TSTP Solution File: ITP214^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP214^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n025.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 03:20:12 EDT 2023
% Result : Theorem 112.47s 112.91s
% Output : Proof 112.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 3.35/3.40 % Problem : ITP214^1 : TPTP v8.1.2. Released v8.1.0.
% 3.35/3.41 % Command : do_cvc5 %s %d
% 3.41/3.62 % Computer : n025.cluster.edu
% 3.41/3.62 % Model : x86_64 x86_64
% 3.41/3.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 3.41/3.62 % Memory : 8042.1875MB
% 3.41/3.62 % OS : Linux 3.10.0-693.el7.x86_64
% 3.41/3.62 % CPULimit : 300
% 3.41/3.62 % WCLimit : 300
% 3.41/3.62 % DateTime : Sun Aug 27 16:56:57 EDT 2023
% 3.41/3.62 % CPUTime :
% 6.88/7.08 %----Proving TH0
% 6.88/7.09 %------------------------------------------------------------------------------
% 6.88/7.09 % File : ITP214^1 : TPTP v8.1.2. Released v8.1.0.
% 6.88/7.09 % Domain : Interactive Theorem Proving
% 6.88/7.09 % Problem : Sledgehammer problem Hoare_Triple 00428_012651
% 6.88/7.09 % Version : [Des22] axioms.
% 6.88/7.09 % English :
% 6.88/7.09
% 6.88/7.09 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 6.88/7.09 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 6.88/7.09 % Source : [Des22]
% 6.88/7.09 % Names : 0025_Hoare_Triple_00428_012651 [Des22]
% 6.88/7.09
% 6.88/7.09 % Status : Theorem
% 6.88/7.09 % Rating : 0.23 v8.1.0
% 6.88/7.09 % Syntax : Number of formulae : 12112 (5171 unt;1845 typ; 0 def)
% 6.88/7.09 % Number of atoms : 29629 (11254 equ; 0 cnn)
% 6.88/7.09 % Maximal formula atoms : 48 ( 2 avg)
% 6.88/7.09 % Number of connectives : 111866 (2669 ~; 470 |;2086 &;95072 @)
% 6.88/7.09 % ( 0 <=>;11569 =>; 0 <=; 0 <~>)
% 6.88/7.09 % Maximal formula depth : 25 ( 6 avg)
% 6.88/7.09 % Number of types : 192 ( 191 usr)
% 6.88/7.09 % Number of type conns : 8544 (8544 >; 0 *; 0 +; 0 <<)
% 6.88/7.09 % Number of symbols : 1657 (1654 usr; 99 con; 0-8 aty)
% 6.88/7.09 % Number of variables : 29524 (3706 ^;25258 !; 560 ?;29524 :)
% 6.88/7.09 % SPC : TH0_THM_EQU_NAR
% 6.88/7.09
% 6.88/7.09 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 6.88/7.09 % from the van Emde Boas Trees session in the Archive of Formal
% 6.88/7.09 % proofs -
% 6.88/7.09 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 6.88/7.09 % 2022-02-17 15:41:40.043
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% 6.88/7.09
% 6.88/7.09 thf(ty_n_t__Nat__Onat,type,
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% 6.88/7.09
% 6.88/7.09 thf(ty_n_t__Int__Oint,type,
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% 6.88/7.09
% 6.88/7.09 thf(ty_n_tf__b,type,
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% 6.88/7.09
% 6.88/7.09 thf(ty_n_tf__a,type,
% 6.88/7.09 a: $tType ).
% 6.88/7.09
% 6.88/7.09 % Explicit typings (1654)
% 6.88/7.09 thf(sy_c_Archimedean__Field_Oceiling_001t__Rat__Orat,type,
% 6.88/7.09 archim2889992004027027881ng_rat: rat > int ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
% 6.88/7.09 archim3151403230148437115or_rat: rat > int ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Archimedean__Field_Ofrac_001t__Rat__Orat,type,
% 6.88/7.09 archimedean_frac_rat: rat > rat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
% 6.88/7.09 archim7778729529865785530nd_rat: rat > int ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Oalloc_001_Eo,type,
% 6.88/7.09 array_alloc_o: list_o > heap_e7401611519738050253t_unit > produc5011041761010125393t_unit ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Oalloc_001t__Int__Oint,type,
% 6.88/7.09 array_alloc_int: list_int > heap_e7401611519738050253t_unit > produc3407818250607552075t_unit ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Oalloc_001t__Nat__Onat,type,
% 6.88/7.09 array_alloc_nat: list_nat > heap_e7401611519738050253t_unit > produc1730305018825802663t_unit ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Olen_001_Eo,type,
% 6.88/7.09 array_len_o: array_o > heap_Time_Heap_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Olen_001t__Int__Oint,type,
% 6.88/7.09 array_len_int: array_int > heap_Time_Heap_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Olen_001t__Nat__Onat,type,
% 6.88/7.09 array_len_nat: array_nat > heap_Time_Heap_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Omake_001_Eo,type,
% 6.88/7.09 array_make_o: nat > ( nat > $o ) > heap_T5660665574680485309rray_o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Omake_001t__Int__Oint,type,
% 6.88/7.09 array_make_int: nat > ( nat > int ) > heap_T1346037964561226099ay_int ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Omake_001t__Nat__Onat,type,
% 6.88/7.09 array_make_nat: nat > ( nat > nat ) > heap_T3836121109492952855ay_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Onth_001_Eo,type,
% 6.88/7.09 array_nth_o: array_o > nat > heap_Time_Heap_o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Onth_001t__Int__Oint,type,
% 6.88/7.09 array_nth_int: array_int > nat > heap_Time_Heap_int ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Onth_001t__Nat__Onat,type,
% 6.88/7.09 array_nth_nat: array_nat > nat > heap_Time_Heap_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Onth_001t__Product____Type__Ounit,type,
% 6.88/7.09 array_7872002506669749220t_unit: array_Product_unit > nat > heap_T5738788834812785303t_unit ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Oof__list_001_Eo,type,
% 6.88/7.09 array_of_list_o: list_o > heap_T5660665574680485309rray_o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Oof__list_001t__Int__Oint,type,
% 6.88/7.09 array_of_list_int: list_int > heap_T1346037964561226099ay_int ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Oof__list_001t__Nat__Onat,type,
% 6.88/7.09 array_of_list_nat: list_nat > heap_T3836121109492952855ay_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Oassn_OAbs__assn,type,
% 6.88/7.09 abs_assn: ( produc3658429121746597890et_nat > $o ) > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Oassn_ORep__assn,type,
% 6.88/7.09 rep_assn: assn > produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Oentails,type,
% 6.88/7.09 entails: assn > assn > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Oin__range,type,
% 6.88/7.09 in_range: produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Oin__range__rel,type,
% 6.88/7.09 in_range_rel: produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Oone__assn__raw,type,
% 6.88/7.09 one_assn_raw: produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Oone__assn__raw__rel,type,
% 6.88/7.09 one_assn_raw_rel: produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Opure__assn,type,
% 6.88/7.09 pure_assn: $o > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Opure__assn__raw_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat,type,
% 6.88/7.09 pure_a825153325127701367it_nat: $o > produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Opure__assn__raw__rel_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat,type,
% 6.88/7.09 pure_a6022498039421069578it_nat: produc6197004810343482825et_nat > produc6197004810343482825et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_OrelH,type,
% 6.88/7.09 relH: set_nat > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Osnga__assn_001_Eo,type,
% 6.88/7.09 snga_assn_o: array_o > list_o > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Osnga__assn_001t__Int__Oint,type,
% 6.88/7.09 snga_assn_int: array_int > list_int > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Osnga__assn_001t__Nat__Onat,type,
% 6.88/7.09 snga_assn_nat: array_nat > list_nat > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Osnga__assn_001t__Product____Type__Ounit,type,
% 6.88/7.09 snga_a4522542871529764173t_unit: array_Product_unit > list_Product_unit > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Osngr__assn_001t__Product____Type__Ounit,type,
% 6.88/7.09 sngr_a5825115052027484668t_unit: ref_Product_unit > product_unit > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Otimes__assn__raw,type,
% 6.88/7.09 times_assn_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Otimes__assn__raw__rel,type,
% 6.88/7.09 times_assn_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Owand__assn,type,
% 6.88/7.09 wand_assn: assn > assn > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Owand__raw,type,
% 6.88/7.09 wand_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Owand__raw__rel,type,
% 6.88/7.09 wand_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Nat__Onat,type,
% 6.88/7.09 bNF_Ca3793111618940312692of_nat: set_nat > set_Pr1261947904930325089at_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001t__Nat__Onat,type,
% 6.88/7.09 bNF_Ca1281551314933786834on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLeq,type,
% 6.88/7.09 bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLess,type,
% 6.88/7.09 bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Int__Oint_001t__Int__Oint,type,
% 6.88/7.09 bNF_Ca1965613569405424510nt_int: set_Pr958786334691620121nt_int > ( int > int ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Int__Oint_001t__Nat__Onat,type,
% 6.88/7.09 bNF_Ca1968104039914474786nt_nat: set_Pr958786334691620121nt_int > ( int > nat ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Int__Oint_001t__Num__Onum,type,
% 6.88/7.09 bNF_Ca7748807862925029228nt_num: set_Pr958786334691620121nt_int > ( int > num ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Int__Oint_001t__Rat__Orat,type,
% 6.88/7.09 bNF_Ca1332973979827979050nt_rat: set_Pr958786334691620121nt_int > ( int > rat ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Int__Oint_001t__Set__Oset_It__Int__Oint_J,type,
% 6.88/7.09 bNF_Ca583493526879471924et_int: set_Pr958786334691620121nt_int > ( int > set_int ) > $o ).
% 6.88/7.09
% 6.88/7.09 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,
% 6.88/7.09 bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 6.88/7.09 bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
% 6.88/7.09
% 6.88/7.09 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,
% 6.88/7.09 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 ).
% 6.88/7.09
% 6.88/7.09 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,
% 6.88/7.09 bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 6.88/7.09 bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 6.88/7.09 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 6.88/7.09
% 6.88/7.09 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,
% 6.88/7.09 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 ).
% 6.88/7.09
% 6.88/7.09 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,
% 6.88/7.09 bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 6.88/7.09
% 6.88/7.09 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,
% 6.88/7.09 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 6.88/7.09 bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 6.88/7.09 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.88/7.09 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 6.88/7.09
% 6.88/7.09 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,
% 6.88/7.09 bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 6.88/7.09
% 6.88/7.09 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,
% 6.88/7.09 bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 6.88/7.09 bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 6.88/7.09
% 6.88/7.09 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,
% 6.88/7.09 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 ).
% 6.88/7.10
% 6.88/7.10 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,
% 6.88/7.10 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 ).
% 6.88/7.10
% 6.88/7.10 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,
% 6.88/7.10 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 ).
% 6.88/7.10
% 6.88/7.10 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,
% 6.88/7.10 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 ).
% 6.88/7.10
% 6.88/7.10 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,
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% 6.88/7.10
% 6.88/7.10 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,
% 6.88/7.10 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 ).
% 6.88/7.10
% 6.88/7.10 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,
% 6.88/7.10 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 ).
% 6.88/7.10
% 6.88/7.10 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,
% 6.88/7.10 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 ).
% 6.88/7.10
% 6.88/7.10 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,
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% 6.88/7.10
% 6.88/7.10 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,
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% 6.88/7.10
% 6.88/7.10 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,
% 6.88/7.10 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 ).
% 6.88/7.10
% 6.88/7.10 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,
% 6.88/7.10 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 ).
% 6.88/7.10
% 6.88/7.10 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,
% 6.88/7.10 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 ).
% 6.88/7.10
% 6.88/7.10 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,
% 6.88/7.10 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 ).
% 6.88/7.10
% 6.88/7.10 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,
% 6.88/7.10 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 ).
% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 6.88/7.10 bNF_re7934895593101944656at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > $o ).
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% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Nat__Onat_001t__Nat__Onat,type,
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% 6.88/7.10 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Nat__Onat,type,
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% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 6.92/7.10
% 6.92/7.10 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_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 comp_C95226695241045696nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > code_integer ) > ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 6.92/7.10 comp_C7449957260575251196nteger: ( code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 comp_C4049556595663050210at_nat: ( code_integer > nat ) > ( nat > code_integer ) > nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 6.92/7.10 comp_i1585864551200866970er_int: ( int > code_integer ) > ( int > int ) > int > code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 6.92/7.10 comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 comp_int_nat_nat: ( int > nat ) > ( nat > int ) > nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Rat__Orat_001t__Int__Oint,type,
% 6.92/7.10 comp_int_rat_int: ( int > rat ) > ( int > int ) > int > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 6.92/7.10 comp_n3898172953802868194er_nat: ( nat > code_integer ) > ( nat > nat ) > nat > code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 6.92/7.10 comp_nat_int_nat: ( nat > int ) > ( nat > nat ) > nat > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat,type,
% 6.92/7.10 comp_n8698576032424989604at_nat: ( nat > multis2468970476368604999at_nat ) > ( nat > nat ) > nat > multis2468970476368604999at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Rat__Orat_001t__Nat__Onat,type,
% 6.92/7.10 comp_nat_rat_nat: ( nat > rat ) > ( nat > nat ) > nat > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Int__Oint_001t__Num__Onum,type,
% 6.92/7.10 comp_num_int_num: ( num > int ) > ( num > num ) > num > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Nat__Onat_001t__Num__Onum,type,
% 6.92/7.10 comp_num_nat_num: ( num > nat ) > ( num > num ) > num > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Num__Onum,type,
% 6.92/7.10 comp_num_num_num: ( num > num ) > ( num > num ) > num > num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 6.92/7.10 comp_n6731957995704128387um_num: ( num > option_num ) > ( num > num ) > num > option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Option__Ooption_I_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_J_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 comp_o7188567781464924208nteger: ( option8057788054806935849nteger > option7428179582072448501nteger ) > ( option_Code_integer > option8057788054806935849nteger ) > option_Code_integer > option7428179582072448501nteger ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Code____Numeral__Ointeger_J_001t__Option__Ooption_I_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_J_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 comp_o9011007105448239796nteger: ( option_Code_integer > option7428179582072448501nteger ) > ( option_Code_integer > option_Code_integer ) > option_Code_integer > option7428179582072448501nteger ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Int__Oint_J_001t__Nat__Onat_001t__Option__Ooption_It__Int__Oint_J,type,
% 6.92/7.10 comp_o5073597352248849069on_int: ( option_int > nat ) > ( option_int > option_int ) > option_int > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Int__Oint_J_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Int__Oint_J,type,
% 6.92/7.10 comp_o4824269118391204861on_int: ( option_int > option_nat ) > ( option_int > option_int ) > option_int > option_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Num__Onum_J_001t__Nat__Onat_001t__Option__Ooption_It__Num__Onum_J,type,
% 6.92/7.10 comp_o6878144249584144265on_num: ( option_num > nat ) > ( option_num > option_num ) > option_num > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 6.92/7.10 comp_o8931257242830428707on_num: ( option_num > option_num ) > ( option_num > option_num ) > option_num > option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__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_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_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 6.92/7.10 comp_P3118722334806803912t_unit: ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > ( heap_e7401611519738050253t_unit > produc8664842809031399944it_nat ) > heap_e7401611519738050253t_unit > option8956607266484857688it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_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_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_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 6.92/7.10 comp_P8552900652980440422t_unit: ( produc3260487557148687353it_nat > option3562590408128118217it_nat ) > ( heap_e7401611519738050253t_unit > produc3260487557148687353it_nat ) > heap_e7401611519738050253t_unit > option3562590408128118217it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 6.92/7.10 comp_P6401406225962756324t_unit: ( produc7388388658123137530it_nat > option4065278094766928714it_nat ) > ( heap_e7401611519738050253t_unit > produc7388388658123137530it_nat ) > heap_e7401611519738050253t_unit > option4065278094766928714it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 comp_rat_nat_nat: ( rat > nat ) > ( nat > rat ) > nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Oid_001_Eo,type,
% 6.92/7.10 id_o: $o > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Oid_001t__Int__Oint,type,
% 6.92/7.10 id_int: int > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 6.92/7.10 id_nat: nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Oid_001t__Num__Onum,type,
% 6.92/7.10 id_num: num > num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 map_fu2496120808607739376eger_o: ( code_integer > int ) > ( ( int > $o ) > code_integer > $o ) > ( int > int > $o ) > code_integer > code_integer > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 map_fu8272188784021352819nteger: ( code_integer > int ) > ( ( int > int ) > code_integer > code_integer ) > ( int > int > int ) > code_integer > code_integer > code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo_001_Eo,type,
% 6.92/7.10 map_fu6957801986076833569nt_o_o: ( code_integer > int ) > ( $o > $o ) > ( int > $o ) > code_integer > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 6.92/7.10 map_fu2599414010547811884nteger: ( code_integer > int ) > ( int > code_integer ) > ( int > int ) > code_integer > code_integer ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 map_fu6256889081107267320ural_o: ( code_natural > nat ) > ( ( nat > $o ) > code_natural > $o ) > ( nat > nat > $o ) > code_natural > code_natural > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 6.92/7.10 map_fu6549440983881763648atural: ( code_natural > nat ) > ( ( nat > nat ) > code_natural > code_natural ) > ( nat > nat > nat ) > code_natural > code_natural > code_natural ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_Eo_001_Eo,type,
% 6.92/7.10 map_fu4892316939951275536at_o_o: ( code_natural > nat ) > ( $o > $o ) > ( nat > $o ) > code_natural > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 6.92/7.10 map_fu1239815594074539274atural: ( code_natural > nat ) > ( nat > code_natural ) > ( nat > nat ) > code_natural > code_natural ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 map_fu7831380289885515383nt_rat: ( int > int ) > ( ( int > product_prod_int_int ) > int > rat ) > ( int > int > product_prod_int_int ) > int > int > rat ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 map_fu3424225382358772769nt_rat: ( int > int ) > ( product_prod_int_int > rat ) > ( int > product_prod_int_int ) > int > rat ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 map_fu6891787308814931657nteger: ( num > num ) > ( ( num > int ) > num > code_integer ) > ( num > num > int ) > num > num > code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 6.92/7.10 map_fu8638147718074629079nteger: ( num > num ) > ( int > code_integer ) > ( num > int ) > num > code_integer ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 map_fu4333342158222067775at_rat: ( rat > product_prod_int_int ) > ( ( product_prod_int_int > product_prod_int_int ) > rat > rat ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > rat > rat > rat ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 map_fu898904425404107465nt_o_o: ( rat > product_prod_int_int ) > ( $o > $o ) > ( product_prod_int_int > $o ) > rat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 6.92/7.10 map_fu5673905371560938248nt_rat: ( rat > product_prod_int_int ) > ( product_prod_int_int > rat ) > ( product_prod_int_int > product_prod_int_int ) > rat > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun__Def_Omax__strict,type,
% 6.92/7.10 fun_max_strict: set_Pr4329608150637261639at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun__Def_Omax__weak,type,
% 6.92/7.10 fun_max_weak: set_Pr4329608150637261639at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun__Def_Omin__strict,type,
% 6.92/7.10 fun_min_strict: set_Pr4329608150637261639at_nat ).
% 6.92/7.10
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% 6.92/7.10
% 6.92/7.10 thf(sy_c_Int_Oring__1__class_OInts_001t__Int__Oint,type,
% 6.92/7.10 ring_1_Ints_int: set_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Int_Oring__1__class_OInts_001t__Rat__Orat,type,
% 6.92/7.10 ring_1_Ints_rat: set_rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 6.92/7.10 ring_18347121197199848620nteger: int > code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 6.92/7.10 ring_1_of_int_int: int > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 6.92/7.10 ring_1_of_int_rat: int > rat ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 inf_in2641120393918057659_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 inf_in3295504058751909687_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_Eo_M_Eo_J,type,
% 6.92/7.10 inf_inf_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 6.92/7.10 inf_inf_int_int_o: ( int > int > $o ) > ( int > int > $o ) > int > int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Int__Oint_M_Eo_J,type,
% 6.92/7.10 inf_inf_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__List__Olist_It__Nat__Onat_J_M_Eo_J,type,
% 6.92/7.10 inf_inf_list_nat_o: ( list_nat > $o ) > ( list_nat > $o ) > list_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 6.92/7.10 inf_inf_nat_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Nat__Onat_M_Eo_J,type,
% 6.92/7.10 inf_inf_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 6.92/7.10 inf_in3604695632404883862_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 6.92/7.10 inf_in5163264567034779214_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 6.92/7.10 inf_inf_set_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
% 6.92/7.10 inf_in5102985939729578038_int_o: ( set_Pr958786334691620121nt_int > $o ) > ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > $o ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 inf_in8051596381320575356_nat_o: ( a > produc6653097349344004940it_nat > $o ) > ( a > produc6653097349344004940it_nat > $o ) > a > produc6653097349344004940it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_Itf__b_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,
% 6.92/7.10 inf_in844129575377303227_nat_o: ( b > produc6653097349344004940it_nat > $o ) > ( b > produc6653097349344004940it_nat > $o ) > b > produc6653097349344004940it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Assertions__Oassn,type,
% 6.92/7.10 inf_inf_assn: assn > assn > assn ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Int__Oint,type,
% 6.92/7.10 inf_inf_int: int > int > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 6.92/7.10 inf_inf_nat: nat > nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Option__Ooption_I_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 6.92/7.10 inf_in7104746047340619750_int_o: option1893999432384633940_int_o > option1893999432384633940_int_o > option1893999432384633940_int_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Option__Ooption_It__Assertions__Oassn_J,type,
% 6.92/7.10 inf_inf_option_assn: option_assn > option_assn > option_assn ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Option__Ooption_It__Nat__Onat_J,type,
% 6.92/7.10 inf_inf_option_nat: option_nat > option_nat > option_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 inf_in7812914138253463912et_nat: option_set_nat > option_set_nat > option_set_nat ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 inf_in777885744494410645at_nat: option8963830502488799655at_nat > option8963830502488799655at_nat > option8963830502488799655at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Product____Type__Ounit,type,
% 6.92/7.10 inf_inf_Product_unit: product_unit > product_unit > product_unit ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Rat__Orat,type,
% 6.92/7.10 inf_inf_rat: rat > rat > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_Eo_J,type,
% 6.92/7.10 inf_inf_set_o: set_o > set_o > set_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Assertions__Oassn_J,type,
% 6.92/7.10 inf_inf_set_assn: set_assn > set_assn > set_assn ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 inf_in1364745209274528805nteger: set_Code_integer > set_Code_integer > set_Code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.10 inf_inf_set_int: set_int > set_int > set_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 6.92/7.10 inf_inf_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.10 inf_inf_set_nat: set_nat > set_nat > set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Num__Onum_J,type,
% 6.92/7.10 inf_inf_set_num: set_num > set_num > set_num ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 inf_in3088352823822785602et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 inf_in1768905781608824518et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 6.92/7.10 inf_in2269163501485487111nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 inf_in1697001100524423349at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 inf_in7913087082777306421at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 inf_in3493107508024165057it_nat: set_Pr7098220151150636591it_nat > set_Pr7098220151150636591it_nat > set_Pr7098220151150636591it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 6.92/7.10 inf_in3995795194662975554it_nat: set_Pr7600907837789447088it_nat > set_Pr7600907837789447088it_nat > set_Pr7600907837789447088it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Rat__Orat_J,type,
% 6.92/7.10 inf_inf_set_rat: set_rat > set_rat > set_rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 inf_inf_set_set_nat: set_set_nat > set_set_nat > set_set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 6.92/7.10 inf_in8396524679539076455nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Assertions__Oassn,type,
% 6.92/7.10 semila8603258263270017530r_assn: ( assn > assn > assn ) > assn > ( assn > assn > $o ) > ( assn > assn > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 6.92/7.10 semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_I_Eo_J,type,
% 6.92/7.10 semila2554085542299052326_set_o: ( set_o > set_o > set_o ) > set_o > ( set_o > set_o > $o ) > ( set_o > set_o > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.10 semila6712789903965657268et_int: ( set_int > set_int > set_int ) > set_int > ( set_int > set_int > $o ) > ( set_int > set_int > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.10 semila1667268886620078168et_nat: ( set_nat > set_nat > set_nat ) > set_nat > ( set_nat > set_nat > $o ) > ( set_nat > set_nat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 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 ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 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 ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 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 ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 sup_su6535292691877529429_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 sup_su1630790145277462993_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_I_Eo_M_Eo_J,type,
% 6.92/7.10 sup_sup_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 6.92/7.10 sup_sup_int_int_o: ( int > int > $o ) > ( int > int > $o ) > int > int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Int__Oint_M_Eo_J,type,
% 6.92/7.10 sup_sup_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__List__Olist_It__Nat__Onat_J_M_Eo_J,type,
% 6.92/7.10 sup_sup_list_nat_o: ( list_nat > $o ) > ( list_nat > $o ) > list_nat > $o ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 sup_su2200014604384089602_nat_o: ( multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ) > ( multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ) > multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 6.92/7.10 sup_sup_nat_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_Eo_J,type,
% 6.92/7.10 sup_sup_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 6.92/7.10 sup_su8463660629351352368_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 sup_su6256023009775730178_nat_o: ( produc4166570645942440679at_nat > $o ) > ( produc4166570645942440679at_nat > $o ) > produc4166570645942440679at_nat > $o ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 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 ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 sup_su2080679670758317954_nat_o: ( produc3843707927480180839at_nat > $o ) > ( produc3843707927480180839at_nat > $o ) > produc3843707927480180839at_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 6.92/7.10 sup_sup_set_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
% 6.92/7.10 sup_su1852724690005176016_int_o: ( set_Pr958786334691620121nt_int > $o ) > ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > $o ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 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 ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 sup_su2191776239474528790_nat_o: ( a > produc6653097349344004940it_nat > $o ) > ( a > produc6653097349344004940it_nat > $o ) > a > produc6653097349344004940it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_Itf__b_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,
% 6.92/7.10 sup_su4207681470386032469_nat_o: ( b > produc6653097349344004940it_nat > $o ) > ( b > produc6653097349344004940it_nat > $o ) > b > produc6653097349344004940it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Assertions__Oassn,type,
% 6.92/7.10 sup_sup_assn: assn > assn > assn ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 6.92/7.10 sup_sup_int: int > int > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 6.92/7.10 sup_sup_nat: nat > nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Int__Oint_J,type,
% 6.92/7.10 sup_sup_option_int: option_int > option_int > option_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Nat__Onat_J,type,
% 6.92/7.10 sup_sup_option_nat: option_nat > option_nat > option_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 sup_su3598758113090618626et_nat: option_set_nat > option_set_nat > option_set_nat ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 sup_su5873096292857799009at_nat: option2498585697089621389at_nat > option2498585697089621389at_nat > option2498585697089621389at_nat ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 sup_su2273273666271716065at_nat: option1583680563626158861at_nat > option1583680563626158861at_nat > option1583680563626158861at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Product____Type__Ounit,type,
% 6.92/7.10 sup_sup_Product_unit: product_unit > product_unit > product_unit ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Rat__Orat,type,
% 6.92/7.10 sup_sup_rat: rat > rat > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_Eo_J,type,
% 6.92/7.10 sup_sup_set_o: set_o > set_o > set_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 sup_su848401254843788991nteger: set_Code_integer > set_Code_integer > set_Code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.10 sup_sup_set_int: set_int > set_int > set_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 6.92/7.10 sup_sup_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.10 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Num__Onum_J,type,
% 6.92/7.10 sup_sup_set_num: set_num > set_num > set_num ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 sup_su8975264963432250076et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 sup_su7128418612487073120et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 6.92/7.10 sup_su6024340866399070445nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 sup_su3035147773818789531at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 sup_su718114333110466843at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 6.92/7.10
% 6.92/7.10 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,
% 6.92/7.10 sup_su3211442154794319707it_nat: set_Pr7098220151150636591it_nat > set_Pr7098220151150636591it_nat > set_Pr7098220151150636591it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 6.92/7.10 sup_su3714129841433130204it_nat: set_Pr7600907837789447088it_nat > set_Pr7600907837789447088it_nat > set_Pr7600907837789447088it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Rat__Orat_J,type,
% 6.92/7.10 sup_sup_set_rat: set_rat > set_rat > set_rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 sup_sup_set_set_nat: set_set_nat > set_set_nat > set_set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 6.92/7.10 sup_su2047564715030645325nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Int__Oint,type,
% 6.92/7.10 lattic8263393255366662781ax_int: set_int > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 6.92/7.10 lattic8265883725875713057ax_nat: set_nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 6.92/7.10 lattic8660852769118194346_int_o: ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ) > ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ) > ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Assertions__Oassn,type,
% 6.92/7.10 lattic5623431474481994958t_assn: ( assn > assn > assn ) > ( assn > assn > $o ) > ( assn > assn > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Int__Oint,type,
% 6.92/7.10 lattic6006661108824415698et_int: ( int > int > int ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Nat__Onat,type,
% 6.92/7.10 lattic6009151579333465974et_nat: ( nat > nat > nat ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Num__Onum,type,
% 6.92/7.10 lattic2566483365489244608et_num: ( num > num > num ) > ( num > num > $o ) > ( num > num > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Rat__Orat,type,
% 6.92/7.10 lattic5374021519246970238et_rat: ( rat > rat > rat ) > ( rat > rat > $o ) > ( rat > rat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.10 lattic8154731777541915528et_int: ( set_int > set_int > set_int ) > ( set_int > set_int > $o ) > ( set_int > set_int > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.10 lattic3109210760196336428et_nat: ( set_nat > set_nat > set_nat ) > ( set_nat > set_nat > $o ) > ( set_nat > set_nat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_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,
% 6.92/7.10 lattic5174734335190411425at_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 ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 lattic6529551498584149819at_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 ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_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,
% 6.92/7.10 lattic6976360593897529633at_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 ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 6.92/7.10 append_int: list_int > list_int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 6.92/7.10 append_nat: list_nat > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Obutlast_001t__Nat__Onat,type,
% 6.92/7.10 butlast_nat: list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 6.92/7.10 drop_nat: nat > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oenumerate_001_Eo,type,
% 6.92/7.10 enumerate_o: nat > list_o > list_P7333126701944960589_nat_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oenumerate_001t__Int__Oint,type,
% 6.92/7.10 enumerate_int: nat > list_int > list_P3521021558325789923at_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oenumerate_001t__Nat__Onat,type,
% 6.92/7.10 enumerate_nat: nat > list_nat > list_P6011104703257516679at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofilter_001t__Nat__Onat,type,
% 6.92/7.10 filter_nat2: ( nat > $o ) > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofind_001_Eo,type,
% 6.92/7.10 find_o: ( $o > $o ) > list_o > option_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofind_001t__Int__Oint,type,
% 6.92/7.10 find_int: ( int > $o ) > list_int > option_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofind_001t__Nat__Onat,type,
% 6.92/7.10 find_nat: ( nat > $o ) > list_nat > option_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofind_001t__Num__Onum,type,
% 6.92/7.10 find_num: ( num > $o ) > list_num > option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofind_001t__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,type,
% 6.92/7.10 find_P5317947125398478060it_nat: ( produc8664842809031399944it_nat > $o ) > list_P626663023886443800it_nat > option8956607266484857688it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofind_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,
% 6.92/7.10 find_P4815471733760996061it_nat: ( produc3260487557148687353it_nat > $o ) > list_P6935614879863011209it_nat > option3562590408128118217it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofind_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 find_P8943372834735446238it_nat: ( produc7388388658123137530it_nat > $o ) > list_P7438302566501821706it_nat > option4065278094766928714it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 6.92/7.10 last_nat: list_nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olinorder__class_Osort__key_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.10 linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olinorder__class_Osort__key_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 6.92/7.10 linord2614967742042102400et_nat: set_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_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,type,
% 6.92/7.10 cons_P6219271836124797827_nat_o: ( produc3658429121746597890et_nat > $o ) > list_P7985473006766602707_nat_o > list_P7985473006766602707_nat_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001_Eo,type,
% 6.92/7.10 cons_o: $o > list_o > list_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 6.92/7.10 cons_int: int > list_int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 6.92/7.10 cons_nat: nat > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Num__Onum,type,
% 6.92/7.10 cons_num: num > list_num > list_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Option__Ooption_It__Num__Onum_J,type,
% 6.92/7.10 cons_option_num: option_num > list_option_num > list_option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_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,
% 6.92/7.10 cons_P6329468272379687876et_nat: produc2732055786443039994et_nat > list_P362550909693114634et_nat > list_P362550909693114634et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_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,
% 6.92/7.10 cons_P3419706843779801160et_nat: produc3925858234332021118et_nat > list_P2321686559999237006et_nat > list_P2321686559999237006et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 cons_P7873165156130251286it_nat: produc6653097349344004940it_nat > list_P131111800688179804it_nat > list_P131111800688179804it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 cons_P2869003950965171916et_nat: produc3658429121746597890et_nat > list_P9062070895058802706et_nat > list_P9062070895058802706et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 6.92/7.10 cons_P3334398858971670639nt_int: product_prod_int_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 6.92/7.10 cons_P7512249878480867347nt_nat: product_prod_int_nat > list_P8198026277950538467nt_nat > list_P8198026277950538467nt_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 6.92/7.10 cons_P2335045147070616083at_int: product_prod_nat_int > list_P3521021558325789923at_int > list_P3521021558325789923at_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 6.92/7.10 cons_P6512896166579812791at_nat: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__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,type,
% 6.92/7.10 cons_P4136552807766418642it_nat: produc8664842809031399944it_nat > list_P626663023886443800it_nat > list_P626663023886443800it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_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,
% 6.92/7.10 cons_P2339423585217329347it_nat: produc3260487557148687353it_nat > list_P6935614879863011209it_nat > list_P6935614879863011209it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 cons_P6467324686191779524it_nat: produc7388388658123137530it_nat > list_P7438302566501821706it_nat > list_P7438302566501821706it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Rat__Orat,type,
% 6.92/7.10 cons_rat: rat > list_rat > list_rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001tf__a,type,
% 6.92/7.10 cons_a: a > list_a > list_a ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001tf__b,type,
% 6.92/7.10 cons_b: b > list_b > list_b ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 6.92/7.10 nil_int: list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 6.92/7.10 nil_nat: list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 6.92/7.10 hd_nat: list_nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 6.92/7.10 set_int2: list_int > set_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001_Eo,type,
% 6.92/7.10 nth_o: list_o > nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 6.92/7.10 nth_int: list_int > nat > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 6.92/7.10 nth_nat: list_nat > nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 6.92/7.10 nth_num: list_num > nat > num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Option__Ooption_It__Num__Onum_J,type,
% 6.92/7.10 nth_option_num: list_option_num > nat > option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 6.92/7.10 nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 6.92/7.10 nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 6.92/7.10 nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 nth_Pr4561283279332054789it_nat: list_P131111800688179804it_nat > nat > produc6653097349344004940it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_M_Eo_J,type,
% 6.92/7.10 nth_Pr7514405829937366042_int_o: list_P5087981734274514673_int_o > nat > product_prod_int_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 6.92/7.10 nth_Pr4439495888332055232nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 6.92/7.10 nth_Pr8617346907841251940nt_nat: list_P8198026277950538467nt_nat > nat > product_prod_int_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 6.92/7.10 nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 6.92/7.10 nth_Pr3440142176431000676at_int: list_P3521021558325789923at_int > nat > product_prod_nat_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 6.92/7.10 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__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,type,
% 6.92/7.10 nth_Pr2956344619228612545it_nat: list_P626663023886443800it_nat > nat > produc8664842809031399944it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_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,
% 6.92/7.10 nth_Pr8687047199098054322it_nat: list_P6935614879863011209it_nat > nat > produc3260487557148687353it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 nth_Pr3591576263217728691it_nat: list_P7438302566501821706it_nat > nat > produc7388388658123137530it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Ounit,type,
% 6.92/7.10 nth_Product_unit: list_Product_unit > nat > product_unit ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Rat__Orat,type,
% 6.92/7.10 nth_rat: list_rat > nat > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001tf__b,type,
% 6.92/7.10 nth_b: list_b > nat > b ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 6.92/7.10 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 6.92/7.10 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 6.92/7.10 product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001t__Int__Oint_001_Eo,type,
% 6.92/7.10 product_int_o: list_int > list_o > list_P5087981734274514673_int_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.10 product_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Nat__Onat,type,
% 6.92/7.10 product_int_nat: list_int > list_nat > list_P8198026277950538467nt_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 6.92/7.10 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Int__Oint,type,
% 6.92/7.10 product_nat_int: list_nat > list_int > list_P3521021558325789923at_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 product_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001tf__b_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 produc1870533552098665926it_nat: list_b > list_P131111800688179804it_nat > list_P7438302566501821706it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Orotate1_001_Eo,type,
% 6.92/7.10 rotate1_o: list_o > list_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Orotate1_001t__Int__Oint,type,
% 6.92/7.10 rotate1_int: list_int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
% 6.92/7.10 rotate1_nat: list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Orotate_001_Eo,type,
% 6.92/7.10 rotate_o: nat > list_o > list_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Orotate_001t__Int__Oint,type,
% 6.92/7.10 rotate_int: nat > list_int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Orotate_001t__Nat__Onat,type,
% 6.92/7.10 rotate_nat: nat > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Osorted__wrt_001_Eo,type,
% 6.92/7.10 sorted_wrt_o: ( $o > $o > $o ) > list_o > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 6.92/7.10 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 6.92/7.10 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Osorted__wrt_001t__Num__Onum,type,
% 6.92/7.10 sorted_wrt_num: ( num > num > $o ) > list_num > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Osorted__wrt_001t__Rat__Orat,type,
% 6.92/7.10 sorted_wrt_rat: ( rat > rat > $o ) > list_rat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 6.92/7.10 take_nat: nat > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oupt,type,
% 6.92/7.10 upt: nat > nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oupto,type,
% 6.92/7.10 upto: int > int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oupto__aux,type,
% 6.92/7.10 upto_aux: int > int > list_int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oupto__rel,type,
% 6.92/7.10 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_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,type,
% 6.92/7.10 zip_Pr8136144321567152340et_nat: list_P7985473006766602707_nat_o > list_P2321686559999237006et_nat > list_P362550909693114634et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_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,type,
% 6.92/7.10 zip_Pr7134870689397686104et_nat: list_P7985473006766602707_nat_o > list_P9062070895058802706et_nat > list_P2321686559999237006et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001_Eo_001_Eo,type,
% 6.92/7.10 zip_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001_Eo_001t__Int__Oint,type,
% 6.92/7.10 zip_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001_Eo_001t__Nat__Onat,type,
% 6.92/7.10 zip_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001t__Int__Oint_001_Eo,type,
% 6.92/7.10 zip_int_o: list_int > list_o > list_P5087981734274514673_int_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.10 zip_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Nat__Onat,type,
% 6.92/7.10 zip_int_nat: list_int > list_nat > list_P8198026277950538467nt_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001t__Nat__Onat_001_Eo,type,
% 6.92/7.10 zip_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Int__Oint,type,
% 6.92/7.10 zip_nat_int: list_nat > list_int > list_P3521021558325789923at_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 zip_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001tf__a_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 zip_a_1859587264247984595it_nat: list_a > list_P131111800688179804it_nat > list_P6935614879863011209it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001tf__b_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 zip_b_5987488365222434772it_nat: list_b > list_P131111800688179804it_nat > list_P7438302566501821706it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_001t__Int__Oint,type,
% 6.92/7.10 eps_Opt_int: ( int > $o ) > option_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_001t__Num__Onum,type,
% 6.92/7.10 eps_Opt_num: ( num > $o ) > option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_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,
% 6.92/7.10 eps_Op6423059015816587746et_nat: ( produc3925858234332021118et_nat > $o ) > option5190343406534369742et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 eps_Op8301357815426737072it_nat: ( produc6653097349344004940it_nat > $o ) > option233860712434008220it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 eps_Op2013419657081471078et_nat: ( produc3658429121746597890et_nat > $o ) > option936205604648967762et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_001t__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,type,
% 6.92/7.10 eps_Op3393321821070424684it_nat: ( produc8664842809031399944it_nat > $o ) > option8956607266484857688it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_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,
% 6.92/7.10 eps_Op1741419982095519837it_nat: ( produc3260487557148687353it_nat > $o ) > option3562590408128118217it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 eps_Op5869321083069970014it_nat: ( produc7388388658123137530it_nat > $o ) > option4065278094766928714it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_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,type,
% 6.92/7.10 biject1468766312547416318et_nat: set_Pr8536935166611901872et_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_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,type,
% 6.92/7.10 biject2615096655818420098et_nat: set_Pr3286484037609594932et_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.10 bijective_int_int: set_Pr958786334691620121nt_int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 biject5714339216877808333at_nat: set_Pr8551490117392284871at_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 bijective_nat_nat: set_Pr1261947904930325089at_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 6.92/7.10 biject3503750217840948301at_nat: set_Pr8693737435421807431at_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_001tf__a_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 biject8592306251674886141it_nat: set_Pr7098220151150636591it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_001tf__b_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 biject3496835315794560510it_nat: set_Pr7600907837789447088it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Odflt__None__set_001_Eo,type,
% 6.92/7.10 dflt_None_set_o: set_o > option_set_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Odflt__None__set_001t__Int__Oint,type,
% 6.92/7.10 dflt_None_set_int: set_int > option_set_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Odflt__None__set_001t__Nat__Onat,type,
% 6.92/7.10 dflt_None_set_nat: set_nat > option_set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Odflt__None__set_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 6.92/7.10 dflt_N6592383573632408824at_nat: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Omap__to__set_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.10 map_to_set_int_int: ( int > option_int ) > set_Pr958786334691620121nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Omap__to__set_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 map_to_set_nat_nat: ( nat > option_nat ) > set_Pr1261947904930325089at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Orel__of_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,type,
% 6.92/7.10 rel_of7774016450764239315et_nat: ( ( produc3658429121746597890et_nat > $o ) > option5190343406534369742et_nat ) > ( produc2732055786443039994et_nat > $o ) > set_Pr8536935166611901872et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Orel__of_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,type,
% 6.92/7.10 rel_of4838799251197538391et_nat: ( ( produc3658429121746597890et_nat > $o ) > option936205604648967762et_nat ) > ( produc3925858234332021118et_nat > $o ) > set_Pr3286484037609594932et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Orel__of_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.10 rel_of_int_int: ( int > option_int ) > ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Orel__of_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 rel_of_nat_nat: ( nat > option_nat ) > ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Orel__of_001tf__a_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 rel_of2761222537318653906it_nat: ( a > option233860712434008220it_nat ) > ( produc3260487557148687353it_nat > $o ) > set_Pr7098220151150636591it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Orel__of_001tf__b_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 rel_of6889123638293104083it_nat: ( b > option233860712434008220it_nat ) > ( produc7388388658123137530it_nat > $o ) > set_Pr7600907837789447088it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oset__to__map_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,type,
% 6.92/7.10 set_to2047380710992656148et_nat: set_Pr8536935166611901872et_nat > ( produc3658429121746597890et_nat > $o ) > option5190343406534369742et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oset__to__map_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,type,
% 6.92/7.10 set_to6040779677306527128et_nat: set_Pr3286484037609594932et_nat > ( produc3658429121746597890et_nat > $o ) > option936205604648967762et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oset__to__map_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.10 set_to_map_int_int: set_Pr958786334691620121nt_int > int > option_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oset__to__map_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 set_to_map_nat_nat: set_Pr1261947904930325089at_nat > nat > option_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oset__to__map_001tf__a_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 set_to2008915276733485075it_nat: set_Pr7098220151150636591it_nat > a > option233860712434008220it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oset__to__map_001tf__b_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 set_to6136816377707935252it_nat: set_Pr7600907837789447088it_nat > b > option233860712434008220it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oslice_001_Eo,type,
% 6.92/7.10 slice_o: nat > nat > list_o > list_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oslice_001t__Int__Oint,type,
% 6.92/7.10 slice_int: nat > nat > list_int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oslice_001t__Nat__Onat,type,
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% 6.92/7.10
% 6.92/7.10 thf(sy_c_Num_Opred__numeral,type,
% 6.92/7.10 pred_numeral: num > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Num_Osqr,type,
% 6.92/7.10 sqr: num > num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ocombine__options_001t__Num__Onum,type,
% 6.92/7.10 combine_options_num: ( num > num > num ) > option_num > option_num > option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ocombine__options_001t__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,type,
% 6.92/7.10 combin4318129983670048329it_nat: ( produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat ) > option8956607266484857688it_nat > option8956607266484857688it_nat > option8956607266484857688it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ocombine__options_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,
% 6.92/7.10 combin5819755802923621690it_nat: ( produc3260487557148687353it_nat > produc3260487557148687353it_nat > produc3260487557148687353it_nat ) > option3562590408128118217it_nat > option3562590408128118217it_nat > option3562590408128118217it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ocombine__options_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 combin724284867043296059it_nat: ( produc7388388658123137530it_nat > produc7388388658123137530it_nat > produc7388388658123137530it_nat ) > option4065278094766928714it_nat > option4065278094766928714it_nat > option4065278094766928714it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 6.92/7.10 none_P2320557853698873699_int_o: option1893999432384633940_int_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Assertions__Oassn,type,
% 6.92/7.10 none_assn: option_assn ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
% 6.92/7.10 none_nat: option_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 6.92/7.10 none_num: option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_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,
% 6.92/7.10 none_P199884684680593241et_nat: option2860828798490689354et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_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,
% 6.92/7.10 none_P4972525538344268765et_nat: option5190343406534369742et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 6.92/7.10 none_P2377608414092835994nt_int: option4624381673175914239nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__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,type,
% 6.92/7.10 none_P9117596204409417319it_nat: option8956607266484857688it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_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,
% 6.92/7.10 none_P2651198173097904984it_nat: option3562590408128118217it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 none_P6779099274072355161it_nat: option4065278094766928714it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Set__Oset_I_Eo_J,type,
% 6.92/7.10 none_set_o: option_set_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.10 none_set_int: option_set_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.10 none_set_nat: option_set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 none_s625347054029921090at_nat: option8963830502488799655at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 6.92/7.10 some_P180497116919641311_int_o: ( product_prod_int_int > $o ) > option1893999432384633940_int_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001_Eo,type,
% 6.92/7.10 some_o: $o > option_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Assertions__Oassn,type,
% 6.92/7.10 some_assn: assn > option_assn ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Int__Oint,type,
% 6.92/7.10 some_int: int > option_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
% 6.92/7.10 some_nat: nat > option_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 6.92/7.10 some_num: num > option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_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,
% 6.92/7.10 some_P1630309045189364437et_nat: produc2732055786443039994et_nat > option2860828798490689354et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_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,
% 6.92/7.10 some_P750831030444334937et_nat: produc3925858234332021118et_nat > option5190343406534369742et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Heap__Oarray_I_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 some_P3509045262911171395it_nat: produc8032495849646651230it_nat > option1013472963438093988it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Heap__Oarray_It__Int__Oint_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 some_P8650484732927216191it_nat: produc7196121022310644452it_nat > option2555668343544256180it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Heap__Oarray_It__Nat__Onat_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 some_P8206036975937309155it_nat: produc6751673265320737416it_nat > option4277301481530639448it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 some_P1054239925786823975it_nat: produc6653097349344004940it_nat > option233860712434008220it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 some_P624177172695371229et_nat: produc3658429121746597890et_nat > option936205604648967762et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 6.92/7.10 some_P4184893108420464158nt_int: product_prod_int_int > option4624381673175914239nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__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,type,
% 6.92/7.10 some_P1914260805536162275it_nat: produc8664842809031399944it_nat > option8956607266484857688it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_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,
% 6.92/7.10 some_P7913643980934408916it_nat: produc3260487557148687353it_nat > option3562590408128118217it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 some_P2818173045054083285it_nat: produc7388388658123137530it_nat > option4065278094766928714it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Rat__Orat,type,
% 6.92/7.10 some_rat: rat > option_rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_I_Eo_J,type,
% 6.92/7.10 some_set_o: set_o > option_set_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.10 some_set_int: set_int > option_set_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.10 some_set_nat: set_nat > option_set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_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,
% 6.92/7.10 some_s287724117700012716at_nat: set_Pr8551490117392284871at_nat > option2498585697089621389at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 some_s147305329494351046at_nat: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_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,
% 6.92/7.10 some_s5890477192898017836at_nat: set_Pr4329608150637261639at_nat > option1583680563626158861at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_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_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 case_o1441893360019914891nteger: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option8057788054806935849nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_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,
% 6.92/7.10 case_o7134296353695833103nteger: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option_Code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Assertions__Oassn,type,
% 6.92/7.10 case_option_o_assn: $o > ( assn > $o ) > option_assn > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Int__Oint,type,
% 6.92/7.10 case_option_o_int: $o > ( int > $o ) > option_int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Nat__Onat,type,
% 6.92/7.10 case_option_o_nat: $o > ( nat > $o ) > option_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Num__Onum,type,
% 6.92/7.10 case_option_o_num: $o > ( num > $o ) > option_num > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__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,type,
% 6.92/7.10 case_o2686588417244861013it_nat: $o > ( produc8664842809031399944it_nat > $o ) > option8956607266484857688it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_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,
% 6.92/7.10 case_o3267218206291580230it_nat: $o > ( produc3260487557148687353it_nat > $o ) > option3562590408128118217it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 case_o7395119307266030407it_nat: $o > ( produc7388388658123137530it_nat > $o ) > option4065278094766928714it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Rat__Orat,type,
% 6.92/7.10 case_option_o_rat: $o > ( rat > $o ) > option_rat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.10 case_o223999843215110191et_int: $o > ( set_int > $o ) > option_set_int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
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% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001t__Code____Numeral__Onatural_001t__Num__Onum,type,
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% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001t__Int__Oint_001t__Num__Onum,type,
% 6.92/7.10 case_option_int_num: int > ( num > int ) > option_num > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001t__Nat__Onat_001t__Int__Oint,type,
% 6.92/7.10 case_option_nat_int: nat > ( int > nat ) > option_int > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001t__Nat__Onat_001t__Num__Onum,type,
% 6.92/7.10 case_option_nat_num: nat > ( num > nat ) > option_num > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
% 6.92/7.10 case_option_num_num: num > ( num > num ) > option_num > num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_I_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 6.92/7.11 case_o670596351732880613_int_o: option1893999432384633940_int_o > ( ( product_prod_int_int > $o ) > option1893999432384633940_int_o ) > option1893999432384633940_int_o > option1893999432384633940_int_o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Assertions__Oassn_J_001t__Assertions__Oassn,type,
% 6.92/7.11 case_o4484465799723439917n_assn: option_assn > ( assn > option_assn ) > option_assn > option_assn ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Int__Oint_J_001t__Int__Oint,type,
% 6.92/7.11 case_o390784466056649525nt_int: option_int > ( int > option_int ) > option_int > option_int ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Nat__Onat_J_001t__Nat__Onat,type,
% 6.92/7.11 case_o7429725398727453821at_nat: option_nat > ( nat > option_nat ) > option_nat > option_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 6.92/7.11 case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_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_001t__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,type,
% 6.92/7.11 case_o2963978774867076333it_nat: option8956607266484857688it_nat > ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > option8956607266484857688it_nat > option8956607266484857688it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_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_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,
% 6.92/7.11 case_o7727800614283616222it_nat: option8956607266484857688it_nat > ( produc3260487557148687353it_nat > option8956607266484857688it_nat ) > option3562590408128118217it_nat > option8956607266484857688it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_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_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 case_o2632329678403290591it_nat: option8956607266484857688it_nat > ( produc7388388658123137530it_nat > option8956607266484857688it_nat ) > option4065278094766928714it_nat > option8956607266484857688it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_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_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,
% 6.92/7.11 case_o6061097939050036047it_nat: option3562590408128118217it_nat > ( produc3260487557148687353it_nat > option3562590408128118217it_nat ) > option3562590408128118217it_nat > option3562590408128118217it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_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_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 case_o965627003169710416it_nat: option3562590408128118217it_nat > ( produc7388388658123137530it_nat > option3562590408128118217it_nat ) > option4065278094766928714it_nat > option3562590408128118217it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_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,
% 6.92/7.11 case_o1773283271472524752it_nat: option4065278094766928714it_nat > ( produc3260487557148687353it_nat > option4065278094766928714it_nat ) > option3562590408128118217it_nat > option4065278094766928714it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 case_o5901184372446974929it_nat: option4065278094766928714it_nat > ( produc7388388658123137530it_nat > option4065278094766928714it_nat ) > option4065278094766928714it_nat > option4065278094766928714it_nat ).
% 6.92/7.11
% 6.92/7.11 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,
% 6.92/7.11 case_o4054078431260844265et_nat: option_set_nat > ( set_nat > option_set_nat ) > option_set_nat > option_set_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_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_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,
% 6.92/7.11 case_o8757249484648823045at_nat: option2498585697089621389at_nat > ( set_Pr8551490117392284871at_nat > option2498585697089621389at_nat ) > option2498585697089621389at_nat > option2498585697089621389at_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 case_o311359030874850053at_nat: option8963830502488799655at_nat > ( set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ) > option8963830502488799655at_nat > option8963830502488799655at_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_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_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,
% 6.92/7.11 case_o9080059180780454917at_nat: option1583680563626158861at_nat > ( set_Pr4329608150637261639at_nat > option1583680563626158861at_nat ) > option1583680563626158861at_nat > option1583680563626158861at_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_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,type,
% 6.92/7.11 map_op3563471509957180299nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option8057788054806935849nteger > option7428179582072448501nteger ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 6.92/7.11 map_op370346339404370627nteger: ( code_integer > code_integer > code_integer ) > option_Code_integer > option8057788054806935849nteger ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_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,type,
% 6.92/7.11 map_op9146685272036663823nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option_Code_integer > option7428179582072448501nteger ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 6.92/7.11 map_op3669829223712506439nteger: ( code_integer > code_integer ) > option_Code_integer > option_Code_integer ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.11 map_option_int_int: ( int > int ) > option_int > option_int ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Int__Oint_001t__Nat__Onat,type,
% 6.92/7.11 map_option_int_nat: ( int > nat ) > option_int > option_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Num__Onum,type,
% 6.92/7.11 map_option_num_num: ( num > num ) > option_num > option_num ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__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,type,
% 6.92/7.11 map_op8118133509425879471it_nat: ( num > produc8664842809031399944it_nat ) > option_num > option8956607266484857688it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_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,
% 6.92/7.11 map_op7586128837645442720it_nat: ( num > produc3260487557148687353it_nat ) > option_num > option3562590408128118217it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 map_op2490657901765117089it_nat: ( num > produc7388388658123137530it_nat ) > option_num > option4065278094766928714it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__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_001t__Num__Onum,type,
% 6.92/7.11 map_op2731889312448867759at_num: ( produc8664842809031399944it_nat > num ) > option8956607266484857688it_nat > option_num ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__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_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 map_op604423251913076367it_nat: ( produc8664842809031399944it_nat > produc7388388658123137530it_nat ) > option8956607266484857688it_nat > option4065278094766928714it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_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_001t__Num__Onum,type,
% 6.92/7.11 map_op5165227558541518752at_num: ( produc3260487557148687353it_nat > num ) > option3562590408128118217it_nat > option_num ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_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_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 map_op7599720869725723008it_nat: ( produc3260487557148687353it_nat > produc7388388658123137530it_nat ) > option3562590408128118217it_nat > option4065278094766928714it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
% 6.92/7.11 map_op6233829773304596897at_num: ( produc7388388658123137530it_nat > num ) > option4065278094766928714it_nat > option_num ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__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,type,
% 6.92/7.11 map_op8924890681001947535it_nat: ( produc7388388658123137530it_nat > produc8664842809031399944it_nat ) > option4065278094766928714it_nat > option8956607266484857688it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_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,
% 6.92/7.11 map_op4453737856117102208it_nat: ( produc7388388658123137530it_nat > produc3260487557148687353it_nat ) > option4065278094766928714it_nat > option3562590408128118217it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 map_op8581638957091552385it_nat: ( produc7388388658123137530it_nat > produc7388388658123137530it_nat ) > option4065278094766928714it_nat > option4065278094766928714it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Osize__option_001t__Int__Oint,type,
% 6.92/7.11 size_option_int: ( int > nat ) > option_int > nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
% 6.92/7.11 size_option_num: ( num > nat ) > option_num > nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Osize__option_001t__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,type,
% 6.92/7.11 size_o29782932136985253it_nat: ( produc8664842809031399944it_nat > nat ) > option8956607266484857688it_nat > nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Osize__option_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,
% 6.92/7.11 size_o1731029420616209814it_nat: ( produc3260487557148687353it_nat > nat ) > option3562590408128118217it_nat > nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 size_o5858930521590659991it_nat: ( produc7388388658123137530it_nat > nat ) > option4065278094766928714it_nat > nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Order__Relation_Olinear__order__on_001t__Nat__Onat,type,
% 6.92/7.11 order_4473980167227706203on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Order__Relation_Opartial__order__on_001t__Nat__Onat,type,
% 6.92/7.11 order_5251275573222108571on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Order__Relation_Opreorder__on_001t__Nat__Onat,type,
% 6.92/7.11 order_4861654808422542329on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Order__Relation_OunderS_001t__Nat__Onat,type,
% 6.92/7.11 order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Order__Relation_Owell__order__on_001t__Nat__Onat,type,
% 6.92/7.11 order_2888998067076097458on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Orderings_Obot__class_Obot_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,
% 6.92/7.11 bot_bo3790638025767943357_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Orderings_Obot__class_Obot_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,
% 6.92/7.11 bot_bo5580076615179976505_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_Eo_M_Eo_J,type,
% 6.92/7.11 bot_bot_o_o: $o > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 6.92/7.11 bot_bot_int_int_o: int > int > $o ).
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% 6.92/7.11 thf(sy_c_Product__Type_OPair_001tf__b_001tf__b,type,
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oarray_It__Nat__Onat_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Heap__Oarray_It__Nat__Onat_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11 produc5645566021302314940it_nat: ( heap_e7401611519738050253t_unit > nat > option3562590408128118217it_nat ) > produc6653097349344004940it_nat > option3562590408128118217it_nat ).
% 6.92/7.11
% 6.92/7.11 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__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 6.92/7.11 produc6148253707941125437it_nat: ( heap_e7401611519738050253t_unit > nat > option4065278094766928714it_nat ) > produc6653097349344004940it_nat > option4065278094766928714it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 6.92/7.11 produc1459180154077124618_int_o: ( int > int > product_prod_int_int > $o ) > product_prod_int_int > product_prod_int_int > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 6.92/7.11 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_I_Eo_J,type,
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.11 produc73460835934605544et_int: ( int > int > set_int ) > product_prod_int_int > set_int ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.11 produc4251311855443802252et_nat: ( int > int > set_nat ) > product_prod_int_int > set_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.11 produc5233655623923918146et_nat: ( int > int > set_set_nat ) > product_prod_int_int > set_set_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
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% 6.92/7.11
% 6.92/7.11 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,
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 6.92/7.11 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 6.92/7.11 produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
% 6.92/7.11 produc2761476792215241774st_nat: ( nat > nat > list_nat ) > product_prod_nat_nat > list_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Ounit_OAbs__unit,type,
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Ounit_ORep__unit,type,
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Random_Oinc__shift,type,
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11 thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.11 member_set_int: set_int > set_set_int > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.11 member_set_nat: set_nat > set_set_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 6.92/7.11 member2340774599025711042nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_P,type,
% 6.92/7.11 p: assn ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_Q,type,
% 6.92/7.11 q: b > assn ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_R,type,
% 6.92/7.11 r: a > assn ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_as____,type,
% 6.92/7.11 as: set_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_f,type,
% 6.92/7.11 f: heap_Time_Heap_a ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_g,type,
% 6.92/7.11 g: a > heap_Time_Heap_b ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_h_H_H____,type,
% 6.92/7.11 h: heap_e7401611519738050253t_unit ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_h_H____,type,
% 6.92/7.11 h2: heap_e7401611519738050253t_unit ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_h____,type,
% 6.92/7.11 h3: heap_e7401611519738050253t_unit ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_rf____,type,
% 6.92/7.11 rf: a ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_rg____,type,
% 6.92/7.11 rg: b ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_t_H_H____,type,
% 6.92/7.11 t: nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_t_H____,type,
% 6.92/7.11 t2: nat ).
% 6.92/7.11
% 6.92/7.11 % Relevant facts (10207)
% 6.92/7.11 thf(fact_0__092_060open_062new__addrs_Ah_H_A_Inew__addrs_Ah_Aas_Ah_H_J_Ah_H_H_A_061_Anew__addrs_Ah_Aas_Ah_H_H_092_060close_062,axiom,
% 6.92/7.11 ( ( hoare_new_addrs @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) @ h )
% 6.92/7.11 = ( hoare_new_addrs @ h3 @ as @ h ) ) ).
% 6.92/7.11
% 6.92/7.11 % \<open>new_addrs h' (new_addrs h as h') h'' = new_addrs h as h''\<close>
% 6.92/7.11 thf(fact_1__092_060open_062_Ih_M_Aas_J_A_092_060Turnstile_062_AP_092_060close_062,axiom,
% 6.92/7.11 rep_assn @ p @ ( produc7507926704131184380et_nat @ h3 @ as ) ).
% 6.92/7.11
% 6.92/7.11 % \<open>(h, as) \<Turnstile> P\<close>
% 6.92/7.11 thf(fact_2_new__addr__refl,axiom,
% 6.92/7.11 ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.11 ( ( hoare_new_addrs @ H @ As @ H )
% 6.92/7.11 = As ) ).
% 6.92/7.11
% 6.92/7.11 % new_addr_refl
% 6.92/7.11 thf(fact_3_POST__G,axiom,
% 6.92/7.11 rep_assn @ ( q @ rg ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) @ h ) ) ).
% 6.92/7.11
% 6.92/7.11 % POST_G
% 6.92/7.11 thf(fact_4_POST__F,axiom,
% 6.92/7.11 rep_assn @ ( r @ rf ) @ ( produc7507926704131184380et_nat @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) ) ).
% 6.92/7.11
% 6.92/7.11 % POST_F
% 6.92/7.11 thf(fact_5_Rep__assn__inject,axiom,
% 6.92/7.11 ! [X: assn,Y: assn] :
% 6.92/7.11 ( ( ( rep_assn @ X )
% 6.92/7.11 = ( rep_assn @ Y ) )
% 6.92/7.11 = ( X = Y ) ) ).
% 6.92/7.11
% 6.92/7.11 % Rep_assn_inject
% 6.92/7.11 thf(fact_6_prod_Oinject,axiom,
% 6.92/7.11 ! [X1: int,X2: int,Y1: int,Y2: int] :
% 6.92/7.11 ( ( ( product_Pair_int_int @ X1 @ X2 )
% 6.92/7.11 = ( product_Pair_int_int @ Y1 @ Y2 ) )
% 6.92/7.11 = ( ( X1 = Y1 )
% 6.92/7.11 & ( X2 = Y2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod.inject
% 6.92/7.11 thf(fact_7_prod_Oinject,axiom,
% 6.92/7.11 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3658429121746597890et_nat,Y1: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( ( produc5001842942810119800et_nat @ X1 @ X2 )
% 6.92/7.11 = ( produc5001842942810119800et_nat @ Y1 @ Y2 ) )
% 6.92/7.11 = ( ( X1 = Y1 )
% 6.92/7.11 & ( X2 = Y2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod.inject
% 6.92/7.11 thf(fact_8_prod_Oinject,axiom,
% 6.92/7.11 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3925858234332021118et_nat,Y1: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( ( produc2245416461498447860et_nat @ X1 @ X2 )
% 6.92/7.11 = ( produc2245416461498447860et_nat @ Y1 @ Y2 ) )
% 6.92/7.11 = ( ( X1 = Y1 )
% 6.92/7.11 & ( X2 = Y2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod.inject
% 6.92/7.11 thf(fact_9_prod_Oinject,axiom,
% 6.92/7.11 ! [X1: b,X2: produc6653097349344004940it_nat,Y1: b,Y2: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( produc4082563078715348724it_nat @ X1 @ X2 )
% 6.92/7.11 = ( produc4082563078715348724it_nat @ Y1 @ Y2 ) )
% 6.92/7.11 = ( ( X1 = Y1 )
% 6.92/7.11 & ( X2 = Y2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod.inject
% 6.92/7.11 thf(fact_10_prod_Oinject,axiom,
% 6.92/7.11 ! [X1: a,X2: produc6653097349344004940it_nat,Y1: a,Y2: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( produc9178034014595674355it_nat @ X1 @ X2 )
% 6.92/7.11 = ( produc9178034014595674355it_nat @ Y1 @ Y2 ) )
% 6.92/7.11 = ( ( X1 = Y1 )
% 6.92/7.11 & ( X2 = Y2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod.inject
% 6.92/7.11 thf(fact_11_old_Oprod_Oinject,axiom,
% 6.92/7.11 ! [A: int,B: int,A2: int,B2: int] :
% 6.92/7.11 ( ( ( product_Pair_int_int @ A @ B )
% 6.92/7.11 = ( product_Pair_int_int @ A2 @ B2 ) )
% 6.92/7.11 = ( ( A = A2 )
% 6.92/7.11 & ( B = B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.inject
% 6.92/7.11 thf(fact_12_old_Oprod_Oinject,axiom,
% 6.92/7.11 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( ( produc5001842942810119800et_nat @ A @ B )
% 6.92/7.11 = ( produc5001842942810119800et_nat @ A2 @ B2 ) )
% 6.92/7.11 = ( ( A = A2 )
% 6.92/7.11 & ( B = B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.inject
% 6.92/7.11 thf(fact_13_old_Oprod_Oinject,axiom,
% 6.92/7.11 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( ( produc2245416461498447860et_nat @ A @ B )
% 6.92/7.11 = ( produc2245416461498447860et_nat @ A2 @ B2 ) )
% 6.92/7.11 = ( ( A = A2 )
% 6.92/7.11 & ( B = B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.inject
% 6.92/7.11 thf(fact_14_old_Oprod_Oinject,axiom,
% 6.92/7.11 ! [A: b,B: produc6653097349344004940it_nat,A2: b,B2: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( produc4082563078715348724it_nat @ A @ B )
% 6.92/7.11 = ( produc4082563078715348724it_nat @ A2 @ B2 ) )
% 6.92/7.11 = ( ( A = A2 )
% 6.92/7.11 & ( B = B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.inject
% 6.92/7.11 thf(fact_15_old_Oprod_Oinject,axiom,
% 6.92/7.11 ! [A: a,B: produc6653097349344004940it_nat,A2: a,B2: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( produc9178034014595674355it_nat @ A @ B )
% 6.92/7.11 = ( produc9178034014595674355it_nat @ A2 @ B2 ) )
% 6.92/7.11 = ( ( A = A2 )
% 6.92/7.11 & ( B = B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.inject
% 6.92/7.11 thf(fact_16_one__assn__raw_Ocases,axiom,
% 6.92/7.11 ! [X: produc3658429121746597890et_nat] :
% 6.92/7.11 ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.11 ( X
% 6.92/7.11 != ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ).
% 6.92/7.11
% 6.92/7.11 % one_assn_raw.cases
% 6.92/7.11 thf(fact_17_times__assn__raw_Ocases,axiom,
% 6.92/7.11 ! [X: produc2732055786443039994et_nat] :
% 6.92/7.11 ~ ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.11 ( X
% 6.92/7.11 != ( produc2245416461498447860et_nat @ P @ ( produc5001842942810119800et_nat @ Q @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % times_assn_raw.cases
% 6.92/7.11 thf(fact_18_prod__induct4,axiom,
% 6.92/7.11 ! [P2: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 6.92/7.11 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: heap_e7401611519738050253t_unit,D: set_nat] : ( P2 @ ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ ( produc7507926704131184380et_nat @ C @ D ) ) ) )
% 6.92/7.11 => ( P2 @ X ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_induct4
% 6.92/7.11 thf(fact_19_prod__induct3,axiom,
% 6.92/7.11 ! [P2: produc3925858234332021118et_nat > $o,X: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ! [A3: produc3658429121746597890et_nat > $o,B3: heap_e7401611519738050253t_unit,C: set_nat] : ( P2 @ ( produc5001842942810119800et_nat @ A3 @ ( produc7507926704131184380et_nat @ B3 @ C ) ) )
% 6.92/7.11 => ( P2 @ X ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_induct3
% 6.92/7.11 thf(fact_20_prod__induct3,axiom,
% 6.92/7.11 ! [P2: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 6.92/7.11 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: produc3658429121746597890et_nat] : ( P2 @ ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ C ) ) )
% 6.92/7.11 => ( P2 @ X ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_induct3
% 6.92/7.11 thf(fact_21_prod__induct3,axiom,
% 6.92/7.11 ! [P2: produc7388388658123137530it_nat > $o,X: produc7388388658123137530it_nat] :
% 6.92/7.11 ( ! [A3: b,B3: heap_e7401611519738050253t_unit,C: nat] : ( P2 @ ( produc4082563078715348724it_nat @ A3 @ ( produc584006145561248582it_nat @ B3 @ C ) ) )
% 6.92/7.11 => ( P2 @ X ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_induct3
% 6.92/7.11 thf(fact_22_prod__induct3,axiom,
% 6.92/7.11 ! [P2: produc3260487557148687353it_nat > $o,X: produc3260487557148687353it_nat] :
% 6.92/7.11 ( ! [A3: a,B3: heap_e7401611519738050253t_unit,C: nat] : ( P2 @ ( produc9178034014595674355it_nat @ A3 @ ( produc584006145561248582it_nat @ B3 @ C ) ) )
% 6.92/7.11 => ( P2 @ X ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_induct3
% 6.92/7.11 thf(fact_23_prod__cases4,axiom,
% 6.92/7.11 ! [Y: produc2732055786443039994et_nat] :
% 6.92/7.11 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: heap_e7401611519738050253t_unit,D: set_nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ ( produc7507926704131184380et_nat @ C @ D ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases4
% 6.92/7.11 thf(fact_24_prod__cases3,axiom,
% 6.92/7.11 ! [Y: produc3925858234332021118et_nat] :
% 6.92/7.11 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: heap_e7401611519738050253t_unit,C: set_nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc5001842942810119800et_nat @ A3 @ ( produc7507926704131184380et_nat @ B3 @ C ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases3
% 6.92/7.11 thf(fact_25_prod__cases3,axiom,
% 6.92/7.11 ! [Y: produc2732055786443039994et_nat] :
% 6.92/7.11 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: produc3658429121746597890et_nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ C ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases3
% 6.92/7.11 thf(fact_26_prod__cases3,axiom,
% 6.92/7.11 ! [Y: produc7388388658123137530it_nat] :
% 6.92/7.11 ~ ! [A3: b,B3: heap_e7401611519738050253t_unit,C: nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc4082563078715348724it_nat @ A3 @ ( produc584006145561248582it_nat @ B3 @ C ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases3
% 6.92/7.11 thf(fact_27_prod__cases3,axiom,
% 6.92/7.11 ! [Y: produc3260487557148687353it_nat] :
% 6.92/7.11 ~ ! [A3: a,B3: heap_e7401611519738050253t_unit,C: nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc9178034014595674355it_nat @ A3 @ ( produc584006145561248582it_nat @ B3 @ C ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases3
% 6.92/7.11 thf(fact_28_Pair__inject,axiom,
% 6.92/7.11 ! [A: int,B: int,A2: int,B2: int] :
% 6.92/7.11 ( ( ( product_Pair_int_int @ A @ B )
% 6.92/7.11 = ( product_Pair_int_int @ A2 @ B2 ) )
% 6.92/7.11 => ~ ( ( A = A2 )
% 6.92/7.11 => ( B != B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Pair_inject
% 6.92/7.11 thf(fact_29_Pair__inject,axiom,
% 6.92/7.11 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( ( produc5001842942810119800et_nat @ A @ B )
% 6.92/7.11 = ( produc5001842942810119800et_nat @ A2 @ B2 ) )
% 6.92/7.11 => ~ ( ( A = A2 )
% 6.92/7.11 => ( B != B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Pair_inject
% 6.92/7.11 thf(fact_30_Pair__inject,axiom,
% 6.92/7.11 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( ( produc2245416461498447860et_nat @ A @ B )
% 6.92/7.11 = ( produc2245416461498447860et_nat @ A2 @ B2 ) )
% 6.92/7.11 => ~ ( ( A = A2 )
% 6.92/7.11 => ( B != B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Pair_inject
% 6.92/7.11 thf(fact_31_Pair__inject,axiom,
% 6.92/7.11 ! [A: b,B: produc6653097349344004940it_nat,A2: b,B2: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( produc4082563078715348724it_nat @ A @ B )
% 6.92/7.11 = ( produc4082563078715348724it_nat @ A2 @ B2 ) )
% 6.92/7.11 => ~ ( ( A = A2 )
% 6.92/7.11 => ( B != B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Pair_inject
% 6.92/7.11 thf(fact_32_Pair__inject,axiom,
% 6.92/7.11 ! [A: a,B: produc6653097349344004940it_nat,A2: a,B2: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( produc9178034014595674355it_nat @ A @ B )
% 6.92/7.11 = ( produc9178034014595674355it_nat @ A2 @ B2 ) )
% 6.92/7.11 => ~ ( ( A = A2 )
% 6.92/7.11 => ( B != B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Pair_inject
% 6.92/7.11 thf(fact_33_prod__cases,axiom,
% 6.92/7.11 ! [P2: product_prod_int_int > $o,P3: product_prod_int_int] :
% 6.92/7.11 ( ! [A3: int,B3: int] : ( P2 @ ( product_Pair_int_int @ A3 @ B3 ) )
% 6.92/7.11 => ( P2 @ P3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases
% 6.92/7.11 thf(fact_34_prod__cases,axiom,
% 6.92/7.11 ! [P2: produc3925858234332021118et_nat > $o,P3: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] : ( P2 @ ( produc5001842942810119800et_nat @ A3 @ B3 ) )
% 6.92/7.11 => ( P2 @ P3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases
% 6.92/7.11 thf(fact_35_prod__cases,axiom,
% 6.92/7.11 ! [P2: produc2732055786443039994et_nat > $o,P3: produc2732055786443039994et_nat] :
% 6.92/7.11 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] : ( P2 @ ( produc2245416461498447860et_nat @ A3 @ B3 ) )
% 6.92/7.11 => ( P2 @ P3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases
% 6.92/7.11 thf(fact_36_prod__cases,axiom,
% 6.92/7.11 ! [P2: produc7388388658123137530it_nat > $o,P3: produc7388388658123137530it_nat] :
% 6.92/7.11 ( ! [A3: b,B3: produc6653097349344004940it_nat] : ( P2 @ ( produc4082563078715348724it_nat @ A3 @ B3 ) )
% 6.92/7.11 => ( P2 @ P3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases
% 6.92/7.11 thf(fact_37_prod__cases,axiom,
% 6.92/7.11 ! [P2: produc3260487557148687353it_nat > $o,P3: produc3260487557148687353it_nat] :
% 6.92/7.11 ( ! [A3: a,B3: produc6653097349344004940it_nat] : ( P2 @ ( produc9178034014595674355it_nat @ A3 @ B3 ) )
% 6.92/7.11 => ( P2 @ P3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases
% 6.92/7.11 thf(fact_38_surj__pair,axiom,
% 6.92/7.11 ! [P3: product_prod_int_int] :
% 6.92/7.11 ? [X3: int,Y3: int] :
% 6.92/7.11 ( P3
% 6.92/7.11 = ( product_Pair_int_int @ X3 @ Y3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % surj_pair
% 6.92/7.11 thf(fact_39_surj__pair,axiom,
% 6.92/7.11 ! [P3: produc3925858234332021118et_nat] :
% 6.92/7.11 ? [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] :
% 6.92/7.11 ( P3
% 6.92/7.11 = ( produc5001842942810119800et_nat @ X3 @ Y3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % surj_pair
% 6.92/7.11 thf(fact_40_surj__pair,axiom,
% 6.92/7.11 ! [P3: produc2732055786443039994et_nat] :
% 6.92/7.11 ? [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] :
% 6.92/7.11 ( P3
% 6.92/7.11 = ( produc2245416461498447860et_nat @ X3 @ Y3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % surj_pair
% 6.92/7.11 thf(fact_41_surj__pair,axiom,
% 6.92/7.11 ! [P3: produc7388388658123137530it_nat] :
% 6.92/7.11 ? [X3: b,Y3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( P3
% 6.92/7.11 = ( produc4082563078715348724it_nat @ X3 @ Y3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % surj_pair
% 6.92/7.11 thf(fact_42_surj__pair,axiom,
% 6.92/7.11 ! [P3: produc3260487557148687353it_nat] :
% 6.92/7.11 ? [X3: a,Y3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( P3
% 6.92/7.11 = ( produc9178034014595674355it_nat @ X3 @ Y3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % surj_pair
% 6.92/7.11 thf(fact_43_bex2I,axiom,
% 6.92/7.11 ! [A: int,B: int,S: set_Pr958786334691620121nt_int,P2: int > int > $o] :
% 6.92/7.11 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ S )
% 6.92/7.11 => ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ S )
% 6.92/7.11 => ( P2 @ A @ B ) )
% 6.92/7.11 => ? [A3: int,B3: int] :
% 6.92/7.11 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A3 @ B3 ) @ S )
% 6.92/7.11 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bex2I
% 6.92/7.11 thf(fact_44_bex2I,axiom,
% 6.92/7.11 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S: set_Pr3286484037609594932et_nat,P2: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 6.92/7.11 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S )
% 6.92/7.11 => ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S )
% 6.92/7.11 => ( P2 @ A @ B ) )
% 6.92/7.11 => ? [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A3 @ B3 ) @ S )
% 6.92/7.11 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bex2I
% 6.92/7.11 thf(fact_45_bex2I,axiom,
% 6.92/7.11 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S: set_Pr8536935166611901872et_nat,P2: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 6.92/7.11 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S )
% 6.92/7.11 => ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S )
% 6.92/7.11 => ( P2 @ A @ B ) )
% 6.92/7.11 => ? [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A3 @ B3 ) @ S )
% 6.92/7.11 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bex2I
% 6.92/7.11 thf(fact_46_bex2I,axiom,
% 6.92/7.11 ! [A: b,B: produc6653097349344004940it_nat,S: set_Pr7600907837789447088it_nat,P2: b > produc6653097349344004940it_nat > $o] :
% 6.92/7.11 ( ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ A @ B ) @ S )
% 6.92/7.11 => ( ( ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ A @ B ) @ S )
% 6.92/7.11 => ( P2 @ A @ B ) )
% 6.92/7.11 => ? [A3: b,B3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ A3 @ B3 ) @ S )
% 6.92/7.11 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bex2I
% 6.92/7.11 thf(fact_47_bex2I,axiom,
% 6.92/7.11 ! [A: a,B: produc6653097349344004940it_nat,S: set_Pr7098220151150636591it_nat,P2: a > produc6653097349344004940it_nat > $o] :
% 6.92/7.11 ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ A @ B ) @ S )
% 6.92/7.11 => ( ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ A @ B ) @ S )
% 6.92/7.11 => ( P2 @ A @ B ) )
% 6.92/7.11 => ? [A3: a,B3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ A3 @ B3 ) @ S )
% 6.92/7.11 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bex2I
% 6.92/7.11 thf(fact_48_old_Oprod_Oexhaust,axiom,
% 6.92/7.11 ! [Y: product_prod_int_int] :
% 6.92/7.11 ~ ! [A3: int,B3: int] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( product_Pair_int_int @ A3 @ B3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.exhaust
% 6.92/7.11 thf(fact_49_old_Oprod_Oexhaust,axiom,
% 6.92/7.11 ! [Y: produc3925858234332021118et_nat] :
% 6.92/7.11 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc5001842942810119800et_nat @ A3 @ B3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.exhaust
% 6.92/7.11 thf(fact_50_old_Oprod_Oexhaust,axiom,
% 6.92/7.11 ! [Y: produc2732055786443039994et_nat] :
% 6.92/7.11 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc2245416461498447860et_nat @ A3 @ B3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.exhaust
% 6.92/7.11 thf(fact_51_old_Oprod_Oexhaust,axiom,
% 6.92/7.11 ! [Y: produc7388388658123137530it_nat] :
% 6.92/7.11 ~ ! [A3: b,B3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc4082563078715348724it_nat @ A3 @ B3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.exhaust
% 6.92/7.11 thf(fact_52_old_Oprod_Oexhaust,axiom,
% 6.92/7.11 ! [Y: produc3260487557148687353it_nat] :
% 6.92/7.11 ~ ! [A3: a,B3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc9178034014595674355it_nat @ A3 @ B3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.exhaust
% 6.92/7.11 thf(fact_53_T1,axiom,
% 6.92/7.11 hoare_hoare_triple_a @ p @ f @ r ).
% 6.92/7.11
% 6.92/7.11 % T1
% 6.92/7.11 thf(fact_54_T2,axiom,
% 6.92/7.11 ! [X: a] : ( hoare_hoare_triple_b @ ( r @ X ) @ ( g @ X ) @ q ) ).
% 6.92/7.11
% 6.92/7.11 % T2
% 6.92/7.11 thf(fact_55_EX__G,axiom,
% 6.92/7.11 ( ( heap_Time_execute_b @ ( g @ rf ) @ h2 )
% 6.92/7.11 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ rg @ ( produc584006145561248582it_nat @ h @ t ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % EX_G
% 6.92/7.11 thf(fact_56_LIM__G,axiom,
% 6.92/7.11 ord_less_eq_nat @ ( lim_Product_unit @ h2 ) @ ( lim_Product_unit @ h ) ).
% 6.92/7.11
% 6.92/7.11 % LIM_G
% 6.92/7.11 thf(fact_57_LIM__F,axiom,
% 6.92/7.11 ord_less_eq_nat @ ( lim_Product_unit @ h3 ) @ ( lim_Product_unit @ h2 ) ).
% 6.92/7.11
% 6.92/7.11 % LIM_F
% 6.92/7.11 thf(fact_58_EX__F,axiom,
% 6.92/7.11 ( ( heap_Time_execute_a @ f @ h3 )
% 6.92/7.11 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ rf @ ( produc584006145561248582it_nat @ h2 @ t2 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % EX_F
% 6.92/7.11 thf(fact_59_mem__Collect__eq,axiom,
% 6.92/7.11 ! [A: $o,P2: $o > $o] :
% 6.92/7.11 ( ( member_o @ A @ ( collect_o @ P2 ) )
% 6.92/7.11 = ( P2 @ A ) ) ).
% 6.92/7.11
% 6.92/7.11 % mem_Collect_eq
% 6.92/7.11 thf(fact_60_mem__Collect__eq,axiom,
% 6.92/7.11 ! [A: list_nat,P2: list_nat > $o] :
% 6.92/7.11 ( ( member_list_nat @ A @ ( collect_list_nat @ P2 ) )
% 6.92/7.11 = ( P2 @ A ) ) ).
% 6.92/7.11
% 6.92/7.11 % mem_Collect_eq
% 6.92/7.11 thf(fact_61_mem__Collect__eq,axiom,
% 6.92/7.11 ! [A: set_Pr958786334691620121nt_int,P2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.11 ( ( member2340774599025711042nt_int @ A @ ( collec5210948495886036740nt_int @ P2 ) )
% 6.92/7.11 = ( P2 @ A ) ) ).
% 6.92/7.11
% 6.92/7.11 % mem_Collect_eq
% 6.92/7.11 thf(fact_62_mem__Collect__eq,axiom,
% 6.92/7.11 ! [A: set_nat,P2: set_nat > $o] :
% 6.92/7.11 ( ( member_set_nat @ A @ ( collect_set_nat @ P2 ) )
% 6.92/7.11 = ( P2 @ A ) ) ).
% 6.92/7.11
% 6.92/7.11 % mem_Collect_eq
% 6.92/7.11 thf(fact_63_mem__Collect__eq,axiom,
% 6.92/7.11 ! [A: nat,P2: nat > $o] :
% 6.92/7.11 ( ( member_nat @ A @ ( collect_nat @ P2 ) )
% 6.92/7.11 = ( P2 @ A ) ) ).
% 6.92/7.11
% 6.92/7.11 % mem_Collect_eq
% 6.92/7.11 thf(fact_64_mem__Collect__eq,axiom,
% 6.92/7.11 ! [A: int,P2: int > $o] :
% 6.92/7.11 ( ( member_int @ A @ ( collect_int @ P2 ) )
% 6.92/7.11 = ( P2 @ A ) ) ).
% 6.92/7.11
% 6.92/7.11 % mem_Collect_eq
% 6.92/7.11 thf(fact_65_Collect__mem__eq,axiom,
% 6.92/7.11 ! [A4: set_o] :
% 6.92/7.11 ( ( collect_o
% 6.92/7.11 @ ^ [X4: $o] : ( member_o @ X4 @ A4 ) )
% 6.92/7.11 = A4 ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_mem_eq
% 6.92/7.11 thf(fact_66_Collect__mem__eq,axiom,
% 6.92/7.11 ! [A4: set_list_nat] :
% 6.92/7.11 ( ( collect_list_nat
% 6.92/7.11 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A4 ) )
% 6.92/7.11 = A4 ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_mem_eq
% 6.92/7.11 thf(fact_67_Collect__mem__eq,axiom,
% 6.92/7.11 ! [A4: set_se6260736226359567993nt_int] :
% 6.92/7.11 ( ( collec5210948495886036740nt_int
% 6.92/7.11 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ A4 ) )
% 6.92/7.11 = A4 ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_mem_eq
% 6.92/7.11 thf(fact_68_Collect__mem__eq,axiom,
% 6.92/7.11 ! [A4: set_set_nat] :
% 6.92/7.11 ( ( collect_set_nat
% 6.92/7.11 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A4 ) )
% 6.92/7.11 = A4 ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_mem_eq
% 6.92/7.11 thf(fact_69_Collect__mem__eq,axiom,
% 6.92/7.11 ! [A4: set_nat] :
% 6.92/7.11 ( ( collect_nat
% 6.92/7.11 @ ^ [X4: nat] : ( member_nat @ X4 @ A4 ) )
% 6.92/7.11 = A4 ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_mem_eq
% 6.92/7.11 thf(fact_70_Collect__mem__eq,axiom,
% 6.92/7.11 ! [A4: set_int] :
% 6.92/7.11 ( ( collect_int
% 6.92/7.11 @ ^ [X4: int] : ( member_int @ X4 @ A4 ) )
% 6.92/7.11 = A4 ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_mem_eq
% 6.92/7.11 thf(fact_71_Collect__cong,axiom,
% 6.92/7.11 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 6.92/7.11 ( ! [X3: list_nat] :
% 6.92/7.11 ( ( P2 @ X3 )
% 6.92/7.11 = ( Q2 @ X3 ) )
% 6.92/7.11 => ( ( collect_list_nat @ P2 )
% 6.92/7.11 = ( collect_list_nat @ Q2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_cong
% 6.92/7.11 thf(fact_72_Collect__cong,axiom,
% 6.92/7.11 ! [P2: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.11 ( ! [X3: set_Pr958786334691620121nt_int] :
% 6.92/7.11 ( ( P2 @ X3 )
% 6.92/7.11 = ( Q2 @ X3 ) )
% 6.92/7.11 => ( ( collec5210948495886036740nt_int @ P2 )
% 6.92/7.11 = ( collec5210948495886036740nt_int @ Q2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_cong
% 6.92/7.11 thf(fact_73_Collect__cong,axiom,
% 6.92/7.11 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 6.92/7.11 ( ! [X3: set_nat] :
% 6.92/7.11 ( ( P2 @ X3 )
% 6.92/7.11 = ( Q2 @ X3 ) )
% 6.92/7.11 => ( ( collect_set_nat @ P2 )
% 6.92/7.11 = ( collect_set_nat @ Q2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_cong
% 6.92/7.11 thf(fact_74_Collect__cong,axiom,
% 6.92/7.11 ! [P2: nat > $o,Q2: nat > $o] :
% 6.92/7.11 ( ! [X3: nat] :
% 6.92/7.11 ( ( P2 @ X3 )
% 6.92/7.11 = ( Q2 @ X3 ) )
% 6.92/7.11 => ( ( collect_nat @ P2 )
% 6.92/7.11 = ( collect_nat @ Q2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_cong
% 6.92/7.11 thf(fact_75_Collect__cong,axiom,
% 6.92/7.11 ! [P2: int > $o,Q2: int > $o] :
% 6.92/7.11 ( ! [X3: int] :
% 6.92/7.11 ( ( P2 @ X3 )
% 6.92/7.11 = ( Q2 @ X3 ) )
% 6.92/7.11 => ( ( collect_int @ P2 )
% 6.92/7.11 = ( collect_int @ Q2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_cong
% 6.92/7.11 thf(fact_76_bijective__def,axiom,
% 6.92/7.11 ( bijective_int_int
% 6.92/7.11 = ( ^ [R: set_Pr958786334691620121nt_int] :
% 6.92/7.11 ( ! [X4: int,Y4: int,Z: int] :
% 6.92/7.11 ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R )
% 6.92/7.11 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Z ) @ R ) )
% 6.92/7.11 => ( Y4 = Z ) )
% 6.92/7.11 & ! [X4: int,Y4: int,Z: int] :
% 6.92/7.11 ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Z ) @ R )
% 6.92/7.11 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y4 @ Z ) @ R ) )
% 6.92/7.11 => ( X4 = Y4 ) ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bijective_def
% 6.92/7.11 thf(fact_77_bijective__def,axiom,
% 6.92/7.11 ( biject2615096655818420098et_nat
% 6.92/7.11 = ( ^ [R: set_Pr3286484037609594932et_nat] :
% 6.92/7.11 ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat,Z: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R )
% 6.92/7.11 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Z ) @ R ) )
% 6.92/7.11 => ( Y4 = Z ) )
% 6.92/7.11 & ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat > $o,Z: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Z ) @ R )
% 6.92/7.11 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ Y4 @ Z ) @ R ) )
% 6.92/7.11 => ( X4 = Y4 ) ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bijective_def
% 6.92/7.11 thf(fact_78_bijective__def,axiom,
% 6.92/7.11 ( biject1468766312547416318et_nat
% 6.92/7.11 = ( ^ [R: set_Pr8536935166611901872et_nat] :
% 6.92/7.11 ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat,Z: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R )
% 6.92/7.11 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Z ) @ R ) )
% 6.92/7.11 => ( Y4 = Z ) )
% 6.92/7.11 & ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat > $o,Z: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Z ) @ R )
% 6.92/7.11 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ Y4 @ Z ) @ R ) )
% 6.92/7.11 => ( X4 = Y4 ) ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bijective_def
% 6.92/7.11 thf(fact_79_bijective__def,axiom,
% 6.92/7.11 ( biject3496835315794560510it_nat
% 6.92/7.11 = ( ^ [R: set_Pr7600907837789447088it_nat] :
% 6.92/7.11 ( ! [X4: b,Y4: produc6653097349344004940it_nat,Z: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Y4 ) @ R )
% 6.92/7.11 & ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Z ) @ R ) )
% 6.92/7.11 => ( Y4 = Z ) )
% 6.92/7.11 & ! [X4: b,Y4: b,Z: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Z ) @ R )
% 6.92/7.11 & ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ Y4 @ Z ) @ R ) )
% 6.92/7.11 => ( X4 = Y4 ) ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bijective_def
% 6.92/7.11 thf(fact_80_bijective__def,axiom,
% 6.92/7.11 ( biject8592306251674886141it_nat
% 6.92/7.11 = ( ^ [R: set_Pr7098220151150636591it_nat] :
% 6.92/7.11 ( ! [X4: a,Y4: produc6653097349344004940it_nat,Z: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ R )
% 6.92/7.11 & ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Z ) @ R ) )
% 6.92/7.11 => ( Y4 = Z ) )
% 6.92/7.11 & ! [X4: a,Y4: a,Z: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Z ) @ R )
% 6.92/7.11 & ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ Y4 @ Z ) @ R ) )
% 6.92/7.11 => ( X4 = Y4 ) ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bijective_def
% 6.92/7.11 thf(fact_81_ssubst__Pair__rhs,axiom,
% 6.92/7.11 ! [R2: int,S2: int,R3: set_Pr958786334691620121nt_int,S3: int] :
% 6.92/7.11 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ R2 @ S2 ) @ R3 )
% 6.92/7.11 => ( ( S3 = S2 )
% 6.92/7.11 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ R2 @ S3 ) @ R3 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ssubst_Pair_rhs
% 6.92/7.11 thf(fact_82_ssubst__Pair__rhs,axiom,
% 6.92/7.11 ! [R2: produc3658429121746597890et_nat > $o,S2: produc3658429121746597890et_nat,R3: set_Pr3286484037609594932et_nat,S3: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R2 @ S2 ) @ R3 )
% 6.92/7.11 => ( ( S3 = S2 )
% 6.92/7.11 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R2 @ S3 ) @ R3 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ssubst_Pair_rhs
% 6.92/7.11 thf(fact_83_ssubst__Pair__rhs,axiom,
% 6.92/7.11 ! [R2: produc3658429121746597890et_nat > $o,S2: produc3925858234332021118et_nat,R3: set_Pr8536935166611901872et_nat,S3: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R2 @ S2 ) @ R3 )
% 6.92/7.11 => ( ( S3 = S2 )
% 6.92/7.11 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R2 @ S3 ) @ R3 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ssubst_Pair_rhs
% 6.92/7.11 thf(fact_84_ssubst__Pair__rhs,axiom,
% 6.92/7.11 ! [R2: b,S2: produc6653097349344004940it_nat,R3: set_Pr7600907837789447088it_nat,S3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ R2 @ S2 ) @ R3 )
% 6.92/7.11 => ( ( S3 = S2 )
% 6.92/7.11 => ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ R2 @ S3 ) @ R3 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ssubst_Pair_rhs
% 6.92/7.11 thf(fact_85_ssubst__Pair__rhs,axiom,
% 6.92/7.11 ! [R2: a,S2: produc6653097349344004940it_nat,R3: set_Pr7098220151150636591it_nat,S3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ R2 @ S2 ) @ R3 )
% 6.92/7.11 => ( ( S3 = S2 )
% 6.92/7.11 => ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ R2 @ S3 ) @ R3 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ssubst_Pair_rhs
% 6.92/7.11 thf(fact_86_curryI,axiom,
% 6.92/7.11 ! [F: product_prod_int_int > $o,A: int,B: int] :
% 6.92/7.11 ( ( F @ ( product_Pair_int_int @ A @ B ) )
% 6.92/7.11 => ( produc175634133007206835_int_o @ F @ A @ B ) ) ).
% 6.92/7.11
% 6.92/7.11 % curryI
% 6.92/7.11 thf(fact_87_curryI,axiom,
% 6.92/7.11 ! [F: produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( F @ ( produc5001842942810119800et_nat @ A @ B ) )
% 6.92/7.11 => ( produc6216949301066131538_nat_o @ F @ A @ B ) ) ).
% 6.92/7.11
% 6.92/7.11 % curryI
% 6.92/7.11 thf(fact_88_curryI,axiom,
% 6.92/7.11 ! [F: produc2732055786443039994et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( F @ ( produc2245416461498447860et_nat @ A @ B ) )
% 6.92/7.11 => ( produc5101573711933517782_nat_o @ F @ A @ B ) ) ).
% 6.92/7.11
% 6.92/7.11 % curryI
% 6.92/7.11 thf(fact_89_curryI,axiom,
% 6.92/7.11 ! [F: produc7388388658123137530it_nat > $o,A: b,B: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( F @ ( produc4082563078715348724it_nat @ A @ B ) )
% 6.92/7.11 => ( produc8043051624866120150_nat_o @ F @ A @ B ) ) ).
% 6.92/7.11
% 6.92/7.11 % curryI
% 6.92/7.11 thf(fact_90_curryI,axiom,
% 6.92/7.11 ! [F: produc3260487557148687353it_nat > $o,A: a,B: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( F @ ( produc9178034014595674355it_nat @ A @ B ) )
% 6.92/7.11 => ( produc3709033845735585303_nat_o @ F @ A @ B ) ) ).
% 6.92/7.11
% 6.92/7.11 % curryI
% 6.92/7.11 thf(fact_91_le__some__optE,axiom,
% 6.92/7.11 ! [M: set_int,X: option_set_int] :
% 6.92/7.11 ( ( ord_le353528952715127954et_int @ ( some_set_int @ M ) @ X )
% 6.92/7.11 => ~ ! [M2: set_int] :
% 6.92/7.11 ( ( X
% 6.92/7.11 = ( some_set_int @ M2 ) )
% 6.92/7.11 => ~ ( ord_less_eq_set_int @ M @ M2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % le_some_optE
% 6.92/7.11 thf(fact_92_le__some__optE,axiom,
% 6.92/7.11 ! [M: rat,X: option_rat] :
% 6.92/7.11 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ M ) @ X )
% 6.92/7.11 => ~ ! [M2: rat] :
% 6.92/7.11 ( ( X
% 6.92/7.11 = ( some_rat @ M2 ) )
% 6.92/7.11 => ~ ( ord_less_eq_rat @ M @ M2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % le_some_optE
% 6.92/7.11 thf(fact_93_le__some__optE,axiom,
% 6.92/7.11 ! [M: num,X: option_num] :
% 6.92/7.11 ( ( ord_le6622620407824499402on_num @ ( some_num @ M ) @ X )
% 6.92/7.11 => ~ ! [M2: num] :
% 6.92/7.11 ( ( X
% 6.92/7.11 = ( some_num @ M2 ) )
% 6.92/7.11 => ~ ( ord_less_eq_num @ M @ M2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % le_some_optE
% 6.92/7.11 thf(fact_94_le__some__optE,axiom,
% 6.92/7.11 ! [M: nat,X: option_nat] :
% 6.92/7.11 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ M ) @ X )
% 6.92/7.11 => ~ ! [M2: nat] :
% 6.92/7.11 ( ( X
% 6.92/7.11 = ( some_nat @ M2 ) )
% 6.92/7.11 => ~ ( ord_less_eq_nat @ M @ M2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % le_some_optE
% 6.92/7.11 thf(fact_95_le__some__optE,axiom,
% 6.92/7.11 ! [M: int,X: option_int] :
% 6.92/7.11 ( ( ord_le1736525451366464988on_int @ ( some_int @ M ) @ X )
% 6.92/7.11 => ~ ! [M2: int] :
% 6.92/7.11 ( ( X
% 6.92/7.11 = ( some_int @ M2 ) )
% 6.92/7.11 => ~ ( ord_less_eq_int @ M @ M2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % le_some_optE
% 6.92/7.11 thf(fact_96_ord__eq__le__eq__trans,axiom,
% 6.92/7.11 ! [A: set_int,B: set_int,C2: set_int,D2: set_int] :
% 6.92/7.11 ( ( A = B )
% 6.92/7.11 => ( ( ord_less_eq_set_int @ B @ C2 )
% 6.92/7.11 => ( ( C2 = D2 )
% 6.92/7.11 => ( ord_less_eq_set_int @ A @ D2 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ord_eq_le_eq_trans
% 6.92/7.11 thf(fact_97_ord__eq__le__eq__trans,axiom,
% 6.92/7.11 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.11 ( ( A = B )
% 6.92/7.11 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.11 => ( ( C2 = D2 )
% 6.92/7.11 => ( ord_less_eq_rat @ A @ D2 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ord_eq_le_eq_trans
% 6.92/7.11 thf(fact_98_ord__eq__le__eq__trans,axiom,
% 6.92/7.11 ! [A: num,B: num,C2: num,D2: num] :
% 6.92/7.11 ( ( A = B )
% 6.92/7.11 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.11 => ( ( C2 = D2 )
% 6.92/7.11 => ( ord_less_eq_num @ A @ D2 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ord_eq_le_eq_trans
% 6.92/7.11 thf(fact_99_ord__eq__le__eq__trans,axiom,
% 6.92/7.11 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.11 ( ( A = B )
% 6.92/7.11 => ( ( ord_less_eq_nat @ B @ C2 )
% 6.92/7.11 => ( ( C2 = D2 )
% 6.92/7.11 => ( ord_less_eq_nat @ A @ D2 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ord_eq_le_eq_trans
% 6.92/7.11 thf(fact_100_ord__eq__le__eq__trans,axiom,
% 6.92/7.11 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.11 ( ( A = B )
% 6.92/7.11 => ( ( ord_less_eq_int @ B @ C2 )
% 6.92/7.11 => ( ( C2 = D2 )
% 6.92/7.11 => ( ord_less_eq_int @ A @ D2 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ord_eq_le_eq_trans
% 6.92/7.11 thf(fact_101_hoare__triple__preI,axiom,
% 6.92/7.11 ! [P2: assn,C2: heap_Time_Heap_a,Q2: a > assn] :
% 6.92/7.11 ( ! [H2: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( rep_assn @ P2 @ H2 )
% 6.92/7.11 => ( hoare_hoare_triple_a @ P2 @ C2 @ Q2 ) )
% 6.92/7.11 => ( hoare_hoare_triple_a @ P2 @ C2 @ Q2 ) ) ).
% 6.92/7.11
% 6.92/7.11 % hoare_triple_preI
% 6.92/7.11 thf(fact_102_hoare__triple__preI,axiom,
% 6.92/7.11 ! [P2: assn,C2: heap_Time_Heap_b,Q2: b > assn] :
% 6.92/7.11 ( ! [H2: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( rep_assn @ P2 @ H2 )
% 6.92/7.11 => ( hoare_hoare_triple_b @ P2 @ C2 @ Q2 ) )
% 6.92/7.11 => ( hoare_hoare_triple_b @ P2 @ C2 @ Q2 ) ) ).
% 6.92/7.11
% 6.92/7.11 % hoare_triple_preI
% 6.92/7.11 thf(fact_103_hoare__triple__preI,axiom,
% 6.92/7.11 ! [P2: assn,C2: heap_T5738788834812785303t_unit,Q2: product_unit > assn] :
% 6.92/7.11 ( ! [H2: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( rep_assn @ P2 @ H2 )
% 6.92/7.11 => ( hoare_8945653483474564448t_unit @ P2 @ C2 @ Q2 ) )
% 6.92/7.11 => ( hoare_8945653483474564448t_unit @ P2 @ C2 @ Q2 ) ) ).
% 6.92/7.11
% 6.92/7.11 % hoare_triple_preI
% 6.92/7.11 thf(fact_104_curryD,axiom,
% 6.92/7.11 ! [F: product_prod_int_int > $o,A: int,B: int] :
% 6.92/7.11 ( ( produc175634133007206835_int_o @ F @ A @ B )
% 6.92/7.11 => ( F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % curryD
% 6.92/7.11 thf(fact_105_curryD,axiom,
% 6.92/7.11 ! [F: produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( produc6216949301066131538_nat_o @ F @ A @ B )
% 6.92/7.11 => ( F @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % curryD
% 6.92/7.11 thf(fact_106_curryD,axiom,
% 6.92/7.11 ! [F: produc2732055786443039994et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 6.92/7.12 ( ( produc5101573711933517782_nat_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryD
% 6.92/7.12 thf(fact_107_curryD,axiom,
% 6.92/7.12 ! [F: produc7388388658123137530it_nat > $o,A: b,B: produc6653097349344004940it_nat] :
% 6.92/7.12 ( ( produc8043051624866120150_nat_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( produc4082563078715348724it_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryD
% 6.92/7.12 thf(fact_108_curryD,axiom,
% 6.92/7.12 ! [F: produc3260487557148687353it_nat > $o,A: a,B: produc6653097349344004940it_nat] :
% 6.92/7.12 ( ( produc3709033845735585303_nat_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( produc9178034014595674355it_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryD
% 6.92/7.12 thf(fact_109_curryE,axiom,
% 6.92/7.12 ! [F: product_prod_int_int > $o,A: int,B: int] :
% 6.92/7.12 ( ( produc175634133007206835_int_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryE
% 6.92/7.12 thf(fact_110_curryE,axiom,
% 6.92/7.12 ! [F: produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 6.92/7.12 ( ( produc6216949301066131538_nat_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryE
% 6.92/7.12 thf(fact_111_curryE,axiom,
% 6.92/7.12 ! [F: produc2732055786443039994et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 6.92/7.12 ( ( produc5101573711933517782_nat_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryE
% 6.92/7.12 thf(fact_112_curryE,axiom,
% 6.92/7.12 ! [F: produc7388388658123137530it_nat > $o,A: b,B: produc6653097349344004940it_nat] :
% 6.92/7.12 ( ( produc8043051624866120150_nat_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( produc4082563078715348724it_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryE
% 6.92/7.12 thf(fact_113_curryE,axiom,
% 6.92/7.12 ! [F: produc3260487557148687353it_nat > $o,A: a,B: produc6653097349344004940it_nat] :
% 6.92/7.12 ( ( produc3709033845735585303_nat_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( produc9178034014595674355it_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryE
% 6.92/7.12 thf(fact_114_less__eq__option__Some,axiom,
% 6.92/7.12 ! [X: set_int,Y: set_int] :
% 6.92/7.12 ( ( ord_le353528952715127954et_int @ ( some_set_int @ X ) @ ( some_set_int @ Y ) )
% 6.92/7.12 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_eq_option_Some
% 6.92/7.12 thf(fact_115_less__eq__option__Some,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ X ) @ ( some_rat @ Y ) )
% 6.92/7.12 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_eq_option_Some
% 6.92/7.12 thf(fact_116_less__eq__option__Some,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( ord_le6622620407824499402on_num @ ( some_num @ X ) @ ( some_num @ Y ) )
% 6.92/7.12 = ( ord_less_eq_num @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_eq_option_Some
% 6.92/7.12 thf(fact_117_less__eq__option__Some,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 6.92/7.12 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_eq_option_Some
% 6.92/7.12 thf(fact_118_less__eq__option__Some,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( ord_le1736525451366464988on_int @ ( some_int @ X ) @ ( some_int @ Y ) )
% 6.92/7.12 = ( ord_less_eq_int @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_eq_option_Some
% 6.92/7.12 thf(fact_119_option_Oinject,axiom,
% 6.92/7.12 ! [X2: produc7388388658123137530it_nat,Y2: produc7388388658123137530it_nat] :
% 6.92/7.12 ( ( ( some_P2818173045054083285it_nat @ X2 )
% 6.92/7.12 = ( some_P2818173045054083285it_nat @ Y2 ) )
% 6.92/7.12 = ( X2 = Y2 ) ) ).
% 6.92/7.12
% 6.92/7.12 % option.inject
% 6.92/7.12 thf(fact_120_option_Oinject,axiom,
% 6.92/7.12 ! [X2: produc3260487557148687353it_nat,Y2: produc3260487557148687353it_nat] :
% 6.92/7.12 ( ( ( some_P7913643980934408916it_nat @ X2 )
% 6.92/7.12 = ( some_P7913643980934408916it_nat @ Y2 ) )
% 6.92/7.12 = ( X2 = Y2 ) ) ).
% 6.92/7.12
% 6.92/7.12 % option.inject
% 6.92/7.12 thf(fact_121_option_Oinject,axiom,
% 6.92/7.12 ! [X2: produc8664842809031399944it_nat,Y2: produc8664842809031399944it_nat] :
% 6.92/7.12 ( ( ( some_P1914260805536162275it_nat @ X2 )
% 6.92/7.12 = ( some_P1914260805536162275it_nat @ Y2 ) )
% 6.92/7.12 = ( X2 = Y2 ) ) ).
% 6.92/7.12
% 6.92/7.12 % option.inject
% 6.92/7.12 thf(fact_122_option_Oinject,axiom,
% 6.92/7.12 ! [X2: num,Y2: num] :
% 6.92/7.12 ( ( ( some_num @ X2 )
% 6.92/7.12 = ( some_num @ Y2 ) )
% 6.92/7.12 = ( X2 = Y2 ) ) ).
% 6.92/7.12
% 6.92/7.12 % option.inject
% 6.92/7.12 thf(fact_123_dual__order_Orefl,axiom,
% 6.92/7.12 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.refl
% 6.92/7.12 thf(fact_124_dual__order_Orefl,axiom,
% 6.92/7.12 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.refl
% 6.92/7.12 thf(fact_125_dual__order_Orefl,axiom,
% 6.92/7.12 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.refl
% 6.92/7.12 thf(fact_126_dual__order_Orefl,axiom,
% 6.92/7.12 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.refl
% 6.92/7.12 thf(fact_127_dual__order_Orefl,axiom,
% 6.92/7.12 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.refl
% 6.92/7.12 thf(fact_128_order__refl,axiom,
% 6.92/7.12 ! [X: set_int] : ( ord_less_eq_set_int @ X @ X ) ).
% 6.92/7.12
% 6.92/7.12 % order_refl
% 6.92/7.12 thf(fact_129_order__refl,axiom,
% 6.92/7.12 ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 6.92/7.12
% 6.92/7.12 % order_refl
% 6.92/7.12 thf(fact_130_order__refl,axiom,
% 6.92/7.12 ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 6.92/7.12
% 6.92/7.12 % order_refl
% 6.92/7.12 thf(fact_131_order__refl,axiom,
% 6.92/7.12 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 6.92/7.12
% 6.92/7.12 % order_refl
% 6.92/7.12 thf(fact_132_order__refl,axiom,
% 6.92/7.12 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 6.92/7.12
% 6.92/7.12 % order_refl
% 6.92/7.12 thf(fact_133__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rg_Ah_H_H_At_H_H_O_A_092_060lbrakk_062execute_A_Ig_Arf_J_Ah_H_A_061_ASome_A_Irg_M_Ah_H_H_M_At_H_H_J_059_A_Ih_H_H_M_Anew__addrs_Ah_H_A_Inew__addrs_Ah_Aas_Ah_H_J_Ah_H_H_J_A_092_060Turnstile_062_AQ_Arg_059_ArelH_A_123a_O_Aa_A_060_Alim_Ah_H_A_092_060and_062_Aa_A_092_060notin_062_Anew__addrs_Ah_Aas_Ah_H_125_Ah_H_Ah_H_H_059_Alim_Ah_H_A_092_060le_062_Alim_Ah_H_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 6.92/7.12 ~ ! [Rg: b,H3: heap_e7401611519738050253t_unit] :
% 6.92/7.12 ( ? [T: nat] :
% 6.92/7.12 ( ( heap_Time_execute_b @ ( g @ rf ) @ h2 )
% 6.92/7.12 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ Rg @ ( produc584006145561248582it_nat @ H3 @ T ) ) ) )
% 6.92/7.12 => ( ( rep_assn @ ( q @ Rg ) @ ( produc7507926704131184380et_nat @ H3 @ ( hoare_new_addrs @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) @ H3 ) ) )
% 6.92/7.12 => ( ( relH
% 6.92/7.12 @ ( collect_nat
% 6.92/7.12 @ ^ [A5: nat] :
% 6.92/7.12 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ h2 ) )
% 6.92/7.12 & ~ ( member_nat @ A5 @ ( hoare_new_addrs @ h3 @ as @ h2 ) ) ) )
% 6.92/7.12 @ h2
% 6.92/7.12 @ H3 )
% 6.92/7.12 => ~ ( ord_less_eq_nat @ ( lim_Product_unit @ h2 ) @ ( lim_Product_unit @ H3 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % \<open>\<And>thesis. (\<And>rg h'' t''. \<lbrakk>execute (g rf) h' = Some (rg, h'', t''); (h'', new_addrs h' (new_addrs h as h') h'') \<Turnstile> Q rg; relH {a. a < lim h' \<and> a \<notin> new_addrs h as h'} h' h''; lim h' \<le> lim h''\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 6.92/7.12 thf(fact_134__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rf_Ah_H_At_H_O_A_092_060lbrakk_062execute_Af_Ah_A_061_ASome_A_Irf_M_Ah_H_M_At_H_J_059_A_Ih_H_M_Anew__addrs_Ah_Aas_Ah_H_J_A_092_060Turnstile_062_AR_Arf_059_ArelH_A_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas_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,
% 6.92/7.12 ~ ! [Rf: a,H4: heap_e7401611519738050253t_unit] :
% 6.92/7.12 ( ? [T2: nat] :
% 6.92/7.12 ( ( heap_Time_execute_a @ f @ h3 )
% 6.92/7.12 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ Rf @ ( produc584006145561248582it_nat @ H4 @ T2 ) ) ) )
% 6.92/7.12 => ( ( rep_assn @ ( r @ Rf ) @ ( produc7507926704131184380et_nat @ H4 @ ( hoare_new_addrs @ h3 @ as @ H4 ) ) )
% 6.92/7.12 => ( ( relH
% 6.92/7.12 @ ( collect_nat
% 6.92/7.12 @ ^ [A5: nat] :
% 6.92/7.12 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ h3 ) )
% 6.92/7.12 & ~ ( member_nat @ A5 @ as ) ) )
% 6.92/7.12 @ h3
% 6.92/7.12 @ H4 )
% 6.92/7.12 => ~ ( ord_less_eq_nat @ ( lim_Product_unit @ h3 ) @ ( lim_Product_unit @ H4 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % \<open>\<And>thesis. (\<And>rf h' t'. \<lbrakk>execute f h = Some (rf, h', t'); (h', new_addrs h as h') \<Turnstile> R rf; relH {a. a < lim h \<and> a \<notin> as} h h'; lim h \<le> lim h'\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 6.92/7.12 thf(fact_135_the__default_Osimps_I1_J,axiom,
% 6.92/7.12 ! [Uu: produc7388388658123137530it_nat,X: produc7388388658123137530it_nat] :
% 6.92/7.12 ( ( the_de4670738602788725795it_nat @ Uu @ ( some_P2818173045054083285it_nat @ X ) )
% 6.92/7.12 = X ) ).
% 6.92/7.12
% 6.92/7.12 % the_default.simps(1)
% 6.92/7.12 thf(fact_136_the__default_Osimps_I1_J,axiom,
% 6.92/7.12 ! [Uu: produc3260487557148687353it_nat,X: produc3260487557148687353it_nat] :
% 6.92/7.12 ( ( the_de542837501814275618it_nat @ Uu @ ( some_P7913643980934408916it_nat @ X ) )
% 6.92/7.12 = X ) ).
% 6.92/7.12
% 6.92/7.12 % the_default.simps(1)
% 6.92/7.12 thf(fact_137_the__default_Osimps_I1_J,axiom,
% 6.92/7.12 ! [Uu: produc8664842809031399944it_nat,X: produc8664842809031399944it_nat] :
% 6.92/7.12 ( ( the_de2487931475039285041it_nat @ Uu @ ( some_P1914260805536162275it_nat @ X ) )
% 6.92/7.12 = X ) ).
% 6.92/7.12
% 6.92/7.12 % the_default.simps(1)
% 6.92/7.12 thf(fact_138_the__default_Osimps_I1_J,axiom,
% 6.92/7.12 ! [Uu: num,X: num] :
% 6.92/7.12 ( ( the_default_num @ Uu @ ( some_num @ X ) )
% 6.92/7.12 = X ) ).
% 6.92/7.12
% 6.92/7.12 % the_default.simps(1)
% 6.92/7.12 thf(fact_139_hoare__triple__effect,axiom,
% 6.92/7.12 ! [P2: assn,C2: heap_Time_Heap_a,Q2: a > assn,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.12 ( ( hoare_hoare_triple_a @ P2 @ C2 @ Q2 )
% 6.92/7.12 => ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.12 => ? [H4: heap_e7401611519738050253t_unit,R4: a,T3: nat] :
% 6.92/7.12 ( ( heap_Time_effect_a @ C2 @ H @ H4 @ R4 @ T3 )
% 6.92/7.12 & ( rep_assn @ ( Q2 @ R4 ) @ ( produc7507926704131184380et_nat @ H4 @ ( hoare_new_addrs @ H @ As @ H4 ) ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % hoare_triple_effect
% 6.92/7.12 thf(fact_140_hoare__triple__effect,axiom,
% 6.92/7.12 ! [P2: assn,C2: heap_Time_Heap_b,Q2: b > assn,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.12 ( ( hoare_hoare_triple_b @ P2 @ C2 @ Q2 )
% 6.92/7.12 => ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.12 => ? [H4: heap_e7401611519738050253t_unit,R4: b,T3: nat] :
% 6.92/7.12 ( ( heap_Time_effect_b @ C2 @ H @ H4 @ R4 @ T3 )
% 6.92/7.12 & ( rep_assn @ ( Q2 @ R4 ) @ ( produc7507926704131184380et_nat @ H4 @ ( hoare_new_addrs @ H @ As @ H4 ) ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % hoare_triple_effect
% 6.92/7.12 thf(fact_141_hoare__triple__effect,axiom,
% 6.92/7.12 ! [P2: assn,C2: heap_T5738788834812785303t_unit,Q2: product_unit > assn,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.12 ( ( hoare_8945653483474564448t_unit @ P2 @ C2 @ Q2 )
% 6.92/7.12 => ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.12 => ? [H4: heap_e7401611519738050253t_unit,R4: product_unit,T3: nat] :
% 6.92/7.12 ( ( heap_T6553295506729943825t_unit @ C2 @ H @ H4 @ R4 @ T3 )
% 6.92/7.12 & ( rep_assn @ ( Q2 @ R4 ) @ ( produc7507926704131184380et_nat @ H4 @ ( hoare_new_addrs @ H @ As @ H4 ) ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % hoare_triple_effect
% 6.92/7.12 thf(fact_142_hoare__triple__success,axiom,
% 6.92/7.12 ! [P2: assn,C2: heap_Time_Heap_a,Q2: a > assn,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.12 ( ( hoare_hoare_triple_a @ P2 @ C2 @ Q2 )
% 6.92/7.12 => ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.12 => ( heap_Time_success_a @ C2 @ H ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % hoare_triple_success
% 6.92/7.12 thf(fact_143_hoare__triple__success,axiom,
% 6.92/7.12 ! [P2: assn,C2: heap_Time_Heap_b,Q2: b > assn,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.12 ( ( hoare_hoare_triple_b @ P2 @ C2 @ Q2 )
% 6.92/7.12 => ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.12 => ( heap_Time_success_b @ C2 @ H ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % hoare_triple_success
% 6.92/7.12 thf(fact_144_hoare__triple__success,axiom,
% 6.92/7.12 ! [P2: assn,C2: heap_T5738788834812785303t_unit,Q2: product_unit > assn,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.12 ( ( hoare_8945653483474564448t_unit @ P2 @ C2 @ Q2 )
% 6.92/7.12 => ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.12 => ( heap_T584514906347983379t_unit @ C2 @ H ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % hoare_triple_success
% 6.92/7.12 thf(fact_145_relChain__def,axiom,
% 6.92/7.12 ( bNF_Ca583493526879471924et_int
% 6.92/7.12 = ( ^ [R5: set_Pr958786334691620121nt_int,As3: int > set_int] :
% 6.92/7.12 ! [I: int,J: int] :
% 6.92/7.12 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R5 )
% 6.92/7.12 => ( ord_less_eq_set_int @ ( As3 @ I ) @ ( As3 @ J ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % relChain_def
% 6.92/7.12 thf(fact_146_relChain__def,axiom,
% 6.92/7.12 ( bNF_Ca1332973979827979050nt_rat
% 6.92/7.12 = ( ^ [R5: set_Pr958786334691620121nt_int,As3: int > rat] :
% 6.92/7.12 ! [I: int,J: int] :
% 6.92/7.12 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R5 )
% 6.92/7.12 => ( ord_less_eq_rat @ ( As3 @ I ) @ ( As3 @ J ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % relChain_def
% 6.92/7.12 thf(fact_147_relChain__def,axiom,
% 6.92/7.12 ( bNF_Ca7748807862925029228nt_num
% 6.92/7.12 = ( ^ [R5: set_Pr958786334691620121nt_int,As3: int > num] :
% 6.92/7.12 ! [I: int,J: int] :
% 6.92/7.12 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R5 )
% 6.92/7.12 => ( ord_less_eq_num @ ( As3 @ I ) @ ( As3 @ J ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % relChain_def
% 6.92/7.12 thf(fact_148_relChain__def,axiom,
% 6.92/7.12 ( bNF_Ca1968104039914474786nt_nat
% 6.92/7.12 = ( ^ [R5: set_Pr958786334691620121nt_int,As3: int > nat] :
% 6.92/7.12 ! [I: int,J: int] :
% 6.92/7.12 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R5 )
% 6.92/7.12 => ( ord_less_eq_nat @ ( As3 @ I ) @ ( As3 @ J ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % relChain_def
% 6.92/7.12 thf(fact_149_relChain__def,axiom,
% 6.92/7.12 ( bNF_Ca1965613569405424510nt_int
% 6.92/7.12 = ( ^ [R5: set_Pr958786334691620121nt_int,As3: int > int] :
% 6.92/7.12 ! [I: int,J: int] :
% 6.92/7.12 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R5 )
% 6.92/7.12 => ( ord_less_eq_int @ ( As3 @ I ) @ ( As3 @ J ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % relChain_def
% 6.92/7.12 thf(fact_150_Heap__eqI,axiom,
% 6.92/7.12 ! [F: heap_Time_Heap_b,G: heap_Time_Heap_b] :
% 6.92/7.12 ( ! [H2: heap_e7401611519738050253t_unit] :
% 6.92/7.12 ( ( heap_Time_execute_b @ F @ H2 )
% 6.92/7.12 = ( heap_Time_execute_b @ G @ H2 ) )
% 6.92/7.12 => ( F = G ) ) ).
% 6.92/7.12
% 6.92/7.12 % Heap_eqI
% 6.92/7.12 thf(fact_151_Heap__eqI,axiom,
% 6.92/7.12 ! [F: heap_Time_Heap_a,G: heap_Time_Heap_a] :
% 6.92/7.12 ( ! [H2: heap_e7401611519738050253t_unit] :
% 6.92/7.12 ( ( heap_Time_execute_a @ F @ H2 )
% 6.92/7.12 = ( heap_Time_execute_a @ G @ H2 ) )
% 6.92/7.12 => ( F = G ) ) ).
% 6.92/7.12
% 6.92/7.12 % Heap_eqI
% 6.92/7.12 thf(fact_152_RH__G,axiom,
% 6.92/7.12 ( relH
% 6.92/7.12 @ ( collect_nat
% 6.92/7.12 @ ^ [A5: nat] :
% 6.92/7.12 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ h2 ) )
% 6.92/7.12 & ~ ( member_nat @ A5 @ ( hoare_new_addrs @ h3 @ as @ h2 ) ) ) )
% 6.92/7.12 @ h2
% 6.92/7.12 @ h ) ).
% 6.92/7.12
% 6.92/7.12 % RH_G
% 6.92/7.12 thf(fact_153_RH__F,axiom,
% 6.92/7.12 ( relH
% 6.92/7.12 @ ( collect_nat
% 6.92/7.12 @ ^ [A5: nat] :
% 6.92/7.12 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ h3 ) )
% 6.92/7.12 & ~ ( member_nat @ A5 @ as ) ) )
% 6.92/7.12 @ h3
% 6.92/7.12 @ h2 ) ).
% 6.92/7.12
% 6.92/7.12 % RH_F
% 6.92/7.12 thf(fact_154_less__option__Some,axiom,
% 6.92/7.12 ! [X: assn,Y: assn] :
% 6.92/7.12 ( ( ord_less_option_assn @ ( some_assn @ X ) @ ( some_assn @ Y ) )
% 6.92/7.12 = ( ord_less_assn @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_option_Some
% 6.92/7.12 thf(fact_155_less__option__Some,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ord_less_option_rat @ ( some_rat @ X ) @ ( some_rat @ Y ) )
% 6.92/7.12 = ( ord_less_rat @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_option_Some
% 6.92/7.12 thf(fact_156_less__option__Some,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( ord_less_option_num @ ( some_num @ X ) @ ( some_num @ Y ) )
% 6.92/7.12 = ( ord_less_num @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_option_Some
% 6.92/7.12 thf(fact_157_less__option__Some,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( ord_less_option_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 6.92/7.12 = ( ord_less_nat @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_option_Some
% 6.92/7.12 thf(fact_158_less__option__Some,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( ord_less_option_int @ ( some_int @ X ) @ ( some_int @ Y ) )
% 6.92/7.12 = ( ord_less_int @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_option_Some
% 6.92/7.12 thf(fact_159_relH__subset,axiom,
% 6.92/7.12 ! [Bs: set_nat,H: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.12 ( ( relH @ Bs @ H @ H5 )
% 6.92/7.12 => ( ( ord_less_eq_set_nat @ As @ Bs )
% 6.92/7.12 => ( relH @ As @ H @ H5 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % relH_subset
% 6.92/7.12 thf(fact_160_lt__ex,axiom,
% 6.92/7.12 ! [X: rat] :
% 6.92/7.12 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X ) ).
% 6.92/7.12
% 6.92/7.12 % lt_ex
% 6.92/7.12 thf(fact_161_lt__ex,axiom,
% 6.92/7.12 ! [X: int] :
% 6.92/7.12 ? [Y3: int] : ( ord_less_int @ Y3 @ X ) ).
% 6.92/7.12
% 6.92/7.12 % lt_ex
% 6.92/7.12 thf(fact_162_gt__ex,axiom,
% 6.92/7.12 ! [X: rat] :
% 6.92/7.12 ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 6.92/7.12
% 6.92/7.12 % gt_ex
% 6.92/7.12 thf(fact_163_gt__ex,axiom,
% 6.92/7.12 ! [X: nat] :
% 6.92/7.12 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 6.92/7.12
% 6.92/7.12 % gt_ex
% 6.92/7.12 thf(fact_164_gt__ex,axiom,
% 6.92/7.12 ! [X: int] :
% 6.92/7.12 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 6.92/7.12
% 6.92/7.12 % gt_ex
% 6.92/7.12 thf(fact_165_dense,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ? [Z2: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X @ Z2 )
% 6.92/7.12 & ( ord_less_rat @ Z2 @ Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dense
% 6.92/7.12 thf(fact_166_less__imp__neq,axiom,
% 6.92/7.12 ! [X: assn,Y: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X @ Y )
% 6.92/7.12 => ( X != Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_imp_neq
% 6.92/7.12 thf(fact_167_less__imp__neq,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ( X != Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_imp_neq
% 6.92/7.12 thf(fact_168_less__imp__neq,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( ord_less_num @ X @ Y )
% 6.92/7.12 => ( X != Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_imp_neq
% 6.92/7.12 thf(fact_169_less__imp__neq,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( ord_less_nat @ X @ Y )
% 6.92/7.12 => ( X != Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_imp_neq
% 6.92/7.12 thf(fact_170_less__imp__neq,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( ord_less_int @ X @ Y )
% 6.92/7.12 => ( X != Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_imp_neq
% 6.92/7.12 thf(fact_171_order_Oasym,axiom,
% 6.92/7.12 ! [A: assn,B: assn] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ~ ( ord_less_assn @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.asym
% 6.92/7.12 thf(fact_172_order_Oasym,axiom,
% 6.92/7.12 ! [A: rat,B: rat] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ~ ( ord_less_rat @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.asym
% 6.92/7.12 thf(fact_173_order_Oasym,axiom,
% 6.92/7.12 ! [A: num,B: num] :
% 6.92/7.12 ( ( ord_less_num @ A @ B )
% 6.92/7.12 => ~ ( ord_less_num @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.asym
% 6.92/7.12 thf(fact_174_order_Oasym,axiom,
% 6.92/7.12 ! [A: nat,B: nat] :
% 6.92/7.12 ( ( ord_less_nat @ A @ B )
% 6.92/7.12 => ~ ( ord_less_nat @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.asym
% 6.92/7.12 thf(fact_175_order_Oasym,axiom,
% 6.92/7.12 ! [A: int,B: int] :
% 6.92/7.12 ( ( ord_less_int @ A @ B )
% 6.92/7.12 => ~ ( ord_less_int @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.asym
% 6.92/7.12 thf(fact_176_ord__eq__less__trans,axiom,
% 6.92/7.12 ! [A: assn,B: assn,C2: assn] :
% 6.92/7.12 ( ( A = B )
% 6.92/7.12 => ( ( ord_less_assn @ B @ C2 )
% 6.92/7.12 => ( ord_less_assn @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_eq_less_trans
% 6.92/7.12 thf(fact_177_ord__eq__less__trans,axiom,
% 6.92/7.12 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.12 ( ( A = B )
% 6.92/7.12 => ( ( ord_less_rat @ B @ C2 )
% 6.92/7.12 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_eq_less_trans
% 6.92/7.12 thf(fact_178_ord__eq__less__trans,axiom,
% 6.92/7.12 ! [A: num,B: num,C2: num] :
% 6.92/7.12 ( ( A = B )
% 6.92/7.12 => ( ( ord_less_num @ B @ C2 )
% 6.92/7.12 => ( ord_less_num @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_eq_less_trans
% 6.92/7.12 thf(fact_179_ord__eq__less__trans,axiom,
% 6.92/7.12 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.12 ( ( A = B )
% 6.92/7.12 => ( ( ord_less_nat @ B @ C2 )
% 6.92/7.12 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_eq_less_trans
% 6.92/7.12 thf(fact_180_ord__eq__less__trans,axiom,
% 6.92/7.12 ! [A: int,B: int,C2: int] :
% 6.92/7.12 ( ( A = B )
% 6.92/7.12 => ( ( ord_less_int @ B @ C2 )
% 6.92/7.12 => ( ord_less_int @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_eq_less_trans
% 6.92/7.12 thf(fact_181_ord__less__eq__trans,axiom,
% 6.92/7.12 ! [A: assn,B: assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ( ( B = C2 )
% 6.92/7.12 => ( ord_less_assn @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_less_eq_trans
% 6.92/7.12 thf(fact_182_ord__less__eq__trans,axiom,
% 6.92/7.12 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ( ( B = C2 )
% 6.92/7.12 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_less_eq_trans
% 6.92/7.12 thf(fact_183_ord__less__eq__trans,axiom,
% 6.92/7.12 ! [A: num,B: num,C2: num] :
% 6.92/7.12 ( ( ord_less_num @ A @ B )
% 6.92/7.12 => ( ( B = C2 )
% 6.92/7.12 => ( ord_less_num @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_less_eq_trans
% 6.92/7.12 thf(fact_184_ord__less__eq__trans,axiom,
% 6.92/7.12 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_nat @ A @ B )
% 6.92/7.12 => ( ( B = C2 )
% 6.92/7.12 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_less_eq_trans
% 6.92/7.12 thf(fact_185_ord__less__eq__trans,axiom,
% 6.92/7.12 ! [A: int,B: int,C2: int] :
% 6.92/7.12 ( ( ord_less_int @ A @ B )
% 6.92/7.12 => ( ( B = C2 )
% 6.92/7.12 => ( ord_less_int @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_less_eq_trans
% 6.92/7.12 thf(fact_186_less__induct,axiom,
% 6.92/7.12 ! [P2: nat > $o,A: nat] :
% 6.92/7.12 ( ! [X3: nat] :
% 6.92/7.12 ( ! [Y5: nat] :
% 6.92/7.12 ( ( ord_less_nat @ Y5 @ X3 )
% 6.92/7.12 => ( P2 @ Y5 ) )
% 6.92/7.12 => ( P2 @ X3 ) )
% 6.92/7.12 => ( P2 @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_induct
% 6.92/7.12 thf(fact_187_antisym__conv3,axiom,
% 6.92/7.12 ! [Y: rat,X: rat] :
% 6.92/7.12 ( ~ ( ord_less_rat @ Y @ X )
% 6.92/7.12 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv3
% 6.92/7.12 thf(fact_188_antisym__conv3,axiom,
% 6.92/7.12 ! [Y: num,X: num] :
% 6.92/7.12 ( ~ ( ord_less_num @ Y @ X )
% 6.92/7.12 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv3
% 6.92/7.12 thf(fact_189_antisym__conv3,axiom,
% 6.92/7.12 ! [Y: nat,X: nat] :
% 6.92/7.12 ( ~ ( ord_less_nat @ Y @ X )
% 6.92/7.12 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv3
% 6.92/7.12 thf(fact_190_antisym__conv3,axiom,
% 6.92/7.12 ! [Y: int,X: int] :
% 6.92/7.12 ( ~ ( ord_less_int @ Y @ X )
% 6.92/7.12 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv3
% 6.92/7.12 thf(fact_191_linorder__cases,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ~ ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ( ( X != Y )
% 6.92/7.12 => ( ord_less_rat @ Y @ X ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_cases
% 6.92/7.12 thf(fact_192_linorder__cases,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ~ ( ord_less_num @ X @ Y )
% 6.92/7.12 => ( ( X != Y )
% 6.92/7.12 => ( ord_less_num @ Y @ X ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_cases
% 6.92/7.12 thf(fact_193_linorder__cases,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ~ ( ord_less_nat @ X @ Y )
% 6.92/7.12 => ( ( X != Y )
% 6.92/7.12 => ( ord_less_nat @ Y @ X ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_cases
% 6.92/7.12 thf(fact_194_linorder__cases,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ~ ( ord_less_int @ X @ Y )
% 6.92/7.12 => ( ( X != Y )
% 6.92/7.12 => ( ord_less_int @ Y @ X ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_cases
% 6.92/7.12 thf(fact_195_dual__order_Oasym,axiom,
% 6.92/7.12 ! [B: assn,A: assn] :
% 6.92/7.12 ( ( ord_less_assn @ B @ A )
% 6.92/7.12 => ~ ( ord_less_assn @ A @ B ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.asym
% 6.92/7.12 thf(fact_196_dual__order_Oasym,axiom,
% 6.92/7.12 ! [B: rat,A: rat] :
% 6.92/7.12 ( ( ord_less_rat @ B @ A )
% 6.92/7.12 => ~ ( ord_less_rat @ A @ B ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.asym
% 6.92/7.12 thf(fact_197_dual__order_Oasym,axiom,
% 6.92/7.12 ! [B: num,A: num] :
% 6.92/7.12 ( ( ord_less_num @ B @ A )
% 6.92/7.12 => ~ ( ord_less_num @ A @ B ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.asym
% 6.92/7.12 thf(fact_198_dual__order_Oasym,axiom,
% 6.92/7.12 ! [B: nat,A: nat] :
% 6.92/7.12 ( ( ord_less_nat @ B @ A )
% 6.92/7.12 => ~ ( ord_less_nat @ A @ B ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.asym
% 6.92/7.12 thf(fact_199_dual__order_Oasym,axiom,
% 6.92/7.12 ! [B: int,A: int] :
% 6.92/7.12 ( ( ord_less_int @ B @ A )
% 6.92/7.12 => ~ ( ord_less_int @ A @ B ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.asym
% 6.92/7.12 thf(fact_200_dual__order_Oirrefl,axiom,
% 6.92/7.12 ! [A: assn] :
% 6.92/7.12 ~ ( ord_less_assn @ A @ A ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.irrefl
% 6.92/7.12 thf(fact_201_dual__order_Oirrefl,axiom,
% 6.92/7.12 ! [A: rat] :
% 6.92/7.12 ~ ( ord_less_rat @ A @ A ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.irrefl
% 6.92/7.12 thf(fact_202_dual__order_Oirrefl,axiom,
% 6.92/7.12 ! [A: num] :
% 6.92/7.12 ~ ( ord_less_num @ A @ A ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.irrefl
% 6.92/7.12 thf(fact_203_dual__order_Oirrefl,axiom,
% 6.92/7.12 ! [A: nat] :
% 6.92/7.12 ~ ( ord_less_nat @ A @ A ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.irrefl
% 6.92/7.12 thf(fact_204_dual__order_Oirrefl,axiom,
% 6.92/7.12 ! [A: int] :
% 6.92/7.12 ~ ( ord_less_int @ A @ A ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.irrefl
% 6.92/7.12 thf(fact_205_exists__least__iff,axiom,
% 6.92/7.12 ( ( ^ [P4: nat > $o] :
% 6.92/7.12 ? [X5: nat] : ( P4 @ X5 ) )
% 6.92/7.12 = ( ^ [P5: nat > $o] :
% 6.92/7.12 ? [N: nat] :
% 6.92/7.12 ( ( P5 @ N )
% 6.92/7.12 & ! [M3: nat] :
% 6.92/7.12 ( ( ord_less_nat @ M3 @ N )
% 6.92/7.12 => ~ ( P5 @ M3 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % exists_least_iff
% 6.92/7.12 thf(fact_206_linorder__less__wlog,axiom,
% 6.92/7.12 ! [P2: rat > rat > $o,A: rat,B: rat] :
% 6.92/7.12 ( ! [A3: rat,B3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ A3 @ B3 )
% 6.92/7.12 => ( P2 @ A3 @ B3 ) )
% 6.92/7.12 => ( ! [A3: rat] : ( P2 @ A3 @ A3 )
% 6.92/7.12 => ( ! [A3: rat,B3: rat] :
% 6.92/7.12 ( ( P2 @ B3 @ A3 )
% 6.92/7.12 => ( P2 @ A3 @ B3 ) )
% 6.92/7.12 => ( P2 @ A @ B ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_less_wlog
% 6.92/7.12 thf(fact_207_linorder__less__wlog,axiom,
% 6.92/7.12 ! [P2: num > num > $o,A: num,B: num] :
% 6.92/7.12 ( ! [A3: num,B3: num] :
% 6.92/7.12 ( ( ord_less_num @ A3 @ B3 )
% 6.92/7.12 => ( P2 @ A3 @ B3 ) )
% 6.92/7.12 => ( ! [A3: num] : ( P2 @ A3 @ A3 )
% 6.92/7.12 => ( ! [A3: num,B3: num] :
% 6.92/7.12 ( ( P2 @ B3 @ A3 )
% 6.92/7.12 => ( P2 @ A3 @ B3 ) )
% 6.92/7.12 => ( P2 @ A @ B ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_less_wlog
% 6.92/7.12 thf(fact_208_linorder__less__wlog,axiom,
% 6.92/7.12 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 6.92/7.12 ( ! [A3: nat,B3: nat] :
% 6.92/7.12 ( ( ord_less_nat @ A3 @ B3 )
% 6.92/7.12 => ( P2 @ A3 @ B3 ) )
% 6.92/7.12 => ( ! [A3: nat] : ( P2 @ A3 @ A3 )
% 6.92/7.12 => ( ! [A3: nat,B3: nat] :
% 6.92/7.12 ( ( P2 @ B3 @ A3 )
% 6.92/7.12 => ( P2 @ A3 @ B3 ) )
% 6.92/7.12 => ( P2 @ A @ B ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_less_wlog
% 6.92/7.12 thf(fact_209_linorder__less__wlog,axiom,
% 6.92/7.12 ! [P2: int > int > $o,A: int,B: int] :
% 6.92/7.12 ( ! [A3: int,B3: int] :
% 6.92/7.12 ( ( ord_less_int @ A3 @ B3 )
% 6.92/7.12 => ( P2 @ A3 @ B3 ) )
% 6.92/7.12 => ( ! [A3: int] : ( P2 @ A3 @ A3 )
% 6.92/7.12 => ( ! [A3: int,B3: int] :
% 6.92/7.12 ( ( P2 @ B3 @ A3 )
% 6.92/7.12 => ( P2 @ A3 @ B3 ) )
% 6.92/7.12 => ( P2 @ A @ B ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_less_wlog
% 6.92/7.12 thf(fact_210_order_Ostrict__trans,axiom,
% 6.92/7.12 ! [A: assn,B: assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ( ( ord_less_assn @ B @ C2 )
% 6.92/7.12 => ( ord_less_assn @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans
% 6.92/7.12 thf(fact_211_order_Ostrict__trans,axiom,
% 6.92/7.12 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ( ( ord_less_rat @ B @ C2 )
% 6.92/7.12 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans
% 6.92/7.12 thf(fact_212_order_Ostrict__trans,axiom,
% 6.92/7.12 ! [A: num,B: num,C2: num] :
% 6.92/7.12 ( ( ord_less_num @ A @ B )
% 6.92/7.12 => ( ( ord_less_num @ B @ C2 )
% 6.92/7.12 => ( ord_less_num @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans
% 6.92/7.12 thf(fact_213_order_Ostrict__trans,axiom,
% 6.92/7.12 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_nat @ A @ B )
% 6.92/7.12 => ( ( ord_less_nat @ B @ C2 )
% 6.92/7.12 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans
% 6.92/7.12 thf(fact_214_order_Ostrict__trans,axiom,
% 6.92/7.12 ! [A: int,B: int,C2: int] :
% 6.92/7.12 ( ( ord_less_int @ A @ B )
% 6.92/7.12 => ( ( ord_less_int @ B @ C2 )
% 6.92/7.12 => ( ord_less_int @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans
% 6.92/7.12 thf(fact_215_not__less__iff__gr__or__eq,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 6.92/7.12 = ( ( ord_less_rat @ Y @ X )
% 6.92/7.12 | ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % not_less_iff_gr_or_eq
% 6.92/7.12 thf(fact_216_not__less__iff__gr__or__eq,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( ~ ( ord_less_num @ X @ Y ) )
% 6.92/7.12 = ( ( ord_less_num @ Y @ X )
% 6.92/7.12 | ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % not_less_iff_gr_or_eq
% 6.92/7.12 thf(fact_217_not__less__iff__gr__or__eq,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 6.92/7.12 = ( ( ord_less_nat @ Y @ X )
% 6.92/7.12 | ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % not_less_iff_gr_or_eq
% 6.92/7.12 thf(fact_218_not__less__iff__gr__or__eq,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( ~ ( ord_less_int @ X @ Y ) )
% 6.92/7.12 = ( ( ord_less_int @ Y @ X )
% 6.92/7.12 | ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % not_less_iff_gr_or_eq
% 6.92/7.12 thf(fact_219_dual__order_Ostrict__trans,axiom,
% 6.92/7.12 ! [B: assn,A: assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_assn @ B @ A )
% 6.92/7.12 => ( ( ord_less_assn @ C2 @ B )
% 6.92/7.12 => ( ord_less_assn @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans
% 6.92/7.12 thf(fact_220_dual__order_Ostrict__trans,axiom,
% 6.92/7.12 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_rat @ B @ A )
% 6.92/7.12 => ( ( ord_less_rat @ C2 @ B )
% 6.92/7.12 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans
% 6.92/7.12 thf(fact_221_dual__order_Ostrict__trans,axiom,
% 6.92/7.12 ! [B: num,A: num,C2: num] :
% 6.92/7.12 ( ( ord_less_num @ B @ A )
% 6.92/7.12 => ( ( ord_less_num @ C2 @ B )
% 6.92/7.12 => ( ord_less_num @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans
% 6.92/7.12 thf(fact_222_dual__order_Ostrict__trans,axiom,
% 6.92/7.12 ! [B: nat,A: nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_nat @ B @ A )
% 6.92/7.12 => ( ( ord_less_nat @ C2 @ B )
% 6.92/7.12 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans
% 6.92/7.12 thf(fact_223_dual__order_Ostrict__trans,axiom,
% 6.92/7.12 ! [B: int,A: int,C2: int] :
% 6.92/7.12 ( ( ord_less_int @ B @ A )
% 6.92/7.12 => ( ( ord_less_int @ C2 @ B )
% 6.92/7.12 => ( ord_less_int @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans
% 6.92/7.12 thf(fact_224_order_Ostrict__implies__not__eq,axiom,
% 6.92/7.12 ! [A: assn,B: assn] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ( A != B ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_implies_not_eq
% 6.92/7.12 thf(fact_225_order_Ostrict__implies__not__eq,axiom,
% 6.92/7.12 ! [A: rat,B: rat] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ( A != B ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_implies_not_eq
% 6.92/7.12 thf(fact_226_order_Ostrict__implies__not__eq,axiom,
% 6.92/7.12 ! [A: num,B: num] :
% 6.92/7.12 ( ( ord_less_num @ A @ B )
% 6.92/7.12 => ( A != B ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_implies_not_eq
% 6.92/7.12 thf(fact_227_order_Ostrict__implies__not__eq,axiom,
% 6.92/7.12 ! [A: nat,B: nat] :
% 6.92/7.12 ( ( ord_less_nat @ A @ B )
% 6.92/7.12 => ( A != B ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_implies_not_eq
% 6.92/7.12 thf(fact_228_order_Ostrict__implies__not__eq,axiom,
% 6.92/7.12 ! [A: int,B: int] :
% 6.92/7.12 ( ( ord_less_int @ A @ B )
% 6.92/7.12 => ( A != B ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_implies_not_eq
% 6.92/7.12 thf(fact_229_dual__order_Ostrict__implies__not__eq,axiom,
% 6.92/7.12 ! [B: assn,A: assn] :
% 6.92/7.12 ( ( ord_less_assn @ B @ A )
% 6.92/7.12 => ( A != B ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_implies_not_eq
% 6.92/7.12 thf(fact_230_dual__order_Ostrict__implies__not__eq,axiom,
% 6.92/7.12 ! [B: rat,A: rat] :
% 6.92/7.12 ( ( ord_less_rat @ B @ A )
% 6.92/7.12 => ( A != B ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_implies_not_eq
% 6.92/7.12 thf(fact_231_dual__order_Ostrict__implies__not__eq,axiom,
% 6.92/7.12 ! [B: num,A: num] :
% 6.92/7.12 ( ( ord_less_num @ B @ A )
% 6.92/7.12 => ( A != B ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_implies_not_eq
% 6.92/7.12 thf(fact_232_dual__order_Ostrict__implies__not__eq,axiom,
% 6.92/7.12 ! [B: nat,A: nat] :
% 6.92/7.12 ( ( ord_less_nat @ B @ A )
% 6.92/7.12 => ( A != B ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_implies_not_eq
% 6.92/7.12 thf(fact_233_dual__order_Ostrict__implies__not__eq,axiom,
% 6.92/7.12 ! [B: int,A: int] :
% 6.92/7.12 ( ( ord_less_int @ B @ A )
% 6.92/7.12 => ( A != B ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_implies_not_eq
% 6.92/7.12 thf(fact_234_linorder__neqE,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( X != Y )
% 6.92/7.12 => ( ~ ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ( ord_less_rat @ Y @ X ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_neqE
% 6.92/7.12 thf(fact_235_linorder__neqE,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( X != Y )
% 6.92/7.12 => ( ~ ( ord_less_num @ X @ Y )
% 6.92/7.12 => ( ord_less_num @ Y @ X ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_neqE
% 6.92/7.12 thf(fact_236_linorder__neqE,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( X != Y )
% 6.92/7.12 => ( ~ ( ord_less_nat @ X @ Y )
% 6.92/7.12 => ( ord_less_nat @ Y @ X ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_neqE
% 6.92/7.12 thf(fact_237_linorder__neqE,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( X != Y )
% 6.92/7.12 => ( ~ ( ord_less_int @ X @ Y )
% 6.92/7.12 => ( ord_less_int @ Y @ X ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_neqE
% 6.92/7.12 thf(fact_238_order__less__asym,axiom,
% 6.92/7.12 ! [X: assn,Y: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X @ Y )
% 6.92/7.12 => ~ ( ord_less_assn @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_asym
% 6.92/7.12 thf(fact_239_order__less__asym,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_asym
% 6.92/7.12 thf(fact_240_order__less__asym,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( ord_less_num @ X @ Y )
% 6.92/7.12 => ~ ( ord_less_num @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_asym
% 6.92/7.12 thf(fact_241_order__less__asym,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( ord_less_nat @ X @ Y )
% 6.92/7.12 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_asym
% 6.92/7.12 thf(fact_242_order__less__asym,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( ord_less_int @ X @ Y )
% 6.92/7.12 => ~ ( ord_less_int @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_asym
% 6.92/7.12 thf(fact_243_linorder__neq__iff,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( X != Y )
% 6.92/7.12 = ( ( ord_less_rat @ X @ Y )
% 6.92/7.12 | ( ord_less_rat @ Y @ X ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_neq_iff
% 6.92/7.12 thf(fact_244_linorder__neq__iff,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( X != Y )
% 6.92/7.12 = ( ( ord_less_num @ X @ Y )
% 6.92/7.12 | ( ord_less_num @ Y @ X ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_neq_iff
% 6.92/7.12 thf(fact_245_linorder__neq__iff,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( X != Y )
% 6.92/7.12 = ( ( ord_less_nat @ X @ Y )
% 6.92/7.12 | ( ord_less_nat @ Y @ X ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_neq_iff
% 6.92/7.12 thf(fact_246_linorder__neq__iff,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( X != Y )
% 6.92/7.12 = ( ( ord_less_int @ X @ Y )
% 6.92/7.12 | ( ord_less_int @ Y @ X ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_neq_iff
% 6.92/7.12 thf(fact_247_order__less__asym_H,axiom,
% 6.92/7.12 ! [A: assn,B: assn] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ~ ( ord_less_assn @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_asym'
% 6.92/7.12 thf(fact_248_order__less__asym_H,axiom,
% 6.92/7.12 ! [A: rat,B: rat] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ~ ( ord_less_rat @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_asym'
% 6.92/7.12 thf(fact_249_order__less__asym_H,axiom,
% 6.92/7.12 ! [A: num,B: num] :
% 6.92/7.12 ( ( ord_less_num @ A @ B )
% 6.92/7.12 => ~ ( ord_less_num @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_asym'
% 6.92/7.12 thf(fact_250_order__less__asym_H,axiom,
% 6.92/7.12 ! [A: nat,B: nat] :
% 6.92/7.12 ( ( ord_less_nat @ A @ B )
% 6.92/7.12 => ~ ( ord_less_nat @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_asym'
% 6.92/7.12 thf(fact_251_order__less__asym_H,axiom,
% 6.92/7.12 ! [A: int,B: int] :
% 6.92/7.12 ( ( ord_less_int @ A @ B )
% 6.92/7.12 => ~ ( ord_less_int @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_asym'
% 6.92/7.12 thf(fact_252_order__less__trans,axiom,
% 6.92/7.12 ! [X: assn,Y: assn,Z3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X @ Y )
% 6.92/7.12 => ( ( ord_less_assn @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_assn @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_trans
% 6.92/7.12 thf(fact_253_order__less__trans,axiom,
% 6.92/7.12 ! [X: rat,Y: rat,Z3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ( ( ord_less_rat @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_rat @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_trans
% 6.92/7.12 thf(fact_254_order__less__trans,axiom,
% 6.92/7.12 ! [X: num,Y: num,Z3: num] :
% 6.92/7.12 ( ( ord_less_num @ X @ Y )
% 6.92/7.12 => ( ( ord_less_num @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_num @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_trans
% 6.92/7.12 thf(fact_255_order__less__trans,axiom,
% 6.92/7.12 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.12 ( ( ord_less_nat @ X @ Y )
% 6.92/7.12 => ( ( ord_less_nat @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_trans
% 6.92/7.12 thf(fact_256_order__less__trans,axiom,
% 6.92/7.12 ! [X: int,Y: int,Z3: int] :
% 6.92/7.12 ( ( ord_less_int @ X @ Y )
% 6.92/7.12 => ( ( ord_less_int @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_trans
% 6.92/7.12 thf(fact_257_ord__eq__less__subst,axiom,
% 6.92/7.12 ! [A: assn,F: assn > assn,B: assn,C2: assn] :
% 6.92/7.12 ( ( A
% 6.92/7.12 = ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_assn @ B @ C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_eq_less_subst
% 6.92/7.12 thf(fact_258_ord__eq__less__subst,axiom,
% 6.92/7.12 ! [A: rat,F: assn > rat,B: assn,C2: assn] :
% 6.92/7.12 ( ( A
% 6.92/7.12 = ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_assn @ B @ C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_eq_less_subst
% 6.92/7.12 thf(fact_259_ord__eq__less__subst,axiom,
% 6.92/7.12 ! [A: num,F: assn > num,B: assn,C2: assn] :
% 6.92/7.12 ( ( A
% 6.92/7.12 = ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_assn @ B @ C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_eq_less_subst
% 6.92/7.12 thf(fact_260_ord__eq__less__subst,axiom,
% 6.92/7.12 ! [A: nat,F: assn > nat,B: assn,C2: assn] :
% 6.92/7.12 ( ( A
% 6.92/7.12 = ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_assn @ B @ C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_eq_less_subst
% 6.92/7.12 thf(fact_261_ord__eq__less__subst,axiom,
% 6.92/7.12 ! [A: int,F: assn > int,B: assn,C2: assn] :
% 6.92/7.12 ( ( A
% 6.92/7.12 = ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_assn @ B @ C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_eq_less_subst
% 6.92/7.12 thf(fact_262_ord__eq__less__subst,axiom,
% 6.92/7.12 ! [A: assn,F: rat > assn,B: rat,C2: rat] :
% 6.92/7.12 ( ( A
% 6.92/7.12 = ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_rat @ B @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_eq_less_subst
% 6.92/7.12 thf(fact_263_ord__eq__less__subst,axiom,
% 6.92/7.12 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 6.92/7.12 ( ( A
% 6.92/7.12 = ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_rat @ B @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_eq_less_subst
% 6.92/7.12 thf(fact_264_ord__eq__less__subst,axiom,
% 6.92/7.12 ! [A: num,F: rat > num,B: rat,C2: rat] :
% 6.92/7.12 ( ( A
% 6.92/7.12 = ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_rat @ B @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_eq_less_subst
% 6.92/7.12 thf(fact_265_ord__eq__less__subst,axiom,
% 6.92/7.12 ! [A: nat,F: rat > nat,B: rat,C2: rat] :
% 6.92/7.12 ( ( A
% 6.92/7.12 = ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_rat @ B @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_eq_less_subst
% 6.92/7.12 thf(fact_266_ord__eq__less__subst,axiom,
% 6.92/7.12 ! [A: int,F: rat > int,B: rat,C2: rat] :
% 6.92/7.12 ( ( A
% 6.92/7.12 = ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_rat @ B @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_eq_less_subst
% 6.92/7.12 thf(fact_267_ord__less__eq__subst,axiom,
% 6.92/7.12 ! [A: assn,B: assn,F: assn > assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ( ( ( F @ B )
% 6.92/7.12 = C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_less_eq_subst
% 6.92/7.12 thf(fact_268_ord__less__eq__subst,axiom,
% 6.92/7.12 ! [A: assn,B: assn,F: assn > rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ( ( ( F @ B )
% 6.92/7.12 = C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_less_eq_subst
% 6.92/7.12 thf(fact_269_ord__less__eq__subst,axiom,
% 6.92/7.12 ! [A: assn,B: assn,F: assn > num,C2: num] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ( ( ( F @ B )
% 6.92/7.12 = C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_less_eq_subst
% 6.92/7.12 thf(fact_270_ord__less__eq__subst,axiom,
% 6.92/7.12 ! [A: assn,B: assn,F: assn > nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ( ( ( F @ B )
% 6.92/7.12 = C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_less_eq_subst
% 6.92/7.12 thf(fact_271_ord__less__eq__subst,axiom,
% 6.92/7.12 ! [A: assn,B: assn,F: assn > int,C2: int] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ( ( ( F @ B )
% 6.92/7.12 = C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_less_eq_subst
% 6.92/7.12 thf(fact_272_ord__less__eq__subst,axiom,
% 6.92/7.12 ! [A: rat,B: rat,F: rat > assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ( ( ( F @ B )
% 6.92/7.12 = C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_less_eq_subst
% 6.92/7.12 thf(fact_273_ord__less__eq__subst,axiom,
% 6.92/7.12 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ( ( ( F @ B )
% 6.92/7.12 = C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_less_eq_subst
% 6.92/7.12 thf(fact_274_ord__less__eq__subst,axiom,
% 6.92/7.12 ! [A: rat,B: rat,F: rat > num,C2: num] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ( ( ( F @ B )
% 6.92/7.12 = C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_less_eq_subst
% 6.92/7.12 thf(fact_275_ord__less__eq__subst,axiom,
% 6.92/7.12 ! [A: rat,B: rat,F: rat > nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ( ( ( F @ B )
% 6.92/7.12 = C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_less_eq_subst
% 6.92/7.12 thf(fact_276_ord__less__eq__subst,axiom,
% 6.92/7.12 ! [A: rat,B: rat,F: rat > int,C2: int] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ( ( ( F @ B )
% 6.92/7.12 = C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % ord_less_eq_subst
% 6.92/7.12 thf(fact_277_order__less__irrefl,axiom,
% 6.92/7.12 ! [X: assn] :
% 6.92/7.12 ~ ( ord_less_assn @ X @ X ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_irrefl
% 6.92/7.12 thf(fact_278_order__less__irrefl,axiom,
% 6.92/7.12 ! [X: rat] :
% 6.92/7.12 ~ ( ord_less_rat @ X @ X ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_irrefl
% 6.92/7.12 thf(fact_279_order__less__irrefl,axiom,
% 6.92/7.12 ! [X: num] :
% 6.92/7.12 ~ ( ord_less_num @ X @ X ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_irrefl
% 6.92/7.12 thf(fact_280_order__less__irrefl,axiom,
% 6.92/7.12 ! [X: nat] :
% 6.92/7.12 ~ ( ord_less_nat @ X @ X ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_irrefl
% 6.92/7.12 thf(fact_281_order__less__irrefl,axiom,
% 6.92/7.12 ! [X: int] :
% 6.92/7.12 ~ ( ord_less_int @ X @ X ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_irrefl
% 6.92/7.12 thf(fact_282_order__less__subst1,axiom,
% 6.92/7.12 ! [A: assn,F: assn > assn,B: assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_assn @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_assn @ B @ C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst1
% 6.92/7.12 thf(fact_283_order__less__subst1,axiom,
% 6.92/7.12 ! [A: assn,F: rat > assn,B: rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_assn @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_rat @ B @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst1
% 6.92/7.12 thf(fact_284_order__less__subst1,axiom,
% 6.92/7.12 ! [A: assn,F: num > assn,B: num,C2: num] :
% 6.92/7.12 ( ( ord_less_assn @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_num @ B @ C2 )
% 6.92/7.12 => ( ! [X3: num,Y3: num] :
% 6.92/7.12 ( ( ord_less_num @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst1
% 6.92/7.12 thf(fact_285_order__less__subst1,axiom,
% 6.92/7.12 ! [A: assn,F: nat > assn,B: nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_assn @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_nat @ B @ C2 )
% 6.92/7.12 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.12 ( ( ord_less_nat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst1
% 6.92/7.12 thf(fact_286_order__less__subst1,axiom,
% 6.92/7.12 ! [A: assn,F: int > assn,B: int,C2: int] :
% 6.92/7.12 ( ( ord_less_assn @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_int @ B @ C2 )
% 6.92/7.12 => ( ! [X3: int,Y3: int] :
% 6.92/7.12 ( ( ord_less_int @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst1
% 6.92/7.12 thf(fact_287_order__less__subst1,axiom,
% 6.92/7.12 ! [A: rat,F: assn > rat,B: assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_rat @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_assn @ B @ C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst1
% 6.92/7.12 thf(fact_288_order__less__subst1,axiom,
% 6.92/7.12 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_rat @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_rat @ B @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst1
% 6.92/7.12 thf(fact_289_order__less__subst1,axiom,
% 6.92/7.12 ! [A: rat,F: num > rat,B: num,C2: num] :
% 6.92/7.12 ( ( ord_less_rat @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_num @ B @ C2 )
% 6.92/7.12 => ( ! [X3: num,Y3: num] :
% 6.92/7.12 ( ( ord_less_num @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst1
% 6.92/7.12 thf(fact_290_order__less__subst1,axiom,
% 6.92/7.12 ! [A: rat,F: nat > rat,B: nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_rat @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_nat @ B @ C2 )
% 6.92/7.12 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.12 ( ( ord_less_nat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst1
% 6.92/7.12 thf(fact_291_order__less__subst1,axiom,
% 6.92/7.12 ! [A: rat,F: int > rat,B: int,C2: int] :
% 6.92/7.12 ( ( ord_less_rat @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_int @ B @ C2 )
% 6.92/7.12 => ( ! [X3: int,Y3: int] :
% 6.92/7.12 ( ( ord_less_int @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst1
% 6.92/7.12 thf(fact_292_order__less__subst2,axiom,
% 6.92/7.12 ! [A: assn,B: assn,F: assn > assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ( ( ord_less_assn @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst2
% 6.92/7.12 thf(fact_293_order__less__subst2,axiom,
% 6.92/7.12 ! [A: assn,B: assn,F: assn > rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ( ( ord_less_rat @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst2
% 6.92/7.12 thf(fact_294_order__less__subst2,axiom,
% 6.92/7.12 ! [A: assn,B: assn,F: assn > num,C2: num] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ( ( ord_less_num @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst2
% 6.92/7.12 thf(fact_295_order__less__subst2,axiom,
% 6.92/7.12 ! [A: assn,B: assn,F: assn > nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst2
% 6.92/7.12 thf(fact_296_order__less__subst2,axiom,
% 6.92/7.12 ! [A: assn,B: assn,F: assn > int,C2: int] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst2
% 6.92/7.12 thf(fact_297_order__less__subst2,axiom,
% 6.92/7.12 ! [A: rat,B: rat,F: rat > assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ( ( ord_less_assn @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst2
% 6.92/7.12 thf(fact_298_order__less__subst2,axiom,
% 6.92/7.12 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ( ( ord_less_rat @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst2
% 6.92/7.12 thf(fact_299_order__less__subst2,axiom,
% 6.92/7.12 ! [A: rat,B: rat,F: rat > num,C2: num] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ( ( ord_less_num @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst2
% 6.92/7.12 thf(fact_300_order__less__subst2,axiom,
% 6.92/7.12 ! [A: rat,B: rat,F: rat > nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst2
% 6.92/7.12 thf(fact_301_order__less__subst2,axiom,
% 6.92/7.12 ! [A: rat,B: rat,F: rat > int,C2: int] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_subst2
% 6.92/7.12 thf(fact_302_order__less__not__sym,axiom,
% 6.92/7.12 ! [X: assn,Y: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X @ Y )
% 6.92/7.12 => ~ ( ord_less_assn @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_not_sym
% 6.92/7.12 thf(fact_303_order__less__not__sym,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_not_sym
% 6.92/7.12 thf(fact_304_order__less__not__sym,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( ord_less_num @ X @ Y )
% 6.92/7.12 => ~ ( ord_less_num @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_not_sym
% 6.92/7.12 thf(fact_305_order__less__not__sym,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( ord_less_nat @ X @ Y )
% 6.92/7.12 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_not_sym
% 6.92/7.12 thf(fact_306_order__less__not__sym,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( ord_less_int @ X @ Y )
% 6.92/7.12 => ~ ( ord_less_int @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_not_sym
% 6.92/7.12 thf(fact_307_order__less__imp__triv,axiom,
% 6.92/7.12 ! [X: assn,Y: assn,P2: $o] :
% 6.92/7.12 ( ( ord_less_assn @ X @ Y )
% 6.92/7.12 => ( ( ord_less_assn @ Y @ X )
% 6.92/7.12 => P2 ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_triv
% 6.92/7.12 thf(fact_308_order__less__imp__triv,axiom,
% 6.92/7.12 ! [X: rat,Y: rat,P2: $o] :
% 6.92/7.12 ( ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ( ( ord_less_rat @ Y @ X )
% 6.92/7.12 => P2 ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_triv
% 6.92/7.12 thf(fact_309_order__less__imp__triv,axiom,
% 6.92/7.12 ! [X: num,Y: num,P2: $o] :
% 6.92/7.12 ( ( ord_less_num @ X @ Y )
% 6.92/7.12 => ( ( ord_less_num @ Y @ X )
% 6.92/7.12 => P2 ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_triv
% 6.92/7.12 thf(fact_310_order__less__imp__triv,axiom,
% 6.92/7.12 ! [X: nat,Y: nat,P2: $o] :
% 6.92/7.12 ( ( ord_less_nat @ X @ Y )
% 6.92/7.12 => ( ( ord_less_nat @ Y @ X )
% 6.92/7.12 => P2 ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_triv
% 6.92/7.12 thf(fact_311_order__less__imp__triv,axiom,
% 6.92/7.12 ! [X: int,Y: int,P2: $o] :
% 6.92/7.12 ( ( ord_less_int @ X @ Y )
% 6.92/7.12 => ( ( ord_less_int @ Y @ X )
% 6.92/7.12 => P2 ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_triv
% 6.92/7.12 thf(fact_312_linorder__less__linear,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X @ Y )
% 6.92/7.12 | ( X = Y )
% 6.92/7.12 | ( ord_less_rat @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_less_linear
% 6.92/7.12 thf(fact_313_linorder__less__linear,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( ord_less_num @ X @ Y )
% 6.92/7.12 | ( X = Y )
% 6.92/7.12 | ( ord_less_num @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_less_linear
% 6.92/7.12 thf(fact_314_linorder__less__linear,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( ord_less_nat @ X @ Y )
% 6.92/7.12 | ( X = Y )
% 6.92/7.12 | ( ord_less_nat @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_less_linear
% 6.92/7.12 thf(fact_315_linorder__less__linear,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( ord_less_int @ X @ Y )
% 6.92/7.12 | ( X = Y )
% 6.92/7.12 | ( ord_less_int @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_less_linear
% 6.92/7.12 thf(fact_316_order__less__imp__not__eq,axiom,
% 6.92/7.12 ! [X: assn,Y: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X @ Y )
% 6.92/7.12 => ( X != Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_not_eq
% 6.92/7.12 thf(fact_317_order__less__imp__not__eq,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ( X != Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_not_eq
% 6.92/7.12 thf(fact_318_order__less__imp__not__eq,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( ord_less_num @ X @ Y )
% 6.92/7.12 => ( X != Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_not_eq
% 6.92/7.12 thf(fact_319_order__less__imp__not__eq,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( ord_less_nat @ X @ Y )
% 6.92/7.12 => ( X != Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_not_eq
% 6.92/7.12 thf(fact_320_order__less__imp__not__eq,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( ord_less_int @ X @ Y )
% 6.92/7.12 => ( X != Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_not_eq
% 6.92/7.12 thf(fact_321_order__less__imp__not__eq2,axiom,
% 6.92/7.12 ! [X: assn,Y: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X @ Y )
% 6.92/7.12 => ( Y != X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_not_eq2
% 6.92/7.12 thf(fact_322_order__less__imp__not__eq2,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ( Y != X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_not_eq2
% 6.92/7.12 thf(fact_323_order__less__imp__not__eq2,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( ord_less_num @ X @ Y )
% 6.92/7.12 => ( Y != X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_not_eq2
% 6.92/7.12 thf(fact_324_order__less__imp__not__eq2,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( ord_less_nat @ X @ Y )
% 6.92/7.12 => ( Y != X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_not_eq2
% 6.92/7.12 thf(fact_325_order__less__imp__not__eq2,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( ord_less_int @ X @ Y )
% 6.92/7.12 => ( Y != X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_not_eq2
% 6.92/7.12 thf(fact_326_order__less__imp__not__less,axiom,
% 6.92/7.12 ! [X: assn,Y: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X @ Y )
% 6.92/7.12 => ~ ( ord_less_assn @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_not_less
% 6.92/7.12 thf(fact_327_order__less__imp__not__less,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_not_less
% 6.92/7.12 thf(fact_328_order__less__imp__not__less,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( ord_less_num @ X @ Y )
% 6.92/7.12 => ~ ( ord_less_num @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_not_less
% 6.92/7.12 thf(fact_329_order__less__imp__not__less,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( ord_less_nat @ X @ Y )
% 6.92/7.12 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_not_less
% 6.92/7.12 thf(fact_330_order__less__imp__not__less,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( ord_less_int @ X @ Y )
% 6.92/7.12 => ~ ( ord_less_int @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_not_less
% 6.92/7.12 thf(fact_331_relH__trans,axiom,
% 6.92/7.12 ! [As: set_nat,H1: heap_e7401611519738050253t_unit,H22: heap_e7401611519738050253t_unit,H32: heap_e7401611519738050253t_unit] :
% 6.92/7.12 ( ( relH @ As @ H1 @ H22 )
% 6.92/7.12 => ( ( relH @ As @ H22 @ H32 )
% 6.92/7.12 => ( relH @ As @ H1 @ H32 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % relH_trans
% 6.92/7.12 thf(fact_332_relH__sym,axiom,
% 6.92/7.12 ! [As: set_nat,H: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 6.92/7.12 ( ( relH @ As @ H @ H5 )
% 6.92/7.12 => ( relH @ As @ H5 @ H ) ) ).
% 6.92/7.12
% 6.92/7.12 % relH_sym
% 6.92/7.12 thf(fact_333_leD,axiom,
% 6.92/7.12 ! [Y: assn,X: assn] :
% 6.92/7.12 ( ( ord_less_eq_assn @ Y @ X )
% 6.92/7.12 => ~ ( ord_less_assn @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % leD
% 6.92/7.12 thf(fact_334_leD,axiom,
% 6.92/7.12 ! [Y: set_int,X: set_int] :
% 6.92/7.12 ( ( ord_less_eq_set_int @ Y @ X )
% 6.92/7.12 => ~ ( ord_less_set_int @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % leD
% 6.92/7.12 thf(fact_335_leD,axiom,
% 6.92/7.12 ! [Y: rat,X: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ Y @ X )
% 6.92/7.12 => ~ ( ord_less_rat @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % leD
% 6.92/7.12 thf(fact_336_leD,axiom,
% 6.92/7.12 ! [Y: num,X: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ Y @ X )
% 6.92/7.12 => ~ ( ord_less_num @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % leD
% 6.92/7.12 thf(fact_337_leD,axiom,
% 6.92/7.12 ! [Y: nat,X: nat] :
% 6.92/7.12 ( ( ord_less_eq_nat @ Y @ X )
% 6.92/7.12 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % leD
% 6.92/7.12 thf(fact_338_leD,axiom,
% 6.92/7.12 ! [Y: int,X: int] :
% 6.92/7.12 ( ( ord_less_eq_int @ Y @ X )
% 6.92/7.12 => ~ ( ord_less_int @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % leD
% 6.92/7.12 thf(fact_339_leI,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ~ ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % leI
% 6.92/7.12 thf(fact_340_leI,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ~ ( ord_less_num @ X @ Y )
% 6.92/7.12 => ( ord_less_eq_num @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % leI
% 6.92/7.12 thf(fact_341_leI,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ~ ( ord_less_nat @ X @ Y )
% 6.92/7.12 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % leI
% 6.92/7.12 thf(fact_342_leI,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ~ ( ord_less_int @ X @ Y )
% 6.92/7.12 => ( ord_less_eq_int @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % leI
% 6.92/7.12 thf(fact_343_nless__le,axiom,
% 6.92/7.12 ! [A: assn,B: assn] :
% 6.92/7.12 ( ( ~ ( ord_less_assn @ A @ B ) )
% 6.92/7.12 = ( ~ ( ord_less_eq_assn @ A @ B )
% 6.92/7.12 | ( A = B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % nless_le
% 6.92/7.12 thf(fact_344_nless__le,axiom,
% 6.92/7.12 ! [A: set_int,B: set_int] :
% 6.92/7.12 ( ( ~ ( ord_less_set_int @ A @ B ) )
% 6.92/7.12 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 6.92/7.12 | ( A = B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % nless_le
% 6.92/7.12 thf(fact_345_nless__le,axiom,
% 6.92/7.12 ! [A: rat,B: rat] :
% 6.92/7.12 ( ( ~ ( ord_less_rat @ A @ B ) )
% 6.92/7.12 = ( ~ ( ord_less_eq_rat @ A @ B )
% 6.92/7.12 | ( A = B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % nless_le
% 6.92/7.12 thf(fact_346_nless__le,axiom,
% 6.92/7.12 ! [A: num,B: num] :
% 6.92/7.12 ( ( ~ ( ord_less_num @ A @ B ) )
% 6.92/7.12 = ( ~ ( ord_less_eq_num @ A @ B )
% 6.92/7.12 | ( A = B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % nless_le
% 6.92/7.12 thf(fact_347_nless__le,axiom,
% 6.92/7.12 ! [A: nat,B: nat] :
% 6.92/7.12 ( ( ~ ( ord_less_nat @ A @ B ) )
% 6.92/7.12 = ( ~ ( ord_less_eq_nat @ A @ B )
% 6.92/7.12 | ( A = B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % nless_le
% 6.92/7.12 thf(fact_348_nless__le,axiom,
% 6.92/7.12 ! [A: int,B: int] :
% 6.92/7.12 ( ( ~ ( ord_less_int @ A @ B ) )
% 6.92/7.12 = ( ~ ( ord_less_eq_int @ A @ B )
% 6.92/7.12 | ( A = B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % nless_le
% 6.92/7.12 thf(fact_349_antisym__conv1,axiom,
% 6.92/7.12 ! [X: assn,Y: assn] :
% 6.92/7.12 ( ~ ( ord_less_assn @ X @ Y )
% 6.92/7.12 => ( ( ord_less_eq_assn @ X @ Y )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv1
% 6.92/7.12 thf(fact_350_antisym__conv1,axiom,
% 6.92/7.12 ! [X: set_int,Y: set_int] :
% 6.92/7.12 ( ~ ( ord_less_set_int @ X @ Y )
% 6.92/7.12 => ( ( ord_less_eq_set_int @ X @ Y )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv1
% 6.92/7.12 thf(fact_351_antisym__conv1,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ~ ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv1
% 6.92/7.12 thf(fact_352_antisym__conv1,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ~ ( ord_less_num @ X @ Y )
% 6.92/7.12 => ( ( ord_less_eq_num @ X @ Y )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv1
% 6.92/7.12 thf(fact_353_antisym__conv1,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ~ ( ord_less_nat @ X @ Y )
% 6.92/7.12 => ( ( ord_less_eq_nat @ X @ Y )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv1
% 6.92/7.12 thf(fact_354_antisym__conv1,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ~ ( ord_less_int @ X @ Y )
% 6.92/7.12 => ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv1
% 6.92/7.12 thf(fact_355_antisym__conv2,axiom,
% 6.92/7.12 ! [X: assn,Y: assn] :
% 6.92/7.12 ( ( ord_less_eq_assn @ X @ Y )
% 6.92/7.12 => ( ( ~ ( ord_less_assn @ X @ Y ) )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv2
% 6.92/7.12 thf(fact_356_antisym__conv2,axiom,
% 6.92/7.12 ! [X: set_int,Y: set_int] :
% 6.92/7.12 ( ( ord_less_eq_set_int @ X @ Y )
% 6.92/7.12 => ( ( ~ ( ord_less_set_int @ X @ Y ) )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv2
% 6.92/7.12 thf(fact_357_antisym__conv2,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.12 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv2
% 6.92/7.12 thf(fact_358_antisym__conv2,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ X @ Y )
% 6.92/7.12 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv2
% 6.92/7.12 thf(fact_359_antisym__conv2,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( ord_less_eq_nat @ X @ Y )
% 6.92/7.12 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv2
% 6.92/7.12 thf(fact_360_antisym__conv2,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.12 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 6.92/7.12 = ( X = Y ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % antisym_conv2
% 6.92/7.12 thf(fact_361_dense__ge,axiom,
% 6.92/7.12 ! [Z3: rat,Y: rat] :
% 6.92/7.12 ( ! [X3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ Z3 @ X3 )
% 6.92/7.12 => ( ord_less_eq_rat @ Y @ X3 ) )
% 6.92/7.12 => ( ord_less_eq_rat @ Y @ Z3 ) ) ).
% 6.92/7.12
% 6.92/7.12 % dense_ge
% 6.92/7.12 thf(fact_362_dense__le,axiom,
% 6.92/7.12 ! [Y: rat,Z3: rat] :
% 6.92/7.12 ( ! [X3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y )
% 6.92/7.12 => ( ord_less_eq_rat @ X3 @ Z3 ) )
% 6.92/7.12 => ( ord_less_eq_rat @ Y @ Z3 ) ) ).
% 6.92/7.12
% 6.92/7.12 % dense_le
% 6.92/7.12 thf(fact_363_less__le__not__le,axiom,
% 6.92/7.12 ( ord_less_assn
% 6.92/7.12 = ( ^ [X4: assn,Y4: assn] :
% 6.92/7.12 ( ( ord_less_eq_assn @ X4 @ Y4 )
% 6.92/7.12 & ~ ( ord_less_eq_assn @ Y4 @ X4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_le_not_le
% 6.92/7.12 thf(fact_364_less__le__not__le,axiom,
% 6.92/7.12 ( ord_less_set_int
% 6.92/7.12 = ( ^ [X4: set_int,Y4: set_int] :
% 6.92/7.12 ( ( ord_less_eq_set_int @ X4 @ Y4 )
% 6.92/7.12 & ~ ( ord_less_eq_set_int @ Y4 @ X4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_le_not_le
% 6.92/7.12 thf(fact_365_less__le__not__le,axiom,
% 6.92/7.12 ( ord_less_rat
% 6.92/7.12 = ( ^ [X4: rat,Y4: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 6.92/7.12 & ~ ( ord_less_eq_rat @ Y4 @ X4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_le_not_le
% 6.92/7.12 thf(fact_366_less__le__not__le,axiom,
% 6.92/7.12 ( ord_less_num
% 6.92/7.12 = ( ^ [X4: num,Y4: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ X4 @ Y4 )
% 6.92/7.12 & ~ ( ord_less_eq_num @ Y4 @ X4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_le_not_le
% 6.92/7.12 thf(fact_367_less__le__not__le,axiom,
% 6.92/7.12 ( ord_less_nat
% 6.92/7.12 = ( ^ [X4: nat,Y4: nat] :
% 6.92/7.12 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 6.92/7.12 & ~ ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_le_not_le
% 6.92/7.12 thf(fact_368_less__le__not__le,axiom,
% 6.92/7.12 ( ord_less_int
% 6.92/7.12 = ( ^ [X4: int,Y4: int] :
% 6.92/7.12 ( ( ord_less_eq_int @ X4 @ Y4 )
% 6.92/7.12 & ~ ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_le_not_le
% 6.92/7.12 thf(fact_369_not__le__imp__less,axiom,
% 6.92/7.12 ! [Y: rat,X: rat] :
% 6.92/7.12 ( ~ ( ord_less_eq_rat @ Y @ X )
% 6.92/7.12 => ( ord_less_rat @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % not_le_imp_less
% 6.92/7.12 thf(fact_370_not__le__imp__less,axiom,
% 6.92/7.12 ! [Y: num,X: num] :
% 6.92/7.12 ( ~ ( ord_less_eq_num @ Y @ X )
% 6.92/7.12 => ( ord_less_num @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % not_le_imp_less
% 6.92/7.12 thf(fact_371_not__le__imp__less,axiom,
% 6.92/7.12 ! [Y: nat,X: nat] :
% 6.92/7.12 ( ~ ( ord_less_eq_nat @ Y @ X )
% 6.92/7.12 => ( ord_less_nat @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % not_le_imp_less
% 6.92/7.12 thf(fact_372_not__le__imp__less,axiom,
% 6.92/7.12 ! [Y: int,X: int] :
% 6.92/7.12 ( ~ ( ord_less_eq_int @ Y @ X )
% 6.92/7.12 => ( ord_less_int @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % not_le_imp_less
% 6.92/7.12 thf(fact_373_order_Oorder__iff__strict,axiom,
% 6.92/7.12 ( ord_less_eq_assn
% 6.92/7.12 = ( ^ [A5: assn,B4: assn] :
% 6.92/7.12 ( ( ord_less_assn @ A5 @ B4 )
% 6.92/7.12 | ( A5 = B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.order_iff_strict
% 6.92/7.12 thf(fact_374_order_Oorder__iff__strict,axiom,
% 6.92/7.12 ( ord_less_eq_set_int
% 6.92/7.12 = ( ^ [A5: set_int,B4: set_int] :
% 6.92/7.12 ( ( ord_less_set_int @ A5 @ B4 )
% 6.92/7.12 | ( A5 = B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.order_iff_strict
% 6.92/7.12 thf(fact_375_order_Oorder__iff__strict,axiom,
% 6.92/7.12 ( ord_less_eq_rat
% 6.92/7.12 = ( ^ [A5: rat,B4: rat] :
% 6.92/7.12 ( ( ord_less_rat @ A5 @ B4 )
% 6.92/7.12 | ( A5 = B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.order_iff_strict
% 6.92/7.12 thf(fact_376_order_Oorder__iff__strict,axiom,
% 6.92/7.12 ( ord_less_eq_num
% 6.92/7.12 = ( ^ [A5: num,B4: num] :
% 6.92/7.12 ( ( ord_less_num @ A5 @ B4 )
% 6.92/7.12 | ( A5 = B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.order_iff_strict
% 6.92/7.12 thf(fact_377_order_Oorder__iff__strict,axiom,
% 6.92/7.12 ( ord_less_eq_nat
% 6.92/7.12 = ( ^ [A5: nat,B4: nat] :
% 6.92/7.12 ( ( ord_less_nat @ A5 @ B4 )
% 6.92/7.12 | ( A5 = B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.order_iff_strict
% 6.92/7.12 thf(fact_378_order_Oorder__iff__strict,axiom,
% 6.92/7.12 ( ord_less_eq_int
% 6.92/7.12 = ( ^ [A5: int,B4: int] :
% 6.92/7.12 ( ( ord_less_int @ A5 @ B4 )
% 6.92/7.12 | ( A5 = B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.order_iff_strict
% 6.92/7.12 thf(fact_379_order_Ostrict__iff__order,axiom,
% 6.92/7.12 ( ord_less_assn
% 6.92/7.12 = ( ^ [A5: assn,B4: assn] :
% 6.92/7.12 ( ( ord_less_eq_assn @ A5 @ B4 )
% 6.92/7.12 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_iff_order
% 6.92/7.12 thf(fact_380_order_Ostrict__iff__order,axiom,
% 6.92/7.12 ( ord_less_set_int
% 6.92/7.12 = ( ^ [A5: set_int,B4: set_int] :
% 6.92/7.12 ( ( ord_less_eq_set_int @ A5 @ B4 )
% 6.92/7.12 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_iff_order
% 6.92/7.12 thf(fact_381_order_Ostrict__iff__order,axiom,
% 6.92/7.12 ( ord_less_rat
% 6.92/7.12 = ( ^ [A5: rat,B4: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ A5 @ B4 )
% 6.92/7.12 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_iff_order
% 6.92/7.12 thf(fact_382_order_Ostrict__iff__order,axiom,
% 6.92/7.12 ( ord_less_num
% 6.92/7.12 = ( ^ [A5: num,B4: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ A5 @ B4 )
% 6.92/7.12 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_iff_order
% 6.92/7.12 thf(fact_383_order_Ostrict__iff__order,axiom,
% 6.92/7.12 ( ord_less_nat
% 6.92/7.12 = ( ^ [A5: nat,B4: nat] :
% 6.92/7.12 ( ( ord_less_eq_nat @ A5 @ B4 )
% 6.92/7.12 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_iff_order
% 6.92/7.12 thf(fact_384_order_Ostrict__iff__order,axiom,
% 6.92/7.12 ( ord_less_int
% 6.92/7.12 = ( ^ [A5: int,B4: int] :
% 6.92/7.12 ( ( ord_less_eq_int @ A5 @ B4 )
% 6.92/7.12 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_iff_order
% 6.92/7.12 thf(fact_385_order_Ostrict__trans1,axiom,
% 6.92/7.12 ! [A: assn,B: assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_eq_assn @ A @ B )
% 6.92/7.12 => ( ( ord_less_assn @ B @ C2 )
% 6.92/7.12 => ( ord_less_assn @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans1
% 6.92/7.12 thf(fact_386_order_Ostrict__trans1,axiom,
% 6.92/7.12 ! [A: set_int,B: set_int,C2: set_int] :
% 6.92/7.12 ( ( ord_less_eq_set_int @ A @ B )
% 6.92/7.12 => ( ( ord_less_set_int @ B @ C2 )
% 6.92/7.12 => ( ord_less_set_int @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans1
% 6.92/7.12 thf(fact_387_order_Ostrict__trans1,axiom,
% 6.92/7.12 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.12 => ( ( ord_less_rat @ B @ C2 )
% 6.92/7.12 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans1
% 6.92/7.12 thf(fact_388_order_Ostrict__trans1,axiom,
% 6.92/7.12 ! [A: num,B: num,C2: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.12 => ( ( ord_less_num @ B @ C2 )
% 6.92/7.12 => ( ord_less_num @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans1
% 6.92/7.12 thf(fact_389_order_Ostrict__trans1,axiom,
% 6.92/7.12 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.12 => ( ( ord_less_nat @ B @ C2 )
% 6.92/7.12 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans1
% 6.92/7.12 thf(fact_390_order_Ostrict__trans1,axiom,
% 6.92/7.12 ! [A: int,B: int,C2: int] :
% 6.92/7.12 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.12 => ( ( ord_less_int @ B @ C2 )
% 6.92/7.12 => ( ord_less_int @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans1
% 6.92/7.12 thf(fact_391_order_Ostrict__trans2,axiom,
% 6.92/7.12 ! [A: assn,B: assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ( ( ord_less_eq_assn @ B @ C2 )
% 6.92/7.12 => ( ord_less_assn @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans2
% 6.92/7.12 thf(fact_392_order_Ostrict__trans2,axiom,
% 6.92/7.12 ! [A: set_int,B: set_int,C2: set_int] :
% 6.92/7.12 ( ( ord_less_set_int @ A @ B )
% 6.92/7.12 => ( ( ord_less_eq_set_int @ B @ C2 )
% 6.92/7.12 => ( ord_less_set_int @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans2
% 6.92/7.12 thf(fact_393_order_Ostrict__trans2,axiom,
% 6.92/7.12 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.12 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans2
% 6.92/7.12 thf(fact_394_order_Ostrict__trans2,axiom,
% 6.92/7.12 ! [A: num,B: num,C2: num] :
% 6.92/7.12 ( ( ord_less_num @ A @ B )
% 6.92/7.12 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.12 => ( ord_less_num @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans2
% 6.92/7.12 thf(fact_395_order_Ostrict__trans2,axiom,
% 6.92/7.12 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_nat @ A @ B )
% 6.92/7.12 => ( ( ord_less_eq_nat @ B @ C2 )
% 6.92/7.12 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans2
% 6.92/7.12 thf(fact_396_order_Ostrict__trans2,axiom,
% 6.92/7.12 ! [A: int,B: int,C2: int] :
% 6.92/7.12 ( ( ord_less_int @ A @ B )
% 6.92/7.12 => ( ( ord_less_eq_int @ B @ C2 )
% 6.92/7.12 => ( ord_less_int @ A @ C2 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_trans2
% 6.92/7.12 thf(fact_397_order_Ostrict__iff__not,axiom,
% 6.92/7.12 ( ord_less_assn
% 6.92/7.12 = ( ^ [A5: assn,B4: assn] :
% 6.92/7.12 ( ( ord_less_eq_assn @ A5 @ B4 )
% 6.92/7.12 & ~ ( ord_less_eq_assn @ B4 @ A5 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_iff_not
% 6.92/7.12 thf(fact_398_order_Ostrict__iff__not,axiom,
% 6.92/7.12 ( ord_less_set_int
% 6.92/7.12 = ( ^ [A5: set_int,B4: set_int] :
% 6.92/7.12 ( ( ord_less_eq_set_int @ A5 @ B4 )
% 6.92/7.12 & ~ ( ord_less_eq_set_int @ B4 @ A5 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_iff_not
% 6.92/7.12 thf(fact_399_order_Ostrict__iff__not,axiom,
% 6.92/7.12 ( ord_less_rat
% 6.92/7.12 = ( ^ [A5: rat,B4: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ A5 @ B4 )
% 6.92/7.12 & ~ ( ord_less_eq_rat @ B4 @ A5 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_iff_not
% 6.92/7.12 thf(fact_400_order_Ostrict__iff__not,axiom,
% 6.92/7.12 ( ord_less_num
% 6.92/7.12 = ( ^ [A5: num,B4: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ A5 @ B4 )
% 6.92/7.12 & ~ ( ord_less_eq_num @ B4 @ A5 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_iff_not
% 6.92/7.12 thf(fact_401_order_Ostrict__iff__not,axiom,
% 6.92/7.12 ( ord_less_nat
% 6.92/7.12 = ( ^ [A5: nat,B4: nat] :
% 6.92/7.12 ( ( ord_less_eq_nat @ A5 @ B4 )
% 6.92/7.12 & ~ ( ord_less_eq_nat @ B4 @ A5 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_iff_not
% 6.92/7.12 thf(fact_402_order_Ostrict__iff__not,axiom,
% 6.92/7.12 ( ord_less_int
% 6.92/7.12 = ( ^ [A5: int,B4: int] :
% 6.92/7.12 ( ( ord_less_eq_int @ A5 @ B4 )
% 6.92/7.12 & ~ ( ord_less_eq_int @ B4 @ A5 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_iff_not
% 6.92/7.12 thf(fact_403_dense__ge__bounded,axiom,
% 6.92/7.12 ! [Z3: rat,X: rat,Y: rat] :
% 6.92/7.12 ( ( ord_less_rat @ Z3 @ X )
% 6.92/7.12 => ( ! [W: rat] :
% 6.92/7.12 ( ( ord_less_rat @ Z3 @ W )
% 6.92/7.12 => ( ( ord_less_rat @ W @ X )
% 6.92/7.12 => ( ord_less_eq_rat @ Y @ W ) ) )
% 6.92/7.12 => ( ord_less_eq_rat @ Y @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dense_ge_bounded
% 6.92/7.12 thf(fact_404_dense__le__bounded,axiom,
% 6.92/7.12 ! [X: rat,Y: rat,Z3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ( ! [W: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X @ W )
% 6.92/7.12 => ( ( ord_less_rat @ W @ Y )
% 6.92/7.12 => ( ord_less_eq_rat @ W @ Z3 ) ) )
% 6.92/7.12 => ( ord_less_eq_rat @ Y @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dense_le_bounded
% 6.92/7.12 thf(fact_405_dual__order_Oorder__iff__strict,axiom,
% 6.92/7.12 ( ord_less_eq_assn
% 6.92/7.12 = ( ^ [B4: assn,A5: assn] :
% 6.92/7.12 ( ( ord_less_assn @ B4 @ A5 )
% 6.92/7.12 | ( A5 = B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.order_iff_strict
% 6.92/7.12 thf(fact_406_dual__order_Oorder__iff__strict,axiom,
% 6.92/7.12 ( ord_less_eq_set_int
% 6.92/7.12 = ( ^ [B4: set_int,A5: set_int] :
% 6.92/7.12 ( ( ord_less_set_int @ B4 @ A5 )
% 6.92/7.12 | ( A5 = B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.order_iff_strict
% 6.92/7.12 thf(fact_407_dual__order_Oorder__iff__strict,axiom,
% 6.92/7.12 ( ord_less_eq_rat
% 6.92/7.12 = ( ^ [B4: rat,A5: rat] :
% 6.92/7.12 ( ( ord_less_rat @ B4 @ A5 )
% 6.92/7.12 | ( A5 = B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.order_iff_strict
% 6.92/7.12 thf(fact_408_dual__order_Oorder__iff__strict,axiom,
% 6.92/7.12 ( ord_less_eq_num
% 6.92/7.12 = ( ^ [B4: num,A5: num] :
% 6.92/7.12 ( ( ord_less_num @ B4 @ A5 )
% 6.92/7.12 | ( A5 = B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.order_iff_strict
% 6.92/7.12 thf(fact_409_dual__order_Oorder__iff__strict,axiom,
% 6.92/7.12 ( ord_less_eq_nat
% 6.92/7.12 = ( ^ [B4: nat,A5: nat] :
% 6.92/7.12 ( ( ord_less_nat @ B4 @ A5 )
% 6.92/7.12 | ( A5 = B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.order_iff_strict
% 6.92/7.12 thf(fact_410_dual__order_Oorder__iff__strict,axiom,
% 6.92/7.12 ( ord_less_eq_int
% 6.92/7.12 = ( ^ [B4: int,A5: int] :
% 6.92/7.12 ( ( ord_less_int @ B4 @ A5 )
% 6.92/7.12 | ( A5 = B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.order_iff_strict
% 6.92/7.12 thf(fact_411_dual__order_Ostrict__iff__order,axiom,
% 6.92/7.12 ( ord_less_assn
% 6.92/7.12 = ( ^ [B4: assn,A5: assn] :
% 6.92/7.12 ( ( ord_less_eq_assn @ B4 @ A5 )
% 6.92/7.12 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_iff_order
% 6.92/7.12 thf(fact_412_dual__order_Ostrict__iff__order,axiom,
% 6.92/7.12 ( ord_less_set_int
% 6.92/7.12 = ( ^ [B4: set_int,A5: set_int] :
% 6.92/7.12 ( ( ord_less_eq_set_int @ B4 @ A5 )
% 6.92/7.12 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_iff_order
% 6.92/7.12 thf(fact_413_dual__order_Ostrict__iff__order,axiom,
% 6.92/7.12 ( ord_less_rat
% 6.92/7.12 = ( ^ [B4: rat,A5: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ B4 @ A5 )
% 6.92/7.12 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_iff_order
% 6.92/7.12 thf(fact_414_dual__order_Ostrict__iff__order,axiom,
% 6.92/7.12 ( ord_less_num
% 6.92/7.12 = ( ^ [B4: num,A5: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ B4 @ A5 )
% 6.92/7.12 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_iff_order
% 6.92/7.12 thf(fact_415_dual__order_Ostrict__iff__order,axiom,
% 6.92/7.12 ( ord_less_nat
% 6.92/7.12 = ( ^ [B4: nat,A5: nat] :
% 6.92/7.12 ( ( ord_less_eq_nat @ B4 @ A5 )
% 6.92/7.12 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_iff_order
% 6.92/7.12 thf(fact_416_dual__order_Ostrict__iff__order,axiom,
% 6.92/7.12 ( ord_less_int
% 6.92/7.12 = ( ^ [B4: int,A5: int] :
% 6.92/7.12 ( ( ord_less_eq_int @ B4 @ A5 )
% 6.92/7.12 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_iff_order
% 6.92/7.12 thf(fact_417_dual__order_Ostrict__trans1,axiom,
% 6.92/7.12 ! [B: assn,A: assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_eq_assn @ B @ A )
% 6.92/7.12 => ( ( ord_less_assn @ C2 @ B )
% 6.92/7.12 => ( ord_less_assn @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans1
% 6.92/7.12 thf(fact_418_dual__order_Ostrict__trans1,axiom,
% 6.92/7.12 ! [B: set_int,A: set_int,C2: set_int] :
% 6.92/7.12 ( ( ord_less_eq_set_int @ B @ A )
% 6.92/7.12 => ( ( ord_less_set_int @ C2 @ B )
% 6.92/7.12 => ( ord_less_set_int @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans1
% 6.92/7.12 thf(fact_419_dual__order_Ostrict__trans1,axiom,
% 6.92/7.12 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.12 => ( ( ord_less_rat @ C2 @ B )
% 6.92/7.12 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans1
% 6.92/7.12 thf(fact_420_dual__order_Ostrict__trans1,axiom,
% 6.92/7.12 ! [B: num,A: num,C2: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ B @ A )
% 6.92/7.12 => ( ( ord_less_num @ C2 @ B )
% 6.92/7.12 => ( ord_less_num @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans1
% 6.92/7.12 thf(fact_421_dual__order_Ostrict__trans1,axiom,
% 6.92/7.12 ! [B: nat,A: nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.12 => ( ( ord_less_nat @ C2 @ B )
% 6.92/7.12 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans1
% 6.92/7.12 thf(fact_422_dual__order_Ostrict__trans1,axiom,
% 6.92/7.12 ! [B: int,A: int,C2: int] :
% 6.92/7.12 ( ( ord_less_eq_int @ B @ A )
% 6.92/7.12 => ( ( ord_less_int @ C2 @ B )
% 6.92/7.12 => ( ord_less_int @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans1
% 6.92/7.12 thf(fact_423_dual__order_Ostrict__trans2,axiom,
% 6.92/7.12 ! [B: assn,A: assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_assn @ B @ A )
% 6.92/7.12 => ( ( ord_less_eq_assn @ C2 @ B )
% 6.92/7.12 => ( ord_less_assn @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans2
% 6.92/7.12 thf(fact_424_dual__order_Ostrict__trans2,axiom,
% 6.92/7.12 ! [B: set_int,A: set_int,C2: set_int] :
% 6.92/7.12 ( ( ord_less_set_int @ B @ A )
% 6.92/7.12 => ( ( ord_less_eq_set_int @ C2 @ B )
% 6.92/7.12 => ( ord_less_set_int @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans2
% 6.92/7.12 thf(fact_425_dual__order_Ostrict__trans2,axiom,
% 6.92/7.12 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_rat @ B @ A )
% 6.92/7.12 => ( ( ord_less_eq_rat @ C2 @ B )
% 6.92/7.12 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans2
% 6.92/7.12 thf(fact_426_dual__order_Ostrict__trans2,axiom,
% 6.92/7.12 ! [B: num,A: num,C2: num] :
% 6.92/7.12 ( ( ord_less_num @ B @ A )
% 6.92/7.12 => ( ( ord_less_eq_num @ C2 @ B )
% 6.92/7.12 => ( ord_less_num @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans2
% 6.92/7.12 thf(fact_427_dual__order_Ostrict__trans2,axiom,
% 6.92/7.12 ! [B: nat,A: nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_nat @ B @ A )
% 6.92/7.12 => ( ( ord_less_eq_nat @ C2 @ B )
% 6.92/7.12 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans2
% 6.92/7.12 thf(fact_428_dual__order_Ostrict__trans2,axiom,
% 6.92/7.12 ! [B: int,A: int,C2: int] :
% 6.92/7.12 ( ( ord_less_int @ B @ A )
% 6.92/7.12 => ( ( ord_less_eq_int @ C2 @ B )
% 6.92/7.12 => ( ord_less_int @ C2 @ A ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_trans2
% 6.92/7.12 thf(fact_429_dual__order_Ostrict__iff__not,axiom,
% 6.92/7.12 ( ord_less_assn
% 6.92/7.12 = ( ^ [B4: assn,A5: assn] :
% 6.92/7.12 ( ( ord_less_eq_assn @ B4 @ A5 )
% 6.92/7.12 & ~ ( ord_less_eq_assn @ A5 @ B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_iff_not
% 6.92/7.12 thf(fact_430_dual__order_Ostrict__iff__not,axiom,
% 6.92/7.12 ( ord_less_set_int
% 6.92/7.12 = ( ^ [B4: set_int,A5: set_int] :
% 6.92/7.12 ( ( ord_less_eq_set_int @ B4 @ A5 )
% 6.92/7.12 & ~ ( ord_less_eq_set_int @ A5 @ B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_iff_not
% 6.92/7.12 thf(fact_431_dual__order_Ostrict__iff__not,axiom,
% 6.92/7.12 ( ord_less_rat
% 6.92/7.12 = ( ^ [B4: rat,A5: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ B4 @ A5 )
% 6.92/7.12 & ~ ( ord_less_eq_rat @ A5 @ B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_iff_not
% 6.92/7.12 thf(fact_432_dual__order_Ostrict__iff__not,axiom,
% 6.92/7.12 ( ord_less_num
% 6.92/7.12 = ( ^ [B4: num,A5: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ B4 @ A5 )
% 6.92/7.12 & ~ ( ord_less_eq_num @ A5 @ B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_iff_not
% 6.92/7.12 thf(fact_433_dual__order_Ostrict__iff__not,axiom,
% 6.92/7.12 ( ord_less_nat
% 6.92/7.12 = ( ^ [B4: nat,A5: nat] :
% 6.92/7.12 ( ( ord_less_eq_nat @ B4 @ A5 )
% 6.92/7.12 & ~ ( ord_less_eq_nat @ A5 @ B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_iff_not
% 6.92/7.12 thf(fact_434_dual__order_Ostrict__iff__not,axiom,
% 6.92/7.12 ( ord_less_int
% 6.92/7.12 = ( ^ [B4: int,A5: int] :
% 6.92/7.12 ( ( ord_less_eq_int @ B4 @ A5 )
% 6.92/7.12 & ~ ( ord_less_eq_int @ A5 @ B4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_iff_not
% 6.92/7.12 thf(fact_435_order_Ostrict__implies__order,axiom,
% 6.92/7.12 ! [A: assn,B: assn] :
% 6.92/7.12 ( ( ord_less_assn @ A @ B )
% 6.92/7.12 => ( ord_less_eq_assn @ A @ B ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_implies_order
% 6.92/7.12 thf(fact_436_order_Ostrict__implies__order,axiom,
% 6.92/7.12 ! [A: set_int,B: set_int] :
% 6.92/7.12 ( ( ord_less_set_int @ A @ B )
% 6.92/7.12 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_implies_order
% 6.92/7.12 thf(fact_437_order_Ostrict__implies__order,axiom,
% 6.92/7.12 ! [A: rat,B: rat] :
% 6.92/7.12 ( ( ord_less_rat @ A @ B )
% 6.92/7.12 => ( ord_less_eq_rat @ A @ B ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_implies_order
% 6.92/7.12 thf(fact_438_order_Ostrict__implies__order,axiom,
% 6.92/7.12 ! [A: num,B: num] :
% 6.92/7.12 ( ( ord_less_num @ A @ B )
% 6.92/7.12 => ( ord_less_eq_num @ A @ B ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_implies_order
% 6.92/7.12 thf(fact_439_order_Ostrict__implies__order,axiom,
% 6.92/7.12 ! [A: nat,B: nat] :
% 6.92/7.12 ( ( ord_less_nat @ A @ B )
% 6.92/7.12 => ( ord_less_eq_nat @ A @ B ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_implies_order
% 6.92/7.12 thf(fact_440_order_Ostrict__implies__order,axiom,
% 6.92/7.12 ! [A: int,B: int] :
% 6.92/7.12 ( ( ord_less_int @ A @ B )
% 6.92/7.12 => ( ord_less_eq_int @ A @ B ) ) ).
% 6.92/7.12
% 6.92/7.12 % order.strict_implies_order
% 6.92/7.12 thf(fact_441_dual__order_Ostrict__implies__order,axiom,
% 6.92/7.12 ! [B: assn,A: assn] :
% 6.92/7.12 ( ( ord_less_assn @ B @ A )
% 6.92/7.12 => ( ord_less_eq_assn @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_implies_order
% 6.92/7.12 thf(fact_442_dual__order_Ostrict__implies__order,axiom,
% 6.92/7.12 ! [B: set_int,A: set_int] :
% 6.92/7.12 ( ( ord_less_set_int @ B @ A )
% 6.92/7.12 => ( ord_less_eq_set_int @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_implies_order
% 6.92/7.12 thf(fact_443_dual__order_Ostrict__implies__order,axiom,
% 6.92/7.12 ! [B: rat,A: rat] :
% 6.92/7.12 ( ( ord_less_rat @ B @ A )
% 6.92/7.12 => ( ord_less_eq_rat @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_implies_order
% 6.92/7.12 thf(fact_444_dual__order_Ostrict__implies__order,axiom,
% 6.92/7.12 ! [B: num,A: num] :
% 6.92/7.12 ( ( ord_less_num @ B @ A )
% 6.92/7.12 => ( ord_less_eq_num @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_implies_order
% 6.92/7.12 thf(fact_445_dual__order_Ostrict__implies__order,axiom,
% 6.92/7.12 ! [B: nat,A: nat] :
% 6.92/7.12 ( ( ord_less_nat @ B @ A )
% 6.92/7.12 => ( ord_less_eq_nat @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_implies_order
% 6.92/7.12 thf(fact_446_dual__order_Ostrict__implies__order,axiom,
% 6.92/7.12 ! [B: int,A: int] :
% 6.92/7.12 ( ( ord_less_int @ B @ A )
% 6.92/7.12 => ( ord_less_eq_int @ B @ A ) ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.strict_implies_order
% 6.92/7.12 thf(fact_447_order__le__less,axiom,
% 6.92/7.12 ( ord_less_eq_assn
% 6.92/7.12 = ( ^ [X4: assn,Y4: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X4 @ Y4 )
% 6.92/7.12 | ( X4 = Y4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less
% 6.92/7.12 thf(fact_448_order__le__less,axiom,
% 6.92/7.12 ( ord_less_eq_set_int
% 6.92/7.12 = ( ^ [X4: set_int,Y4: set_int] :
% 6.92/7.12 ( ( ord_less_set_int @ X4 @ Y4 )
% 6.92/7.12 | ( X4 = Y4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less
% 6.92/7.12 thf(fact_449_order__le__less,axiom,
% 6.92/7.12 ( ord_less_eq_rat
% 6.92/7.12 = ( ^ [X4: rat,Y4: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X4 @ Y4 )
% 6.92/7.12 | ( X4 = Y4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less
% 6.92/7.12 thf(fact_450_order__le__less,axiom,
% 6.92/7.12 ( ord_less_eq_num
% 6.92/7.12 = ( ^ [X4: num,Y4: num] :
% 6.92/7.12 ( ( ord_less_num @ X4 @ Y4 )
% 6.92/7.12 | ( X4 = Y4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less
% 6.92/7.12 thf(fact_451_order__le__less,axiom,
% 6.92/7.12 ( ord_less_eq_nat
% 6.92/7.12 = ( ^ [X4: nat,Y4: nat] :
% 6.92/7.12 ( ( ord_less_nat @ X4 @ Y4 )
% 6.92/7.12 | ( X4 = Y4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less
% 6.92/7.12 thf(fact_452_order__le__less,axiom,
% 6.92/7.12 ( ord_less_eq_int
% 6.92/7.12 = ( ^ [X4: int,Y4: int] :
% 6.92/7.12 ( ( ord_less_int @ X4 @ Y4 )
% 6.92/7.12 | ( X4 = Y4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less
% 6.92/7.12 thf(fact_453_order__less__le,axiom,
% 6.92/7.12 ( ord_less_assn
% 6.92/7.12 = ( ^ [X4: assn,Y4: assn] :
% 6.92/7.12 ( ( ord_less_eq_assn @ X4 @ Y4 )
% 6.92/7.12 & ( X4 != Y4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_le
% 6.92/7.12 thf(fact_454_order__less__le,axiom,
% 6.92/7.12 ( ord_less_set_int
% 6.92/7.12 = ( ^ [X4: set_int,Y4: set_int] :
% 6.92/7.12 ( ( ord_less_eq_set_int @ X4 @ Y4 )
% 6.92/7.12 & ( X4 != Y4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_le
% 6.92/7.12 thf(fact_455_order__less__le,axiom,
% 6.92/7.12 ( ord_less_rat
% 6.92/7.12 = ( ^ [X4: rat,Y4: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 6.92/7.12 & ( X4 != Y4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_le
% 6.92/7.12 thf(fact_456_order__less__le,axiom,
% 6.92/7.12 ( ord_less_num
% 6.92/7.12 = ( ^ [X4: num,Y4: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ X4 @ Y4 )
% 6.92/7.12 & ( X4 != Y4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_le
% 6.92/7.12 thf(fact_457_order__less__le,axiom,
% 6.92/7.12 ( ord_less_nat
% 6.92/7.12 = ( ^ [X4: nat,Y4: nat] :
% 6.92/7.12 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 6.92/7.12 & ( X4 != Y4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_le
% 6.92/7.12 thf(fact_458_order__less__le,axiom,
% 6.92/7.12 ( ord_less_int
% 6.92/7.12 = ( ^ [X4: int,Y4: int] :
% 6.92/7.12 ( ( ord_less_eq_int @ X4 @ Y4 )
% 6.92/7.12 & ( X4 != Y4 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_le
% 6.92/7.12 thf(fact_459_linorder__not__le,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 6.92/7.12 = ( ord_less_rat @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_not_le
% 6.92/7.12 thf(fact_460_linorder__not__le,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( ~ ( ord_less_eq_num @ X @ Y ) )
% 6.92/7.12 = ( ord_less_num @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_not_le
% 6.92/7.12 thf(fact_461_linorder__not__le,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 6.92/7.12 = ( ord_less_nat @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_not_le
% 6.92/7.12 thf(fact_462_linorder__not__le,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 6.92/7.12 = ( ord_less_int @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_not_le
% 6.92/7.12 thf(fact_463_linorder__not__less,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 6.92/7.12 = ( ord_less_eq_rat @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_not_less
% 6.92/7.12 thf(fact_464_linorder__not__less,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( ~ ( ord_less_num @ X @ Y ) )
% 6.92/7.12 = ( ord_less_eq_num @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_not_less
% 6.92/7.12 thf(fact_465_linorder__not__less,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 6.92/7.12 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_not_less
% 6.92/7.12 thf(fact_466_linorder__not__less,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( ~ ( ord_less_int @ X @ Y ) )
% 6.92/7.12 = ( ord_less_eq_int @ Y @ X ) ) ).
% 6.92/7.12
% 6.92/7.12 % linorder_not_less
% 6.92/7.12 thf(fact_467_order__less__imp__le,axiom,
% 6.92/7.12 ! [X: assn,Y: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X @ Y )
% 6.92/7.12 => ( ord_less_eq_assn @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_le
% 6.92/7.12 thf(fact_468_order__less__imp__le,axiom,
% 6.92/7.12 ! [X: set_int,Y: set_int] :
% 6.92/7.12 ( ( ord_less_set_int @ X @ Y )
% 6.92/7.12 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_le
% 6.92/7.12 thf(fact_469_order__less__imp__le,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_le
% 6.92/7.12 thf(fact_470_order__less__imp__le,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( ord_less_num @ X @ Y )
% 6.92/7.12 => ( ord_less_eq_num @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_le
% 6.92/7.12 thf(fact_471_order__less__imp__le,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( ord_less_nat @ X @ Y )
% 6.92/7.12 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_le
% 6.92/7.12 thf(fact_472_order__less__imp__le,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( ord_less_int @ X @ Y )
% 6.92/7.12 => ( ord_less_eq_int @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_imp_le
% 6.92/7.12 thf(fact_473_order__le__neq__trans,axiom,
% 6.92/7.12 ! [A: assn,B: assn] :
% 6.92/7.12 ( ( ord_less_eq_assn @ A @ B )
% 6.92/7.12 => ( ( A != B )
% 6.92/7.12 => ( ord_less_assn @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_neq_trans
% 6.92/7.12 thf(fact_474_order__le__neq__trans,axiom,
% 6.92/7.12 ! [A: set_int,B: set_int] :
% 6.92/7.12 ( ( ord_less_eq_set_int @ A @ B )
% 6.92/7.12 => ( ( A != B )
% 6.92/7.12 => ( ord_less_set_int @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_neq_trans
% 6.92/7.12 thf(fact_475_order__le__neq__trans,axiom,
% 6.92/7.12 ! [A: rat,B: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.12 => ( ( A != B )
% 6.92/7.12 => ( ord_less_rat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_neq_trans
% 6.92/7.12 thf(fact_476_order__le__neq__trans,axiom,
% 6.92/7.12 ! [A: num,B: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.12 => ( ( A != B )
% 6.92/7.12 => ( ord_less_num @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_neq_trans
% 6.92/7.12 thf(fact_477_order__le__neq__trans,axiom,
% 6.92/7.12 ! [A: nat,B: nat] :
% 6.92/7.12 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.12 => ( ( A != B )
% 6.92/7.12 => ( ord_less_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_neq_trans
% 6.92/7.12 thf(fact_478_order__le__neq__trans,axiom,
% 6.92/7.12 ! [A: int,B: int] :
% 6.92/7.12 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.12 => ( ( A != B )
% 6.92/7.12 => ( ord_less_int @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_neq_trans
% 6.92/7.12 thf(fact_479_order__neq__le__trans,axiom,
% 6.92/7.12 ! [A: assn,B: assn] :
% 6.92/7.12 ( ( A != B )
% 6.92/7.12 => ( ( ord_less_eq_assn @ A @ B )
% 6.92/7.12 => ( ord_less_assn @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_neq_le_trans
% 6.92/7.12 thf(fact_480_order__neq__le__trans,axiom,
% 6.92/7.12 ! [A: set_int,B: set_int] :
% 6.92/7.12 ( ( A != B )
% 6.92/7.12 => ( ( ord_less_eq_set_int @ A @ B )
% 6.92/7.12 => ( ord_less_set_int @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_neq_le_trans
% 6.92/7.12 thf(fact_481_order__neq__le__trans,axiom,
% 6.92/7.12 ! [A: rat,B: rat] :
% 6.92/7.12 ( ( A != B )
% 6.92/7.12 => ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.12 => ( ord_less_rat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_neq_le_trans
% 6.92/7.12 thf(fact_482_order__neq__le__trans,axiom,
% 6.92/7.12 ! [A: num,B: num] :
% 6.92/7.12 ( ( A != B )
% 6.92/7.12 => ( ( ord_less_eq_num @ A @ B )
% 6.92/7.12 => ( ord_less_num @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_neq_le_trans
% 6.92/7.12 thf(fact_483_order__neq__le__trans,axiom,
% 6.92/7.12 ! [A: nat,B: nat] :
% 6.92/7.12 ( ( A != B )
% 6.92/7.12 => ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.12 => ( ord_less_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_neq_le_trans
% 6.92/7.12 thf(fact_484_order__neq__le__trans,axiom,
% 6.92/7.12 ! [A: int,B: int] :
% 6.92/7.12 ( ( A != B )
% 6.92/7.12 => ( ( ord_less_eq_int @ A @ B )
% 6.92/7.12 => ( ord_less_int @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_neq_le_trans
% 6.92/7.12 thf(fact_485_order__le__less__trans,axiom,
% 6.92/7.12 ! [X: assn,Y: assn,Z3: assn] :
% 6.92/7.12 ( ( ord_less_eq_assn @ X @ Y )
% 6.92/7.12 => ( ( ord_less_assn @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_assn @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_trans
% 6.92/7.12 thf(fact_486_order__le__less__trans,axiom,
% 6.92/7.12 ! [X: set_int,Y: set_int,Z3: set_int] :
% 6.92/7.12 ( ( ord_less_eq_set_int @ X @ Y )
% 6.92/7.12 => ( ( ord_less_set_int @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_set_int @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_trans
% 6.92/7.12 thf(fact_487_order__le__less__trans,axiom,
% 6.92/7.12 ! [X: rat,Y: rat,Z3: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.12 => ( ( ord_less_rat @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_rat @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_trans
% 6.92/7.12 thf(fact_488_order__le__less__trans,axiom,
% 6.92/7.12 ! [X: num,Y: num,Z3: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ X @ Y )
% 6.92/7.12 => ( ( ord_less_num @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_num @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_trans
% 6.92/7.12 thf(fact_489_order__le__less__trans,axiom,
% 6.92/7.12 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.12 ( ( ord_less_eq_nat @ X @ Y )
% 6.92/7.12 => ( ( ord_less_nat @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_trans
% 6.92/7.12 thf(fact_490_order__le__less__trans,axiom,
% 6.92/7.12 ! [X: int,Y: int,Z3: int] :
% 6.92/7.12 ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.12 => ( ( ord_less_int @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_trans
% 6.92/7.12 thf(fact_491_order__less__le__trans,axiom,
% 6.92/7.12 ! [X: assn,Y: assn,Z3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X @ Y )
% 6.92/7.12 => ( ( ord_less_eq_assn @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_assn @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_le_trans
% 6.92/7.12 thf(fact_492_order__less__le__trans,axiom,
% 6.92/7.12 ! [X: set_int,Y: set_int,Z3: set_int] :
% 6.92/7.12 ( ( ord_less_set_int @ X @ Y )
% 6.92/7.12 => ( ( ord_less_eq_set_int @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_set_int @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_le_trans
% 6.92/7.12 thf(fact_493_order__less__le__trans,axiom,
% 6.92/7.12 ! [X: rat,Y: rat,Z3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X @ Y )
% 6.92/7.12 => ( ( ord_less_eq_rat @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_rat @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_le_trans
% 6.92/7.12 thf(fact_494_order__less__le__trans,axiom,
% 6.92/7.12 ! [X: num,Y: num,Z3: num] :
% 6.92/7.12 ( ( ord_less_num @ X @ Y )
% 6.92/7.12 => ( ( ord_less_eq_num @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_num @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_le_trans
% 6.92/7.12 thf(fact_495_order__less__le__trans,axiom,
% 6.92/7.12 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.12 ( ( ord_less_nat @ X @ Y )
% 6.92/7.12 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_le_trans
% 6.92/7.12 thf(fact_496_order__less__le__trans,axiom,
% 6.92/7.12 ! [X: int,Y: int,Z3: int] :
% 6.92/7.12 ( ( ord_less_int @ X @ Y )
% 6.92/7.12 => ( ( ord_less_eq_int @ Y @ Z3 )
% 6.92/7.12 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_less_le_trans
% 6.92/7.12 thf(fact_497_order__le__less__subst1,axiom,
% 6.92/7.12 ! [A: assn,F: assn > assn,B: assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_eq_assn @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_assn @ B @ C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst1
% 6.92/7.12 thf(fact_498_order__le__less__subst1,axiom,
% 6.92/7.12 ! [A: assn,F: rat > assn,B: rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_eq_assn @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_rat @ B @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst1
% 6.92/7.12 thf(fact_499_order__le__less__subst1,axiom,
% 6.92/7.12 ! [A: assn,F: num > assn,B: num,C2: num] :
% 6.92/7.12 ( ( ord_less_eq_assn @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_num @ B @ C2 )
% 6.92/7.12 => ( ! [X3: num,Y3: num] :
% 6.92/7.12 ( ( ord_less_num @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst1
% 6.92/7.12 thf(fact_500_order__le__less__subst1,axiom,
% 6.92/7.12 ! [A: assn,F: nat > assn,B: nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_eq_assn @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_nat @ B @ C2 )
% 6.92/7.12 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.12 ( ( ord_less_nat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst1
% 6.92/7.12 thf(fact_501_order__le__less__subst1,axiom,
% 6.92/7.12 ! [A: assn,F: int > assn,B: int,C2: int] :
% 6.92/7.12 ( ( ord_less_eq_assn @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_int @ B @ C2 )
% 6.92/7.12 => ( ! [X3: int,Y3: int] :
% 6.92/7.12 ( ( ord_less_int @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst1
% 6.92/7.12 thf(fact_502_order__le__less__subst1,axiom,
% 6.92/7.12 ! [A: rat,F: assn > rat,B: assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_assn @ B @ C2 )
% 6.92/7.12 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.12 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst1
% 6.92/7.12 thf(fact_503_order__le__less__subst1,axiom,
% 6.92/7.12 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_rat @ B @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst1
% 6.92/7.12 thf(fact_504_order__le__less__subst1,axiom,
% 6.92/7.12 ! [A: rat,F: num > rat,B: num,C2: num] :
% 6.92/7.12 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_num @ B @ C2 )
% 6.92/7.12 => ( ! [X3: num,Y3: num] :
% 6.92/7.12 ( ( ord_less_num @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst1
% 6.92/7.12 thf(fact_505_order__le__less__subst1,axiom,
% 6.92/7.12 ! [A: rat,F: nat > rat,B: nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_nat @ B @ C2 )
% 6.92/7.12 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.12 ( ( ord_less_nat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst1
% 6.92/7.12 thf(fact_506_order__le__less__subst1,axiom,
% 6.92/7.12 ! [A: rat,F: int > rat,B: int,C2: int] :
% 6.92/7.12 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 6.92/7.12 => ( ( ord_less_int @ B @ C2 )
% 6.92/7.12 => ( ! [X3: int,Y3: int] :
% 6.92/7.12 ( ( ord_less_int @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst1
% 6.92/7.12 thf(fact_507_order__le__less__subst2,axiom,
% 6.92/7.12 ! [A: rat,B: rat,F: rat > assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.12 => ( ( ord_less_assn @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_eq_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst2
% 6.92/7.12 thf(fact_508_order__le__less__subst2,axiom,
% 6.92/7.12 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.12 => ( ( ord_less_rat @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst2
% 6.92/7.12 thf(fact_509_order__le__less__subst2,axiom,
% 6.92/7.12 ! [A: rat,B: rat,F: rat > num,C2: num] :
% 6.92/7.12 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.12 => ( ( ord_less_num @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst2
% 6.92/7.12 thf(fact_510_order__le__less__subst2,axiom,
% 6.92/7.12 ! [A: rat,B: rat,F: rat > nat,C2: nat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.12 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst2
% 6.92/7.12 thf(fact_511_order__le__less__subst2,axiom,
% 6.92/7.12 ! [A: rat,B: rat,F: rat > int,C2: int] :
% 6.92/7.12 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.12 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.12 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst2
% 6.92/7.12 thf(fact_512_order__le__less__subst2,axiom,
% 6.92/7.12 ! [A: num,B: num,F: num > assn,C2: assn] :
% 6.92/7.12 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.12 => ( ( ord_less_assn @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: num,Y3: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_eq_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_assn @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst2
% 6.92/7.12 thf(fact_513_order__le__less__subst2,axiom,
% 6.92/7.12 ! [A: num,B: num,F: num > rat,C2: rat] :
% 6.92/7.12 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.12 => ( ( ord_less_rat @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: num,Y3: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.12 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % order_le_less_subst2
% 6.92/7.12 thf(fact_514_order__le__less__subst2,axiom,
% 6.92/7.12 ! [A: num,B: num,F: num > num,C2: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.12 => ( ( ord_less_num @ ( F @ B ) @ C2 )
% 6.92/7.12 => ( ! [X3: num,Y3: num] :
% 6.92/7.12 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.12 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_le_less_subst2
% 6.92/7.13 thf(fact_515_order__le__less__subst2,axiom,
% 6.92/7.13 ! [A: num,B: num,F: num > nat,C2: nat] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.13 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_le_less_subst2
% 6.92/7.13 thf(fact_516_order__le__less__subst2,axiom,
% 6.92/7.13 ! [A: num,B: num,F: num > int,C2: int] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.13 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_le_less_subst2
% 6.92/7.13 thf(fact_517_order__less__le__subst1,axiom,
% 6.92/7.13 ! [A: assn,F: rat > assn,B: rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_assn @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_assn @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst1
% 6.92/7.13 thf(fact_518_order__less__le__subst1,axiom,
% 6.92/7.13 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_rat @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst1
% 6.92/7.13 thf(fact_519_order__less__le__subst1,axiom,
% 6.92/7.13 ! [A: num,F: rat > num,B: rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_num @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst1
% 6.92/7.13 thf(fact_520_order__less__le__subst1,axiom,
% 6.92/7.13 ! [A: nat,F: rat > nat,B: rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_nat @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst1
% 6.92/7.13 thf(fact_521_order__less__le__subst1,axiom,
% 6.92/7.13 ! [A: int,F: rat > int,B: rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_int @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst1
% 6.92/7.13 thf(fact_522_order__less__le__subst1,axiom,
% 6.92/7.13 ! [A: assn,F: num > assn,B: num,C2: num] :
% 6.92/7.13 ( ( ord_less_assn @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_assn @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst1
% 6.92/7.13 thf(fact_523_order__less__le__subst1,axiom,
% 6.92/7.13 ! [A: rat,F: num > rat,B: num,C2: num] :
% 6.92/7.13 ( ( ord_less_rat @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst1
% 6.92/7.13 thf(fact_524_order__less__le__subst1,axiom,
% 6.92/7.13 ! [A: num,F: num > num,B: num,C2: num] :
% 6.92/7.13 ( ( ord_less_num @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst1
% 6.92/7.13 thf(fact_525_order__less__le__subst1,axiom,
% 6.92/7.13 ! [A: nat,F: num > nat,B: num,C2: num] :
% 6.92/7.13 ( ( ord_less_nat @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst1
% 6.92/7.13 thf(fact_526_order__less__le__subst1,axiom,
% 6.92/7.13 ! [A: int,F: num > int,B: num,C2: num] :
% 6.92/7.13 ( ( ord_less_int @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst1
% 6.92/7.13 thf(fact_527_order__less__le__subst2,axiom,
% 6.92/7.13 ! [A: assn,B: assn,F: assn > assn,C2: assn] :
% 6.92/7.13 ( ( ord_less_assn @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_assn @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.13 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_assn @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst2
% 6.92/7.13 thf(fact_528_order__less__le__subst2,axiom,
% 6.92/7.13 ! [A: rat,B: rat,F: rat > assn,C2: assn] :
% 6.92/7.13 ( ( ord_less_rat @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_assn @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_assn @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst2
% 6.92/7.13 thf(fact_529_order__less__le__subst2,axiom,
% 6.92/7.13 ! [A: num,B: num,F: num > assn,C2: assn] :
% 6.92/7.13 ( ( ord_less_num @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_assn @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_assn @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst2
% 6.92/7.13 thf(fact_530_order__less__le__subst2,axiom,
% 6.92/7.13 ! [A: nat,B: nat,F: nat > assn,C2: assn] :
% 6.92/7.13 ( ( ord_less_nat @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_assn @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.13 ( ( ord_less_nat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_assn @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst2
% 6.92/7.13 thf(fact_531_order__less__le__subst2,axiom,
% 6.92/7.13 ! [A: int,B: int,F: int > assn,C2: assn] :
% 6.92/7.13 ( ( ord_less_int @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_assn @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: int,Y3: int] :
% 6.92/7.13 ( ( ord_less_int @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_assn @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst2
% 6.92/7.13 thf(fact_532_order__less__le__subst2,axiom,
% 6.92/7.13 ! [A: assn,B: assn,F: assn > rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_assn @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: assn,Y3: assn] :
% 6.92/7.13 ( ( ord_less_assn @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst2
% 6.92/7.13 thf(fact_533_order__less__le__subst2,axiom,
% 6.92/7.13 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_rat @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst2
% 6.92/7.13 thf(fact_534_order__less__le__subst2,axiom,
% 6.92/7.13 ! [A: num,B: num,F: num > rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_num @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst2
% 6.92/7.13 thf(fact_535_order__less__le__subst2,axiom,
% 6.92/7.13 ! [A: nat,B: nat,F: nat > rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_nat @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.13 ( ( ord_less_nat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst2
% 6.92/7.13 thf(fact_536_order__less__le__subst2,axiom,
% 6.92/7.13 ! [A: int,B: int,F: int > rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_int @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: int,Y3: int] :
% 6.92/7.13 ( ( ord_less_int @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_less_le_subst2
% 6.92/7.13 thf(fact_537_linorder__le__less__linear,axiom,
% 6.92/7.13 ! [X: rat,Y: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.13 | ( ord_less_rat @ Y @ X ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_le_less_linear
% 6.92/7.13 thf(fact_538_linorder__le__less__linear,axiom,
% 6.92/7.13 ! [X: num,Y: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X @ Y )
% 6.92/7.13 | ( ord_less_num @ Y @ X ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_le_less_linear
% 6.92/7.13 thf(fact_539_linorder__le__less__linear,axiom,
% 6.92/7.13 ! [X: nat,Y: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ X @ Y )
% 6.92/7.13 | ( ord_less_nat @ Y @ X ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_le_less_linear
% 6.92/7.13 thf(fact_540_linorder__le__less__linear,axiom,
% 6.92/7.13 ! [X: int,Y: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.13 | ( ord_less_int @ Y @ X ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_le_less_linear
% 6.92/7.13 thf(fact_541_order__le__imp__less__or__eq,axiom,
% 6.92/7.13 ! [X: assn,Y: assn] :
% 6.92/7.13 ( ( ord_less_eq_assn @ X @ Y )
% 6.92/7.13 => ( ( ord_less_assn @ X @ Y )
% 6.92/7.13 | ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_le_imp_less_or_eq
% 6.92/7.13 thf(fact_542_order__le__imp__less__or__eq,axiom,
% 6.92/7.13 ! [X: set_int,Y: set_int] :
% 6.92/7.13 ( ( ord_less_eq_set_int @ X @ Y )
% 6.92/7.13 => ( ( ord_less_set_int @ X @ Y )
% 6.92/7.13 | ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_le_imp_less_or_eq
% 6.92/7.13 thf(fact_543_order__le__imp__less__or__eq,axiom,
% 6.92/7.13 ! [X: rat,Y: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.13 => ( ( ord_less_rat @ X @ Y )
% 6.92/7.13 | ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_le_imp_less_or_eq
% 6.92/7.13 thf(fact_544_order__le__imp__less__or__eq,axiom,
% 6.92/7.13 ! [X: num,Y: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X @ Y )
% 6.92/7.13 => ( ( ord_less_num @ X @ Y )
% 6.92/7.13 | ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_le_imp_less_or_eq
% 6.92/7.13 thf(fact_545_order__le__imp__less__or__eq,axiom,
% 6.92/7.13 ! [X: nat,Y: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ X @ Y )
% 6.92/7.13 => ( ( ord_less_nat @ X @ Y )
% 6.92/7.13 | ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_le_imp_less_or_eq
% 6.92/7.13 thf(fact_546_order__le__imp__less__or__eq,axiom,
% 6.92/7.13 ! [X: int,Y: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.13 => ( ( ord_less_int @ X @ Y )
% 6.92/7.13 | ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_le_imp_less_or_eq
% 6.92/7.13 thf(fact_547_exists__leI,axiom,
% 6.92/7.13 ! [N2: nat,P2: nat > $o] :
% 6.92/7.13 ( ( ! [N3: nat] :
% 6.92/7.13 ( ( ord_less_nat @ N3 @ N2 )
% 6.92/7.13 => ~ ( P2 @ N3 ) )
% 6.92/7.13 => ( P2 @ N2 ) )
% 6.92/7.13 => ? [N4: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ N4 @ N2 )
% 6.92/7.13 & ( P2 @ N4 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % exists_leI
% 6.92/7.13 thf(fact_548_mod__relH,axiom,
% 6.92/7.13 ! [As: set_nat,H: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,P2: assn] :
% 6.92/7.13 ( ( relH @ As @ H @ H5 )
% 6.92/7.13 => ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.13 = ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H5 @ As ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % mod_relH
% 6.92/7.13 thf(fact_549_hoare__triple__def,axiom,
% 6.92/7.13 ( hoare_hoare_triple_a
% 6.92/7.13 = ( ^ [P5: assn,C3: heap_Time_Heap_a,Q3: a > assn] :
% 6.92/7.13 ! [H6: heap_e7401611519738050253t_unit,As4: set_nat] :
% 6.92/7.13 ( ( rep_assn @ P5 @ ( produc7507926704131184380et_nat @ H6 @ As4 ) )
% 6.92/7.13 => ? [R5: a,H7: heap_e7401611519738050253t_unit] :
% 6.92/7.13 ( ? [T4: nat] :
% 6.92/7.13 ( ( heap_Time_execute_a @ C3 @ H6 )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R5 @ ( produc584006145561248582it_nat @ H7 @ T4 ) ) ) )
% 6.92/7.13 & ( rep_assn @ ( Q3 @ R5 ) @ ( produc7507926704131184380et_nat @ H7 @ ( hoare_new_addrs @ H6 @ As4 @ H7 ) ) )
% 6.92/7.13 & ( relH
% 6.92/7.13 @ ( collect_nat
% 6.92/7.13 @ ^ [A5: nat] :
% 6.92/7.13 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ H6 ) )
% 6.92/7.13 & ~ ( member_nat @ A5 @ As4 ) ) )
% 6.92/7.13 @ H6
% 6.92/7.13 @ H7 )
% 6.92/7.13 & ( ord_less_eq_nat @ ( lim_Product_unit @ H6 ) @ ( lim_Product_unit @ H7 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % hoare_triple_def
% 6.92/7.13 thf(fact_550_hoare__triple__def,axiom,
% 6.92/7.13 ( hoare_hoare_triple_b
% 6.92/7.13 = ( ^ [P5: assn,C3: heap_Time_Heap_b,Q3: b > assn] :
% 6.92/7.13 ! [H6: heap_e7401611519738050253t_unit,As4: set_nat] :
% 6.92/7.13 ( ( rep_assn @ P5 @ ( produc7507926704131184380et_nat @ H6 @ As4 ) )
% 6.92/7.13 => ? [R5: b,H7: heap_e7401611519738050253t_unit] :
% 6.92/7.13 ( ? [T4: nat] :
% 6.92/7.13 ( ( heap_Time_execute_b @ C3 @ H6 )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ R5 @ ( produc584006145561248582it_nat @ H7 @ T4 ) ) ) )
% 6.92/7.13 & ( rep_assn @ ( Q3 @ R5 ) @ ( produc7507926704131184380et_nat @ H7 @ ( hoare_new_addrs @ H6 @ As4 @ H7 ) ) )
% 6.92/7.13 & ( relH
% 6.92/7.13 @ ( collect_nat
% 6.92/7.13 @ ^ [A5: nat] :
% 6.92/7.13 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ H6 ) )
% 6.92/7.13 & ~ ( member_nat @ A5 @ As4 ) ) )
% 6.92/7.13 @ H6
% 6.92/7.13 @ H7 )
% 6.92/7.13 & ( ord_less_eq_nat @ ( lim_Product_unit @ H6 ) @ ( lim_Product_unit @ H7 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % hoare_triple_def
% 6.92/7.13 thf(fact_551_hoare__triple__def,axiom,
% 6.92/7.13 ( hoare_8945653483474564448t_unit
% 6.92/7.13 = ( ^ [P5: assn,C3: heap_T5738788834812785303t_unit,Q3: product_unit > assn] :
% 6.92/7.13 ! [H6: heap_e7401611519738050253t_unit,As4: set_nat] :
% 6.92/7.13 ( ( rep_assn @ P5 @ ( produc7507926704131184380et_nat @ H6 @ As4 ) )
% 6.92/7.13 => ? [R5: product_unit,H7: heap_e7401611519738050253t_unit] :
% 6.92/7.13 ( ? [T4: nat] :
% 6.92/7.13 ( ( heap_T875086893843062177t_unit @ C3 @ H6 )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R5 @ ( produc584006145561248582it_nat @ H7 @ T4 ) ) ) )
% 6.92/7.13 & ( rep_assn @ ( Q3 @ R5 ) @ ( produc7507926704131184380et_nat @ H7 @ ( hoare_new_addrs @ H6 @ As4 @ H7 ) ) )
% 6.92/7.13 & ( relH
% 6.92/7.13 @ ( collect_nat
% 6.92/7.13 @ ^ [A5: nat] :
% 6.92/7.13 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ H6 ) )
% 6.92/7.13 & ~ ( member_nat @ A5 @ As4 ) ) )
% 6.92/7.13 @ H6
% 6.92/7.13 @ H7 )
% 6.92/7.13 & ( ord_less_eq_nat @ ( lim_Product_unit @ H6 ) @ ( lim_Product_unit @ H7 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % hoare_triple_def
% 6.92/7.13 thf(fact_552_hoare__tripleI,axiom,
% 6.92/7.13 ! [P2: assn,C2: heap_Time_Heap_a,Q2: a > assn] :
% 6.92/7.13 ( ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.13 ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.13 => ? [R6: a,H8: heap_e7401611519738050253t_unit,T5: nat] :
% 6.92/7.13 ( ( ( heap_Time_execute_a @ C2 @ H2 )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R6 @ ( produc584006145561248582it_nat @ H8 @ T5 ) ) ) )
% 6.92/7.13 & ( rep_assn @ ( Q2 @ R6 ) @ ( produc7507926704131184380et_nat @ H8 @ ( hoare_new_addrs @ H2 @ As2 @ H8 ) ) )
% 6.92/7.13 & ( relH
% 6.92/7.13 @ ( collect_nat
% 6.92/7.13 @ ^ [A5: nat] :
% 6.92/7.13 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ H2 ) )
% 6.92/7.13 & ~ ( member_nat @ A5 @ As2 ) ) )
% 6.92/7.13 @ H2
% 6.92/7.13 @ H8 )
% 6.92/7.13 & ( ord_less_eq_nat @ ( lim_Product_unit @ H2 ) @ ( lim_Product_unit @ H8 ) ) ) )
% 6.92/7.13 => ( hoare_hoare_triple_a @ P2 @ C2 @ Q2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % hoare_tripleI
% 6.92/7.13 thf(fact_553_hoare__tripleI,axiom,
% 6.92/7.13 ! [P2: assn,C2: heap_Time_Heap_b,Q2: b > assn] :
% 6.92/7.13 ( ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.13 ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.13 => ? [R6: b,H8: heap_e7401611519738050253t_unit,T5: nat] :
% 6.92/7.13 ( ( ( heap_Time_execute_b @ C2 @ H2 )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ R6 @ ( produc584006145561248582it_nat @ H8 @ T5 ) ) ) )
% 6.92/7.13 & ( rep_assn @ ( Q2 @ R6 ) @ ( produc7507926704131184380et_nat @ H8 @ ( hoare_new_addrs @ H2 @ As2 @ H8 ) ) )
% 6.92/7.13 & ( relH
% 6.92/7.13 @ ( collect_nat
% 6.92/7.13 @ ^ [A5: nat] :
% 6.92/7.13 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ H2 ) )
% 6.92/7.13 & ~ ( member_nat @ A5 @ As2 ) ) )
% 6.92/7.13 @ H2
% 6.92/7.13 @ H8 )
% 6.92/7.13 & ( ord_less_eq_nat @ ( lim_Product_unit @ H2 ) @ ( lim_Product_unit @ H8 ) ) ) )
% 6.92/7.13 => ( hoare_hoare_triple_b @ P2 @ C2 @ Q2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % hoare_tripleI
% 6.92/7.13 thf(fact_554_hoare__tripleI,axiom,
% 6.92/7.13 ! [P2: assn,C2: heap_T5738788834812785303t_unit,Q2: product_unit > assn] :
% 6.92/7.13 ( ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.13 ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.13 => ? [R6: product_unit,H8: heap_e7401611519738050253t_unit,T5: nat] :
% 6.92/7.13 ( ( ( heap_T875086893843062177t_unit @ C2 @ H2 )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R6 @ ( produc584006145561248582it_nat @ H8 @ T5 ) ) ) )
% 6.92/7.13 & ( rep_assn @ ( Q2 @ R6 ) @ ( produc7507926704131184380et_nat @ H8 @ ( hoare_new_addrs @ H2 @ As2 @ H8 ) ) )
% 6.92/7.13 & ( relH
% 6.92/7.13 @ ( collect_nat
% 6.92/7.13 @ ^ [A5: nat] :
% 6.92/7.13 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ H2 ) )
% 6.92/7.13 & ~ ( member_nat @ A5 @ As2 ) ) )
% 6.92/7.13 @ H2
% 6.92/7.13 @ H8 )
% 6.92/7.13 & ( ord_less_eq_nat @ ( lim_Product_unit @ H2 ) @ ( lim_Product_unit @ H8 ) ) ) )
% 6.92/7.13 => ( hoare_8945653483474564448t_unit @ P2 @ C2 @ Q2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % hoare_tripleI
% 6.92/7.13 thf(fact_555_hoare__tripleE,axiom,
% 6.92/7.13 ! [P2: assn,C2: heap_Time_Heap_a,Q2: a > assn,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.13 ( ( hoare_hoare_triple_a @ P2 @ C2 @ Q2 )
% 6.92/7.13 => ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.13 => ~ ! [R4: a,H4: heap_e7401611519738050253t_unit] :
% 6.92/7.13 ( ? [T3: nat] :
% 6.92/7.13 ( ( heap_Time_execute_a @ C2 @ H )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R4 @ ( produc584006145561248582it_nat @ H4 @ T3 ) ) ) )
% 6.92/7.13 => ( ( rep_assn @ ( Q2 @ R4 ) @ ( produc7507926704131184380et_nat @ H4 @ ( hoare_new_addrs @ H @ As @ H4 ) ) )
% 6.92/7.13 => ( ( relH
% 6.92/7.13 @ ( collect_nat
% 6.92/7.13 @ ^ [A5: nat] :
% 6.92/7.13 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ H ) )
% 6.92/7.13 & ~ ( member_nat @ A5 @ As ) ) )
% 6.92/7.13 @ H
% 6.92/7.13 @ H4 )
% 6.92/7.13 => ~ ( ord_less_eq_nat @ ( lim_Product_unit @ H ) @ ( lim_Product_unit @ H4 ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % hoare_tripleE
% 6.92/7.13 thf(fact_556_hoare__tripleE,axiom,
% 6.92/7.13 ! [P2: assn,C2: heap_Time_Heap_b,Q2: b > assn,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.13 ( ( hoare_hoare_triple_b @ P2 @ C2 @ Q2 )
% 6.92/7.13 => ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.13 => ~ ! [R4: b,H4: heap_e7401611519738050253t_unit] :
% 6.92/7.13 ( ? [T3: nat] :
% 6.92/7.13 ( ( heap_Time_execute_b @ C2 @ H )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ R4 @ ( produc584006145561248582it_nat @ H4 @ T3 ) ) ) )
% 6.92/7.13 => ( ( rep_assn @ ( Q2 @ R4 ) @ ( produc7507926704131184380et_nat @ H4 @ ( hoare_new_addrs @ H @ As @ H4 ) ) )
% 6.92/7.13 => ( ( relH
% 6.92/7.13 @ ( collect_nat
% 6.92/7.13 @ ^ [A5: nat] :
% 6.92/7.13 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ H ) )
% 6.92/7.13 & ~ ( member_nat @ A5 @ As ) ) )
% 6.92/7.13 @ H
% 6.92/7.13 @ H4 )
% 6.92/7.13 => ~ ( ord_less_eq_nat @ ( lim_Product_unit @ H ) @ ( lim_Product_unit @ H4 ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % hoare_tripleE
% 6.92/7.13 thf(fact_557_hoare__tripleE,axiom,
% 6.92/7.13 ! [P2: assn,C2: heap_T5738788834812785303t_unit,Q2: product_unit > assn,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.13 ( ( hoare_8945653483474564448t_unit @ P2 @ C2 @ Q2 )
% 6.92/7.13 => ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.13 => ~ ! [R4: product_unit,H4: heap_e7401611519738050253t_unit] :
% 6.92/7.13 ( ? [T3: nat] :
% 6.92/7.13 ( ( heap_T875086893843062177t_unit @ C2 @ H )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R4 @ ( produc584006145561248582it_nat @ H4 @ T3 ) ) ) )
% 6.92/7.13 => ( ( rep_assn @ ( Q2 @ R4 ) @ ( produc7507926704131184380et_nat @ H4 @ ( hoare_new_addrs @ H @ As @ H4 ) ) )
% 6.92/7.13 => ( ( relH
% 6.92/7.13 @ ( collect_nat
% 6.92/7.13 @ ^ [A5: nat] :
% 6.92/7.13 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ H ) )
% 6.92/7.13 & ~ ( member_nat @ A5 @ As ) ) )
% 6.92/7.13 @ H
% 6.92/7.13 @ H4 )
% 6.92/7.13 => ~ ( ord_less_eq_nat @ ( lim_Product_unit @ H ) @ ( lim_Product_unit @ H4 ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % hoare_tripleE
% 6.92/7.13 thf(fact_558_successE,axiom,
% 6.92/7.13 ! [F: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 6.92/7.13 ( ( heap_T584514906347983379t_unit @ F @ H )
% 6.92/7.13 => ~ ! [R4: product_unit,H4: produc6653097349344004940it_nat] :
% 6.92/7.13 ( ( heap_T875086893843062177t_unit @ F @ H )
% 6.92/7.13 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R4 @ H4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % successE
% 6.92/7.13 thf(fact_559_successE,axiom,
% 6.92/7.13 ! [F: heap_Time_Heap_b,H: heap_e7401611519738050253t_unit] :
% 6.92/7.13 ( ( heap_Time_success_b @ F @ H )
% 6.92/7.13 => ~ ! [R4: b,H4: produc6653097349344004940it_nat] :
% 6.92/7.13 ( ( heap_Time_execute_b @ F @ H )
% 6.92/7.13 != ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ R4 @ H4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % successE
% 6.92/7.13 thf(fact_560_successE,axiom,
% 6.92/7.13 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit] :
% 6.92/7.13 ( ( heap_Time_success_a @ F @ H )
% 6.92/7.13 => ~ ! [R4: a,H4: produc6653097349344004940it_nat] :
% 6.92/7.13 ( ( heap_Time_execute_a @ F @ H )
% 6.92/7.13 != ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R4 @ H4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % successE
% 6.92/7.13 thf(fact_561_nle__le,axiom,
% 6.92/7.13 ! [A: rat,B: rat] :
% 6.92/7.13 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 6.92/7.13 = ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.13 & ( B != A ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % nle_le
% 6.92/7.13 thf(fact_562_nle__le,axiom,
% 6.92/7.13 ! [A: num,B: num] :
% 6.92/7.13 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 6.92/7.13 = ( ( ord_less_eq_num @ B @ A )
% 6.92/7.13 & ( B != A ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % nle_le
% 6.92/7.13 thf(fact_563_nle__le,axiom,
% 6.92/7.13 ! [A: nat,B: nat] :
% 6.92/7.13 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 6.92/7.13 = ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.13 & ( B != A ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % nle_le
% 6.92/7.13 thf(fact_564_nle__le,axiom,
% 6.92/7.13 ! [A: int,B: int] :
% 6.92/7.13 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 6.92/7.13 = ( ( ord_less_eq_int @ B @ A )
% 6.92/7.13 & ( B != A ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % nle_le
% 6.92/7.13 thf(fact_565_le__cases3,axiom,
% 6.92/7.13 ! [X: rat,Y: rat,Z3: rat] :
% 6.92/7.13 ( ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.13 => ~ ( ord_less_eq_rat @ Y @ Z3 ) )
% 6.92/7.13 => ( ( ( ord_less_eq_rat @ Y @ X )
% 6.92/7.13 => ~ ( ord_less_eq_rat @ X @ Z3 ) )
% 6.92/7.13 => ( ( ( ord_less_eq_rat @ X @ Z3 )
% 6.92/7.13 => ~ ( ord_less_eq_rat @ Z3 @ Y ) )
% 6.92/7.13 => ( ( ( ord_less_eq_rat @ Z3 @ Y )
% 6.92/7.13 => ~ ( ord_less_eq_rat @ Y @ X ) )
% 6.92/7.13 => ( ( ( ord_less_eq_rat @ Y @ Z3 )
% 6.92/7.13 => ~ ( ord_less_eq_rat @ Z3 @ X ) )
% 6.92/7.13 => ~ ( ( ord_less_eq_rat @ Z3 @ X )
% 6.92/7.13 => ~ ( ord_less_eq_rat @ X @ Y ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % le_cases3
% 6.92/7.13 thf(fact_566_le__cases3,axiom,
% 6.92/7.13 ! [X: num,Y: num,Z3: num] :
% 6.92/7.13 ( ( ( ord_less_eq_num @ X @ Y )
% 6.92/7.13 => ~ ( ord_less_eq_num @ Y @ Z3 ) )
% 6.92/7.13 => ( ( ( ord_less_eq_num @ Y @ X )
% 6.92/7.13 => ~ ( ord_less_eq_num @ X @ Z3 ) )
% 6.92/7.13 => ( ( ( ord_less_eq_num @ X @ Z3 )
% 6.92/7.13 => ~ ( ord_less_eq_num @ Z3 @ Y ) )
% 6.92/7.13 => ( ( ( ord_less_eq_num @ Z3 @ Y )
% 6.92/7.13 => ~ ( ord_less_eq_num @ Y @ X ) )
% 6.92/7.13 => ( ( ( ord_less_eq_num @ Y @ Z3 )
% 6.92/7.13 => ~ ( ord_less_eq_num @ Z3 @ X ) )
% 6.92/7.13 => ~ ( ( ord_less_eq_num @ Z3 @ X )
% 6.92/7.13 => ~ ( ord_less_eq_num @ X @ Y ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % le_cases3
% 6.92/7.13 thf(fact_567_le__cases3,axiom,
% 6.92/7.13 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.13 ( ( ( ord_less_eq_nat @ X @ Y )
% 6.92/7.13 => ~ ( ord_less_eq_nat @ Y @ Z3 ) )
% 6.92/7.13 => ( ( ( ord_less_eq_nat @ Y @ X )
% 6.92/7.13 => ~ ( ord_less_eq_nat @ X @ Z3 ) )
% 6.92/7.13 => ( ( ( ord_less_eq_nat @ X @ Z3 )
% 6.92/7.13 => ~ ( ord_less_eq_nat @ Z3 @ Y ) )
% 6.92/7.13 => ( ( ( ord_less_eq_nat @ Z3 @ Y )
% 6.92/7.13 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 6.92/7.13 => ( ( ( ord_less_eq_nat @ Y @ Z3 )
% 6.92/7.13 => ~ ( ord_less_eq_nat @ Z3 @ X ) )
% 6.92/7.13 => ~ ( ( ord_less_eq_nat @ Z3 @ X )
% 6.92/7.13 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % le_cases3
% 6.92/7.13 thf(fact_568_le__cases3,axiom,
% 6.92/7.13 ! [X: int,Y: int,Z3: int] :
% 6.92/7.13 ( ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.13 => ~ ( ord_less_eq_int @ Y @ Z3 ) )
% 6.92/7.13 => ( ( ( ord_less_eq_int @ Y @ X )
% 6.92/7.13 => ~ ( ord_less_eq_int @ X @ Z3 ) )
% 6.92/7.13 => ( ( ( ord_less_eq_int @ X @ Z3 )
% 6.92/7.13 => ~ ( ord_less_eq_int @ Z3 @ Y ) )
% 6.92/7.13 => ( ( ( ord_less_eq_int @ Z3 @ Y )
% 6.92/7.13 => ~ ( ord_less_eq_int @ Y @ X ) )
% 6.92/7.13 => ( ( ( ord_less_eq_int @ Y @ Z3 )
% 6.92/7.13 => ~ ( ord_less_eq_int @ Z3 @ X ) )
% 6.92/7.13 => ~ ( ( ord_less_eq_int @ Z3 @ X )
% 6.92/7.13 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % le_cases3
% 6.92/7.13 thf(fact_569_order__class_Oorder__eq__iff,axiom,
% 6.92/7.13 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 6.92/7.13 = ( ^ [X4: set_int,Y4: set_int] :
% 6.92/7.13 ( ( ord_less_eq_set_int @ X4 @ Y4 )
% 6.92/7.13 & ( ord_less_eq_set_int @ Y4 @ X4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_class.order_eq_iff
% 6.92/7.13 thf(fact_570_order__class_Oorder__eq__iff,axiom,
% 6.92/7.13 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 6.92/7.13 = ( ^ [X4: rat,Y4: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 6.92/7.13 & ( ord_less_eq_rat @ Y4 @ X4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_class.order_eq_iff
% 6.92/7.13 thf(fact_571_order__class_Oorder__eq__iff,axiom,
% 6.92/7.13 ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 6.92/7.13 = ( ^ [X4: num,Y4: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X4 @ Y4 )
% 6.92/7.13 & ( ord_less_eq_num @ Y4 @ X4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_class.order_eq_iff
% 6.92/7.13 thf(fact_572_order__class_Oorder__eq__iff,axiom,
% 6.92/7.13 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 6.92/7.13 = ( ^ [X4: nat,Y4: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 6.92/7.13 & ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_class.order_eq_iff
% 6.92/7.13 thf(fact_573_order__class_Oorder__eq__iff,axiom,
% 6.92/7.13 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 6.92/7.13 = ( ^ [X4: int,Y4: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ X4 @ Y4 )
% 6.92/7.13 & ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_class.order_eq_iff
% 6.92/7.13 thf(fact_574_ord__eq__le__trans,axiom,
% 6.92/7.13 ! [A: set_int,B: set_int,C2: set_int] :
% 6.92/7.13 ( ( A = B )
% 6.92/7.13 => ( ( ord_less_eq_set_int @ B @ C2 )
% 6.92/7.13 => ( ord_less_eq_set_int @ A @ C2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_eq_le_trans
% 6.92/7.13 thf(fact_575_ord__eq__le__trans,axiom,
% 6.92/7.13 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.13 ( ( A = B )
% 6.92/7.13 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.13 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_eq_le_trans
% 6.92/7.13 thf(fact_576_ord__eq__le__trans,axiom,
% 6.92/7.13 ! [A: num,B: num,C2: num] :
% 6.92/7.13 ( ( A = B )
% 6.92/7.13 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.13 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_eq_le_trans
% 6.92/7.13 thf(fact_577_ord__eq__le__trans,axiom,
% 6.92/7.13 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.13 ( ( A = B )
% 6.92/7.13 => ( ( ord_less_eq_nat @ B @ C2 )
% 6.92/7.13 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_eq_le_trans
% 6.92/7.13 thf(fact_578_ord__eq__le__trans,axiom,
% 6.92/7.13 ! [A: int,B: int,C2: int] :
% 6.92/7.13 ( ( A = B )
% 6.92/7.13 => ( ( ord_less_eq_int @ B @ C2 )
% 6.92/7.13 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_eq_le_trans
% 6.92/7.13 thf(fact_579_ord__le__eq__trans,axiom,
% 6.92/7.13 ! [A: set_int,B: set_int,C2: set_int] :
% 6.92/7.13 ( ( ord_less_eq_set_int @ A @ B )
% 6.92/7.13 => ( ( B = C2 )
% 6.92/7.13 => ( ord_less_eq_set_int @ A @ C2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_le_eq_trans
% 6.92/7.13 thf(fact_580_ord__le__eq__trans,axiom,
% 6.92/7.13 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.13 => ( ( B = C2 )
% 6.92/7.13 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_le_eq_trans
% 6.92/7.13 thf(fact_581_ord__le__eq__trans,axiom,
% 6.92/7.13 ! [A: num,B: num,C2: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.13 => ( ( B = C2 )
% 6.92/7.13 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_le_eq_trans
% 6.92/7.13 thf(fact_582_ord__le__eq__trans,axiom,
% 6.92/7.13 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.13 => ( ( B = C2 )
% 6.92/7.13 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_le_eq_trans
% 6.92/7.13 thf(fact_583_ord__le__eq__trans,axiom,
% 6.92/7.13 ! [A: int,B: int,C2: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.13 => ( ( B = C2 )
% 6.92/7.13 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_le_eq_trans
% 6.92/7.13 thf(fact_584_order__antisym,axiom,
% 6.92/7.13 ! [X: set_int,Y: set_int] :
% 6.92/7.13 ( ( ord_less_eq_set_int @ X @ Y )
% 6.92/7.13 => ( ( ord_less_eq_set_int @ Y @ X )
% 6.92/7.13 => ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_antisym
% 6.92/7.13 thf(fact_585_order__antisym,axiom,
% 6.92/7.13 ! [X: rat,Y: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.13 => ( ( ord_less_eq_rat @ Y @ X )
% 6.92/7.13 => ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_antisym
% 6.92/7.13 thf(fact_586_order__antisym,axiom,
% 6.92/7.13 ! [X: num,Y: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X @ Y )
% 6.92/7.13 => ( ( ord_less_eq_num @ Y @ X )
% 6.92/7.13 => ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_antisym
% 6.92/7.13 thf(fact_587_order__antisym,axiom,
% 6.92/7.13 ! [X: nat,Y: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ X @ Y )
% 6.92/7.13 => ( ( ord_less_eq_nat @ Y @ X )
% 6.92/7.13 => ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_antisym
% 6.92/7.13 thf(fact_588_order__antisym,axiom,
% 6.92/7.13 ! [X: int,Y: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.13 => ( ( ord_less_eq_int @ Y @ X )
% 6.92/7.13 => ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_antisym
% 6.92/7.13 thf(fact_589_order_Otrans,axiom,
% 6.92/7.13 ! [A: set_int,B: set_int,C2: set_int] :
% 6.92/7.13 ( ( ord_less_eq_set_int @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_set_int @ B @ C2 )
% 6.92/7.13 => ( ord_less_eq_set_int @ A @ C2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order.trans
% 6.92/7.13 thf(fact_590_order_Otrans,axiom,
% 6.92/7.13 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.13 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order.trans
% 6.92/7.13 thf(fact_591_order_Otrans,axiom,
% 6.92/7.13 ! [A: num,B: num,C2: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.13 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order.trans
% 6.92/7.13 thf(fact_592_order_Otrans,axiom,
% 6.92/7.13 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_nat @ B @ C2 )
% 6.92/7.13 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order.trans
% 6.92/7.13 thf(fact_593_order_Otrans,axiom,
% 6.92/7.13 ! [A: int,B: int,C2: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_int @ B @ C2 )
% 6.92/7.13 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order.trans
% 6.92/7.13 thf(fact_594_order__trans,axiom,
% 6.92/7.13 ! [X: set_int,Y: set_int,Z3: set_int] :
% 6.92/7.13 ( ( ord_less_eq_set_int @ X @ Y )
% 6.92/7.13 => ( ( ord_less_eq_set_int @ Y @ Z3 )
% 6.92/7.13 => ( ord_less_eq_set_int @ X @ Z3 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_trans
% 6.92/7.13 thf(fact_595_order__trans,axiom,
% 6.92/7.13 ! [X: rat,Y: rat,Z3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.13 => ( ( ord_less_eq_rat @ Y @ Z3 )
% 6.92/7.13 => ( ord_less_eq_rat @ X @ Z3 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_trans
% 6.92/7.13 thf(fact_596_order__trans,axiom,
% 6.92/7.13 ! [X: num,Y: num,Z3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X @ Y )
% 6.92/7.13 => ( ( ord_less_eq_num @ Y @ Z3 )
% 6.92/7.13 => ( ord_less_eq_num @ X @ Z3 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_trans
% 6.92/7.13 thf(fact_597_order__trans,axiom,
% 6.92/7.13 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ X @ Y )
% 6.92/7.13 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 6.92/7.13 => ( ord_less_eq_nat @ X @ Z3 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_trans
% 6.92/7.13 thf(fact_598_order__trans,axiom,
% 6.92/7.13 ! [X: int,Y: int,Z3: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.13 => ( ( ord_less_eq_int @ Y @ Z3 )
% 6.92/7.13 => ( ord_less_eq_int @ X @ Z3 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_trans
% 6.92/7.13 thf(fact_599_linorder__wlog,axiom,
% 6.92/7.13 ! [P2: rat > rat > $o,A: rat,B: rat] :
% 6.92/7.13 ( ! [A3: rat,B3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A3 @ B3 )
% 6.92/7.13 => ( P2 @ A3 @ B3 ) )
% 6.92/7.13 => ( ! [A3: rat,B3: rat] :
% 6.92/7.13 ( ( P2 @ B3 @ A3 )
% 6.92/7.13 => ( P2 @ A3 @ B3 ) )
% 6.92/7.13 => ( P2 @ A @ B ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_wlog
% 6.92/7.13 thf(fact_600_linorder__wlog,axiom,
% 6.92/7.13 ! [P2: num > num > $o,A: num,B: num] :
% 6.92/7.13 ( ! [A3: num,B3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ A3 @ B3 )
% 6.92/7.13 => ( P2 @ A3 @ B3 ) )
% 6.92/7.13 => ( ! [A3: num,B3: num] :
% 6.92/7.13 ( ( P2 @ B3 @ A3 )
% 6.92/7.13 => ( P2 @ A3 @ B3 ) )
% 6.92/7.13 => ( P2 @ A @ B ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_wlog
% 6.92/7.13 thf(fact_601_linorder__wlog,axiom,
% 6.92/7.13 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 6.92/7.13 ( ! [A3: nat,B3: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ A3 @ B3 )
% 6.92/7.13 => ( P2 @ A3 @ B3 ) )
% 6.92/7.13 => ( ! [A3: nat,B3: nat] :
% 6.92/7.13 ( ( P2 @ B3 @ A3 )
% 6.92/7.13 => ( P2 @ A3 @ B3 ) )
% 6.92/7.13 => ( P2 @ A @ B ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_wlog
% 6.92/7.13 thf(fact_602_linorder__wlog,axiom,
% 6.92/7.13 ! [P2: int > int > $o,A: int,B: int] :
% 6.92/7.13 ( ! [A3: int,B3: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ A3 @ B3 )
% 6.92/7.13 => ( P2 @ A3 @ B3 ) )
% 6.92/7.13 => ( ! [A3: int,B3: int] :
% 6.92/7.13 ( ( P2 @ B3 @ A3 )
% 6.92/7.13 => ( P2 @ A3 @ B3 ) )
% 6.92/7.13 => ( P2 @ A @ B ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_wlog
% 6.92/7.13 thf(fact_603_dual__order_Oeq__iff,axiom,
% 6.92/7.13 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 6.92/7.13 = ( ^ [A5: set_int,B4: set_int] :
% 6.92/7.13 ( ( ord_less_eq_set_int @ B4 @ A5 )
% 6.92/7.13 & ( ord_less_eq_set_int @ A5 @ B4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % dual_order.eq_iff
% 6.92/7.13 thf(fact_604_dual__order_Oeq__iff,axiom,
% 6.92/7.13 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 6.92/7.13 = ( ^ [A5: rat,B4: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ B4 @ A5 )
% 6.92/7.13 & ( ord_less_eq_rat @ A5 @ B4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % dual_order.eq_iff
% 6.92/7.13 thf(fact_605_dual__order_Oeq__iff,axiom,
% 6.92/7.13 ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 6.92/7.13 = ( ^ [A5: num,B4: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ B4 @ A5 )
% 6.92/7.13 & ( ord_less_eq_num @ A5 @ B4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % dual_order.eq_iff
% 6.92/7.13 thf(fact_606_dual__order_Oeq__iff,axiom,
% 6.92/7.13 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 6.92/7.13 = ( ^ [A5: nat,B4: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ B4 @ A5 )
% 6.92/7.13 & ( ord_less_eq_nat @ A5 @ B4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % dual_order.eq_iff
% 6.92/7.13 thf(fact_607_dual__order_Oeq__iff,axiom,
% 6.92/7.13 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 6.92/7.13 = ( ^ [A5: int,B4: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ B4 @ A5 )
% 6.92/7.13 & ( ord_less_eq_int @ A5 @ B4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % dual_order.eq_iff
% 6.92/7.13 thf(fact_608_dual__order_Oantisym,axiom,
% 6.92/7.13 ! [B: set_int,A: set_int] :
% 6.92/7.13 ( ( ord_less_eq_set_int @ B @ A )
% 6.92/7.13 => ( ( ord_less_eq_set_int @ A @ B )
% 6.92/7.13 => ( A = B ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % dual_order.antisym
% 6.92/7.13 thf(fact_609_dual__order_Oantisym,axiom,
% 6.92/7.13 ! [B: rat,A: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.13 => ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.13 => ( A = B ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % dual_order.antisym
% 6.92/7.13 thf(fact_610_dual__order_Oantisym,axiom,
% 6.92/7.13 ! [B: num,A: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ B @ A )
% 6.92/7.13 => ( ( ord_less_eq_num @ A @ B )
% 6.92/7.13 => ( A = B ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % dual_order.antisym
% 6.92/7.13 thf(fact_611_dual__order_Oantisym,axiom,
% 6.92/7.13 ! [B: nat,A: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.13 => ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.13 => ( A = B ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % dual_order.antisym
% 6.92/7.13 thf(fact_612_dual__order_Oantisym,axiom,
% 6.92/7.13 ! [B: int,A: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ B @ A )
% 6.92/7.13 => ( ( ord_less_eq_int @ A @ B )
% 6.92/7.13 => ( A = B ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % dual_order.antisym
% 6.92/7.13 thf(fact_613_dual__order_Otrans,axiom,
% 6.92/7.13 ! [B: set_int,A: set_int,C2: set_int] :
% 6.92/7.13 ( ( ord_less_eq_set_int @ B @ A )
% 6.92/7.13 => ( ( ord_less_eq_set_int @ C2 @ B )
% 6.92/7.13 => ( ord_less_eq_set_int @ C2 @ A ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % dual_order.trans
% 6.92/7.13 thf(fact_614_dual__order_Otrans,axiom,
% 6.92/7.13 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.13 => ( ( ord_less_eq_rat @ C2 @ B )
% 6.92/7.13 => ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % dual_order.trans
% 6.92/7.13 thf(fact_615_dual__order_Otrans,axiom,
% 6.92/7.13 ! [B: num,A: num,C2: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ B @ A )
% 6.92/7.13 => ( ( ord_less_eq_num @ C2 @ B )
% 6.92/7.13 => ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % dual_order.trans
% 6.92/7.13 thf(fact_616_dual__order_Otrans,axiom,
% 6.92/7.13 ! [B: nat,A: nat,C2: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.13 => ( ( ord_less_eq_nat @ C2 @ B )
% 6.92/7.13 => ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % dual_order.trans
% 6.92/7.13 thf(fact_617_dual__order_Otrans,axiom,
% 6.92/7.13 ! [B: int,A: int,C2: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ B @ A )
% 6.92/7.13 => ( ( ord_less_eq_int @ C2 @ B )
% 6.92/7.13 => ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % dual_order.trans
% 6.92/7.13 thf(fact_618_antisym,axiom,
% 6.92/7.13 ! [A: set_int,B: set_int] :
% 6.92/7.13 ( ( ord_less_eq_set_int @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_set_int @ B @ A )
% 6.92/7.13 => ( A = B ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % antisym
% 6.92/7.13 thf(fact_619_antisym,axiom,
% 6.92/7.13 ! [A: rat,B: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.13 => ( A = B ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % antisym
% 6.92/7.13 thf(fact_620_antisym,axiom,
% 6.92/7.13 ! [A: num,B: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_num @ B @ A )
% 6.92/7.13 => ( A = B ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % antisym
% 6.92/7.13 thf(fact_621_antisym,axiom,
% 6.92/7.13 ! [A: nat,B: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.13 => ( A = B ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % antisym
% 6.92/7.13 thf(fact_622_antisym,axiom,
% 6.92/7.13 ! [A: int,B: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_int @ B @ A )
% 6.92/7.13 => ( A = B ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % antisym
% 6.92/7.13 thf(fact_623_Orderings_Oorder__eq__iff,axiom,
% 6.92/7.13 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 6.92/7.13 = ( ^ [A5: set_int,B4: set_int] :
% 6.92/7.13 ( ( ord_less_eq_set_int @ A5 @ B4 )
% 6.92/7.13 & ( ord_less_eq_set_int @ B4 @ A5 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % Orderings.order_eq_iff
% 6.92/7.13 thf(fact_624_Orderings_Oorder__eq__iff,axiom,
% 6.92/7.13 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 6.92/7.13 = ( ^ [A5: rat,B4: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A5 @ B4 )
% 6.92/7.13 & ( ord_less_eq_rat @ B4 @ A5 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % Orderings.order_eq_iff
% 6.92/7.13 thf(fact_625_Orderings_Oorder__eq__iff,axiom,
% 6.92/7.13 ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 6.92/7.13 = ( ^ [A5: num,B4: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ A5 @ B4 )
% 6.92/7.13 & ( ord_less_eq_num @ B4 @ A5 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % Orderings.order_eq_iff
% 6.92/7.13 thf(fact_626_Orderings_Oorder__eq__iff,axiom,
% 6.92/7.13 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 6.92/7.13 = ( ^ [A5: nat,B4: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ A5 @ B4 )
% 6.92/7.13 & ( ord_less_eq_nat @ B4 @ A5 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % Orderings.order_eq_iff
% 6.92/7.13 thf(fact_627_Orderings_Oorder__eq__iff,axiom,
% 6.92/7.13 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 6.92/7.13 = ( ^ [A5: int,B4: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ A5 @ B4 )
% 6.92/7.13 & ( ord_less_eq_int @ B4 @ A5 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % Orderings.order_eq_iff
% 6.92/7.13 thf(fact_628_order__subst1,axiom,
% 6.92/7.13 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst1
% 6.92/7.13 thf(fact_629_order__subst1,axiom,
% 6.92/7.13 ! [A: rat,F: num > rat,B: num,C2: num] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst1
% 6.92/7.13 thf(fact_630_order__subst1,axiom,
% 6.92/7.13 ! [A: rat,F: nat > rat,B: nat,C2: nat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_nat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst1
% 6.92/7.13 thf(fact_631_order__subst1,axiom,
% 6.92/7.13 ! [A: rat,F: int > rat,B: int,C2: int] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_int @ B @ C2 )
% 6.92/7.13 => ( ! [X3: int,Y3: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst1
% 6.92/7.13 thf(fact_632_order__subst1,axiom,
% 6.92/7.13 ! [A: num,F: rat > num,B: rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst1
% 6.92/7.13 thf(fact_633_order__subst1,axiom,
% 6.92/7.13 ! [A: num,F: num > num,B: num,C2: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst1
% 6.92/7.13 thf(fact_634_order__subst1,axiom,
% 6.92/7.13 ! [A: num,F: nat > num,B: nat,C2: nat] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_nat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst1
% 6.92/7.13 thf(fact_635_order__subst1,axiom,
% 6.92/7.13 ! [A: num,F: int > num,B: int,C2: int] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_int @ B @ C2 )
% 6.92/7.13 => ( ! [X3: int,Y3: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst1
% 6.92/7.13 thf(fact_636_order__subst1,axiom,
% 6.92/7.13 ! [A: nat,F: rat > nat,B: rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst1
% 6.92/7.13 thf(fact_637_order__subst1,axiom,
% 6.92/7.13 ! [A: nat,F: num > nat,B: num,C2: num] :
% 6.92/7.13 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst1
% 6.92/7.13 thf(fact_638_order__subst2,axiom,
% 6.92/7.13 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst2
% 6.92/7.13 thf(fact_639_order__subst2,axiom,
% 6.92/7.13 ! [A: rat,B: rat,F: rat > num,C2: num] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_num @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst2
% 6.92/7.13 thf(fact_640_order__subst2,axiom,
% 6.92/7.13 ! [A: rat,B: rat,F: rat > nat,C2: nat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst2
% 6.92/7.13 thf(fact_641_order__subst2,axiom,
% 6.92/7.13 ! [A: rat,B: rat,F: rat > int,C2: int] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst2
% 6.92/7.13 thf(fact_642_order__subst2,axiom,
% 6.92/7.13 ! [A: num,B: num,F: num > rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst2
% 6.92/7.13 thf(fact_643_order__subst2,axiom,
% 6.92/7.13 ! [A: num,B: num,F: num > num,C2: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_num @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst2
% 6.92/7.13 thf(fact_644_order__subst2,axiom,
% 6.92/7.13 ! [A: num,B: num,F: num > nat,C2: nat] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst2
% 6.92/7.13 thf(fact_645_order__subst2,axiom,
% 6.92/7.13 ! [A: num,B: num,F: num > int,C2: int] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst2
% 6.92/7.13 thf(fact_646_order__subst2,axiom,
% 6.92/7.13 ! [A: nat,B: nat,F: nat > rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst2
% 6.92/7.13 thf(fact_647_order__subst2,axiom,
% 6.92/7.13 ! [A: nat,B: nat,F: nat > num,C2: num] :
% 6.92/7.13 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.13 => ( ( ord_less_eq_num @ ( F @ B ) @ C2 )
% 6.92/7.13 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_subst2
% 6.92/7.13 thf(fact_648_order__eq__refl,axiom,
% 6.92/7.13 ! [X: set_int,Y: set_int] :
% 6.92/7.13 ( ( X = Y )
% 6.92/7.13 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_eq_refl
% 6.92/7.13 thf(fact_649_order__eq__refl,axiom,
% 6.92/7.13 ! [X: rat,Y: rat] :
% 6.92/7.13 ( ( X = Y )
% 6.92/7.13 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_eq_refl
% 6.92/7.13 thf(fact_650_order__eq__refl,axiom,
% 6.92/7.13 ! [X: num,Y: num] :
% 6.92/7.13 ( ( X = Y )
% 6.92/7.13 => ( ord_less_eq_num @ X @ Y ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_eq_refl
% 6.92/7.13 thf(fact_651_order__eq__refl,axiom,
% 6.92/7.13 ! [X: nat,Y: nat] :
% 6.92/7.13 ( ( X = Y )
% 6.92/7.13 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_eq_refl
% 6.92/7.13 thf(fact_652_order__eq__refl,axiom,
% 6.92/7.13 ! [X: int,Y: int] :
% 6.92/7.13 ( ( X = Y )
% 6.92/7.13 => ( ord_less_eq_int @ X @ Y ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_eq_refl
% 6.92/7.13 thf(fact_653_linorder__linear,axiom,
% 6.92/7.13 ! [X: rat,Y: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.13 | ( ord_less_eq_rat @ Y @ X ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_linear
% 6.92/7.13 thf(fact_654_linorder__linear,axiom,
% 6.92/7.13 ! [X: num,Y: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X @ Y )
% 6.92/7.13 | ( ord_less_eq_num @ Y @ X ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_linear
% 6.92/7.13 thf(fact_655_linorder__linear,axiom,
% 6.92/7.13 ! [X: nat,Y: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ X @ Y )
% 6.92/7.13 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_linear
% 6.92/7.13 thf(fact_656_linorder__linear,axiom,
% 6.92/7.13 ! [X: int,Y: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.13 | ( ord_less_eq_int @ Y @ X ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_linear
% 6.92/7.13 thf(fact_657_ord__eq__le__subst,axiom,
% 6.92/7.13 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 6.92/7.13 ( ( A
% 6.92/7.13 = ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_eq_le_subst
% 6.92/7.13 thf(fact_658_ord__eq__le__subst,axiom,
% 6.92/7.13 ! [A: num,F: rat > num,B: rat,C2: rat] :
% 6.92/7.13 ( ( A
% 6.92/7.13 = ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_eq_le_subst
% 6.92/7.13 thf(fact_659_ord__eq__le__subst,axiom,
% 6.92/7.13 ! [A: nat,F: rat > nat,B: rat,C2: rat] :
% 6.92/7.13 ( ( A
% 6.92/7.13 = ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_eq_le_subst
% 6.92/7.13 thf(fact_660_ord__eq__le__subst,axiom,
% 6.92/7.13 ! [A: int,F: rat > int,B: rat,C2: rat] :
% 6.92/7.13 ( ( A
% 6.92/7.13 = ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_eq_le_subst
% 6.92/7.13 thf(fact_661_ord__eq__le__subst,axiom,
% 6.92/7.13 ! [A: rat,F: num > rat,B: num,C2: num] :
% 6.92/7.13 ( ( A
% 6.92/7.13 = ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_eq_le_subst
% 6.92/7.13 thf(fact_662_ord__eq__le__subst,axiom,
% 6.92/7.13 ! [A: num,F: num > num,B: num,C2: num] :
% 6.92/7.13 ( ( A
% 6.92/7.13 = ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_eq_le_subst
% 6.92/7.13 thf(fact_663_ord__eq__le__subst,axiom,
% 6.92/7.13 ! [A: nat,F: num > nat,B: num,C2: num] :
% 6.92/7.13 ( ( A
% 6.92/7.13 = ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_eq_le_subst
% 6.92/7.13 thf(fact_664_ord__eq__le__subst,axiom,
% 6.92/7.13 ! [A: int,F: num > int,B: num,C2: num] :
% 6.92/7.13 ( ( A
% 6.92/7.13 = ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_eq_le_subst
% 6.92/7.13 thf(fact_665_ord__eq__le__subst,axiom,
% 6.92/7.13 ! [A: rat,F: nat > rat,B: nat,C2: nat] :
% 6.92/7.13 ( ( A
% 6.92/7.13 = ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_nat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_eq_le_subst
% 6.92/7.13 thf(fact_666_ord__eq__le__subst,axiom,
% 6.92/7.13 ! [A: num,F: nat > num,B: nat,C2: nat] :
% 6.92/7.13 ( ( A
% 6.92/7.13 = ( F @ B ) )
% 6.92/7.13 => ( ( ord_less_eq_nat @ B @ C2 )
% 6.92/7.13 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_eq_le_subst
% 6.92/7.13 thf(fact_667_ord__le__eq__subst,axiom,
% 6.92/7.13 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.13 => ( ( ( F @ B )
% 6.92/7.13 = C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_le_eq_subst
% 6.92/7.13 thf(fact_668_ord__le__eq__subst,axiom,
% 6.92/7.13 ! [A: rat,B: rat,F: rat > num,C2: num] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.13 => ( ( ( F @ B )
% 6.92/7.13 = C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_le_eq_subst
% 6.92/7.13 thf(fact_669_ord__le__eq__subst,axiom,
% 6.92/7.13 ! [A: rat,B: rat,F: rat > nat,C2: nat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.13 => ( ( ( F @ B )
% 6.92/7.13 = C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_le_eq_subst
% 6.92/7.13 thf(fact_670_ord__le__eq__subst,axiom,
% 6.92/7.13 ! [A: rat,B: rat,F: rat > int,C2: int] :
% 6.92/7.13 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.13 => ( ( ( F @ B )
% 6.92/7.13 = C2 )
% 6.92/7.13 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_le_eq_subst
% 6.92/7.13 thf(fact_671_ord__le__eq__subst,axiom,
% 6.92/7.13 ! [A: num,B: num,F: num > rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.13 => ( ( ( F @ B )
% 6.92/7.13 = C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_le_eq_subst
% 6.92/7.13 thf(fact_672_ord__le__eq__subst,axiom,
% 6.92/7.13 ! [A: num,B: num,F: num > num,C2: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.13 => ( ( ( F @ B )
% 6.92/7.13 = C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_le_eq_subst
% 6.92/7.13 thf(fact_673_ord__le__eq__subst,axiom,
% 6.92/7.13 ! [A: num,B: num,F: num > nat,C2: nat] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.13 => ( ( ( F @ B )
% 6.92/7.13 = C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_le_eq_subst
% 6.92/7.13 thf(fact_674_ord__le__eq__subst,axiom,
% 6.92/7.13 ! [A: num,B: num,F: num > int,C2: int] :
% 6.92/7.13 ( ( ord_less_eq_num @ A @ B )
% 6.92/7.13 => ( ( ( F @ B )
% 6.92/7.13 = C2 )
% 6.92/7.13 => ( ! [X3: num,Y3: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_le_eq_subst
% 6.92/7.13 thf(fact_675_ord__le__eq__subst,axiom,
% 6.92/7.13 ! [A: nat,B: nat,F: nat > rat,C2: rat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.13 => ( ( ( F @ B )
% 6.92/7.13 = C2 )
% 6.92/7.13 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_le_eq_subst
% 6.92/7.13 thf(fact_676_ord__le__eq__subst,axiom,
% 6.92/7.13 ! [A: nat,B: nat,F: nat > num,C2: num] :
% 6.92/7.13 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.13 => ( ( ( F @ B )
% 6.92/7.13 = C2 )
% 6.92/7.13 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 6.92/7.13 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % ord_le_eq_subst
% 6.92/7.13 thf(fact_677_linorder__le__cases,axiom,
% 6.92/7.13 ! [X: rat,Y: rat] :
% 6.92/7.13 ( ~ ( ord_less_eq_rat @ X @ Y )
% 6.92/7.13 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_le_cases
% 6.92/7.13 thf(fact_678_linorder__le__cases,axiom,
% 6.92/7.13 ! [X: num,Y: num] :
% 6.92/7.13 ( ~ ( ord_less_eq_num @ X @ Y )
% 6.92/7.13 => ( ord_less_eq_num @ Y @ X ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_le_cases
% 6.92/7.13 thf(fact_679_linorder__le__cases,axiom,
% 6.92/7.13 ! [X: nat,Y: nat] :
% 6.92/7.13 ( ~ ( ord_less_eq_nat @ X @ Y )
% 6.92/7.13 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_le_cases
% 6.92/7.13 thf(fact_680_linorder__le__cases,axiom,
% 6.92/7.13 ! [X: int,Y: int] :
% 6.92/7.13 ( ~ ( ord_less_eq_int @ X @ Y )
% 6.92/7.13 => ( ord_less_eq_int @ Y @ X ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_le_cases
% 6.92/7.13 thf(fact_681_order__antisym__conv,axiom,
% 6.92/7.13 ! [Y: set_int,X: set_int] :
% 6.92/7.13 ( ( ord_less_eq_set_int @ Y @ X )
% 6.92/7.13 => ( ( ord_less_eq_set_int @ X @ Y )
% 6.92/7.13 = ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_antisym_conv
% 6.92/7.13 thf(fact_682_order__antisym__conv,axiom,
% 6.92/7.13 ! [Y: rat,X: rat] :
% 6.92/7.13 ( ( ord_less_eq_rat @ Y @ X )
% 6.92/7.13 => ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.13 = ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_antisym_conv
% 6.92/7.13 thf(fact_683_order__antisym__conv,axiom,
% 6.92/7.13 ! [Y: num,X: num] :
% 6.92/7.13 ( ( ord_less_eq_num @ Y @ X )
% 6.92/7.13 => ( ( ord_less_eq_num @ X @ Y )
% 6.92/7.13 = ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_antisym_conv
% 6.92/7.13 thf(fact_684_order__antisym__conv,axiom,
% 6.92/7.13 ! [Y: nat,X: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ Y @ X )
% 6.92/7.13 => ( ( ord_less_eq_nat @ X @ Y )
% 6.92/7.13 = ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_antisym_conv
% 6.92/7.13 thf(fact_685_order__antisym__conv,axiom,
% 6.92/7.13 ! [Y: int,X: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ Y @ X )
% 6.92/7.13 => ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.13 = ( X = Y ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % order_antisym_conv
% 6.92/7.13 thf(fact_686_effect__def,axiom,
% 6.92/7.13 ( heap_T6553295506729943825t_unit
% 6.92/7.13 = ( ^ [C3: heap_T5738788834812785303t_unit,H6: heap_e7401611519738050253t_unit,H7: heap_e7401611519738050253t_unit,R5: product_unit,N: nat] :
% 6.92/7.13 ( ( heap_T875086893843062177t_unit @ C3 @ H6 )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R5 @ ( produc584006145561248582it_nat @ H7 @ N ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % effect_def
% 6.92/7.13 thf(fact_687_effect__def,axiom,
% 6.92/7.13 ( heap_Time_effect_b
% 6.92/7.13 = ( ^ [C3: heap_Time_Heap_b,H6: heap_e7401611519738050253t_unit,H7: heap_e7401611519738050253t_unit,R5: b,N: nat] :
% 6.92/7.13 ( ( heap_Time_execute_b @ C3 @ H6 )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ R5 @ ( produc584006145561248582it_nat @ H7 @ N ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % effect_def
% 6.92/7.13 thf(fact_688_effect__def,axiom,
% 6.92/7.13 ( heap_Time_effect_a
% 6.92/7.13 = ( ^ [C3: heap_Time_Heap_a,H6: heap_e7401611519738050253t_unit,H7: heap_e7401611519738050253t_unit,R5: a,N: nat] :
% 6.92/7.13 ( ( heap_Time_execute_a @ C3 @ H6 )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R5 @ ( produc584006145561248582it_nat @ H7 @ N ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % effect_def
% 6.92/7.13 thf(fact_689_effectI,axiom,
% 6.92/7.13 ! [C2: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,R2: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat] :
% 6.92/7.13 ( ( ( heap_T875086893843062177t_unit @ C2 @ H )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( heap_T6553295506729943825t_unit @ C2 @ H @ H5 @ R2 @ N2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % effectI
% 6.92/7.13 thf(fact_690_effectI,axiom,
% 6.92/7.13 ! [C2: heap_Time_Heap_b,H: heap_e7401611519738050253t_unit,R2: b,H5: heap_e7401611519738050253t_unit,N2: nat] :
% 6.92/7.13 ( ( ( heap_Time_execute_b @ C2 @ H )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ R2 @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( heap_Time_effect_b @ C2 @ H @ H5 @ R2 @ N2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % effectI
% 6.92/7.13 thf(fact_691_effectI,axiom,
% 6.92/7.13 ! [C2: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,R2: a,H5: heap_e7401611519738050253t_unit,N2: nat] :
% 6.92/7.13 ( ( ( heap_Time_execute_a @ C2 @ H )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R2 @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( heap_Time_effect_a @ C2 @ H @ H5 @ R2 @ N2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % effectI
% 6.92/7.13 thf(fact_692_nat__less__le,axiom,
% 6.92/7.13 ( ord_less_nat
% 6.92/7.13 = ( ^ [M3: nat,N: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ M3 @ N )
% 6.92/7.13 & ( M3 != N ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % nat_less_le
% 6.92/7.13 thf(fact_693_less__imp__le__nat,axiom,
% 6.92/7.13 ! [M: nat,N2: nat] :
% 6.92/7.13 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.13 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % less_imp_le_nat
% 6.92/7.13 thf(fact_694_le__eq__less__or__eq,axiom,
% 6.92/7.13 ( ord_less_eq_nat
% 6.92/7.13 = ( ^ [M3: nat,N: nat] :
% 6.92/7.13 ( ( ord_less_nat @ M3 @ N )
% 6.92/7.13 | ( M3 = N ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % le_eq_less_or_eq
% 6.92/7.13 thf(fact_695_less__or__eq__imp__le,axiom,
% 6.92/7.13 ! [M: nat,N2: nat] :
% 6.92/7.13 ( ( ( ord_less_nat @ M @ N2 )
% 6.92/7.13 | ( M = N2 ) )
% 6.92/7.13 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % less_or_eq_imp_le
% 6.92/7.13 thf(fact_696_le__neq__implies__less,axiom,
% 6.92/7.13 ! [M: nat,N2: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.13 => ( ( M != N2 )
% 6.92/7.13 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % le_neq_implies_less
% 6.92/7.13 thf(fact_697_less__mono__imp__le__mono,axiom,
% 6.92/7.13 ! [F: nat > nat,I2: nat,J2: nat] :
% 6.92/7.13 ( ! [I3: nat,J3: nat] :
% 6.92/7.13 ( ( ord_less_nat @ I3 @ J3 )
% 6.92/7.13 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J3 ) ) )
% 6.92/7.13 => ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.13 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J2 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % less_mono_imp_le_mono
% 6.92/7.13 thf(fact_698_nat__descend__induct,axiom,
% 6.92/7.13 ! [N2: nat,P2: nat > $o,M: nat] :
% 6.92/7.13 ( ! [K: nat] :
% 6.92/7.13 ( ( ord_less_nat @ N2 @ K )
% 6.92/7.13 => ( P2 @ K ) )
% 6.92/7.13 => ( ! [K: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ K @ N2 )
% 6.92/7.13 => ( ! [I4: nat] :
% 6.92/7.13 ( ( ord_less_nat @ K @ I4 )
% 6.92/7.13 => ( P2 @ I4 ) )
% 6.92/7.13 => ( P2 @ K ) ) )
% 6.92/7.13 => ( P2 @ M ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % nat_descend_induct
% 6.92/7.13 thf(fact_699_minf_I8_J,axiom,
% 6.92/7.13 ! [T6: rat] :
% 6.92/7.13 ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ X6 @ Z2 )
% 6.92/7.13 => ~ ( ord_less_eq_rat @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(8)
% 6.92/7.13 thf(fact_700_minf_I8_J,axiom,
% 6.92/7.13 ! [T6: num] :
% 6.92/7.13 ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ X6 @ Z2 )
% 6.92/7.13 => ~ ( ord_less_eq_num @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(8)
% 6.92/7.13 thf(fact_701_minf_I8_J,axiom,
% 6.92/7.13 ! [T6: nat] :
% 6.92/7.13 ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ X6 @ Z2 )
% 6.92/7.13 => ~ ( ord_less_eq_nat @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(8)
% 6.92/7.13 thf(fact_702_minf_I8_J,axiom,
% 6.92/7.13 ! [T6: int] :
% 6.92/7.13 ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ X6 @ Z2 )
% 6.92/7.13 => ~ ( ord_less_eq_int @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(8)
% 6.92/7.13 thf(fact_703_minf_I6_J,axiom,
% 6.92/7.13 ! [T6: rat] :
% 6.92/7.13 ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ X6 @ Z2 )
% 6.92/7.13 => ( ord_less_eq_rat @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(6)
% 6.92/7.13 thf(fact_704_minf_I6_J,axiom,
% 6.92/7.13 ! [T6: num] :
% 6.92/7.13 ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ X6 @ Z2 )
% 6.92/7.13 => ( ord_less_eq_num @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(6)
% 6.92/7.13 thf(fact_705_minf_I6_J,axiom,
% 6.92/7.13 ! [T6: nat] :
% 6.92/7.13 ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ X6 @ Z2 )
% 6.92/7.13 => ( ord_less_eq_nat @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(6)
% 6.92/7.13 thf(fact_706_minf_I6_J,axiom,
% 6.92/7.13 ! [T6: int] :
% 6.92/7.13 ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ X6 @ Z2 )
% 6.92/7.13 => ( ord_less_eq_int @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(6)
% 6.92/7.13 thf(fact_707_pinf_I8_J,axiom,
% 6.92/7.13 ! [T6: rat] :
% 6.92/7.13 ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ Z2 @ X6 )
% 6.92/7.13 => ( ord_less_eq_rat @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(8)
% 6.92/7.13 thf(fact_708_pinf_I8_J,axiom,
% 6.92/7.13 ! [T6: num] :
% 6.92/7.13 ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ Z2 @ X6 )
% 6.92/7.13 => ( ord_less_eq_num @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(8)
% 6.92/7.13 thf(fact_709_pinf_I8_J,axiom,
% 6.92/7.13 ! [T6: nat] :
% 6.92/7.13 ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ Z2 @ X6 )
% 6.92/7.13 => ( ord_less_eq_nat @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(8)
% 6.92/7.13 thf(fact_710_pinf_I8_J,axiom,
% 6.92/7.13 ! [T6: int] :
% 6.92/7.13 ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ Z2 @ X6 )
% 6.92/7.13 => ( ord_less_eq_int @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(8)
% 6.92/7.13 thf(fact_711_subset__Collect__conv,axiom,
% 6.92/7.13 ! [S: set_list_nat,P2: list_nat > $o] :
% 6.92/7.13 ( ( ord_le6045566169113846134st_nat @ S @ ( collect_list_nat @ P2 ) )
% 6.92/7.13 = ( ! [X4: list_nat] :
% 6.92/7.13 ( ( member_list_nat @ X4 @ S )
% 6.92/7.13 => ( P2 @ X4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % subset_Collect_conv
% 6.92/7.13 thf(fact_712_subset__Collect__conv,axiom,
% 6.92/7.13 ! [S: set_se6260736226359567993nt_int,P2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.13 ( ( ord_le483042692224249369nt_int @ S @ ( collec5210948495886036740nt_int @ P2 ) )
% 6.92/7.13 = ( ! [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.13 ( ( member2340774599025711042nt_int @ X4 @ S )
% 6.92/7.13 => ( P2 @ X4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % subset_Collect_conv
% 6.92/7.13 thf(fact_713_subset__Collect__conv,axiom,
% 6.92/7.13 ! [S: set_set_nat,P2: set_nat > $o] :
% 6.92/7.13 ( ( ord_le6893508408891458716et_nat @ S @ ( collect_set_nat @ P2 ) )
% 6.92/7.13 = ( ! [X4: set_nat] :
% 6.92/7.13 ( ( member_set_nat @ X4 @ S )
% 6.92/7.13 => ( P2 @ X4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % subset_Collect_conv
% 6.92/7.13 thf(fact_714_subset__Collect__conv,axiom,
% 6.92/7.13 ! [S: set_nat,P2: nat > $o] :
% 6.92/7.13 ( ( ord_less_eq_set_nat @ S @ ( collect_nat @ P2 ) )
% 6.92/7.13 = ( ! [X4: nat] :
% 6.92/7.13 ( ( member_nat @ X4 @ S )
% 6.92/7.13 => ( P2 @ X4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % subset_Collect_conv
% 6.92/7.13 thf(fact_715_subset__Collect__conv,axiom,
% 6.92/7.13 ! [S: set_int,P2: int > $o] :
% 6.92/7.13 ( ( ord_less_eq_set_int @ S @ ( collect_int @ P2 ) )
% 6.92/7.13 = ( ! [X4: int] :
% 6.92/7.13 ( ( member_int @ X4 @ S )
% 6.92/7.13 => ( P2 @ X4 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % subset_Collect_conv
% 6.92/7.13 thf(fact_716_Collect__restrict,axiom,
% 6.92/7.13 ! [X7: set_o,P2: $o > $o] :
% 6.92/7.13 ( ord_less_eq_set_o
% 6.92/7.13 @ ( collect_o
% 6.92/7.13 @ ^ [X4: $o] :
% 6.92/7.13 ( ( member_o @ X4 @ X7 )
% 6.92/7.13 & ( P2 @ X4 ) ) )
% 6.92/7.13 @ X7 ) ).
% 6.92/7.13
% 6.92/7.13 % Collect_restrict
% 6.92/7.13 thf(fact_717_Collect__restrict,axiom,
% 6.92/7.13 ! [X7: set_list_nat,P2: list_nat > $o] :
% 6.92/7.13 ( ord_le6045566169113846134st_nat
% 6.92/7.13 @ ( collect_list_nat
% 6.92/7.13 @ ^ [X4: list_nat] :
% 6.92/7.13 ( ( member_list_nat @ X4 @ X7 )
% 6.92/7.13 & ( P2 @ X4 ) ) )
% 6.92/7.13 @ X7 ) ).
% 6.92/7.13
% 6.92/7.13 % Collect_restrict
% 6.92/7.13 thf(fact_718_Collect__restrict,axiom,
% 6.92/7.13 ! [X7: set_se6260736226359567993nt_int,P2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.13 ( ord_le483042692224249369nt_int
% 6.92/7.13 @ ( collec5210948495886036740nt_int
% 6.92/7.13 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.13 ( ( member2340774599025711042nt_int @ X4 @ X7 )
% 6.92/7.13 & ( P2 @ X4 ) ) )
% 6.92/7.13 @ X7 ) ).
% 6.92/7.13
% 6.92/7.13 % Collect_restrict
% 6.92/7.13 thf(fact_719_Collect__restrict,axiom,
% 6.92/7.13 ! [X7: set_set_nat,P2: set_nat > $o] :
% 6.92/7.13 ( ord_le6893508408891458716et_nat
% 6.92/7.13 @ ( collect_set_nat
% 6.92/7.13 @ ^ [X4: set_nat] :
% 6.92/7.13 ( ( member_set_nat @ X4 @ X7 )
% 6.92/7.13 & ( P2 @ X4 ) ) )
% 6.92/7.13 @ X7 ) ).
% 6.92/7.13
% 6.92/7.13 % Collect_restrict
% 6.92/7.13 thf(fact_720_Collect__restrict,axiom,
% 6.92/7.13 ! [X7: set_nat,P2: nat > $o] :
% 6.92/7.13 ( ord_less_eq_set_nat
% 6.92/7.13 @ ( collect_nat
% 6.92/7.13 @ ^ [X4: nat] :
% 6.92/7.13 ( ( member_nat @ X4 @ X7 )
% 6.92/7.13 & ( P2 @ X4 ) ) )
% 6.92/7.13 @ X7 ) ).
% 6.92/7.13
% 6.92/7.13 % Collect_restrict
% 6.92/7.13 thf(fact_721_Collect__restrict,axiom,
% 6.92/7.13 ! [X7: set_int,P2: int > $o] :
% 6.92/7.13 ( ord_less_eq_set_int
% 6.92/7.13 @ ( collect_int
% 6.92/7.13 @ ^ [X4: int] :
% 6.92/7.13 ( ( member_int @ X4 @ X7 )
% 6.92/7.13 & ( P2 @ X4 ) ) )
% 6.92/7.13 @ X7 ) ).
% 6.92/7.13
% 6.92/7.13 % Collect_restrict
% 6.92/7.13 thf(fact_722_prop__restrict,axiom,
% 6.92/7.13 ! [X: $o,Z5: set_o,X7: set_o,P2: $o > $o] :
% 6.92/7.13 ( ( member_o @ X @ Z5 )
% 6.92/7.13 => ( ( ord_less_eq_set_o @ Z5
% 6.92/7.13 @ ( collect_o
% 6.92/7.13 @ ^ [X4: $o] :
% 6.92/7.13 ( ( member_o @ X4 @ X7 )
% 6.92/7.13 & ( P2 @ X4 ) ) ) )
% 6.92/7.13 => ( P2 @ X ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % prop_restrict
% 6.92/7.13 thf(fact_723_prop__restrict,axiom,
% 6.92/7.13 ! [X: list_nat,Z5: set_list_nat,X7: set_list_nat,P2: list_nat > $o] :
% 6.92/7.13 ( ( member_list_nat @ X @ Z5 )
% 6.92/7.13 => ( ( ord_le6045566169113846134st_nat @ Z5
% 6.92/7.13 @ ( collect_list_nat
% 6.92/7.13 @ ^ [X4: list_nat] :
% 6.92/7.13 ( ( member_list_nat @ X4 @ X7 )
% 6.92/7.13 & ( P2 @ X4 ) ) ) )
% 6.92/7.13 => ( P2 @ X ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % prop_restrict
% 6.92/7.13 thf(fact_724_prop__restrict,axiom,
% 6.92/7.13 ! [X: set_Pr958786334691620121nt_int,Z5: set_se6260736226359567993nt_int,X7: set_se6260736226359567993nt_int,P2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.13 ( ( member2340774599025711042nt_int @ X @ Z5 )
% 6.92/7.13 => ( ( ord_le483042692224249369nt_int @ Z5
% 6.92/7.13 @ ( collec5210948495886036740nt_int
% 6.92/7.13 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.13 ( ( member2340774599025711042nt_int @ X4 @ X7 )
% 6.92/7.13 & ( P2 @ X4 ) ) ) )
% 6.92/7.13 => ( P2 @ X ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % prop_restrict
% 6.92/7.13 thf(fact_725_prop__restrict,axiom,
% 6.92/7.13 ! [X: set_nat,Z5: set_set_nat,X7: set_set_nat,P2: set_nat > $o] :
% 6.92/7.13 ( ( member_set_nat @ X @ Z5 )
% 6.92/7.13 => ( ( ord_le6893508408891458716et_nat @ Z5
% 6.92/7.13 @ ( collect_set_nat
% 6.92/7.13 @ ^ [X4: set_nat] :
% 6.92/7.13 ( ( member_set_nat @ X4 @ X7 )
% 6.92/7.13 & ( P2 @ X4 ) ) ) )
% 6.92/7.13 => ( P2 @ X ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % prop_restrict
% 6.92/7.13 thf(fact_726_prop__restrict,axiom,
% 6.92/7.13 ! [X: nat,Z5: set_nat,X7: set_nat,P2: nat > $o] :
% 6.92/7.13 ( ( member_nat @ X @ Z5 )
% 6.92/7.13 => ( ( ord_less_eq_set_nat @ Z5
% 6.92/7.13 @ ( collect_nat
% 6.92/7.13 @ ^ [X4: nat] :
% 6.92/7.13 ( ( member_nat @ X4 @ X7 )
% 6.92/7.13 & ( P2 @ X4 ) ) ) )
% 6.92/7.13 => ( P2 @ X ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % prop_restrict
% 6.92/7.13 thf(fact_727_prop__restrict,axiom,
% 6.92/7.13 ! [X: int,Z5: set_int,X7: set_int,P2: int > $o] :
% 6.92/7.13 ( ( member_int @ X @ Z5 )
% 6.92/7.13 => ( ( ord_less_eq_set_int @ Z5
% 6.92/7.13 @ ( collect_int
% 6.92/7.13 @ ^ [X4: int] :
% 6.92/7.13 ( ( member_int @ X4 @ X7 )
% 6.92/7.13 & ( P2 @ X4 ) ) ) )
% 6.92/7.13 => ( P2 @ X ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % prop_restrict
% 6.92/7.13 thf(fact_728_pinf_I1_J,axiom,
% 6.92/7.13 ! [P2: rat > $o,P6: rat > $o,Q2: rat > $o,Q4: rat > $o] :
% 6.92/7.13 ( ? [Z6: rat] :
% 6.92/7.13 ! [X3: rat] :
% 6.92/7.13 ( ( ord_less_rat @ Z6 @ X3 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: rat] :
% 6.92/7.13 ! [X3: rat] :
% 6.92/7.13 ( ( ord_less_rat @ Z6 @ X3 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ Z2 @ X6 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 & ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 & ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(1)
% 6.92/7.13 thf(fact_729_pinf_I1_J,axiom,
% 6.92/7.13 ! [P2: num > $o,P6: num > $o,Q2: num > $o,Q4: num > $o] :
% 6.92/7.13 ( ? [Z6: num] :
% 6.92/7.13 ! [X3: num] :
% 6.92/7.13 ( ( ord_less_num @ Z6 @ X3 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: num] :
% 6.92/7.13 ! [X3: num] :
% 6.92/7.13 ( ( ord_less_num @ Z6 @ X3 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ Z2 @ X6 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 & ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 & ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(1)
% 6.92/7.13 thf(fact_730_pinf_I1_J,axiom,
% 6.92/7.13 ! [P2: nat > $o,P6: nat > $o,Q2: nat > $o,Q4: nat > $o] :
% 6.92/7.13 ( ? [Z6: nat] :
% 6.92/7.13 ! [X3: nat] :
% 6.92/7.13 ( ( ord_less_nat @ Z6 @ X3 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: nat] :
% 6.92/7.13 ! [X3: nat] :
% 6.92/7.13 ( ( ord_less_nat @ Z6 @ X3 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ Z2 @ X6 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 & ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 & ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(1)
% 6.92/7.13 thf(fact_731_pinf_I1_J,axiom,
% 6.92/7.13 ! [P2: int > $o,P6: int > $o,Q2: int > $o,Q4: int > $o] :
% 6.92/7.13 ( ? [Z6: int] :
% 6.92/7.13 ! [X3: int] :
% 6.92/7.13 ( ( ord_less_int @ Z6 @ X3 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: int] :
% 6.92/7.13 ! [X3: int] :
% 6.92/7.13 ( ( ord_less_int @ Z6 @ X3 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ Z2 @ X6 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 & ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 & ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(1)
% 6.92/7.13 thf(fact_732_pinf_I2_J,axiom,
% 6.92/7.13 ! [P2: rat > $o,P6: rat > $o,Q2: rat > $o,Q4: rat > $o] :
% 6.92/7.13 ( ? [Z6: rat] :
% 6.92/7.13 ! [X3: rat] :
% 6.92/7.13 ( ( ord_less_rat @ Z6 @ X3 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: rat] :
% 6.92/7.13 ! [X3: rat] :
% 6.92/7.13 ( ( ord_less_rat @ Z6 @ X3 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ Z2 @ X6 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 | ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 | ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(2)
% 6.92/7.13 thf(fact_733_pinf_I2_J,axiom,
% 6.92/7.13 ! [P2: num > $o,P6: num > $o,Q2: num > $o,Q4: num > $o] :
% 6.92/7.13 ( ? [Z6: num] :
% 6.92/7.13 ! [X3: num] :
% 6.92/7.13 ( ( ord_less_num @ Z6 @ X3 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: num] :
% 6.92/7.13 ! [X3: num] :
% 6.92/7.13 ( ( ord_less_num @ Z6 @ X3 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ Z2 @ X6 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 | ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 | ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(2)
% 6.92/7.13 thf(fact_734_pinf_I2_J,axiom,
% 6.92/7.13 ! [P2: nat > $o,P6: nat > $o,Q2: nat > $o,Q4: nat > $o] :
% 6.92/7.13 ( ? [Z6: nat] :
% 6.92/7.13 ! [X3: nat] :
% 6.92/7.13 ( ( ord_less_nat @ Z6 @ X3 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: nat] :
% 6.92/7.13 ! [X3: nat] :
% 6.92/7.13 ( ( ord_less_nat @ Z6 @ X3 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ Z2 @ X6 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 | ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 | ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(2)
% 6.92/7.13 thf(fact_735_pinf_I2_J,axiom,
% 6.92/7.13 ! [P2: int > $o,P6: int > $o,Q2: int > $o,Q4: int > $o] :
% 6.92/7.13 ( ? [Z6: int] :
% 6.92/7.13 ! [X3: int] :
% 6.92/7.13 ( ( ord_less_int @ Z6 @ X3 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: int] :
% 6.92/7.13 ! [X3: int] :
% 6.92/7.13 ( ( ord_less_int @ Z6 @ X3 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ Z2 @ X6 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 | ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 | ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(2)
% 6.92/7.13 thf(fact_736_pinf_I3_J,axiom,
% 6.92/7.13 ! [T6: rat] :
% 6.92/7.13 ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ Z2 @ X6 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(3)
% 6.92/7.13 thf(fact_737_pinf_I3_J,axiom,
% 6.92/7.13 ! [T6: num] :
% 6.92/7.13 ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ Z2 @ X6 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(3)
% 6.92/7.13 thf(fact_738_pinf_I3_J,axiom,
% 6.92/7.13 ! [T6: nat] :
% 6.92/7.13 ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ Z2 @ X6 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(3)
% 6.92/7.13 thf(fact_739_pinf_I3_J,axiom,
% 6.92/7.13 ! [T6: int] :
% 6.92/7.13 ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ Z2 @ X6 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(3)
% 6.92/7.13 thf(fact_740_pinf_I4_J,axiom,
% 6.92/7.13 ! [T6: rat] :
% 6.92/7.13 ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ Z2 @ X6 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(4)
% 6.92/7.13 thf(fact_741_pinf_I4_J,axiom,
% 6.92/7.13 ! [T6: num] :
% 6.92/7.13 ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ Z2 @ X6 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(4)
% 6.92/7.13 thf(fact_742_pinf_I4_J,axiom,
% 6.92/7.13 ! [T6: nat] :
% 6.92/7.13 ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ Z2 @ X6 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(4)
% 6.92/7.13 thf(fact_743_pinf_I4_J,axiom,
% 6.92/7.13 ! [T6: int] :
% 6.92/7.13 ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ Z2 @ X6 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(4)
% 6.92/7.13 thf(fact_744_pinf_I5_J,axiom,
% 6.92/7.13 ! [T6: rat] :
% 6.92/7.13 ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ Z2 @ X6 )
% 6.92/7.13 => ~ ( ord_less_rat @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(5)
% 6.92/7.13 thf(fact_745_pinf_I5_J,axiom,
% 6.92/7.13 ! [T6: num] :
% 6.92/7.13 ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ Z2 @ X6 )
% 6.92/7.13 => ~ ( ord_less_num @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(5)
% 6.92/7.13 thf(fact_746_pinf_I5_J,axiom,
% 6.92/7.13 ! [T6: nat] :
% 6.92/7.13 ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ Z2 @ X6 )
% 6.92/7.13 => ~ ( ord_less_nat @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(5)
% 6.92/7.13 thf(fact_747_pinf_I5_J,axiom,
% 6.92/7.13 ! [T6: int] :
% 6.92/7.13 ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ Z2 @ X6 )
% 6.92/7.13 => ~ ( ord_less_int @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(5)
% 6.92/7.13 thf(fact_748_pinf_I7_J,axiom,
% 6.92/7.13 ! [T6: rat] :
% 6.92/7.13 ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ Z2 @ X6 )
% 6.92/7.13 => ( ord_less_rat @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(7)
% 6.92/7.13 thf(fact_749_pinf_I7_J,axiom,
% 6.92/7.13 ! [T6: num] :
% 6.92/7.13 ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ Z2 @ X6 )
% 6.92/7.13 => ( ord_less_num @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(7)
% 6.92/7.13 thf(fact_750_pinf_I7_J,axiom,
% 6.92/7.13 ! [T6: nat] :
% 6.92/7.13 ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ Z2 @ X6 )
% 6.92/7.13 => ( ord_less_nat @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(7)
% 6.92/7.13 thf(fact_751_pinf_I7_J,axiom,
% 6.92/7.13 ! [T6: int] :
% 6.92/7.13 ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ Z2 @ X6 )
% 6.92/7.13 => ( ord_less_int @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(7)
% 6.92/7.13 thf(fact_752_minf_I1_J,axiom,
% 6.92/7.13 ! [P2: rat > $o,P6: rat > $o,Q2: rat > $o,Q4: rat > $o] :
% 6.92/7.13 ( ? [Z6: rat] :
% 6.92/7.13 ! [X3: rat] :
% 6.92/7.13 ( ( ord_less_rat @ X3 @ Z6 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: rat] :
% 6.92/7.13 ! [X3: rat] :
% 6.92/7.13 ( ( ord_less_rat @ X3 @ Z6 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ X6 @ Z2 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 & ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 & ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(1)
% 6.92/7.13 thf(fact_753_minf_I1_J,axiom,
% 6.92/7.13 ! [P2: num > $o,P6: num > $o,Q2: num > $o,Q4: num > $o] :
% 6.92/7.13 ( ? [Z6: num] :
% 6.92/7.13 ! [X3: num] :
% 6.92/7.13 ( ( ord_less_num @ X3 @ Z6 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: num] :
% 6.92/7.13 ! [X3: num] :
% 6.92/7.13 ( ( ord_less_num @ X3 @ Z6 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ X6 @ Z2 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 & ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 & ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(1)
% 6.92/7.13 thf(fact_754_minf_I1_J,axiom,
% 6.92/7.13 ! [P2: nat > $o,P6: nat > $o,Q2: nat > $o,Q4: nat > $o] :
% 6.92/7.13 ( ? [Z6: nat] :
% 6.92/7.13 ! [X3: nat] :
% 6.92/7.13 ( ( ord_less_nat @ X3 @ Z6 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: nat] :
% 6.92/7.13 ! [X3: nat] :
% 6.92/7.13 ( ( ord_less_nat @ X3 @ Z6 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ X6 @ Z2 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 & ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 & ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(1)
% 6.92/7.13 thf(fact_755_minf_I1_J,axiom,
% 6.92/7.13 ! [P2: int > $o,P6: int > $o,Q2: int > $o,Q4: int > $o] :
% 6.92/7.13 ( ? [Z6: int] :
% 6.92/7.13 ! [X3: int] :
% 6.92/7.13 ( ( ord_less_int @ X3 @ Z6 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: int] :
% 6.92/7.13 ! [X3: int] :
% 6.92/7.13 ( ( ord_less_int @ X3 @ Z6 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ X6 @ Z2 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 & ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 & ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(1)
% 6.92/7.13 thf(fact_756_minf_I2_J,axiom,
% 6.92/7.13 ! [P2: rat > $o,P6: rat > $o,Q2: rat > $o,Q4: rat > $o] :
% 6.92/7.13 ( ? [Z6: rat] :
% 6.92/7.13 ! [X3: rat] :
% 6.92/7.13 ( ( ord_less_rat @ X3 @ Z6 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: rat] :
% 6.92/7.13 ! [X3: rat] :
% 6.92/7.13 ( ( ord_less_rat @ X3 @ Z6 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ X6 @ Z2 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 | ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 | ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(2)
% 6.92/7.13 thf(fact_757_minf_I2_J,axiom,
% 6.92/7.13 ! [P2: num > $o,P6: num > $o,Q2: num > $o,Q4: num > $o] :
% 6.92/7.13 ( ? [Z6: num] :
% 6.92/7.13 ! [X3: num] :
% 6.92/7.13 ( ( ord_less_num @ X3 @ Z6 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: num] :
% 6.92/7.13 ! [X3: num] :
% 6.92/7.13 ( ( ord_less_num @ X3 @ Z6 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ X6 @ Z2 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 | ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 | ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(2)
% 6.92/7.13 thf(fact_758_minf_I2_J,axiom,
% 6.92/7.13 ! [P2: nat > $o,P6: nat > $o,Q2: nat > $o,Q4: nat > $o] :
% 6.92/7.13 ( ? [Z6: nat] :
% 6.92/7.13 ! [X3: nat] :
% 6.92/7.13 ( ( ord_less_nat @ X3 @ Z6 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: nat] :
% 6.92/7.13 ! [X3: nat] :
% 6.92/7.13 ( ( ord_less_nat @ X3 @ Z6 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ X6 @ Z2 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 | ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 | ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(2)
% 6.92/7.13 thf(fact_759_minf_I2_J,axiom,
% 6.92/7.13 ! [P2: int > $o,P6: int > $o,Q2: int > $o,Q4: int > $o] :
% 6.92/7.13 ( ? [Z6: int] :
% 6.92/7.13 ! [X3: int] :
% 6.92/7.13 ( ( ord_less_int @ X3 @ Z6 )
% 6.92/7.13 => ( ( P2 @ X3 )
% 6.92/7.13 = ( P6 @ X3 ) ) )
% 6.92/7.13 => ( ? [Z6: int] :
% 6.92/7.13 ! [X3: int] :
% 6.92/7.13 ( ( ord_less_int @ X3 @ Z6 )
% 6.92/7.13 => ( ( Q2 @ X3 )
% 6.92/7.13 = ( Q4 @ X3 ) ) )
% 6.92/7.13 => ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ X6 @ Z2 )
% 6.92/7.13 => ( ( ( P2 @ X6 )
% 6.92/7.13 | ( Q2 @ X6 ) )
% 6.92/7.13 = ( ( P6 @ X6 )
% 6.92/7.13 | ( Q4 @ X6 ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(2)
% 6.92/7.13 thf(fact_760_minf_I3_J,axiom,
% 6.92/7.13 ! [T6: rat] :
% 6.92/7.13 ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ X6 @ Z2 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(3)
% 6.92/7.13 thf(fact_761_minf_I3_J,axiom,
% 6.92/7.13 ! [T6: num] :
% 6.92/7.13 ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ X6 @ Z2 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(3)
% 6.92/7.13 thf(fact_762_minf_I3_J,axiom,
% 6.92/7.13 ! [T6: nat] :
% 6.92/7.13 ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ X6 @ Z2 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(3)
% 6.92/7.13 thf(fact_763_minf_I3_J,axiom,
% 6.92/7.13 ! [T6: int] :
% 6.92/7.13 ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ X6 @ Z2 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(3)
% 6.92/7.13 thf(fact_764_minf_I4_J,axiom,
% 6.92/7.13 ! [T6: rat] :
% 6.92/7.13 ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ X6 @ Z2 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(4)
% 6.92/7.13 thf(fact_765_minf_I4_J,axiom,
% 6.92/7.13 ! [T6: num] :
% 6.92/7.13 ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ X6 @ Z2 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(4)
% 6.92/7.13 thf(fact_766_minf_I4_J,axiom,
% 6.92/7.13 ! [T6: nat] :
% 6.92/7.13 ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ X6 @ Z2 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(4)
% 6.92/7.13 thf(fact_767_minf_I4_J,axiom,
% 6.92/7.13 ! [T6: int] :
% 6.92/7.13 ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ X6 @ Z2 )
% 6.92/7.13 => ( X6 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(4)
% 6.92/7.13 thf(fact_768_minf_I5_J,axiom,
% 6.92/7.13 ! [T6: rat] :
% 6.92/7.13 ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ X6 @ Z2 )
% 6.92/7.13 => ( ord_less_rat @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(5)
% 6.92/7.13 thf(fact_769_minf_I5_J,axiom,
% 6.92/7.13 ! [T6: num] :
% 6.92/7.13 ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ X6 @ Z2 )
% 6.92/7.13 => ( ord_less_num @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(5)
% 6.92/7.13 thf(fact_770_minf_I5_J,axiom,
% 6.92/7.13 ! [T6: nat] :
% 6.92/7.13 ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ X6 @ Z2 )
% 6.92/7.13 => ( ord_less_nat @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(5)
% 6.92/7.13 thf(fact_771_minf_I5_J,axiom,
% 6.92/7.13 ! [T6: int] :
% 6.92/7.13 ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ X6 @ Z2 )
% 6.92/7.13 => ( ord_less_int @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(5)
% 6.92/7.13 thf(fact_772_minf_I7_J,axiom,
% 6.92/7.13 ! [T6: rat] :
% 6.92/7.13 ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ X6 @ Z2 )
% 6.92/7.13 => ~ ( ord_less_rat @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(7)
% 6.92/7.13 thf(fact_773_minf_I7_J,axiom,
% 6.92/7.13 ! [T6: num] :
% 6.92/7.13 ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ X6 @ Z2 )
% 6.92/7.13 => ~ ( ord_less_num @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(7)
% 6.92/7.13 thf(fact_774_minf_I7_J,axiom,
% 6.92/7.13 ! [T6: nat] :
% 6.92/7.13 ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ X6 @ Z2 )
% 6.92/7.13 => ~ ( ord_less_nat @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(7)
% 6.92/7.13 thf(fact_775_minf_I7_J,axiom,
% 6.92/7.13 ! [T6: int] :
% 6.92/7.13 ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ X6 @ Z2 )
% 6.92/7.13 => ~ ( ord_less_int @ T6 @ X6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % minf(7)
% 6.92/7.13 thf(fact_776_linorder__neqE__nat,axiom,
% 6.92/7.13 ! [X: nat,Y: nat] :
% 6.92/7.13 ( ( X != Y )
% 6.92/7.13 => ( ~ ( ord_less_nat @ X @ Y )
% 6.92/7.13 => ( ord_less_nat @ Y @ X ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % linorder_neqE_nat
% 6.92/7.13 thf(fact_777_infinite__descent,axiom,
% 6.92/7.13 ! [P2: nat > $o,N2: nat] :
% 6.92/7.13 ( ! [N5: nat] :
% 6.92/7.13 ( ~ ( P2 @ N5 )
% 6.92/7.13 => ? [M4: nat] :
% 6.92/7.13 ( ( ord_less_nat @ M4 @ N5 )
% 6.92/7.13 & ~ ( P2 @ M4 ) ) )
% 6.92/7.13 => ( P2 @ N2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % infinite_descent
% 6.92/7.13 thf(fact_778_nat__less__induct,axiom,
% 6.92/7.13 ! [P2: nat > $o,N2: nat] :
% 6.92/7.13 ( ! [N5: nat] :
% 6.92/7.13 ( ! [M4: nat] :
% 6.92/7.13 ( ( ord_less_nat @ M4 @ N5 )
% 6.92/7.13 => ( P2 @ M4 ) )
% 6.92/7.13 => ( P2 @ N5 ) )
% 6.92/7.13 => ( P2 @ N2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % nat_less_induct
% 6.92/7.13 thf(fact_779_less__irrefl__nat,axiom,
% 6.92/7.13 ! [N2: nat] :
% 6.92/7.13 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 6.92/7.13
% 6.92/7.13 % less_irrefl_nat
% 6.92/7.13 thf(fact_780_less__not__refl3,axiom,
% 6.92/7.13 ! [S2: nat,T6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ S2 @ T6 )
% 6.92/7.13 => ( S2 != T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % less_not_refl3
% 6.92/7.13 thf(fact_781_less__not__refl2,axiom,
% 6.92/7.13 ! [N2: nat,M: nat] :
% 6.92/7.13 ( ( ord_less_nat @ N2 @ M )
% 6.92/7.13 => ( M != N2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % less_not_refl2
% 6.92/7.13 thf(fact_782_less__not__refl,axiom,
% 6.92/7.13 ! [N2: nat] :
% 6.92/7.13 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 6.92/7.13
% 6.92/7.13 % less_not_refl
% 6.92/7.13 thf(fact_783_nat__neq__iff,axiom,
% 6.92/7.13 ! [M: nat,N2: nat] :
% 6.92/7.13 ( ( M != N2 )
% 6.92/7.13 = ( ( ord_less_nat @ M @ N2 )
% 6.92/7.13 | ( ord_less_nat @ N2 @ M ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % nat_neq_iff
% 6.92/7.13 thf(fact_784_Nat_Oex__has__greatest__nat,axiom,
% 6.92/7.13 ! [P2: nat > $o,K2: nat,B: nat] :
% 6.92/7.13 ( ( P2 @ K2 )
% 6.92/7.13 => ( ! [Y3: nat] :
% 6.92/7.13 ( ( P2 @ Y3 )
% 6.92/7.13 => ( ord_less_eq_nat @ Y3 @ B ) )
% 6.92/7.13 => ? [X3: nat] :
% 6.92/7.13 ( ( P2 @ X3 )
% 6.92/7.13 & ! [Y5: nat] :
% 6.92/7.13 ( ( P2 @ Y5 )
% 6.92/7.13 => ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % Nat.ex_has_greatest_nat
% 6.92/7.13 thf(fact_785_nat__le__linear,axiom,
% 6.92/7.13 ! [M: nat,N2: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.13 | ( ord_less_eq_nat @ N2 @ M ) ) ).
% 6.92/7.13
% 6.92/7.13 % nat_le_linear
% 6.92/7.13 thf(fact_786_le__antisym,axiom,
% 6.92/7.13 ! [M: nat,N2: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.13 => ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.13 => ( M = N2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % le_antisym
% 6.92/7.13 thf(fact_787_eq__imp__le,axiom,
% 6.92/7.13 ! [M: nat,N2: nat] :
% 6.92/7.13 ( ( M = N2 )
% 6.92/7.13 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % eq_imp_le
% 6.92/7.13 thf(fact_788_le__trans,axiom,
% 6.92/7.13 ! [I2: nat,J2: nat,K2: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.13 => ( ( ord_less_eq_nat @ J2 @ K2 )
% 6.92/7.13 => ( ord_less_eq_nat @ I2 @ K2 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % le_trans
% 6.92/7.13 thf(fact_789_le__refl,axiom,
% 6.92/7.13 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ N2 ) ).
% 6.92/7.13
% 6.92/7.13 % le_refl
% 6.92/7.13 thf(fact_790_pinf_I6_J,axiom,
% 6.92/7.13 ! [T6: rat] :
% 6.92/7.13 ? [Z2: rat] :
% 6.92/7.13 ! [X6: rat] :
% 6.92/7.13 ( ( ord_less_rat @ Z2 @ X6 )
% 6.92/7.13 => ~ ( ord_less_eq_rat @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(6)
% 6.92/7.13 thf(fact_791_pinf_I6_J,axiom,
% 6.92/7.13 ! [T6: num] :
% 6.92/7.13 ? [Z2: num] :
% 6.92/7.13 ! [X6: num] :
% 6.92/7.13 ( ( ord_less_num @ Z2 @ X6 )
% 6.92/7.13 => ~ ( ord_less_eq_num @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(6)
% 6.92/7.13 thf(fact_792_pinf_I6_J,axiom,
% 6.92/7.13 ! [T6: nat] :
% 6.92/7.13 ? [Z2: nat] :
% 6.92/7.13 ! [X6: nat] :
% 6.92/7.13 ( ( ord_less_nat @ Z2 @ X6 )
% 6.92/7.13 => ~ ( ord_less_eq_nat @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(6)
% 6.92/7.13 thf(fact_793_pinf_I6_J,axiom,
% 6.92/7.13 ! [T6: int] :
% 6.92/7.13 ? [Z2: int] :
% 6.92/7.13 ! [X6: int] :
% 6.92/7.13 ( ( ord_less_int @ Z2 @ X6 )
% 6.92/7.13 => ~ ( ord_less_eq_int @ X6 @ T6 ) ) ).
% 6.92/7.13
% 6.92/7.13 % pinf(6)
% 6.92/7.13 thf(fact_794_execute__bind_I1_J,axiom,
% 6.92/7.13 ! [F: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_Time_Heap_b] :
% 6.92/7.13 ( ( ( heap_T875086893843062177t_unit @ F @ H )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( ( heap_Time_execute_b @ ( heap_T757603679106148409unit_b @ F @ G ) @ H )
% 6.92/7.13 = ( heap_T7616092557645711336rame_b @ N2 @ ( heap_Time_execute_b @ ( G @ X ) @ H5 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % execute_bind(1)
% 6.92/7.13 thf(fact_795_execute__bind_I1_J,axiom,
% 6.92/7.13 ! [F: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_Time_Heap_a] :
% 6.92/7.13 ( ( ( heap_T875086893843062177t_unit @ F @ H )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( ( heap_Time_execute_a @ ( heap_T757603679106148408unit_a @ F @ G ) @ H )
% 6.92/7.13 = ( heap_T7616092557645711335rame_a @ N2 @ ( heap_Time_execute_a @ ( G @ X ) @ H5 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % execute_bind(1)
% 6.92/7.13 thf(fact_796_execute__bind_I1_J,axiom,
% 6.92/7.13 ! [F: heap_Time_Heap_b,H: heap_e7401611519738050253t_unit,X: b,H5: heap_e7401611519738050253t_unit,N2: nat,G: b > heap_Time_Heap_b] :
% 6.92/7.13 ( ( ( heap_Time_execute_b @ F @ H )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( ( heap_Time_execute_b @ ( heap_Time_bind_b_b @ F @ G ) @ H )
% 6.92/7.13 = ( heap_T7616092557645711336rame_b @ N2 @ ( heap_Time_execute_b @ ( G @ X ) @ H5 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % execute_bind(1)
% 6.92/7.13 thf(fact_797_execute__bind_I1_J,axiom,
% 6.92/7.13 ! [F: heap_Time_Heap_b,H: heap_e7401611519738050253t_unit,X: b,H5: heap_e7401611519738050253t_unit,N2: nat,G: b > heap_Time_Heap_a] :
% 6.92/7.13 ( ( ( heap_Time_execute_b @ F @ H )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( ( heap_Time_execute_a @ ( heap_Time_bind_b_a @ F @ G ) @ H )
% 6.92/7.13 = ( heap_T7616092557645711335rame_a @ N2 @ ( heap_Time_execute_a @ ( G @ X ) @ H5 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % execute_bind(1)
% 6.92/7.13 thf(fact_798_execute__bind_I1_J,axiom,
% 6.92/7.13 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,X: a,H5: heap_e7401611519738050253t_unit,N2: nat,G: a > heap_Time_Heap_b] :
% 6.92/7.13 ( ( ( heap_Time_execute_a @ F @ H )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( ( heap_Time_execute_b @ ( heap_Time_bind_a_b @ F @ G ) @ H )
% 6.92/7.13 = ( heap_T7616092557645711336rame_b @ N2 @ ( heap_Time_execute_b @ ( G @ X ) @ H5 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % execute_bind(1)
% 6.92/7.13 thf(fact_799_execute__bind_I1_J,axiom,
% 6.92/7.13 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,X: a,H5: heap_e7401611519738050253t_unit,N2: nat,G: a > heap_Time_Heap_a] :
% 6.92/7.13 ( ( ( heap_Time_execute_a @ F @ H )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( ( heap_Time_execute_a @ ( heap_Time_bind_a_a @ F @ G ) @ H )
% 6.92/7.13 = ( heap_T7616092557645711335rame_a @ N2 @ ( heap_Time_execute_a @ ( G @ X ) @ H5 ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % execute_bind(1)
% 6.92/7.13 thf(fact_800_subset__antisym,axiom,
% 6.92/7.13 ! [A4: set_int,B5: set_int] :
% 6.92/7.13 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.13 => ( ( ord_less_eq_set_int @ B5 @ A4 )
% 6.92/7.13 => ( A4 = B5 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % subset_antisym
% 6.92/7.13 thf(fact_801_psubsetI,axiom,
% 6.92/7.13 ! [A4: set_int,B5: set_int] :
% 6.92/7.13 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.13 => ( ( A4 != B5 )
% 6.92/7.13 => ( ord_less_set_int @ A4 @ B5 ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % psubsetI
% 6.92/7.13 thf(fact_802_subsetI,axiom,
% 6.92/7.13 ! [A4: set_o,B5: set_o] :
% 6.92/7.13 ( ! [X3: $o] :
% 6.92/7.13 ( ( member_o @ X3 @ A4 )
% 6.92/7.13 => ( member_o @ X3 @ B5 ) )
% 6.92/7.13 => ( ord_less_eq_set_o @ A4 @ B5 ) ) ).
% 6.92/7.13
% 6.92/7.13 % subsetI
% 6.92/7.13 thf(fact_803_subsetI,axiom,
% 6.92/7.13 ! [A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.13 ( ! [X3: set_Pr958786334691620121nt_int] :
% 6.92/7.13 ( ( member2340774599025711042nt_int @ X3 @ A4 )
% 6.92/7.13 => ( member2340774599025711042nt_int @ X3 @ B5 ) )
% 6.92/7.13 => ( ord_le483042692224249369nt_int @ A4 @ B5 ) ) ).
% 6.92/7.13
% 6.92/7.13 % subsetI
% 6.92/7.13 thf(fact_804_subsetI,axiom,
% 6.92/7.13 ! [A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.13 ( ! [X3: set_nat] :
% 6.92/7.13 ( ( member_set_nat @ X3 @ A4 )
% 6.92/7.13 => ( member_set_nat @ X3 @ B5 ) )
% 6.92/7.13 => ( ord_le6893508408891458716et_nat @ A4 @ B5 ) ) ).
% 6.92/7.13
% 6.92/7.13 % subsetI
% 6.92/7.13 thf(fact_805_subsetI,axiom,
% 6.92/7.13 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.13 ( ! [X3: nat] :
% 6.92/7.13 ( ( member_nat @ X3 @ A4 )
% 6.92/7.13 => ( member_nat @ X3 @ B5 ) )
% 6.92/7.13 => ( ord_less_eq_set_nat @ A4 @ B5 ) ) ).
% 6.92/7.13
% 6.92/7.13 % subsetI
% 6.92/7.13 thf(fact_806_subsetI,axiom,
% 6.92/7.13 ! [A4: set_int,B5: set_int] :
% 6.92/7.13 ( ! [X3: int] :
% 6.92/7.13 ( ( member_int @ X3 @ A4 )
% 6.92/7.13 => ( member_int @ X3 @ B5 ) )
% 6.92/7.13 => ( ord_less_eq_set_int @ A4 @ B5 ) ) ).
% 6.92/7.13
% 6.92/7.13 % subsetI
% 6.92/7.13 thf(fact_807_complete__interval,axiom,
% 6.92/7.13 ! [A: nat,B: nat,P2: nat > $o] :
% 6.92/7.13 ( ( ord_less_nat @ A @ B )
% 6.92/7.13 => ( ( P2 @ A )
% 6.92/7.13 => ( ~ ( P2 @ B )
% 6.92/7.13 => ? [C: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ A @ C )
% 6.92/7.13 & ( ord_less_eq_nat @ C @ B )
% 6.92/7.13 & ! [X6: nat] :
% 6.92/7.13 ( ( ( ord_less_eq_nat @ A @ X6 )
% 6.92/7.13 & ( ord_less_nat @ X6 @ C ) )
% 6.92/7.13 => ( P2 @ X6 ) )
% 6.92/7.13 & ! [D3: nat] :
% 6.92/7.13 ( ! [X3: nat] :
% 6.92/7.13 ( ( ( ord_less_eq_nat @ A @ X3 )
% 6.92/7.13 & ( ord_less_nat @ X3 @ D3 ) )
% 6.92/7.13 => ( P2 @ X3 ) )
% 6.92/7.13 => ( ord_less_eq_nat @ D3 @ C ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % complete_interval
% 6.92/7.13 thf(fact_808_complete__interval,axiom,
% 6.92/7.13 ! [A: int,B: int,P2: int > $o] :
% 6.92/7.13 ( ( ord_less_int @ A @ B )
% 6.92/7.13 => ( ( P2 @ A )
% 6.92/7.13 => ( ~ ( P2 @ B )
% 6.92/7.13 => ? [C: int] :
% 6.92/7.13 ( ( ord_less_eq_int @ A @ C )
% 6.92/7.13 & ( ord_less_eq_int @ C @ B )
% 6.92/7.13 & ! [X6: int] :
% 6.92/7.13 ( ( ( ord_less_eq_int @ A @ X6 )
% 6.92/7.13 & ( ord_less_int @ X6 @ C ) )
% 6.92/7.13 => ( P2 @ X6 ) )
% 6.92/7.13 & ! [D3: int] :
% 6.92/7.13 ( ! [X3: int] :
% 6.92/7.13 ( ( ( ord_less_eq_int @ A @ X3 )
% 6.92/7.13 & ( ord_less_int @ X3 @ D3 ) )
% 6.92/7.13 => ( P2 @ X3 ) )
% 6.92/7.13 => ( ord_less_eq_int @ D3 @ C ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % complete_interval
% 6.92/7.13 thf(fact_809_verit__comp__simplify1_I3_J,axiom,
% 6.92/7.13 ! [B2: rat,A2: rat] :
% 6.92/7.13 ( ( ~ ( ord_less_eq_rat @ B2 @ A2 ) )
% 6.92/7.13 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % verit_comp_simplify1(3)
% 6.92/7.13 thf(fact_810_verit__comp__simplify1_I3_J,axiom,
% 6.92/7.13 ! [B2: num,A2: num] :
% 6.92/7.13 ( ( ~ ( ord_less_eq_num @ B2 @ A2 ) )
% 6.92/7.13 = ( ord_less_num @ A2 @ B2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % verit_comp_simplify1(3)
% 6.92/7.13 thf(fact_811_verit__comp__simplify1_I3_J,axiom,
% 6.92/7.13 ! [B2: nat,A2: nat] :
% 6.92/7.13 ( ( ~ ( ord_less_eq_nat @ B2 @ A2 ) )
% 6.92/7.13 = ( ord_less_nat @ A2 @ B2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % verit_comp_simplify1(3)
% 6.92/7.13 thf(fact_812_verit__comp__simplify1_I3_J,axiom,
% 6.92/7.13 ! [B2: int,A2: int] :
% 6.92/7.13 ( ( ~ ( ord_less_eq_int @ B2 @ A2 ) )
% 6.92/7.13 = ( ord_less_int @ A2 @ B2 ) ) ).
% 6.92/7.13
% 6.92/7.13 % verit_comp_simplify1(3)
% 6.92/7.13 thf(fact_813_execute__bind__eq__SomeI,axiom,
% 6.92/7.13 ! [F: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_T5738788834812785303t_unit,Y: product_unit,H9: heap_e7401611519738050253t_unit,N6: nat] :
% 6.92/7.13 ( ( ( heap_T875086893843062177t_unit @ F @ H )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( ( ( heap_T875086893843062177t_unit @ ( G @ X ) @ H5 )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ N6 ) ) ) )
% 6.92/7.13 => ( ( heap_T875086893843062177t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ H )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % execute_bind_eq_SomeI
% 6.92/7.13 thf(fact_814_execute__bind__eq__SomeI,axiom,
% 6.92/7.13 ! [F: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_Time_Heap_b,Y: b,H9: heap_e7401611519738050253t_unit,N6: nat] :
% 6.92/7.13 ( ( ( heap_T875086893843062177t_unit @ F @ H )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( ( ( heap_Time_execute_b @ ( G @ X ) @ H5 )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ N6 ) ) ) )
% 6.92/7.13 => ( ( heap_Time_execute_b @ ( heap_T757603679106148409unit_b @ F @ G ) @ H )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % execute_bind_eq_SomeI
% 6.92/7.13 thf(fact_815_execute__bind__eq__SomeI,axiom,
% 6.92/7.13 ! [F: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,X: product_unit,H5: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_Time_Heap_a,Y: a,H9: heap_e7401611519738050253t_unit,N6: nat] :
% 6.92/7.13 ( ( ( heap_T875086893843062177t_unit @ F @ H )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( ( ( heap_Time_execute_a @ ( G @ X ) @ H5 )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ N6 ) ) ) )
% 6.92/7.13 => ( ( heap_Time_execute_a @ ( heap_T757603679106148408unit_a @ F @ G ) @ H )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % execute_bind_eq_SomeI
% 6.92/7.13 thf(fact_816_execute__bind__eq__SomeI,axiom,
% 6.92/7.13 ! [F: heap_Time_Heap_b,H: heap_e7401611519738050253t_unit,X: b,H5: heap_e7401611519738050253t_unit,N2: nat,G: b > heap_T5738788834812785303t_unit,Y: product_unit,H9: heap_e7401611519738050253t_unit,N6: nat] :
% 6.92/7.13 ( ( ( heap_Time_execute_b @ F @ H )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( ( ( heap_T875086893843062177t_unit @ ( G @ X ) @ H5 )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ N6 ) ) ) )
% 6.92/7.13 => ( ( heap_T875086893843062177t_unit @ ( heap_T3413130826733729493t_unit @ F @ G ) @ H )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % execute_bind_eq_SomeI
% 6.92/7.13 thf(fact_817_execute__bind__eq__SomeI,axiom,
% 6.92/7.13 ! [F: heap_Time_Heap_b,H: heap_e7401611519738050253t_unit,X: b,H5: heap_e7401611519738050253t_unit,N2: nat,G: b > heap_Time_Heap_b,Y: b,H9: heap_e7401611519738050253t_unit,N6: nat] :
% 6.92/7.13 ( ( ( heap_Time_execute_b @ F @ H )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( ( ( heap_Time_execute_b @ ( G @ X ) @ H5 )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ N6 ) ) ) )
% 6.92/7.13 => ( ( heap_Time_execute_b @ ( heap_Time_bind_b_b @ F @ G ) @ H )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % execute_bind_eq_SomeI
% 6.92/7.13 thf(fact_818_execute__bind__eq__SomeI,axiom,
% 6.92/7.13 ! [F: heap_Time_Heap_b,H: heap_e7401611519738050253t_unit,X: b,H5: heap_e7401611519738050253t_unit,N2: nat,G: b > heap_Time_Heap_a,Y: a,H9: heap_e7401611519738050253t_unit,N6: nat] :
% 6.92/7.13 ( ( ( heap_Time_execute_b @ F @ H )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( ( ( heap_Time_execute_a @ ( G @ X ) @ H5 )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ N6 ) ) ) )
% 6.92/7.13 => ( ( heap_Time_execute_a @ ( heap_Time_bind_b_a @ F @ G ) @ H )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % execute_bind_eq_SomeI
% 6.92/7.13 thf(fact_819_execute__bind__eq__SomeI,axiom,
% 6.92/7.13 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,X: a,H5: heap_e7401611519738050253t_unit,N2: nat,G: a > heap_T5738788834812785303t_unit,Y: product_unit,H9: heap_e7401611519738050253t_unit,N6: nat] :
% 6.92/7.13 ( ( ( heap_Time_execute_a @ F @ H )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( ( ( heap_T875086893843062177t_unit @ ( G @ X ) @ H5 )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ N6 ) ) ) )
% 6.92/7.13 => ( ( heap_T875086893843062177t_unit @ ( heap_T8685611227969916822t_unit @ F @ G ) @ H )
% 6.92/7.13 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % execute_bind_eq_SomeI
% 6.92/7.13 thf(fact_820_execute__bind__eq__SomeI,axiom,
% 6.92/7.13 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,X: a,H5: heap_e7401611519738050253t_unit,N2: nat,G: a > heap_Time_Heap_b,Y: b,H9: heap_e7401611519738050253t_unit,N6: nat] :
% 6.92/7.13 ( ( ( heap_Time_execute_a @ F @ H )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( ( ( heap_Time_execute_b @ ( G @ X ) @ H5 )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ N6 ) ) ) )
% 6.92/7.13 => ( ( heap_Time_execute_b @ ( heap_Time_bind_a_b @ F @ G ) @ H )
% 6.92/7.13 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % execute_bind_eq_SomeI
% 6.92/7.13 thf(fact_821_execute__bind__eq__SomeI,axiom,
% 6.92/7.13 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,X: a,H5: heap_e7401611519738050253t_unit,N2: nat,G: a > heap_Time_Heap_a,Y: a,H9: heap_e7401611519738050253t_unit,N6: nat] :
% 6.92/7.13 ( ( ( heap_Time_execute_a @ F @ H )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ X @ ( produc584006145561248582it_nat @ H5 @ N2 ) ) ) )
% 6.92/7.13 => ( ( ( heap_Time_execute_a @ ( G @ X ) @ H5 )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ N6 ) ) ) )
% 6.92/7.13 => ( ( heap_Time_execute_a @ ( heap_Time_bind_a_a @ F @ G ) @ H )
% 6.92/7.13 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % execute_bind_eq_SomeI
% 6.92/7.13 thf(fact_822_new__addrs__def,axiom,
% 6.92/7.13 ( hoare_new_addrs
% 6.92/7.13 = ( ^ [H6: heap_e7401611519738050253t_unit,As4: set_nat,H7: heap_e7401611519738050253t_unit] :
% 6.92/7.13 ( sup_sup_set_nat @ As4
% 6.92/7.13 @ ( collect_nat
% 6.92/7.13 @ ^ [A5: nat] :
% 6.92/7.13 ( ( ord_less_eq_nat @ ( lim_Product_unit @ H6 ) @ A5 )
% 6.92/7.13 & ( ord_less_nat @ A5 @ ( lim_Product_unit @ H7 ) ) ) ) ) ) ) ).
% 6.92/7.13
% 6.92/7.13 % new_addrs_def
% 6.92/7.13 thf(fact_823_subset__Collect__iff,axiom,
% 6.92/7.13 ! [B5: set_o,A4: set_o,P2: $o > $o] :
% 6.92/7.13 ( ( ord_less_eq_set_o @ B5 @ A4 )
% 6.92/7.13 => ( ( ord_less_eq_set_o @ B5
% 6.92/7.13 @ ( collect_o
% 6.92/7.13 @ ^ [X4: $o] :
% 6.92/7.13 ( ( member_o @ X4 @ A4 )
% 6.92/7.13 & ( P2 @ X4 ) ) ) )
% 6.92/7.13 = ( ! [X4: $o] :
% 6.92/7.13 ( ( member_o @ X4 @ B5 )
% 6.92/7.13 => ( P2 @ X4 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_Collect_iff
% 6.92/7.14 thf(fact_824_subset__Collect__iff,axiom,
% 6.92/7.14 ! [B5: set_list_nat,A4: set_list_nat,P2: list_nat > $o] :
% 6.92/7.14 ( ( ord_le6045566169113846134st_nat @ B5 @ A4 )
% 6.92/7.14 => ( ( ord_le6045566169113846134st_nat @ B5
% 6.92/7.14 @ ( collect_list_nat
% 6.92/7.14 @ ^ [X4: list_nat] :
% 6.92/7.14 ( ( member_list_nat @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) ) )
% 6.92/7.14 = ( ! [X4: list_nat] :
% 6.92/7.14 ( ( member_list_nat @ X4 @ B5 )
% 6.92/7.14 => ( P2 @ X4 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_Collect_iff
% 6.92/7.14 thf(fact_825_subset__Collect__iff,axiom,
% 6.92/7.14 ! [B5: set_se6260736226359567993nt_int,A4: set_se6260736226359567993nt_int,P2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.14 ( ( ord_le483042692224249369nt_int @ B5 @ A4 )
% 6.92/7.14 => ( ( ord_le483042692224249369nt_int @ B5
% 6.92/7.14 @ ( collec5210948495886036740nt_int
% 6.92/7.14 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( member2340774599025711042nt_int @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) ) )
% 6.92/7.14 = ( ! [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( member2340774599025711042nt_int @ X4 @ B5 )
% 6.92/7.14 => ( P2 @ X4 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_Collect_iff
% 6.92/7.14 thf(fact_826_subset__Collect__iff,axiom,
% 6.92/7.14 ! [B5: set_set_nat,A4: set_set_nat,P2: set_nat > $o] :
% 6.92/7.14 ( ( ord_le6893508408891458716et_nat @ B5 @ A4 )
% 6.92/7.14 => ( ( ord_le6893508408891458716et_nat @ B5
% 6.92/7.14 @ ( collect_set_nat
% 6.92/7.14 @ ^ [X4: set_nat] :
% 6.92/7.14 ( ( member_set_nat @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) ) )
% 6.92/7.14 = ( ! [X4: set_nat] :
% 6.92/7.14 ( ( member_set_nat @ X4 @ B5 )
% 6.92/7.14 => ( P2 @ X4 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_Collect_iff
% 6.92/7.14 thf(fact_827_subset__Collect__iff,axiom,
% 6.92/7.14 ! [B5: set_nat,A4: set_nat,P2: nat > $o] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 6.92/7.14 => ( ( ord_less_eq_set_nat @ B5
% 6.92/7.14 @ ( collect_nat
% 6.92/7.14 @ ^ [X4: nat] :
% 6.92/7.14 ( ( member_nat @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) ) )
% 6.92/7.14 = ( ! [X4: nat] :
% 6.92/7.14 ( ( member_nat @ X4 @ B5 )
% 6.92/7.14 => ( P2 @ X4 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_Collect_iff
% 6.92/7.14 thf(fact_828_subset__Collect__iff,axiom,
% 6.92/7.14 ! [B5: set_int,A4: set_int,P2: int > $o] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 6.92/7.14 => ( ( ord_less_eq_set_int @ B5
% 6.92/7.14 @ ( collect_int
% 6.92/7.14 @ ^ [X4: int] :
% 6.92/7.14 ( ( member_int @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) ) )
% 6.92/7.14 = ( ! [X4: int] :
% 6.92/7.14 ( ( member_int @ X4 @ B5 )
% 6.92/7.14 => ( P2 @ X4 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_Collect_iff
% 6.92/7.14 thf(fact_829_subset__CollectI,axiom,
% 6.92/7.14 ! [B5: set_o,A4: set_o,Q2: $o > $o,P2: $o > $o] :
% 6.92/7.14 ( ( ord_less_eq_set_o @ B5 @ A4 )
% 6.92/7.14 => ( ! [X3: $o] :
% 6.92/7.14 ( ( member_o @ X3 @ B5 )
% 6.92/7.14 => ( ( Q2 @ X3 )
% 6.92/7.14 => ( P2 @ X3 ) ) )
% 6.92/7.14 => ( ord_less_eq_set_o
% 6.92/7.14 @ ( collect_o
% 6.92/7.14 @ ^ [X4: $o] :
% 6.92/7.14 ( ( member_o @ X4 @ B5 )
% 6.92/7.14 & ( Q2 @ X4 ) ) )
% 6.92/7.14 @ ( collect_o
% 6.92/7.14 @ ^ [X4: $o] :
% 6.92/7.14 ( ( member_o @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_CollectI
% 6.92/7.14 thf(fact_830_subset__CollectI,axiom,
% 6.92/7.14 ! [B5: set_list_nat,A4: set_list_nat,Q2: list_nat > $o,P2: list_nat > $o] :
% 6.92/7.14 ( ( ord_le6045566169113846134st_nat @ B5 @ A4 )
% 6.92/7.14 => ( ! [X3: list_nat] :
% 6.92/7.14 ( ( member_list_nat @ X3 @ B5 )
% 6.92/7.14 => ( ( Q2 @ X3 )
% 6.92/7.14 => ( P2 @ X3 ) ) )
% 6.92/7.14 => ( ord_le6045566169113846134st_nat
% 6.92/7.14 @ ( collect_list_nat
% 6.92/7.14 @ ^ [X4: list_nat] :
% 6.92/7.14 ( ( member_list_nat @ X4 @ B5 )
% 6.92/7.14 & ( Q2 @ X4 ) ) )
% 6.92/7.14 @ ( collect_list_nat
% 6.92/7.14 @ ^ [X4: list_nat] :
% 6.92/7.14 ( ( member_list_nat @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_CollectI
% 6.92/7.14 thf(fact_831_subset__CollectI,axiom,
% 6.92/7.14 ! [B5: set_se6260736226359567993nt_int,A4: set_se6260736226359567993nt_int,Q2: set_Pr958786334691620121nt_int > $o,P2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.14 ( ( ord_le483042692224249369nt_int @ B5 @ A4 )
% 6.92/7.14 => ( ! [X3: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( member2340774599025711042nt_int @ X3 @ B5 )
% 6.92/7.14 => ( ( Q2 @ X3 )
% 6.92/7.14 => ( P2 @ X3 ) ) )
% 6.92/7.14 => ( ord_le483042692224249369nt_int
% 6.92/7.14 @ ( collec5210948495886036740nt_int
% 6.92/7.14 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( member2340774599025711042nt_int @ X4 @ B5 )
% 6.92/7.14 & ( Q2 @ X4 ) ) )
% 6.92/7.14 @ ( collec5210948495886036740nt_int
% 6.92/7.14 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( member2340774599025711042nt_int @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_CollectI
% 6.92/7.14 thf(fact_832_subset__CollectI,axiom,
% 6.92/7.14 ! [B5: set_set_nat,A4: set_set_nat,Q2: set_nat > $o,P2: set_nat > $o] :
% 6.92/7.14 ( ( ord_le6893508408891458716et_nat @ B5 @ A4 )
% 6.92/7.14 => ( ! [X3: set_nat] :
% 6.92/7.14 ( ( member_set_nat @ X3 @ B5 )
% 6.92/7.14 => ( ( Q2 @ X3 )
% 6.92/7.14 => ( P2 @ X3 ) ) )
% 6.92/7.14 => ( ord_le6893508408891458716et_nat
% 6.92/7.14 @ ( collect_set_nat
% 6.92/7.14 @ ^ [X4: set_nat] :
% 6.92/7.14 ( ( member_set_nat @ X4 @ B5 )
% 6.92/7.14 & ( Q2 @ X4 ) ) )
% 6.92/7.14 @ ( collect_set_nat
% 6.92/7.14 @ ^ [X4: set_nat] :
% 6.92/7.14 ( ( member_set_nat @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_CollectI
% 6.92/7.14 thf(fact_833_subset__CollectI,axiom,
% 6.92/7.14 ! [B5: set_nat,A4: set_nat,Q2: nat > $o,P2: nat > $o] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 6.92/7.14 => ( ! [X3: nat] :
% 6.92/7.14 ( ( member_nat @ X3 @ B5 )
% 6.92/7.14 => ( ( Q2 @ X3 )
% 6.92/7.14 => ( P2 @ X3 ) ) )
% 6.92/7.14 => ( ord_less_eq_set_nat
% 6.92/7.14 @ ( collect_nat
% 6.92/7.14 @ ^ [X4: nat] :
% 6.92/7.14 ( ( member_nat @ X4 @ B5 )
% 6.92/7.14 & ( Q2 @ X4 ) ) )
% 6.92/7.14 @ ( collect_nat
% 6.92/7.14 @ ^ [X4: nat] :
% 6.92/7.14 ( ( member_nat @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_CollectI
% 6.92/7.14 thf(fact_834_subset__CollectI,axiom,
% 6.92/7.14 ! [B5: set_int,A4: set_int,Q2: int > $o,P2: int > $o] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 6.92/7.14 => ( ! [X3: int] :
% 6.92/7.14 ( ( member_int @ X3 @ B5 )
% 6.92/7.14 => ( ( Q2 @ X3 )
% 6.92/7.14 => ( P2 @ X3 ) ) )
% 6.92/7.14 => ( ord_less_eq_set_int
% 6.92/7.14 @ ( collect_int
% 6.92/7.14 @ ^ [X4: int] :
% 6.92/7.14 ( ( member_int @ X4 @ B5 )
% 6.92/7.14 & ( Q2 @ X4 ) ) )
% 6.92/7.14 @ ( collect_int
% 6.92/7.14 @ ^ [X4: int] :
% 6.92/7.14 ( ( member_int @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_CollectI
% 6.92/7.14 thf(fact_835_conj__subset__def,axiom,
% 6.92/7.14 ! [A4: set_list_nat,P2: list_nat > $o,Q2: list_nat > $o] :
% 6.92/7.14 ( ( ord_le6045566169113846134st_nat @ A4
% 6.92/7.14 @ ( collect_list_nat
% 6.92/7.14 @ ^ [X4: list_nat] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 & ( Q2 @ X4 ) ) ) )
% 6.92/7.14 = ( ( ord_le6045566169113846134st_nat @ A4 @ ( collect_list_nat @ P2 ) )
% 6.92/7.14 & ( ord_le6045566169113846134st_nat @ A4 @ ( collect_list_nat @ Q2 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % conj_subset_def
% 6.92/7.14 thf(fact_836_conj__subset__def,axiom,
% 6.92/7.14 ! [A4: set_se6260736226359567993nt_int,P2: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.14 ( ( ord_le483042692224249369nt_int @ A4
% 6.92/7.14 @ ( collec5210948495886036740nt_int
% 6.92/7.14 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 & ( Q2 @ X4 ) ) ) )
% 6.92/7.14 = ( ( ord_le483042692224249369nt_int @ A4 @ ( collec5210948495886036740nt_int @ P2 ) )
% 6.92/7.14 & ( ord_le483042692224249369nt_int @ A4 @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % conj_subset_def
% 6.92/7.14 thf(fact_837_conj__subset__def,axiom,
% 6.92/7.14 ! [A4: set_set_nat,P2: set_nat > $o,Q2: set_nat > $o] :
% 6.92/7.14 ( ( ord_le6893508408891458716et_nat @ A4
% 6.92/7.14 @ ( collect_set_nat
% 6.92/7.14 @ ^ [X4: set_nat] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 & ( Q2 @ X4 ) ) ) )
% 6.92/7.14 = ( ( ord_le6893508408891458716et_nat @ A4 @ ( collect_set_nat @ P2 ) )
% 6.92/7.14 & ( ord_le6893508408891458716et_nat @ A4 @ ( collect_set_nat @ Q2 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % conj_subset_def
% 6.92/7.14 thf(fact_838_conj__subset__def,axiom,
% 6.92/7.14 ! [A4: set_nat,P2: nat > $o,Q2: nat > $o] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ A4
% 6.92/7.14 @ ( collect_nat
% 6.92/7.14 @ ^ [X4: nat] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 & ( Q2 @ X4 ) ) ) )
% 6.92/7.14 = ( ( ord_less_eq_set_nat @ A4 @ ( collect_nat @ P2 ) )
% 6.92/7.14 & ( ord_less_eq_set_nat @ A4 @ ( collect_nat @ Q2 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % conj_subset_def
% 6.92/7.14 thf(fact_839_conj__subset__def,axiom,
% 6.92/7.14 ! [A4: set_int,P2: int > $o,Q2: int > $o] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ A4
% 6.92/7.14 @ ( collect_int
% 6.92/7.14 @ ^ [X4: int] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 & ( Q2 @ X4 ) ) ) )
% 6.92/7.14 = ( ( ord_less_eq_set_int @ A4 @ ( collect_int @ P2 ) )
% 6.92/7.14 & ( ord_less_eq_set_int @ A4 @ ( collect_int @ Q2 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % conj_subset_def
% 6.92/7.14 thf(fact_840_UnCI,axiom,
% 6.92/7.14 ! [C2: $o,B5: set_o,A4: set_o] :
% 6.92/7.14 ( ( ~ ( member_o @ C2 @ B5 )
% 6.92/7.14 => ( member_o @ C2 @ A4 ) )
% 6.92/7.14 => ( member_o @ C2 @ ( sup_sup_set_o @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnCI
% 6.92/7.14 thf(fact_841_UnCI,axiom,
% 6.92/7.14 ! [C2: set_Pr958786334691620121nt_int,B5: set_se6260736226359567993nt_int,A4: set_se6260736226359567993nt_int] :
% 6.92/7.14 ( ( ~ ( member2340774599025711042nt_int @ C2 @ B5 )
% 6.92/7.14 => ( member2340774599025711042nt_int @ C2 @ A4 ) )
% 6.92/7.14 => ( member2340774599025711042nt_int @ C2 @ ( sup_su2047564715030645325nt_int @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnCI
% 6.92/7.14 thf(fact_842_UnCI,axiom,
% 6.92/7.14 ! [C2: set_nat,B5: set_set_nat,A4: set_set_nat] :
% 6.92/7.14 ( ( ~ ( member_set_nat @ C2 @ B5 )
% 6.92/7.14 => ( member_set_nat @ C2 @ A4 ) )
% 6.92/7.14 => ( member_set_nat @ C2 @ ( sup_sup_set_set_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnCI
% 6.92/7.14 thf(fact_843_UnCI,axiom,
% 6.92/7.14 ! [C2: int,B5: set_int,A4: set_int] :
% 6.92/7.14 ( ( ~ ( member_int @ C2 @ B5 )
% 6.92/7.14 => ( member_int @ C2 @ A4 ) )
% 6.92/7.14 => ( member_int @ C2 @ ( sup_sup_set_int @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnCI
% 6.92/7.14 thf(fact_844_UnCI,axiom,
% 6.92/7.14 ! [C2: produc4166570645942440679at_nat,B5: set_Pr8551490117392284871at_nat,A4: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( ~ ( member6689249552917799696at_nat @ C2 @ B5 )
% 6.92/7.14 => ( member6689249552917799696at_nat @ C2 @ A4 ) )
% 6.92/7.14 => ( member6689249552917799696at_nat @ C2 @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnCI
% 6.92/7.14 thf(fact_845_UnCI,axiom,
% 6.92/7.14 ! [C2: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( ~ ( member8757157785044589968at_nat @ C2 @ B5 )
% 6.92/7.14 => ( member8757157785044589968at_nat @ C2 @ A4 ) )
% 6.92/7.14 => ( member8757157785044589968at_nat @ C2 @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnCI
% 6.92/7.14 thf(fact_846_UnCI,axiom,
% 6.92/7.14 ! [C2: nat,B5: set_nat,A4: set_nat] :
% 6.92/7.14 ( ( ~ ( member_nat @ C2 @ B5 )
% 6.92/7.14 => ( member_nat @ C2 @ A4 ) )
% 6.92/7.14 => ( member_nat @ C2 @ ( sup_sup_set_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnCI
% 6.92/7.14 thf(fact_847_Un__iff,axiom,
% 6.92/7.14 ! [C2: $o,A4: set_o,B5: set_o] :
% 6.92/7.14 ( ( member_o @ C2 @ ( sup_sup_set_o @ A4 @ B5 ) )
% 6.92/7.14 = ( ( member_o @ C2 @ A4 )
% 6.92/7.14 | ( member_o @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_iff
% 6.92/7.14 thf(fact_848_Un__iff,axiom,
% 6.92/7.14 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.14 ( ( member2340774599025711042nt_int @ C2 @ ( sup_su2047564715030645325nt_int @ A4 @ B5 ) )
% 6.92/7.14 = ( ( member2340774599025711042nt_int @ C2 @ A4 )
% 6.92/7.14 | ( member2340774599025711042nt_int @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_iff
% 6.92/7.14 thf(fact_849_Un__iff,axiom,
% 6.92/7.14 ! [C2: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.14 ( ( member_set_nat @ C2 @ ( sup_sup_set_set_nat @ A4 @ B5 ) )
% 6.92/7.14 = ( ( member_set_nat @ C2 @ A4 )
% 6.92/7.14 | ( member_set_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_iff
% 6.92/7.14 thf(fact_850_Un__iff,axiom,
% 6.92/7.14 ! [C2: int,A4: set_int,B5: set_int] :
% 6.92/7.14 ( ( member_int @ C2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.92/7.14 = ( ( member_int @ C2 @ A4 )
% 6.92/7.14 | ( member_int @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_iff
% 6.92/7.14 thf(fact_851_Un__iff,axiom,
% 6.92/7.14 ! [C2: produc4166570645942440679at_nat,A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( member6689249552917799696at_nat @ C2 @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) )
% 6.92/7.14 = ( ( member6689249552917799696at_nat @ C2 @ A4 )
% 6.92/7.14 | ( member6689249552917799696at_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_iff
% 6.92/7.14 thf(fact_852_Un__iff,axiom,
% 6.92/7.14 ! [C2: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( member8757157785044589968at_nat @ C2 @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 6.92/7.14 = ( ( member8757157785044589968at_nat @ C2 @ A4 )
% 6.92/7.14 | ( member8757157785044589968at_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_iff
% 6.92/7.14 thf(fact_853_Un__iff,axiom,
% 6.92/7.14 ! [C2: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.14 ( ( member_nat @ C2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.92/7.14 = ( ( member_nat @ C2 @ A4 )
% 6.92/7.14 | ( member_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_iff
% 6.92/7.14 thf(fact_854_nat__add__left__cancel__less,axiom,
% 6.92/7.14 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.14 ( ( ord_less_nat @ ( plus_plus_nat @ K2 @ M ) @ ( plus_plus_nat @ K2 @ N2 ) )
% 6.92/7.14 = ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % nat_add_left_cancel_less
% 6.92/7.14 thf(fact_855_Un__subset__iff,axiom,
% 6.92/7.14 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.14 = ( ( ord_le8081472938463900775at_nat @ A4 @ C4 )
% 6.92/7.14 & ( ord_le8081472938463900775at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_subset_iff
% 6.92/7.14 thf(fact_856_Un__subset__iff,axiom,
% 6.92/7.14 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.14 = ( ( ord_le1268244103169919719at_nat @ A4 @ C4 )
% 6.92/7.14 & ( ord_le1268244103169919719at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_subset_iff
% 6.92/7.14 thf(fact_857_Un__subset__iff,axiom,
% 6.92/7.14 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.14 = ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.92/7.14 & ( ord_less_eq_set_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_subset_iff
% 6.92/7.14 thf(fact_858_Un__subset__iff,axiom,
% 6.92/7.14 ! [A4: set_int,B5: set_int,C4: set_int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ ( sup_sup_set_int @ A4 @ B5 ) @ C4 )
% 6.92/7.14 = ( ( ord_less_eq_set_int @ A4 @ C4 )
% 6.92/7.14 & ( ord_less_eq_set_int @ B5 @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_subset_iff
% 6.92/7.14 thf(fact_859_nat__add__left__cancel__le,axiom,
% 6.92/7.14 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.14 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K2 @ M ) @ ( plus_plus_nat @ K2 @ N2 ) )
% 6.92/7.14 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % nat_add_left_cancel_le
% 6.92/7.14 thf(fact_860_sup__Some,axiom,
% 6.92/7.14 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su5873096292857799009at_nat @ ( some_s287724117700012716at_nat @ X ) @ ( some_s287724117700012716at_nat @ Y ) )
% 6.92/7.14 = ( some_s287724117700012716at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_Some
% 6.92/7.14 thf(fact_861_sup__Some,axiom,
% 6.92/7.14 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su2273273666271716065at_nat @ ( some_s5890477192898017836at_nat @ X ) @ ( some_s5890477192898017836at_nat @ Y ) )
% 6.92/7.14 = ( some_s5890477192898017836at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_Some
% 6.92/7.14 thf(fact_862_sup__Some,axiom,
% 6.92/7.14 ! [X: set_nat,Y: set_nat] :
% 6.92/7.14 ( ( sup_su3598758113090618626et_nat @ ( some_set_nat @ X ) @ ( some_set_nat @ Y ) )
% 6.92/7.14 = ( some_set_nat @ ( sup_sup_set_nat @ X @ Y ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_Some
% 6.92/7.14 thf(fact_863_sup__Some,axiom,
% 6.92/7.14 ! [X: nat,Y: nat] :
% 6.92/7.14 ( ( sup_sup_option_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 6.92/7.14 = ( some_nat @ ( sup_sup_nat @ X @ Y ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_Some
% 6.92/7.14 thf(fact_864_sup__Some,axiom,
% 6.92/7.14 ! [X: int,Y: int] :
% 6.92/7.14 ( ( sup_sup_option_int @ ( some_int @ X ) @ ( some_int @ Y ) )
% 6.92/7.14 = ( some_int @ ( sup_sup_int @ X @ Y ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_Some
% 6.92/7.14 thf(fact_865_relH__dist__union,axiom,
% 6.92/7.14 ! [As: set_nat,As5: set_nat,H: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 6.92/7.14 ( ( relH @ ( sup_sup_set_nat @ As @ As5 ) @ H @ H5 )
% 6.92/7.14 = ( ( relH @ As @ H @ H5 )
% 6.92/7.14 & ( relH @ As5 @ H @ H5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % relH_dist_union
% 6.92/7.14 thf(fact_866_psubsetD,axiom,
% 6.92/7.14 ! [A4: set_o,B5: set_o,C2: $o] :
% 6.92/7.14 ( ( ord_less_set_o @ A4 @ B5 )
% 6.92/7.14 => ( ( member_o @ C2 @ A4 )
% 6.92/7.14 => ( member_o @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % psubsetD
% 6.92/7.14 thf(fact_867_psubsetD,axiom,
% 6.92/7.14 ! [A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int,C2: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( ord_le1924305788584680229nt_int @ A4 @ B5 )
% 6.92/7.14 => ( ( member2340774599025711042nt_int @ C2 @ A4 )
% 6.92/7.14 => ( member2340774599025711042nt_int @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % psubsetD
% 6.92/7.14 thf(fact_868_psubsetD,axiom,
% 6.92/7.14 ! [A4: set_set_nat,B5: set_set_nat,C2: set_nat] :
% 6.92/7.14 ( ( ord_less_set_set_nat @ A4 @ B5 )
% 6.92/7.14 => ( ( member_set_nat @ C2 @ A4 )
% 6.92/7.14 => ( member_set_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % psubsetD
% 6.92/7.14 thf(fact_869_psubsetD,axiom,
% 6.92/7.14 ! [A4: set_nat,B5: set_nat,C2: nat] :
% 6.92/7.14 ( ( ord_less_set_nat @ A4 @ B5 )
% 6.92/7.14 => ( ( member_nat @ C2 @ A4 )
% 6.92/7.14 => ( member_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % psubsetD
% 6.92/7.14 thf(fact_870_psubsetD,axiom,
% 6.92/7.14 ! [A4: set_int,B5: set_int,C2: int] :
% 6.92/7.14 ( ( ord_less_set_int @ A4 @ B5 )
% 6.92/7.14 => ( ( member_int @ C2 @ A4 )
% 6.92/7.14 => ( member_int @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % psubsetD
% 6.92/7.14 thf(fact_871_less__set__def,axiom,
% 6.92/7.14 ( ord_less_set_o
% 6.92/7.14 = ( ^ [A6: set_o,B6: set_o] :
% 6.92/7.14 ( ord_less_o_o
% 6.92/7.14 @ ^ [X4: $o] : ( member_o @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: $o] : ( member_o @ X4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % less_set_def
% 6.92/7.14 thf(fact_872_less__set__def,axiom,
% 6.92/7.14 ( ord_le1924305788584680229nt_int
% 6.92/7.14 = ( ^ [A6: set_se6260736226359567993nt_int,B6: set_se6260736226359567993nt_int] :
% 6.92/7.14 ( ord_le2688692977766382584_int_o
% 6.92/7.14 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % less_set_def
% 6.92/7.14 thf(fact_873_less__set__def,axiom,
% 6.92/7.14 ( ord_less_set_set_nat
% 6.92/7.14 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 6.92/7.14 ( ord_less_set_nat_o
% 6.92/7.14 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % less_set_def
% 6.92/7.14 thf(fact_874_less__set__def,axiom,
% 6.92/7.14 ( ord_less_set_nat
% 6.92/7.14 = ( ^ [A6: set_nat,B6: set_nat] :
% 6.92/7.14 ( ord_less_nat_o
% 6.92/7.14 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % less_set_def
% 6.92/7.14 thf(fact_875_less__set__def,axiom,
% 6.92/7.14 ( ord_less_set_int
% 6.92/7.14 = ( ^ [A6: set_int,B6: set_int] :
% 6.92/7.14 ( ord_less_int_o
% 6.92/7.14 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % less_set_def
% 6.92/7.14 thf(fact_876_UnE,axiom,
% 6.92/7.14 ! [C2: $o,A4: set_o,B5: set_o] :
% 6.92/7.14 ( ( member_o @ C2 @ ( sup_sup_set_o @ A4 @ B5 ) )
% 6.92/7.14 => ( ~ ( member_o @ C2 @ A4 )
% 6.92/7.14 => ( member_o @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnE
% 6.92/7.14 thf(fact_877_UnE,axiom,
% 6.92/7.14 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.14 ( ( member2340774599025711042nt_int @ C2 @ ( sup_su2047564715030645325nt_int @ A4 @ B5 ) )
% 6.92/7.14 => ( ~ ( member2340774599025711042nt_int @ C2 @ A4 )
% 6.92/7.14 => ( member2340774599025711042nt_int @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnE
% 6.92/7.14 thf(fact_878_UnE,axiom,
% 6.92/7.14 ! [C2: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.14 ( ( member_set_nat @ C2 @ ( sup_sup_set_set_nat @ A4 @ B5 ) )
% 6.92/7.14 => ( ~ ( member_set_nat @ C2 @ A4 )
% 6.92/7.14 => ( member_set_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnE
% 6.92/7.14 thf(fact_879_UnE,axiom,
% 6.92/7.14 ! [C2: int,A4: set_int,B5: set_int] :
% 6.92/7.14 ( ( member_int @ C2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.92/7.14 => ( ~ ( member_int @ C2 @ A4 )
% 6.92/7.14 => ( member_int @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnE
% 6.92/7.14 thf(fact_880_UnE,axiom,
% 6.92/7.14 ! [C2: produc4166570645942440679at_nat,A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( member6689249552917799696at_nat @ C2 @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) )
% 6.92/7.14 => ( ~ ( member6689249552917799696at_nat @ C2 @ A4 )
% 6.92/7.14 => ( member6689249552917799696at_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnE
% 6.92/7.14 thf(fact_881_UnE,axiom,
% 6.92/7.14 ! [C2: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( member8757157785044589968at_nat @ C2 @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 6.92/7.14 => ( ~ ( member8757157785044589968at_nat @ C2 @ A4 )
% 6.92/7.14 => ( member8757157785044589968at_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnE
% 6.92/7.14 thf(fact_882_UnE,axiom,
% 6.92/7.14 ! [C2: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.14 ( ( member_nat @ C2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.92/7.14 => ( ~ ( member_nat @ C2 @ A4 )
% 6.92/7.14 => ( member_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnE
% 6.92/7.14 thf(fact_883_UnI1,axiom,
% 6.92/7.14 ! [C2: $o,A4: set_o,B5: set_o] :
% 6.92/7.14 ( ( member_o @ C2 @ A4 )
% 6.92/7.14 => ( member_o @ C2 @ ( sup_sup_set_o @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnI1
% 6.92/7.14 thf(fact_884_UnI1,axiom,
% 6.92/7.14 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.14 ( ( member2340774599025711042nt_int @ C2 @ A4 )
% 6.92/7.14 => ( member2340774599025711042nt_int @ C2 @ ( sup_su2047564715030645325nt_int @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnI1
% 6.92/7.14 thf(fact_885_UnI1,axiom,
% 6.92/7.14 ! [C2: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.14 ( ( member_set_nat @ C2 @ A4 )
% 6.92/7.14 => ( member_set_nat @ C2 @ ( sup_sup_set_set_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnI1
% 6.92/7.14 thf(fact_886_UnI1,axiom,
% 6.92/7.14 ! [C2: int,A4: set_int,B5: set_int] :
% 6.92/7.14 ( ( member_int @ C2 @ A4 )
% 6.92/7.14 => ( member_int @ C2 @ ( sup_sup_set_int @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnI1
% 6.92/7.14 thf(fact_887_UnI1,axiom,
% 6.92/7.14 ! [C2: produc4166570645942440679at_nat,A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( member6689249552917799696at_nat @ C2 @ A4 )
% 6.92/7.14 => ( member6689249552917799696at_nat @ C2 @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnI1
% 6.92/7.14 thf(fact_888_UnI1,axiom,
% 6.92/7.14 ! [C2: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( member8757157785044589968at_nat @ C2 @ A4 )
% 6.92/7.14 => ( member8757157785044589968at_nat @ C2 @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnI1
% 6.92/7.14 thf(fact_889_UnI1,axiom,
% 6.92/7.14 ! [C2: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.14 ( ( member_nat @ C2 @ A4 )
% 6.92/7.14 => ( member_nat @ C2 @ ( sup_sup_set_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnI1
% 6.92/7.14 thf(fact_890_UnI2,axiom,
% 6.92/7.14 ! [C2: $o,B5: set_o,A4: set_o] :
% 6.92/7.14 ( ( member_o @ C2 @ B5 )
% 6.92/7.14 => ( member_o @ C2 @ ( sup_sup_set_o @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnI2
% 6.92/7.14 thf(fact_891_UnI2,axiom,
% 6.92/7.14 ! [C2: set_Pr958786334691620121nt_int,B5: set_se6260736226359567993nt_int,A4: set_se6260736226359567993nt_int] :
% 6.92/7.14 ( ( member2340774599025711042nt_int @ C2 @ B5 )
% 6.92/7.14 => ( member2340774599025711042nt_int @ C2 @ ( sup_su2047564715030645325nt_int @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnI2
% 6.92/7.14 thf(fact_892_UnI2,axiom,
% 6.92/7.14 ! [C2: set_nat,B5: set_set_nat,A4: set_set_nat] :
% 6.92/7.14 ( ( member_set_nat @ C2 @ B5 )
% 6.92/7.14 => ( member_set_nat @ C2 @ ( sup_sup_set_set_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnI2
% 6.92/7.14 thf(fact_893_UnI2,axiom,
% 6.92/7.14 ! [C2: int,B5: set_int,A4: set_int] :
% 6.92/7.14 ( ( member_int @ C2 @ B5 )
% 6.92/7.14 => ( member_int @ C2 @ ( sup_sup_set_int @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnI2
% 6.92/7.14 thf(fact_894_UnI2,axiom,
% 6.92/7.14 ! [C2: produc4166570645942440679at_nat,B5: set_Pr8551490117392284871at_nat,A4: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( member6689249552917799696at_nat @ C2 @ B5 )
% 6.92/7.14 => ( member6689249552917799696at_nat @ C2 @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnI2
% 6.92/7.14 thf(fact_895_UnI2,axiom,
% 6.92/7.14 ! [C2: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( member8757157785044589968at_nat @ C2 @ B5 )
% 6.92/7.14 => ( member8757157785044589968at_nat @ C2 @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnI2
% 6.92/7.14 thf(fact_896_UnI2,axiom,
% 6.92/7.14 ! [C2: nat,B5: set_nat,A4: set_nat] :
% 6.92/7.14 ( ( member_nat @ C2 @ B5 )
% 6.92/7.14 => ( member_nat @ C2 @ ( sup_sup_set_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % UnI2
% 6.92/7.14 thf(fact_897_bex__Un,axiom,
% 6.92/7.14 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,P2: produc4166570645942440679at_nat > $o] :
% 6.92/7.14 ( ( ? [X4: produc4166570645942440679at_nat] :
% 6.92/7.14 ( ( member6689249552917799696at_nat @ X4 @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) )
% 6.92/7.14 & ( P2 @ X4 ) ) )
% 6.92/7.14 = ( ? [X4: produc4166570645942440679at_nat] :
% 6.92/7.14 ( ( member6689249552917799696at_nat @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) )
% 6.92/7.14 | ? [X4: produc4166570645942440679at_nat] :
% 6.92/7.14 ( ( member6689249552917799696at_nat @ X4 @ B5 )
% 6.92/7.14 & ( P2 @ X4 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % bex_Un
% 6.92/7.14 thf(fact_898_bex__Un,axiom,
% 6.92/7.14 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,P2: produc3843707927480180839at_nat > $o] :
% 6.92/7.14 ( ( ? [X4: produc3843707927480180839at_nat] :
% 6.92/7.14 ( ( member8757157785044589968at_nat @ X4 @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 6.92/7.14 & ( P2 @ X4 ) ) )
% 6.92/7.14 = ( ? [X4: produc3843707927480180839at_nat] :
% 6.92/7.14 ( ( member8757157785044589968at_nat @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) )
% 6.92/7.14 | ? [X4: produc3843707927480180839at_nat] :
% 6.92/7.14 ( ( member8757157785044589968at_nat @ X4 @ B5 )
% 6.92/7.14 & ( P2 @ X4 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % bex_Un
% 6.92/7.14 thf(fact_899_bex__Un,axiom,
% 6.92/7.14 ! [A4: set_nat,B5: set_nat,P2: nat > $o] :
% 6.92/7.14 ( ( ? [X4: nat] :
% 6.92/7.14 ( ( member_nat @ X4 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.92/7.14 & ( P2 @ X4 ) ) )
% 6.92/7.14 = ( ? [X4: nat] :
% 6.92/7.14 ( ( member_nat @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) )
% 6.92/7.14 | ? [X4: nat] :
% 6.92/7.14 ( ( member_nat @ X4 @ B5 )
% 6.92/7.14 & ( P2 @ X4 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % bex_Un
% 6.92/7.14 thf(fact_900_ball__Un,axiom,
% 6.92/7.14 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,P2: produc4166570645942440679at_nat > $o] :
% 6.92/7.14 ( ( ! [X4: produc4166570645942440679at_nat] :
% 6.92/7.14 ( ( member6689249552917799696at_nat @ X4 @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) )
% 6.92/7.14 => ( P2 @ X4 ) ) )
% 6.92/7.14 = ( ! [X4: produc4166570645942440679at_nat] :
% 6.92/7.14 ( ( member6689249552917799696at_nat @ X4 @ A4 )
% 6.92/7.14 => ( P2 @ X4 ) )
% 6.92/7.14 & ! [X4: produc4166570645942440679at_nat] :
% 6.92/7.14 ( ( member6689249552917799696at_nat @ X4 @ B5 )
% 6.92/7.14 => ( P2 @ X4 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % ball_Un
% 6.92/7.14 thf(fact_901_ball__Un,axiom,
% 6.92/7.14 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,P2: produc3843707927480180839at_nat > $o] :
% 6.92/7.14 ( ( ! [X4: produc3843707927480180839at_nat] :
% 6.92/7.14 ( ( member8757157785044589968at_nat @ X4 @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 6.92/7.14 => ( P2 @ X4 ) ) )
% 6.92/7.14 = ( ! [X4: produc3843707927480180839at_nat] :
% 6.92/7.14 ( ( member8757157785044589968at_nat @ X4 @ A4 )
% 6.92/7.14 => ( P2 @ X4 ) )
% 6.92/7.14 & ! [X4: produc3843707927480180839at_nat] :
% 6.92/7.14 ( ( member8757157785044589968at_nat @ X4 @ B5 )
% 6.92/7.14 => ( P2 @ X4 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % ball_Un
% 6.92/7.14 thf(fact_902_ball__Un,axiom,
% 6.92/7.14 ! [A4: set_nat,B5: set_nat,P2: nat > $o] :
% 6.92/7.14 ( ( ! [X4: nat] :
% 6.92/7.14 ( ( member_nat @ X4 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.92/7.14 => ( P2 @ X4 ) ) )
% 6.92/7.14 = ( ! [X4: nat] :
% 6.92/7.14 ( ( member_nat @ X4 @ A4 )
% 6.92/7.14 => ( P2 @ X4 ) )
% 6.92/7.14 & ! [X4: nat] :
% 6.92/7.14 ( ( member_nat @ X4 @ B5 )
% 6.92/7.14 => ( P2 @ X4 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % ball_Un
% 6.92/7.14 thf(fact_903_Un__assoc,axiom,
% 6.92/7.14 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.14 = ( sup_su3035147773818789531at_nat @ A4 @ ( sup_su3035147773818789531at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_assoc
% 6.92/7.14 thf(fact_904_Un__assoc,axiom,
% 6.92/7.14 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.14 = ( sup_su5525570899277871387at_nat @ A4 @ ( sup_su5525570899277871387at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_assoc
% 6.92/7.14 thf(fact_905_Un__assoc,axiom,
% 6.92/7.14 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.14 = ( sup_sup_set_nat @ A4 @ ( sup_sup_set_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_assoc
% 6.92/7.14 thf(fact_906_Un__absorb,axiom,
% 6.92/7.14 ! [A4: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ A4 @ A4 )
% 6.92/7.14 = A4 ) ).
% 6.92/7.14
% 6.92/7.14 % Un_absorb
% 6.92/7.14 thf(fact_907_Un__absorb,axiom,
% 6.92/7.14 ! [A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ A4 @ A4 )
% 6.92/7.14 = A4 ) ).
% 6.92/7.14
% 6.92/7.14 % Un_absorb
% 6.92/7.14 thf(fact_908_Un__absorb,axiom,
% 6.92/7.14 ! [A4: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ A4 @ A4 )
% 6.92/7.14 = A4 ) ).
% 6.92/7.14
% 6.92/7.14 % Un_absorb
% 6.92/7.14 thf(fact_909_Un__commute,axiom,
% 6.92/7.14 ( sup_su3035147773818789531at_nat
% 6.92/7.14 = ( ^ [A6: set_Pr8551490117392284871at_nat,B6: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ B6 @ A6 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_commute
% 6.92/7.14 thf(fact_910_Un__commute,axiom,
% 6.92/7.14 ( sup_su5525570899277871387at_nat
% 6.92/7.14 = ( ^ [A6: set_Pr4329608150637261639at_nat,B6: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ B6 @ A6 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_commute
% 6.92/7.14 thf(fact_911_Un__commute,axiom,
% 6.92/7.14 ( sup_sup_set_nat
% 6.92/7.14 = ( ^ [A6: set_nat,B6: set_nat] : ( sup_sup_set_nat @ B6 @ A6 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_commute
% 6.92/7.14 thf(fact_912_Un__left__absorb,axiom,
% 6.92/7.14 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ A4 @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) )
% 6.92/7.14 = ( sup_su3035147773818789531at_nat @ A4 @ B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_left_absorb
% 6.92/7.14 thf(fact_913_Un__left__absorb,axiom,
% 6.92/7.14 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ A4 @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 6.92/7.14 = ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_left_absorb
% 6.92/7.14 thf(fact_914_Un__left__absorb,axiom,
% 6.92/7.14 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ A4 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.92/7.14 = ( sup_sup_set_nat @ A4 @ B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_left_absorb
% 6.92/7.14 thf(fact_915_Un__left__commute,axiom,
% 6.92/7.14 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ A4 @ ( sup_su3035147773818789531at_nat @ B5 @ C4 ) )
% 6.92/7.14 = ( sup_su3035147773818789531at_nat @ B5 @ ( sup_su3035147773818789531at_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_left_commute
% 6.92/7.14 thf(fact_916_Un__left__commute,axiom,
% 6.92/7.14 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ A4 @ ( sup_su5525570899277871387at_nat @ B5 @ C4 ) )
% 6.92/7.14 = ( sup_su5525570899277871387at_nat @ B5 @ ( sup_su5525570899277871387at_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_left_commute
% 6.92/7.14 thf(fact_917_Un__left__commute,axiom,
% 6.92/7.14 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ A4 @ ( sup_sup_set_nat @ B5 @ C4 ) )
% 6.92/7.14 = ( sup_sup_set_nat @ B5 @ ( sup_sup_set_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_left_commute
% 6.92/7.14 thf(fact_918_Collect__disj__eq,axiom,
% 6.92/7.14 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 6.92/7.14 ( ( collect_list_nat
% 6.92/7.14 @ ^ [X4: list_nat] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 | ( Q2 @ X4 ) ) )
% 6.92/7.14 = ( sup_sup_set_list_nat @ ( collect_list_nat @ P2 ) @ ( collect_list_nat @ Q2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_disj_eq
% 6.92/7.14 thf(fact_919_Collect__disj__eq,axiom,
% 6.92/7.14 ! [P2: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.14 ( ( collec5210948495886036740nt_int
% 6.92/7.14 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 | ( Q2 @ X4 ) ) )
% 6.92/7.14 = ( sup_su2047564715030645325nt_int @ ( collec5210948495886036740nt_int @ P2 ) @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_disj_eq
% 6.92/7.14 thf(fact_920_Collect__disj__eq,axiom,
% 6.92/7.14 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 6.92/7.14 ( ( collect_set_nat
% 6.92/7.14 @ ^ [X4: set_nat] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 | ( Q2 @ X4 ) ) )
% 6.92/7.14 = ( sup_sup_set_set_nat @ ( collect_set_nat @ P2 ) @ ( collect_set_nat @ Q2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_disj_eq
% 6.92/7.14 thf(fact_921_Collect__disj__eq,axiom,
% 6.92/7.14 ! [P2: int > $o,Q2: int > $o] :
% 6.92/7.14 ( ( collect_int
% 6.92/7.14 @ ^ [X4: int] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 | ( Q2 @ X4 ) ) )
% 6.92/7.14 = ( sup_sup_set_int @ ( collect_int @ P2 ) @ ( collect_int @ Q2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_disj_eq
% 6.92/7.14 thf(fact_922_Collect__disj__eq,axiom,
% 6.92/7.14 ! [P2: produc4166570645942440679at_nat > $o,Q2: produc4166570645942440679at_nat > $o] :
% 6.92/7.14 ( ( collec5204685387357076818at_nat
% 6.92/7.14 @ ^ [X4: produc4166570645942440679at_nat] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 | ( Q2 @ X4 ) ) )
% 6.92/7.14 = ( sup_su3035147773818789531at_nat @ ( collec5204685387357076818at_nat @ P2 ) @ ( collec5204685387357076818at_nat @ Q2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_disj_eq
% 6.92/7.14 thf(fact_923_Collect__disj__eq,axiom,
% 6.92/7.14 ! [P2: produc3843707927480180839at_nat > $o,Q2: produc3843707927480180839at_nat > $o] :
% 6.92/7.14 ( ( collec6321179662152712658at_nat
% 6.92/7.14 @ ^ [X4: produc3843707927480180839at_nat] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 | ( Q2 @ X4 ) ) )
% 6.92/7.14 = ( sup_su5525570899277871387at_nat @ ( collec6321179662152712658at_nat @ P2 ) @ ( collec6321179662152712658at_nat @ Q2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_disj_eq
% 6.92/7.14 thf(fact_924_Collect__disj__eq,axiom,
% 6.92/7.14 ! [P2: nat > $o,Q2: nat > $o] :
% 6.92/7.14 ( ( collect_nat
% 6.92/7.14 @ ^ [X4: nat] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 | ( Q2 @ X4 ) ) )
% 6.92/7.14 = ( sup_sup_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_disj_eq
% 6.92/7.14 thf(fact_925_Un__def,axiom,
% 6.92/7.14 ( sup_sup_set_o
% 6.92/7.14 = ( ^ [A6: set_o,B6: set_o] :
% 6.92/7.14 ( collect_o
% 6.92/7.14 @ ^ [X4: $o] :
% 6.92/7.14 ( ( member_o @ X4 @ A6 )
% 6.92/7.14 | ( member_o @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_def
% 6.92/7.14 thf(fact_926_Un__def,axiom,
% 6.92/7.14 ( sup_sup_set_list_nat
% 6.92/7.14 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 6.92/7.14 ( collect_list_nat
% 6.92/7.14 @ ^ [X4: list_nat] :
% 6.92/7.14 ( ( member_list_nat @ X4 @ A6 )
% 6.92/7.14 | ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_def
% 6.92/7.14 thf(fact_927_Un__def,axiom,
% 6.92/7.14 ( sup_su2047564715030645325nt_int
% 6.92/7.14 = ( ^ [A6: set_se6260736226359567993nt_int,B6: set_se6260736226359567993nt_int] :
% 6.92/7.14 ( collec5210948495886036740nt_int
% 6.92/7.14 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( member2340774599025711042nt_int @ X4 @ A6 )
% 6.92/7.14 | ( member2340774599025711042nt_int @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_def
% 6.92/7.14 thf(fact_928_Un__def,axiom,
% 6.92/7.14 ( sup_sup_set_set_nat
% 6.92/7.14 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 6.92/7.14 ( collect_set_nat
% 6.92/7.14 @ ^ [X4: set_nat] :
% 6.92/7.14 ( ( member_set_nat @ X4 @ A6 )
% 6.92/7.14 | ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_def
% 6.92/7.14 thf(fact_929_Un__def,axiom,
% 6.92/7.14 ( sup_sup_set_int
% 6.92/7.14 = ( ^ [A6: set_int,B6: set_int] :
% 6.92/7.14 ( collect_int
% 6.92/7.14 @ ^ [X4: int] :
% 6.92/7.14 ( ( member_int @ X4 @ A6 )
% 6.92/7.14 | ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_def
% 6.92/7.14 thf(fact_930_Un__def,axiom,
% 6.92/7.14 ( sup_su3035147773818789531at_nat
% 6.92/7.14 = ( ^ [A6: set_Pr8551490117392284871at_nat,B6: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( collec5204685387357076818at_nat
% 6.92/7.14 @ ^ [X4: produc4166570645942440679at_nat] :
% 6.92/7.14 ( ( member6689249552917799696at_nat @ X4 @ A6 )
% 6.92/7.14 | ( member6689249552917799696at_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_def
% 6.92/7.14 thf(fact_931_Un__def,axiom,
% 6.92/7.14 ( sup_su5525570899277871387at_nat
% 6.92/7.14 = ( ^ [A6: set_Pr4329608150637261639at_nat,B6: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( collec6321179662152712658at_nat
% 6.92/7.14 @ ^ [X4: produc3843707927480180839at_nat] :
% 6.92/7.14 ( ( member8757157785044589968at_nat @ X4 @ A6 )
% 6.92/7.14 | ( member8757157785044589968at_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_def
% 6.92/7.14 thf(fact_932_Un__def,axiom,
% 6.92/7.14 ( sup_sup_set_nat
% 6.92/7.14 = ( ^ [A6: set_nat,B6: set_nat] :
% 6.92/7.14 ( collect_nat
% 6.92/7.14 @ ^ [X4: nat] :
% 6.92/7.14 ( ( member_nat @ X4 @ A6 )
% 6.92/7.14 | ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_def
% 6.92/7.14 thf(fact_933_Un__mono,axiom,
% 6.92/7.14 ! [A4: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,D4: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( ord_le8081472938463900775at_nat @ A4 @ C4 )
% 6.92/7.14 => ( ( ord_le8081472938463900775at_nat @ B5 @ D4 )
% 6.92/7.14 => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) @ ( sup_su3035147773818789531at_nat @ C4 @ D4 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_mono
% 6.92/7.14 thf(fact_934_Un__mono,axiom,
% 6.92/7.14 ! [A4: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,D4: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( ord_le1268244103169919719at_nat @ A4 @ C4 )
% 6.92/7.14 => ( ( ord_le1268244103169919719at_nat @ B5 @ D4 )
% 6.92/7.14 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) @ ( sup_su5525570899277871387at_nat @ C4 @ D4 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_mono
% 6.92/7.14 thf(fact_935_Un__mono,axiom,
% 6.92/7.14 ! [A4: set_nat,C4: set_nat,B5: set_nat,D4: set_nat] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.92/7.14 => ( ( ord_less_eq_set_nat @ B5 @ D4 )
% 6.92/7.14 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A4 @ B5 ) @ ( sup_sup_set_nat @ C4 @ D4 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_mono
% 6.92/7.14 thf(fact_936_Un__mono,axiom,
% 6.92/7.14 ! [A4: set_int,C4: set_int,B5: set_int,D4: set_int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ A4 @ C4 )
% 6.92/7.14 => ( ( ord_less_eq_set_int @ B5 @ D4 )
% 6.92/7.14 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ A4 @ B5 ) @ ( sup_sup_set_int @ C4 @ D4 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_mono
% 6.92/7.14 thf(fact_937_Un__least,axiom,
% 6.92/7.14 ! [A4: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( ord_le8081472938463900775at_nat @ A4 @ C4 )
% 6.92/7.14 => ( ( ord_le8081472938463900775at_nat @ B5 @ C4 )
% 6.92/7.14 => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_least
% 6.92/7.14 thf(fact_938_Un__least,axiom,
% 6.92/7.14 ! [A4: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( ord_le1268244103169919719at_nat @ A4 @ C4 )
% 6.92/7.14 => ( ( ord_le1268244103169919719at_nat @ B5 @ C4 )
% 6.92/7.14 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_least
% 6.92/7.14 thf(fact_939_Un__least,axiom,
% 6.92/7.14 ! [A4: set_nat,C4: set_nat,B5: set_nat] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.92/7.14 => ( ( ord_less_eq_set_nat @ B5 @ C4 )
% 6.92/7.14 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A4 @ B5 ) @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_least
% 6.92/7.14 thf(fact_940_Un__least,axiom,
% 6.92/7.14 ! [A4: set_int,C4: set_int,B5: set_int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ A4 @ C4 )
% 6.92/7.14 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 6.92/7.14 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ A4 @ B5 ) @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_least
% 6.92/7.14 thf(fact_941_Un__upper1,axiom,
% 6.92/7.14 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ A4 @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_upper1
% 6.92/7.14 thf(fact_942_Un__upper1,axiom,
% 6.92/7.14 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ A4 @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_upper1
% 6.92/7.14 thf(fact_943_Un__upper1,axiom,
% 6.92/7.14 ! [A4: set_nat,B5: set_nat] : ( ord_less_eq_set_nat @ A4 @ ( sup_sup_set_nat @ A4 @ B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_upper1
% 6.92/7.14 thf(fact_944_Un__upper1,axiom,
% 6.92/7.14 ! [A4: set_int,B5: set_int] : ( ord_less_eq_set_int @ A4 @ ( sup_sup_set_int @ A4 @ B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_upper1
% 6.92/7.14 thf(fact_945_Un__upper2,axiom,
% 6.92/7.14 ! [B5: set_Pr8551490117392284871at_nat,A4: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ B5 @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_upper2
% 6.92/7.14 thf(fact_946_Un__upper2,axiom,
% 6.92/7.14 ! [B5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ B5 @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_upper2
% 6.92/7.14 thf(fact_947_Un__upper2,axiom,
% 6.92/7.14 ! [B5: set_nat,A4: set_nat] : ( ord_less_eq_set_nat @ B5 @ ( sup_sup_set_nat @ A4 @ B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_upper2
% 6.92/7.14 thf(fact_948_Un__upper2,axiom,
% 6.92/7.14 ! [B5: set_int,A4: set_int] : ( ord_less_eq_set_int @ B5 @ ( sup_sup_set_int @ A4 @ B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_upper2
% 6.92/7.14 thf(fact_949_Un__absorb1,axiom,
% 6.92/7.14 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( ord_le8081472938463900775at_nat @ A4 @ B5 )
% 6.92/7.14 => ( ( sup_su3035147773818789531at_nat @ A4 @ B5 )
% 6.92/7.14 = B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_absorb1
% 6.92/7.14 thf(fact_950_Un__absorb1,axiom,
% 6.92/7.14 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( ord_le1268244103169919719at_nat @ A4 @ B5 )
% 6.92/7.14 => ( ( sup_su5525570899277871387at_nat @ A4 @ B5 )
% 6.92/7.14 = B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_absorb1
% 6.92/7.14 thf(fact_951_Un__absorb1,axiom,
% 6.92/7.14 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.92/7.14 => ( ( sup_sup_set_nat @ A4 @ B5 )
% 6.92/7.14 = B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_absorb1
% 6.92/7.14 thf(fact_952_Un__absorb1,axiom,
% 6.92/7.14 ! [A4: set_int,B5: set_int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.14 => ( ( sup_sup_set_int @ A4 @ B5 )
% 6.92/7.14 = B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_absorb1
% 6.92/7.14 thf(fact_953_Un__absorb2,axiom,
% 6.92/7.14 ! [B5: set_Pr8551490117392284871at_nat,A4: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( ord_le8081472938463900775at_nat @ B5 @ A4 )
% 6.92/7.14 => ( ( sup_su3035147773818789531at_nat @ A4 @ B5 )
% 6.92/7.14 = A4 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_absorb2
% 6.92/7.14 thf(fact_954_Un__absorb2,axiom,
% 6.92/7.14 ! [B5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( ord_le1268244103169919719at_nat @ B5 @ A4 )
% 6.92/7.14 => ( ( sup_su5525570899277871387at_nat @ A4 @ B5 )
% 6.92/7.14 = A4 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_absorb2
% 6.92/7.14 thf(fact_955_Un__absorb2,axiom,
% 6.92/7.14 ! [B5: set_nat,A4: set_nat] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 6.92/7.14 => ( ( sup_sup_set_nat @ A4 @ B5 )
% 6.92/7.14 = A4 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_absorb2
% 6.92/7.14 thf(fact_956_Un__absorb2,axiom,
% 6.92/7.14 ! [B5: set_int,A4: set_int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 6.92/7.14 => ( ( sup_sup_set_int @ A4 @ B5 )
% 6.92/7.14 = A4 ) ) ).
% 6.92/7.14
% 6.92/7.14 % Un_absorb2
% 6.92/7.14 thf(fact_957_subset__UnE,axiom,
% 6.92/7.14 ! [C4: set_Pr8551490117392284871at_nat,A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( ord_le8081472938463900775at_nat @ C4 @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) )
% 6.92/7.14 => ~ ! [A7: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( ord_le8081472938463900775at_nat @ A7 @ A4 )
% 6.92/7.14 => ! [B7: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( ord_le8081472938463900775at_nat @ B7 @ B5 )
% 6.92/7.14 => ( C4
% 6.92/7.14 != ( sup_su3035147773818789531at_nat @ A7 @ B7 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_UnE
% 6.92/7.14 thf(fact_958_subset__UnE,axiom,
% 6.92/7.14 ! [C4: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( ord_le1268244103169919719at_nat @ C4 @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 6.92/7.14 => ~ ! [A7: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( ord_le1268244103169919719at_nat @ A7 @ A4 )
% 6.92/7.14 => ! [B7: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( ord_le1268244103169919719at_nat @ B7 @ B5 )
% 6.92/7.14 => ( C4
% 6.92/7.14 != ( sup_su5525570899277871387at_nat @ A7 @ B7 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_UnE
% 6.92/7.14 thf(fact_959_subset__UnE,axiom,
% 6.92/7.14 ! [C4: set_nat,A4: set_nat,B5: set_nat] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ C4 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.92/7.14 => ~ ! [A7: set_nat] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ A7 @ A4 )
% 6.92/7.14 => ! [B7: set_nat] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ B7 @ B5 )
% 6.92/7.14 => ( C4
% 6.92/7.14 != ( sup_sup_set_nat @ A7 @ B7 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_UnE
% 6.92/7.14 thf(fact_960_subset__UnE,axiom,
% 6.92/7.14 ! [C4: set_int,A4: set_int,B5: set_int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ C4 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.92/7.14 => ~ ! [A7: set_int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ A7 @ A4 )
% 6.92/7.14 => ! [B7: set_int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ B7 @ B5 )
% 6.92/7.14 => ( C4
% 6.92/7.14 != ( sup_sup_set_int @ A7 @ B7 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_UnE
% 6.92/7.14 thf(fact_961_subset__Un__eq,axiom,
% 6.92/7.14 ( ord_le8081472938463900775at_nat
% 6.92/7.14 = ( ^ [A6: set_Pr8551490117392284871at_nat,B6: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ A6 @ B6 )
% 6.92/7.14 = B6 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_Un_eq
% 6.92/7.14 thf(fact_962_subset__Un__eq,axiom,
% 6.92/7.14 ( ord_le1268244103169919719at_nat
% 6.92/7.14 = ( ^ [A6: set_Pr4329608150637261639at_nat,B6: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ A6 @ B6 )
% 6.92/7.14 = B6 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_Un_eq
% 6.92/7.14 thf(fact_963_subset__Un__eq,axiom,
% 6.92/7.14 ( ord_less_eq_set_nat
% 6.92/7.14 = ( ^ [A6: set_nat,B6: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ A6 @ B6 )
% 6.92/7.14 = B6 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_Un_eq
% 6.92/7.14 thf(fact_964_subset__Un__eq,axiom,
% 6.92/7.14 ( ord_less_eq_set_int
% 6.92/7.14 = ( ^ [A6: set_int,B6: set_int] :
% 6.92/7.14 ( ( sup_sup_set_int @ A6 @ B6 )
% 6.92/7.14 = B6 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_Un_eq
% 6.92/7.14 thf(fact_965_add__lessD1,axiom,
% 6.92/7.14 ! [I2: nat,J2: nat,K2: nat] :
% 6.92/7.14 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J2 ) @ K2 )
% 6.92/7.14 => ( ord_less_nat @ I2 @ K2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_lessD1
% 6.92/7.14 thf(fact_966_add__less__mono,axiom,
% 6.92/7.14 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 6.92/7.14 ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.14 => ( ( ord_less_nat @ K2 @ L )
% 6.92/7.14 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_less_mono
% 6.92/7.14 thf(fact_967_not__add__less1,axiom,
% 6.92/7.14 ! [I2: nat,J2: nat] :
% 6.92/7.14 ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J2 ) @ I2 ) ).
% 6.92/7.14
% 6.92/7.14 % not_add_less1
% 6.92/7.14 thf(fact_968_not__add__less2,axiom,
% 6.92/7.14 ! [J2: nat,I2: nat] :
% 6.92/7.14 ~ ( ord_less_nat @ ( plus_plus_nat @ J2 @ I2 ) @ I2 ) ).
% 6.92/7.14
% 6.92/7.14 % not_add_less2
% 6.92/7.14 thf(fact_969_add__less__mono1,axiom,
% 6.92/7.14 ! [I2: nat,J2: nat,K2: nat] :
% 6.92/7.14 ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.14 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ K2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_less_mono1
% 6.92/7.14 thf(fact_970_trans__less__add1,axiom,
% 6.92/7.14 ! [I2: nat,J2: nat,M: nat] :
% 6.92/7.14 ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.14 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J2 @ M ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % trans_less_add1
% 6.92/7.14 thf(fact_971_trans__less__add2,axiom,
% 6.92/7.14 ! [I2: nat,J2: nat,M: nat] :
% 6.92/7.14 ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.14 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % trans_less_add2
% 6.92/7.14 thf(fact_972_less__add__eq__less,axiom,
% 6.92/7.14 ! [K2: nat,L: nat,M: nat,N2: nat] :
% 6.92/7.14 ( ( ord_less_nat @ K2 @ L )
% 6.92/7.14 => ( ( ( plus_plus_nat @ M @ L )
% 6.92/7.14 = ( plus_plus_nat @ K2 @ N2 ) )
% 6.92/7.14 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % less_add_eq_less
% 6.92/7.14 thf(fact_973_add__leE,axiom,
% 6.92/7.14 ! [M: nat,K2: nat,N2: nat] :
% 6.92/7.14 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K2 ) @ N2 )
% 6.92/7.14 => ~ ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.14 => ~ ( ord_less_eq_nat @ K2 @ N2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_leE
% 6.92/7.14 thf(fact_974_le__add1,axiom,
% 6.92/7.14 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) ) ).
% 6.92/7.14
% 6.92/7.14 % le_add1
% 6.92/7.14 thf(fact_975_le__add2,axiom,
% 6.92/7.14 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % le_add2
% 6.92/7.14 thf(fact_976_add__leD1,axiom,
% 6.92/7.14 ! [M: nat,K2: nat,N2: nat] :
% 6.92/7.14 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K2 ) @ N2 )
% 6.92/7.14 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_leD1
% 6.92/7.14 thf(fact_977_add__leD2,axiom,
% 6.92/7.14 ! [M: nat,K2: nat,N2: nat] :
% 6.92/7.14 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K2 ) @ N2 )
% 6.92/7.14 => ( ord_less_eq_nat @ K2 @ N2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_leD2
% 6.92/7.14 thf(fact_978_le__Suc__ex,axiom,
% 6.92/7.14 ! [K2: nat,L: nat] :
% 6.92/7.14 ( ( ord_less_eq_nat @ K2 @ L )
% 6.92/7.14 => ? [N5: nat] :
% 6.92/7.14 ( L
% 6.92/7.14 = ( plus_plus_nat @ K2 @ N5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % le_Suc_ex
% 6.92/7.14 thf(fact_979_add__le__mono,axiom,
% 6.92/7.14 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 6.92/7.14 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.14 => ( ( ord_less_eq_nat @ K2 @ L )
% 6.92/7.14 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_le_mono
% 6.92/7.14 thf(fact_980_add__le__mono1,axiom,
% 6.92/7.14 ! [I2: nat,J2: nat,K2: nat] :
% 6.92/7.14 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.14 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ K2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_le_mono1
% 6.92/7.14 thf(fact_981_trans__le__add1,axiom,
% 6.92/7.14 ! [I2: nat,J2: nat,M: nat] :
% 6.92/7.14 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.14 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J2 @ M ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % trans_le_add1
% 6.92/7.14 thf(fact_982_trans__le__add2,axiom,
% 6.92/7.14 ! [I2: nat,J2: nat,M: nat] :
% 6.92/7.14 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.14 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % trans_le_add2
% 6.92/7.14 thf(fact_983_nat__le__iff__add,axiom,
% 6.92/7.14 ( ord_less_eq_nat
% 6.92/7.14 = ( ^ [M3: nat,N: nat] :
% 6.92/7.14 ? [K3: nat] :
% 6.92/7.14 ( N
% 6.92/7.14 = ( plus_plus_nat @ M3 @ K3 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % nat_le_iff_add
% 6.92/7.14 thf(fact_984_timeFrame_Osimps_I1_J,axiom,
% 6.92/7.14 ! [N2: nat,R2: b,H: heap_e7401611519738050253t_unit,N6: nat] :
% 6.92/7.14 ( ( heap_T7616092557645711336rame_b @ N2 @ ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ R2 @ ( produc584006145561248582it_nat @ H @ N6 ) ) ) )
% 6.92/7.14 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ R2 @ ( produc584006145561248582it_nat @ H @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % timeFrame.simps(1)
% 6.92/7.14 thf(fact_985_timeFrame_Osimps_I1_J,axiom,
% 6.92/7.14 ! [N2: nat,R2: a,H: heap_e7401611519738050253t_unit,N6: nat] :
% 6.92/7.14 ( ( heap_T7616092557645711335rame_a @ N2 @ ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R2 @ ( produc584006145561248582it_nat @ H @ N6 ) ) ) )
% 6.92/7.14 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R2 @ ( produc584006145561248582it_nat @ H @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % timeFrame.simps(1)
% 6.92/7.14 thf(fact_986_timeFrame_Osimps_I1_J,axiom,
% 6.92/7.14 ! [N2: nat,R2: product_unit,H: heap_e7401611519738050253t_unit,N6: nat] :
% 6.92/7.14 ( ( heap_T3616969660504097270t_unit @ N2 @ ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H @ N6 ) ) ) )
% 6.92/7.14 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % timeFrame.simps(1)
% 6.92/7.14 thf(fact_987_mono__nat__linear__lb,axiom,
% 6.92/7.14 ! [F: nat > nat,M: nat,K2: nat] :
% 6.92/7.14 ( ! [M5: nat,N5: nat] :
% 6.92/7.14 ( ( ord_less_nat @ M5 @ N5 )
% 6.92/7.14 => ( ord_less_nat @ ( F @ M5 ) @ ( F @ N5 ) ) )
% 6.92/7.14 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K2 ) @ ( F @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % mono_nat_linear_lb
% 6.92/7.14 thf(fact_988_verit__comp__simplify1_I2_J,axiom,
% 6.92/7.14 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 6.92/7.14
% 6.92/7.14 % verit_comp_simplify1(2)
% 6.92/7.14 thf(fact_989_verit__comp__simplify1_I2_J,axiom,
% 6.92/7.14 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 6.92/7.14
% 6.92/7.14 % verit_comp_simplify1(2)
% 6.92/7.14 thf(fact_990_verit__comp__simplify1_I2_J,axiom,
% 6.92/7.14 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 6.92/7.14
% 6.92/7.14 % verit_comp_simplify1(2)
% 6.92/7.14 thf(fact_991_verit__comp__simplify1_I2_J,axiom,
% 6.92/7.14 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 6.92/7.14
% 6.92/7.14 % verit_comp_simplify1(2)
% 6.92/7.14 thf(fact_992_verit__comp__simplify1_I2_J,axiom,
% 6.92/7.14 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 6.92/7.14
% 6.92/7.14 % verit_comp_simplify1(2)
% 6.92/7.14 thf(fact_993_verit__la__disequality,axiom,
% 6.92/7.14 ! [A: rat,B: rat] :
% 6.92/7.14 ( ( A = B )
% 6.92/7.14 | ~ ( ord_less_eq_rat @ A @ B )
% 6.92/7.14 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 6.92/7.14
% 6.92/7.14 % verit_la_disequality
% 6.92/7.14 thf(fact_994_verit__la__disequality,axiom,
% 6.92/7.14 ! [A: num,B: num] :
% 6.92/7.14 ( ( A = B )
% 6.92/7.14 | ~ ( ord_less_eq_num @ A @ B )
% 6.92/7.14 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 6.92/7.14
% 6.92/7.14 % verit_la_disequality
% 6.92/7.14 thf(fact_995_verit__la__disequality,axiom,
% 6.92/7.14 ! [A: nat,B: nat] :
% 6.92/7.14 ( ( A = B )
% 6.92/7.14 | ~ ( ord_less_eq_nat @ A @ B )
% 6.92/7.14 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 6.92/7.14
% 6.92/7.14 % verit_la_disequality
% 6.92/7.14 thf(fact_996_verit__la__disequality,axiom,
% 6.92/7.14 ! [A: int,B: int] :
% 6.92/7.14 ( ( A = B )
% 6.92/7.14 | ~ ( ord_less_eq_int @ A @ B )
% 6.92/7.14 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 6.92/7.14
% 6.92/7.14 % verit_la_disequality
% 6.92/7.14 thf(fact_997_verit__comp__simplify1_I1_J,axiom,
% 6.92/7.14 ! [A: assn] :
% 6.92/7.14 ~ ( ord_less_assn @ A @ A ) ).
% 6.92/7.14
% 6.92/7.14 % verit_comp_simplify1(1)
% 6.92/7.14 thf(fact_998_verit__comp__simplify1_I1_J,axiom,
% 6.92/7.14 ! [A: rat] :
% 6.92/7.14 ~ ( ord_less_rat @ A @ A ) ).
% 6.92/7.14
% 6.92/7.14 % verit_comp_simplify1(1)
% 6.92/7.14 thf(fact_999_verit__comp__simplify1_I1_J,axiom,
% 6.92/7.14 ! [A: num] :
% 6.92/7.14 ~ ( ord_less_num @ A @ A ) ).
% 6.92/7.14
% 6.92/7.14 % verit_comp_simplify1(1)
% 6.92/7.14 thf(fact_1000_verit__comp__simplify1_I1_J,axiom,
% 6.92/7.14 ! [A: nat] :
% 6.92/7.14 ~ ( ord_less_nat @ A @ A ) ).
% 6.92/7.14
% 6.92/7.14 % verit_comp_simplify1(1)
% 6.92/7.14 thf(fact_1001_verit__comp__simplify1_I1_J,axiom,
% 6.92/7.14 ! [A: int] :
% 6.92/7.14 ~ ( ord_less_int @ A @ A ) ).
% 6.92/7.14
% 6.92/7.14 % verit_comp_simplify1(1)
% 6.92/7.14 thf(fact_1002_in__mono,axiom,
% 6.92/7.14 ! [A4: set_o,B5: set_o,X: $o] :
% 6.92/7.14 ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.92/7.14 => ( ( member_o @ X @ A4 )
% 6.92/7.14 => ( member_o @ X @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % in_mono
% 6.92/7.14 thf(fact_1003_in__mono,axiom,
% 6.92/7.14 ! [A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( ord_le483042692224249369nt_int @ A4 @ B5 )
% 6.92/7.14 => ( ( member2340774599025711042nt_int @ X @ A4 )
% 6.92/7.14 => ( member2340774599025711042nt_int @ X @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % in_mono
% 6.92/7.14 thf(fact_1004_in__mono,axiom,
% 6.92/7.14 ! [A4: set_set_nat,B5: set_set_nat,X: set_nat] :
% 6.92/7.14 ( ( ord_le6893508408891458716et_nat @ A4 @ B5 )
% 6.92/7.14 => ( ( member_set_nat @ X @ A4 )
% 6.92/7.14 => ( member_set_nat @ X @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % in_mono
% 6.92/7.14 thf(fact_1005_in__mono,axiom,
% 6.92/7.14 ! [A4: set_nat,B5: set_nat,X: nat] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.92/7.14 => ( ( member_nat @ X @ A4 )
% 6.92/7.14 => ( member_nat @ X @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % in_mono
% 6.92/7.14 thf(fact_1006_in__mono,axiom,
% 6.92/7.14 ! [A4: set_int,B5: set_int,X: int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.14 => ( ( member_int @ X @ A4 )
% 6.92/7.14 => ( member_int @ X @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % in_mono
% 6.92/7.14 thf(fact_1007_subsetD,axiom,
% 6.92/7.14 ! [A4: set_o,B5: set_o,C2: $o] :
% 6.92/7.14 ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.92/7.14 => ( ( member_o @ C2 @ A4 )
% 6.92/7.14 => ( member_o @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subsetD
% 6.92/7.14 thf(fact_1008_subsetD,axiom,
% 6.92/7.14 ! [A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int,C2: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( ord_le483042692224249369nt_int @ A4 @ B5 )
% 6.92/7.14 => ( ( member2340774599025711042nt_int @ C2 @ A4 )
% 6.92/7.14 => ( member2340774599025711042nt_int @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subsetD
% 6.92/7.14 thf(fact_1009_subsetD,axiom,
% 6.92/7.14 ! [A4: set_set_nat,B5: set_set_nat,C2: set_nat] :
% 6.92/7.14 ( ( ord_le6893508408891458716et_nat @ A4 @ B5 )
% 6.92/7.14 => ( ( member_set_nat @ C2 @ A4 )
% 6.92/7.14 => ( member_set_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subsetD
% 6.92/7.14 thf(fact_1010_subsetD,axiom,
% 6.92/7.14 ! [A4: set_nat,B5: set_nat,C2: nat] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.92/7.14 => ( ( member_nat @ C2 @ A4 )
% 6.92/7.14 => ( member_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subsetD
% 6.92/7.14 thf(fact_1011_subsetD,axiom,
% 6.92/7.14 ! [A4: set_int,B5: set_int,C2: int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.14 => ( ( member_int @ C2 @ A4 )
% 6.92/7.14 => ( member_int @ C2 @ B5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subsetD
% 6.92/7.14 thf(fact_1012_psubsetE,axiom,
% 6.92/7.14 ! [A4: set_int,B5: set_int] :
% 6.92/7.14 ( ( ord_less_set_int @ A4 @ B5 )
% 6.92/7.14 => ~ ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.14 => ( ord_less_eq_set_int @ B5 @ A4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % psubsetE
% 6.92/7.14 thf(fact_1013_equalityE,axiom,
% 6.92/7.14 ! [A4: set_int,B5: set_int] :
% 6.92/7.14 ( ( A4 = B5 )
% 6.92/7.14 => ~ ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.14 => ~ ( ord_less_eq_set_int @ B5 @ A4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % equalityE
% 6.92/7.14 thf(fact_1014_subset__eq,axiom,
% 6.92/7.14 ( ord_less_eq_set_o
% 6.92/7.14 = ( ^ [A6: set_o,B6: set_o] :
% 6.92/7.14 ! [X4: $o] :
% 6.92/7.14 ( ( member_o @ X4 @ A6 )
% 6.92/7.14 => ( member_o @ X4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_eq
% 6.92/7.14 thf(fact_1015_subset__eq,axiom,
% 6.92/7.14 ( ord_le483042692224249369nt_int
% 6.92/7.14 = ( ^ [A6: set_se6260736226359567993nt_int,B6: set_se6260736226359567993nt_int] :
% 6.92/7.14 ! [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( member2340774599025711042nt_int @ X4 @ A6 )
% 6.92/7.14 => ( member2340774599025711042nt_int @ X4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_eq
% 6.92/7.14 thf(fact_1016_subset__eq,axiom,
% 6.92/7.14 ( ord_le6893508408891458716et_nat
% 6.92/7.14 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 6.92/7.14 ! [X4: set_nat] :
% 6.92/7.14 ( ( member_set_nat @ X4 @ A6 )
% 6.92/7.14 => ( member_set_nat @ X4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_eq
% 6.92/7.14 thf(fact_1017_subset__eq,axiom,
% 6.92/7.14 ( ord_less_eq_set_nat
% 6.92/7.14 = ( ^ [A6: set_nat,B6: set_nat] :
% 6.92/7.14 ! [X4: nat] :
% 6.92/7.14 ( ( member_nat @ X4 @ A6 )
% 6.92/7.14 => ( member_nat @ X4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_eq
% 6.92/7.14 thf(fact_1018_subset__eq,axiom,
% 6.92/7.14 ( ord_less_eq_set_int
% 6.92/7.14 = ( ^ [A6: set_int,B6: set_int] :
% 6.92/7.14 ! [X4: int] :
% 6.92/7.14 ( ( member_int @ X4 @ A6 )
% 6.92/7.14 => ( member_int @ X4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_eq
% 6.92/7.14 thf(fact_1019_equalityD1,axiom,
% 6.92/7.14 ! [A4: set_int,B5: set_int] :
% 6.92/7.14 ( ( A4 = B5 )
% 6.92/7.14 => ( ord_less_eq_set_int @ A4 @ B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % equalityD1
% 6.92/7.14 thf(fact_1020_equalityD2,axiom,
% 6.92/7.14 ! [A4: set_int,B5: set_int] :
% 6.92/7.14 ( ( A4 = B5 )
% 6.92/7.14 => ( ord_less_eq_set_int @ B5 @ A4 ) ) ).
% 6.92/7.14
% 6.92/7.14 % equalityD2
% 6.92/7.14 thf(fact_1021_psubset__eq,axiom,
% 6.92/7.14 ( ord_less_set_int
% 6.92/7.14 = ( ^ [A6: set_int,B6: set_int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 6.92/7.14 & ( A6 != B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % psubset_eq
% 6.92/7.14 thf(fact_1022_subset__iff,axiom,
% 6.92/7.14 ( ord_less_eq_set_o
% 6.92/7.14 = ( ^ [A6: set_o,B6: set_o] :
% 6.92/7.14 ! [T4: $o] :
% 6.92/7.14 ( ( member_o @ T4 @ A6 )
% 6.92/7.14 => ( member_o @ T4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_iff
% 6.92/7.14 thf(fact_1023_subset__iff,axiom,
% 6.92/7.14 ( ord_le483042692224249369nt_int
% 6.92/7.14 = ( ^ [A6: set_se6260736226359567993nt_int,B6: set_se6260736226359567993nt_int] :
% 6.92/7.14 ! [T4: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( member2340774599025711042nt_int @ T4 @ A6 )
% 6.92/7.14 => ( member2340774599025711042nt_int @ T4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_iff
% 6.92/7.14 thf(fact_1024_subset__iff,axiom,
% 6.92/7.14 ( ord_le6893508408891458716et_nat
% 6.92/7.14 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 6.92/7.14 ! [T4: set_nat] :
% 6.92/7.14 ( ( member_set_nat @ T4 @ A6 )
% 6.92/7.14 => ( member_set_nat @ T4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_iff
% 6.92/7.14 thf(fact_1025_subset__iff,axiom,
% 6.92/7.14 ( ord_less_eq_set_nat
% 6.92/7.14 = ( ^ [A6: set_nat,B6: set_nat] :
% 6.92/7.14 ! [T4: nat] :
% 6.92/7.14 ( ( member_nat @ T4 @ A6 )
% 6.92/7.14 => ( member_nat @ T4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_iff
% 6.92/7.14 thf(fact_1026_subset__iff,axiom,
% 6.92/7.14 ( ord_less_eq_set_int
% 6.92/7.14 = ( ^ [A6: set_int,B6: set_int] :
% 6.92/7.14 ! [T4: int] :
% 6.92/7.14 ( ( member_int @ T4 @ A6 )
% 6.92/7.14 => ( member_int @ T4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_iff
% 6.92/7.14 thf(fact_1027_subset__refl,axiom,
% 6.92/7.14 ! [A4: set_int] : ( ord_less_eq_set_int @ A4 @ A4 ) ).
% 6.92/7.14
% 6.92/7.14 % subset_refl
% 6.92/7.14 thf(fact_1028_Collect__mono,axiom,
% 6.92/7.14 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 6.92/7.14 ( ! [X3: list_nat] :
% 6.92/7.14 ( ( P2 @ X3 )
% 6.92/7.14 => ( Q2 @ X3 ) )
% 6.92/7.14 => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P2 ) @ ( collect_list_nat @ Q2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_mono
% 6.92/7.14 thf(fact_1029_Collect__mono,axiom,
% 6.92/7.14 ! [P2: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.14 ( ! [X3: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( P2 @ X3 )
% 6.92/7.14 => ( Q2 @ X3 ) )
% 6.92/7.14 => ( ord_le483042692224249369nt_int @ ( collec5210948495886036740nt_int @ P2 ) @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_mono
% 6.92/7.14 thf(fact_1030_Collect__mono,axiom,
% 6.92/7.14 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 6.92/7.14 ( ! [X3: set_nat] :
% 6.92/7.14 ( ( P2 @ X3 )
% 6.92/7.14 => ( Q2 @ X3 ) )
% 6.92/7.14 => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P2 ) @ ( collect_set_nat @ Q2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_mono
% 6.92/7.14 thf(fact_1031_Collect__mono,axiom,
% 6.92/7.14 ! [P2: nat > $o,Q2: nat > $o] :
% 6.92/7.14 ( ! [X3: nat] :
% 6.92/7.14 ( ( P2 @ X3 )
% 6.92/7.14 => ( Q2 @ X3 ) )
% 6.92/7.14 => ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_mono
% 6.92/7.14 thf(fact_1032_Collect__mono,axiom,
% 6.92/7.14 ! [P2: int > $o,Q2: int > $o] :
% 6.92/7.14 ( ! [X3: int] :
% 6.92/7.14 ( ( P2 @ X3 )
% 6.92/7.14 => ( Q2 @ X3 ) )
% 6.92/7.14 => ( ord_less_eq_set_int @ ( collect_int @ P2 ) @ ( collect_int @ Q2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_mono
% 6.92/7.14 thf(fact_1033_subset__trans,axiom,
% 6.92/7.14 ! [A4: set_int,B5: set_int,C4: set_int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.14 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 6.92/7.14 => ( ord_less_eq_set_int @ A4 @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_trans
% 6.92/7.14 thf(fact_1034_set__eq__subset,axiom,
% 6.92/7.14 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 6.92/7.14 = ( ^ [A6: set_int,B6: set_int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 6.92/7.14 & ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % set_eq_subset
% 6.92/7.14 thf(fact_1035_Collect__mono__iff,axiom,
% 6.92/7.14 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 6.92/7.14 ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P2 ) @ ( collect_list_nat @ Q2 ) )
% 6.92/7.14 = ( ! [X4: list_nat] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 => ( Q2 @ X4 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_mono_iff
% 6.92/7.14 thf(fact_1036_Collect__mono__iff,axiom,
% 6.92/7.14 ! [P2: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.14 ( ( ord_le483042692224249369nt_int @ ( collec5210948495886036740nt_int @ P2 ) @ ( collec5210948495886036740nt_int @ Q2 ) )
% 6.92/7.14 = ( ! [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 => ( Q2 @ X4 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_mono_iff
% 6.92/7.14 thf(fact_1037_Collect__mono__iff,axiom,
% 6.92/7.14 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 6.92/7.14 ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P2 ) @ ( collect_set_nat @ Q2 ) )
% 6.92/7.14 = ( ! [X4: set_nat] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 => ( Q2 @ X4 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_mono_iff
% 6.92/7.14 thf(fact_1038_Collect__mono__iff,axiom,
% 6.92/7.14 ! [P2: nat > $o,Q2: nat > $o] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q2 ) )
% 6.92/7.14 = ( ! [X4: nat] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 => ( Q2 @ X4 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_mono_iff
% 6.92/7.14 thf(fact_1039_Collect__mono__iff,axiom,
% 6.92/7.14 ! [P2: int > $o,Q2: int > $o] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ ( collect_int @ P2 ) @ ( collect_int @ Q2 ) )
% 6.92/7.14 = ( ! [X4: int] :
% 6.92/7.14 ( ( P2 @ X4 )
% 6.92/7.14 => ( Q2 @ X4 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_mono_iff
% 6.92/7.14 thf(fact_1040_psubset__imp__subset,axiom,
% 6.92/7.14 ! [A4: set_int,B5: set_int] :
% 6.92/7.14 ( ( ord_less_set_int @ A4 @ B5 )
% 6.92/7.14 => ( ord_less_eq_set_int @ A4 @ B5 ) ) ).
% 6.92/7.14
% 6.92/7.14 % psubset_imp_subset
% 6.92/7.14 thf(fact_1041_psubset__subset__trans,axiom,
% 6.92/7.14 ! [A4: set_int,B5: set_int,C4: set_int] :
% 6.92/7.14 ( ( ord_less_set_int @ A4 @ B5 )
% 6.92/7.14 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 6.92/7.14 => ( ord_less_set_int @ A4 @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % psubset_subset_trans
% 6.92/7.14 thf(fact_1042_subset__not__subset__eq,axiom,
% 6.92/7.14 ( ord_less_set_int
% 6.92/7.14 = ( ^ [A6: set_int,B6: set_int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 6.92/7.14 & ~ ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_not_subset_eq
% 6.92/7.14 thf(fact_1043_subset__psubset__trans,axiom,
% 6.92/7.14 ! [A4: set_int,B5: set_int,C4: set_int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.14 => ( ( ord_less_set_int @ B5 @ C4 )
% 6.92/7.14 => ( ord_less_set_int @ A4 @ C4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_psubset_trans
% 6.92/7.14 thf(fact_1044_subset__iff__psubset__eq,axiom,
% 6.92/7.14 ( ord_less_eq_set_int
% 6.92/7.14 = ( ^ [A6: set_int,B6: set_int] :
% 6.92/7.14 ( ( ord_less_set_int @ A6 @ B6 )
% 6.92/7.14 | ( A6 = B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % subset_iff_psubset_eq
% 6.92/7.14 thf(fact_1045_Collect__subset,axiom,
% 6.92/7.14 ! [A4: set_o,P2: $o > $o] :
% 6.92/7.14 ( ord_less_eq_set_o
% 6.92/7.14 @ ( collect_o
% 6.92/7.14 @ ^ [X4: $o] :
% 6.92/7.14 ( ( member_o @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) )
% 6.92/7.14 @ A4 ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_subset
% 6.92/7.14 thf(fact_1046_Collect__subset,axiom,
% 6.92/7.14 ! [A4: set_list_nat,P2: list_nat > $o] :
% 6.92/7.14 ( ord_le6045566169113846134st_nat
% 6.92/7.14 @ ( collect_list_nat
% 6.92/7.14 @ ^ [X4: list_nat] :
% 6.92/7.14 ( ( member_list_nat @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) )
% 6.92/7.14 @ A4 ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_subset
% 6.92/7.14 thf(fact_1047_Collect__subset,axiom,
% 6.92/7.14 ! [A4: set_se6260736226359567993nt_int,P2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.14 ( ord_le483042692224249369nt_int
% 6.92/7.14 @ ( collec5210948495886036740nt_int
% 6.92/7.14 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.14 ( ( member2340774599025711042nt_int @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) )
% 6.92/7.14 @ A4 ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_subset
% 6.92/7.14 thf(fact_1048_Collect__subset,axiom,
% 6.92/7.14 ! [A4: set_set_nat,P2: set_nat > $o] :
% 6.92/7.14 ( ord_le6893508408891458716et_nat
% 6.92/7.14 @ ( collect_set_nat
% 6.92/7.14 @ ^ [X4: set_nat] :
% 6.92/7.14 ( ( member_set_nat @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) )
% 6.92/7.14 @ A4 ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_subset
% 6.92/7.14 thf(fact_1049_Collect__subset,axiom,
% 6.92/7.14 ! [A4: set_nat,P2: nat > $o] :
% 6.92/7.14 ( ord_less_eq_set_nat
% 6.92/7.14 @ ( collect_nat
% 6.92/7.14 @ ^ [X4: nat] :
% 6.92/7.14 ( ( member_nat @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) )
% 6.92/7.14 @ A4 ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_subset
% 6.92/7.14 thf(fact_1050_Collect__subset,axiom,
% 6.92/7.14 ! [A4: set_int,P2: int > $o] :
% 6.92/7.14 ( ord_less_eq_set_int
% 6.92/7.14 @ ( collect_int
% 6.92/7.14 @ ^ [X4: int] :
% 6.92/7.14 ( ( member_int @ X4 @ A4 )
% 6.92/7.14 & ( P2 @ X4 ) ) )
% 6.92/7.14 @ A4 ) ).
% 6.92/7.14
% 6.92/7.14 % Collect_subset
% 6.92/7.14 thf(fact_1051_less__eq__set__def,axiom,
% 6.92/7.14 ( ord_less_eq_set_o
% 6.92/7.14 = ( ^ [A6: set_o,B6: set_o] :
% 6.92/7.14 ( ord_less_eq_o_o
% 6.92/7.14 @ ^ [X4: $o] : ( member_o @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: $o] : ( member_o @ X4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % less_eq_set_def
% 6.92/7.14 thf(fact_1052_less__eq__set__def,axiom,
% 6.92/7.14 ( ord_le483042692224249369nt_int
% 6.92/7.14 = ( ^ [A6: set_se6260736226359567993nt_int,B6: set_se6260736226359567993nt_int] :
% 6.92/7.14 ( ord_le8334417538754933252_int_o
% 6.92/7.14 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % less_eq_set_def
% 6.92/7.14 thf(fact_1053_less__eq__set__def,axiom,
% 6.92/7.14 ( ord_le6893508408891458716et_nat
% 6.92/7.14 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 6.92/7.14 ( ord_le3964352015994296041_nat_o
% 6.92/7.14 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % less_eq_set_def
% 6.92/7.14 thf(fact_1054_less__eq__set__def,axiom,
% 6.92/7.14 ( ord_less_eq_set_nat
% 6.92/7.14 = ( ^ [A6: set_nat,B6: set_nat] :
% 6.92/7.14 ( ord_less_eq_nat_o
% 6.92/7.14 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % less_eq_set_def
% 6.92/7.14 thf(fact_1055_less__eq__set__def,axiom,
% 6.92/7.14 ( ord_less_eq_set_int
% 6.92/7.14 = ( ^ [A6: set_int,B6: set_int] :
% 6.92/7.14 ( ord_less_eq_int_o
% 6.92/7.14 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % less_eq_set_def
% 6.92/7.14 thf(fact_1056_le__sup__iff,axiom,
% 6.92/7.14 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( ( ord_le8081472938463900775at_nat @ X @ Z3 )
% 6.92/7.14 & ( ord_le8081472938463900775at_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % le_sup_iff
% 6.92/7.14 thf(fact_1057_le__sup__iff,axiom,
% 6.92/7.14 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( ( ord_le1268244103169919719at_nat @ X @ Z3 )
% 6.92/7.14 & ( ord_le1268244103169919719at_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % le_sup_iff
% 6.92/7.14 thf(fact_1058_le__sup__iff,axiom,
% 6.92/7.14 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( ( ord_less_eq_set_nat @ X @ Z3 )
% 6.92/7.14 & ( ord_less_eq_set_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % le_sup_iff
% 6.92/7.14 thf(fact_1059_le__sup__iff,axiom,
% 6.92/7.14 ! [X: set_int,Y: set_int,Z3: set_int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ ( sup_sup_set_int @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( ( ord_less_eq_set_int @ X @ Z3 )
% 6.92/7.14 & ( ord_less_eq_set_int @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % le_sup_iff
% 6.92/7.14 thf(fact_1060_le__sup__iff,axiom,
% 6.92/7.14 ! [X: rat,Y: rat,Z3: rat] :
% 6.92/7.14 ( ( ord_less_eq_rat @ ( sup_sup_rat @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( ( ord_less_eq_rat @ X @ Z3 )
% 6.92/7.14 & ( ord_less_eq_rat @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % le_sup_iff
% 6.92/7.14 thf(fact_1061_le__sup__iff,axiom,
% 6.92/7.14 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.14 ( ( ord_less_eq_nat @ ( sup_sup_nat @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( ( ord_less_eq_nat @ X @ Z3 )
% 6.92/7.14 & ( ord_less_eq_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % le_sup_iff
% 6.92/7.14 thf(fact_1062_le__sup__iff,axiom,
% 6.92/7.14 ! [X: int,Y: int,Z3: int] :
% 6.92/7.14 ( ( ord_less_eq_int @ ( sup_sup_int @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( ( ord_less_eq_int @ X @ Z3 )
% 6.92/7.14 & ( ord_less_eq_int @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % le_sup_iff
% 6.92/7.14 thf(fact_1063_sup_Obounded__iff,axiom,
% 6.92/7.14 ! [B: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ B @ C2 ) @ A )
% 6.92/7.14 = ( ( ord_le8081472938463900775at_nat @ B @ A )
% 6.92/7.14 & ( ord_le8081472938463900775at_nat @ C2 @ A ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.bounded_iff
% 6.92/7.14 thf(fact_1064_sup_Obounded__iff,axiom,
% 6.92/7.14 ! [B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B @ C2 ) @ A )
% 6.92/7.14 = ( ( ord_le1268244103169919719at_nat @ B @ A )
% 6.92/7.14 & ( ord_le1268244103169919719at_nat @ C2 @ A ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.bounded_iff
% 6.92/7.14 thf(fact_1065_sup_Obounded__iff,axiom,
% 6.92/7.14 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 6.92/7.14 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C2 ) @ A )
% 6.92/7.14 = ( ( ord_less_eq_set_nat @ B @ A )
% 6.92/7.14 & ( ord_less_eq_set_nat @ C2 @ A ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.bounded_iff
% 6.92/7.14 thf(fact_1066_sup_Obounded__iff,axiom,
% 6.92/7.14 ! [B: set_int,C2: set_int,A: set_int] :
% 6.92/7.14 ( ( ord_less_eq_set_int @ ( sup_sup_set_int @ B @ C2 ) @ A )
% 6.92/7.14 = ( ( ord_less_eq_set_int @ B @ A )
% 6.92/7.14 & ( ord_less_eq_set_int @ C2 @ A ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.bounded_iff
% 6.92/7.14 thf(fact_1067_sup_Obounded__iff,axiom,
% 6.92/7.14 ! [B: rat,C2: rat,A: rat] :
% 6.92/7.14 ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C2 ) @ A )
% 6.92/7.14 = ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.14 & ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.bounded_iff
% 6.92/7.14 thf(fact_1068_sup_Obounded__iff,axiom,
% 6.92/7.14 ! [B: nat,C2: nat,A: nat] :
% 6.92/7.14 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C2 ) @ A )
% 6.92/7.14 = ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.14 & ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.bounded_iff
% 6.92/7.14 thf(fact_1069_sup_Obounded__iff,axiom,
% 6.92/7.14 ! [B: int,C2: int,A: int] :
% 6.92/7.14 ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C2 ) @ A )
% 6.92/7.14 = ( ( ord_less_eq_int @ B @ A )
% 6.92/7.14 & ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.bounded_iff
% 6.92/7.14 thf(fact_1070_add__less__cancel__left,axiom,
% 6.92/7.14 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.14 ( ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 6.92/7.14 = ( ord_less_rat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_less_cancel_left
% 6.92/7.14 thf(fact_1071_add__less__cancel__left,axiom,
% 6.92/7.14 ! [C2: nat,A: nat,B: nat] :
% 6.92/7.14 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 6.92/7.14 = ( ord_less_nat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_less_cancel_left
% 6.92/7.14 thf(fact_1072_add__less__cancel__left,axiom,
% 6.92/7.14 ! [C2: int,A: int,B: int] :
% 6.92/7.14 ( ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 6.92/7.14 = ( ord_less_int @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_less_cancel_left
% 6.92/7.14 thf(fact_1073_add__less__cancel__right,axiom,
% 6.92/7.14 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.14 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 6.92/7.14 = ( ord_less_rat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_less_cancel_right
% 6.92/7.14 thf(fact_1074_add__less__cancel__right,axiom,
% 6.92/7.14 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.14 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 6.92/7.14 = ( ord_less_nat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_less_cancel_right
% 6.92/7.14 thf(fact_1075_add__less__cancel__right,axiom,
% 6.92/7.14 ! [A: int,C2: int,B: int] :
% 6.92/7.14 ( ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 6.92/7.14 = ( ord_less_int @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_less_cancel_right
% 6.92/7.14 thf(fact_1076_add__le__cancel__left,axiom,
% 6.92/7.14 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.14 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 6.92/7.14 = ( ord_less_eq_rat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_le_cancel_left
% 6.92/7.14 thf(fact_1077_add__le__cancel__left,axiom,
% 6.92/7.14 ! [C2: nat,A: nat,B: nat] :
% 6.92/7.14 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 6.92/7.14 = ( ord_less_eq_nat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_le_cancel_left
% 6.92/7.14 thf(fact_1078_add__le__cancel__left,axiom,
% 6.92/7.14 ! [C2: int,A: int,B: int] :
% 6.92/7.14 ( ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 6.92/7.14 = ( ord_less_eq_int @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_le_cancel_left
% 6.92/7.14 thf(fact_1079_add__le__cancel__right,axiom,
% 6.92/7.14 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.14 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 6.92/7.14 = ( ord_less_eq_rat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_le_cancel_right
% 6.92/7.14 thf(fact_1080_add__le__cancel__right,axiom,
% 6.92/7.14 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.14 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 6.92/7.14 = ( ord_less_eq_nat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_le_cancel_right
% 6.92/7.14 thf(fact_1081_add__le__cancel__right,axiom,
% 6.92/7.14 ! [A: int,C2: int,B: int] :
% 6.92/7.14 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 6.92/7.14 = ( ord_less_eq_int @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_le_cancel_right
% 6.92/7.14 thf(fact_1082_add__less__le__mono,axiom,
% 6.92/7.14 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.14 ( ( ord_less_rat @ A @ B )
% 6.92/7.14 => ( ( ord_less_eq_rat @ C2 @ D2 )
% 6.92/7.14 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_less_le_mono
% 6.92/7.14 thf(fact_1083_add__less__le__mono,axiom,
% 6.92/7.14 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.14 ( ( ord_less_nat @ A @ B )
% 6.92/7.14 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 6.92/7.14 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_less_le_mono
% 6.92/7.14 thf(fact_1084_add__less__le__mono,axiom,
% 6.92/7.14 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.14 ( ( ord_less_int @ A @ B )
% 6.92/7.14 => ( ( ord_less_eq_int @ C2 @ D2 )
% 6.92/7.14 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_less_le_mono
% 6.92/7.14 thf(fact_1085_add__le__less__mono,axiom,
% 6.92/7.14 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.14 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.14 => ( ( ord_less_rat @ C2 @ D2 )
% 6.92/7.14 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_le_less_mono
% 6.92/7.14 thf(fact_1086_add__le__less__mono,axiom,
% 6.92/7.14 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.14 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.14 => ( ( ord_less_nat @ C2 @ D2 )
% 6.92/7.14 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_le_less_mono
% 6.92/7.14 thf(fact_1087_add__le__less__mono,axiom,
% 6.92/7.14 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.14 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.14 => ( ( ord_less_int @ C2 @ D2 )
% 6.92/7.14 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_le_less_mono
% 6.92/7.14 thf(fact_1088_add__mono__thms__linordered__field_I3_J,axiom,
% 6.92/7.14 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 6.92/7.14 ( ( ( ord_less_rat @ I2 @ J2 )
% 6.92/7.14 & ( ord_less_eq_rat @ K2 @ L ) )
% 6.92/7.14 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_mono_thms_linordered_field(3)
% 6.92/7.14 thf(fact_1089_add__mono__thms__linordered__field_I3_J,axiom,
% 6.92/7.14 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 6.92/7.14 ( ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.14 & ( ord_less_eq_nat @ K2 @ L ) )
% 6.92/7.14 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_mono_thms_linordered_field(3)
% 6.92/7.14 thf(fact_1090_add__mono__thms__linordered__field_I3_J,axiom,
% 6.92/7.14 ! [I2: int,J2: int,K2: int,L: int] :
% 6.92/7.14 ( ( ( ord_less_int @ I2 @ J2 )
% 6.92/7.14 & ( ord_less_eq_int @ K2 @ L ) )
% 6.92/7.14 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_mono_thms_linordered_field(3)
% 6.92/7.14 thf(fact_1091_add__mono__thms__linordered__field_I4_J,axiom,
% 6.92/7.14 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 6.92/7.14 ( ( ( ord_less_eq_rat @ I2 @ J2 )
% 6.92/7.14 & ( ord_less_rat @ K2 @ L ) )
% 6.92/7.14 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_mono_thms_linordered_field(4)
% 6.92/7.14 thf(fact_1092_add__mono__thms__linordered__field_I4_J,axiom,
% 6.92/7.14 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 6.92/7.14 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.14 & ( ord_less_nat @ K2 @ L ) )
% 6.92/7.14 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_mono_thms_linordered_field(4)
% 6.92/7.14 thf(fact_1093_add__mono__thms__linordered__field_I4_J,axiom,
% 6.92/7.14 ! [I2: int,J2: int,K2: int,L: int] :
% 6.92/7.14 ( ( ( ord_less_eq_int @ I2 @ J2 )
% 6.92/7.14 & ( ord_less_int @ K2 @ L ) )
% 6.92/7.14 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_mono_thms_linordered_field(4)
% 6.92/7.14 thf(fact_1094_sup_Oidem,axiom,
% 6.92/7.14 ! [A: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ A @ A )
% 6.92/7.14 = A ) ).
% 6.92/7.14
% 6.92/7.14 % sup.idem
% 6.92/7.14 thf(fact_1095_sup_Oidem,axiom,
% 6.92/7.14 ! [A: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ A @ A )
% 6.92/7.14 = A ) ).
% 6.92/7.14
% 6.92/7.14 % sup.idem
% 6.92/7.14 thf(fact_1096_sup_Oidem,axiom,
% 6.92/7.14 ! [A: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ A @ A )
% 6.92/7.14 = A ) ).
% 6.92/7.14
% 6.92/7.14 % sup.idem
% 6.92/7.14 thf(fact_1097_sup_Oidem,axiom,
% 6.92/7.14 ! [A: nat] :
% 6.92/7.14 ( ( sup_sup_nat @ A @ A )
% 6.92/7.14 = A ) ).
% 6.92/7.14
% 6.92/7.14 % sup.idem
% 6.92/7.14 thf(fact_1098_sup_Oidem,axiom,
% 6.92/7.14 ! [A: int] :
% 6.92/7.14 ( ( sup_sup_int @ A @ A )
% 6.92/7.14 = A ) ).
% 6.92/7.14
% 6.92/7.14 % sup.idem
% 6.92/7.14 thf(fact_1099_add__right__cancel,axiom,
% 6.92/7.14 ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,C2: multis2468970476368604999at_nat] :
% 6.92/7.14 ( ( ( plus_p7104986032573967614at_nat @ B @ A )
% 6.92/7.14 = ( plus_p7104986032573967614at_nat @ C2 @ A ) )
% 6.92/7.14 = ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_right_cancel
% 6.92/7.14 thf(fact_1100_add__right__cancel,axiom,
% 6.92/7.14 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.14 ( ( ( plus_plus_rat @ B @ A )
% 6.92/7.14 = ( plus_plus_rat @ C2 @ A ) )
% 6.92/7.14 = ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_right_cancel
% 6.92/7.14 thf(fact_1101_add__right__cancel,axiom,
% 6.92/7.14 ! [B: nat,A: nat,C2: nat] :
% 6.92/7.14 ( ( ( plus_plus_nat @ B @ A )
% 6.92/7.14 = ( plus_plus_nat @ C2 @ A ) )
% 6.92/7.14 = ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_right_cancel
% 6.92/7.14 thf(fact_1102_add__right__cancel,axiom,
% 6.92/7.14 ! [B: int,A: int,C2: int] :
% 6.92/7.14 ( ( ( plus_plus_int @ B @ A )
% 6.92/7.14 = ( plus_plus_int @ C2 @ A ) )
% 6.92/7.14 = ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_right_cancel
% 6.92/7.14 thf(fact_1103_add__left__cancel,axiom,
% 6.92/7.14 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C2: multis2468970476368604999at_nat] :
% 6.92/7.14 ( ( ( plus_p7104986032573967614at_nat @ A @ B )
% 6.92/7.14 = ( plus_p7104986032573967614at_nat @ A @ C2 ) )
% 6.92/7.14 = ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_left_cancel
% 6.92/7.14 thf(fact_1104_add__left__cancel,axiom,
% 6.92/7.14 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.14 ( ( ( plus_plus_rat @ A @ B )
% 6.92/7.14 = ( plus_plus_rat @ A @ C2 ) )
% 6.92/7.14 = ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_left_cancel
% 6.92/7.14 thf(fact_1105_add__left__cancel,axiom,
% 6.92/7.14 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.14 ( ( ( plus_plus_nat @ A @ B )
% 6.92/7.14 = ( plus_plus_nat @ A @ C2 ) )
% 6.92/7.14 = ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_left_cancel
% 6.92/7.14 thf(fact_1106_add__left__cancel,axiom,
% 6.92/7.14 ! [A: int,B: int,C2: int] :
% 6.92/7.14 ( ( ( plus_plus_int @ A @ B )
% 6.92/7.14 = ( plus_plus_int @ A @ C2 ) )
% 6.92/7.14 = ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_left_cancel
% 6.92/7.14 thf(fact_1107_sup_Oright__idem,axiom,
% 6.92/7.14 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ B )
% 6.92/7.14 = ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.right_idem
% 6.92/7.14 thf(fact_1108_sup_Oright__idem,axiom,
% 6.92/7.14 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ B )
% 6.92/7.14 = ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.right_idem
% 6.92/7.14 thf(fact_1109_sup_Oright__idem,axiom,
% 6.92/7.14 ! [A: set_nat,B: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B ) @ B )
% 6.92/7.14 = ( sup_sup_set_nat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.right_idem
% 6.92/7.14 thf(fact_1110_sup_Oright__idem,axiom,
% 6.92/7.14 ! [A: nat,B: nat] :
% 6.92/7.14 ( ( sup_sup_nat @ ( sup_sup_nat @ A @ B ) @ B )
% 6.92/7.14 = ( sup_sup_nat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.right_idem
% 6.92/7.14 thf(fact_1111_sup_Oright__idem,axiom,
% 6.92/7.14 ! [A: int,B: int] :
% 6.92/7.14 ( ( sup_sup_int @ ( sup_sup_int @ A @ B ) @ B )
% 6.92/7.14 = ( sup_sup_int @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.right_idem
% 6.92/7.14 thf(fact_1112_sup__left__idem,axiom,
% 6.92/7.14 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 6.92/7.14 = ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_left_idem
% 6.92/7.14 thf(fact_1113_sup__left__idem,axiom,
% 6.92/7.14 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 6.92/7.14 = ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_left_idem
% 6.92/7.14 thf(fact_1114_sup__left__idem,axiom,
% 6.92/7.14 ! [X: set_nat,Y: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 6.92/7.14 = ( sup_sup_set_nat @ X @ Y ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_left_idem
% 6.92/7.14 thf(fact_1115_sup__left__idem,axiom,
% 6.92/7.14 ! [X: nat,Y: nat] :
% 6.92/7.14 ( ( sup_sup_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 6.92/7.14 = ( sup_sup_nat @ X @ Y ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_left_idem
% 6.92/7.14 thf(fact_1116_sup__left__idem,axiom,
% 6.92/7.14 ! [X: int,Y: int] :
% 6.92/7.14 ( ( sup_sup_int @ X @ ( sup_sup_int @ X @ Y ) )
% 6.92/7.14 = ( sup_sup_int @ X @ Y ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_left_idem
% 6.92/7.14 thf(fact_1117_sup_Oleft__idem,axiom,
% 6.92/7.14 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ A @ ( sup_su3035147773818789531at_nat @ A @ B ) )
% 6.92/7.14 = ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.left_idem
% 6.92/7.14 thf(fact_1118_sup_Oleft__idem,axiom,
% 6.92/7.14 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ A @ ( sup_su5525570899277871387at_nat @ A @ B ) )
% 6.92/7.14 = ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.left_idem
% 6.92/7.14 thf(fact_1119_sup_Oleft__idem,axiom,
% 6.92/7.14 ! [A: set_nat,B: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) )
% 6.92/7.14 = ( sup_sup_set_nat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.left_idem
% 6.92/7.14 thf(fact_1120_sup_Oleft__idem,axiom,
% 6.92/7.14 ! [A: nat,B: nat] :
% 6.92/7.14 ( ( sup_sup_nat @ A @ ( sup_sup_nat @ A @ B ) )
% 6.92/7.14 = ( sup_sup_nat @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.left_idem
% 6.92/7.14 thf(fact_1121_sup_Oleft__idem,axiom,
% 6.92/7.14 ! [A: int,B: int] :
% 6.92/7.14 ( ( sup_sup_int @ A @ ( sup_sup_int @ A @ B ) )
% 6.92/7.14 = ( sup_sup_int @ A @ B ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.left_idem
% 6.92/7.14 thf(fact_1122_sup__idem,axiom,
% 6.92/7.14 ! [X: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ X @ X )
% 6.92/7.14 = X ) ).
% 6.92/7.14
% 6.92/7.14 % sup_idem
% 6.92/7.14 thf(fact_1123_sup__idem,axiom,
% 6.92/7.14 ! [X: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ X @ X )
% 6.92/7.14 = X ) ).
% 6.92/7.14
% 6.92/7.14 % sup_idem
% 6.92/7.14 thf(fact_1124_sup__idem,axiom,
% 6.92/7.14 ! [X: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ X @ X )
% 6.92/7.14 = X ) ).
% 6.92/7.14
% 6.92/7.14 % sup_idem
% 6.92/7.14 thf(fact_1125_sup__idem,axiom,
% 6.92/7.14 ! [X: nat] :
% 6.92/7.14 ( ( sup_sup_nat @ X @ X )
% 6.92/7.14 = X ) ).
% 6.92/7.14
% 6.92/7.14 % sup_idem
% 6.92/7.14 thf(fact_1126_sup__idem,axiom,
% 6.92/7.14 ! [X: int] :
% 6.92/7.14 ( ( sup_sup_int @ X @ X )
% 6.92/7.14 = X ) ).
% 6.92/7.14
% 6.92/7.14 % sup_idem
% 6.92/7.14 thf(fact_1127_mod__or__dist,axiom,
% 6.92/7.14 ! [P2: assn,Q2: assn,H: produc3658429121746597890et_nat] :
% 6.92/7.14 ( ( rep_assn @ ( sup_sup_assn @ P2 @ Q2 ) @ H )
% 6.92/7.14 = ( ( rep_assn @ P2 @ H )
% 6.92/7.14 | ( rep_assn @ Q2 @ H ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % mod_or_dist
% 6.92/7.14 thf(fact_1128_sup__set__def,axiom,
% 6.92/7.14 ( sup_sup_set_o
% 6.92/7.14 = ( ^ [A6: set_o,B6: set_o] :
% 6.92/7.14 ( collect_o
% 6.92/7.14 @ ( sup_sup_o_o
% 6.92/7.14 @ ^ [X4: $o] : ( member_o @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: $o] : ( member_o @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_set_def
% 6.92/7.14 thf(fact_1129_sup__set__def,axiom,
% 6.92/7.14 ( sup_sup_set_list_nat
% 6.92/7.14 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 6.92/7.14 ( collect_list_nat
% 6.92/7.14 @ ( sup_sup_list_nat_o
% 6.92/7.14 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_set_def
% 6.92/7.14 thf(fact_1130_sup__set__def,axiom,
% 6.92/7.14 ( sup_su2047564715030645325nt_int
% 6.92/7.14 = ( ^ [A6: set_se6260736226359567993nt_int,B6: set_se6260736226359567993nt_int] :
% 6.92/7.14 ( collec5210948495886036740nt_int
% 6.92/7.14 @ ( sup_su1852724690005176016_int_o
% 6.92/7.14 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_set_def
% 6.92/7.14 thf(fact_1131_sup__set__def,axiom,
% 6.92/7.14 ( sup_sup_set_set_nat
% 6.92/7.14 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 6.92/7.14 ( collect_set_nat
% 6.92/7.14 @ ( sup_sup_set_nat_o
% 6.92/7.14 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_set_def
% 6.92/7.14 thf(fact_1132_sup__set__def,axiom,
% 6.92/7.14 ( sup_sup_set_int
% 6.92/7.14 = ( ^ [A6: set_int,B6: set_int] :
% 6.92/7.14 ( collect_int
% 6.92/7.14 @ ( sup_sup_int_o
% 6.92/7.14 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_set_def
% 6.92/7.14 thf(fact_1133_sup__set__def,axiom,
% 6.92/7.14 ( sup_su3035147773818789531at_nat
% 6.92/7.14 = ( ^ [A6: set_Pr8551490117392284871at_nat,B6: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( collec5204685387357076818at_nat
% 6.92/7.14 @ ( sup_su6256023009775730178_nat_o
% 6.92/7.14 @ ^ [X4: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_set_def
% 6.92/7.14 thf(fact_1134_sup__set__def,axiom,
% 6.92/7.14 ( sup_su5525570899277871387at_nat
% 6.92/7.14 = ( ^ [A6: set_Pr4329608150637261639at_nat,B6: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( collec6321179662152712658at_nat
% 6.92/7.14 @ ( sup_su2080679670758317954_nat_o
% 6.92/7.14 @ ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_set_def
% 6.92/7.14 thf(fact_1135_sup__set__def,axiom,
% 6.92/7.14 ( sup_sup_set_nat
% 6.92/7.14 = ( ^ [A6: set_nat,B6: set_nat] :
% 6.92/7.14 ( collect_nat
% 6.92/7.14 @ ( sup_sup_nat_o
% 6.92/7.14 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 6.92/7.14 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_set_def
% 6.92/7.14 thf(fact_1136_add__right__imp__eq,axiom,
% 6.92/7.14 ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,C2: multis2468970476368604999at_nat] :
% 6.92/7.14 ( ( ( plus_p7104986032573967614at_nat @ B @ A )
% 6.92/7.14 = ( plus_p7104986032573967614at_nat @ C2 @ A ) )
% 6.92/7.14 => ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_right_imp_eq
% 6.92/7.14 thf(fact_1137_add__right__imp__eq,axiom,
% 6.92/7.14 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.14 ( ( ( plus_plus_rat @ B @ A )
% 6.92/7.14 = ( plus_plus_rat @ C2 @ A ) )
% 6.92/7.14 => ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_right_imp_eq
% 6.92/7.14 thf(fact_1138_add__right__imp__eq,axiom,
% 6.92/7.14 ! [B: nat,A: nat,C2: nat] :
% 6.92/7.14 ( ( ( plus_plus_nat @ B @ A )
% 6.92/7.14 = ( plus_plus_nat @ C2 @ A ) )
% 6.92/7.14 => ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_right_imp_eq
% 6.92/7.14 thf(fact_1139_add__right__imp__eq,axiom,
% 6.92/7.14 ! [B: int,A: int,C2: int] :
% 6.92/7.14 ( ( ( plus_plus_int @ B @ A )
% 6.92/7.14 = ( plus_plus_int @ C2 @ A ) )
% 6.92/7.14 => ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_right_imp_eq
% 6.92/7.14 thf(fact_1140_add__left__imp__eq,axiom,
% 6.92/7.14 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C2: multis2468970476368604999at_nat] :
% 6.92/7.14 ( ( ( plus_p7104986032573967614at_nat @ A @ B )
% 6.92/7.14 = ( plus_p7104986032573967614at_nat @ A @ C2 ) )
% 6.92/7.14 => ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_left_imp_eq
% 6.92/7.14 thf(fact_1141_add__left__imp__eq,axiom,
% 6.92/7.14 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.14 ( ( ( plus_plus_rat @ A @ B )
% 6.92/7.14 = ( plus_plus_rat @ A @ C2 ) )
% 6.92/7.14 => ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_left_imp_eq
% 6.92/7.14 thf(fact_1142_add__left__imp__eq,axiom,
% 6.92/7.14 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.14 ( ( ( plus_plus_nat @ A @ B )
% 6.92/7.14 = ( plus_plus_nat @ A @ C2 ) )
% 6.92/7.14 => ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_left_imp_eq
% 6.92/7.14 thf(fact_1143_add__left__imp__eq,axiom,
% 6.92/7.14 ! [A: int,B: int,C2: int] :
% 6.92/7.14 ( ( ( plus_plus_int @ A @ B )
% 6.92/7.14 = ( plus_plus_int @ A @ C2 ) )
% 6.92/7.14 => ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_left_imp_eq
% 6.92/7.14 thf(fact_1144_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 6.92/7.14 ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,C2: multis2468970476368604999at_nat] :
% 6.92/7.14 ( ( plus_p7104986032573967614at_nat @ B @ ( plus_p7104986032573967614at_nat @ A @ C2 ) )
% 6.92/7.14 = ( plus_p7104986032573967614at_nat @ A @ ( plus_p7104986032573967614at_nat @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % ab_semigroup_add_class.add.left_commute
% 6.92/7.14 thf(fact_1145_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 6.92/7.14 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.14 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C2 ) )
% 6.92/7.14 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % ab_semigroup_add_class.add.left_commute
% 6.92/7.14 thf(fact_1146_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 6.92/7.14 ! [B: nat,A: nat,C2: nat] :
% 6.92/7.14 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C2 ) )
% 6.92/7.14 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % ab_semigroup_add_class.add.left_commute
% 6.92/7.14 thf(fact_1147_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 6.92/7.14 ! [B: int,A: int,C2: int] :
% 6.92/7.14 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C2 ) )
% 6.92/7.14 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % ab_semigroup_add_class.add.left_commute
% 6.92/7.14 thf(fact_1148_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 6.92/7.14 ( plus_p7104986032573967614at_nat
% 6.92/7.14 = ( ^ [A5: multis2468970476368604999at_nat,B4: multis2468970476368604999at_nat] : ( plus_p7104986032573967614at_nat @ B4 @ A5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % ab_semigroup_add_class.add.commute
% 6.92/7.14 thf(fact_1149_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 6.92/7.14 ( plus_plus_rat
% 6.92/7.14 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ B4 @ A5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % ab_semigroup_add_class.add.commute
% 6.92/7.14 thf(fact_1150_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 6.92/7.14 ( plus_plus_nat
% 6.92/7.14 = ( ^ [A5: nat,B4: nat] : ( plus_plus_nat @ B4 @ A5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % ab_semigroup_add_class.add.commute
% 6.92/7.14 thf(fact_1151_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 6.92/7.14 ( plus_plus_int
% 6.92/7.14 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ B4 @ A5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % ab_semigroup_add_class.add.commute
% 6.92/7.14 thf(fact_1152_add_Oright__cancel,axiom,
% 6.92/7.14 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.14 ( ( ( plus_plus_rat @ B @ A )
% 6.92/7.14 = ( plus_plus_rat @ C2 @ A ) )
% 6.92/7.14 = ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add.right_cancel
% 6.92/7.14 thf(fact_1153_add_Oright__cancel,axiom,
% 6.92/7.14 ! [B: int,A: int,C2: int] :
% 6.92/7.14 ( ( ( plus_plus_int @ B @ A )
% 6.92/7.14 = ( plus_plus_int @ C2 @ A ) )
% 6.92/7.14 = ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add.right_cancel
% 6.92/7.14 thf(fact_1154_add_Oleft__cancel,axiom,
% 6.92/7.14 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.14 ( ( ( plus_plus_rat @ A @ B )
% 6.92/7.14 = ( plus_plus_rat @ A @ C2 ) )
% 6.92/7.14 = ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add.left_cancel
% 6.92/7.14 thf(fact_1155_add_Oleft__cancel,axiom,
% 6.92/7.14 ! [A: int,B: int,C2: int] :
% 6.92/7.14 ( ( ( plus_plus_int @ A @ B )
% 6.92/7.14 = ( plus_plus_int @ A @ C2 ) )
% 6.92/7.14 = ( B = C2 ) ) ).
% 6.92/7.14
% 6.92/7.14 % add.left_cancel
% 6.92/7.14 thf(fact_1156_add_Oassoc,axiom,
% 6.92/7.14 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C2: multis2468970476368604999at_nat] :
% 6.92/7.14 ( ( plus_p7104986032573967614at_nat @ ( plus_p7104986032573967614at_nat @ A @ B ) @ C2 )
% 6.92/7.14 = ( plus_p7104986032573967614at_nat @ A @ ( plus_p7104986032573967614at_nat @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add.assoc
% 6.92/7.14 thf(fact_1157_add_Oassoc,axiom,
% 6.92/7.14 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.14 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 6.92/7.14 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add.assoc
% 6.92/7.14 thf(fact_1158_add_Oassoc,axiom,
% 6.92/7.14 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.14 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 6.92/7.14 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add.assoc
% 6.92/7.14 thf(fact_1159_add_Oassoc,axiom,
% 6.92/7.14 ! [A: int,B: int,C2: int] :
% 6.92/7.14 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 6.92/7.14 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add.assoc
% 6.92/7.14 thf(fact_1160_group__cancel_Oadd2,axiom,
% 6.92/7.14 ! [B5: multis2468970476368604999at_nat,K2: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat] :
% 6.92/7.14 ( ( B5
% 6.92/7.14 = ( plus_p7104986032573967614at_nat @ K2 @ B ) )
% 6.92/7.14 => ( ( plus_p7104986032573967614at_nat @ A @ B5 )
% 6.92/7.14 = ( plus_p7104986032573967614at_nat @ K2 @ ( plus_p7104986032573967614at_nat @ A @ B ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % group_cancel.add2
% 6.92/7.14 thf(fact_1161_group__cancel_Oadd2,axiom,
% 6.92/7.14 ! [B5: rat,K2: rat,B: rat,A: rat] :
% 6.92/7.14 ( ( B5
% 6.92/7.14 = ( plus_plus_rat @ K2 @ B ) )
% 6.92/7.14 => ( ( plus_plus_rat @ A @ B5 )
% 6.92/7.14 = ( plus_plus_rat @ K2 @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % group_cancel.add2
% 6.92/7.14 thf(fact_1162_group__cancel_Oadd2,axiom,
% 6.92/7.14 ! [B5: nat,K2: nat,B: nat,A: nat] :
% 6.92/7.14 ( ( B5
% 6.92/7.14 = ( plus_plus_nat @ K2 @ B ) )
% 6.92/7.14 => ( ( plus_plus_nat @ A @ B5 )
% 6.92/7.14 = ( plus_plus_nat @ K2 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % group_cancel.add2
% 6.92/7.14 thf(fact_1163_group__cancel_Oadd2,axiom,
% 6.92/7.14 ! [B5: int,K2: int,B: int,A: int] :
% 6.92/7.14 ( ( B5
% 6.92/7.14 = ( plus_plus_int @ K2 @ B ) )
% 6.92/7.14 => ( ( plus_plus_int @ A @ B5 )
% 6.92/7.14 = ( plus_plus_int @ K2 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % group_cancel.add2
% 6.92/7.14 thf(fact_1164_group__cancel_Oadd1,axiom,
% 6.92/7.14 ! [A4: multis2468970476368604999at_nat,K2: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 6.92/7.14 ( ( A4
% 6.92/7.14 = ( plus_p7104986032573967614at_nat @ K2 @ A ) )
% 6.92/7.14 => ( ( plus_p7104986032573967614at_nat @ A4 @ B )
% 6.92/7.14 = ( plus_p7104986032573967614at_nat @ K2 @ ( plus_p7104986032573967614at_nat @ A @ B ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % group_cancel.add1
% 6.92/7.14 thf(fact_1165_group__cancel_Oadd1,axiom,
% 6.92/7.14 ! [A4: rat,K2: rat,A: rat,B: rat] :
% 6.92/7.14 ( ( A4
% 6.92/7.14 = ( plus_plus_rat @ K2 @ A ) )
% 6.92/7.14 => ( ( plus_plus_rat @ A4 @ B )
% 6.92/7.14 = ( plus_plus_rat @ K2 @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % group_cancel.add1
% 6.92/7.14 thf(fact_1166_group__cancel_Oadd1,axiom,
% 6.92/7.14 ! [A4: nat,K2: nat,A: nat,B: nat] :
% 6.92/7.14 ( ( A4
% 6.92/7.14 = ( plus_plus_nat @ K2 @ A ) )
% 6.92/7.14 => ( ( plus_plus_nat @ A4 @ B )
% 6.92/7.14 = ( plus_plus_nat @ K2 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % group_cancel.add1
% 6.92/7.14 thf(fact_1167_group__cancel_Oadd1,axiom,
% 6.92/7.14 ! [A4: int,K2: int,A: int,B: int] :
% 6.92/7.14 ( ( A4
% 6.92/7.14 = ( plus_plus_int @ K2 @ A ) )
% 6.92/7.14 => ( ( plus_plus_int @ A4 @ B )
% 6.92/7.14 = ( plus_plus_int @ K2 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % group_cancel.add1
% 6.92/7.14 thf(fact_1168_add__mono__thms__linordered__semiring_I4_J,axiom,
% 6.92/7.14 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 6.92/7.14 ( ( ( I2 = J2 )
% 6.92/7.14 & ( K2 = L ) )
% 6.92/7.14 => ( ( plus_plus_rat @ I2 @ K2 )
% 6.92/7.14 = ( plus_plus_rat @ J2 @ L ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_mono_thms_linordered_semiring(4)
% 6.92/7.14 thf(fact_1169_add__mono__thms__linordered__semiring_I4_J,axiom,
% 6.92/7.14 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 6.92/7.14 ( ( ( I2 = J2 )
% 6.92/7.14 & ( K2 = L ) )
% 6.92/7.14 => ( ( plus_plus_nat @ I2 @ K2 )
% 6.92/7.14 = ( plus_plus_nat @ J2 @ L ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_mono_thms_linordered_semiring(4)
% 6.92/7.14 thf(fact_1170_add__mono__thms__linordered__semiring_I4_J,axiom,
% 6.92/7.14 ! [I2: int,J2: int,K2: int,L: int] :
% 6.92/7.14 ( ( ( I2 = J2 )
% 6.92/7.14 & ( K2 = L ) )
% 6.92/7.14 => ( ( plus_plus_int @ I2 @ K2 )
% 6.92/7.14 = ( plus_plus_int @ J2 @ L ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % add_mono_thms_linordered_semiring(4)
% 6.92/7.14 thf(fact_1171_sup__left__commute,axiom,
% 6.92/7.14 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z3 ) )
% 6.92/7.14 = ( sup_su3035147773818789531at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_left_commute
% 6.92/7.14 thf(fact_1172_sup__left__commute,axiom,
% 6.92/7.14 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z3 ) )
% 6.92/7.14 = ( sup_su5525570899277871387at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_left_commute
% 6.92/7.14 thf(fact_1173_sup__left__commute,axiom,
% 6.92/7.14 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z3 ) )
% 6.92/7.14 = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_left_commute
% 6.92/7.14 thf(fact_1174_sup__left__commute,axiom,
% 6.92/7.14 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.14 ( ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z3 ) )
% 6.92/7.14 = ( sup_sup_nat @ Y @ ( sup_sup_nat @ X @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_left_commute
% 6.92/7.14 thf(fact_1175_sup__left__commute,axiom,
% 6.92/7.14 ! [X: int,Y: int,Z3: int] :
% 6.92/7.14 ( ( sup_sup_int @ X @ ( sup_sup_int @ Y @ Z3 ) )
% 6.92/7.14 = ( sup_sup_int @ Y @ ( sup_sup_int @ X @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_left_commute
% 6.92/7.14 thf(fact_1176_sup_Oleft__commute,axiom,
% 6.92/7.14 ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ B @ ( sup_su3035147773818789531at_nat @ A @ C2 ) )
% 6.92/7.14 = ( sup_su3035147773818789531at_nat @ A @ ( sup_su3035147773818789531at_nat @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.left_commute
% 6.92/7.14 thf(fact_1177_sup_Oleft__commute,axiom,
% 6.92/7.14 ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ B @ ( sup_su5525570899277871387at_nat @ A @ C2 ) )
% 6.92/7.14 = ( sup_su5525570899277871387at_nat @ A @ ( sup_su5525570899277871387at_nat @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.left_commute
% 6.92/7.14 thf(fact_1178_sup_Oleft__commute,axiom,
% 6.92/7.14 ! [B: set_nat,A: set_nat,C2: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ B @ ( sup_sup_set_nat @ A @ C2 ) )
% 6.92/7.14 = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.left_commute
% 6.92/7.14 thf(fact_1179_sup_Oleft__commute,axiom,
% 6.92/7.14 ! [B: nat,A: nat,C2: nat] :
% 6.92/7.14 ( ( sup_sup_nat @ B @ ( sup_sup_nat @ A @ C2 ) )
% 6.92/7.14 = ( sup_sup_nat @ A @ ( sup_sup_nat @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.left_commute
% 6.92/7.14 thf(fact_1180_sup_Oleft__commute,axiom,
% 6.92/7.14 ! [B: int,A: int,C2: int] :
% 6.92/7.14 ( ( sup_sup_int @ B @ ( sup_sup_int @ A @ C2 ) )
% 6.92/7.14 = ( sup_sup_int @ A @ ( sup_sup_int @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.left_commute
% 6.92/7.14 thf(fact_1181_sup__commute,axiom,
% 6.92/7.14 ( sup_su3035147773818789531at_nat
% 6.92/7.14 = ( ^ [X4: set_Pr8551490117392284871at_nat,Y4: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ Y4 @ X4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_commute
% 6.92/7.14 thf(fact_1182_sup__commute,axiom,
% 6.92/7.14 ( sup_su5525570899277871387at_nat
% 6.92/7.14 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ Y4 @ X4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_commute
% 6.92/7.14 thf(fact_1183_sup__commute,axiom,
% 6.92/7.14 ( sup_sup_set_nat
% 6.92/7.14 = ( ^ [X4: set_nat,Y4: set_nat] : ( sup_sup_set_nat @ Y4 @ X4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_commute
% 6.92/7.14 thf(fact_1184_sup__commute,axiom,
% 6.92/7.14 ( sup_sup_nat
% 6.92/7.14 = ( ^ [X4: nat,Y4: nat] : ( sup_sup_nat @ Y4 @ X4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_commute
% 6.92/7.14 thf(fact_1185_sup__commute,axiom,
% 6.92/7.14 ( sup_sup_int
% 6.92/7.14 = ( ^ [X4: int,Y4: int] : ( sup_sup_int @ Y4 @ X4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_commute
% 6.92/7.14 thf(fact_1186_sup_Ocommute,axiom,
% 6.92/7.14 ( sup_su3035147773818789531at_nat
% 6.92/7.14 = ( ^ [A5: set_Pr8551490117392284871at_nat,B4: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ B4 @ A5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.commute
% 6.92/7.14 thf(fact_1187_sup_Ocommute,axiom,
% 6.92/7.14 ( sup_su5525570899277871387at_nat
% 6.92/7.14 = ( ^ [A5: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ B4 @ A5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.commute
% 6.92/7.14 thf(fact_1188_sup_Ocommute,axiom,
% 6.92/7.14 ( sup_sup_set_nat
% 6.92/7.14 = ( ^ [A5: set_nat,B4: set_nat] : ( sup_sup_set_nat @ B4 @ A5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.commute
% 6.92/7.14 thf(fact_1189_sup_Ocommute,axiom,
% 6.92/7.14 ( sup_sup_nat
% 6.92/7.14 = ( ^ [A5: nat,B4: nat] : ( sup_sup_nat @ B4 @ A5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.commute
% 6.92/7.14 thf(fact_1190_sup_Ocommute,axiom,
% 6.92/7.14 ( sup_sup_int
% 6.92/7.14 = ( ^ [A5: int,B4: int] : ( sup_sup_int @ B4 @ A5 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.commute
% 6.92/7.14 thf(fact_1191_sup__assoc,axiom,
% 6.92/7.14 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_assoc
% 6.92/7.14 thf(fact_1192_sup__assoc,axiom,
% 6.92/7.14 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_assoc
% 6.92/7.14 thf(fact_1193_sup__assoc,axiom,
% 6.92/7.14 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_assoc
% 6.92/7.14 thf(fact_1194_sup__assoc,axiom,
% 6.92/7.14 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.14 ( ( sup_sup_nat @ ( sup_sup_nat @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_assoc
% 6.92/7.14 thf(fact_1195_sup__assoc,axiom,
% 6.92/7.14 ! [X: int,Y: int,Z3: int] :
% 6.92/7.14 ( ( sup_sup_int @ ( sup_sup_int @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( sup_sup_int @ X @ ( sup_sup_int @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup_assoc
% 6.92/7.14 thf(fact_1196_sup_Oassoc,axiom,
% 6.92/7.14 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ C2 )
% 6.92/7.14 = ( sup_su3035147773818789531at_nat @ A @ ( sup_su3035147773818789531at_nat @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.assoc
% 6.92/7.14 thf(fact_1197_sup_Oassoc,axiom,
% 6.92/7.14 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ C2 )
% 6.92/7.14 = ( sup_su5525570899277871387at_nat @ A @ ( sup_su5525570899277871387at_nat @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.assoc
% 6.92/7.14 thf(fact_1198_sup_Oassoc,axiom,
% 6.92/7.14 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B ) @ C2 )
% 6.92/7.14 = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.assoc
% 6.92/7.14 thf(fact_1199_sup_Oassoc,axiom,
% 6.92/7.14 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.14 ( ( sup_sup_nat @ ( sup_sup_nat @ A @ B ) @ C2 )
% 6.92/7.14 = ( sup_sup_nat @ A @ ( sup_sup_nat @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.assoc
% 6.92/7.14 thf(fact_1200_sup_Oassoc,axiom,
% 6.92/7.14 ! [A: int,B: int,C2: int] :
% 6.92/7.14 ( ( sup_sup_int @ ( sup_sup_int @ A @ B ) @ C2 )
% 6.92/7.14 = ( sup_sup_int @ A @ ( sup_sup_int @ B @ C2 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % sup.assoc
% 6.92/7.14 thf(fact_1201_inf__sup__aci_I5_J,axiom,
% 6.92/7.14 ( sup_su3035147773818789531at_nat
% 6.92/7.14 = ( ^ [X4: set_Pr8551490117392284871at_nat,Y4: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ Y4 @ X4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % inf_sup_aci(5)
% 6.92/7.14 thf(fact_1202_inf__sup__aci_I5_J,axiom,
% 6.92/7.14 ( sup_su5525570899277871387at_nat
% 6.92/7.14 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ Y4 @ X4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % inf_sup_aci(5)
% 6.92/7.14 thf(fact_1203_inf__sup__aci_I5_J,axiom,
% 6.92/7.14 ( sup_sup_set_nat
% 6.92/7.14 = ( ^ [X4: set_nat,Y4: set_nat] : ( sup_sup_set_nat @ Y4 @ X4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % inf_sup_aci(5)
% 6.92/7.14 thf(fact_1204_inf__sup__aci_I5_J,axiom,
% 6.92/7.14 ( sup_sup_nat
% 6.92/7.14 = ( ^ [X4: nat,Y4: nat] : ( sup_sup_nat @ Y4 @ X4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % inf_sup_aci(5)
% 6.92/7.14 thf(fact_1205_inf__sup__aci_I5_J,axiom,
% 6.92/7.14 ( sup_sup_int
% 6.92/7.14 = ( ^ [X4: int,Y4: int] : ( sup_sup_int @ Y4 @ X4 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % inf_sup_aci(5)
% 6.92/7.14 thf(fact_1206_inf__sup__aci_I6_J,axiom,
% 6.92/7.14 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % inf_sup_aci(6)
% 6.92/7.14 thf(fact_1207_inf__sup__aci_I6_J,axiom,
% 6.92/7.14 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % inf_sup_aci(6)
% 6.92/7.14 thf(fact_1208_inf__sup__aci_I6_J,axiom,
% 6.92/7.14 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % inf_sup_aci(6)
% 6.92/7.14 thf(fact_1209_inf__sup__aci_I6_J,axiom,
% 6.92/7.14 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.14 ( ( sup_sup_nat @ ( sup_sup_nat @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % inf_sup_aci(6)
% 6.92/7.14 thf(fact_1210_inf__sup__aci_I6_J,axiom,
% 6.92/7.14 ! [X: int,Y: int,Z3: int] :
% 6.92/7.14 ( ( sup_sup_int @ ( sup_sup_int @ X @ Y ) @ Z3 )
% 6.92/7.14 = ( sup_sup_int @ X @ ( sup_sup_int @ Y @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % inf_sup_aci(6)
% 6.92/7.14 thf(fact_1211_inf__sup__aci_I7_J,axiom,
% 6.92/7.14 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] :
% 6.92/7.14 ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z3 ) )
% 6.92/7.14 = ( sup_su3035147773818789531at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % inf_sup_aci(7)
% 6.92/7.14 thf(fact_1212_inf__sup__aci_I7_J,axiom,
% 6.92/7.14 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] :
% 6.92/7.14 ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z3 ) )
% 6.92/7.14 = ( sup_su5525570899277871387at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % inf_sup_aci(7)
% 6.92/7.14 thf(fact_1213_inf__sup__aci_I7_J,axiom,
% 6.92/7.14 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 6.92/7.14 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z3 ) )
% 6.92/7.14 = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % inf_sup_aci(7)
% 6.92/7.14 thf(fact_1214_inf__sup__aci_I7_J,axiom,
% 6.92/7.14 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.14 ( ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z3 ) )
% 6.92/7.14 = ( sup_sup_nat @ Y @ ( sup_sup_nat @ X @ Z3 ) ) ) ).
% 6.92/7.14
% 6.92/7.14 % inf_sup_aci(7)
% 6.92/7.14 thf(fact_1215_inf__sup__aci_I7_J,axiom,
% 6.92/7.14 ! [X: int,Y: int,Z3: int] :
% 6.92/7.15 ( ( sup_sup_int @ X @ ( sup_sup_int @ Y @ Z3 ) )
% 6.92/7.15 = ( sup_sup_int @ Y @ ( sup_sup_int @ X @ Z3 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_aci(7)
% 6.92/7.15 thf(fact_1216_inf__sup__aci_I8_J,axiom,
% 6.92/7.15 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 6.92/7.15 = ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_aci(8)
% 6.92/7.15 thf(fact_1217_inf__sup__aci_I8_J,axiom,
% 6.92/7.15 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 6.92/7.15 = ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_aci(8)
% 6.92/7.15 thf(fact_1218_inf__sup__aci_I8_J,axiom,
% 6.92/7.15 ! [X: set_nat,Y: set_nat] :
% 6.92/7.15 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 6.92/7.15 = ( sup_sup_set_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_aci(8)
% 6.92/7.15 thf(fact_1219_inf__sup__aci_I8_J,axiom,
% 6.92/7.15 ! [X: nat,Y: nat] :
% 6.92/7.15 ( ( sup_sup_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 6.92/7.15 = ( sup_sup_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_aci(8)
% 6.92/7.15 thf(fact_1220_inf__sup__aci_I8_J,axiom,
% 6.92/7.15 ! [X: int,Y: int] :
% 6.92/7.15 ( ( sup_sup_int @ X @ ( sup_sup_int @ X @ Y ) )
% 6.92/7.15 = ( sup_sup_int @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_aci(8)
% 6.92/7.15 thf(fact_1221_add__le__imp__le__right,axiom,
% 6.92/7.15 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 6.92/7.15 => ( ord_less_eq_rat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_le_imp_le_right
% 6.92/7.15 thf(fact_1222_add__le__imp__le__right,axiom,
% 6.92/7.15 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 6.92/7.15 => ( ord_less_eq_nat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_le_imp_le_right
% 6.92/7.15 thf(fact_1223_add__le__imp__le__right,axiom,
% 6.92/7.15 ! [A: int,C2: int,B: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 6.92/7.15 => ( ord_less_eq_int @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_le_imp_le_right
% 6.92/7.15 thf(fact_1224_add__le__imp__le__left,axiom,
% 6.92/7.15 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 6.92/7.15 => ( ord_less_eq_rat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_le_imp_le_left
% 6.92/7.15 thf(fact_1225_add__le__imp__le__left,axiom,
% 6.92/7.15 ! [C2: nat,A: nat,B: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 6.92/7.15 => ( ord_less_eq_nat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_le_imp_le_left
% 6.92/7.15 thf(fact_1226_add__le__imp__le__left,axiom,
% 6.92/7.15 ! [C2: int,A: int,B: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 6.92/7.15 => ( ord_less_eq_int @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_le_imp_le_left
% 6.92/7.15 thf(fact_1227_le__iff__add,axiom,
% 6.92/7.15 ( ord_less_eq_nat
% 6.92/7.15 = ( ^ [A5: nat,B4: nat] :
% 6.92/7.15 ? [C3: nat] :
% 6.92/7.15 ( B4
% 6.92/7.15 = ( plus_plus_nat @ A5 @ C3 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_iff_add
% 6.92/7.15 thf(fact_1228_add__right__mono,axiom,
% 6.92/7.15 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.15 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_right_mono
% 6.92/7.15 thf(fact_1229_add__right__mono,axiom,
% 6.92/7.15 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.15 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_right_mono
% 6.92/7.15 thf(fact_1230_add__right__mono,axiom,
% 6.92/7.15 ! [A: int,B: int,C2: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.15 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_right_mono
% 6.92/7.15 thf(fact_1231_less__eqE,axiom,
% 6.92/7.15 ! [A: nat,B: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.15 => ~ ! [C: nat] :
% 6.92/7.15 ( B
% 6.92/7.15 != ( plus_plus_nat @ A @ C ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_eqE
% 6.92/7.15 thf(fact_1232_add__left__mono,axiom,
% 6.92/7.15 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.15 => ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_left_mono
% 6.92/7.15 thf(fact_1233_add__left__mono,axiom,
% 6.92/7.15 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.15 => ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_left_mono
% 6.92/7.15 thf(fact_1234_add__left__mono,axiom,
% 6.92/7.15 ! [A: int,B: int,C2: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.15 => ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_left_mono
% 6.92/7.15 thf(fact_1235_add__mono,axiom,
% 6.92/7.15 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.15 => ( ( ord_less_eq_rat @ C2 @ D2 )
% 6.92/7.15 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono
% 6.92/7.15 thf(fact_1236_add__mono,axiom,
% 6.92/7.15 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.15 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 6.92/7.15 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono
% 6.92/7.15 thf(fact_1237_add__mono,axiom,
% 6.92/7.15 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.15 => ( ( ord_less_eq_int @ C2 @ D2 )
% 6.92/7.15 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono
% 6.92/7.15 thf(fact_1238_add__mono__thms__linordered__semiring_I1_J,axiom,
% 6.92/7.15 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 6.92/7.15 ( ( ( ord_less_eq_rat @ I2 @ J2 )
% 6.92/7.15 & ( ord_less_eq_rat @ K2 @ L ) )
% 6.92/7.15 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_semiring(1)
% 6.92/7.15 thf(fact_1239_add__mono__thms__linordered__semiring_I1_J,axiom,
% 6.92/7.15 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 6.92/7.15 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.15 & ( ord_less_eq_nat @ K2 @ L ) )
% 6.92/7.15 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_semiring(1)
% 6.92/7.15 thf(fact_1240_add__mono__thms__linordered__semiring_I1_J,axiom,
% 6.92/7.15 ! [I2: int,J2: int,K2: int,L: int] :
% 6.92/7.15 ( ( ( ord_less_eq_int @ I2 @ J2 )
% 6.92/7.15 & ( ord_less_eq_int @ K2 @ L ) )
% 6.92/7.15 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_semiring(1)
% 6.92/7.15 thf(fact_1241_add__mono__thms__linordered__semiring_I2_J,axiom,
% 6.92/7.15 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 6.92/7.15 ( ( ( I2 = J2 )
% 6.92/7.15 & ( ord_less_eq_rat @ K2 @ L ) )
% 6.92/7.15 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_semiring(2)
% 6.92/7.15 thf(fact_1242_add__mono__thms__linordered__semiring_I2_J,axiom,
% 6.92/7.15 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 6.92/7.15 ( ( ( I2 = J2 )
% 6.92/7.15 & ( ord_less_eq_nat @ K2 @ L ) )
% 6.92/7.15 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_semiring(2)
% 6.92/7.15 thf(fact_1243_add__mono__thms__linordered__semiring_I2_J,axiom,
% 6.92/7.15 ! [I2: int,J2: int,K2: int,L: int] :
% 6.92/7.15 ( ( ( I2 = J2 )
% 6.92/7.15 & ( ord_less_eq_int @ K2 @ L ) )
% 6.92/7.15 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_semiring(2)
% 6.92/7.15 thf(fact_1244_add__mono__thms__linordered__semiring_I3_J,axiom,
% 6.92/7.15 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 6.92/7.15 ( ( ( ord_less_eq_rat @ I2 @ J2 )
% 6.92/7.15 & ( K2 = L ) )
% 6.92/7.15 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_semiring(3)
% 6.92/7.15 thf(fact_1245_add__mono__thms__linordered__semiring_I3_J,axiom,
% 6.92/7.15 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 6.92/7.15 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.15 & ( K2 = L ) )
% 6.92/7.15 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_semiring(3)
% 6.92/7.15 thf(fact_1246_add__mono__thms__linordered__semiring_I3_J,axiom,
% 6.92/7.15 ! [I2: int,J2: int,K2: int,L: int] :
% 6.92/7.15 ( ( ( ord_less_eq_int @ I2 @ J2 )
% 6.92/7.15 & ( K2 = L ) )
% 6.92/7.15 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_semiring(3)
% 6.92/7.15 thf(fact_1247_add__less__imp__less__right,axiom,
% 6.92/7.15 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.15 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 6.92/7.15 => ( ord_less_rat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_less_imp_less_right
% 6.92/7.15 thf(fact_1248_add__less__imp__less__right,axiom,
% 6.92/7.15 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.15 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 6.92/7.15 => ( ord_less_nat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_less_imp_less_right
% 6.92/7.15 thf(fact_1249_add__less__imp__less__right,axiom,
% 6.92/7.15 ! [A: int,C2: int,B: int] :
% 6.92/7.15 ( ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 6.92/7.15 => ( ord_less_int @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_less_imp_less_right
% 6.92/7.15 thf(fact_1250_add__less__imp__less__left,axiom,
% 6.92/7.15 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.15 ( ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 6.92/7.15 => ( ord_less_rat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_less_imp_less_left
% 6.92/7.15 thf(fact_1251_add__less__imp__less__left,axiom,
% 6.92/7.15 ! [C2: nat,A: nat,B: nat] :
% 6.92/7.15 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 6.92/7.15 => ( ord_less_nat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_less_imp_less_left
% 6.92/7.15 thf(fact_1252_add__less__imp__less__left,axiom,
% 6.92/7.15 ! [C2: int,A: int,B: int] :
% 6.92/7.15 ( ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 6.92/7.15 => ( ord_less_int @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_less_imp_less_left
% 6.92/7.15 thf(fact_1253_add__strict__right__mono,axiom,
% 6.92/7.15 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.15 ( ( ord_less_rat @ A @ B )
% 6.92/7.15 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_strict_right_mono
% 6.92/7.15 thf(fact_1254_add__strict__right__mono,axiom,
% 6.92/7.15 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.15 ( ( ord_less_nat @ A @ B )
% 6.92/7.15 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_strict_right_mono
% 6.92/7.15 thf(fact_1255_add__strict__right__mono,axiom,
% 6.92/7.15 ! [A: int,B: int,C2: int] :
% 6.92/7.15 ( ( ord_less_int @ A @ B )
% 6.92/7.15 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_strict_right_mono
% 6.92/7.15 thf(fact_1256_add__strict__left__mono,axiom,
% 6.92/7.15 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.15 ( ( ord_less_rat @ A @ B )
% 6.92/7.15 => ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_strict_left_mono
% 6.92/7.15 thf(fact_1257_add__strict__left__mono,axiom,
% 6.92/7.15 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.15 ( ( ord_less_nat @ A @ B )
% 6.92/7.15 => ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_strict_left_mono
% 6.92/7.15 thf(fact_1258_add__strict__left__mono,axiom,
% 6.92/7.15 ! [A: int,B: int,C2: int] :
% 6.92/7.15 ( ( ord_less_int @ A @ B )
% 6.92/7.15 => ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_strict_left_mono
% 6.92/7.15 thf(fact_1259_add__strict__mono,axiom,
% 6.92/7.15 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.15 ( ( ord_less_rat @ A @ B )
% 6.92/7.15 => ( ( ord_less_rat @ C2 @ D2 )
% 6.92/7.15 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_strict_mono
% 6.92/7.15 thf(fact_1260_add__strict__mono,axiom,
% 6.92/7.15 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.15 ( ( ord_less_nat @ A @ B )
% 6.92/7.15 => ( ( ord_less_nat @ C2 @ D2 )
% 6.92/7.15 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_strict_mono
% 6.92/7.15 thf(fact_1261_add__strict__mono,axiom,
% 6.92/7.15 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.15 ( ( ord_less_int @ A @ B )
% 6.92/7.15 => ( ( ord_less_int @ C2 @ D2 )
% 6.92/7.15 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_strict_mono
% 6.92/7.15 thf(fact_1262_add__mono__thms__linordered__field_I1_J,axiom,
% 6.92/7.15 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 6.92/7.15 ( ( ( ord_less_rat @ I2 @ J2 )
% 6.92/7.15 & ( K2 = L ) )
% 6.92/7.15 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_field(1)
% 6.92/7.15 thf(fact_1263_add__mono__thms__linordered__field_I1_J,axiom,
% 6.92/7.15 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 6.92/7.15 ( ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.15 & ( K2 = L ) )
% 6.92/7.15 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_field(1)
% 6.92/7.15 thf(fact_1264_add__mono__thms__linordered__field_I1_J,axiom,
% 6.92/7.15 ! [I2: int,J2: int,K2: int,L: int] :
% 6.92/7.15 ( ( ( ord_less_int @ I2 @ J2 )
% 6.92/7.15 & ( K2 = L ) )
% 6.92/7.15 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_field(1)
% 6.92/7.15 thf(fact_1265_add__mono__thms__linordered__field_I2_J,axiom,
% 6.92/7.15 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 6.92/7.15 ( ( ( I2 = J2 )
% 6.92/7.15 & ( ord_less_rat @ K2 @ L ) )
% 6.92/7.15 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_field(2)
% 6.92/7.15 thf(fact_1266_add__mono__thms__linordered__field_I2_J,axiom,
% 6.92/7.15 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 6.92/7.15 ( ( ( I2 = J2 )
% 6.92/7.15 & ( ord_less_nat @ K2 @ L ) )
% 6.92/7.15 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_field(2)
% 6.92/7.15 thf(fact_1267_add__mono__thms__linordered__field_I2_J,axiom,
% 6.92/7.15 ! [I2: int,J2: int,K2: int,L: int] :
% 6.92/7.15 ( ( ( I2 = J2 )
% 6.92/7.15 & ( ord_less_int @ K2 @ L ) )
% 6.92/7.15 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_field(2)
% 6.92/7.15 thf(fact_1268_add__mono__thms__linordered__field_I5_J,axiom,
% 6.92/7.15 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 6.92/7.15 ( ( ( ord_less_rat @ I2 @ J2 )
% 6.92/7.15 & ( ord_less_rat @ K2 @ L ) )
% 6.92/7.15 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_field(5)
% 6.92/7.15 thf(fact_1269_add__mono__thms__linordered__field_I5_J,axiom,
% 6.92/7.15 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 6.92/7.15 ( ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.15 & ( ord_less_nat @ K2 @ L ) )
% 6.92/7.15 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_field(5)
% 6.92/7.15 thf(fact_1270_add__mono__thms__linordered__field_I5_J,axiom,
% 6.92/7.15 ! [I2: int,J2: int,K2: int,L: int] :
% 6.92/7.15 ( ( ( ord_less_int @ I2 @ J2 )
% 6.92/7.15 & ( ord_less_int @ K2 @ L ) )
% 6.92/7.15 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % add_mono_thms_linordered_field(5)
% 6.92/7.15 thf(fact_1271_sup_OcoboundedI2,axiom,
% 6.92/7.15 ! [C2: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ C2 @ B )
% 6.92/7.15 => ( ord_le8081472938463900775at_nat @ C2 @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.coboundedI2
% 6.92/7.15 thf(fact_1272_sup_OcoboundedI2,axiom,
% 6.92/7.15 ! [C2: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ C2 @ B )
% 6.92/7.15 => ( ord_le1268244103169919719at_nat @ C2 @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.coboundedI2
% 6.92/7.15 thf(fact_1273_sup_OcoboundedI2,axiom,
% 6.92/7.15 ! [C2: set_nat,B: set_nat,A: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ C2 @ B )
% 6.92/7.15 => ( ord_less_eq_set_nat @ C2 @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.coboundedI2
% 6.92/7.15 thf(fact_1274_sup_OcoboundedI2,axiom,
% 6.92/7.15 ! [C2: set_int,B: set_int,A: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ C2 @ B )
% 6.92/7.15 => ( ord_less_eq_set_int @ C2 @ ( sup_sup_set_int @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.coboundedI2
% 6.92/7.15 thf(fact_1275_sup_OcoboundedI2,axiom,
% 6.92/7.15 ! [C2: rat,B: rat,A: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ C2 @ B )
% 6.92/7.15 => ( ord_less_eq_rat @ C2 @ ( sup_sup_rat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.coboundedI2
% 6.92/7.15 thf(fact_1276_sup_OcoboundedI2,axiom,
% 6.92/7.15 ! [C2: nat,B: nat,A: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ C2 @ B )
% 6.92/7.15 => ( ord_less_eq_nat @ C2 @ ( sup_sup_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.coboundedI2
% 6.92/7.15 thf(fact_1277_sup_OcoboundedI2,axiom,
% 6.92/7.15 ! [C2: int,B: int,A: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ C2 @ B )
% 6.92/7.15 => ( ord_less_eq_int @ C2 @ ( sup_sup_int @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.coboundedI2
% 6.92/7.15 thf(fact_1278_sup_OcoboundedI1,axiom,
% 6.92/7.15 ! [C2: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ C2 @ A )
% 6.92/7.15 => ( ord_le8081472938463900775at_nat @ C2 @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.coboundedI1
% 6.92/7.15 thf(fact_1279_sup_OcoboundedI1,axiom,
% 6.92/7.15 ! [C2: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ C2 @ A )
% 6.92/7.15 => ( ord_le1268244103169919719at_nat @ C2 @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.coboundedI1
% 6.92/7.15 thf(fact_1280_sup_OcoboundedI1,axiom,
% 6.92/7.15 ! [C2: set_nat,A: set_nat,B: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ C2 @ A )
% 6.92/7.15 => ( ord_less_eq_set_nat @ C2 @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.coboundedI1
% 6.92/7.15 thf(fact_1281_sup_OcoboundedI1,axiom,
% 6.92/7.15 ! [C2: set_int,A: set_int,B: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ C2 @ A )
% 6.92/7.15 => ( ord_less_eq_set_int @ C2 @ ( sup_sup_set_int @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.coboundedI1
% 6.92/7.15 thf(fact_1282_sup_OcoboundedI1,axiom,
% 6.92/7.15 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ C2 @ A )
% 6.92/7.15 => ( ord_less_eq_rat @ C2 @ ( sup_sup_rat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.coboundedI1
% 6.92/7.15 thf(fact_1283_sup_OcoboundedI1,axiom,
% 6.92/7.15 ! [C2: nat,A: nat,B: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ C2 @ A )
% 6.92/7.15 => ( ord_less_eq_nat @ C2 @ ( sup_sup_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.coboundedI1
% 6.92/7.15 thf(fact_1284_sup_OcoboundedI1,axiom,
% 6.92/7.15 ! [C2: int,A: int,B: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ C2 @ A )
% 6.92/7.15 => ( ord_less_eq_int @ C2 @ ( sup_sup_int @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.coboundedI1
% 6.92/7.15 thf(fact_1285_sup_Oabsorb__iff2,axiom,
% 6.92/7.15 ( ord_le8081472938463900775at_nat
% 6.92/7.15 = ( ^ [A5: set_Pr8551490117392284871at_nat,B4: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( sup_su3035147773818789531at_nat @ A5 @ B4 )
% 6.92/7.15 = B4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb_iff2
% 6.92/7.15 thf(fact_1286_sup_Oabsorb__iff2,axiom,
% 6.92/7.15 ( ord_le1268244103169919719at_nat
% 6.92/7.15 = ( ^ [A5: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( sup_su5525570899277871387at_nat @ A5 @ B4 )
% 6.92/7.15 = B4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb_iff2
% 6.92/7.15 thf(fact_1287_sup_Oabsorb__iff2,axiom,
% 6.92/7.15 ( ord_less_eq_set_nat
% 6.92/7.15 = ( ^ [A5: set_nat,B4: set_nat] :
% 6.92/7.15 ( ( sup_sup_set_nat @ A5 @ B4 )
% 6.92/7.15 = B4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb_iff2
% 6.92/7.15 thf(fact_1288_sup_Oabsorb__iff2,axiom,
% 6.92/7.15 ( ord_less_eq_set_int
% 6.92/7.15 = ( ^ [A5: set_int,B4: set_int] :
% 6.92/7.15 ( ( sup_sup_set_int @ A5 @ B4 )
% 6.92/7.15 = B4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb_iff2
% 6.92/7.15 thf(fact_1289_sup_Oabsorb__iff2,axiom,
% 6.92/7.15 ( ord_less_eq_rat
% 6.92/7.15 = ( ^ [A5: rat,B4: rat] :
% 6.92/7.15 ( ( sup_sup_rat @ A5 @ B4 )
% 6.92/7.15 = B4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb_iff2
% 6.92/7.15 thf(fact_1290_sup_Oabsorb__iff2,axiom,
% 6.92/7.15 ( ord_less_eq_nat
% 6.92/7.15 = ( ^ [A5: nat,B4: nat] :
% 6.92/7.15 ( ( sup_sup_nat @ A5 @ B4 )
% 6.92/7.15 = B4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb_iff2
% 6.92/7.15 thf(fact_1291_sup_Oabsorb__iff2,axiom,
% 6.92/7.15 ( ord_less_eq_int
% 6.92/7.15 = ( ^ [A5: int,B4: int] :
% 6.92/7.15 ( ( sup_sup_int @ A5 @ B4 )
% 6.92/7.15 = B4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb_iff2
% 6.92/7.15 thf(fact_1292_sup_Oabsorb__iff1,axiom,
% 6.92/7.15 ( ord_le8081472938463900775at_nat
% 6.92/7.15 = ( ^ [B4: set_Pr8551490117392284871at_nat,A5: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( sup_su3035147773818789531at_nat @ A5 @ B4 )
% 6.92/7.15 = A5 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb_iff1
% 6.92/7.15 thf(fact_1293_sup_Oabsorb__iff1,axiom,
% 6.92/7.15 ( ord_le1268244103169919719at_nat
% 6.92/7.15 = ( ^ [B4: set_Pr4329608150637261639at_nat,A5: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( sup_su5525570899277871387at_nat @ A5 @ B4 )
% 6.92/7.15 = A5 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb_iff1
% 6.92/7.15 thf(fact_1294_sup_Oabsorb__iff1,axiom,
% 6.92/7.15 ( ord_less_eq_set_nat
% 6.92/7.15 = ( ^ [B4: set_nat,A5: set_nat] :
% 6.92/7.15 ( ( sup_sup_set_nat @ A5 @ B4 )
% 6.92/7.15 = A5 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb_iff1
% 6.92/7.15 thf(fact_1295_sup_Oabsorb__iff1,axiom,
% 6.92/7.15 ( ord_less_eq_set_int
% 6.92/7.15 = ( ^ [B4: set_int,A5: set_int] :
% 6.92/7.15 ( ( sup_sup_set_int @ A5 @ B4 )
% 6.92/7.15 = A5 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb_iff1
% 6.92/7.15 thf(fact_1296_sup_Oabsorb__iff1,axiom,
% 6.92/7.15 ( ord_less_eq_rat
% 6.92/7.15 = ( ^ [B4: rat,A5: rat] :
% 6.92/7.15 ( ( sup_sup_rat @ A5 @ B4 )
% 6.92/7.15 = A5 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb_iff1
% 6.92/7.15 thf(fact_1297_sup_Oabsorb__iff1,axiom,
% 6.92/7.15 ( ord_less_eq_nat
% 6.92/7.15 = ( ^ [B4: nat,A5: nat] :
% 6.92/7.15 ( ( sup_sup_nat @ A5 @ B4 )
% 6.92/7.15 = A5 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb_iff1
% 6.92/7.15 thf(fact_1298_sup_Oabsorb__iff1,axiom,
% 6.92/7.15 ( ord_less_eq_int
% 6.92/7.15 = ( ^ [B4: int,A5: int] :
% 6.92/7.15 ( ( sup_sup_int @ A5 @ B4 )
% 6.92/7.15 = A5 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb_iff1
% 6.92/7.15 thf(fact_1299_sup_Ocobounded2,axiom,
% 6.92/7.15 ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ B @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.cobounded2
% 6.92/7.15 thf(fact_1300_sup_Ocobounded2,axiom,
% 6.92/7.15 ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ B @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.cobounded2
% 6.92/7.15 thf(fact_1301_sup_Ocobounded2,axiom,
% 6.92/7.15 ! [B: set_nat,A: set_nat] : ( ord_less_eq_set_nat @ B @ ( sup_sup_set_nat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.cobounded2
% 6.92/7.15 thf(fact_1302_sup_Ocobounded2,axiom,
% 6.92/7.15 ! [B: set_int,A: set_int] : ( ord_less_eq_set_int @ B @ ( sup_sup_set_int @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.cobounded2
% 6.92/7.15 thf(fact_1303_sup_Ocobounded2,axiom,
% 6.92/7.15 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( sup_sup_rat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.cobounded2
% 6.92/7.15 thf(fact_1304_sup_Ocobounded2,axiom,
% 6.92/7.15 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( sup_sup_nat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.cobounded2
% 6.92/7.15 thf(fact_1305_sup_Ocobounded2,axiom,
% 6.92/7.15 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( sup_sup_int @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.cobounded2
% 6.92/7.15 thf(fact_1306_sup_Ocobounded1,axiom,
% 6.92/7.15 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ A @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.cobounded1
% 6.92/7.15 thf(fact_1307_sup_Ocobounded1,axiom,
% 6.92/7.15 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ A @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.cobounded1
% 6.92/7.15 thf(fact_1308_sup_Ocobounded1,axiom,
% 6.92/7.15 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.cobounded1
% 6.92/7.15 thf(fact_1309_sup_Ocobounded1,axiom,
% 6.92/7.15 ! [A: set_int,B: set_int] : ( ord_less_eq_set_int @ A @ ( sup_sup_set_int @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.cobounded1
% 6.92/7.15 thf(fact_1310_sup_Ocobounded1,axiom,
% 6.92/7.15 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( sup_sup_rat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.cobounded1
% 6.92/7.15 thf(fact_1311_sup_Ocobounded1,axiom,
% 6.92/7.15 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( sup_sup_nat @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.cobounded1
% 6.92/7.15 thf(fact_1312_sup_Ocobounded1,axiom,
% 6.92/7.15 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ A @ B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.cobounded1
% 6.92/7.15 thf(fact_1313_sup_Oorder__iff,axiom,
% 6.92/7.15 ( ord_le8081472938463900775at_nat
% 6.92/7.15 = ( ^ [B4: set_Pr8551490117392284871at_nat,A5: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( A5
% 6.92/7.15 = ( sup_su3035147773818789531at_nat @ A5 @ B4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.order_iff
% 6.92/7.15 thf(fact_1314_sup_Oorder__iff,axiom,
% 6.92/7.15 ( ord_le1268244103169919719at_nat
% 6.92/7.15 = ( ^ [B4: set_Pr4329608150637261639at_nat,A5: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( A5
% 6.92/7.15 = ( sup_su5525570899277871387at_nat @ A5 @ B4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.order_iff
% 6.92/7.15 thf(fact_1315_sup_Oorder__iff,axiom,
% 6.92/7.15 ( ord_less_eq_set_nat
% 6.92/7.15 = ( ^ [B4: set_nat,A5: set_nat] :
% 6.92/7.15 ( A5
% 6.92/7.15 = ( sup_sup_set_nat @ A5 @ B4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.order_iff
% 6.92/7.15 thf(fact_1316_sup_Oorder__iff,axiom,
% 6.92/7.15 ( ord_less_eq_set_int
% 6.92/7.15 = ( ^ [B4: set_int,A5: set_int] :
% 6.92/7.15 ( A5
% 6.92/7.15 = ( sup_sup_set_int @ A5 @ B4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.order_iff
% 6.92/7.15 thf(fact_1317_sup_Oorder__iff,axiom,
% 6.92/7.15 ( ord_less_eq_rat
% 6.92/7.15 = ( ^ [B4: rat,A5: rat] :
% 6.92/7.15 ( A5
% 6.92/7.15 = ( sup_sup_rat @ A5 @ B4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.order_iff
% 6.92/7.15 thf(fact_1318_sup_Oorder__iff,axiom,
% 6.92/7.15 ( ord_less_eq_nat
% 6.92/7.15 = ( ^ [B4: nat,A5: nat] :
% 6.92/7.15 ( A5
% 6.92/7.15 = ( sup_sup_nat @ A5 @ B4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.order_iff
% 6.92/7.15 thf(fact_1319_sup_Oorder__iff,axiom,
% 6.92/7.15 ( ord_less_eq_int
% 6.92/7.15 = ( ^ [B4: int,A5: int] :
% 6.92/7.15 ( A5
% 6.92/7.15 = ( sup_sup_int @ A5 @ B4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.order_iff
% 6.92/7.15 thf(fact_1320_sup_OboundedI,axiom,
% 6.92/7.15 ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ B @ A )
% 6.92/7.15 => ( ( ord_le8081472938463900775at_nat @ C2 @ A )
% 6.92/7.15 => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ B @ C2 ) @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.boundedI
% 6.92/7.15 thf(fact_1321_sup_OboundedI,axiom,
% 6.92/7.15 ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ B @ A )
% 6.92/7.15 => ( ( ord_le1268244103169919719at_nat @ C2 @ A )
% 6.92/7.15 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B @ C2 ) @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.boundedI
% 6.92/7.15 thf(fact_1322_sup_OboundedI,axiom,
% 6.92/7.15 ! [B: set_nat,A: set_nat,C2: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ B @ A )
% 6.92/7.15 => ( ( ord_less_eq_set_nat @ C2 @ A )
% 6.92/7.15 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C2 ) @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.boundedI
% 6.92/7.15 thf(fact_1323_sup_OboundedI,axiom,
% 6.92/7.15 ! [B: set_int,A: set_int,C2: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ B @ A )
% 6.92/7.15 => ( ( ord_less_eq_set_int @ C2 @ A )
% 6.92/7.15 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ B @ C2 ) @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.boundedI
% 6.92/7.15 thf(fact_1324_sup_OboundedI,axiom,
% 6.92/7.15 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.15 => ( ( ord_less_eq_rat @ C2 @ A )
% 6.92/7.15 => ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C2 ) @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.boundedI
% 6.92/7.15 thf(fact_1325_sup_OboundedI,axiom,
% 6.92/7.15 ! [B: nat,A: nat,C2: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.15 => ( ( ord_less_eq_nat @ C2 @ A )
% 6.92/7.15 => ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C2 ) @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.boundedI
% 6.92/7.15 thf(fact_1326_sup_OboundedI,axiom,
% 6.92/7.15 ! [B: int,A: int,C2: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ B @ A )
% 6.92/7.15 => ( ( ord_less_eq_int @ C2 @ A )
% 6.92/7.15 => ( ord_less_eq_int @ ( sup_sup_int @ B @ C2 ) @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.boundedI
% 6.92/7.15 thf(fact_1327_sup_OboundedE,axiom,
% 6.92/7.15 ! [B: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ B @ C2 ) @ A )
% 6.92/7.15 => ~ ( ( ord_le8081472938463900775at_nat @ B @ A )
% 6.92/7.15 => ~ ( ord_le8081472938463900775at_nat @ C2 @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.boundedE
% 6.92/7.15 thf(fact_1328_sup_OboundedE,axiom,
% 6.92/7.15 ! [B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B @ C2 ) @ A )
% 6.92/7.15 => ~ ( ( ord_le1268244103169919719at_nat @ B @ A )
% 6.92/7.15 => ~ ( ord_le1268244103169919719at_nat @ C2 @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.boundedE
% 6.92/7.15 thf(fact_1329_sup_OboundedE,axiom,
% 6.92/7.15 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C2 ) @ A )
% 6.92/7.15 => ~ ( ( ord_less_eq_set_nat @ B @ A )
% 6.92/7.15 => ~ ( ord_less_eq_set_nat @ C2 @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.boundedE
% 6.92/7.15 thf(fact_1330_sup_OboundedE,axiom,
% 6.92/7.15 ! [B: set_int,C2: set_int,A: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ ( sup_sup_set_int @ B @ C2 ) @ A )
% 6.92/7.15 => ~ ( ( ord_less_eq_set_int @ B @ A )
% 6.92/7.15 => ~ ( ord_less_eq_set_int @ C2 @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.boundedE
% 6.92/7.15 thf(fact_1331_sup_OboundedE,axiom,
% 6.92/7.15 ! [B: rat,C2: rat,A: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C2 ) @ A )
% 6.92/7.15 => ~ ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.15 => ~ ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.boundedE
% 6.92/7.15 thf(fact_1332_sup_OboundedE,axiom,
% 6.92/7.15 ! [B: nat,C2: nat,A: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C2 ) @ A )
% 6.92/7.15 => ~ ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.15 => ~ ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.boundedE
% 6.92/7.15 thf(fact_1333_sup_OboundedE,axiom,
% 6.92/7.15 ! [B: int,C2: int,A: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C2 ) @ A )
% 6.92/7.15 => ~ ( ( ord_less_eq_int @ B @ A )
% 6.92/7.15 => ~ ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.boundedE
% 6.92/7.15 thf(fact_1334_sup__absorb2,axiom,
% 6.92/7.15 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ X @ Y )
% 6.92/7.15 => ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 6.92/7.15 = Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_absorb2
% 6.92/7.15 thf(fact_1335_sup__absorb2,axiom,
% 6.92/7.15 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ X @ Y )
% 6.92/7.15 => ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 6.92/7.15 = Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_absorb2
% 6.92/7.15 thf(fact_1336_sup__absorb2,axiom,
% 6.92/7.15 ! [X: set_nat,Y: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ X @ Y )
% 6.92/7.15 => ( ( sup_sup_set_nat @ X @ Y )
% 6.92/7.15 = Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_absorb2
% 6.92/7.15 thf(fact_1337_sup__absorb2,axiom,
% 6.92/7.15 ! [X: set_int,Y: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ X @ Y )
% 6.92/7.15 => ( ( sup_sup_set_int @ X @ Y )
% 6.92/7.15 = Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_absorb2
% 6.92/7.15 thf(fact_1338_sup__absorb2,axiom,
% 6.92/7.15 ! [X: rat,Y: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.15 => ( ( sup_sup_rat @ X @ Y )
% 6.92/7.15 = Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_absorb2
% 6.92/7.15 thf(fact_1339_sup__absorb2,axiom,
% 6.92/7.15 ! [X: nat,Y: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ X @ Y )
% 6.92/7.15 => ( ( sup_sup_nat @ X @ Y )
% 6.92/7.15 = Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_absorb2
% 6.92/7.15 thf(fact_1340_sup__absorb2,axiom,
% 6.92/7.15 ! [X: int,Y: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.15 => ( ( sup_sup_int @ X @ Y )
% 6.92/7.15 = Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_absorb2
% 6.92/7.15 thf(fact_1341_sup__absorb1,axiom,
% 6.92/7.15 ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ Y @ X )
% 6.92/7.15 => ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 6.92/7.15 = X ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_absorb1
% 6.92/7.15 thf(fact_1342_sup__absorb1,axiom,
% 6.92/7.15 ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ Y @ X )
% 6.92/7.15 => ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 6.92/7.15 = X ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_absorb1
% 6.92/7.15 thf(fact_1343_sup__absorb1,axiom,
% 6.92/7.15 ! [Y: set_nat,X: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ Y @ X )
% 6.92/7.15 => ( ( sup_sup_set_nat @ X @ Y )
% 6.92/7.15 = X ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_absorb1
% 6.92/7.15 thf(fact_1344_sup__absorb1,axiom,
% 6.92/7.15 ! [Y: set_int,X: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ Y @ X )
% 6.92/7.15 => ( ( sup_sup_set_int @ X @ Y )
% 6.92/7.15 = X ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_absorb1
% 6.92/7.15 thf(fact_1345_sup__absorb1,axiom,
% 6.92/7.15 ! [Y: rat,X: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ Y @ X )
% 6.92/7.15 => ( ( sup_sup_rat @ X @ Y )
% 6.92/7.15 = X ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_absorb1
% 6.92/7.15 thf(fact_1346_sup__absorb1,axiom,
% 6.92/7.15 ! [Y: nat,X: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ Y @ X )
% 6.92/7.15 => ( ( sup_sup_nat @ X @ Y )
% 6.92/7.15 = X ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_absorb1
% 6.92/7.15 thf(fact_1347_sup__absorb1,axiom,
% 6.92/7.15 ! [Y: int,X: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ Y @ X )
% 6.92/7.15 => ( ( sup_sup_int @ X @ Y )
% 6.92/7.15 = X ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_absorb1
% 6.92/7.15 thf(fact_1348_sup_Oabsorb2,axiom,
% 6.92/7.15 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ A @ B )
% 6.92/7.15 => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 6.92/7.15 = B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb2
% 6.92/7.15 thf(fact_1349_sup_Oabsorb2,axiom,
% 6.92/7.15 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ A @ B )
% 6.92/7.15 => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 6.92/7.15 = B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb2
% 6.92/7.15 thf(fact_1350_sup_Oabsorb2,axiom,
% 6.92/7.15 ! [A: set_nat,B: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ A @ B )
% 6.92/7.15 => ( ( sup_sup_set_nat @ A @ B )
% 6.92/7.15 = B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb2
% 6.92/7.15 thf(fact_1351_sup_Oabsorb2,axiom,
% 6.92/7.15 ! [A: set_int,B: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ A @ B )
% 6.92/7.15 => ( ( sup_sup_set_int @ A @ B )
% 6.92/7.15 = B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb2
% 6.92/7.15 thf(fact_1352_sup_Oabsorb2,axiom,
% 6.92/7.15 ! [A: rat,B: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.15 => ( ( sup_sup_rat @ A @ B )
% 6.92/7.15 = B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb2
% 6.92/7.15 thf(fact_1353_sup_Oabsorb2,axiom,
% 6.92/7.15 ! [A: nat,B: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.15 => ( ( sup_sup_nat @ A @ B )
% 6.92/7.15 = B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb2
% 6.92/7.15 thf(fact_1354_sup_Oabsorb2,axiom,
% 6.92/7.15 ! [A: int,B: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.15 => ( ( sup_sup_int @ A @ B )
% 6.92/7.15 = B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb2
% 6.92/7.15 thf(fact_1355_sup_Oabsorb1,axiom,
% 6.92/7.15 ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ B @ A )
% 6.92/7.15 => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 6.92/7.15 = A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb1
% 6.92/7.15 thf(fact_1356_sup_Oabsorb1,axiom,
% 6.92/7.15 ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ B @ A )
% 6.92/7.15 => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 6.92/7.15 = A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb1
% 6.92/7.15 thf(fact_1357_sup_Oabsorb1,axiom,
% 6.92/7.15 ! [B: set_nat,A: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ B @ A )
% 6.92/7.15 => ( ( sup_sup_set_nat @ A @ B )
% 6.92/7.15 = A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb1
% 6.92/7.15 thf(fact_1358_sup_Oabsorb1,axiom,
% 6.92/7.15 ! [B: set_int,A: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ B @ A )
% 6.92/7.15 => ( ( sup_sup_set_int @ A @ B )
% 6.92/7.15 = A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb1
% 6.92/7.15 thf(fact_1359_sup_Oabsorb1,axiom,
% 6.92/7.15 ! [B: rat,A: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.15 => ( ( sup_sup_rat @ A @ B )
% 6.92/7.15 = A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb1
% 6.92/7.15 thf(fact_1360_sup_Oabsorb1,axiom,
% 6.92/7.15 ! [B: nat,A: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.15 => ( ( sup_sup_nat @ A @ B )
% 6.92/7.15 = A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb1
% 6.92/7.15 thf(fact_1361_sup_Oabsorb1,axiom,
% 6.92/7.15 ! [B: int,A: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ B @ A )
% 6.92/7.15 => ( ( sup_sup_int @ A @ B )
% 6.92/7.15 = A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb1
% 6.92/7.15 thf(fact_1362_sup__unique,axiom,
% 6.92/7.15 ! [F: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ! [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ X3 @ ( F @ X3 @ Y3 ) )
% 6.92/7.15 => ( ! [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y3 @ ( F @ X3 @ Y3 ) )
% 6.92/7.15 => ( ! [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat,Z2: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ Y3 @ X3 )
% 6.92/7.15 => ( ( ord_le8081472938463900775at_nat @ Z2 @ X3 )
% 6.92/7.15 => ( ord_le8081472938463900775at_nat @ ( F @ Y3 @ Z2 ) @ X3 ) ) )
% 6.92/7.15 => ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 6.92/7.15 = ( F @ X @ Y ) ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_unique
% 6.92/7.15 thf(fact_1363_sup__unique,axiom,
% 6.92/7.15 ! [F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ! [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X3 @ ( F @ X3 @ Y3 ) )
% 6.92/7.15 => ( ! [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y3 @ ( F @ X3 @ Y3 ) )
% 6.92/7.15 => ( ! [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ Y3 @ X3 )
% 6.92/7.15 => ( ( ord_le1268244103169919719at_nat @ Z2 @ X3 )
% 6.92/7.15 => ( ord_le1268244103169919719at_nat @ ( F @ Y3 @ Z2 ) @ X3 ) ) )
% 6.92/7.15 => ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 6.92/7.15 = ( F @ X @ Y ) ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_unique
% 6.92/7.15 thf(fact_1364_sup__unique,axiom,
% 6.92/7.15 ! [F: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 6.92/7.15 ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ X3 @ ( F @ X3 @ Y3 ) )
% 6.92/7.15 => ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ Y3 @ ( F @ X3 @ Y3 ) )
% 6.92/7.15 => ( ! [X3: set_nat,Y3: set_nat,Z2: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ Y3 @ X3 )
% 6.92/7.15 => ( ( ord_less_eq_set_nat @ Z2 @ X3 )
% 6.92/7.15 => ( ord_less_eq_set_nat @ ( F @ Y3 @ Z2 ) @ X3 ) ) )
% 6.92/7.15 => ( ( sup_sup_set_nat @ X @ Y )
% 6.92/7.15 = ( F @ X @ Y ) ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_unique
% 6.92/7.15 thf(fact_1365_sup__unique,axiom,
% 6.92/7.15 ! [F: set_int > set_int > set_int,X: set_int,Y: set_int] :
% 6.92/7.15 ( ! [X3: set_int,Y3: set_int] : ( ord_less_eq_set_int @ X3 @ ( F @ X3 @ Y3 ) )
% 6.92/7.15 => ( ! [X3: set_int,Y3: set_int] : ( ord_less_eq_set_int @ Y3 @ ( F @ X3 @ Y3 ) )
% 6.92/7.15 => ( ! [X3: set_int,Y3: set_int,Z2: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ Y3 @ X3 )
% 6.92/7.15 => ( ( ord_less_eq_set_int @ Z2 @ X3 )
% 6.92/7.15 => ( ord_less_eq_set_int @ ( F @ Y3 @ Z2 ) @ X3 ) ) )
% 6.92/7.15 => ( ( sup_sup_set_int @ X @ Y )
% 6.92/7.15 = ( F @ X @ Y ) ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_unique
% 6.92/7.15 thf(fact_1366_sup__unique,axiom,
% 6.92/7.15 ! [F: rat > rat > rat,X: rat,Y: rat] :
% 6.92/7.15 ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ X3 @ ( F @ X3 @ Y3 ) )
% 6.92/7.15 => ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ Y3 @ ( F @ X3 @ Y3 ) )
% 6.92/7.15 => ( ! [X3: rat,Y3: rat,Z2: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ Y3 @ X3 )
% 6.92/7.15 => ( ( ord_less_eq_rat @ Z2 @ X3 )
% 6.92/7.15 => ( ord_less_eq_rat @ ( F @ Y3 @ Z2 ) @ X3 ) ) )
% 6.92/7.15 => ( ( sup_sup_rat @ X @ Y )
% 6.92/7.15 = ( F @ X @ Y ) ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_unique
% 6.92/7.15 thf(fact_1367_sup__unique,axiom,
% 6.92/7.15 ! [F: nat > nat > nat,X: nat,Y: nat] :
% 6.92/7.15 ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ X3 @ ( F @ X3 @ Y3 ) )
% 6.92/7.15 => ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ ( F @ X3 @ Y3 ) )
% 6.92/7.15 => ( ! [X3: nat,Y3: nat,Z2: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ Y3 @ X3 )
% 6.92/7.15 => ( ( ord_less_eq_nat @ Z2 @ X3 )
% 6.92/7.15 => ( ord_less_eq_nat @ ( F @ Y3 @ Z2 ) @ X3 ) ) )
% 6.92/7.15 => ( ( sup_sup_nat @ X @ Y )
% 6.92/7.15 = ( F @ X @ Y ) ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_unique
% 6.92/7.15 thf(fact_1368_sup__unique,axiom,
% 6.92/7.15 ! [F: int > int > int,X: int,Y: int] :
% 6.92/7.15 ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ X3 @ ( F @ X3 @ Y3 ) )
% 6.92/7.15 => ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ Y3 @ ( F @ X3 @ Y3 ) )
% 6.92/7.15 => ( ! [X3: int,Y3: int,Z2: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ Y3 @ X3 )
% 6.92/7.15 => ( ( ord_less_eq_int @ Z2 @ X3 )
% 6.92/7.15 => ( ord_less_eq_int @ ( F @ Y3 @ Z2 ) @ X3 ) ) )
% 6.92/7.15 => ( ( sup_sup_int @ X @ Y )
% 6.92/7.15 = ( F @ X @ Y ) ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_unique
% 6.92/7.15 thf(fact_1369_sup_OorderI,axiom,
% 6.92/7.15 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( A
% 6.92/7.15 = ( sup_su3035147773818789531at_nat @ A @ B ) )
% 6.92/7.15 => ( ord_le8081472938463900775at_nat @ B @ A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.orderI
% 6.92/7.15 thf(fact_1370_sup_OorderI,axiom,
% 6.92/7.15 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( A
% 6.92/7.15 = ( sup_su5525570899277871387at_nat @ A @ B ) )
% 6.92/7.15 => ( ord_le1268244103169919719at_nat @ B @ A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.orderI
% 6.92/7.15 thf(fact_1371_sup_OorderI,axiom,
% 6.92/7.15 ! [A: set_nat,B: set_nat] :
% 6.92/7.15 ( ( A
% 6.92/7.15 = ( sup_sup_set_nat @ A @ B ) )
% 6.92/7.15 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.orderI
% 6.92/7.15 thf(fact_1372_sup_OorderI,axiom,
% 6.92/7.15 ! [A: set_int,B: set_int] :
% 6.92/7.15 ( ( A
% 6.92/7.15 = ( sup_sup_set_int @ A @ B ) )
% 6.92/7.15 => ( ord_less_eq_set_int @ B @ A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.orderI
% 6.92/7.15 thf(fact_1373_sup_OorderI,axiom,
% 6.92/7.15 ! [A: rat,B: rat] :
% 6.92/7.15 ( ( A
% 6.92/7.15 = ( sup_sup_rat @ A @ B ) )
% 6.92/7.15 => ( ord_less_eq_rat @ B @ A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.orderI
% 6.92/7.15 thf(fact_1374_sup_OorderI,axiom,
% 6.92/7.15 ! [A: nat,B: nat] :
% 6.92/7.15 ( ( A
% 6.92/7.15 = ( sup_sup_nat @ A @ B ) )
% 6.92/7.15 => ( ord_less_eq_nat @ B @ A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.orderI
% 6.92/7.15 thf(fact_1375_sup_OorderI,axiom,
% 6.92/7.15 ! [A: int,B: int] :
% 6.92/7.15 ( ( A
% 6.92/7.15 = ( sup_sup_int @ A @ B ) )
% 6.92/7.15 => ( ord_less_eq_int @ B @ A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.orderI
% 6.92/7.15 thf(fact_1376_sup_OorderE,axiom,
% 6.92/7.15 ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ B @ A )
% 6.92/7.15 => ( A
% 6.92/7.15 = ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.orderE
% 6.92/7.15 thf(fact_1377_sup_OorderE,axiom,
% 6.92/7.15 ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ B @ A )
% 6.92/7.15 => ( A
% 6.92/7.15 = ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.orderE
% 6.92/7.15 thf(fact_1378_sup_OorderE,axiom,
% 6.92/7.15 ! [B: set_nat,A: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ B @ A )
% 6.92/7.15 => ( A
% 6.92/7.15 = ( sup_sup_set_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.orderE
% 6.92/7.15 thf(fact_1379_sup_OorderE,axiom,
% 6.92/7.15 ! [B: set_int,A: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ B @ A )
% 6.92/7.15 => ( A
% 6.92/7.15 = ( sup_sup_set_int @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.orderE
% 6.92/7.15 thf(fact_1380_sup_OorderE,axiom,
% 6.92/7.15 ! [B: rat,A: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.15 => ( A
% 6.92/7.15 = ( sup_sup_rat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.orderE
% 6.92/7.15 thf(fact_1381_sup_OorderE,axiom,
% 6.92/7.15 ! [B: nat,A: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.15 => ( A
% 6.92/7.15 = ( sup_sup_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.orderE
% 6.92/7.15 thf(fact_1382_sup_OorderE,axiom,
% 6.92/7.15 ! [B: int,A: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ B @ A )
% 6.92/7.15 => ( A
% 6.92/7.15 = ( sup_sup_int @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.orderE
% 6.92/7.15 thf(fact_1383_le__iff__sup,axiom,
% 6.92/7.15 ( ord_le8081472938463900775at_nat
% 6.92/7.15 = ( ^ [X4: set_Pr8551490117392284871at_nat,Y4: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( sup_su3035147773818789531at_nat @ X4 @ Y4 )
% 6.92/7.15 = Y4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_iff_sup
% 6.92/7.15 thf(fact_1384_le__iff__sup,axiom,
% 6.92/7.15 ( ord_le1268244103169919719at_nat
% 6.92/7.15 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( sup_su5525570899277871387at_nat @ X4 @ Y4 )
% 6.92/7.15 = Y4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_iff_sup
% 6.92/7.15 thf(fact_1385_le__iff__sup,axiom,
% 6.92/7.15 ( ord_less_eq_set_nat
% 6.92/7.15 = ( ^ [X4: set_nat,Y4: set_nat] :
% 6.92/7.15 ( ( sup_sup_set_nat @ X4 @ Y4 )
% 6.92/7.15 = Y4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_iff_sup
% 6.92/7.15 thf(fact_1386_le__iff__sup,axiom,
% 6.92/7.15 ( ord_less_eq_set_int
% 6.92/7.15 = ( ^ [X4: set_int,Y4: set_int] :
% 6.92/7.15 ( ( sup_sup_set_int @ X4 @ Y4 )
% 6.92/7.15 = Y4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_iff_sup
% 6.92/7.15 thf(fact_1387_le__iff__sup,axiom,
% 6.92/7.15 ( ord_less_eq_rat
% 6.92/7.15 = ( ^ [X4: rat,Y4: rat] :
% 6.92/7.15 ( ( sup_sup_rat @ X4 @ Y4 )
% 6.92/7.15 = Y4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_iff_sup
% 6.92/7.15 thf(fact_1388_le__iff__sup,axiom,
% 6.92/7.15 ( ord_less_eq_nat
% 6.92/7.15 = ( ^ [X4: nat,Y4: nat] :
% 6.92/7.15 ( ( sup_sup_nat @ X4 @ Y4 )
% 6.92/7.15 = Y4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_iff_sup
% 6.92/7.15 thf(fact_1389_le__iff__sup,axiom,
% 6.92/7.15 ( ord_less_eq_int
% 6.92/7.15 = ( ^ [X4: int,Y4: int] :
% 6.92/7.15 ( ( sup_sup_int @ X4 @ Y4 )
% 6.92/7.15 = Y4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_iff_sup
% 6.92/7.15 thf(fact_1390_sup__least,axiom,
% 6.92/7.15 ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ Y @ X )
% 6.92/7.15 => ( ( ord_le8081472938463900775at_nat @ Z3 @ X )
% 6.92/7.15 => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ Y @ Z3 ) @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_least
% 6.92/7.15 thf(fact_1391_sup__least,axiom,
% 6.92/7.15 ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ Y @ X )
% 6.92/7.15 => ( ( ord_le1268244103169919719at_nat @ Z3 @ X )
% 6.92/7.15 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ Y @ Z3 ) @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_least
% 6.92/7.15 thf(fact_1392_sup__least,axiom,
% 6.92/7.15 ! [Y: set_nat,X: set_nat,Z3: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ Y @ X )
% 6.92/7.15 => ( ( ord_less_eq_set_nat @ Z3 @ X )
% 6.92/7.15 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ Y @ Z3 ) @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_least
% 6.92/7.15 thf(fact_1393_sup__least,axiom,
% 6.92/7.15 ! [Y: set_int,X: set_int,Z3: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ Y @ X )
% 6.92/7.15 => ( ( ord_less_eq_set_int @ Z3 @ X )
% 6.92/7.15 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ Y @ Z3 ) @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_least
% 6.92/7.15 thf(fact_1394_sup__least,axiom,
% 6.92/7.15 ! [Y: rat,X: rat,Z3: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ Y @ X )
% 6.92/7.15 => ( ( ord_less_eq_rat @ Z3 @ X )
% 6.92/7.15 => ( ord_less_eq_rat @ ( sup_sup_rat @ Y @ Z3 ) @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_least
% 6.92/7.15 thf(fact_1395_sup__least,axiom,
% 6.92/7.15 ! [Y: nat,X: nat,Z3: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ Y @ X )
% 6.92/7.15 => ( ( ord_less_eq_nat @ Z3 @ X )
% 6.92/7.15 => ( ord_less_eq_nat @ ( sup_sup_nat @ Y @ Z3 ) @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_least
% 6.92/7.15 thf(fact_1396_sup__least,axiom,
% 6.92/7.15 ! [Y: int,X: int,Z3: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ Y @ X )
% 6.92/7.15 => ( ( ord_less_eq_int @ Z3 @ X )
% 6.92/7.15 => ( ord_less_eq_int @ ( sup_sup_int @ Y @ Z3 ) @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_least
% 6.92/7.15 thf(fact_1397_sup__mono,axiom,
% 6.92/7.15 ! [A: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,D2: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ A @ C2 )
% 6.92/7.15 => ( ( ord_le8081472938463900775at_nat @ B @ D2 )
% 6.92/7.15 => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ ( sup_su3035147773818789531at_nat @ C2 @ D2 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_mono
% 6.92/7.15 thf(fact_1398_sup__mono,axiom,
% 6.92/7.15 ! [A: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,D2: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ A @ C2 )
% 6.92/7.15 => ( ( ord_le1268244103169919719at_nat @ B @ D2 )
% 6.92/7.15 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ ( sup_su5525570899277871387at_nat @ C2 @ D2 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_mono
% 6.92/7.15 thf(fact_1399_sup__mono,axiom,
% 6.92/7.15 ! [A: set_nat,C2: set_nat,B: set_nat,D2: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ A @ C2 )
% 6.92/7.15 => ( ( ord_less_eq_set_nat @ B @ D2 )
% 6.92/7.15 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ ( sup_sup_set_nat @ C2 @ D2 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_mono
% 6.92/7.15 thf(fact_1400_sup__mono,axiom,
% 6.92/7.15 ! [A: set_int,C2: set_int,B: set_int,D2: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ A @ C2 )
% 6.92/7.15 => ( ( ord_less_eq_set_int @ B @ D2 )
% 6.92/7.15 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ A @ B ) @ ( sup_sup_set_int @ C2 @ D2 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_mono
% 6.92/7.15 thf(fact_1401_sup__mono,axiom,
% 6.92/7.15 ! [A: rat,C2: rat,B: rat,D2: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ A @ C2 )
% 6.92/7.15 => ( ( ord_less_eq_rat @ B @ D2 )
% 6.92/7.15 => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ ( sup_sup_rat @ C2 @ D2 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_mono
% 6.92/7.15 thf(fact_1402_sup__mono,axiom,
% 6.92/7.15 ! [A: nat,C2: nat,B: nat,D2: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ A @ C2 )
% 6.92/7.15 => ( ( ord_less_eq_nat @ B @ D2 )
% 6.92/7.15 => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ ( sup_sup_nat @ C2 @ D2 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_mono
% 6.92/7.15 thf(fact_1403_sup__mono,axiom,
% 6.92/7.15 ! [A: int,C2: int,B: int,D2: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ A @ C2 )
% 6.92/7.15 => ( ( ord_less_eq_int @ B @ D2 )
% 6.92/7.15 => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ ( sup_sup_int @ C2 @ D2 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_mono
% 6.92/7.15 thf(fact_1404_sup_Omono,axiom,
% 6.92/7.15 ! [C2: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,D2: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ C2 @ A )
% 6.92/7.15 => ( ( ord_le8081472938463900775at_nat @ D2 @ B )
% 6.92/7.15 => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ C2 @ D2 ) @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.mono
% 6.92/7.15 thf(fact_1405_sup_Omono,axiom,
% 6.92/7.15 ! [C2: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,D2: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ C2 @ A )
% 6.92/7.15 => ( ( ord_le1268244103169919719at_nat @ D2 @ B )
% 6.92/7.15 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ C2 @ D2 ) @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.mono
% 6.92/7.15 thf(fact_1406_sup_Omono,axiom,
% 6.92/7.15 ! [C2: set_nat,A: set_nat,D2: set_nat,B: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ C2 @ A )
% 6.92/7.15 => ( ( ord_less_eq_set_nat @ D2 @ B )
% 6.92/7.15 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ C2 @ D2 ) @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.mono
% 6.92/7.15 thf(fact_1407_sup_Omono,axiom,
% 6.92/7.15 ! [C2: set_int,A: set_int,D2: set_int,B: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ C2 @ A )
% 6.92/7.15 => ( ( ord_less_eq_set_int @ D2 @ B )
% 6.92/7.15 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ C2 @ D2 ) @ ( sup_sup_set_int @ A @ B ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.mono
% 6.92/7.15 thf(fact_1408_sup_Omono,axiom,
% 6.92/7.15 ! [C2: rat,A: rat,D2: rat,B: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ C2 @ A )
% 6.92/7.15 => ( ( ord_less_eq_rat @ D2 @ B )
% 6.92/7.15 => ( ord_less_eq_rat @ ( sup_sup_rat @ C2 @ D2 ) @ ( sup_sup_rat @ A @ B ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.mono
% 6.92/7.15 thf(fact_1409_sup_Omono,axiom,
% 6.92/7.15 ! [C2: nat,A: nat,D2: nat,B: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ C2 @ A )
% 6.92/7.15 => ( ( ord_less_eq_nat @ D2 @ B )
% 6.92/7.15 => ( ord_less_eq_nat @ ( sup_sup_nat @ C2 @ D2 ) @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.mono
% 6.92/7.15 thf(fact_1410_sup_Omono,axiom,
% 6.92/7.15 ! [C2: int,A: int,D2: int,B: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ C2 @ A )
% 6.92/7.15 => ( ( ord_less_eq_int @ D2 @ B )
% 6.92/7.15 => ( ord_less_eq_int @ ( sup_sup_int @ C2 @ D2 ) @ ( sup_sup_int @ A @ B ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.mono
% 6.92/7.15 thf(fact_1411_le__supI2,axiom,
% 6.92/7.15 ! [X: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ X @ B )
% 6.92/7.15 => ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI2
% 6.92/7.15 thf(fact_1412_le__supI2,axiom,
% 6.92/7.15 ! [X: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ X @ B )
% 6.92/7.15 => ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI2
% 6.92/7.15 thf(fact_1413_le__supI2,axiom,
% 6.92/7.15 ! [X: set_nat,B: set_nat,A: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ X @ B )
% 6.92/7.15 => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI2
% 6.92/7.15 thf(fact_1414_le__supI2,axiom,
% 6.92/7.15 ! [X: set_int,B: set_int,A: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ X @ B )
% 6.92/7.15 => ( ord_less_eq_set_int @ X @ ( sup_sup_set_int @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI2
% 6.92/7.15 thf(fact_1415_le__supI2,axiom,
% 6.92/7.15 ! [X: rat,B: rat,A: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ X @ B )
% 6.92/7.15 => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI2
% 6.92/7.15 thf(fact_1416_le__supI2,axiom,
% 6.92/7.15 ! [X: nat,B: nat,A: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ X @ B )
% 6.92/7.15 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI2
% 6.92/7.15 thf(fact_1417_le__supI2,axiom,
% 6.92/7.15 ! [X: int,B: int,A: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ X @ B )
% 6.92/7.15 => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI2
% 6.92/7.15 thf(fact_1418_le__supI1,axiom,
% 6.92/7.15 ! [X: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ X @ A )
% 6.92/7.15 => ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI1
% 6.92/7.15 thf(fact_1419_le__supI1,axiom,
% 6.92/7.15 ! [X: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ X @ A )
% 6.92/7.15 => ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI1
% 6.92/7.15 thf(fact_1420_le__supI1,axiom,
% 6.92/7.15 ! [X: set_nat,A: set_nat,B: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ X @ A )
% 6.92/7.15 => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI1
% 6.92/7.15 thf(fact_1421_le__supI1,axiom,
% 6.92/7.15 ! [X: set_int,A: set_int,B: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ X @ A )
% 6.92/7.15 => ( ord_less_eq_set_int @ X @ ( sup_sup_set_int @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI1
% 6.92/7.15 thf(fact_1422_le__supI1,axiom,
% 6.92/7.15 ! [X: rat,A: rat,B: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ X @ A )
% 6.92/7.15 => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI1
% 6.92/7.15 thf(fact_1423_le__supI1,axiom,
% 6.92/7.15 ! [X: nat,A: nat,B: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ X @ A )
% 6.92/7.15 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI1
% 6.92/7.15 thf(fact_1424_le__supI1,axiom,
% 6.92/7.15 ! [X: int,A: int,B: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ X @ A )
% 6.92/7.15 => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI1
% 6.92/7.15 thf(fact_1425_sup__ge2,axiom,
% 6.92/7.15 ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_ge2
% 6.92/7.15 thf(fact_1426_sup__ge2,axiom,
% 6.92/7.15 ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_ge2
% 6.92/7.15 thf(fact_1427_sup__ge2,axiom,
% 6.92/7.15 ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_ge2
% 6.92/7.15 thf(fact_1428_sup__ge2,axiom,
% 6.92/7.15 ! [Y: set_int,X: set_int] : ( ord_less_eq_set_int @ Y @ ( sup_sup_set_int @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_ge2
% 6.92/7.15 thf(fact_1429_sup__ge2,axiom,
% 6.92/7.15 ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_ge2
% 6.92/7.15 thf(fact_1430_sup__ge2,axiom,
% 6.92/7.15 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_ge2
% 6.92/7.15 thf(fact_1431_sup__ge2,axiom,
% 6.92/7.15 ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_ge2
% 6.92/7.15 thf(fact_1432_sup__ge1,axiom,
% 6.92/7.15 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_ge1
% 6.92/7.15 thf(fact_1433_sup__ge1,axiom,
% 6.92/7.15 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_ge1
% 6.92/7.15 thf(fact_1434_sup__ge1,axiom,
% 6.92/7.15 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_ge1
% 6.92/7.15 thf(fact_1435_sup__ge1,axiom,
% 6.92/7.15 ! [X: set_int,Y: set_int] : ( ord_less_eq_set_int @ X @ ( sup_sup_set_int @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_ge1
% 6.92/7.15 thf(fact_1436_sup__ge1,axiom,
% 6.92/7.15 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_ge1
% 6.92/7.15 thf(fact_1437_sup__ge1,axiom,
% 6.92/7.15 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_ge1
% 6.92/7.15 thf(fact_1438_sup__ge1,axiom,
% 6.92/7.15 ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_ge1
% 6.92/7.15 thf(fact_1439_le__supI,axiom,
% 6.92/7.15 ! [A: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ A @ X )
% 6.92/7.15 => ( ( ord_le8081472938463900775at_nat @ B @ X )
% 6.92/7.15 => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI
% 6.92/7.15 thf(fact_1440_le__supI,axiom,
% 6.92/7.15 ! [A: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ A @ X )
% 6.92/7.15 => ( ( ord_le1268244103169919719at_nat @ B @ X )
% 6.92/7.15 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI
% 6.92/7.15 thf(fact_1441_le__supI,axiom,
% 6.92/7.15 ! [A: set_nat,X: set_nat,B: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ A @ X )
% 6.92/7.15 => ( ( ord_less_eq_set_nat @ B @ X )
% 6.92/7.15 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI
% 6.92/7.15 thf(fact_1442_le__supI,axiom,
% 6.92/7.15 ! [A: set_int,X: set_int,B: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ A @ X )
% 6.92/7.15 => ( ( ord_less_eq_set_int @ B @ X )
% 6.92/7.15 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ A @ B ) @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI
% 6.92/7.15 thf(fact_1443_le__supI,axiom,
% 6.92/7.15 ! [A: rat,X: rat,B: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ A @ X )
% 6.92/7.15 => ( ( ord_less_eq_rat @ B @ X )
% 6.92/7.15 => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI
% 6.92/7.15 thf(fact_1444_le__supI,axiom,
% 6.92/7.15 ! [A: nat,X: nat,B: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ A @ X )
% 6.92/7.15 => ( ( ord_less_eq_nat @ B @ X )
% 6.92/7.15 => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI
% 6.92/7.15 thf(fact_1445_le__supI,axiom,
% 6.92/7.15 ! [A: int,X: int,B: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ A @ X )
% 6.92/7.15 => ( ( ord_less_eq_int @ B @ X )
% 6.92/7.15 => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supI
% 6.92/7.15 thf(fact_1446_le__supE,axiom,
% 6.92/7.15 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ X )
% 6.92/7.15 => ~ ( ( ord_le8081472938463900775at_nat @ A @ X )
% 6.92/7.15 => ~ ( ord_le8081472938463900775at_nat @ B @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supE
% 6.92/7.15 thf(fact_1447_le__supE,axiom,
% 6.92/7.15 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ X )
% 6.92/7.15 => ~ ( ( ord_le1268244103169919719at_nat @ A @ X )
% 6.92/7.15 => ~ ( ord_le1268244103169919719at_nat @ B @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supE
% 6.92/7.15 thf(fact_1448_le__supE,axiom,
% 6.92/7.15 ! [A: set_nat,B: set_nat,X: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X )
% 6.92/7.15 => ~ ( ( ord_less_eq_set_nat @ A @ X )
% 6.92/7.15 => ~ ( ord_less_eq_set_nat @ B @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supE
% 6.92/7.15 thf(fact_1449_le__supE,axiom,
% 6.92/7.15 ! [A: set_int,B: set_int,X: set_int] :
% 6.92/7.15 ( ( ord_less_eq_set_int @ ( sup_sup_set_int @ A @ B ) @ X )
% 6.92/7.15 => ~ ( ( ord_less_eq_set_int @ A @ X )
% 6.92/7.15 => ~ ( ord_less_eq_set_int @ B @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supE
% 6.92/7.15 thf(fact_1450_le__supE,axiom,
% 6.92/7.15 ! [A: rat,B: rat,X: rat] :
% 6.92/7.15 ( ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X )
% 6.92/7.15 => ~ ( ( ord_less_eq_rat @ A @ X )
% 6.92/7.15 => ~ ( ord_less_eq_rat @ B @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supE
% 6.92/7.15 thf(fact_1451_le__supE,axiom,
% 6.92/7.15 ! [A: nat,B: nat,X: nat] :
% 6.92/7.15 ( ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X )
% 6.92/7.15 => ~ ( ( ord_less_eq_nat @ A @ X )
% 6.92/7.15 => ~ ( ord_less_eq_nat @ B @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supE
% 6.92/7.15 thf(fact_1452_le__supE,axiom,
% 6.92/7.15 ! [A: int,B: int,X: int] :
% 6.92/7.15 ( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X )
% 6.92/7.15 => ~ ( ( ord_less_eq_int @ A @ X )
% 6.92/7.15 => ~ ( ord_less_eq_int @ B @ X ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % le_supE
% 6.92/7.15 thf(fact_1453_inf__sup__ord_I3_J,axiom,
% 6.92/7.15 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_ord(3)
% 6.92/7.15 thf(fact_1454_inf__sup__ord_I3_J,axiom,
% 6.92/7.15 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_ord(3)
% 6.92/7.15 thf(fact_1455_inf__sup__ord_I3_J,axiom,
% 6.92/7.15 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_ord(3)
% 6.92/7.15 thf(fact_1456_inf__sup__ord_I3_J,axiom,
% 6.92/7.15 ! [X: set_int,Y: set_int] : ( ord_less_eq_set_int @ X @ ( sup_sup_set_int @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_ord(3)
% 6.92/7.15 thf(fact_1457_inf__sup__ord_I3_J,axiom,
% 6.92/7.15 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_ord(3)
% 6.92/7.15 thf(fact_1458_inf__sup__ord_I3_J,axiom,
% 6.92/7.15 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_ord(3)
% 6.92/7.15 thf(fact_1459_inf__sup__ord_I3_J,axiom,
% 6.92/7.15 ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_ord(3)
% 6.92/7.15 thf(fact_1460_inf__sup__ord_I4_J,axiom,
% 6.92/7.15 ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_ord(4)
% 6.92/7.15 thf(fact_1461_inf__sup__ord_I4_J,axiom,
% 6.92/7.15 ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_ord(4)
% 6.92/7.15 thf(fact_1462_inf__sup__ord_I4_J,axiom,
% 6.92/7.15 ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_ord(4)
% 6.92/7.15 thf(fact_1463_inf__sup__ord_I4_J,axiom,
% 6.92/7.15 ! [Y: set_int,X: set_int] : ( ord_less_eq_set_int @ Y @ ( sup_sup_set_int @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_ord(4)
% 6.92/7.15 thf(fact_1464_inf__sup__ord_I4_J,axiom,
% 6.92/7.15 ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_ord(4)
% 6.92/7.15 thf(fact_1465_inf__sup__ord_I4_J,axiom,
% 6.92/7.15 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_ord(4)
% 6.92/7.15 thf(fact_1466_inf__sup__ord_I4_J,axiom,
% 6.92/7.15 ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 6.92/7.15
% 6.92/7.15 % inf_sup_ord(4)
% 6.92/7.15 thf(fact_1467_sup_Ostrict__coboundedI2,axiom,
% 6.92/7.15 ! [C2: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le7642048601412989811at_nat @ C2 @ B )
% 6.92/7.15 => ( ord_le7642048601412989811at_nat @ C2 @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_coboundedI2
% 6.92/7.15 thf(fact_1468_sup_Ostrict__coboundedI2,axiom,
% 6.92/7.15 ! [C2: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le2604355607129572851at_nat @ C2 @ B )
% 6.92/7.15 => ( ord_le2604355607129572851at_nat @ C2 @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_coboundedI2
% 6.92/7.15 thf(fact_1469_sup_Ostrict__coboundedI2,axiom,
% 6.92/7.15 ! [C2: set_nat,B: set_nat,A: set_nat] :
% 6.92/7.15 ( ( ord_less_set_nat @ C2 @ B )
% 6.92/7.15 => ( ord_less_set_nat @ C2 @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_coboundedI2
% 6.92/7.15 thf(fact_1470_sup_Ostrict__coboundedI2,axiom,
% 6.92/7.15 ! [C2: assn,B: assn,A: assn] :
% 6.92/7.15 ( ( ord_less_assn @ C2 @ B )
% 6.92/7.15 => ( ord_less_assn @ C2 @ ( sup_sup_assn @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_coboundedI2
% 6.92/7.15 thf(fact_1471_sup_Ostrict__coboundedI2,axiom,
% 6.92/7.15 ! [C2: rat,B: rat,A: rat] :
% 6.92/7.15 ( ( ord_less_rat @ C2 @ B )
% 6.92/7.15 => ( ord_less_rat @ C2 @ ( sup_sup_rat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_coboundedI2
% 6.92/7.15 thf(fact_1472_sup_Ostrict__coboundedI2,axiom,
% 6.92/7.15 ! [C2: nat,B: nat,A: nat] :
% 6.92/7.15 ( ( ord_less_nat @ C2 @ B )
% 6.92/7.15 => ( ord_less_nat @ C2 @ ( sup_sup_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_coboundedI2
% 6.92/7.15 thf(fact_1473_sup_Ostrict__coboundedI2,axiom,
% 6.92/7.15 ! [C2: int,B: int,A: int] :
% 6.92/7.15 ( ( ord_less_int @ C2 @ B )
% 6.92/7.15 => ( ord_less_int @ C2 @ ( sup_sup_int @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_coboundedI2
% 6.92/7.15 thf(fact_1474_sup_Ostrict__coboundedI1,axiom,
% 6.92/7.15 ! [C2: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le7642048601412989811at_nat @ C2 @ A )
% 6.92/7.15 => ( ord_le7642048601412989811at_nat @ C2 @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_coboundedI1
% 6.92/7.15 thf(fact_1475_sup_Ostrict__coboundedI1,axiom,
% 6.92/7.15 ! [C2: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le2604355607129572851at_nat @ C2 @ A )
% 6.92/7.15 => ( ord_le2604355607129572851at_nat @ C2 @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_coboundedI1
% 6.92/7.15 thf(fact_1476_sup_Ostrict__coboundedI1,axiom,
% 6.92/7.15 ! [C2: set_nat,A: set_nat,B: set_nat] :
% 6.92/7.15 ( ( ord_less_set_nat @ C2 @ A )
% 6.92/7.15 => ( ord_less_set_nat @ C2 @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_coboundedI1
% 6.92/7.15 thf(fact_1477_sup_Ostrict__coboundedI1,axiom,
% 6.92/7.15 ! [C2: assn,A: assn,B: assn] :
% 6.92/7.15 ( ( ord_less_assn @ C2 @ A )
% 6.92/7.15 => ( ord_less_assn @ C2 @ ( sup_sup_assn @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_coboundedI1
% 6.92/7.15 thf(fact_1478_sup_Ostrict__coboundedI1,axiom,
% 6.92/7.15 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.15 ( ( ord_less_rat @ C2 @ A )
% 6.92/7.15 => ( ord_less_rat @ C2 @ ( sup_sup_rat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_coboundedI1
% 6.92/7.15 thf(fact_1479_sup_Ostrict__coboundedI1,axiom,
% 6.92/7.15 ! [C2: nat,A: nat,B: nat] :
% 6.92/7.15 ( ( ord_less_nat @ C2 @ A )
% 6.92/7.15 => ( ord_less_nat @ C2 @ ( sup_sup_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_coboundedI1
% 6.92/7.15 thf(fact_1480_sup_Ostrict__coboundedI1,axiom,
% 6.92/7.15 ! [C2: int,A: int,B: int] :
% 6.92/7.15 ( ( ord_less_int @ C2 @ A )
% 6.92/7.15 => ( ord_less_int @ C2 @ ( sup_sup_int @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_coboundedI1
% 6.92/7.15 thf(fact_1481_sup_Ostrict__order__iff,axiom,
% 6.92/7.15 ( ord_le7642048601412989811at_nat
% 6.92/7.15 = ( ^ [B4: set_Pr8551490117392284871at_nat,A5: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( A5
% 6.92/7.15 = ( sup_su3035147773818789531at_nat @ A5 @ B4 ) )
% 6.92/7.15 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_order_iff
% 6.92/7.15 thf(fact_1482_sup_Ostrict__order__iff,axiom,
% 6.92/7.15 ( ord_le2604355607129572851at_nat
% 6.92/7.15 = ( ^ [B4: set_Pr4329608150637261639at_nat,A5: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( A5
% 6.92/7.15 = ( sup_su5525570899277871387at_nat @ A5 @ B4 ) )
% 6.92/7.15 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_order_iff
% 6.92/7.15 thf(fact_1483_sup_Ostrict__order__iff,axiom,
% 6.92/7.15 ( ord_less_set_nat
% 6.92/7.15 = ( ^ [B4: set_nat,A5: set_nat] :
% 6.92/7.15 ( ( A5
% 6.92/7.15 = ( sup_sup_set_nat @ A5 @ B4 ) )
% 6.92/7.15 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_order_iff
% 6.92/7.15 thf(fact_1484_sup_Ostrict__order__iff,axiom,
% 6.92/7.15 ( ord_less_assn
% 6.92/7.15 = ( ^ [B4: assn,A5: assn] :
% 6.92/7.15 ( ( A5
% 6.92/7.15 = ( sup_sup_assn @ A5 @ B4 ) )
% 6.92/7.15 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_order_iff
% 6.92/7.15 thf(fact_1485_sup_Ostrict__order__iff,axiom,
% 6.92/7.15 ( ord_less_rat
% 6.92/7.15 = ( ^ [B4: rat,A5: rat] :
% 6.92/7.15 ( ( A5
% 6.92/7.15 = ( sup_sup_rat @ A5 @ B4 ) )
% 6.92/7.15 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_order_iff
% 6.92/7.15 thf(fact_1486_sup_Ostrict__order__iff,axiom,
% 6.92/7.15 ( ord_less_nat
% 6.92/7.15 = ( ^ [B4: nat,A5: nat] :
% 6.92/7.15 ( ( A5
% 6.92/7.15 = ( sup_sup_nat @ A5 @ B4 ) )
% 6.92/7.15 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_order_iff
% 6.92/7.15 thf(fact_1487_sup_Ostrict__order__iff,axiom,
% 6.92/7.15 ( ord_less_int
% 6.92/7.15 = ( ^ [B4: int,A5: int] :
% 6.92/7.15 ( ( A5
% 6.92/7.15 = ( sup_sup_int @ A5 @ B4 ) )
% 6.92/7.15 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_order_iff
% 6.92/7.15 thf(fact_1488_sup_Ostrict__boundedE,axiom,
% 6.92/7.15 ! [B: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le7642048601412989811at_nat @ ( sup_su3035147773818789531at_nat @ B @ C2 ) @ A )
% 6.92/7.15 => ~ ( ( ord_le7642048601412989811at_nat @ B @ A )
% 6.92/7.15 => ~ ( ord_le7642048601412989811at_nat @ C2 @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_boundedE
% 6.92/7.15 thf(fact_1489_sup_Ostrict__boundedE,axiom,
% 6.92/7.15 ! [B: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le2604355607129572851at_nat @ ( sup_su5525570899277871387at_nat @ B @ C2 ) @ A )
% 6.92/7.15 => ~ ( ( ord_le2604355607129572851at_nat @ B @ A )
% 6.92/7.15 => ~ ( ord_le2604355607129572851at_nat @ C2 @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_boundedE
% 6.92/7.15 thf(fact_1490_sup_Ostrict__boundedE,axiom,
% 6.92/7.15 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 6.92/7.15 ( ( ord_less_set_nat @ ( sup_sup_set_nat @ B @ C2 ) @ A )
% 6.92/7.15 => ~ ( ( ord_less_set_nat @ B @ A )
% 6.92/7.15 => ~ ( ord_less_set_nat @ C2 @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_boundedE
% 6.92/7.15 thf(fact_1491_sup_Ostrict__boundedE,axiom,
% 6.92/7.15 ! [B: assn,C2: assn,A: assn] :
% 6.92/7.15 ( ( ord_less_assn @ ( sup_sup_assn @ B @ C2 ) @ A )
% 6.92/7.15 => ~ ( ( ord_less_assn @ B @ A )
% 6.92/7.15 => ~ ( ord_less_assn @ C2 @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_boundedE
% 6.92/7.15 thf(fact_1492_sup_Ostrict__boundedE,axiom,
% 6.92/7.15 ! [B: rat,C2: rat,A: rat] :
% 6.92/7.15 ( ( ord_less_rat @ ( sup_sup_rat @ B @ C2 ) @ A )
% 6.92/7.15 => ~ ( ( ord_less_rat @ B @ A )
% 6.92/7.15 => ~ ( ord_less_rat @ C2 @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_boundedE
% 6.92/7.15 thf(fact_1493_sup_Ostrict__boundedE,axiom,
% 6.92/7.15 ! [B: nat,C2: nat,A: nat] :
% 6.92/7.15 ( ( ord_less_nat @ ( sup_sup_nat @ B @ C2 ) @ A )
% 6.92/7.15 => ~ ( ( ord_less_nat @ B @ A )
% 6.92/7.15 => ~ ( ord_less_nat @ C2 @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_boundedE
% 6.92/7.15 thf(fact_1494_sup_Ostrict__boundedE,axiom,
% 6.92/7.15 ! [B: int,C2: int,A: int] :
% 6.92/7.15 ( ( ord_less_int @ ( sup_sup_int @ B @ C2 ) @ A )
% 6.92/7.15 => ~ ( ( ord_less_int @ B @ A )
% 6.92/7.15 => ~ ( ord_less_int @ C2 @ A ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.strict_boundedE
% 6.92/7.15 thf(fact_1495_sup_Oabsorb4,axiom,
% 6.92/7.15 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le7642048601412989811at_nat @ A @ B )
% 6.92/7.15 => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 6.92/7.15 = B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb4
% 6.92/7.15 thf(fact_1496_sup_Oabsorb4,axiom,
% 6.92/7.15 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le2604355607129572851at_nat @ A @ B )
% 6.92/7.15 => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 6.92/7.15 = B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb4
% 6.92/7.15 thf(fact_1497_sup_Oabsorb4,axiom,
% 6.92/7.15 ! [A: set_nat,B: set_nat] :
% 6.92/7.15 ( ( ord_less_set_nat @ A @ B )
% 6.92/7.15 => ( ( sup_sup_set_nat @ A @ B )
% 6.92/7.15 = B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb4
% 6.92/7.15 thf(fact_1498_sup_Oabsorb4,axiom,
% 6.92/7.15 ! [A: assn,B: assn] :
% 6.92/7.15 ( ( ord_less_assn @ A @ B )
% 6.92/7.15 => ( ( sup_sup_assn @ A @ B )
% 6.92/7.15 = B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb4
% 6.92/7.15 thf(fact_1499_sup_Oabsorb4,axiom,
% 6.92/7.15 ! [A: rat,B: rat] :
% 6.92/7.15 ( ( ord_less_rat @ A @ B )
% 6.92/7.15 => ( ( sup_sup_rat @ A @ B )
% 6.92/7.15 = B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb4
% 6.92/7.15 thf(fact_1500_sup_Oabsorb4,axiom,
% 6.92/7.15 ! [A: nat,B: nat] :
% 6.92/7.15 ( ( ord_less_nat @ A @ B )
% 6.92/7.15 => ( ( sup_sup_nat @ A @ B )
% 6.92/7.15 = B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb4
% 6.92/7.15 thf(fact_1501_sup_Oabsorb4,axiom,
% 6.92/7.15 ! [A: int,B: int] :
% 6.92/7.15 ( ( ord_less_int @ A @ B )
% 6.92/7.15 => ( ( sup_sup_int @ A @ B )
% 6.92/7.15 = B ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb4
% 6.92/7.15 thf(fact_1502_sup_Oabsorb3,axiom,
% 6.92/7.15 ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le7642048601412989811at_nat @ B @ A )
% 6.92/7.15 => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 6.92/7.15 = A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb3
% 6.92/7.15 thf(fact_1503_sup_Oabsorb3,axiom,
% 6.92/7.15 ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le2604355607129572851at_nat @ B @ A )
% 6.92/7.15 => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 6.92/7.15 = A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb3
% 6.92/7.15 thf(fact_1504_sup_Oabsorb3,axiom,
% 6.92/7.15 ! [B: set_nat,A: set_nat] :
% 6.92/7.15 ( ( ord_less_set_nat @ B @ A )
% 6.92/7.15 => ( ( sup_sup_set_nat @ A @ B )
% 6.92/7.15 = A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb3
% 6.92/7.15 thf(fact_1505_sup_Oabsorb3,axiom,
% 6.92/7.15 ! [B: assn,A: assn] :
% 6.92/7.15 ( ( ord_less_assn @ B @ A )
% 6.92/7.15 => ( ( sup_sup_assn @ A @ B )
% 6.92/7.15 = A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb3
% 6.92/7.15 thf(fact_1506_sup_Oabsorb3,axiom,
% 6.92/7.15 ! [B: rat,A: rat] :
% 6.92/7.15 ( ( ord_less_rat @ B @ A )
% 6.92/7.15 => ( ( sup_sup_rat @ A @ B )
% 6.92/7.15 = A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb3
% 6.92/7.15 thf(fact_1507_sup_Oabsorb3,axiom,
% 6.92/7.15 ! [B: nat,A: nat] :
% 6.92/7.15 ( ( ord_less_nat @ B @ A )
% 6.92/7.15 => ( ( sup_sup_nat @ A @ B )
% 6.92/7.15 = A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb3
% 6.92/7.15 thf(fact_1508_sup_Oabsorb3,axiom,
% 6.92/7.15 ! [B: int,A: int] :
% 6.92/7.15 ( ( ord_less_int @ B @ A )
% 6.92/7.15 => ( ( sup_sup_int @ A @ B )
% 6.92/7.15 = A ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup.absorb3
% 6.92/7.15 thf(fact_1509_less__supI2,axiom,
% 6.92/7.15 ! [X: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le7642048601412989811at_nat @ X @ B )
% 6.92/7.15 => ( ord_le7642048601412989811at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_supI2
% 6.92/7.15 thf(fact_1510_less__supI2,axiom,
% 6.92/7.15 ! [X: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le2604355607129572851at_nat @ X @ B )
% 6.92/7.15 => ( ord_le2604355607129572851at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_supI2
% 6.92/7.15 thf(fact_1511_less__supI2,axiom,
% 6.92/7.15 ! [X: set_nat,B: set_nat,A: set_nat] :
% 6.92/7.15 ( ( ord_less_set_nat @ X @ B )
% 6.92/7.15 => ( ord_less_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_supI2
% 6.92/7.15 thf(fact_1512_less__supI2,axiom,
% 6.92/7.15 ! [X: assn,B: assn,A: assn] :
% 6.92/7.15 ( ( ord_less_assn @ X @ B )
% 6.92/7.15 => ( ord_less_assn @ X @ ( sup_sup_assn @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_supI2
% 6.92/7.15 thf(fact_1513_less__supI2,axiom,
% 6.92/7.15 ! [X: rat,B: rat,A: rat] :
% 6.92/7.15 ( ( ord_less_rat @ X @ B )
% 6.92/7.15 => ( ord_less_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_supI2
% 6.92/7.15 thf(fact_1514_less__supI2,axiom,
% 6.92/7.15 ! [X: nat,B: nat,A: nat] :
% 6.92/7.15 ( ( ord_less_nat @ X @ B )
% 6.92/7.15 => ( ord_less_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_supI2
% 6.92/7.15 thf(fact_1515_less__supI2,axiom,
% 6.92/7.15 ! [X: int,B: int,A: int] :
% 6.92/7.15 ( ( ord_less_int @ X @ B )
% 6.92/7.15 => ( ord_less_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_supI2
% 6.92/7.15 thf(fact_1516_less__supI1,axiom,
% 6.92/7.15 ! [X: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( ord_le7642048601412989811at_nat @ X @ A )
% 6.92/7.15 => ( ord_le7642048601412989811at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_supI1
% 6.92/7.15 thf(fact_1517_less__supI1,axiom,
% 6.92/7.15 ! [X: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( ord_le2604355607129572851at_nat @ X @ A )
% 6.92/7.15 => ( ord_le2604355607129572851at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_supI1
% 6.92/7.15 thf(fact_1518_less__supI1,axiom,
% 6.92/7.15 ! [X: set_nat,A: set_nat,B: set_nat] :
% 6.92/7.15 ( ( ord_less_set_nat @ X @ A )
% 6.92/7.15 => ( ord_less_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_supI1
% 6.92/7.15 thf(fact_1519_less__supI1,axiom,
% 6.92/7.15 ! [X: assn,A: assn,B: assn] :
% 6.92/7.15 ( ( ord_less_assn @ X @ A )
% 6.92/7.15 => ( ord_less_assn @ X @ ( sup_sup_assn @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_supI1
% 6.92/7.15 thf(fact_1520_less__supI1,axiom,
% 6.92/7.15 ! [X: rat,A: rat,B: rat] :
% 6.92/7.15 ( ( ord_less_rat @ X @ A )
% 6.92/7.15 => ( ord_less_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_supI1
% 6.92/7.15 thf(fact_1521_less__supI1,axiom,
% 6.92/7.15 ! [X: nat,A: nat,B: nat] :
% 6.92/7.15 ( ( ord_less_nat @ X @ A )
% 6.92/7.15 => ( ord_less_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_supI1
% 6.92/7.15 thf(fact_1522_less__supI1,axiom,
% 6.92/7.15 ! [X: int,A: int,B: int] :
% 6.92/7.15 ( ( ord_less_int @ X @ A )
% 6.92/7.15 => ( ord_less_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_supI1
% 6.92/7.15 thf(fact_1523_pred__subset__eq,axiom,
% 6.92/7.15 ! [R3: set_o,S: set_o] :
% 6.92/7.15 ( ( ord_less_eq_o_o
% 6.92/7.15 @ ^ [X4: $o] : ( member_o @ X4 @ R3 )
% 6.92/7.15 @ ^ [X4: $o] : ( member_o @ X4 @ S ) )
% 6.92/7.15 = ( ord_less_eq_set_o @ R3 @ S ) ) ).
% 6.92/7.15
% 6.92/7.15 % pred_subset_eq
% 6.92/7.15 thf(fact_1524_pred__subset__eq,axiom,
% 6.92/7.15 ! [R3: set_se6260736226359567993nt_int,S: set_se6260736226359567993nt_int] :
% 6.92/7.15 ( ( ord_le8334417538754933252_int_o
% 6.92/7.15 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ R3 )
% 6.92/7.15 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ S ) )
% 6.92/7.15 = ( ord_le483042692224249369nt_int @ R3 @ S ) ) ).
% 6.92/7.15
% 6.92/7.15 % pred_subset_eq
% 6.92/7.15 thf(fact_1525_pred__subset__eq,axiom,
% 6.92/7.15 ! [R3: set_set_nat,S: set_set_nat] :
% 6.92/7.15 ( ( ord_le3964352015994296041_nat_o
% 6.92/7.15 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ R3 )
% 6.92/7.15 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ S ) )
% 6.92/7.15 = ( ord_le6893508408891458716et_nat @ R3 @ S ) ) ).
% 6.92/7.15
% 6.92/7.15 % pred_subset_eq
% 6.92/7.15 thf(fact_1526_pred__subset__eq,axiom,
% 6.92/7.15 ! [R3: set_nat,S: set_nat] :
% 6.92/7.15 ( ( ord_less_eq_nat_o
% 6.92/7.15 @ ^ [X4: nat] : ( member_nat @ X4 @ R3 )
% 6.92/7.15 @ ^ [X4: nat] : ( member_nat @ X4 @ S ) )
% 6.92/7.15 = ( ord_less_eq_set_nat @ R3 @ S ) ) ).
% 6.92/7.15
% 6.92/7.15 % pred_subset_eq
% 6.92/7.15 thf(fact_1527_pred__subset__eq,axiom,
% 6.92/7.15 ! [R3: set_int,S: set_int] :
% 6.92/7.15 ( ( ord_less_eq_int_o
% 6.92/7.15 @ ^ [X4: int] : ( member_int @ X4 @ R3 )
% 6.92/7.15 @ ^ [X4: int] : ( member_int @ X4 @ S ) )
% 6.92/7.15 = ( ord_less_eq_set_int @ R3 @ S ) ) ).
% 6.92/7.15
% 6.92/7.15 % pred_subset_eq
% 6.92/7.15 thf(fact_1528_timeFrame_Oelims,axiom,
% 6.92/7.15 ! [X: nat,Xa: option4065278094766928714it_nat,Y: option4065278094766928714it_nat] :
% 6.92/7.15 ( ( ( heap_T7616092557645711336rame_b @ X @ Xa )
% 6.92/7.15 = Y )
% 6.92/7.15 => ( ! [R4: b,H2: heap_e7401611519738050253t_unit,N4: nat] :
% 6.92/7.15 ( ( Xa
% 6.92/7.15 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ N4 ) ) ) )
% 6.92/7.15 => ( Y
% 6.92/7.15 != ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ ( plus_plus_nat @ X @ N4 ) ) ) ) ) )
% 6.92/7.15 => ~ ( ( Xa = none_P6779099274072355161it_nat )
% 6.92/7.15 => ( Y != none_P6779099274072355161it_nat ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % timeFrame.elims
% 6.92/7.15 thf(fact_1529_timeFrame_Oelims,axiom,
% 6.92/7.15 ! [X: nat,Xa: option3562590408128118217it_nat,Y: option3562590408128118217it_nat] :
% 6.92/7.15 ( ( ( heap_T7616092557645711335rame_a @ X @ Xa )
% 6.92/7.15 = Y )
% 6.92/7.15 => ( ! [R4: a,H2: heap_e7401611519738050253t_unit,N4: nat] :
% 6.92/7.15 ( ( Xa
% 6.92/7.15 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ N4 ) ) ) )
% 6.92/7.15 => ( Y
% 6.92/7.15 != ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ ( plus_plus_nat @ X @ N4 ) ) ) ) ) )
% 6.92/7.15 => ~ ( ( Xa = none_P2651198173097904984it_nat )
% 6.92/7.15 => ( Y != none_P2651198173097904984it_nat ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % timeFrame.elims
% 6.92/7.15 thf(fact_1530_timeFrame_Oelims,axiom,
% 6.92/7.15 ! [X: nat,Xa: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
% 6.92/7.15 ( ( ( heap_T3616969660504097270t_unit @ X @ Xa )
% 6.92/7.15 = Y )
% 6.92/7.15 => ( ! [R4: product_unit,H2: heap_e7401611519738050253t_unit,N4: nat] :
% 6.92/7.15 ( ( Xa
% 6.92/7.15 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ N4 ) ) ) )
% 6.92/7.15 => ( Y
% 6.92/7.15 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ ( plus_plus_nat @ X @ N4 ) ) ) ) ) )
% 6.92/7.15 => ~ ( ( Xa = none_P9117596204409417319it_nat )
% 6.92/7.15 => ( Y != none_P9117596204409417319it_nat ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % timeFrame.elims
% 6.92/7.15 thf(fact_1531_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.15 ( lattic5174734335190411425at_nat @ sup_su3035147773818789531at_nat
% 6.92/7.15 @ ^ [X4: set_Pr8551490117392284871at_nat,Y4: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y4 @ X4 )
% 6.92/7.15 @ ^ [X4: set_Pr8551490117392284871at_nat,Y4: set_Pr8551490117392284871at_nat] : ( ord_le7642048601412989811at_nat @ Y4 @ X4 ) ) ).
% 6.92/7.15
% 6.92/7.15 % Sup_fin.semilattice_order_set_axioms
% 6.92/7.15 thf(fact_1532_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.15 ( lattic6976360593897529633at_nat @ sup_su5525570899277871387at_nat
% 6.92/7.15 @ ^ [X4: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y4 @ X4 )
% 6.92/7.15 @ ^ [X4: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] : ( ord_le2604355607129572851at_nat @ Y4 @ X4 ) ) ).
% 6.92/7.15
% 6.92/7.15 % Sup_fin.semilattice_order_set_axioms
% 6.92/7.15 thf(fact_1533_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.15 ( lattic3109210760196336428et_nat @ sup_sup_set_nat
% 6.92/7.15 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ Y4 @ X4 )
% 6.92/7.15 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_set_nat @ Y4 @ X4 ) ) ).
% 6.92/7.15
% 6.92/7.15 % Sup_fin.semilattice_order_set_axioms
% 6.92/7.15 thf(fact_1534_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.15 ( lattic5623431474481994958t_assn @ sup_sup_assn
% 6.92/7.15 @ ^ [X4: assn,Y4: assn] : ( ord_less_eq_assn @ Y4 @ X4 )
% 6.92/7.15 @ ^ [X4: assn,Y4: assn] : ( ord_less_assn @ Y4 @ X4 ) ) ).
% 6.92/7.15
% 6.92/7.15 % Sup_fin.semilattice_order_set_axioms
% 6.92/7.15 thf(fact_1535_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.15 ( lattic8154731777541915528et_int @ sup_sup_set_int
% 6.92/7.15 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_eq_set_int @ Y4 @ X4 )
% 6.92/7.15 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_set_int @ Y4 @ X4 ) ) ).
% 6.92/7.15
% 6.92/7.15 % Sup_fin.semilattice_order_set_axioms
% 6.92/7.15 thf(fact_1536_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.15 ( lattic5374021519246970238et_rat @ sup_sup_rat
% 6.92/7.15 @ ^ [X4: rat,Y4: rat] : ( ord_less_eq_rat @ Y4 @ X4 )
% 6.92/7.15 @ ^ [X4: rat,Y4: rat] : ( ord_less_rat @ Y4 @ X4 ) ) ).
% 6.92/7.15
% 6.92/7.15 % Sup_fin.semilattice_order_set_axioms
% 6.92/7.15 thf(fact_1537_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.15 ( lattic6009151579333465974et_nat @ sup_sup_nat
% 6.92/7.15 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 6.92/7.15 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 ) ) ).
% 6.92/7.15
% 6.92/7.15 % Sup_fin.semilattice_order_set_axioms
% 6.92/7.15 thf(fact_1538_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.15 ( lattic6006661108824415698et_int @ sup_sup_int
% 6.92/7.15 @ ^ [X4: int,Y4: int] : ( ord_less_eq_int @ Y4 @ X4 )
% 6.92/7.15 @ ^ [X4: int,Y4: int] : ( ord_less_int @ Y4 @ X4 ) ) ).
% 6.92/7.15
% 6.92/7.15 % Sup_fin.semilattice_order_set_axioms
% 6.92/7.15 thf(fact_1539_sup__option__def,axiom,
% 6.92/7.15 ( sup_su5873096292857799009at_nat
% 6.92/7.15 = ( ^ [X4: option2498585697089621389at_nat,Y4: option2498585697089621389at_nat] :
% 6.92/7.15 ( case_o8757249484648823045at_nat @ Y4
% 6.92/7.15 @ ^ [X8: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( case_o8757249484648823045at_nat @ X4
% 6.92/7.15 @ ^ [Z: set_Pr8551490117392284871at_nat] : ( some_s287724117700012716at_nat @ ( sup_su3035147773818789531at_nat @ X8 @ Z ) )
% 6.92/7.15 @ Y4 )
% 6.92/7.15 @ X4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_option_def
% 6.92/7.15 thf(fact_1540_sup__option__def,axiom,
% 6.92/7.15 ( sup_su2273273666271716065at_nat
% 6.92/7.15 = ( ^ [X4: option1583680563626158861at_nat,Y4: option1583680563626158861at_nat] :
% 6.92/7.15 ( case_o9080059180780454917at_nat @ Y4
% 6.92/7.15 @ ^ [X8: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( case_o9080059180780454917at_nat @ X4
% 6.92/7.15 @ ^ [Z: set_Pr4329608150637261639at_nat] : ( some_s5890477192898017836at_nat @ ( sup_su5525570899277871387at_nat @ X8 @ Z ) )
% 6.92/7.15 @ Y4 )
% 6.92/7.15 @ X4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_option_def
% 6.92/7.15 thf(fact_1541_sup__option__def,axiom,
% 6.92/7.15 ( sup_su3598758113090618626et_nat
% 6.92/7.15 = ( ^ [X4: option_set_nat,Y4: option_set_nat] :
% 6.92/7.15 ( case_o4054078431260844265et_nat @ Y4
% 6.92/7.15 @ ^ [X8: set_nat] :
% 6.92/7.15 ( case_o4054078431260844265et_nat @ X4
% 6.92/7.15 @ ^ [Z: set_nat] : ( some_set_nat @ ( sup_sup_set_nat @ X8 @ Z ) )
% 6.92/7.15 @ Y4 )
% 6.92/7.15 @ X4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_option_def
% 6.92/7.15 thf(fact_1542_sup__option__def,axiom,
% 6.92/7.15 ( sup_sup_option_nat
% 6.92/7.15 = ( ^ [X4: option_nat,Y4: option_nat] :
% 6.92/7.15 ( case_o7429725398727453821at_nat @ Y4
% 6.92/7.15 @ ^ [X8: nat] :
% 6.92/7.15 ( case_o7429725398727453821at_nat @ X4
% 6.92/7.15 @ ^ [Z: nat] : ( some_nat @ ( sup_sup_nat @ X8 @ Z ) )
% 6.92/7.15 @ Y4 )
% 6.92/7.15 @ X4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_option_def
% 6.92/7.15 thf(fact_1543_sup__option__def,axiom,
% 6.92/7.15 ( sup_sup_option_int
% 6.92/7.15 = ( ^ [X4: option_int,Y4: option_int] :
% 6.92/7.15 ( case_o390784466056649525nt_int @ Y4
% 6.92/7.15 @ ^ [X8: int] :
% 6.92/7.15 ( case_o390784466056649525nt_int @ X4
% 6.92/7.15 @ ^ [Z: int] : ( some_int @ ( sup_sup_int @ X8 @ Z ) )
% 6.92/7.15 @ Y4 )
% 6.92/7.15 @ X4 ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_option_def
% 6.92/7.15 thf(fact_1544_sup__Un__eq,axiom,
% 6.92/7.15 ! [R3: set_o,S: set_o] :
% 6.92/7.15 ( ( sup_sup_o_o
% 6.92/7.15 @ ^ [X4: $o] : ( member_o @ X4 @ R3 )
% 6.92/7.15 @ ^ [X4: $o] : ( member_o @ X4 @ S ) )
% 6.92/7.15 = ( ^ [X4: $o] : ( member_o @ X4 @ ( sup_sup_set_o @ R3 @ S ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_Un_eq
% 6.92/7.15 thf(fact_1545_sup__Un__eq,axiom,
% 6.92/7.15 ! [R3: set_se6260736226359567993nt_int,S: set_se6260736226359567993nt_int] :
% 6.92/7.15 ( ( sup_su1852724690005176016_int_o
% 6.92/7.15 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ R3 )
% 6.92/7.15 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ S ) )
% 6.92/7.15 = ( ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ ( sup_su2047564715030645325nt_int @ R3 @ S ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_Un_eq
% 6.92/7.15 thf(fact_1546_sup__Un__eq,axiom,
% 6.92/7.15 ! [R3: set_set_nat,S: set_set_nat] :
% 6.92/7.15 ( ( sup_sup_set_nat_o
% 6.92/7.15 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ R3 )
% 6.92/7.15 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ S ) )
% 6.92/7.15 = ( ^ [X4: set_nat] : ( member_set_nat @ X4 @ ( sup_sup_set_set_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_Un_eq
% 6.92/7.15 thf(fact_1547_sup__Un__eq,axiom,
% 6.92/7.15 ! [R3: set_int,S: set_int] :
% 6.92/7.15 ( ( sup_sup_int_o
% 6.92/7.15 @ ^ [X4: int] : ( member_int @ X4 @ R3 )
% 6.92/7.15 @ ^ [X4: int] : ( member_int @ X4 @ S ) )
% 6.92/7.15 = ( ^ [X4: int] : ( member_int @ X4 @ ( sup_sup_set_int @ R3 @ S ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_Un_eq
% 6.92/7.15 thf(fact_1548_sup__Un__eq,axiom,
% 6.92/7.15 ! [R3: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( sup_su6256023009775730178_nat_o
% 6.92/7.15 @ ^ [X4: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X4 @ R3 )
% 6.92/7.15 @ ^ [X4: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X4 @ S ) )
% 6.92/7.15 = ( ^ [X4: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X4 @ ( sup_su3035147773818789531at_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_Un_eq
% 6.92/7.15 thf(fact_1549_sup__Un__eq,axiom,
% 6.92/7.15 ! [R3: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( sup_su2080679670758317954_nat_o
% 6.92/7.15 @ ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ R3 )
% 6.92/7.15 @ ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ S ) )
% 6.92/7.15 = ( ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ ( sup_su5525570899277871387at_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_Un_eq
% 6.92/7.15 thf(fact_1550_sup__Un__eq,axiom,
% 6.92/7.15 ! [R3: set_nat,S: set_nat] :
% 6.92/7.15 ( ( sup_sup_nat_o
% 6.92/7.15 @ ^ [X4: nat] : ( member_nat @ X4 @ R3 )
% 6.92/7.15 @ ^ [X4: nat] : ( member_nat @ X4 @ S ) )
% 6.92/7.15 = ( ^ [X4: nat] : ( member_nat @ X4 @ ( sup_sup_set_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_Un_eq
% 6.92/7.15 thf(fact_1551_sup__Un__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
% 6.92/7.15 ( ( sup_sup_int_int_o
% 6.92/7.15 @ ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R3 )
% 6.92/7.15 @ ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ S ) )
% 6.92/7.15 = ( ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ ( sup_su6024340866399070445nt_int @ R3 @ S ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_Un_eq2
% 6.92/7.15 thf(fact_1552_sup__Un__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 6.92/7.15 ( ( sup_su1630790145277462993_nat_o
% 6.92/7.15 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R3 )
% 6.92/7.15 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ S ) )
% 6.92/7.15 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ ( sup_su7128418612487073120et_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_Un_eq2
% 6.92/7.15 thf(fact_1553_sup__Un__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 6.92/7.15 ( ( sup_su6535292691877529429_nat_o
% 6.92/7.15 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R3 )
% 6.92/7.15 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ S ) )
% 6.92/7.15 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ ( sup_su8975264963432250076et_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_Un_eq2
% 6.92/7.15 thf(fact_1554_sup__Un__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr7600907837789447088it_nat,S: set_Pr7600907837789447088it_nat] :
% 6.92/7.15 ( ( sup_su4207681470386032469_nat_o
% 6.92/7.15 @ ^ [X4: b,Y4: produc6653097349344004940it_nat] : ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Y4 ) @ R3 )
% 6.92/7.15 @ ^ [X4: b,Y4: produc6653097349344004940it_nat] : ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Y4 ) @ S ) )
% 6.92/7.15 = ( ^ [X4: b,Y4: produc6653097349344004940it_nat] : ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Y4 ) @ ( sup_su3714129841433130204it_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_Un_eq2
% 6.92/7.15 thf(fact_1555_sup__Un__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr7098220151150636591it_nat,S: set_Pr7098220151150636591it_nat] :
% 6.92/7.15 ( ( sup_su2191776239474528790_nat_o
% 6.92/7.15 @ ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ R3 )
% 6.92/7.15 @ ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ S ) )
% 6.92/7.15 = ( ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ ( sup_su3211442154794319707it_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_Un_eq2
% 6.92/7.15 thf(fact_1556_sup__Un__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 6.92/7.15 ( ( sup_su2200014604384089602_nat_o
% 6.92/7.15 @ ^ [X4: multis2468970476368604999at_nat,Y4: multis2468970476368604999at_nat] : ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ X4 @ Y4 ) @ R3 )
% 6.92/7.15 @ ^ [X4: multis2468970476368604999at_nat,Y4: multis2468970476368604999at_nat] : ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ X4 @ Y4 ) @ S ) )
% 6.92/7.15 = ( ^ [X4: multis2468970476368604999at_nat,Y4: multis2468970476368604999at_nat] : ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ X4 @ Y4 ) @ ( sup_su3035147773818789531at_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_Un_eq2
% 6.92/7.15 thf(fact_1557_sup__Un__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 6.92/7.15 ( ( sup_su7519161239522478338_nat_o
% 6.92/7.15 @ ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y4 ) @ R3 )
% 6.92/7.15 @ ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y4 ) @ S ) )
% 6.92/7.15 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y4 ) @ ( sup_su5525570899277871387at_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % sup_Un_eq2
% 6.92/7.15 thf(fact_1558_pred__subset__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
% 6.92/7.15 ( ( ord_le6741204236512500942_int_o
% 6.92/7.15 @ ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R3 )
% 6.92/7.15 @ ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ S ) )
% 6.92/7.15 = ( ord_le2843351958646193337nt_int @ R3 @ S ) ) ).
% 6.92/7.15
% 6.92/7.15 % pred_subset_eq2
% 6.92/7.15 thf(fact_1559_pred__subset__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 6.92/7.15 ( ( ord_le8000401564054156549_nat_o
% 6.92/7.15 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R3 )
% 6.92/7.15 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ S ) )
% 6.92/7.15 = ( ord_le5966269811547037844et_nat @ R3 @ S ) ) ).
% 6.92/7.15
% 6.92/7.15 % pred_subset_eq2
% 6.92/7.15 thf(fact_1560_pred__subset__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 6.92/7.15 ( ( ord_le6753239538765779593_nat_o
% 6.92/7.15 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R3 )
% 6.92/7.15 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ S ) )
% 6.92/7.15 = ( ord_le4763372923235995152et_nat @ R3 @ S ) ) ).
% 6.92/7.15
% 6.92/7.15 % pred_subset_eq2
% 6.92/7.15 thf(fact_1561_pred__subset__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr7600907837789447088it_nat,S: set_Pr7600907837789447088it_nat] :
% 6.92/7.15 ( ( ord_le785348814064375433_nat_o
% 6.92/7.15 @ ^ [X4: b,Y4: produc6653097349344004940it_nat] : ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Y4 ) @ R3 )
% 6.92/7.15 @ ^ [X4: b,Y4: produc6653097349344004940it_nat] : ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Y4 ) @ S ) )
% 6.92/7.15 = ( ord_le4980869671742669840it_nat @ R3 @ S ) ) ).
% 6.92/7.15
% 6.92/7.15 % pred_subset_eq2
% 6.92/7.15 thf(fact_1562_pred__subset__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr7098220151150636591it_nat,S: set_Pr7098220151150636591it_nat] :
% 6.92/7.15 ( ( ord_le7992815620007647562_nat_o
% 6.92/7.15 @ ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ R3 )
% 6.92/7.15 @ ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ S ) )
% 6.92/7.15 = ( ord_le4478181985103859343it_nat @ R3 @ S ) ) ).
% 6.92/7.15
% 6.92/7.15 % pred_subset_eq2
% 6.92/7.15 thf(fact_1563_pred__equals__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
% 6.92/7.15 ( ( ( ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R3 ) )
% 6.92/7.15 = ( ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ S ) ) )
% 6.92/7.15 = ( R3 = S ) ) ).
% 6.92/7.15
% 6.92/7.15 % pred_equals_eq2
% 6.92/7.15 thf(fact_1564_pred__equals__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 6.92/7.15 ( ( ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R3 ) )
% 6.92/7.15 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ S ) ) )
% 6.92/7.15 = ( R3 = S ) ) ).
% 6.92/7.15
% 6.92/7.15 % pred_equals_eq2
% 6.92/7.15 thf(fact_1565_pred__equals__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 6.92/7.15 ( ( ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R3 ) )
% 6.92/7.15 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ S ) ) )
% 6.92/7.15 = ( R3 = S ) ) ).
% 6.92/7.15
% 6.92/7.15 % pred_equals_eq2
% 6.92/7.15 thf(fact_1566_pred__equals__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr7600907837789447088it_nat,S: set_Pr7600907837789447088it_nat] :
% 6.92/7.15 ( ( ( ^ [X4: b,Y4: produc6653097349344004940it_nat] : ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Y4 ) @ R3 ) )
% 6.92/7.15 = ( ^ [X4: b,Y4: produc6653097349344004940it_nat] : ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Y4 ) @ S ) ) )
% 6.92/7.15 = ( R3 = S ) ) ).
% 6.92/7.15
% 6.92/7.15 % pred_equals_eq2
% 6.92/7.15 thf(fact_1567_pred__equals__eq2,axiom,
% 6.92/7.15 ! [R3: set_Pr7098220151150636591it_nat,S: set_Pr7098220151150636591it_nat] :
% 6.92/7.15 ( ( ( ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ R3 ) )
% 6.92/7.15 = ( ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ S ) ) )
% 6.92/7.15 = ( R3 = S ) ) ).
% 6.92/7.15
% 6.92/7.15 % pred_equals_eq2
% 6.92/7.15 thf(fact_1568_execute__guard_I2_J,axiom,
% 6.92/7.15 ! [P2: heap_e7401611519738050253t_unit > $o,H: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] :
% 6.92/7.15 ( ( P2 @ H )
% 6.92/7.15 => ( ( heap_T875086893843062177t_unit @ ( heap_T8440541562793052209t_unit @ P2 @ F ) @ H )
% 6.92/7.15 = ( some_P1914260805536162275it_nat @ ( F @ H ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % execute_guard(2)
% 6.92/7.15 thf(fact_1569_execute__guard_I2_J,axiom,
% 6.92/7.15 ! [P2: heap_e7401611519738050253t_unit > $o,H: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc7388388658123137530it_nat] :
% 6.92/7.15 ( ( P2 @ H )
% 6.92/7.15 => ( ( heap_Time_execute_b @ ( heap_Time_guard_b @ P2 @ F ) @ H )
% 6.92/7.15 = ( some_P2818173045054083285it_nat @ ( F @ H ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % execute_guard(2)
% 6.92/7.15 thf(fact_1570_execute__guard_I2_J,axiom,
% 6.92/7.15 ! [P2: heap_e7401611519738050253t_unit > $o,H: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc3260487557148687353it_nat] :
% 6.92/7.15 ( ( P2 @ H )
% 6.92/7.15 => ( ( heap_Time_execute_a @ ( heap_Time_guard_a @ P2 @ F ) @ H )
% 6.92/7.15 = ( some_P7913643980934408916it_nat @ ( F @ H ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % execute_guard(2)
% 6.92/7.15 thf(fact_1571_some__opt__eq__trivial,axiom,
% 6.92/7.15 ! [X: produc7388388658123137530it_nat] :
% 6.92/7.15 ( ( eps_Op5869321083069970014it_nat
% 6.92/7.15 @ ^ [Y4: produc7388388658123137530it_nat] : ( Y4 = X ) )
% 6.92/7.15 = ( some_P2818173045054083285it_nat @ X ) ) ).
% 6.92/7.15
% 6.92/7.15 % some_opt_eq_trivial
% 6.92/7.15 thf(fact_1572_some__opt__eq__trivial,axiom,
% 6.92/7.15 ! [X: produc3260487557148687353it_nat] :
% 6.92/7.15 ( ( eps_Op1741419982095519837it_nat
% 6.92/7.15 @ ^ [Y4: produc3260487557148687353it_nat] : ( Y4 = X ) )
% 6.92/7.15 = ( some_P7913643980934408916it_nat @ X ) ) ).
% 6.92/7.15
% 6.92/7.15 % some_opt_eq_trivial
% 6.92/7.15 thf(fact_1573_some__opt__eq__trivial,axiom,
% 6.92/7.15 ! [X: produc8664842809031399944it_nat] :
% 6.92/7.15 ( ( eps_Op3393321821070424684it_nat
% 6.92/7.15 @ ^ [Y4: produc8664842809031399944it_nat] : ( Y4 = X ) )
% 6.92/7.15 = ( some_P1914260805536162275it_nat @ X ) ) ).
% 6.92/7.15
% 6.92/7.15 % some_opt_eq_trivial
% 6.92/7.15 thf(fact_1574_some__opt__eq__trivial,axiom,
% 6.92/7.15 ! [X: num] :
% 6.92/7.15 ( ( eps_Opt_num
% 6.92/7.15 @ ^ [Y4: num] : ( Y4 = X ) )
% 6.92/7.15 = ( some_num @ X ) ) ).
% 6.92/7.15
% 6.92/7.15 % some_opt_eq_trivial
% 6.92/7.15 thf(fact_1575_not__None__eq,axiom,
% 6.92/7.15 ! [X: option4065278094766928714it_nat] :
% 6.92/7.15 ( ( X != none_P6779099274072355161it_nat )
% 6.92/7.15 = ( ? [Y4: produc7388388658123137530it_nat] :
% 6.92/7.15 ( X
% 6.92/7.15 = ( some_P2818173045054083285it_nat @ Y4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % not_None_eq
% 6.92/7.15 thf(fact_1576_not__None__eq,axiom,
% 6.92/7.15 ! [X: option3562590408128118217it_nat] :
% 6.92/7.15 ( ( X != none_P2651198173097904984it_nat )
% 6.92/7.15 = ( ? [Y4: produc3260487557148687353it_nat] :
% 6.92/7.15 ( X
% 6.92/7.15 = ( some_P7913643980934408916it_nat @ Y4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % not_None_eq
% 6.92/7.15 thf(fact_1577_not__None__eq,axiom,
% 6.92/7.15 ! [X: option8956607266484857688it_nat] :
% 6.92/7.15 ( ( X != none_P9117596204409417319it_nat )
% 6.92/7.15 = ( ? [Y4: produc8664842809031399944it_nat] :
% 6.92/7.15 ( X
% 6.92/7.15 = ( some_P1914260805536162275it_nat @ Y4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % not_None_eq
% 6.92/7.15 thf(fact_1578_not__None__eq,axiom,
% 6.92/7.15 ! [X: option_num] :
% 6.92/7.15 ( ( X != none_num )
% 6.92/7.15 = ( ? [Y4: num] :
% 6.92/7.15 ( X
% 6.92/7.15 = ( some_num @ Y4 ) ) ) ) ).
% 6.92/7.15
% 6.92/7.15 % not_None_eq
% 6.92/7.15 thf(fact_1579_not__Some__eq,axiom,
% 6.92/7.15 ! [X: option4065278094766928714it_nat] :
% 6.92/7.15 ( ( ! [Y4: produc7388388658123137530it_nat] :
% 6.92/7.15 ( X
% 6.92/7.15 != ( some_P2818173045054083285it_nat @ Y4 ) ) )
% 6.92/7.15 = ( X = none_P6779099274072355161it_nat ) ) ).
% 6.92/7.15
% 6.92/7.15 % not_Some_eq
% 6.92/7.15 thf(fact_1580_not__Some__eq,axiom,
% 6.92/7.15 ! [X: option3562590408128118217it_nat] :
% 6.92/7.15 ( ( ! [Y4: produc3260487557148687353it_nat] :
% 6.92/7.15 ( X
% 6.92/7.15 != ( some_P7913643980934408916it_nat @ Y4 ) ) )
% 6.92/7.15 = ( X = none_P2651198173097904984it_nat ) ) ).
% 6.92/7.15
% 6.92/7.15 % not_Some_eq
% 6.92/7.15 thf(fact_1581_not__Some__eq,axiom,
% 6.92/7.15 ! [X: option8956607266484857688it_nat] :
% 6.92/7.15 ( ( ! [Y4: produc8664842809031399944it_nat] :
% 6.92/7.15 ( X
% 6.92/7.15 != ( some_P1914260805536162275it_nat @ Y4 ) ) )
% 6.92/7.15 = ( X = none_P9117596204409417319it_nat ) ) ).
% 6.92/7.15
% 6.92/7.15 % not_Some_eq
% 6.92/7.15 thf(fact_1582_not__Some__eq,axiom,
% 6.92/7.15 ! [X: option_num] :
% 6.92/7.15 ( ( ! [Y4: num] :
% 6.92/7.15 ( X
% 6.92/7.15 != ( some_num @ Y4 ) ) )
% 6.92/7.15 = ( X = none_num ) ) ).
% 6.92/7.15
% 6.92/7.15 % not_Some_eq
% 6.92/7.15 thf(fact_1583_some__opt__sym__eq__trivial,axiom,
% 6.92/7.15 ! [X: produc7388388658123137530it_nat] :
% 6.92/7.15 ( ( eps_Op5869321083069970014it_nat
% 6.92/7.15 @ ( ^ [Y6: produc7388388658123137530it_nat,Z4: produc7388388658123137530it_nat] : ( Y6 = Z4 )
% 6.92/7.15 @ X ) )
% 6.92/7.15 = ( some_P2818173045054083285it_nat @ X ) ) ).
% 6.92/7.15
% 6.92/7.15 % some_opt_sym_eq_trivial
% 6.92/7.15 thf(fact_1584_some__opt__sym__eq__trivial,axiom,
% 6.92/7.15 ! [X: produc3260487557148687353it_nat] :
% 6.92/7.15 ( ( eps_Op1741419982095519837it_nat
% 6.92/7.15 @ ( ^ [Y6: produc3260487557148687353it_nat,Z4: produc3260487557148687353it_nat] : ( Y6 = Z4 )
% 6.92/7.15 @ X ) )
% 6.92/7.15 = ( some_P7913643980934408916it_nat @ X ) ) ).
% 6.92/7.15
% 6.92/7.15 % some_opt_sym_eq_trivial
% 6.92/7.15 thf(fact_1585_some__opt__sym__eq__trivial,axiom,
% 6.92/7.15 ! [X: produc8664842809031399944it_nat] :
% 6.92/7.15 ( ( eps_Op3393321821070424684it_nat
% 6.92/7.15 @ ( ^ [Y6: produc8664842809031399944it_nat,Z4: produc8664842809031399944it_nat] : ( Y6 = Z4 )
% 6.92/7.15 @ X ) )
% 6.92/7.15 = ( some_P1914260805536162275it_nat @ X ) ) ).
% 6.92/7.15
% 6.92/7.15 % some_opt_sym_eq_trivial
% 6.92/7.15 thf(fact_1586_some__opt__sym__eq__trivial,axiom,
% 6.92/7.15 ! [X: num] :
% 6.92/7.15 ( ( eps_Opt_num
% 6.92/7.15 @ ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 )
% 6.92/7.15 @ X ) )
% 6.92/7.15 = ( some_num @ X ) ) ).
% 6.92/7.15
% 6.92/7.15 % some_opt_sym_eq_trivial
% 6.92/7.15 thf(fact_1587_less__eq__option__None__code,axiom,
% 6.92/7.15 ! [X: option_num] : ( ord_le6622620407824499402on_num @ none_num @ X ) ).
% 6.92/7.15
% 6.92/7.15 % less_eq_option_None_code
% 6.92/7.15 thf(fact_1588_less__option__None,axiom,
% 6.92/7.15 ! [X: option_num] :
% 6.92/7.15 ~ ( ord_less_option_num @ X @ none_num ) ).
% 6.92/7.15
% 6.92/7.15 % less_option_None
% 6.92/7.15 thf(fact_1589_some__opt__false__trivial,axiom,
% 6.92/7.15 ( ( eps_Opt_num
% 6.92/7.15 @ ^ [Uu2: num] : $false )
% 6.92/7.15 = none_num ) ).
% 6.92/7.15
% 6.92/7.15 % some_opt_false_trivial
% 6.92/7.15 thf(fact_1590_not__Some__eq2,axiom,
% 6.92/7.15 ! [V: option4624381673175914239nt_int] :
% 6.92/7.15 ( ( ! [X4: int,Y4: int] :
% 6.92/7.15 ( V
% 6.92/7.15 != ( some_P4184893108420464158nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) ) ) )
% 6.92/7.15 = ( V = none_P2377608414092835994nt_int ) ) ).
% 6.92/7.15
% 6.92/7.15 % not_Some_eq2
% 6.92/7.15 thf(fact_1591_not__Some__eq2,axiom,
% 6.92/7.15 ! [V: option5190343406534369742et_nat] :
% 6.92/7.15 ( ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] :
% 6.92/7.15 ( V
% 6.92/7.15 != ( some_P750831030444334937et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) ) ) )
% 6.92/7.15 = ( V = none_P4972525538344268765et_nat ) ) ).
% 6.92/7.15
% 6.92/7.15 % not_Some_eq2
% 6.92/7.15 thf(fact_1592_not__Some__eq2,axiom,
% 6.92/7.15 ! [V: option2860828798490689354et_nat] :
% 6.92/7.15 ( ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] :
% 6.92/7.15 ( V
% 6.92/7.15 != ( some_P1630309045189364437et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) ) ) )
% 6.92/7.15 = ( V = none_P199884684680593241et_nat ) ) ).
% 6.92/7.15
% 6.92/7.15 % not_Some_eq2
% 6.92/7.15 thf(fact_1593_not__Some__eq2,axiom,
% 6.92/7.15 ! [V: option4065278094766928714it_nat] :
% 6.92/7.15 ( ( ! [X4: b,Y4: produc6653097349344004940it_nat] :
% 6.92/7.15 ( V
% 6.92/7.15 != ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ X4 @ Y4 ) ) ) )
% 6.92/7.15 = ( V = none_P6779099274072355161it_nat ) ) ).
% 6.92/7.15
% 6.92/7.15 % not_Some_eq2
% 6.92/7.15 thf(fact_1594_not__Some__eq2,axiom,
% 6.92/7.15 ! [V: option3562590408128118217it_nat] :
% 6.92/7.15 ( ( ! [X4: a,Y4: produc6653097349344004940it_nat] :
% 6.92/7.15 ( V
% 6.92/7.15 != ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) ) ) )
% 6.92/7.15 = ( V = none_P2651198173097904984it_nat ) ) ).
% 6.92/7.15
% 6.92/7.15 % not_Some_eq2
% 6.92/7.15 thf(fact_1595_not__Some__eq2,axiom,
% 6.92/7.15 ! [V: option8956607266484857688it_nat] :
% 6.92/7.15 ( ( ! [X4: product_unit,Y4: produc6653097349344004940it_nat] :
% 6.92/7.15 ( V
% 6.92/7.15 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X4 @ Y4 ) ) ) )
% 6.92/7.15 = ( V = none_P9117596204409417319it_nat ) ) ).
% 6.92/7.15
% 6.92/7.15 % not_Some_eq2
% 6.92/7.15 thf(fact_1596_less__eq__option__Some__None,axiom,
% 6.92/7.15 ! [X: num] :
% 6.92/7.15 ~ ( ord_le6622620407824499402on_num @ ( some_num @ X ) @ none_num ) ).
% 6.92/7.15
% 6.92/7.15 % less_eq_option_Some_None
% 6.92/7.15 thf(fact_1597_less__option__None__Some__code,axiom,
% 6.92/7.15 ! [X: num] : ( ord_less_option_num @ none_num @ ( some_num @ X ) ) ).
% 6.92/7.15
% 6.92/7.15 % less_option_None_Some_code
% 6.92/7.15 thf(fact_1598_option_Osimps_I4_J,axiom,
% 6.92/7.15 ! [F1: int,F2: num > int] :
% 6.92/7.15 ( ( case_option_int_num @ F1 @ F2 @ none_num )
% 6.92/7.15 = F1 ) ).
% 6.92/7.15
% 6.92/7.15 % option.simps(4)
% 6.92/7.15 thf(fact_1599_option_Osimps_I4_J,axiom,
% 6.92/7.15 ! [F1: option_num,F2: num > option_num] :
% 6.92/7.15 ( ( case_o6005452278849405969um_num @ F1 @ F2 @ none_num )
% 6.92/7.15 = F1 ) ).
% 6.92/7.15
% 6.92/7.15 % option.simps(4)
% 6.92/7.15 thf(fact_1600_option_Osimps_I4_J,axiom,
% 6.92/7.15 ! [F1: num,F2: num > num] :
% 6.92/7.15 ( ( case_option_num_num @ F1 @ F2 @ none_num )
% 6.92/7.15 = F1 ) ).
% 6.92/7.15
% 6.92/7.15 % option.simps(4)
% 6.92/7.15 thf(fact_1601_execute__guard_I1_J,axiom,
% 6.92/7.15 ! [P2: heap_e7401611519738050253t_unit > $o,H: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc7388388658123137530it_nat] :
% 6.92/7.15 ( ~ ( P2 @ H )
% 6.92/7.15 => ( ( heap_Time_execute_b @ ( heap_Time_guard_b @ P2 @ F ) @ H )
% 6.92/7.15 = none_P6779099274072355161it_nat ) ) ).
% 6.92/7.15
% 6.92/7.15 % execute_guard(1)
% 6.92/7.15 thf(fact_1602_execute__guard_I1_J,axiom,
% 6.92/7.15 ! [P2: heap_e7401611519738050253t_unit > $o,H: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc3260487557148687353it_nat] :
% 6.92/7.15 ( ~ ( P2 @ H )
% 6.92/7.15 => ( ( heap_Time_execute_a @ ( heap_Time_guard_a @ P2 @ F ) @ H )
% 6.92/7.15 = none_P2651198173097904984it_nat ) ) ).
% 6.92/7.15
% 6.92/7.15 % execute_guard(1)
% 6.92/7.15 thf(fact_1603_execute__raise,axiom,
% 6.92/7.15 ! [S2: list_char] :
% 6.92/7.15 ( ( heap_Time_execute_b @ ( heap_Time_raise_b @ S2 ) )
% 6.92/7.15 = ( ^ [Uu2: heap_e7401611519738050253t_unit] : none_P6779099274072355161it_nat ) ) ).
% 6.92/7.15
% 6.92/7.15 % execute_raise
% 6.92/7.15 thf(fact_1604_execute__raise,axiom,
% 6.92/7.15 ! [S2: list_char] :
% 6.92/7.15 ( ( heap_Time_execute_a @ ( heap_Time_raise_a @ S2 ) )
% 6.92/7.15 = ( ^ [Uu2: heap_e7401611519738050253t_unit] : none_P2651198173097904984it_nat ) ) ).
% 6.92/7.15
% 6.92/7.15 % execute_raise
% 6.92/7.15 thf(fact_1605_option_Ocase__distrib,axiom,
% 6.92/7.15 ! [H: int > int,F1: int,F2: num > int,Option: option_num] :
% 6.92/7.15 ( ( H @ ( case_option_int_num @ F1 @ F2 @ Option ) )
% 6.92/7.15 = ( case_option_int_num @ ( H @ F1 )
% 6.92/7.15 @ ^ [X4: num] : ( H @ ( F2 @ X4 ) )
% 6.92/7.15 @ Option ) ) ).
% 6.92/7.15
% 6.92/7.15 % option.case_distrib
% 6.92/7.15 thf(fact_1606_option_Ocase__distrib,axiom,
% 6.92/7.16 ! [H: int > option_num,F1: int,F2: num > int,Option: option_num] :
% 6.92/7.16 ( ( H @ ( case_option_int_num @ F1 @ F2 @ Option ) )
% 6.92/7.16 = ( case_o6005452278849405969um_num @ ( H @ F1 )
% 6.92/7.16 @ ^ [X4: num] : ( H @ ( F2 @ X4 ) )
% 6.92/7.16 @ Option ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.case_distrib
% 6.92/7.16 thf(fact_1607_option_Ocase__distrib,axiom,
% 6.92/7.16 ! [H: int > num,F1: int,F2: num > int,Option: option_num] :
% 6.92/7.16 ( ( H @ ( case_option_int_num @ F1 @ F2 @ Option ) )
% 6.92/7.16 = ( case_option_num_num @ ( H @ F1 )
% 6.92/7.16 @ ^ [X4: num] : ( H @ ( F2 @ X4 ) )
% 6.92/7.16 @ Option ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.case_distrib
% 6.92/7.16 thf(fact_1608_option_Ocase__distrib,axiom,
% 6.92/7.16 ! [H: option_num > int,F1: option_num,F2: num > option_num,Option: option_num] :
% 6.92/7.16 ( ( H @ ( case_o6005452278849405969um_num @ F1 @ F2 @ Option ) )
% 6.92/7.16 = ( case_option_int_num @ ( H @ F1 )
% 6.92/7.16 @ ^ [X4: num] : ( H @ ( F2 @ X4 ) )
% 6.92/7.16 @ Option ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.case_distrib
% 6.92/7.16 thf(fact_1609_option_Ocase__distrib,axiom,
% 6.92/7.16 ! [H: option_num > option_num,F1: option_num,F2: num > option_num,Option: option_num] :
% 6.92/7.16 ( ( H @ ( case_o6005452278849405969um_num @ F1 @ F2 @ Option ) )
% 6.92/7.16 = ( case_o6005452278849405969um_num @ ( H @ F1 )
% 6.92/7.16 @ ^ [X4: num] : ( H @ ( F2 @ X4 ) )
% 6.92/7.16 @ Option ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.case_distrib
% 6.92/7.16 thf(fact_1610_option_Ocase__distrib,axiom,
% 6.92/7.16 ! [H: option_num > num,F1: option_num,F2: num > option_num,Option: option_num] :
% 6.92/7.16 ( ( H @ ( case_o6005452278849405969um_num @ F1 @ F2 @ Option ) )
% 6.92/7.16 = ( case_option_num_num @ ( H @ F1 )
% 6.92/7.16 @ ^ [X4: num] : ( H @ ( F2 @ X4 ) )
% 6.92/7.16 @ Option ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.case_distrib
% 6.92/7.16 thf(fact_1611_option_Ocase__distrib,axiom,
% 6.92/7.16 ! [H: num > int,F1: num,F2: num > num,Option: option_num] :
% 6.92/7.16 ( ( H @ ( case_option_num_num @ F1 @ F2 @ Option ) )
% 6.92/7.16 = ( case_option_int_num @ ( H @ F1 )
% 6.92/7.16 @ ^ [X4: num] : ( H @ ( F2 @ X4 ) )
% 6.92/7.16 @ Option ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.case_distrib
% 6.92/7.16 thf(fact_1612_option_Ocase__distrib,axiom,
% 6.92/7.16 ! [H: num > option_num,F1: num,F2: num > num,Option: option_num] :
% 6.92/7.16 ( ( H @ ( case_option_num_num @ F1 @ F2 @ Option ) )
% 6.92/7.16 = ( case_o6005452278849405969um_num @ ( H @ F1 )
% 6.92/7.16 @ ^ [X4: num] : ( H @ ( F2 @ X4 ) )
% 6.92/7.16 @ Option ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.case_distrib
% 6.92/7.16 thf(fact_1613_option_Ocase__distrib,axiom,
% 6.92/7.16 ! [H: num > num,F1: num,F2: num > num,Option: option_num] :
% 6.92/7.16 ( ( H @ ( case_option_num_num @ F1 @ F2 @ Option ) )
% 6.92/7.16 = ( case_option_num_num @ ( H @ F1 )
% 6.92/7.16 @ ^ [X4: num] : ( H @ ( F2 @ X4 ) )
% 6.92/7.16 @ Option ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.case_distrib
% 6.92/7.16 thf(fact_1614_option_Odistinct_I1_J,axiom,
% 6.92/7.16 ! [X2: produc7388388658123137530it_nat] :
% 6.92/7.16 ( none_P6779099274072355161it_nat
% 6.92/7.16 != ( some_P2818173045054083285it_nat @ X2 ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.distinct(1)
% 6.92/7.16 thf(fact_1615_option_Odistinct_I1_J,axiom,
% 6.92/7.16 ! [X2: produc3260487557148687353it_nat] :
% 6.92/7.16 ( none_P2651198173097904984it_nat
% 6.92/7.16 != ( some_P7913643980934408916it_nat @ X2 ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.distinct(1)
% 6.92/7.16 thf(fact_1616_option_Odistinct_I1_J,axiom,
% 6.92/7.16 ! [X2: produc8664842809031399944it_nat] :
% 6.92/7.16 ( none_P9117596204409417319it_nat
% 6.92/7.16 != ( some_P1914260805536162275it_nat @ X2 ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.distinct(1)
% 6.92/7.16 thf(fact_1617_option_Odistinct_I1_J,axiom,
% 6.92/7.16 ! [X2: num] :
% 6.92/7.16 ( none_num
% 6.92/7.16 != ( some_num @ X2 ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.distinct(1)
% 6.92/7.16 thf(fact_1618_option_OdiscI,axiom,
% 6.92/7.16 ! [Option: option4065278094766928714it_nat,X2: produc7388388658123137530it_nat] :
% 6.92/7.16 ( ( Option
% 6.92/7.16 = ( some_P2818173045054083285it_nat @ X2 ) )
% 6.92/7.16 => ( Option != none_P6779099274072355161it_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.discI
% 6.92/7.16 thf(fact_1619_option_OdiscI,axiom,
% 6.92/7.16 ! [Option: option3562590408128118217it_nat,X2: produc3260487557148687353it_nat] :
% 6.92/7.16 ( ( Option
% 6.92/7.16 = ( some_P7913643980934408916it_nat @ X2 ) )
% 6.92/7.16 => ( Option != none_P2651198173097904984it_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.discI
% 6.92/7.16 thf(fact_1620_option_OdiscI,axiom,
% 6.92/7.16 ! [Option: option8956607266484857688it_nat,X2: produc8664842809031399944it_nat] :
% 6.92/7.16 ( ( Option
% 6.92/7.16 = ( some_P1914260805536162275it_nat @ X2 ) )
% 6.92/7.16 => ( Option != none_P9117596204409417319it_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.discI
% 6.92/7.16 thf(fact_1621_option_OdiscI,axiom,
% 6.92/7.16 ! [Option: option_num,X2: num] :
% 6.92/7.16 ( ( Option
% 6.92/7.16 = ( some_num @ X2 ) )
% 6.92/7.16 => ( Option != none_num ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.discI
% 6.92/7.16 thf(fact_1622_option_Oexhaust,axiom,
% 6.92/7.16 ! [Y: option4065278094766928714it_nat] :
% 6.92/7.16 ( ( Y != none_P6779099274072355161it_nat )
% 6.92/7.16 => ~ ! [X22: produc7388388658123137530it_nat] :
% 6.92/7.16 ( Y
% 6.92/7.16 != ( some_P2818173045054083285it_nat @ X22 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.exhaust
% 6.92/7.16 thf(fact_1623_option_Oexhaust,axiom,
% 6.92/7.16 ! [Y: option3562590408128118217it_nat] :
% 6.92/7.16 ( ( Y != none_P2651198173097904984it_nat )
% 6.92/7.16 => ~ ! [X22: produc3260487557148687353it_nat] :
% 6.92/7.16 ( Y
% 6.92/7.16 != ( some_P7913643980934408916it_nat @ X22 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.exhaust
% 6.92/7.16 thf(fact_1624_option_Oexhaust,axiom,
% 6.92/7.16 ! [Y: option8956607266484857688it_nat] :
% 6.92/7.16 ( ( Y != none_P9117596204409417319it_nat )
% 6.92/7.16 => ~ ! [X22: produc8664842809031399944it_nat] :
% 6.92/7.16 ( Y
% 6.92/7.16 != ( some_P1914260805536162275it_nat @ X22 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.exhaust
% 6.92/7.16 thf(fact_1625_option_Oexhaust,axiom,
% 6.92/7.16 ! [Y: option_num] :
% 6.92/7.16 ( ( Y != none_num )
% 6.92/7.16 => ~ ! [X22: num] :
% 6.92/7.16 ( Y
% 6.92/7.16 != ( some_num @ X22 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.exhaust
% 6.92/7.16 thf(fact_1626_split__option__ex,axiom,
% 6.92/7.16 ( ( ^ [P4: option4065278094766928714it_nat > $o] :
% 6.92/7.16 ? [X5: option4065278094766928714it_nat] : ( P4 @ X5 ) )
% 6.92/7.16 = ( ^ [P5: option4065278094766928714it_nat > $o] :
% 6.92/7.16 ( ( P5 @ none_P6779099274072355161it_nat )
% 6.92/7.16 | ? [X4: produc7388388658123137530it_nat] : ( P5 @ ( some_P2818173045054083285it_nat @ X4 ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % split_option_ex
% 6.92/7.16 thf(fact_1627_split__option__ex,axiom,
% 6.92/7.16 ( ( ^ [P4: option3562590408128118217it_nat > $o] :
% 6.92/7.16 ? [X5: option3562590408128118217it_nat] : ( P4 @ X5 ) )
% 6.92/7.16 = ( ^ [P5: option3562590408128118217it_nat > $o] :
% 6.92/7.16 ( ( P5 @ none_P2651198173097904984it_nat )
% 6.92/7.16 | ? [X4: produc3260487557148687353it_nat] : ( P5 @ ( some_P7913643980934408916it_nat @ X4 ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % split_option_ex
% 6.92/7.16 thf(fact_1628_split__option__ex,axiom,
% 6.92/7.16 ( ( ^ [P4: option8956607266484857688it_nat > $o] :
% 6.92/7.16 ? [X5: option8956607266484857688it_nat] : ( P4 @ X5 ) )
% 6.92/7.16 = ( ^ [P5: option8956607266484857688it_nat > $o] :
% 6.92/7.16 ( ( P5 @ none_P9117596204409417319it_nat )
% 6.92/7.16 | ? [X4: produc8664842809031399944it_nat] : ( P5 @ ( some_P1914260805536162275it_nat @ X4 ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % split_option_ex
% 6.92/7.16 thf(fact_1629_split__option__ex,axiom,
% 6.92/7.16 ( ( ^ [P4: option_num > $o] :
% 6.92/7.16 ? [X5: option_num] : ( P4 @ X5 ) )
% 6.92/7.16 = ( ^ [P5: option_num > $o] :
% 6.92/7.16 ( ( P5 @ none_num )
% 6.92/7.16 | ? [X4: num] : ( P5 @ ( some_num @ X4 ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % split_option_ex
% 6.92/7.16 thf(fact_1630_split__option__all,axiom,
% 6.92/7.16 ( ( ^ [P4: option4065278094766928714it_nat > $o] :
% 6.92/7.16 ! [X5: option4065278094766928714it_nat] : ( P4 @ X5 ) )
% 6.92/7.16 = ( ^ [P5: option4065278094766928714it_nat > $o] :
% 6.92/7.16 ( ( P5 @ none_P6779099274072355161it_nat )
% 6.92/7.16 & ! [X4: produc7388388658123137530it_nat] : ( P5 @ ( some_P2818173045054083285it_nat @ X4 ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % split_option_all
% 6.92/7.16 thf(fact_1631_split__option__all,axiom,
% 6.92/7.16 ( ( ^ [P4: option3562590408128118217it_nat > $o] :
% 6.92/7.16 ! [X5: option3562590408128118217it_nat] : ( P4 @ X5 ) )
% 6.92/7.16 = ( ^ [P5: option3562590408128118217it_nat > $o] :
% 6.92/7.16 ( ( P5 @ none_P2651198173097904984it_nat )
% 6.92/7.16 & ! [X4: produc3260487557148687353it_nat] : ( P5 @ ( some_P7913643980934408916it_nat @ X4 ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % split_option_all
% 6.92/7.16 thf(fact_1632_split__option__all,axiom,
% 6.92/7.16 ( ( ^ [P4: option8956607266484857688it_nat > $o] :
% 6.92/7.16 ! [X5: option8956607266484857688it_nat] : ( P4 @ X5 ) )
% 6.92/7.16 = ( ^ [P5: option8956607266484857688it_nat > $o] :
% 6.92/7.16 ( ( P5 @ none_P9117596204409417319it_nat )
% 6.92/7.16 & ! [X4: produc8664842809031399944it_nat] : ( P5 @ ( some_P1914260805536162275it_nat @ X4 ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % split_option_all
% 6.92/7.16 thf(fact_1633_split__option__all,axiom,
% 6.92/7.16 ( ( ^ [P4: option_num > $o] :
% 6.92/7.16 ! [X5: option_num] : ( P4 @ X5 ) )
% 6.92/7.16 = ( ^ [P5: option_num > $o] :
% 6.92/7.16 ( ( P5 @ none_num )
% 6.92/7.16 & ! [X4: num] : ( P5 @ ( some_num @ X4 ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % split_option_all
% 6.92/7.16 thf(fact_1634_combine__options__cases,axiom,
% 6.92/7.16 ! [X: option_num,P2: option_num > option_num > $o,Y: option_num] :
% 6.92/7.16 ( ( ( X = none_num )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ( ( Y = none_num )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ! [A3: num,B3: num] :
% 6.92/7.16 ( ( X
% 6.92/7.16 = ( some_num @ A3 ) )
% 6.92/7.16 => ( ( Y
% 6.92/7.16 = ( some_num @ B3 ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_cases
% 6.92/7.16 thf(fact_1635_combine__options__cases,axiom,
% 6.92/7.16 ! [X: option4065278094766928714it_nat,P2: option4065278094766928714it_nat > option_num > $o,Y: option_num] :
% 6.92/7.16 ( ( ( X = none_P6779099274072355161it_nat )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ( ( Y = none_num )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ! [A3: produc7388388658123137530it_nat,B3: num] :
% 6.92/7.16 ( ( X
% 6.92/7.16 = ( some_P2818173045054083285it_nat @ A3 ) )
% 6.92/7.16 => ( ( Y
% 6.92/7.16 = ( some_num @ B3 ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_cases
% 6.92/7.16 thf(fact_1636_combine__options__cases,axiom,
% 6.92/7.16 ! [X: option3562590408128118217it_nat,P2: option3562590408128118217it_nat > option_num > $o,Y: option_num] :
% 6.92/7.16 ( ( ( X = none_P2651198173097904984it_nat )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ( ( Y = none_num )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ! [A3: produc3260487557148687353it_nat,B3: num] :
% 6.92/7.16 ( ( X
% 6.92/7.16 = ( some_P7913643980934408916it_nat @ A3 ) )
% 6.92/7.16 => ( ( Y
% 6.92/7.16 = ( some_num @ B3 ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_cases
% 6.92/7.16 thf(fact_1637_combine__options__cases,axiom,
% 6.92/7.16 ! [X: option8956607266484857688it_nat,P2: option8956607266484857688it_nat > option_num > $o,Y: option_num] :
% 6.92/7.16 ( ( ( X = none_P9117596204409417319it_nat )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ( ( Y = none_num )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ! [A3: produc8664842809031399944it_nat,B3: num] :
% 6.92/7.16 ( ( X
% 6.92/7.16 = ( some_P1914260805536162275it_nat @ A3 ) )
% 6.92/7.16 => ( ( Y
% 6.92/7.16 = ( some_num @ B3 ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_cases
% 6.92/7.16 thf(fact_1638_combine__options__cases,axiom,
% 6.92/7.16 ! [X: option_num,P2: option_num > option4065278094766928714it_nat > $o,Y: option4065278094766928714it_nat] :
% 6.92/7.16 ( ( ( X = none_num )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ( ( Y = none_P6779099274072355161it_nat )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ! [A3: num,B3: produc7388388658123137530it_nat] :
% 6.92/7.16 ( ( X
% 6.92/7.16 = ( some_num @ A3 ) )
% 6.92/7.16 => ( ( Y
% 6.92/7.16 = ( some_P2818173045054083285it_nat @ B3 ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_cases
% 6.92/7.16 thf(fact_1639_combine__options__cases,axiom,
% 6.92/7.16 ! [X: option_num,P2: option_num > option3562590408128118217it_nat > $o,Y: option3562590408128118217it_nat] :
% 6.92/7.16 ( ( ( X = none_num )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ( ( Y = none_P2651198173097904984it_nat )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ! [A3: num,B3: produc3260487557148687353it_nat] :
% 6.92/7.16 ( ( X
% 6.92/7.16 = ( some_num @ A3 ) )
% 6.92/7.16 => ( ( Y
% 6.92/7.16 = ( some_P7913643980934408916it_nat @ B3 ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_cases
% 6.92/7.16 thf(fact_1640_combine__options__cases,axiom,
% 6.92/7.16 ! [X: option_num,P2: option_num > option8956607266484857688it_nat > $o,Y: option8956607266484857688it_nat] :
% 6.92/7.16 ( ( ( X = none_num )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ( ( Y = none_P9117596204409417319it_nat )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ! [A3: num,B3: produc8664842809031399944it_nat] :
% 6.92/7.16 ( ( X
% 6.92/7.16 = ( some_num @ A3 ) )
% 6.92/7.16 => ( ( Y
% 6.92/7.16 = ( some_P1914260805536162275it_nat @ B3 ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_cases
% 6.92/7.16 thf(fact_1641_combine__options__cases,axiom,
% 6.92/7.16 ! [X: option4065278094766928714it_nat,P2: option4065278094766928714it_nat > option4065278094766928714it_nat > $o,Y: option4065278094766928714it_nat] :
% 6.92/7.16 ( ( ( X = none_P6779099274072355161it_nat )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ( ( Y = none_P6779099274072355161it_nat )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ! [A3: produc7388388658123137530it_nat,B3: produc7388388658123137530it_nat] :
% 6.92/7.16 ( ( X
% 6.92/7.16 = ( some_P2818173045054083285it_nat @ A3 ) )
% 6.92/7.16 => ( ( Y
% 6.92/7.16 = ( some_P2818173045054083285it_nat @ B3 ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_cases
% 6.92/7.16 thf(fact_1642_combine__options__cases,axiom,
% 6.92/7.16 ! [X: option4065278094766928714it_nat,P2: option4065278094766928714it_nat > option3562590408128118217it_nat > $o,Y: option3562590408128118217it_nat] :
% 6.92/7.16 ( ( ( X = none_P6779099274072355161it_nat )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ( ( Y = none_P2651198173097904984it_nat )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ! [A3: produc7388388658123137530it_nat,B3: produc3260487557148687353it_nat] :
% 6.92/7.16 ( ( X
% 6.92/7.16 = ( some_P2818173045054083285it_nat @ A3 ) )
% 6.92/7.16 => ( ( Y
% 6.92/7.16 = ( some_P7913643980934408916it_nat @ B3 ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_cases
% 6.92/7.16 thf(fact_1643_combine__options__cases,axiom,
% 6.92/7.16 ! [X: option4065278094766928714it_nat,P2: option4065278094766928714it_nat > option8956607266484857688it_nat > $o,Y: option8956607266484857688it_nat] :
% 6.92/7.16 ( ( ( X = none_P6779099274072355161it_nat )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ( ( Y = none_P9117596204409417319it_nat )
% 6.92/7.16 => ( P2 @ X @ Y ) )
% 6.92/7.16 => ( ! [A3: produc7388388658123137530it_nat,B3: produc8664842809031399944it_nat] :
% 6.92/7.16 ( ( X
% 6.92/7.16 = ( some_P2818173045054083285it_nat @ A3 ) )
% 6.92/7.16 => ( ( Y
% 6.92/7.16 = ( some_P1914260805536162275it_nat @ B3 ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) )
% 6.92/7.16 => ( P2 @ X @ Y ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_cases
% 6.92/7.16 thf(fact_1644_less__eq__option__None__is__None,axiom,
% 6.92/7.16 ! [X: option_num] :
% 6.92/7.16 ( ( ord_le6622620407824499402on_num @ X @ none_num )
% 6.92/7.16 => ( X = none_num ) ) ).
% 6.92/7.16
% 6.92/7.16 % less_eq_option_None_is_None
% 6.92/7.16 thf(fact_1645_less__eq__option__None,axiom,
% 6.92/7.16 ! [X: option_num] : ( ord_le6622620407824499402on_num @ none_num @ X ) ).
% 6.92/7.16
% 6.92/7.16 % less_eq_option_None
% 6.92/7.16 thf(fact_1646_option_Osimps_I5_J,axiom,
% 6.92/7.16 ! [F1: int,F2: num > int,X2: num] :
% 6.92/7.16 ( ( case_option_int_num @ F1 @ F2 @ ( some_num @ X2 ) )
% 6.92/7.16 = ( F2 @ X2 ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.simps(5)
% 6.92/7.16 thf(fact_1647_option_Osimps_I5_J,axiom,
% 6.92/7.16 ! [F1: option_num,F2: num > option_num,X2: num] :
% 6.92/7.16 ( ( case_o6005452278849405969um_num @ F1 @ F2 @ ( some_num @ X2 ) )
% 6.92/7.16 = ( F2 @ X2 ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.simps(5)
% 6.92/7.16 thf(fact_1648_option_Osimps_I5_J,axiom,
% 6.92/7.16 ! [F1: num,F2: num > num,X2: num] :
% 6.92/7.16 ( ( case_option_num_num @ F1 @ F2 @ ( some_num @ X2 ) )
% 6.92/7.16 = ( F2 @ X2 ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.simps(5)
% 6.92/7.16 thf(fact_1649_the__default_Osimps_I2_J,axiom,
% 6.92/7.16 ! [X: num] :
% 6.92/7.16 ( ( the_default_num @ X @ none_num )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % the_default.simps(2)
% 6.92/7.16 thf(fact_1650_Eps__Opt__eq__Some__implies,axiom,
% 6.92/7.16 ! [P2: produc7388388658123137530it_nat > $o,X: produc7388388658123137530it_nat] :
% 6.92/7.16 ( ( ( eps_Op5869321083069970014it_nat @ P2 )
% 6.92/7.16 = ( some_P2818173045054083285it_nat @ X ) )
% 6.92/7.16 => ( P2 @ X ) ) ).
% 6.92/7.16
% 6.92/7.16 % Eps_Opt_eq_Some_implies
% 6.92/7.16 thf(fact_1651_Eps__Opt__eq__Some__implies,axiom,
% 6.92/7.16 ! [P2: produc3260487557148687353it_nat > $o,X: produc3260487557148687353it_nat] :
% 6.92/7.16 ( ( ( eps_Op1741419982095519837it_nat @ P2 )
% 6.92/7.16 = ( some_P7913643980934408916it_nat @ X ) )
% 6.92/7.16 => ( P2 @ X ) ) ).
% 6.92/7.16
% 6.92/7.16 % Eps_Opt_eq_Some_implies
% 6.92/7.16 thf(fact_1652_Eps__Opt__eq__Some__implies,axiom,
% 6.92/7.16 ! [P2: produc8664842809031399944it_nat > $o,X: produc8664842809031399944it_nat] :
% 6.92/7.16 ( ( ( eps_Op3393321821070424684it_nat @ P2 )
% 6.92/7.16 = ( some_P1914260805536162275it_nat @ X ) )
% 6.92/7.16 => ( P2 @ X ) ) ).
% 6.92/7.16
% 6.92/7.16 % Eps_Opt_eq_Some_implies
% 6.92/7.16 thf(fact_1653_Eps__Opt__eq__Some__implies,axiom,
% 6.92/7.16 ! [P2: num > $o,X: num] :
% 6.92/7.16 ( ( ( eps_Opt_num @ P2 )
% 6.92/7.16 = ( some_num @ X ) )
% 6.92/7.16 => ( P2 @ X ) ) ).
% 6.92/7.16
% 6.92/7.16 % Eps_Opt_eq_Some_implies
% 6.92/7.16 thf(fact_1654_Eps__Opt__eq__Some,axiom,
% 6.92/7.16 ! [P2: produc7388388658123137530it_nat > $o,X: produc7388388658123137530it_nat] :
% 6.92/7.16 ( ! [X9: produc7388388658123137530it_nat] :
% 6.92/7.16 ( ( P2 @ X )
% 6.92/7.16 => ( ( P2 @ X9 )
% 6.92/7.16 => ( X9 = X ) ) )
% 6.92/7.16 => ( ( ( eps_Op5869321083069970014it_nat @ P2 )
% 6.92/7.16 = ( some_P2818173045054083285it_nat @ X ) )
% 6.92/7.16 = ( P2 @ X ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Eps_Opt_eq_Some
% 6.92/7.16 thf(fact_1655_Eps__Opt__eq__Some,axiom,
% 6.92/7.16 ! [P2: produc3260487557148687353it_nat > $o,X: produc3260487557148687353it_nat] :
% 6.92/7.16 ( ! [X9: produc3260487557148687353it_nat] :
% 6.92/7.16 ( ( P2 @ X )
% 6.92/7.16 => ( ( P2 @ X9 )
% 6.92/7.16 => ( X9 = X ) ) )
% 6.92/7.16 => ( ( ( eps_Op1741419982095519837it_nat @ P2 )
% 6.92/7.16 = ( some_P7913643980934408916it_nat @ X ) )
% 6.92/7.16 = ( P2 @ X ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Eps_Opt_eq_Some
% 6.92/7.16 thf(fact_1656_Eps__Opt__eq__Some,axiom,
% 6.92/7.16 ! [P2: produc8664842809031399944it_nat > $o,X: produc8664842809031399944it_nat] :
% 6.92/7.16 ( ! [X9: produc8664842809031399944it_nat] :
% 6.92/7.16 ( ( P2 @ X )
% 6.92/7.16 => ( ( P2 @ X9 )
% 6.92/7.16 => ( X9 = X ) ) )
% 6.92/7.16 => ( ( ( eps_Op3393321821070424684it_nat @ P2 )
% 6.92/7.16 = ( some_P1914260805536162275it_nat @ X ) )
% 6.92/7.16 = ( P2 @ X ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Eps_Opt_eq_Some
% 6.92/7.16 thf(fact_1657_Eps__Opt__eq__Some,axiom,
% 6.92/7.16 ! [P2: num > $o,X: num] :
% 6.92/7.16 ( ! [X9: num] :
% 6.92/7.16 ( ( P2 @ X )
% 6.92/7.16 => ( ( P2 @ X9 )
% 6.92/7.16 => ( X9 = X ) ) )
% 6.92/7.16 => ( ( ( eps_Opt_num @ P2 )
% 6.92/7.16 = ( some_num @ X ) )
% 6.92/7.16 = ( P2 @ X ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Eps_Opt_eq_Some
% 6.92/7.16 thf(fact_1658_execute__bind_I2_J,axiom,
% 6.92/7.16 ! [F: heap_Time_Heap_b,H: heap_e7401611519738050253t_unit,G: b > heap_Time_Heap_b] :
% 6.92/7.16 ( ( ( heap_Time_execute_b @ F @ H )
% 6.92/7.16 = none_P6779099274072355161it_nat )
% 6.92/7.16 => ( ( heap_Time_execute_b @ ( heap_Time_bind_b_b @ F @ G ) @ H )
% 6.92/7.16 = none_P6779099274072355161it_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % execute_bind(2)
% 6.92/7.16 thf(fact_1659_execute__bind_I2_J,axiom,
% 6.92/7.16 ! [F: heap_Time_Heap_b,H: heap_e7401611519738050253t_unit,G: b > heap_Time_Heap_a] :
% 6.92/7.16 ( ( ( heap_Time_execute_b @ F @ H )
% 6.92/7.16 = none_P6779099274072355161it_nat )
% 6.92/7.16 => ( ( heap_Time_execute_a @ ( heap_Time_bind_b_a @ F @ G ) @ H )
% 6.92/7.16 = none_P2651198173097904984it_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % execute_bind(2)
% 6.92/7.16 thf(fact_1660_execute__bind_I2_J,axiom,
% 6.92/7.16 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,G: a > heap_Time_Heap_b] :
% 6.92/7.16 ( ( ( heap_Time_execute_a @ F @ H )
% 6.92/7.16 = none_P2651198173097904984it_nat )
% 6.92/7.16 => ( ( heap_Time_execute_b @ ( heap_Time_bind_a_b @ F @ G ) @ H )
% 6.92/7.16 = none_P6779099274072355161it_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % execute_bind(2)
% 6.92/7.16 thf(fact_1661_execute__bind_I2_J,axiom,
% 6.92/7.16 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,G: a > heap_Time_Heap_a] :
% 6.92/7.16 ( ( ( heap_Time_execute_a @ F @ H )
% 6.92/7.16 = none_P2651198173097904984it_nat )
% 6.92/7.16 => ( ( heap_Time_execute_a @ ( heap_Time_bind_a_a @ F @ G ) @ H )
% 6.92/7.16 = none_P2651198173097904984it_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % execute_bind(2)
% 6.92/7.16 thf(fact_1662_success__def,axiom,
% 6.92/7.16 ( heap_Time_success_b
% 6.92/7.16 = ( ^ [F3: heap_Time_Heap_b,H6: heap_e7401611519738050253t_unit] :
% 6.92/7.16 ( ( heap_Time_execute_b @ F3 @ H6 )
% 6.92/7.16 != none_P6779099274072355161it_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % success_def
% 6.92/7.16 thf(fact_1663_success__def,axiom,
% 6.92/7.16 ( heap_Time_success_a
% 6.92/7.16 = ( ^ [F3: heap_Time_Heap_a,H6: heap_e7401611519738050253t_unit] :
% 6.92/7.16 ( ( heap_Time_execute_a @ F3 @ H6 )
% 6.92/7.16 != none_P2651198173097904984it_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % success_def
% 6.92/7.16 thf(fact_1664_successI,axiom,
% 6.92/7.16 ! [F: heap_Time_Heap_b,H: heap_e7401611519738050253t_unit] :
% 6.92/7.16 ( ( ( heap_Time_execute_b @ F @ H )
% 6.92/7.16 != none_P6779099274072355161it_nat )
% 6.92/7.16 => ( heap_Time_success_b @ F @ H ) ) ).
% 6.92/7.16
% 6.92/7.16 % successI
% 6.92/7.16 thf(fact_1665_successI,axiom,
% 6.92/7.16 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit] :
% 6.92/7.16 ( ( ( heap_Time_execute_a @ F @ H )
% 6.92/7.16 != none_P2651198173097904984it_nat )
% 6.92/7.16 => ( heap_Time_success_a @ F @ H ) ) ).
% 6.92/7.16
% 6.92/7.16 % successI
% 6.92/7.16 thf(fact_1666_less__option__None__is__Some,axiom,
% 6.92/7.16 ! [X: option_num] :
% 6.92/7.16 ( ( ord_less_option_num @ none_num @ X )
% 6.92/7.16 => ? [Z2: num] :
% 6.92/7.16 ( X
% 6.92/7.16 = ( some_num @ Z2 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % less_option_None_is_Some
% 6.92/7.16 thf(fact_1667_less__option__None__Some,axiom,
% 6.92/7.16 ! [X: num] : ( ord_less_option_num @ none_num @ ( some_num @ X ) ) ).
% 6.92/7.16
% 6.92/7.16 % less_option_None_Some
% 6.92/7.16 thf(fact_1668_subrelI,axiom,
% 6.92/7.16 ! [R2: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 6.92/7.16 ( ! [X3: int,Y3: int] :
% 6.92/7.16 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ R2 )
% 6.92/7.16 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ S2 ) )
% 6.92/7.16 => ( ord_le2843351958646193337nt_int @ R2 @ S2 ) ) ).
% 6.92/7.16
% 6.92/7.16 % subrelI
% 6.92/7.16 thf(fact_1669_subrelI,axiom,
% 6.92/7.16 ! [R2: set_Pr3286484037609594932et_nat,S2: set_Pr3286484037609594932et_nat] :
% 6.92/7.16 ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] :
% 6.92/7.16 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R2 )
% 6.92/7.16 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S2 ) )
% 6.92/7.16 => ( ord_le5966269811547037844et_nat @ R2 @ S2 ) ) ).
% 6.92/7.16
% 6.92/7.16 % subrelI
% 6.92/7.16 thf(fact_1670_subrelI,axiom,
% 6.92/7.16 ! [R2: set_Pr8536935166611901872et_nat,S2: set_Pr8536935166611901872et_nat] :
% 6.92/7.16 ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] :
% 6.92/7.16 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R2 )
% 6.92/7.16 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S2 ) )
% 6.92/7.16 => ( ord_le4763372923235995152et_nat @ R2 @ S2 ) ) ).
% 6.92/7.16
% 6.92/7.16 % subrelI
% 6.92/7.16 thf(fact_1671_subrelI,axiom,
% 6.92/7.16 ! [R2: set_Pr7600907837789447088it_nat,S2: set_Pr7600907837789447088it_nat] :
% 6.92/7.16 ( ! [X3: b,Y3: produc6653097349344004940it_nat] :
% 6.92/7.16 ( ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X3 @ Y3 ) @ R2 )
% 6.92/7.16 => ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X3 @ Y3 ) @ S2 ) )
% 6.92/7.16 => ( ord_le4980869671742669840it_nat @ R2 @ S2 ) ) ).
% 6.92/7.16
% 6.92/7.16 % subrelI
% 6.92/7.16 thf(fact_1672_subrelI,axiom,
% 6.92/7.16 ! [R2: set_Pr7098220151150636591it_nat,S2: set_Pr7098220151150636591it_nat] :
% 6.92/7.16 ( ! [X3: a,Y3: produc6653097349344004940it_nat] :
% 6.92/7.16 ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X3 @ Y3 ) @ R2 )
% 6.92/7.16 => ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X3 @ Y3 ) @ S2 ) )
% 6.92/7.16 => ( ord_le4478181985103859343it_nat @ R2 @ S2 ) ) ).
% 6.92/7.16
% 6.92/7.16 % subrelI
% 6.92/7.16 thf(fact_1673_Heap__cases,axiom,
% 6.92/7.16 ! [F: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 6.92/7.16 ( ! [X3: product_unit,H4: produc6653097349344004940it_nat] :
% 6.92/7.16 ( ( heap_T875086893843062177t_unit @ F @ H )
% 6.92/7.16 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X3 @ H4 ) ) )
% 6.92/7.16 => ( ( heap_T875086893843062177t_unit @ F @ H )
% 6.92/7.16 = none_P9117596204409417319it_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % Heap_cases
% 6.92/7.16 thf(fact_1674_Heap__cases,axiom,
% 6.92/7.16 ! [F: heap_Time_Heap_b,H: heap_e7401611519738050253t_unit] :
% 6.92/7.16 ( ! [X3: b,H4: produc6653097349344004940it_nat] :
% 6.92/7.16 ( ( heap_Time_execute_b @ F @ H )
% 6.92/7.16 != ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ X3 @ H4 ) ) )
% 6.92/7.16 => ( ( heap_Time_execute_b @ F @ H )
% 6.92/7.16 = none_P6779099274072355161it_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % Heap_cases
% 6.92/7.16 thf(fact_1675_Heap__cases,axiom,
% 6.92/7.16 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit] :
% 6.92/7.16 ( ! [X3: a,H4: produc6653097349344004940it_nat] :
% 6.92/7.16 ( ( heap_Time_execute_a @ F @ H )
% 6.92/7.16 != ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ X3 @ H4 ) ) )
% 6.92/7.16 => ( ( heap_Time_execute_a @ F @ H )
% 6.92/7.16 = none_P2651198173097904984it_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % Heap_cases
% 6.92/7.16 thf(fact_1676_timeFrame_Ocases,axiom,
% 6.92/7.16 ! [X: produc2207270350733924475it_nat] :
% 6.92/7.16 ( ! [N5: nat,R4: b,H2: heap_e7401611519738050253t_unit,N4: nat] :
% 6.92/7.16 ( X
% 6.92/7.16 != ( produc4613957359643799859it_nat @ N5 @ ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ N4 ) ) ) ) )
% 6.92/7.16 => ~ ! [N5: nat] :
% 6.92/7.16 ( X
% 6.92/7.16 != ( produc4613957359643799859it_nat @ N5 @ none_P6779099274072355161it_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % timeFrame.cases
% 6.92/7.16 thf(fact_1677_timeFrame_Ocases,axiom,
% 6.92/7.16 ! [X: produc4453839368661128058it_nat] :
% 6.92/7.16 ( ! [N5: nat,R4: a,H2: heap_e7401611519738050253t_unit,N4: nat] :
% 6.92/7.16 ( X
% 6.92/7.16 != ( produc4111269673004989362it_nat @ N5 @ ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ N4 ) ) ) ) )
% 6.92/7.16 => ~ ! [N5: nat] :
% 6.92/7.16 ( X
% 6.92/7.16 != ( produc4111269673004989362it_nat @ N5 @ none_P2651198173097904984it_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % timeFrame.cases
% 6.92/7.16 thf(fact_1678_timeFrame_Ocases,axiom,
% 6.92/7.16 ! [X: produc3911288613690379145it_nat] :
% 6.92/7.16 ( ! [N5: nat,R4: product_unit,H2: heap_e7401611519738050253t_unit,N4: nat] :
% 6.92/7.16 ( X
% 6.92/7.16 != ( produc638857205735767105it_nat @ N5 @ ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ N4 ) ) ) ) )
% 6.92/7.16 => ~ ! [N5: nat] :
% 6.92/7.16 ( X
% 6.92/7.16 != ( produc638857205735767105it_nat @ N5 @ none_P9117596204409417319it_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % timeFrame.cases
% 6.92/7.16 thf(fact_1679_timeFrame_Opelims,axiom,
% 6.92/7.16 ! [X: nat,Xa: option4065278094766928714it_nat,Y: option4065278094766928714it_nat] :
% 6.92/7.16 ( ( ( heap_T7616092557645711336rame_b @ X @ Xa )
% 6.92/7.16 = Y )
% 6.92/7.16 => ( ( accp_P4016523247509365636it_nat @ heap_T8132184524487034139_rel_b @ ( produc4613957359643799859it_nat @ X @ Xa ) )
% 6.92/7.16 => ( ! [R4: b,H2: heap_e7401611519738050253t_unit,N4: nat] :
% 6.92/7.16 ( ( Xa
% 6.92/7.16 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ N4 ) ) ) )
% 6.92/7.16 => ( ( Y
% 6.92/7.16 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ ( plus_plus_nat @ X @ N4 ) ) ) ) )
% 6.92/7.16 => ~ ( accp_P4016523247509365636it_nat @ heap_T8132184524487034139_rel_b @ ( produc4613957359643799859it_nat @ X @ ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ N4 ) ) ) ) ) ) )
% 6.92/7.16 => ~ ( ( Xa = none_P6779099274072355161it_nat )
% 6.92/7.16 => ( ( Y = none_P6779099274072355161it_nat )
% 6.92/7.16 => ~ ( accp_P4016523247509365636it_nat @ heap_T8132184524487034139_rel_b @ ( produc4613957359643799859it_nat @ X @ none_P6779099274072355161it_nat ) ) ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % timeFrame.pelims
% 6.92/7.16 thf(fact_1680_timeFrame_Opelims,axiom,
% 6.92/7.16 ! [X: nat,Xa: option3562590408128118217it_nat,Y: option3562590408128118217it_nat] :
% 6.92/7.16 ( ( ( heap_T7616092557645711335rame_a @ X @ Xa )
% 6.92/7.16 = Y )
% 6.92/7.16 => ( ( accp_P6263092265436569219it_nat @ heap_T8132184524487034138_rel_a @ ( produc4111269673004989362it_nat @ X @ Xa ) )
% 6.92/7.16 => ( ! [R4: a,H2: heap_e7401611519738050253t_unit,N4: nat] :
% 6.92/7.16 ( ( Xa
% 6.92/7.16 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ N4 ) ) ) )
% 6.92/7.16 => ( ( Y
% 6.92/7.16 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ ( plus_plus_nat @ X @ N4 ) ) ) ) )
% 6.92/7.16 => ~ ( accp_P6263092265436569219it_nat @ heap_T8132184524487034138_rel_a @ ( produc4111269673004989362it_nat @ X @ ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ N4 ) ) ) ) ) ) )
% 6.92/7.16 => ~ ( ( Xa = none_P2651198173097904984it_nat )
% 6.92/7.16 => ( ( Y = none_P2651198173097904984it_nat )
% 6.92/7.16 => ~ ( accp_P6263092265436569219it_nat @ heap_T8132184524487034138_rel_a @ ( produc4111269673004989362it_nat @ X @ none_P2651198173097904984it_nat ) ) ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % timeFrame.pelims
% 6.92/7.16 thf(fact_1681_timeFrame_Opelims,axiom,
% 6.92/7.16 ! [X: nat,Xa: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
% 6.92/7.16 ( ( ( heap_T3616969660504097270t_unit @ X @ Xa )
% 6.92/7.16 = Y )
% 6.92/7.16 => ( ( accp_P414730952086964626it_nat @ heap_T996182799752388649t_unit @ ( produc638857205735767105it_nat @ X @ Xa ) )
% 6.92/7.16 => ( ! [R4: product_unit,H2: heap_e7401611519738050253t_unit,N4: nat] :
% 6.92/7.16 ( ( Xa
% 6.92/7.16 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ N4 ) ) ) )
% 6.92/7.16 => ( ( Y
% 6.92/7.16 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ ( plus_plus_nat @ X @ N4 ) ) ) ) )
% 6.92/7.16 => ~ ( accp_P414730952086964626it_nat @ heap_T996182799752388649t_unit @ ( produc638857205735767105it_nat @ X @ ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R4 @ ( produc584006145561248582it_nat @ H2 @ N4 ) ) ) ) ) ) )
% 6.92/7.16 => ~ ( ( Xa = none_P9117596204409417319it_nat )
% 6.92/7.16 => ( ( Y = none_P9117596204409417319it_nat )
% 6.92/7.16 => ~ ( accp_P414730952086964626it_nat @ heap_T996182799752388649t_unit @ ( produc638857205735767105it_nat @ X @ none_P9117596204409417319it_nat ) ) ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % timeFrame.pelims
% 6.92/7.16 thf(fact_1682_disjE__realizer2,axiom,
% 6.92/7.16 ! [P2: $o,Q2: num > $o,X: option_num,R3: int > $o,F: int,G: num > int] :
% 6.92/7.16 ( ( case_option_o_num @ P2 @ Q2 @ X )
% 6.92/7.16 => ( ( P2
% 6.92/7.16 => ( R3 @ F ) )
% 6.92/7.16 => ( ! [Q5: num] :
% 6.92/7.16 ( ( Q2 @ Q5 )
% 6.92/7.16 => ( R3 @ ( G @ Q5 ) ) )
% 6.92/7.16 => ( R3 @ ( case_option_int_num @ F @ G @ X ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % disjE_realizer2
% 6.92/7.16 thf(fact_1683_disjE__realizer2,axiom,
% 6.92/7.16 ! [P2: $o,Q2: num > $o,X: option_num,R3: option_num > $o,F: option_num,G: num > option_num] :
% 6.92/7.16 ( ( case_option_o_num @ P2 @ Q2 @ X )
% 6.92/7.16 => ( ( P2
% 6.92/7.16 => ( R3 @ F ) )
% 6.92/7.16 => ( ! [Q5: num] :
% 6.92/7.16 ( ( Q2 @ Q5 )
% 6.92/7.16 => ( R3 @ ( G @ Q5 ) ) )
% 6.92/7.16 => ( R3 @ ( case_o6005452278849405969um_num @ F @ G @ X ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % disjE_realizer2
% 6.92/7.16 thf(fact_1684_disjE__realizer2,axiom,
% 6.92/7.16 ! [P2: $o,Q2: num > $o,X: option_num,R3: num > $o,F: num,G: num > num] :
% 6.92/7.16 ( ( case_option_o_num @ P2 @ Q2 @ X )
% 6.92/7.16 => ( ( P2
% 6.92/7.16 => ( R3 @ F ) )
% 6.92/7.16 => ( ! [Q5: num] :
% 6.92/7.16 ( ( Q2 @ Q5 )
% 6.92/7.16 => ( R3 @ ( G @ Q5 ) ) )
% 6.92/7.16 => ( R3 @ ( case_option_num_num @ F @ G @ X ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % disjE_realizer2
% 6.92/7.16 thf(fact_1685_set__to__map__def,axiom,
% 6.92/7.16 ( set_to_map_int_int
% 6.92/7.16 = ( ^ [S4: set_Pr958786334691620121nt_int,K3: int] :
% 6.92/7.16 ( eps_Opt_int
% 6.92/7.16 @ ^ [V2: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ K3 @ V2 ) @ S4 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % set_to_map_def
% 6.92/7.16 thf(fact_1686_set__to__map__def,axiom,
% 6.92/7.16 ( set_to6040779677306527128et_nat
% 6.92/7.16 = ( ^ [S4: set_Pr3286484037609594932et_nat,K3: produc3658429121746597890et_nat > $o] :
% 6.92/7.16 ( eps_Op2013419657081471078et_nat
% 6.92/7.16 @ ^ [V2: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ K3 @ V2 ) @ S4 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % set_to_map_def
% 6.92/7.16 thf(fact_1687_set__to__map__def,axiom,
% 6.92/7.16 ( set_to2047380710992656148et_nat
% 6.92/7.16 = ( ^ [S4: set_Pr8536935166611901872et_nat,K3: produc3658429121746597890et_nat > $o] :
% 6.92/7.16 ( eps_Op6423059015816587746et_nat
% 6.92/7.16 @ ^ [V2: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ K3 @ V2 ) @ S4 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % set_to_map_def
% 6.92/7.16 thf(fact_1688_set__to__map__def,axiom,
% 6.92/7.16 ( set_to6136816377707935252it_nat
% 6.92/7.16 = ( ^ [S4: set_Pr7600907837789447088it_nat,K3: b] :
% 6.92/7.16 ( eps_Op8301357815426737072it_nat
% 6.92/7.16 @ ^ [V2: produc6653097349344004940it_nat] : ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ K3 @ V2 ) @ S4 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % set_to_map_def
% 6.92/7.16 thf(fact_1689_set__to__map__def,axiom,
% 6.92/7.16 ( set_to2008915276733485075it_nat
% 6.92/7.16 = ( ^ [S4: set_Pr7098220151150636591it_nat,K3: a] :
% 6.92/7.16 ( eps_Op8301357815426737072it_nat
% 6.92/7.16 @ ^ [V2: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ K3 @ V2 ) @ S4 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % set_to_map_def
% 6.92/7.16 thf(fact_1690_guard__def,axiom,
% 6.92/7.16 ( heap_Time_guard_b
% 6.92/7.16 = ( ^ [P5: heap_e7401611519738050253t_unit > $o,F3: heap_e7401611519738050253t_unit > produc7388388658123137530it_nat] :
% 6.92/7.16 ( heap_Time_Heap_b2
% 6.92/7.16 @ ^ [H6: heap_e7401611519738050253t_unit] : ( if_opt7386294288321364996it_nat @ ( P5 @ H6 ) @ ( some_P2818173045054083285it_nat @ ( F3 @ H6 ) ) @ none_P6779099274072355161it_nat ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % guard_def
% 6.92/7.16 thf(fact_1691_guard__def,axiom,
% 6.92/7.16 ( heap_Time_guard_a
% 6.92/7.16 = ( ^ [P5: heap_e7401611519738050253t_unit > $o,F3: heap_e7401611519738050253t_unit > produc3260487557148687353it_nat] :
% 6.92/7.16 ( heap_Time_Heap_a2
% 6.92/7.16 @ ^ [H6: heap_e7401611519738050253t_unit] : ( if_opt6883606601682554499it_nat @ ( P5 @ H6 ) @ ( some_P7913643980934408916it_nat @ ( F3 @ H6 ) ) @ none_P2651198173097904984it_nat ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % guard_def
% 6.92/7.16 thf(fact_1692_guard__def,axiom,
% 6.92/7.16 ( heap_T8440541562793052209t_unit
% 6.92/7.16 = ( ^ [P5: heap_e7401611519738050253t_unit > $o,F3: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] :
% 6.92/7.16 ( heap_T6183433275982383450t_unit
% 6.92/7.16 @ ^ [H6: heap_e7401611519738050253t_unit] : ( if_opt1729522071442692626it_nat @ ( P5 @ H6 ) @ ( some_P1914260805536162275it_nat @ ( F3 @ H6 ) ) @ none_P9117596204409417319it_nat ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % guard_def
% 6.92/7.16 thf(fact_1693_Heap_Oinject,axiom,
% 6.92/7.16 ! [X: heap_e7401611519738050253t_unit > option8956607266484857688it_nat,Ya: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 6.92/7.16 ( ( ( heap_T6183433275982383450t_unit @ X )
% 6.92/7.16 = ( heap_T6183433275982383450t_unit @ Ya ) )
% 6.92/7.16 = ( X = Ya ) ) ).
% 6.92/7.16
% 6.92/7.16 % Heap.inject
% 6.92/7.16 thf(fact_1694_Heap__execute,axiom,
% 6.92/7.16 ! [F: heap_Time_Heap_b] :
% 6.92/7.16 ( ( heap_Time_Heap_b2 @ ( heap_Time_execute_b @ F ) )
% 6.92/7.16 = F ) ).
% 6.92/7.16
% 6.92/7.16 % Heap_execute
% 6.92/7.16 thf(fact_1695_Heap__execute,axiom,
% 6.92/7.16 ! [F: heap_Time_Heap_a] :
% 6.92/7.16 ( ( heap_Time_Heap_a2 @ ( heap_Time_execute_a @ F ) )
% 6.92/7.16 = F ) ).
% 6.92/7.16
% 6.92/7.16 % Heap_execute
% 6.92/7.16 thf(fact_1696_Heap__execute,axiom,
% 6.92/7.16 ! [F: heap_T5738788834812785303t_unit] :
% 6.92/7.16 ( ( heap_T6183433275982383450t_unit @ ( heap_T875086893843062177t_unit @ F ) )
% 6.92/7.16 = F ) ).
% 6.92/7.16
% 6.92/7.16 % Heap_execute
% 6.92/7.16 thf(fact_1697_Heap_Oexhaust,axiom,
% 6.92/7.16 ! [Y: heap_T5738788834812785303t_unit] :
% 6.92/7.16 ~ ! [X3: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 6.92/7.16 ( Y
% 6.92/7.16 != ( heap_T6183433275982383450t_unit @ X3 ) ) ).
% 6.92/7.16
% 6.92/7.16 % Heap.exhaust
% 6.92/7.16 thf(fact_1698_execute_Osimps,axiom,
% 6.92/7.16 ! [F: heap_e7401611519738050253t_unit > option4065278094766928714it_nat] :
% 6.92/7.16 ( ( heap_Time_execute_b @ ( heap_Time_Heap_b2 @ F ) )
% 6.92/7.16 = F ) ).
% 6.92/7.16
% 6.92/7.16 % execute.simps
% 6.92/7.16 thf(fact_1699_execute_Osimps,axiom,
% 6.92/7.16 ! [F: heap_e7401611519738050253t_unit > option3562590408128118217it_nat] :
% 6.92/7.16 ( ( heap_Time_execute_a @ ( heap_Time_Heap_a2 @ F ) )
% 6.92/7.16 = F ) ).
% 6.92/7.16
% 6.92/7.16 % execute.simps
% 6.92/7.16 thf(fact_1700_execute_Osimps,axiom,
% 6.92/7.16 ! [F: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 6.92/7.16 ( ( heap_T875086893843062177t_unit @ ( heap_T6183433275982383450t_unit @ F ) )
% 6.92/7.16 = F ) ).
% 6.92/7.16
% 6.92/7.16 % execute.simps
% 6.92/7.16 thf(fact_1701_option_Odisc__eq__case_I2_J,axiom,
% 6.92/7.16 ! [Option: option_num] :
% 6.92/7.16 ( ( Option != none_num )
% 6.92/7.16 = ( case_option_o_num @ $false
% 6.92/7.16 @ ^ [Uu2: num] : $true
% 6.92/7.16 @ Option ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.disc_eq_case(2)
% 6.92/7.16 thf(fact_1702_option_Odisc__eq__case_I1_J,axiom,
% 6.92/7.16 ! [Option: option_num] :
% 6.92/7.16 ( ( Option = none_num )
% 6.92/7.16 = ( case_option_o_num @ $true
% 6.92/7.16 @ ^ [Uu2: num] : $false
% 6.92/7.16 @ Option ) ) ).
% 6.92/7.16
% 6.92/7.16 % option.disc_eq_case(1)
% 6.92/7.16 thf(fact_1703_case__optionE,axiom,
% 6.92/7.16 ! [P2: $o,Q2: produc7388388658123137530it_nat > $o,X: option4065278094766928714it_nat] :
% 6.92/7.16 ( ( case_o7395119307266030407it_nat @ P2 @ Q2 @ X )
% 6.92/7.16 => ( ( ( X = none_P6779099274072355161it_nat )
% 6.92/7.16 => ~ P2 )
% 6.92/7.16 => ~ ! [Y3: produc7388388658123137530it_nat] :
% 6.92/7.16 ( ( X
% 6.92/7.16 = ( some_P2818173045054083285it_nat @ Y3 ) )
% 6.92/7.16 => ~ ( Q2 @ Y3 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % case_optionE
% 6.92/7.16 thf(fact_1704_case__optionE,axiom,
% 6.92/7.16 ! [P2: $o,Q2: produc3260487557148687353it_nat > $o,X: option3562590408128118217it_nat] :
% 6.92/7.16 ( ( case_o3267218206291580230it_nat @ P2 @ Q2 @ X )
% 6.92/7.16 => ( ( ( X = none_P2651198173097904984it_nat )
% 6.92/7.16 => ~ P2 )
% 6.92/7.16 => ~ ! [Y3: produc3260487557148687353it_nat] :
% 6.92/7.16 ( ( X
% 6.92/7.16 = ( some_P7913643980934408916it_nat @ Y3 ) )
% 6.92/7.16 => ~ ( Q2 @ Y3 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % case_optionE
% 6.92/7.16 thf(fact_1705_case__optionE,axiom,
% 6.92/7.16 ! [P2: $o,Q2: produc8664842809031399944it_nat > $o,X: option8956607266484857688it_nat] :
% 6.92/7.16 ( ( case_o2686588417244861013it_nat @ P2 @ Q2 @ X )
% 6.92/7.16 => ( ( ( X = none_P9117596204409417319it_nat )
% 6.92/7.16 => ~ P2 )
% 6.92/7.16 => ~ ! [Y3: produc8664842809031399944it_nat] :
% 6.92/7.16 ( ( X
% 6.92/7.16 = ( some_P1914260805536162275it_nat @ Y3 ) )
% 6.92/7.16 => ~ ( Q2 @ Y3 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % case_optionE
% 6.92/7.16 thf(fact_1706_case__optionE,axiom,
% 6.92/7.16 ! [P2: $o,Q2: num > $o,X: option_num] :
% 6.92/7.16 ( ( case_option_o_num @ P2 @ Q2 @ X )
% 6.92/7.16 => ( ( ( X = none_num )
% 6.92/7.16 => ~ P2 )
% 6.92/7.16 => ~ ! [Y3: num] :
% 6.92/7.16 ( ( X
% 6.92/7.16 = ( some_num @ Y3 ) )
% 6.92/7.16 => ~ ( Q2 @ Y3 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % case_optionE
% 6.92/7.16 thf(fact_1707_boolean__algebra__cancel_Osup2,axiom,
% 6.92/7.16 ! [B5: set_Pr8551490117392284871at_nat,K2: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 6.92/7.16 ( ( B5
% 6.92/7.16 = ( sup_su3035147773818789531at_nat @ K2 @ B ) )
% 6.92/7.16 => ( ( sup_su3035147773818789531at_nat @ A @ B5 )
% 6.92/7.16 = ( sup_su3035147773818789531at_nat @ K2 @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra_cancel.sup2
% 6.92/7.16 thf(fact_1708_boolean__algebra__cancel_Osup2,axiom,
% 6.92/7.16 ! [B5: set_Pr4329608150637261639at_nat,K2: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 6.92/7.16 ( ( B5
% 6.92/7.16 = ( sup_su5525570899277871387at_nat @ K2 @ B ) )
% 6.92/7.16 => ( ( sup_su5525570899277871387at_nat @ A @ B5 )
% 6.92/7.16 = ( sup_su5525570899277871387at_nat @ K2 @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra_cancel.sup2
% 6.92/7.16 thf(fact_1709_boolean__algebra__cancel_Osup2,axiom,
% 6.92/7.16 ! [B5: set_nat,K2: set_nat,B: set_nat,A: set_nat] :
% 6.92/7.16 ( ( B5
% 6.92/7.16 = ( sup_sup_set_nat @ K2 @ B ) )
% 6.92/7.16 => ( ( sup_sup_set_nat @ A @ B5 )
% 6.92/7.16 = ( sup_sup_set_nat @ K2 @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra_cancel.sup2
% 6.92/7.16 thf(fact_1710_boolean__algebra__cancel_Osup2,axiom,
% 6.92/7.16 ! [B5: nat,K2: nat,B: nat,A: nat] :
% 6.92/7.16 ( ( B5
% 6.92/7.16 = ( sup_sup_nat @ K2 @ B ) )
% 6.92/7.16 => ( ( sup_sup_nat @ A @ B5 )
% 6.92/7.16 = ( sup_sup_nat @ K2 @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra_cancel.sup2
% 6.92/7.16 thf(fact_1711_boolean__algebra__cancel_Osup2,axiom,
% 6.92/7.16 ! [B5: int,K2: int,B: int,A: int] :
% 6.92/7.16 ( ( B5
% 6.92/7.16 = ( sup_sup_int @ K2 @ B ) )
% 6.92/7.16 => ( ( sup_sup_int @ A @ B5 )
% 6.92/7.16 = ( sup_sup_int @ K2 @ ( sup_sup_int @ A @ B ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra_cancel.sup2
% 6.92/7.16 thf(fact_1712_boolean__algebra__cancel_Osup1,axiom,
% 6.92/7.16 ! [A4: set_Pr8551490117392284871at_nat,K2: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 6.92/7.16 ( ( A4
% 6.92/7.16 = ( sup_su3035147773818789531at_nat @ K2 @ A ) )
% 6.92/7.16 => ( ( sup_su3035147773818789531at_nat @ A4 @ B )
% 6.92/7.16 = ( sup_su3035147773818789531at_nat @ K2 @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra_cancel.sup1
% 6.92/7.16 thf(fact_1713_boolean__algebra__cancel_Osup1,axiom,
% 6.92/7.16 ! [A4: set_Pr4329608150637261639at_nat,K2: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 6.92/7.16 ( ( A4
% 6.92/7.16 = ( sup_su5525570899277871387at_nat @ K2 @ A ) )
% 6.92/7.16 => ( ( sup_su5525570899277871387at_nat @ A4 @ B )
% 6.92/7.16 = ( sup_su5525570899277871387at_nat @ K2 @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra_cancel.sup1
% 6.92/7.16 thf(fact_1714_boolean__algebra__cancel_Osup1,axiom,
% 6.92/7.16 ! [A4: set_nat,K2: set_nat,A: set_nat,B: set_nat] :
% 6.92/7.16 ( ( A4
% 6.92/7.16 = ( sup_sup_set_nat @ K2 @ A ) )
% 6.92/7.16 => ( ( sup_sup_set_nat @ A4 @ B )
% 6.92/7.16 = ( sup_sup_set_nat @ K2 @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra_cancel.sup1
% 6.92/7.16 thf(fact_1715_boolean__algebra__cancel_Osup1,axiom,
% 6.92/7.16 ! [A4: nat,K2: nat,A: nat,B: nat] :
% 6.92/7.16 ( ( A4
% 6.92/7.16 = ( sup_sup_nat @ K2 @ A ) )
% 6.92/7.16 => ( ( sup_sup_nat @ A4 @ B )
% 6.92/7.16 = ( sup_sup_nat @ K2 @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra_cancel.sup1
% 6.92/7.16 thf(fact_1716_boolean__algebra__cancel_Osup1,axiom,
% 6.92/7.16 ! [A4: int,K2: int,A: int,B: int] :
% 6.92/7.16 ( ( A4
% 6.92/7.16 = ( sup_sup_int @ K2 @ A ) )
% 6.92/7.16 => ( ( sup_sup_int @ A4 @ B )
% 6.92/7.16 = ( sup_sup_int @ K2 @ ( sup_sup_int @ A @ B ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra_cancel.sup1
% 6.92/7.16 thf(fact_1717_less__eq__option__def,axiom,
% 6.92/7.16 ( ord_le353528952715127954et_int
% 6.92/7.16 = ( ^ [X4: option_set_int,Y4: option_set_int] :
% 6.92/7.16 ( case_o223999843215110191et_int @ $true
% 6.92/7.16 @ ^ [Z: set_int] : ( case_o223999843215110191et_int @ $false @ ( ord_less_eq_set_int @ Z ) @ Y4 )
% 6.92/7.16 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % less_eq_option_def
% 6.92/7.16 thf(fact_1718_less__eq__option__def,axiom,
% 6.92/7.16 ( ord_le2406147912482264968on_rat
% 6.92/7.16 = ( ^ [X4: option_rat,Y4: option_rat] :
% 6.92/7.16 ( case_option_o_rat @ $true
% 6.92/7.16 @ ^ [Z: rat] : ( case_option_o_rat @ $false @ ( ord_less_eq_rat @ Z ) @ Y4 )
% 6.92/7.16 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % less_eq_option_def
% 6.92/7.16 thf(fact_1719_less__eq__option__def,axiom,
% 6.92/7.16 ( ord_le6622620407824499402on_num
% 6.92/7.16 = ( ^ [X4: option_num,Y4: option_num] :
% 6.92/7.16 ( case_option_o_num @ $true
% 6.92/7.16 @ ^ [Z: num] : ( case_option_o_num @ $false @ ( ord_less_eq_num @ Z ) @ Y4 )
% 6.92/7.16 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % less_eq_option_def
% 6.92/7.16 thf(fact_1720_less__eq__option__def,axiom,
% 6.92/7.16 ( ord_le5914376470875661696on_nat
% 6.92/7.16 = ( ^ [X4: option_nat,Y4: option_nat] :
% 6.92/7.16 ( case_option_o_nat @ $true
% 6.92/7.16 @ ^ [Z: nat] : ( case_option_o_nat @ $false @ ( ord_less_eq_nat @ Z ) @ Y4 )
% 6.92/7.16 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % less_eq_option_def
% 6.92/7.16 thf(fact_1721_less__eq__option__def,axiom,
% 6.92/7.16 ( ord_le1736525451366464988on_int
% 6.92/7.16 = ( ^ [X4: option_int,Y4: option_int] :
% 6.92/7.16 ( case_option_o_int @ $true
% 6.92/7.16 @ ^ [Z: int] : ( case_option_o_int @ $false @ ( ord_less_eq_int @ Z ) @ Y4 )
% 6.92/7.16 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % less_eq_option_def
% 6.92/7.16 thf(fact_1722_less__option__def,axiom,
% 6.92/7.16 ( ord_less_option_assn
% 6.92/7.16 = ( ^ [X4: option_assn] :
% 6.92/7.16 ( case_option_o_assn @ $false
% 6.92/7.16 @ ^ [Y4: assn] :
% 6.92/7.16 ( case_option_o_assn @ $true
% 6.92/7.16 @ ^ [Z: assn] : ( ord_less_assn @ Z @ Y4 )
% 6.92/7.16 @ X4 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % less_option_def
% 6.92/7.16 thf(fact_1723_less__option__def,axiom,
% 6.92/7.16 ( ord_less_option_rat
% 6.92/7.16 = ( ^ [X4: option_rat] :
% 6.92/7.16 ( case_option_o_rat @ $false
% 6.92/7.16 @ ^ [Y4: rat] :
% 6.92/7.16 ( case_option_o_rat @ $true
% 6.92/7.16 @ ^ [Z: rat] : ( ord_less_rat @ Z @ Y4 )
% 6.92/7.16 @ X4 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % less_option_def
% 6.92/7.16 thf(fact_1724_less__option__def,axiom,
% 6.92/7.16 ( ord_less_option_num
% 6.92/7.16 = ( ^ [X4: option_num] :
% 6.92/7.16 ( case_option_o_num @ $false
% 6.92/7.16 @ ^ [Y4: num] :
% 6.92/7.16 ( case_option_o_num @ $true
% 6.92/7.16 @ ^ [Z: num] : ( ord_less_num @ Z @ Y4 )
% 6.92/7.16 @ X4 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % less_option_def
% 6.92/7.16 thf(fact_1725_less__option__def,axiom,
% 6.92/7.16 ( ord_less_option_nat
% 6.92/7.16 = ( ^ [X4: option_nat] :
% 6.92/7.16 ( case_option_o_nat @ $false
% 6.92/7.16 @ ^ [Y4: nat] :
% 6.92/7.16 ( case_option_o_nat @ $true
% 6.92/7.16 @ ^ [Z: nat] : ( ord_less_nat @ Z @ Y4 )
% 6.92/7.16 @ X4 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % less_option_def
% 6.92/7.16 thf(fact_1726_less__option__def,axiom,
% 6.92/7.16 ( ord_less_option_int
% 6.92/7.16 = ( ^ [X4: option_int] :
% 6.92/7.16 ( case_option_o_int @ $false
% 6.92/7.16 @ ^ [Y4: int] :
% 6.92/7.16 ( case_option_o_int @ $true
% 6.92/7.16 @ ^ [Z: int] : ( ord_less_int @ Z @ Y4 )
% 6.92/7.16 @ X4 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % less_option_def
% 6.92/7.16 thf(fact_1727_raise__def,axiom,
% 6.92/7.16 ( heap_T2927564422264180874t_unit
% 6.92/7.16 = ( ^ [S5: list_char] :
% 6.92/7.16 ( heap_T6183433275982383450t_unit
% 6.92/7.16 @ ^ [Uu2: heap_e7401611519738050253t_unit] : none_P9117596204409417319it_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % raise_def
% 6.92/7.16 thf(fact_1728_accp__subset,axiom,
% 6.92/7.16 ! [R1: product_prod_num_num > product_prod_num_num > $o,R22: product_prod_num_num > product_prod_num_num > $o] :
% 6.92/7.16 ( ( ord_le2556027599737686990_num_o @ R1 @ R22 )
% 6.92/7.16 => ( ord_le2239182809043710856_num_o @ ( accp_P3113834385874906142um_num @ R22 ) @ ( accp_P3113834385874906142um_num @ R1 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % accp_subset
% 6.92/7.16 thf(fact_1729_accp__subset,axiom,
% 6.92/7.16 ! [R1: product_prod_nat_nat > product_prod_nat_nat > $o,R22: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 6.92/7.16 ( ( ord_le5604493270027003598_nat_o @ R1 @ R22 )
% 6.92/7.16 => ( ord_le704812498762024988_nat_o @ ( accp_P4275260045618599050at_nat @ R22 ) @ ( accp_P4275260045618599050at_nat @ R1 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % accp_subset
% 6.92/7.16 thf(fact_1730_accp__subset,axiom,
% 6.92/7.16 ! [R1: product_prod_int_int > product_prod_int_int > $o,R22: product_prod_int_int > product_prod_int_int > $o] :
% 6.92/7.16 ( ( ord_le1598226405681992910_int_o @ R1 @ R22 )
% 6.92/7.16 => ( ord_le8369615600986905444_int_o @ ( accp_P1096762738010456898nt_int @ R22 ) @ ( accp_P1096762738010456898nt_int @ R1 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % accp_subset
% 6.92/7.16 thf(fact_1731_accp__subset,axiom,
% 6.92/7.16 ! [R1: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,R22: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o] :
% 6.92/7.16 ( ( ord_le7226304311989208114_nat_o @ R1 @ R22 )
% 6.92/7.16 => ( ord_le1658592502415435381_nat_o @ ( accp_P1862375125659990705et_nat @ R22 ) @ ( accp_P1862375125659990705et_nat @ R1 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % accp_subset
% 6.92/7.16 thf(fact_1732_accp__subset,axiom,
% 6.92/7.16 ! [R1: nat > nat > $o,R22: nat > nat > $o] :
% 6.92/7.16 ( ( ord_le2646555220125990790_nat_o @ R1 @ R22 )
% 6.92/7.16 => ( ord_less_eq_nat_o @ ( accp_nat @ R22 ) @ ( accp_nat @ R1 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % accp_subset
% 6.92/7.16 thf(fact_1733_accp__subset__induct,axiom,
% 6.92/7.16 ! [D4: product_prod_num_num > $o,R3: product_prod_num_num > product_prod_num_num > $o,X: product_prod_num_num,P2: product_prod_num_num > $o] :
% 6.92/7.16 ( ( ord_le2239182809043710856_num_o @ D4 @ ( accp_P3113834385874906142um_num @ R3 ) )
% 6.92/7.16 => ( ! [X3: product_prod_num_num,Z2: product_prod_num_num] :
% 6.92/7.16 ( ( D4 @ X3 )
% 6.92/7.16 => ( ( R3 @ Z2 @ X3 )
% 6.92/7.16 => ( D4 @ Z2 ) ) )
% 6.92/7.16 => ( ( D4 @ X )
% 6.92/7.16 => ( ! [X3: product_prod_num_num] :
% 6.92/7.16 ( ( D4 @ X3 )
% 6.92/7.16 => ( ! [Z6: product_prod_num_num] :
% 6.92/7.16 ( ( R3 @ Z6 @ X3 )
% 6.92/7.16 => ( P2 @ Z6 ) )
% 6.92/7.16 => ( P2 @ X3 ) ) )
% 6.92/7.16 => ( P2 @ X ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % accp_subset_induct
% 6.92/7.16 thf(fact_1734_accp__subset__induct,axiom,
% 6.92/7.16 ! [D4: product_prod_nat_nat > $o,R3: product_prod_nat_nat > product_prod_nat_nat > $o,X: product_prod_nat_nat,P2: product_prod_nat_nat > $o] :
% 6.92/7.16 ( ( ord_le704812498762024988_nat_o @ D4 @ ( accp_P4275260045618599050at_nat @ R3 ) )
% 6.92/7.16 => ( ! [X3: product_prod_nat_nat,Z2: product_prod_nat_nat] :
% 6.92/7.16 ( ( D4 @ X3 )
% 6.92/7.16 => ( ( R3 @ Z2 @ X3 )
% 6.92/7.16 => ( D4 @ Z2 ) ) )
% 6.92/7.16 => ( ( D4 @ X )
% 6.92/7.16 => ( ! [X3: product_prod_nat_nat] :
% 6.92/7.16 ( ( D4 @ X3 )
% 6.92/7.16 => ( ! [Z6: product_prod_nat_nat] :
% 6.92/7.16 ( ( R3 @ Z6 @ X3 )
% 6.92/7.16 => ( P2 @ Z6 ) )
% 6.92/7.16 => ( P2 @ X3 ) ) )
% 6.92/7.16 => ( P2 @ X ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % accp_subset_induct
% 6.92/7.16 thf(fact_1735_accp__subset__induct,axiom,
% 6.92/7.16 ! [D4: product_prod_int_int > $o,R3: product_prod_int_int > product_prod_int_int > $o,X: product_prod_int_int,P2: product_prod_int_int > $o] :
% 6.92/7.16 ( ( ord_le8369615600986905444_int_o @ D4 @ ( accp_P1096762738010456898nt_int @ R3 ) )
% 6.92/7.16 => ( ! [X3: product_prod_int_int,Z2: product_prod_int_int] :
% 6.92/7.16 ( ( D4 @ X3 )
% 6.92/7.16 => ( ( R3 @ Z2 @ X3 )
% 6.92/7.16 => ( D4 @ Z2 ) ) )
% 6.92/7.16 => ( ( D4 @ X )
% 6.92/7.16 => ( ! [X3: product_prod_int_int] :
% 6.92/7.16 ( ( D4 @ X3 )
% 6.92/7.16 => ( ! [Z6: product_prod_int_int] :
% 6.92/7.16 ( ( R3 @ Z6 @ X3 )
% 6.92/7.16 => ( P2 @ Z6 ) )
% 6.92/7.16 => ( P2 @ X3 ) ) )
% 6.92/7.16 => ( P2 @ X ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % accp_subset_induct
% 6.92/7.16 thf(fact_1736_accp__subset__induct,axiom,
% 6.92/7.16 ! [D4: produc2732055786443039994et_nat > $o,R3: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat,P2: produc2732055786443039994et_nat > $o] :
% 6.92/7.16 ( ( ord_le1658592502415435381_nat_o @ D4 @ ( accp_P1862375125659990705et_nat @ R3 ) )
% 6.92/7.16 => ( ! [X3: produc2732055786443039994et_nat,Z2: produc2732055786443039994et_nat] :
% 6.92/7.16 ( ( D4 @ X3 )
% 6.92/7.16 => ( ( R3 @ Z2 @ X3 )
% 6.92/7.16 => ( D4 @ Z2 ) ) )
% 6.92/7.16 => ( ( D4 @ X )
% 6.92/7.16 => ( ! [X3: produc2732055786443039994et_nat] :
% 6.92/7.16 ( ( D4 @ X3 )
% 6.92/7.16 => ( ! [Z6: produc2732055786443039994et_nat] :
% 6.92/7.16 ( ( R3 @ Z6 @ X3 )
% 6.92/7.16 => ( P2 @ Z6 ) )
% 6.92/7.16 => ( P2 @ X3 ) ) )
% 6.92/7.16 => ( P2 @ X ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % accp_subset_induct
% 6.92/7.16 thf(fact_1737_accp__subset__induct,axiom,
% 6.92/7.16 ! [D4: nat > $o,R3: nat > nat > $o,X: nat,P2: nat > $o] :
% 6.92/7.16 ( ( ord_less_eq_nat_o @ D4 @ ( accp_nat @ R3 ) )
% 6.92/7.16 => ( ! [X3: nat,Z2: nat] :
% 6.92/7.16 ( ( D4 @ X3 )
% 6.92/7.16 => ( ( R3 @ Z2 @ X3 )
% 6.92/7.16 => ( D4 @ Z2 ) ) )
% 6.92/7.16 => ( ( D4 @ X )
% 6.92/7.16 => ( ! [X3: nat] :
% 6.92/7.16 ( ( D4 @ X3 )
% 6.92/7.16 => ( ! [Z6: nat] :
% 6.92/7.16 ( ( R3 @ Z6 @ X3 )
% 6.92/7.16 => ( P2 @ Z6 ) )
% 6.92/7.16 => ( P2 @ X3 ) ) )
% 6.92/7.16 => ( P2 @ X ) ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % accp_subset_induct
% 6.92/7.16 thf(fact_1738_execute__assert_I2_J,axiom,
% 6.92/7.16 ! [P2: b > $o,X: b,H: heap_e7401611519738050253t_unit] :
% 6.92/7.16 ( ~ ( P2 @ X )
% 6.92/7.16 => ( ( heap_Time_execute_b @ ( heap_Time_assert_b @ P2 @ X ) @ H )
% 6.92/7.16 = none_P6779099274072355161it_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % execute_assert(2)
% 6.92/7.16 thf(fact_1739_execute__assert_I2_J,axiom,
% 6.92/7.16 ! [P2: a > $o,X: a,H: heap_e7401611519738050253t_unit] :
% 6.92/7.16 ( ~ ( P2 @ X )
% 6.92/7.16 => ( ( heap_Time_execute_a @ ( heap_Time_assert_a @ P2 @ X ) @ H )
% 6.92/7.16 = none_P2651198173097904984it_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % execute_assert(2)
% 6.92/7.16 thf(fact_1740_mod__h__bot__iff_I7_J,axiom,
% 6.92/7.16 ! [P2: assn,Q2: assn,H: heap_e7401611519738050253t_unit] :
% 6.92/7.16 ( ( rep_assn @ ( sup_sup_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 6.92/7.16 = ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 6.92/7.16 | ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % mod_h_bot_iff(7)
% 6.92/7.16 thf(fact_1741_combine__options__def,axiom,
% 6.92/7.16 ( combin724284867043296059it_nat
% 6.92/7.16 = ( ^ [F3: produc7388388658123137530it_nat > produc7388388658123137530it_nat > produc7388388658123137530it_nat,X4: option4065278094766928714it_nat,Y4: option4065278094766928714it_nat] :
% 6.92/7.16 ( case_o5901184372446974929it_nat @ Y4
% 6.92/7.16 @ ^ [Z: produc7388388658123137530it_nat] :
% 6.92/7.16 ( case_o5901184372446974929it_nat @ ( some_P2818173045054083285it_nat @ Z )
% 6.92/7.16 @ ^ [Aa: produc7388388658123137530it_nat] : ( some_P2818173045054083285it_nat @ ( F3 @ Z @ Aa ) )
% 6.92/7.16 @ Y4 )
% 6.92/7.16 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_def
% 6.92/7.16 thf(fact_1742_combine__options__def,axiom,
% 6.92/7.16 ( combin5819755802923621690it_nat
% 6.92/7.16 = ( ^ [F3: produc3260487557148687353it_nat > produc3260487557148687353it_nat > produc3260487557148687353it_nat,X4: option3562590408128118217it_nat,Y4: option3562590408128118217it_nat] :
% 6.92/7.16 ( case_o6061097939050036047it_nat @ Y4
% 6.92/7.16 @ ^ [Z: produc3260487557148687353it_nat] :
% 6.92/7.16 ( case_o6061097939050036047it_nat @ ( some_P7913643980934408916it_nat @ Z )
% 6.92/7.16 @ ^ [Aa: produc3260487557148687353it_nat] : ( some_P7913643980934408916it_nat @ ( F3 @ Z @ Aa ) )
% 6.92/7.16 @ Y4 )
% 6.92/7.16 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_def
% 6.92/7.16 thf(fact_1743_combine__options__def,axiom,
% 6.92/7.16 ( combin4318129983670048329it_nat
% 6.92/7.16 = ( ^ [F3: produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat,X4: option8956607266484857688it_nat,Y4: option8956607266484857688it_nat] :
% 6.92/7.16 ( case_o2963978774867076333it_nat @ Y4
% 6.92/7.16 @ ^ [Z: produc8664842809031399944it_nat] :
% 6.92/7.16 ( case_o2963978774867076333it_nat @ ( some_P1914260805536162275it_nat @ Z )
% 6.92/7.16 @ ^ [Aa: produc8664842809031399944it_nat] : ( some_P1914260805536162275it_nat @ ( F3 @ Z @ Aa ) )
% 6.92/7.16 @ Y4 )
% 6.92/7.16 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_def
% 6.92/7.16 thf(fact_1744_combine__options__def,axiom,
% 6.92/7.16 ( combine_options_num
% 6.92/7.16 = ( ^ [F3: num > num > num,X4: option_num,Y4: option_num] :
% 6.92/7.16 ( case_o6005452278849405969um_num @ Y4
% 6.92/7.16 @ ^ [Z: num] :
% 6.92/7.16 ( case_o6005452278849405969um_num @ ( some_num @ Z )
% 6.92/7.16 @ ^ [Aa: num] : ( some_num @ ( F3 @ Z @ Aa ) )
% 6.92/7.16 @ Y4 )
% 6.92/7.16 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_def
% 6.92/7.16 thf(fact_1745_reflcl__set__eq,axiom,
% 6.92/7.16 ! [R2: set_Pr8693737435421807431at_nat] :
% 6.92/7.16 ( ( sup_su362511073950362882_nat_o
% 6.92/7.16 @ ^ [X4: product_prod_nat_nat,Y4: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y4 ) @ R2 )
% 6.92/7.16 @ ^ [Y6: product_prod_nat_nat,Z4: product_prod_nat_nat] : ( Y6 = Z4 ) )
% 6.92/7.16 = ( ^ [X4: product_prod_nat_nat,Y4: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y4 ) @ ( sup_su718114333110466843at_nat @ R2 @ id_Pro2258643101195443293at_nat ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % reflcl_set_eq
% 6.92/7.16 thf(fact_1746_reflcl__set__eq,axiom,
% 6.92/7.16 ! [R2: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( sup_sup_nat_nat_o
% 6.92/7.16 @ ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R2 )
% 6.92/7.16 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 6.92/7.16 = ( ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ ( sup_su6327502436637775413at_nat @ R2 @ id_nat2 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % reflcl_set_eq
% 6.92/7.16 thf(fact_1747_reflcl__set__eq,axiom,
% 6.92/7.16 ! [R2: set_Pr958786334691620121nt_int] :
% 6.92/7.16 ( ( sup_sup_int_int_o
% 6.92/7.16 @ ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R2 )
% 6.92/7.16 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 6.92/7.16 = ( ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ ( sup_su6024340866399070445nt_int @ R2 @ id_int2 ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % reflcl_set_eq
% 6.92/7.16 thf(fact_1748_reflcl__set__eq,axiom,
% 6.92/7.16 ! [R2: set_Pr8551490117392284871at_nat] :
% 6.92/7.16 ( ( sup_su2200014604384089602_nat_o
% 6.92/7.16 @ ^ [X4: multis2468970476368604999at_nat,Y4: multis2468970476368604999at_nat] : ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ X4 @ Y4 ) @ R2 )
% 6.92/7.16 @ ^ [Y6: multis2468970476368604999at_nat,Z4: multis2468970476368604999at_nat] : ( Y6 = Z4 ) )
% 6.92/7.16 = ( ^ [X4: multis2468970476368604999at_nat,Y4: multis2468970476368604999at_nat] : ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ X4 @ Y4 ) @ ( sup_su3035147773818789531at_nat @ R2 @ id_mul2649389997224486051at_nat ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % reflcl_set_eq
% 6.92/7.16 thf(fact_1749_reflcl__set__eq,axiom,
% 6.92/7.16 ! [R2: set_Pr4329608150637261639at_nat] :
% 6.92/7.16 ( ( sup_su7519161239522478338_nat_o
% 6.92/7.16 @ ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y4 ) @ R2 )
% 6.92/7.16 @ ^ [Y6: set_Pr1261947904930325089at_nat,Z4: set_Pr1261947904930325089at_nat] : ( Y6 = Z4 ) )
% 6.92/7.16 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y4 ) @ ( sup_su5525570899277871387at_nat @ R2 @ id_set1796276052702428605at_nat ) ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % reflcl_set_eq
% 6.92/7.16 thf(fact_1750_in__measure,axiom,
% 6.92/7.16 ! [X: int,Y: int,F: int > nat] :
% 6.92/7.16 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measure_int @ F ) )
% 6.92/7.16 = ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % in_measure
% 6.92/7.16 thf(fact_1751_wait__bind__decon,axiom,
% 6.92/7.16 ! [P2: assn,M: heap_Time_Heap_a,Q2: a > assn,N2: nat] :
% 6.92/7.16 ( ( hoare_hoare_triple_a @ P2 @ M @ Q2 )
% 6.92/7.16 => ( hoare_hoare_triple_a @ P2
% 6.92/7.16 @ ( heap_T757603679106148408unit_a @ ( heap_Time_wait @ N2 )
% 6.92/7.16 @ ^ [Uu2: product_unit] : M )
% 6.92/7.16 @ Q2 ) ) ).
% 6.92/7.16
% 6.92/7.16 % wait_bind_decon
% 6.92/7.16 thf(fact_1752_wait__bind__decon,axiom,
% 6.92/7.16 ! [P2: assn,M: heap_Time_Heap_b,Q2: b > assn,N2: nat] :
% 6.92/7.16 ( ( hoare_hoare_triple_b @ P2 @ M @ Q2 )
% 6.92/7.16 => ( hoare_hoare_triple_b @ P2
% 6.92/7.16 @ ( heap_T757603679106148409unit_b @ ( heap_Time_wait @ N2 )
% 6.92/7.16 @ ^ [Uu2: product_unit] : M )
% 6.92/7.16 @ Q2 ) ) ).
% 6.92/7.16
% 6.92/7.16 % wait_bind_decon
% 6.92/7.16 thf(fact_1753_wait__bind__decon,axiom,
% 6.92/7.16 ! [P2: assn,M: heap_T5738788834812785303t_unit,Q2: product_unit > assn,N2: nat] :
% 6.92/7.16 ( ( hoare_8945653483474564448t_unit @ P2 @ M @ Q2 )
% 6.92/7.16 => ( hoare_8945653483474564448t_unit @ P2
% 6.92/7.16 @ ( heap_T2633723481742716231t_unit @ ( heap_Time_wait @ N2 )
% 6.92/7.16 @ ^ [Uu2: product_unit] : M )
% 6.92/7.16 @ Q2 ) ) ).
% 6.92/7.16
% 6.92/7.16 % wait_bind_decon
% 6.92/7.16 thf(fact_1754_empty__Collect__eq,axiom,
% 6.92/7.16 ! [P2: list_nat > $o] :
% 6.92/7.16 ( ( bot_bot_set_list_nat
% 6.92/7.16 = ( collect_list_nat @ P2 ) )
% 6.92/7.16 = ( ! [X4: list_nat] :
% 6.92/7.16 ~ ( P2 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % empty_Collect_eq
% 6.92/7.16 thf(fact_1755_empty__Collect__eq,axiom,
% 6.92/7.16 ! [P2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.16 ( ( bot_bo1488462491386950373nt_int
% 6.92/7.16 = ( collec5210948495886036740nt_int @ P2 ) )
% 6.92/7.16 = ( ! [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.16 ~ ( P2 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % empty_Collect_eq
% 6.92/7.16 thf(fact_1756_empty__Collect__eq,axiom,
% 6.92/7.16 ! [P2: set_nat > $o] :
% 6.92/7.16 ( ( bot_bot_set_set_nat
% 6.92/7.16 = ( collect_set_nat @ P2 ) )
% 6.92/7.16 = ( ! [X4: set_nat] :
% 6.92/7.16 ~ ( P2 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % empty_Collect_eq
% 6.92/7.16 thf(fact_1757_empty__Collect__eq,axiom,
% 6.92/7.16 ! [P2: product_prod_nat_nat > $o] :
% 6.92/7.16 ( ( bot_bo2099793752762293965at_nat
% 6.92/7.16 = ( collec3392354462482085612at_nat @ P2 ) )
% 6.92/7.16 = ( ! [X4: product_prod_nat_nat] :
% 6.92/7.16 ~ ( P2 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % empty_Collect_eq
% 6.92/7.16 thf(fact_1758_empty__Collect__eq,axiom,
% 6.92/7.16 ! [P2: $o > $o] :
% 6.92/7.16 ( ( bot_bot_set_o
% 6.92/7.16 = ( collect_o @ P2 ) )
% 6.92/7.16 = ( ! [X4: $o] :
% 6.92/7.16 ~ ( P2 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % empty_Collect_eq
% 6.92/7.16 thf(fact_1759_empty__Collect__eq,axiom,
% 6.92/7.16 ! [P2: nat > $o] :
% 6.92/7.16 ( ( bot_bot_set_nat
% 6.92/7.16 = ( collect_nat @ P2 ) )
% 6.92/7.16 = ( ! [X4: nat] :
% 6.92/7.16 ~ ( P2 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % empty_Collect_eq
% 6.92/7.16 thf(fact_1760_empty__Collect__eq,axiom,
% 6.92/7.16 ! [P2: int > $o] :
% 6.92/7.16 ( ( bot_bot_set_int
% 6.92/7.16 = ( collect_int @ P2 ) )
% 6.92/7.16 = ( ! [X4: int] :
% 6.92/7.16 ~ ( P2 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % empty_Collect_eq
% 6.92/7.16 thf(fact_1761_Collect__empty__eq,axiom,
% 6.92/7.16 ! [P2: list_nat > $o] :
% 6.92/7.16 ( ( ( collect_list_nat @ P2 )
% 6.92/7.16 = bot_bot_set_list_nat )
% 6.92/7.16 = ( ! [X4: list_nat] :
% 6.92/7.16 ~ ( P2 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Collect_empty_eq
% 6.92/7.16 thf(fact_1762_Collect__empty__eq,axiom,
% 6.92/7.16 ! [P2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.16 ( ( ( collec5210948495886036740nt_int @ P2 )
% 6.92/7.16 = bot_bo1488462491386950373nt_int )
% 6.92/7.16 = ( ! [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.16 ~ ( P2 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Collect_empty_eq
% 6.92/7.16 thf(fact_1763_Collect__empty__eq,axiom,
% 6.92/7.16 ! [P2: set_nat > $o] :
% 6.92/7.16 ( ( ( collect_set_nat @ P2 )
% 6.92/7.16 = bot_bot_set_set_nat )
% 6.92/7.16 = ( ! [X4: set_nat] :
% 6.92/7.16 ~ ( P2 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Collect_empty_eq
% 6.92/7.16 thf(fact_1764_Collect__empty__eq,axiom,
% 6.92/7.16 ! [P2: product_prod_nat_nat > $o] :
% 6.92/7.16 ( ( ( collec3392354462482085612at_nat @ P2 )
% 6.92/7.16 = bot_bo2099793752762293965at_nat )
% 6.92/7.16 = ( ! [X4: product_prod_nat_nat] :
% 6.92/7.16 ~ ( P2 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Collect_empty_eq
% 6.92/7.16 thf(fact_1765_Collect__empty__eq,axiom,
% 6.92/7.16 ! [P2: $o > $o] :
% 6.92/7.16 ( ( ( collect_o @ P2 )
% 6.92/7.16 = bot_bot_set_o )
% 6.92/7.16 = ( ! [X4: $o] :
% 6.92/7.16 ~ ( P2 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Collect_empty_eq
% 6.92/7.16 thf(fact_1766_Collect__empty__eq,axiom,
% 6.92/7.16 ! [P2: nat > $o] :
% 6.92/7.16 ( ( ( collect_nat @ P2 )
% 6.92/7.16 = bot_bot_set_nat )
% 6.92/7.16 = ( ! [X4: nat] :
% 6.92/7.16 ~ ( P2 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Collect_empty_eq
% 6.92/7.16 thf(fact_1767_Collect__empty__eq,axiom,
% 6.92/7.16 ! [P2: int > $o] :
% 6.92/7.16 ( ( ( collect_int @ P2 )
% 6.92/7.16 = bot_bot_set_int )
% 6.92/7.16 = ( ! [X4: int] :
% 6.92/7.16 ~ ( P2 @ X4 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Collect_empty_eq
% 6.92/7.16 thf(fact_1768_all__not__in__conv,axiom,
% 6.92/7.16 ! [A4: set_se6260736226359567993nt_int] :
% 6.92/7.16 ( ( ! [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.16 ~ ( member2340774599025711042nt_int @ X4 @ A4 ) )
% 6.92/7.16 = ( A4 = bot_bo1488462491386950373nt_int ) ) ).
% 6.92/7.16
% 6.92/7.16 % all_not_in_conv
% 6.92/7.16 thf(fact_1769_all__not__in__conv,axiom,
% 6.92/7.16 ! [A4: set_set_nat] :
% 6.92/7.16 ( ( ! [X4: set_nat] :
% 6.92/7.16 ~ ( member_set_nat @ X4 @ A4 ) )
% 6.92/7.16 = ( A4 = bot_bot_set_set_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % all_not_in_conv
% 6.92/7.16 thf(fact_1770_all__not__in__conv,axiom,
% 6.92/7.16 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( ! [X4: product_prod_nat_nat] :
% 6.92/7.16 ~ ( member8440522571783428010at_nat @ X4 @ A4 ) )
% 6.92/7.16 = ( A4 = bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % all_not_in_conv
% 6.92/7.16 thf(fact_1771_all__not__in__conv,axiom,
% 6.92/7.16 ! [A4: set_o] :
% 6.92/7.16 ( ( ! [X4: $o] :
% 6.92/7.16 ~ ( member_o @ X4 @ A4 ) )
% 6.92/7.16 = ( A4 = bot_bot_set_o ) ) ).
% 6.92/7.16
% 6.92/7.16 % all_not_in_conv
% 6.92/7.16 thf(fact_1772_all__not__in__conv,axiom,
% 6.92/7.16 ! [A4: set_nat] :
% 6.92/7.16 ( ( ! [X4: nat] :
% 6.92/7.16 ~ ( member_nat @ X4 @ A4 ) )
% 6.92/7.16 = ( A4 = bot_bot_set_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % all_not_in_conv
% 6.92/7.16 thf(fact_1773_all__not__in__conv,axiom,
% 6.92/7.16 ! [A4: set_int] :
% 6.92/7.16 ( ( ! [X4: int] :
% 6.92/7.16 ~ ( member_int @ X4 @ A4 ) )
% 6.92/7.16 = ( A4 = bot_bot_set_int ) ) ).
% 6.92/7.16
% 6.92/7.16 % all_not_in_conv
% 6.92/7.16 thf(fact_1774_empty__iff,axiom,
% 6.92/7.16 ! [C2: set_Pr958786334691620121nt_int] :
% 6.92/7.16 ~ ( member2340774599025711042nt_int @ C2 @ bot_bo1488462491386950373nt_int ) ).
% 6.92/7.16
% 6.92/7.16 % empty_iff
% 6.92/7.16 thf(fact_1775_empty__iff,axiom,
% 6.92/7.16 ! [C2: set_nat] :
% 6.92/7.16 ~ ( member_set_nat @ C2 @ bot_bot_set_set_nat ) ).
% 6.92/7.16
% 6.92/7.16 % empty_iff
% 6.92/7.16 thf(fact_1776_empty__iff,axiom,
% 6.92/7.16 ! [C2: product_prod_nat_nat] :
% 6.92/7.16 ~ ( member8440522571783428010at_nat @ C2 @ bot_bo2099793752762293965at_nat ) ).
% 6.92/7.16
% 6.92/7.16 % empty_iff
% 6.92/7.16 thf(fact_1777_empty__iff,axiom,
% 6.92/7.16 ! [C2: $o] :
% 6.92/7.16 ~ ( member_o @ C2 @ bot_bot_set_o ) ).
% 6.92/7.16
% 6.92/7.16 % empty_iff
% 6.92/7.16 thf(fact_1778_empty__iff,axiom,
% 6.92/7.16 ! [C2: nat] :
% 6.92/7.16 ~ ( member_nat @ C2 @ bot_bot_set_nat ) ).
% 6.92/7.16
% 6.92/7.16 % empty_iff
% 6.92/7.16 thf(fact_1779_empty__iff,axiom,
% 6.92/7.16 ! [C2: int] :
% 6.92/7.16 ~ ( member_int @ C2 @ bot_bot_set_int ) ).
% 6.92/7.16
% 6.92/7.16 % empty_iff
% 6.92/7.16 thf(fact_1780_subset__empty,axiom,
% 6.92/7.16 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( ord_le3146513528884898305at_nat @ A4 @ bot_bo2099793752762293965at_nat )
% 6.92/7.16 = ( A4 = bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % subset_empty
% 6.92/7.16 thf(fact_1781_subset__empty,axiom,
% 6.92/7.16 ! [A4: set_o] :
% 6.92/7.16 ( ( ord_less_eq_set_o @ A4 @ bot_bot_set_o )
% 6.92/7.16 = ( A4 = bot_bot_set_o ) ) ).
% 6.92/7.16
% 6.92/7.16 % subset_empty
% 6.92/7.16 thf(fact_1782_subset__empty,axiom,
% 6.92/7.16 ! [A4: set_nat] :
% 6.92/7.16 ( ( ord_less_eq_set_nat @ A4 @ bot_bot_set_nat )
% 6.92/7.16 = ( A4 = bot_bot_set_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % subset_empty
% 6.92/7.16 thf(fact_1783_subset__empty,axiom,
% 6.92/7.16 ! [A4: set_int] :
% 6.92/7.16 ( ( ord_less_eq_set_int @ A4 @ bot_bot_set_int )
% 6.92/7.16 = ( A4 = bot_bot_set_int ) ) ).
% 6.92/7.16
% 6.92/7.16 % subset_empty
% 6.92/7.16 thf(fact_1784_empty__subsetI,axiom,
% 6.92/7.16 ! [A4: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ bot_bo2099793752762293965at_nat @ A4 ) ).
% 6.92/7.16
% 6.92/7.16 % empty_subsetI
% 6.92/7.16 thf(fact_1785_empty__subsetI,axiom,
% 6.92/7.16 ! [A4: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A4 ) ).
% 6.92/7.16
% 6.92/7.16 % empty_subsetI
% 6.92/7.16 thf(fact_1786_empty__subsetI,axiom,
% 6.92/7.16 ! [A4: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A4 ) ).
% 6.92/7.16
% 6.92/7.16 % empty_subsetI
% 6.92/7.16 thf(fact_1787_empty__subsetI,axiom,
% 6.92/7.16 ! [A4: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A4 ) ).
% 6.92/7.16
% 6.92/7.16 % empty_subsetI
% 6.92/7.16 thf(fact_1788_sup__bot__left,axiom,
% 6.92/7.16 ! [X: set_Pr8551490117392284871at_nat] :
% 6.92/7.16 ( ( sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat @ X )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot_left
% 6.92/7.16 thf(fact_1789_sup__bot__left,axiom,
% 6.92/7.16 ! [X: set_Pr4329608150637261639at_nat] :
% 6.92/7.16 ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ X )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot_left
% 6.92/7.16 thf(fact_1790_sup__bot__left,axiom,
% 6.92/7.16 ! [X: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ X )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot_left
% 6.92/7.16 thf(fact_1791_sup__bot__left,axiom,
% 6.92/7.16 ! [X: set_o] :
% 6.92/7.16 ( ( sup_sup_set_o @ bot_bot_set_o @ X )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot_left
% 6.92/7.16 thf(fact_1792_sup__bot__left,axiom,
% 6.92/7.16 ! [X: set_nat] :
% 6.92/7.16 ( ( sup_sup_set_nat @ bot_bot_set_nat @ X )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot_left
% 6.92/7.16 thf(fact_1793_sup__bot__left,axiom,
% 6.92/7.16 ! [X: set_int] :
% 6.92/7.16 ( ( sup_sup_set_int @ bot_bot_set_int @ X )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot_left
% 6.92/7.16 thf(fact_1794_sup__bot__right,axiom,
% 6.92/7.16 ! [X: set_Pr8551490117392284871at_nat] :
% 6.92/7.16 ( ( sup_su3035147773818789531at_nat @ X @ bot_bo8422036546324065075at_nat )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot_right
% 6.92/7.16 thf(fact_1795_sup__bot__right,axiom,
% 6.92/7.16 ! [X: set_Pr4329608150637261639at_nat] :
% 6.92/7.16 ( ( sup_su5525570899277871387at_nat @ X @ bot_bo228742789529271731at_nat )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot_right
% 6.92/7.16 thf(fact_1796_sup__bot__right,axiom,
% 6.92/7.16 ! [X: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( sup_su6327502436637775413at_nat @ X @ bot_bo2099793752762293965at_nat )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot_right
% 6.92/7.16 thf(fact_1797_sup__bot__right,axiom,
% 6.92/7.16 ! [X: set_o] :
% 6.92/7.16 ( ( sup_sup_set_o @ X @ bot_bot_set_o )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot_right
% 6.92/7.16 thf(fact_1798_sup__bot__right,axiom,
% 6.92/7.16 ! [X: set_nat] :
% 6.92/7.16 ( ( sup_sup_set_nat @ X @ bot_bot_set_nat )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot_right
% 6.92/7.16 thf(fact_1799_sup__bot__right,axiom,
% 6.92/7.16 ! [X: set_int] :
% 6.92/7.16 ( ( sup_sup_set_int @ X @ bot_bot_set_int )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot_right
% 6.92/7.16 thf(fact_1800_bot__eq__sup__iff,axiom,
% 6.92/7.16 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 6.92/7.16 ( ( bot_bo8422036546324065075at_nat
% 6.92/7.16 = ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 6.92/7.16 = ( ( X = bot_bo8422036546324065075at_nat )
% 6.92/7.16 & ( Y = bot_bo8422036546324065075at_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot_eq_sup_iff
% 6.92/7.16 thf(fact_1801_bot__eq__sup__iff,axiom,
% 6.92/7.16 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 6.92/7.16 ( ( bot_bo228742789529271731at_nat
% 6.92/7.16 = ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 6.92/7.16 = ( ( X = bot_bo228742789529271731at_nat )
% 6.92/7.16 & ( Y = bot_bo228742789529271731at_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot_eq_sup_iff
% 6.92/7.16 thf(fact_1802_bot__eq__sup__iff,axiom,
% 6.92/7.16 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( bot_bo2099793752762293965at_nat
% 6.92/7.16 = ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 6.92/7.16 = ( ( X = bot_bo2099793752762293965at_nat )
% 6.92/7.16 & ( Y = bot_bo2099793752762293965at_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot_eq_sup_iff
% 6.92/7.16 thf(fact_1803_bot__eq__sup__iff,axiom,
% 6.92/7.16 ! [X: set_o,Y: set_o] :
% 6.92/7.16 ( ( bot_bot_set_o
% 6.92/7.16 = ( sup_sup_set_o @ X @ Y ) )
% 6.92/7.16 = ( ( X = bot_bot_set_o )
% 6.92/7.16 & ( Y = bot_bot_set_o ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot_eq_sup_iff
% 6.92/7.16 thf(fact_1804_bot__eq__sup__iff,axiom,
% 6.92/7.16 ! [X: set_nat,Y: set_nat] :
% 6.92/7.16 ( ( bot_bot_set_nat
% 6.92/7.16 = ( sup_sup_set_nat @ X @ Y ) )
% 6.92/7.16 = ( ( X = bot_bot_set_nat )
% 6.92/7.16 & ( Y = bot_bot_set_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot_eq_sup_iff
% 6.92/7.16 thf(fact_1805_bot__eq__sup__iff,axiom,
% 6.92/7.16 ! [X: set_int,Y: set_int] :
% 6.92/7.16 ( ( bot_bot_set_int
% 6.92/7.16 = ( sup_sup_set_int @ X @ Y ) )
% 6.92/7.16 = ( ( X = bot_bot_set_int )
% 6.92/7.16 & ( Y = bot_bot_set_int ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot_eq_sup_iff
% 6.92/7.16 thf(fact_1806_sup__eq__bot__iff,axiom,
% 6.92/7.16 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 6.92/7.16 ( ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 6.92/7.16 = bot_bo8422036546324065075at_nat )
% 6.92/7.16 = ( ( X = bot_bo8422036546324065075at_nat )
% 6.92/7.16 & ( Y = bot_bo8422036546324065075at_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_eq_bot_iff
% 6.92/7.16 thf(fact_1807_sup__eq__bot__iff,axiom,
% 6.92/7.16 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 6.92/7.16 ( ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 6.92/7.16 = bot_bo228742789529271731at_nat )
% 6.92/7.16 = ( ( X = bot_bo228742789529271731at_nat )
% 6.92/7.16 & ( Y = bot_bo228742789529271731at_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_eq_bot_iff
% 6.92/7.16 thf(fact_1808_sup__eq__bot__iff,axiom,
% 6.92/7.16 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( ( sup_su6327502436637775413at_nat @ X @ Y )
% 6.92/7.16 = bot_bo2099793752762293965at_nat )
% 6.92/7.16 = ( ( X = bot_bo2099793752762293965at_nat )
% 6.92/7.16 & ( Y = bot_bo2099793752762293965at_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_eq_bot_iff
% 6.92/7.16 thf(fact_1809_sup__eq__bot__iff,axiom,
% 6.92/7.16 ! [X: set_o,Y: set_o] :
% 6.92/7.16 ( ( ( sup_sup_set_o @ X @ Y )
% 6.92/7.16 = bot_bot_set_o )
% 6.92/7.16 = ( ( X = bot_bot_set_o )
% 6.92/7.16 & ( Y = bot_bot_set_o ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_eq_bot_iff
% 6.92/7.16 thf(fact_1810_sup__eq__bot__iff,axiom,
% 6.92/7.16 ! [X: set_nat,Y: set_nat] :
% 6.92/7.16 ( ( ( sup_sup_set_nat @ X @ Y )
% 6.92/7.16 = bot_bot_set_nat )
% 6.92/7.16 = ( ( X = bot_bot_set_nat )
% 6.92/7.16 & ( Y = bot_bot_set_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_eq_bot_iff
% 6.92/7.16 thf(fact_1811_sup__eq__bot__iff,axiom,
% 6.92/7.16 ! [X: set_int,Y: set_int] :
% 6.92/7.16 ( ( ( sup_sup_set_int @ X @ Y )
% 6.92/7.16 = bot_bot_set_int )
% 6.92/7.16 = ( ( X = bot_bot_set_int )
% 6.92/7.16 & ( Y = bot_bot_set_int ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_eq_bot_iff
% 6.92/7.16 thf(fact_1812_sup__bot_Oeq__neutr__iff,axiom,
% 6.92/7.16 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 6.92/7.16 ( ( ( sup_su3035147773818789531at_nat @ A @ B )
% 6.92/7.16 = bot_bo8422036546324065075at_nat )
% 6.92/7.16 = ( ( A = bot_bo8422036546324065075at_nat )
% 6.92/7.16 & ( B = bot_bo8422036546324065075at_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.eq_neutr_iff
% 6.92/7.16 thf(fact_1813_sup__bot_Oeq__neutr__iff,axiom,
% 6.92/7.16 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 6.92/7.16 ( ( ( sup_su5525570899277871387at_nat @ A @ B )
% 6.92/7.16 = bot_bo228742789529271731at_nat )
% 6.92/7.16 = ( ( A = bot_bo228742789529271731at_nat )
% 6.92/7.16 & ( B = bot_bo228742789529271731at_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.eq_neutr_iff
% 6.92/7.16 thf(fact_1814_sup__bot_Oeq__neutr__iff,axiom,
% 6.92/7.16 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( ( sup_su6327502436637775413at_nat @ A @ B )
% 6.92/7.16 = bot_bo2099793752762293965at_nat )
% 6.92/7.16 = ( ( A = bot_bo2099793752762293965at_nat )
% 6.92/7.16 & ( B = bot_bo2099793752762293965at_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.eq_neutr_iff
% 6.92/7.16 thf(fact_1815_sup__bot_Oeq__neutr__iff,axiom,
% 6.92/7.16 ! [A: set_o,B: set_o] :
% 6.92/7.16 ( ( ( sup_sup_set_o @ A @ B )
% 6.92/7.16 = bot_bot_set_o )
% 6.92/7.16 = ( ( A = bot_bot_set_o )
% 6.92/7.16 & ( B = bot_bot_set_o ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.eq_neutr_iff
% 6.92/7.16 thf(fact_1816_sup__bot_Oeq__neutr__iff,axiom,
% 6.92/7.16 ! [A: set_nat,B: set_nat] :
% 6.92/7.16 ( ( ( sup_sup_set_nat @ A @ B )
% 6.92/7.16 = bot_bot_set_nat )
% 6.92/7.16 = ( ( A = bot_bot_set_nat )
% 6.92/7.16 & ( B = bot_bot_set_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.eq_neutr_iff
% 6.92/7.16 thf(fact_1817_sup__bot_Oeq__neutr__iff,axiom,
% 6.92/7.16 ! [A: set_int,B: set_int] :
% 6.92/7.16 ( ( ( sup_sup_set_int @ A @ B )
% 6.92/7.16 = bot_bot_set_int )
% 6.92/7.16 = ( ( A = bot_bot_set_int )
% 6.92/7.16 & ( B = bot_bot_set_int ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.eq_neutr_iff
% 6.92/7.16 thf(fact_1818_sup__bot_Oleft__neutral,axiom,
% 6.92/7.16 ! [A: set_Pr8551490117392284871at_nat] :
% 6.92/7.16 ( ( sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat @ A )
% 6.92/7.16 = A ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.left_neutral
% 6.92/7.16 thf(fact_1819_sup__bot_Oleft__neutral,axiom,
% 6.92/7.16 ! [A: set_Pr4329608150637261639at_nat] :
% 6.92/7.16 ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ A )
% 6.92/7.16 = A ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.left_neutral
% 6.92/7.16 thf(fact_1820_sup__bot_Oleft__neutral,axiom,
% 6.92/7.16 ! [A: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ A )
% 6.92/7.16 = A ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.left_neutral
% 6.92/7.16 thf(fact_1821_sup__bot_Oleft__neutral,axiom,
% 6.92/7.16 ! [A: set_o] :
% 6.92/7.16 ( ( sup_sup_set_o @ bot_bot_set_o @ A )
% 6.92/7.16 = A ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.left_neutral
% 6.92/7.16 thf(fact_1822_sup__bot_Oleft__neutral,axiom,
% 6.92/7.16 ! [A: set_nat] :
% 6.92/7.16 ( ( sup_sup_set_nat @ bot_bot_set_nat @ A )
% 6.92/7.16 = A ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.left_neutral
% 6.92/7.16 thf(fact_1823_sup__bot_Oleft__neutral,axiom,
% 6.92/7.16 ! [A: set_int] :
% 6.92/7.16 ( ( sup_sup_set_int @ bot_bot_set_int @ A )
% 6.92/7.16 = A ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.left_neutral
% 6.92/7.16 thf(fact_1824_sup__bot_Oneutr__eq__iff,axiom,
% 6.92/7.16 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 6.92/7.16 ( ( bot_bo8422036546324065075at_nat
% 6.92/7.16 = ( sup_su3035147773818789531at_nat @ A @ B ) )
% 6.92/7.16 = ( ( A = bot_bo8422036546324065075at_nat )
% 6.92/7.16 & ( B = bot_bo8422036546324065075at_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.neutr_eq_iff
% 6.92/7.16 thf(fact_1825_sup__bot_Oneutr__eq__iff,axiom,
% 6.92/7.16 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 6.92/7.16 ( ( bot_bo228742789529271731at_nat
% 6.92/7.16 = ( sup_su5525570899277871387at_nat @ A @ B ) )
% 6.92/7.16 = ( ( A = bot_bo228742789529271731at_nat )
% 6.92/7.16 & ( B = bot_bo228742789529271731at_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.neutr_eq_iff
% 6.92/7.16 thf(fact_1826_sup__bot_Oneutr__eq__iff,axiom,
% 6.92/7.16 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( bot_bo2099793752762293965at_nat
% 6.92/7.16 = ( sup_su6327502436637775413at_nat @ A @ B ) )
% 6.92/7.16 = ( ( A = bot_bo2099793752762293965at_nat )
% 6.92/7.16 & ( B = bot_bo2099793752762293965at_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.neutr_eq_iff
% 6.92/7.16 thf(fact_1827_sup__bot_Oneutr__eq__iff,axiom,
% 6.92/7.16 ! [A: set_o,B: set_o] :
% 6.92/7.16 ( ( bot_bot_set_o
% 6.92/7.16 = ( sup_sup_set_o @ A @ B ) )
% 6.92/7.16 = ( ( A = bot_bot_set_o )
% 6.92/7.16 & ( B = bot_bot_set_o ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.neutr_eq_iff
% 6.92/7.16 thf(fact_1828_sup__bot_Oneutr__eq__iff,axiom,
% 6.92/7.16 ! [A: set_nat,B: set_nat] :
% 6.92/7.16 ( ( bot_bot_set_nat
% 6.92/7.16 = ( sup_sup_set_nat @ A @ B ) )
% 6.92/7.16 = ( ( A = bot_bot_set_nat )
% 6.92/7.16 & ( B = bot_bot_set_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.neutr_eq_iff
% 6.92/7.16 thf(fact_1829_sup__bot_Oneutr__eq__iff,axiom,
% 6.92/7.16 ! [A: set_int,B: set_int] :
% 6.92/7.16 ( ( bot_bot_set_int
% 6.92/7.16 = ( sup_sup_set_int @ A @ B ) )
% 6.92/7.16 = ( ( A = bot_bot_set_int )
% 6.92/7.16 & ( B = bot_bot_set_int ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.neutr_eq_iff
% 6.92/7.16 thf(fact_1830_sup__bot_Oright__neutral,axiom,
% 6.92/7.16 ! [A: set_Pr8551490117392284871at_nat] :
% 6.92/7.16 ( ( sup_su3035147773818789531at_nat @ A @ bot_bo8422036546324065075at_nat )
% 6.92/7.16 = A ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.right_neutral
% 6.92/7.16 thf(fact_1831_sup__bot_Oright__neutral,axiom,
% 6.92/7.16 ! [A: set_Pr4329608150637261639at_nat] :
% 6.92/7.16 ( ( sup_su5525570899277871387at_nat @ A @ bot_bo228742789529271731at_nat )
% 6.92/7.16 = A ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.right_neutral
% 6.92/7.16 thf(fact_1832_sup__bot_Oright__neutral,axiom,
% 6.92/7.16 ! [A: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( sup_su6327502436637775413at_nat @ A @ bot_bo2099793752762293965at_nat )
% 6.92/7.16 = A ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.right_neutral
% 6.92/7.16 thf(fact_1833_sup__bot_Oright__neutral,axiom,
% 6.92/7.16 ! [A: set_o] :
% 6.92/7.16 ( ( sup_sup_set_o @ A @ bot_bot_set_o )
% 6.92/7.16 = A ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.right_neutral
% 6.92/7.16 thf(fact_1834_sup__bot_Oright__neutral,axiom,
% 6.92/7.16 ! [A: set_nat] :
% 6.92/7.16 ( ( sup_sup_set_nat @ A @ bot_bot_set_nat )
% 6.92/7.16 = A ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.right_neutral
% 6.92/7.16 thf(fact_1835_sup__bot_Oright__neutral,axiom,
% 6.92/7.16 ! [A: set_int] :
% 6.92/7.16 ( ( sup_sup_set_int @ A @ bot_bot_set_int )
% 6.92/7.16 = A ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.right_neutral
% 6.92/7.16 thf(fact_1836_Un__empty,axiom,
% 6.92/7.16 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.16 ( ( ( sup_su3035147773818789531at_nat @ A4 @ B5 )
% 6.92/7.16 = bot_bo8422036546324065075at_nat )
% 6.92/7.16 = ( ( A4 = bot_bo8422036546324065075at_nat )
% 6.92/7.16 & ( B5 = bot_bo8422036546324065075at_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty
% 6.92/7.16 thf(fact_1837_Un__empty,axiom,
% 6.92/7.16 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.16 ( ( ( sup_su5525570899277871387at_nat @ A4 @ B5 )
% 6.92/7.16 = bot_bo228742789529271731at_nat )
% 6.92/7.16 = ( ( A4 = bot_bo228742789529271731at_nat )
% 6.92/7.16 & ( B5 = bot_bo228742789529271731at_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty
% 6.92/7.16 thf(fact_1838_Un__empty,axiom,
% 6.92/7.16 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( ( sup_su6327502436637775413at_nat @ A4 @ B5 )
% 6.92/7.16 = bot_bo2099793752762293965at_nat )
% 6.92/7.16 = ( ( A4 = bot_bo2099793752762293965at_nat )
% 6.92/7.16 & ( B5 = bot_bo2099793752762293965at_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty
% 6.92/7.16 thf(fact_1839_Un__empty,axiom,
% 6.92/7.16 ! [A4: set_o,B5: set_o] :
% 6.92/7.16 ( ( ( sup_sup_set_o @ A4 @ B5 )
% 6.92/7.16 = bot_bot_set_o )
% 6.92/7.16 = ( ( A4 = bot_bot_set_o )
% 6.92/7.16 & ( B5 = bot_bot_set_o ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty
% 6.92/7.16 thf(fact_1840_Un__empty,axiom,
% 6.92/7.16 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.16 ( ( ( sup_sup_set_nat @ A4 @ B5 )
% 6.92/7.16 = bot_bot_set_nat )
% 6.92/7.16 = ( ( A4 = bot_bot_set_nat )
% 6.92/7.16 & ( B5 = bot_bot_set_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty
% 6.92/7.16 thf(fact_1841_Un__empty,axiom,
% 6.92/7.16 ! [A4: set_int,B5: set_int] :
% 6.92/7.16 ( ( ( sup_sup_set_int @ A4 @ B5 )
% 6.92/7.16 = bot_bot_set_int )
% 6.92/7.16 = ( ( A4 = bot_bot_set_int )
% 6.92/7.16 & ( B5 = bot_bot_set_int ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty
% 6.92/7.16 thf(fact_1842_pair__in__Id__conv,axiom,
% 6.92/7.16 ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 6.92/7.16 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ id_Pro2258643101195443293at_nat )
% 6.92/7.16 = ( A = B ) ) ).
% 6.92/7.16
% 6.92/7.16 % pair_in_Id_conv
% 6.92/7.16 thf(fact_1843_pair__in__Id__conv,axiom,
% 6.92/7.16 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 6.92/7.16 ( ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ A @ B ) @ id_mul2649389997224486051at_nat )
% 6.92/7.16 = ( A = B ) ) ).
% 6.92/7.16
% 6.92/7.16 % pair_in_Id_conv
% 6.92/7.16 thf(fact_1844_pair__in__Id__conv,axiom,
% 6.92/7.16 ! [A: nat,B: nat] :
% 6.92/7.16 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ id_nat2 )
% 6.92/7.16 = ( A = B ) ) ).
% 6.92/7.16
% 6.92/7.16 % pair_in_Id_conv
% 6.92/7.16 thf(fact_1845_pair__in__Id__conv,axiom,
% 6.92/7.16 ! [A: int,B: int] :
% 6.92/7.16 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ id_int2 )
% 6.92/7.16 = ( A = B ) ) ).
% 6.92/7.16
% 6.92/7.16 % pair_in_Id_conv
% 6.92/7.16 thf(fact_1846_IdI,axiom,
% 6.92/7.16 ! [A: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ A ) @ id_Pro2258643101195443293at_nat ) ).
% 6.92/7.16
% 6.92/7.16 % IdI
% 6.92/7.16 thf(fact_1847_IdI,axiom,
% 6.92/7.16 ! [A: multis2468970476368604999at_nat] : ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ A @ A ) @ id_mul2649389997224486051at_nat ) ).
% 6.92/7.16
% 6.92/7.16 % IdI
% 6.92/7.16 thf(fact_1848_IdI,axiom,
% 6.92/7.16 ! [A: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A ) @ id_nat2 ) ).
% 6.92/7.16
% 6.92/7.16 % IdI
% 6.92/7.16 thf(fact_1849_IdI,axiom,
% 6.92/7.16 ! [A: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ A ) @ id_int2 ) ).
% 6.92/7.16
% 6.92/7.16 % IdI
% 6.92/7.16 thf(fact_1850_combine__options__simps_I3_J,axiom,
% 6.92/7.16 ! [F: produc7388388658123137530it_nat > produc7388388658123137530it_nat > produc7388388658123137530it_nat,A: produc7388388658123137530it_nat,B: produc7388388658123137530it_nat] :
% 6.92/7.16 ( ( combin724284867043296059it_nat @ F @ ( some_P2818173045054083285it_nat @ A ) @ ( some_P2818173045054083285it_nat @ B ) )
% 6.92/7.16 = ( some_P2818173045054083285it_nat @ ( F @ A @ B ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_simps(3)
% 6.92/7.16 thf(fact_1851_combine__options__simps_I3_J,axiom,
% 6.92/7.16 ! [F: produc3260487557148687353it_nat > produc3260487557148687353it_nat > produc3260487557148687353it_nat,A: produc3260487557148687353it_nat,B: produc3260487557148687353it_nat] :
% 6.92/7.16 ( ( combin5819755802923621690it_nat @ F @ ( some_P7913643980934408916it_nat @ A ) @ ( some_P7913643980934408916it_nat @ B ) )
% 6.92/7.16 = ( some_P7913643980934408916it_nat @ ( F @ A @ B ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_simps(3)
% 6.92/7.16 thf(fact_1852_combine__options__simps_I3_J,axiom,
% 6.92/7.16 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat,A: produc8664842809031399944it_nat,B: produc8664842809031399944it_nat] :
% 6.92/7.16 ( ( combin4318129983670048329it_nat @ F @ ( some_P1914260805536162275it_nat @ A ) @ ( some_P1914260805536162275it_nat @ B ) )
% 6.92/7.16 = ( some_P1914260805536162275it_nat @ ( F @ A @ B ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_simps(3)
% 6.92/7.16 thf(fact_1853_combine__options__simps_I3_J,axiom,
% 6.92/7.16 ! [F: num > num > num,A: num,B: num] :
% 6.92/7.16 ( ( combine_options_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 6.92/7.16 = ( some_num @ ( F @ A @ B ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_simps(3)
% 6.92/7.16 thf(fact_1854_combine__options__simps_I1_J,axiom,
% 6.92/7.16 ! [F: num > num > num,Y: option_num] :
% 6.92/7.16 ( ( combine_options_num @ F @ none_num @ Y )
% 6.92/7.16 = Y ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_simps(1)
% 6.92/7.16 thf(fact_1855_combine__options__simps_I2_J,axiom,
% 6.92/7.16 ! [F: num > num > num,X: option_num] :
% 6.92/7.16 ( ( combine_options_num @ F @ X @ none_num )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % combine_options_simps(2)
% 6.92/7.16 thf(fact_1856_bijective__Id,axiom,
% 6.92/7.16 biject3503750217840948301at_nat @ id_Pro2258643101195443293at_nat ).
% 6.92/7.16
% 6.92/7.16 % bijective_Id
% 6.92/7.16 thf(fact_1857_bijective__Id,axiom,
% 6.92/7.16 biject5714339216877808333at_nat @ id_mul2649389997224486051at_nat ).
% 6.92/7.16
% 6.92/7.16 % bijective_Id
% 6.92/7.16 thf(fact_1858_bijective__Id,axiom,
% 6.92/7.16 bijective_nat_nat @ id_nat2 ).
% 6.92/7.16
% 6.92/7.16 % bijective_Id
% 6.92/7.16 thf(fact_1859_memb__imp__not__empty,axiom,
% 6.92/7.16 ! [X: set_Pr958786334691620121nt_int,S: set_se6260736226359567993nt_int] :
% 6.92/7.16 ( ( member2340774599025711042nt_int @ X @ S )
% 6.92/7.16 => ( S != bot_bo1488462491386950373nt_int ) ) ).
% 6.92/7.16
% 6.92/7.16 % memb_imp_not_empty
% 6.92/7.16 thf(fact_1860_memb__imp__not__empty,axiom,
% 6.92/7.16 ! [X: set_nat,S: set_set_nat] :
% 6.92/7.16 ( ( member_set_nat @ X @ S )
% 6.92/7.16 => ( S != bot_bot_set_set_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % memb_imp_not_empty
% 6.92/7.16 thf(fact_1861_memb__imp__not__empty,axiom,
% 6.92/7.16 ! [X: product_prod_nat_nat,S: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( member8440522571783428010at_nat @ X @ S )
% 6.92/7.16 => ( S != bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % memb_imp_not_empty
% 6.92/7.16 thf(fact_1862_memb__imp__not__empty,axiom,
% 6.92/7.16 ! [X: $o,S: set_o] :
% 6.92/7.16 ( ( member_o @ X @ S )
% 6.92/7.16 => ( S != bot_bot_set_o ) ) ).
% 6.92/7.16
% 6.92/7.16 % memb_imp_not_empty
% 6.92/7.16 thf(fact_1863_memb__imp__not__empty,axiom,
% 6.92/7.16 ! [X: nat,S: set_nat] :
% 6.92/7.16 ( ( member_nat @ X @ S )
% 6.92/7.16 => ( S != bot_bot_set_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % memb_imp_not_empty
% 6.92/7.16 thf(fact_1864_memb__imp__not__empty,axiom,
% 6.92/7.16 ! [X: int,S: set_int] :
% 6.92/7.16 ( ( member_int @ X @ S )
% 6.92/7.16 => ( S != bot_bot_set_int ) ) ).
% 6.92/7.16
% 6.92/7.16 % memb_imp_not_empty
% 6.92/7.16 thf(fact_1865_set__notEmptyE,axiom,
% 6.92/7.16 ! [S: set_se6260736226359567993nt_int] :
% 6.92/7.16 ( ( S != bot_bo1488462491386950373nt_int )
% 6.92/7.16 => ~ ! [X3: set_Pr958786334691620121nt_int] :
% 6.92/7.16 ~ ( member2340774599025711042nt_int @ X3 @ S ) ) ).
% 6.92/7.16
% 6.92/7.16 % set_notEmptyE
% 6.92/7.16 thf(fact_1866_set__notEmptyE,axiom,
% 6.92/7.16 ! [S: set_set_nat] :
% 6.92/7.16 ( ( S != bot_bot_set_set_nat )
% 6.92/7.16 => ~ ! [X3: set_nat] :
% 6.92/7.16 ~ ( member_set_nat @ X3 @ S ) ) ).
% 6.92/7.16
% 6.92/7.16 % set_notEmptyE
% 6.92/7.16 thf(fact_1867_set__notEmptyE,axiom,
% 6.92/7.16 ! [S: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( S != bot_bo2099793752762293965at_nat )
% 6.92/7.16 => ~ ! [X3: product_prod_nat_nat] :
% 6.92/7.16 ~ ( member8440522571783428010at_nat @ X3 @ S ) ) ).
% 6.92/7.16
% 6.92/7.16 % set_notEmptyE
% 6.92/7.16 thf(fact_1868_set__notEmptyE,axiom,
% 6.92/7.16 ! [S: set_o] :
% 6.92/7.16 ( ( S != bot_bot_set_o )
% 6.92/7.16 => ~ ! [X3: $o] :
% 6.92/7.16 ~ ( member_o @ X3 @ S ) ) ).
% 6.92/7.16
% 6.92/7.16 % set_notEmptyE
% 6.92/7.16 thf(fact_1869_set__notEmptyE,axiom,
% 6.92/7.16 ! [S: set_nat] :
% 6.92/7.16 ( ( S != bot_bot_set_nat )
% 6.92/7.16 => ~ ! [X3: nat] :
% 6.92/7.16 ~ ( member_nat @ X3 @ S ) ) ).
% 6.92/7.16
% 6.92/7.16 % set_notEmptyE
% 6.92/7.16 thf(fact_1870_set__notEmptyE,axiom,
% 6.92/7.16 ! [S: set_int] :
% 6.92/7.16 ( ( S != bot_bot_set_int )
% 6.92/7.16 => ~ ! [X3: int] :
% 6.92/7.16 ~ ( member_int @ X3 @ S ) ) ).
% 6.92/7.16
% 6.92/7.16 % set_notEmptyE
% 6.92/7.16 thf(fact_1871_ex__in__conv,axiom,
% 6.92/7.16 ! [A4: set_se6260736226359567993nt_int] :
% 6.92/7.16 ( ( ? [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ A4 ) )
% 6.92/7.16 = ( A4 != bot_bo1488462491386950373nt_int ) ) ).
% 6.92/7.16
% 6.92/7.16 % ex_in_conv
% 6.92/7.16 thf(fact_1872_ex__in__conv,axiom,
% 6.92/7.16 ! [A4: set_set_nat] :
% 6.92/7.16 ( ( ? [X4: set_nat] : ( member_set_nat @ X4 @ A4 ) )
% 6.92/7.16 = ( A4 != bot_bot_set_set_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % ex_in_conv
% 6.92/7.16 thf(fact_1873_ex__in__conv,axiom,
% 6.92/7.16 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( ? [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ A4 ) )
% 6.92/7.16 = ( A4 != bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % ex_in_conv
% 6.92/7.16 thf(fact_1874_ex__in__conv,axiom,
% 6.92/7.16 ! [A4: set_o] :
% 6.92/7.16 ( ( ? [X4: $o] : ( member_o @ X4 @ A4 ) )
% 6.92/7.16 = ( A4 != bot_bot_set_o ) ) ).
% 6.92/7.16
% 6.92/7.16 % ex_in_conv
% 6.92/7.16 thf(fact_1875_ex__in__conv,axiom,
% 6.92/7.16 ! [A4: set_nat] :
% 6.92/7.16 ( ( ? [X4: nat] : ( member_nat @ X4 @ A4 ) )
% 6.92/7.16 = ( A4 != bot_bot_set_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % ex_in_conv
% 6.92/7.16 thf(fact_1876_ex__in__conv,axiom,
% 6.92/7.16 ! [A4: set_int] :
% 6.92/7.16 ( ( ? [X4: int] : ( member_int @ X4 @ A4 ) )
% 6.92/7.16 = ( A4 != bot_bot_set_int ) ) ).
% 6.92/7.16
% 6.92/7.16 % ex_in_conv
% 6.92/7.16 thf(fact_1877_equals0I,axiom,
% 6.92/7.16 ! [A4: set_se6260736226359567993nt_int] :
% 6.92/7.16 ( ! [Y3: set_Pr958786334691620121nt_int] :
% 6.92/7.16 ~ ( member2340774599025711042nt_int @ Y3 @ A4 )
% 6.92/7.16 => ( A4 = bot_bo1488462491386950373nt_int ) ) ).
% 6.92/7.16
% 6.92/7.16 % equals0I
% 6.92/7.16 thf(fact_1878_equals0I,axiom,
% 6.92/7.16 ! [A4: set_set_nat] :
% 6.92/7.16 ( ! [Y3: set_nat] :
% 6.92/7.16 ~ ( member_set_nat @ Y3 @ A4 )
% 6.92/7.16 => ( A4 = bot_bot_set_set_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % equals0I
% 6.92/7.16 thf(fact_1879_equals0I,axiom,
% 6.92/7.16 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ! [Y3: product_prod_nat_nat] :
% 6.92/7.16 ~ ( member8440522571783428010at_nat @ Y3 @ A4 )
% 6.92/7.16 => ( A4 = bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % equals0I
% 6.92/7.16 thf(fact_1880_equals0I,axiom,
% 6.92/7.16 ! [A4: set_o] :
% 6.92/7.16 ( ! [Y3: $o] :
% 6.92/7.16 ~ ( member_o @ Y3 @ A4 )
% 6.92/7.16 => ( A4 = bot_bot_set_o ) ) ).
% 6.92/7.16
% 6.92/7.16 % equals0I
% 6.92/7.16 thf(fact_1881_equals0I,axiom,
% 6.92/7.16 ! [A4: set_nat] :
% 6.92/7.16 ( ! [Y3: nat] :
% 6.92/7.16 ~ ( member_nat @ Y3 @ A4 )
% 6.92/7.16 => ( A4 = bot_bot_set_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % equals0I
% 6.92/7.16 thf(fact_1882_equals0I,axiom,
% 6.92/7.16 ! [A4: set_int] :
% 6.92/7.16 ( ! [Y3: int] :
% 6.92/7.16 ~ ( member_int @ Y3 @ A4 )
% 6.92/7.16 => ( A4 = bot_bot_set_int ) ) ).
% 6.92/7.16
% 6.92/7.16 % equals0I
% 6.92/7.16 thf(fact_1883_equals0D,axiom,
% 6.92/7.16 ! [A4: set_se6260736226359567993nt_int,A: set_Pr958786334691620121nt_int] :
% 6.92/7.16 ( ( A4 = bot_bo1488462491386950373nt_int )
% 6.92/7.16 => ~ ( member2340774599025711042nt_int @ A @ A4 ) ) ).
% 6.92/7.16
% 6.92/7.16 % equals0D
% 6.92/7.16 thf(fact_1884_equals0D,axiom,
% 6.92/7.16 ! [A4: set_set_nat,A: set_nat] :
% 6.92/7.16 ( ( A4 = bot_bot_set_set_nat )
% 6.92/7.16 => ~ ( member_set_nat @ A @ A4 ) ) ).
% 6.92/7.16
% 6.92/7.16 % equals0D
% 6.92/7.16 thf(fact_1885_equals0D,axiom,
% 6.92/7.16 ! [A4: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 6.92/7.16 ( ( A4 = bot_bo2099793752762293965at_nat )
% 6.92/7.16 => ~ ( member8440522571783428010at_nat @ A @ A4 ) ) ).
% 6.92/7.16
% 6.92/7.16 % equals0D
% 6.92/7.16 thf(fact_1886_equals0D,axiom,
% 6.92/7.16 ! [A4: set_o,A: $o] :
% 6.92/7.16 ( ( A4 = bot_bot_set_o )
% 6.92/7.16 => ~ ( member_o @ A @ A4 ) ) ).
% 6.92/7.16
% 6.92/7.16 % equals0D
% 6.92/7.16 thf(fact_1887_equals0D,axiom,
% 6.92/7.16 ! [A4: set_nat,A: nat] :
% 6.92/7.16 ( ( A4 = bot_bot_set_nat )
% 6.92/7.16 => ~ ( member_nat @ A @ A4 ) ) ).
% 6.92/7.16
% 6.92/7.16 % equals0D
% 6.92/7.16 thf(fact_1888_equals0D,axiom,
% 6.92/7.16 ! [A4: set_int,A: int] :
% 6.92/7.16 ( ( A4 = bot_bot_set_int )
% 6.92/7.16 => ~ ( member_int @ A @ A4 ) ) ).
% 6.92/7.16
% 6.92/7.16 % equals0D
% 6.92/7.16 thf(fact_1889_emptyE,axiom,
% 6.92/7.16 ! [A: set_Pr958786334691620121nt_int] :
% 6.92/7.16 ~ ( member2340774599025711042nt_int @ A @ bot_bo1488462491386950373nt_int ) ).
% 6.92/7.16
% 6.92/7.16 % emptyE
% 6.92/7.16 thf(fact_1890_emptyE,axiom,
% 6.92/7.16 ! [A: set_nat] :
% 6.92/7.16 ~ ( member_set_nat @ A @ bot_bot_set_set_nat ) ).
% 6.92/7.16
% 6.92/7.16 % emptyE
% 6.92/7.16 thf(fact_1891_emptyE,axiom,
% 6.92/7.16 ! [A: product_prod_nat_nat] :
% 6.92/7.16 ~ ( member8440522571783428010at_nat @ A @ bot_bo2099793752762293965at_nat ) ).
% 6.92/7.16
% 6.92/7.16 % emptyE
% 6.92/7.16 thf(fact_1892_emptyE,axiom,
% 6.92/7.16 ! [A: $o] :
% 6.92/7.16 ~ ( member_o @ A @ bot_bot_set_o ) ).
% 6.92/7.16
% 6.92/7.16 % emptyE
% 6.92/7.16 thf(fact_1893_emptyE,axiom,
% 6.92/7.16 ! [A: nat] :
% 6.92/7.16 ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 6.92/7.16
% 6.92/7.16 % emptyE
% 6.92/7.16 thf(fact_1894_emptyE,axiom,
% 6.92/7.16 ! [A: int] :
% 6.92/7.16 ~ ( member_int @ A @ bot_bot_set_int ) ).
% 6.92/7.16
% 6.92/7.16 % emptyE
% 6.92/7.16 thf(fact_1895_Set_Oempty__def,axiom,
% 6.92/7.16 ( bot_bot_set_list_nat
% 6.92/7.16 = ( collect_list_nat
% 6.92/7.16 @ ^ [X4: list_nat] : $false ) ) ).
% 6.92/7.16
% 6.92/7.16 % Set.empty_def
% 6.92/7.16 thf(fact_1896_Set_Oempty__def,axiom,
% 6.92/7.16 ( bot_bo1488462491386950373nt_int
% 6.92/7.16 = ( collec5210948495886036740nt_int
% 6.92/7.16 @ ^ [X4: set_Pr958786334691620121nt_int] : $false ) ) ).
% 6.92/7.16
% 6.92/7.16 % Set.empty_def
% 6.92/7.16 thf(fact_1897_Set_Oempty__def,axiom,
% 6.92/7.16 ( bot_bot_set_set_nat
% 6.92/7.16 = ( collect_set_nat
% 6.92/7.16 @ ^ [X4: set_nat] : $false ) ) ).
% 6.92/7.16
% 6.92/7.16 % Set.empty_def
% 6.92/7.16 thf(fact_1898_Set_Oempty__def,axiom,
% 6.92/7.16 ( bot_bo2099793752762293965at_nat
% 6.92/7.16 = ( collec3392354462482085612at_nat
% 6.92/7.16 @ ^ [X4: product_prod_nat_nat] : $false ) ) ).
% 6.92/7.16
% 6.92/7.16 % Set.empty_def
% 6.92/7.16 thf(fact_1899_Set_Oempty__def,axiom,
% 6.92/7.16 ( bot_bot_set_o
% 6.92/7.16 = ( collect_o
% 6.92/7.16 @ ^ [X4: $o] : $false ) ) ).
% 6.92/7.16
% 6.92/7.16 % Set.empty_def
% 6.92/7.16 thf(fact_1900_Set_Oempty__def,axiom,
% 6.92/7.16 ( bot_bot_set_nat
% 6.92/7.16 = ( collect_nat
% 6.92/7.16 @ ^ [X4: nat] : $false ) ) ).
% 6.92/7.16
% 6.92/7.16 % Set.empty_def
% 6.92/7.16 thf(fact_1901_Set_Oempty__def,axiom,
% 6.92/7.16 ( bot_bot_set_int
% 6.92/7.16 = ( collect_int
% 6.92/7.16 @ ^ [X4: int] : $false ) ) ).
% 6.92/7.16
% 6.92/7.16 % Set.empty_def
% 6.92/7.16 thf(fact_1902_bot_Oextremum,axiom,
% 6.92/7.16 ! [A: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ bot_bo2099793752762293965at_nat @ A ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum
% 6.92/7.16 thf(fact_1903_bot_Oextremum,axiom,
% 6.92/7.16 ! [A: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum
% 6.92/7.16 thf(fact_1904_bot_Oextremum,axiom,
% 6.92/7.16 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum
% 6.92/7.16 thf(fact_1905_bot_Oextremum,axiom,
% 6.92/7.16 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum
% 6.92/7.16 thf(fact_1906_bot_Oextremum,axiom,
% 6.92/7.16 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum
% 6.92/7.16 thf(fact_1907_bot_Oextremum__unique,axiom,
% 6.92/7.16 ! [A: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( ord_le3146513528884898305at_nat @ A @ bot_bo2099793752762293965at_nat )
% 6.92/7.16 = ( A = bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_unique
% 6.92/7.16 thf(fact_1908_bot_Oextremum__unique,axiom,
% 6.92/7.16 ! [A: set_o] :
% 6.92/7.16 ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 6.92/7.16 = ( A = bot_bot_set_o ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_unique
% 6.92/7.16 thf(fact_1909_bot_Oextremum__unique,axiom,
% 6.92/7.16 ! [A: set_nat] :
% 6.92/7.16 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 6.92/7.16 = ( A = bot_bot_set_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_unique
% 6.92/7.16 thf(fact_1910_bot_Oextremum__unique,axiom,
% 6.92/7.16 ! [A: set_int] :
% 6.92/7.16 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 6.92/7.16 = ( A = bot_bot_set_int ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_unique
% 6.92/7.16 thf(fact_1911_bot_Oextremum__unique,axiom,
% 6.92/7.16 ! [A: nat] :
% 6.92/7.16 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 6.92/7.16 = ( A = bot_bot_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_unique
% 6.92/7.16 thf(fact_1912_bot_Oextremum__uniqueI,axiom,
% 6.92/7.16 ! [A: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( ord_le3146513528884898305at_nat @ A @ bot_bo2099793752762293965at_nat )
% 6.92/7.16 => ( A = bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_uniqueI
% 6.92/7.16 thf(fact_1913_bot_Oextremum__uniqueI,axiom,
% 6.92/7.16 ! [A: set_o] :
% 6.92/7.16 ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 6.92/7.16 => ( A = bot_bot_set_o ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_uniqueI
% 6.92/7.16 thf(fact_1914_bot_Oextremum__uniqueI,axiom,
% 6.92/7.16 ! [A: set_nat] :
% 6.92/7.16 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 6.92/7.16 => ( A = bot_bot_set_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_uniqueI
% 6.92/7.16 thf(fact_1915_bot_Oextremum__uniqueI,axiom,
% 6.92/7.16 ! [A: set_int] :
% 6.92/7.16 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 6.92/7.16 => ( A = bot_bot_set_int ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_uniqueI
% 6.92/7.16 thf(fact_1916_bot_Oextremum__uniqueI,axiom,
% 6.92/7.16 ! [A: nat] :
% 6.92/7.16 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 6.92/7.16 => ( A = bot_bot_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_uniqueI
% 6.92/7.16 thf(fact_1917_bot_Oextremum__strict,axiom,
% 6.92/7.16 ! [A: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ~ ( ord_le7866589430770878221at_nat @ A @ bot_bo2099793752762293965at_nat ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_strict
% 6.92/7.16 thf(fact_1918_bot_Oextremum__strict,axiom,
% 6.92/7.16 ! [A: set_o] :
% 6.92/7.16 ~ ( ord_less_set_o @ A @ bot_bot_set_o ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_strict
% 6.92/7.16 thf(fact_1919_bot_Oextremum__strict,axiom,
% 6.92/7.16 ! [A: set_nat] :
% 6.92/7.16 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_strict
% 6.92/7.16 thf(fact_1920_bot_Oextremum__strict,axiom,
% 6.92/7.16 ! [A: set_int] :
% 6.92/7.16 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_strict
% 6.92/7.16 thf(fact_1921_bot_Oextremum__strict,axiom,
% 6.92/7.16 ! [A: assn] :
% 6.92/7.16 ~ ( ord_less_assn @ A @ bot_bot_assn ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_strict
% 6.92/7.16 thf(fact_1922_bot_Oextremum__strict,axiom,
% 6.92/7.16 ! [A: nat] :
% 6.92/7.16 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 6.92/7.16
% 6.92/7.16 % bot.extremum_strict
% 6.92/7.16 thf(fact_1923_bot_Onot__eq__extremum,axiom,
% 6.92/7.16 ! [A: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( A != bot_bo2099793752762293965at_nat )
% 6.92/7.16 = ( ord_le7866589430770878221at_nat @ bot_bo2099793752762293965at_nat @ A ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.not_eq_extremum
% 6.92/7.16 thf(fact_1924_bot_Onot__eq__extremum,axiom,
% 6.92/7.16 ! [A: set_o] :
% 6.92/7.16 ( ( A != bot_bot_set_o )
% 6.92/7.16 = ( ord_less_set_o @ bot_bot_set_o @ A ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.not_eq_extremum
% 6.92/7.16 thf(fact_1925_bot_Onot__eq__extremum,axiom,
% 6.92/7.16 ! [A: set_nat] :
% 6.92/7.16 ( ( A != bot_bot_set_nat )
% 6.92/7.16 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.not_eq_extremum
% 6.92/7.16 thf(fact_1926_bot_Onot__eq__extremum,axiom,
% 6.92/7.16 ! [A: set_int] :
% 6.92/7.16 ( ( A != bot_bot_set_int )
% 6.92/7.16 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.not_eq_extremum
% 6.92/7.16 thf(fact_1927_bot_Onot__eq__extremum,axiom,
% 6.92/7.16 ! [A: assn] :
% 6.92/7.16 ( ( A != bot_bot_assn )
% 6.92/7.16 = ( ord_less_assn @ bot_bot_assn @ A ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.not_eq_extremum
% 6.92/7.16 thf(fact_1928_bot_Onot__eq__extremum,axiom,
% 6.92/7.16 ! [A: nat] :
% 6.92/7.16 ( ( A != bot_bot_nat )
% 6.92/7.16 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 6.92/7.16
% 6.92/7.16 % bot.not_eq_extremum
% 6.92/7.16 thf(fact_1929_boolean__algebra_Odisj__zero__right,axiom,
% 6.92/7.16 ! [X: set_Pr8551490117392284871at_nat] :
% 6.92/7.16 ( ( sup_su3035147773818789531at_nat @ X @ bot_bo8422036546324065075at_nat )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra.disj_zero_right
% 6.92/7.16 thf(fact_1930_boolean__algebra_Odisj__zero__right,axiom,
% 6.92/7.16 ! [X: set_Pr4329608150637261639at_nat] :
% 6.92/7.16 ( ( sup_su5525570899277871387at_nat @ X @ bot_bo228742789529271731at_nat )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra.disj_zero_right
% 6.92/7.16 thf(fact_1931_boolean__algebra_Odisj__zero__right,axiom,
% 6.92/7.16 ! [X: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( sup_su6327502436637775413at_nat @ X @ bot_bo2099793752762293965at_nat )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra.disj_zero_right
% 6.92/7.16 thf(fact_1932_boolean__algebra_Odisj__zero__right,axiom,
% 6.92/7.16 ! [X: set_o] :
% 6.92/7.16 ( ( sup_sup_set_o @ X @ bot_bot_set_o )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra.disj_zero_right
% 6.92/7.16 thf(fact_1933_boolean__algebra_Odisj__zero__right,axiom,
% 6.92/7.16 ! [X: set_nat] :
% 6.92/7.16 ( ( sup_sup_set_nat @ X @ bot_bot_set_nat )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra.disj_zero_right
% 6.92/7.16 thf(fact_1934_boolean__algebra_Odisj__zero__right,axiom,
% 6.92/7.16 ! [X: set_int] :
% 6.92/7.16 ( ( sup_sup_set_int @ X @ bot_bot_set_int )
% 6.92/7.16 = X ) ).
% 6.92/7.16
% 6.92/7.16 % boolean_algebra.disj_zero_right
% 6.92/7.16 thf(fact_1935_IdE,axiom,
% 6.92/7.16 ! [P3: produc859450856879609959at_nat] :
% 6.92/7.16 ( ( member8206827879206165904at_nat @ P3 @ id_Pro2258643101195443293at_nat )
% 6.92/7.16 => ~ ! [X3: product_prod_nat_nat] :
% 6.92/7.16 ( P3
% 6.92/7.16 != ( produc6161850002892822231at_nat @ X3 @ X3 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % IdE
% 6.92/7.16 thf(fact_1936_IdE,axiom,
% 6.92/7.16 ! [P3: produc4166570645942440679at_nat] :
% 6.92/7.16 ( ( member6689249552917799696at_nat @ P3 @ id_mul2649389997224486051at_nat )
% 6.92/7.16 => ~ ! [X3: multis2468970476368604999at_nat] :
% 6.92/7.16 ( P3
% 6.92/7.16 != ( produc4348348721325984599at_nat @ X3 @ X3 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % IdE
% 6.92/7.16 thf(fact_1937_IdE,axiom,
% 6.92/7.16 ! [P3: product_prod_nat_nat] :
% 6.92/7.16 ( ( member8440522571783428010at_nat @ P3 @ id_nat2 )
% 6.92/7.16 => ~ ! [X3: nat] :
% 6.92/7.16 ( P3
% 6.92/7.16 != ( product_Pair_nat_nat @ X3 @ X3 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % IdE
% 6.92/7.16 thf(fact_1938_IdE,axiom,
% 6.92/7.16 ! [P3: product_prod_int_int] :
% 6.92/7.16 ( ( member5262025264175285858nt_int @ P3 @ id_int2 )
% 6.92/7.16 => ~ ! [X3: int] :
% 6.92/7.16 ( P3
% 6.92/7.16 != ( product_Pair_int_int @ X3 @ X3 ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % IdE
% 6.92/7.16 thf(fact_1939_BNF__Greatest__Fixpoint_OIdD,axiom,
% 6.92/7.16 ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 6.92/7.16 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ id_Pro2258643101195443293at_nat )
% 6.92/7.16 => ( A = B ) ) ).
% 6.92/7.16
% 6.92/7.16 % BNF_Greatest_Fixpoint.IdD
% 6.92/7.16 thf(fact_1940_BNF__Greatest__Fixpoint_OIdD,axiom,
% 6.92/7.16 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 6.92/7.16 ( ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ A @ B ) @ id_mul2649389997224486051at_nat )
% 6.92/7.16 => ( A = B ) ) ).
% 6.92/7.16
% 6.92/7.16 % BNF_Greatest_Fixpoint.IdD
% 6.92/7.16 thf(fact_1941_BNF__Greatest__Fixpoint_OIdD,axiom,
% 6.92/7.16 ! [A: nat,B: nat] :
% 6.92/7.16 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ id_nat2 )
% 6.92/7.16 => ( A = B ) ) ).
% 6.92/7.16
% 6.92/7.16 % BNF_Greatest_Fixpoint.IdD
% 6.92/7.16 thf(fact_1942_BNF__Greatest__Fixpoint_OIdD,axiom,
% 6.92/7.16 ! [A: int,B: int] :
% 6.92/7.16 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ id_int2 )
% 6.92/7.16 => ( A = B ) ) ).
% 6.92/7.16
% 6.92/7.16 % BNF_Greatest_Fixpoint.IdD
% 6.92/7.16 thf(fact_1943_subset__emptyI,axiom,
% 6.92/7.16 ! [A4: set_se6260736226359567993nt_int] :
% 6.92/7.16 ( ! [X3: set_Pr958786334691620121nt_int] :
% 6.92/7.16 ~ ( member2340774599025711042nt_int @ X3 @ A4 )
% 6.92/7.16 => ( ord_le483042692224249369nt_int @ A4 @ bot_bo1488462491386950373nt_int ) ) ).
% 6.92/7.16
% 6.92/7.16 % subset_emptyI
% 6.92/7.16 thf(fact_1944_subset__emptyI,axiom,
% 6.92/7.16 ! [A4: set_set_nat] :
% 6.92/7.16 ( ! [X3: set_nat] :
% 6.92/7.16 ~ ( member_set_nat @ X3 @ A4 )
% 6.92/7.16 => ( ord_le6893508408891458716et_nat @ A4 @ bot_bot_set_set_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % subset_emptyI
% 6.92/7.16 thf(fact_1945_subset__emptyI,axiom,
% 6.92/7.16 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ! [X3: product_prod_nat_nat] :
% 6.92/7.16 ~ ( member8440522571783428010at_nat @ X3 @ A4 )
% 6.92/7.16 => ( ord_le3146513528884898305at_nat @ A4 @ bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % subset_emptyI
% 6.92/7.16 thf(fact_1946_subset__emptyI,axiom,
% 6.92/7.16 ! [A4: set_o] :
% 6.92/7.16 ( ! [X3: $o] :
% 6.92/7.16 ~ ( member_o @ X3 @ A4 )
% 6.92/7.16 => ( ord_less_eq_set_o @ A4 @ bot_bot_set_o ) ) ).
% 6.92/7.16
% 6.92/7.16 % subset_emptyI
% 6.92/7.16 thf(fact_1947_subset__emptyI,axiom,
% 6.92/7.16 ! [A4: set_nat] :
% 6.92/7.16 ( ! [X3: nat] :
% 6.92/7.16 ~ ( member_nat @ X3 @ A4 )
% 6.92/7.16 => ( ord_less_eq_set_nat @ A4 @ bot_bot_set_nat ) ) ).
% 6.92/7.16
% 6.92/7.16 % subset_emptyI
% 6.92/7.16 thf(fact_1948_subset__emptyI,axiom,
% 6.92/7.16 ! [A4: set_int] :
% 6.92/7.16 ( ! [X3: int] :
% 6.92/7.16 ~ ( member_int @ X3 @ A4 )
% 6.92/7.16 => ( ord_less_eq_set_int @ A4 @ bot_bot_set_int ) ) ).
% 6.92/7.16
% 6.92/7.16 % subset_emptyI
% 6.92/7.16 thf(fact_1949_Un__empty__left,axiom,
% 6.92/7.16 ! [B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.16 ( ( sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat @ B5 )
% 6.92/7.16 = B5 ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty_left
% 6.92/7.16 thf(fact_1950_Un__empty__left,axiom,
% 6.92/7.16 ! [B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.16 ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ B5 )
% 6.92/7.16 = B5 ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty_left
% 6.92/7.16 thf(fact_1951_Un__empty__left,axiom,
% 6.92/7.16 ! [B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ B5 )
% 6.92/7.16 = B5 ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty_left
% 6.92/7.16 thf(fact_1952_Un__empty__left,axiom,
% 6.92/7.16 ! [B5: set_o] :
% 6.92/7.16 ( ( sup_sup_set_o @ bot_bot_set_o @ B5 )
% 6.92/7.16 = B5 ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty_left
% 6.92/7.16 thf(fact_1953_Un__empty__left,axiom,
% 6.92/7.16 ! [B5: set_nat] :
% 6.92/7.16 ( ( sup_sup_set_nat @ bot_bot_set_nat @ B5 )
% 6.92/7.16 = B5 ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty_left
% 6.92/7.16 thf(fact_1954_Un__empty__left,axiom,
% 6.92/7.16 ! [B5: set_int] :
% 6.92/7.16 ( ( sup_sup_set_int @ bot_bot_set_int @ B5 )
% 6.92/7.16 = B5 ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty_left
% 6.92/7.16 thf(fact_1955_Un__empty__right,axiom,
% 6.92/7.16 ! [A4: set_Pr8551490117392284871at_nat] :
% 6.92/7.16 ( ( sup_su3035147773818789531at_nat @ A4 @ bot_bo8422036546324065075at_nat )
% 6.92/7.16 = A4 ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty_right
% 6.92/7.16 thf(fact_1956_Un__empty__right,axiom,
% 6.92/7.16 ! [A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.16 ( ( sup_su5525570899277871387at_nat @ A4 @ bot_bo228742789529271731at_nat )
% 6.92/7.16 = A4 ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty_right
% 6.92/7.16 thf(fact_1957_Un__empty__right,axiom,
% 6.92/7.16 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ( ( sup_su6327502436637775413at_nat @ A4 @ bot_bo2099793752762293965at_nat )
% 6.92/7.16 = A4 ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty_right
% 6.92/7.16 thf(fact_1958_Un__empty__right,axiom,
% 6.92/7.16 ! [A4: set_o] :
% 6.92/7.16 ( ( sup_sup_set_o @ A4 @ bot_bot_set_o )
% 6.92/7.16 = A4 ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty_right
% 6.92/7.16 thf(fact_1959_Un__empty__right,axiom,
% 6.92/7.16 ! [A4: set_nat] :
% 6.92/7.16 ( ( sup_sup_set_nat @ A4 @ bot_bot_set_nat )
% 6.92/7.16 = A4 ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty_right
% 6.92/7.16 thf(fact_1960_Un__empty__right,axiom,
% 6.92/7.16 ! [A4: set_int] :
% 6.92/7.16 ( ( sup_sup_set_int @ A4 @ bot_bot_set_int )
% 6.92/7.16 = A4 ) ).
% 6.92/7.16
% 6.92/7.16 % Un_empty_right
% 6.92/7.16 thf(fact_1961_not__psubset__empty,axiom,
% 6.92/7.16 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.16 ~ ( ord_le7866589430770878221at_nat @ A4 @ bot_bo2099793752762293965at_nat ) ).
% 6.92/7.16
% 6.92/7.16 % not_psubset_empty
% 6.92/7.16 thf(fact_1962_not__psubset__empty,axiom,
% 6.92/7.16 ! [A4: set_o] :
% 6.92/7.16 ~ ( ord_less_set_o @ A4 @ bot_bot_set_o ) ).
% 6.92/7.16
% 6.92/7.16 % not_psubset_empty
% 6.92/7.16 thf(fact_1963_not__psubset__empty,axiom,
% 6.92/7.16 ! [A4: set_nat] :
% 6.92/7.16 ~ ( ord_less_set_nat @ A4 @ bot_bot_set_nat ) ).
% 6.92/7.16
% 6.92/7.16 % not_psubset_empty
% 6.92/7.16 thf(fact_1964_not__psubset__empty,axiom,
% 6.92/7.16 ! [A4: set_int] :
% 6.92/7.16 ~ ( ord_less_set_int @ A4 @ bot_bot_set_int ) ).
% 6.92/7.16
% 6.92/7.16 % not_psubset_empty
% 6.92/7.16 thf(fact_1965_mod__h__bot__indep,axiom,
% 6.92/7.16 ! [P2: assn,H: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 6.92/7.16 ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 6.92/7.16 = ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H5 @ bot_bot_set_nat ) ) ) ).
% 6.92/7.16
% 6.92/7.16 % mod_h_bot_indep
% 6.92/7.16 thf(fact_1966_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 6.92/7.16 ( semila5207306265035627125at_nat @ sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat
% 6.92/7.16 @ ^ [X4: set_Pr8551490117392284871at_nat,Y4: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y4 @ X4 )
% 6.92/7.16 @ ^ [X4: set_Pr8551490117392284871at_nat,Y4: set_Pr8551490117392284871at_nat] : ( ord_le7642048601412989811at_nat @ Y4 @ X4 ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.semilattice_neutr_order_axioms
% 6.92/7.16 thf(fact_1967_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 6.92/7.16 ( semila6534579987270727413at_nat @ sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat
% 6.92/7.16 @ ^ [X4: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y4 @ X4 )
% 6.92/7.16 @ ^ [X4: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] : ( ord_le2604355607129572851at_nat @ Y4 @ X4 ) ) ).
% 6.92/7.16
% 6.92/7.16 % sup_bot.semilattice_neutr_order_axioms
% 6.92/7.16 thf(fact_1968_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 6.92/7.16 ( semila4918476307565957903at_nat @ sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat
% 6.92/7.17 @ ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ Y4 @ X4 )
% 6.92/7.17 @ ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( ord_le7866589430770878221at_nat @ Y4 @ X4 ) ) ).
% 6.92/7.17
% 6.92/7.17 % sup_bot.semilattice_neutr_order_axioms
% 6.92/7.17 thf(fact_1969_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 6.92/7.17 ( semila2554085542299052326_set_o @ sup_sup_set_o @ bot_bot_set_o
% 6.92/7.17 @ ^ [X4: set_o,Y4: set_o] : ( ord_less_eq_set_o @ Y4 @ X4 )
% 6.92/7.17 @ ^ [X4: set_o,Y4: set_o] : ( ord_less_set_o @ Y4 @ X4 ) ) ).
% 6.92/7.17
% 6.92/7.17 % sup_bot.semilattice_neutr_order_axioms
% 6.92/7.17 thf(fact_1970_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 6.92/7.17 ( semila1667268886620078168et_nat @ sup_sup_set_nat @ bot_bot_set_nat
% 6.92/7.17 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ Y4 @ X4 )
% 6.92/7.17 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_set_nat @ Y4 @ X4 ) ) ).
% 6.92/7.17
% 6.92/7.17 % sup_bot.semilattice_neutr_order_axioms
% 6.92/7.17 thf(fact_1971_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 6.92/7.17 ( semila8603258263270017530r_assn @ sup_sup_assn @ bot_bot_assn
% 6.92/7.17 @ ^ [X4: assn,Y4: assn] : ( ord_less_eq_assn @ Y4 @ X4 )
% 6.92/7.17 @ ^ [X4: assn,Y4: assn] : ( ord_less_assn @ Y4 @ X4 ) ) ).
% 6.92/7.17
% 6.92/7.17 % sup_bot.semilattice_neutr_order_axioms
% 6.92/7.17 thf(fact_1972_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 6.92/7.17 ( semila6712789903965657268et_int @ sup_sup_set_int @ bot_bot_set_int
% 6.92/7.17 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_eq_set_int @ Y4 @ X4 )
% 6.92/7.17 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_set_int @ Y4 @ X4 ) ) ).
% 6.92/7.17
% 6.92/7.17 % sup_bot.semilattice_neutr_order_axioms
% 6.92/7.17 thf(fact_1973_execute__assert_I1_J,axiom,
% 6.92/7.17 ! [P2: product_unit > $o,X: product_unit,H: heap_e7401611519738050253t_unit] :
% 6.92/7.17 ( ( P2 @ X )
% 6.92/7.17 => ( ( heap_T875086893843062177t_unit @ ( heap_T4208721593536448476t_unit @ P2 @ X ) @ H )
% 6.92/7.17 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_assert(1)
% 6.92/7.17 thf(fact_1974_execute__assert_I1_J,axiom,
% 6.92/7.17 ! [P2: b > $o,X: b,H: heap_e7401611519738050253t_unit] :
% 6.92/7.17 ( ( P2 @ X )
% 6.92/7.17 => ( ( heap_Time_execute_b @ ( heap_Time_assert_b @ P2 @ X ) @ H )
% 6.92/7.17 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ X @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_assert(1)
% 6.92/7.17 thf(fact_1975_execute__assert_I1_J,axiom,
% 6.92/7.17 ! [P2: a > $o,X: a,H: heap_e7401611519738050253t_unit] :
% 6.92/7.17 ( ( P2 @ X )
% 6.92/7.17 => ( ( heap_Time_execute_a @ ( heap_Time_assert_a @ P2 @ X ) @ H )
% 6.92/7.17 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ X @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_assert(1)
% 6.92/7.17 thf(fact_1976_the__dflt__None__empty,axiom,
% 6.92/7.17 ( ( dflt_N6592383573632408824at_nat @ bot_bo2099793752762293965at_nat )
% 6.92/7.17 = none_s625347054029921090at_nat ) ).
% 6.92/7.17
% 6.92/7.17 % the_dflt_None_empty
% 6.92/7.17 thf(fact_1977_the__dflt__None__empty,axiom,
% 6.92/7.17 ( ( dflt_None_set_o @ bot_bot_set_o )
% 6.92/7.17 = none_set_o ) ).
% 6.92/7.17
% 6.92/7.17 % the_dflt_None_empty
% 6.92/7.17 thf(fact_1978_the__dflt__None__empty,axiom,
% 6.92/7.17 ( ( dflt_None_set_nat @ bot_bot_set_nat )
% 6.92/7.17 = none_set_nat ) ).
% 6.92/7.17
% 6.92/7.17 % the_dflt_None_empty
% 6.92/7.17 thf(fact_1979_the__dflt__None__empty,axiom,
% 6.92/7.17 ( ( dflt_None_set_int @ bot_bot_set_int )
% 6.92/7.17 = none_set_int ) ).
% 6.92/7.17
% 6.92/7.17 % the_dflt_None_empty
% 6.92/7.17 thf(fact_1980_the__dflt__None__nonempty,axiom,
% 6.92/7.17 ! [S: set_Pr1261947904930325089at_nat] :
% 6.92/7.17 ( ( S != bot_bo2099793752762293965at_nat )
% 6.92/7.17 => ( ( dflt_N6592383573632408824at_nat @ S )
% 6.92/7.17 = ( some_s147305329494351046at_nat @ S ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % the_dflt_None_nonempty
% 6.92/7.17 thf(fact_1981_the__dflt__None__nonempty,axiom,
% 6.92/7.17 ! [S: set_o] :
% 6.92/7.17 ( ( S != bot_bot_set_o )
% 6.92/7.17 => ( ( dflt_None_set_o @ S )
% 6.92/7.17 = ( some_set_o @ S ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % the_dflt_None_nonempty
% 6.92/7.17 thf(fact_1982_the__dflt__None__nonempty,axiom,
% 6.92/7.17 ! [S: set_nat] :
% 6.92/7.17 ( ( S != bot_bot_set_nat )
% 6.92/7.17 => ( ( dflt_None_set_nat @ S )
% 6.92/7.17 = ( some_set_nat @ S ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % the_dflt_None_nonempty
% 6.92/7.17 thf(fact_1983_the__dflt__None__nonempty,axiom,
% 6.92/7.17 ! [S: set_int] :
% 6.92/7.17 ( ( S != bot_bot_set_int )
% 6.92/7.17 => ( ( dflt_None_set_int @ S )
% 6.92/7.17 = ( some_set_int @ S ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % the_dflt_None_nonempty
% 6.92/7.17 thf(fact_1984_the__dflt__None__set,axiom,
% 6.92/7.17 ! [X: set_Pr1261947904930325089at_nat] :
% 6.92/7.17 ( ( the_de3668382347305825784at_nat @ bot_bo2099793752762293965at_nat @ ( dflt_N6592383573632408824at_nat @ X ) )
% 6.92/7.17 = X ) ).
% 6.92/7.17
% 6.92/7.17 % the_dflt_None_set
% 6.92/7.17 thf(fact_1985_the__dflt__None__set,axiom,
% 6.92/7.17 ! [X: set_o] :
% 6.92/7.17 ( ( the_default_set_o @ bot_bot_set_o @ ( dflt_None_set_o @ X ) )
% 6.92/7.17 = X ) ).
% 6.92/7.17
% 6.92/7.17 % the_dflt_None_set
% 6.92/7.17 thf(fact_1986_the__dflt__None__set,axiom,
% 6.92/7.17 ! [X: set_nat] :
% 6.92/7.17 ( ( the_default_set_nat @ bot_bot_set_nat @ ( dflt_None_set_nat @ X ) )
% 6.92/7.17 = X ) ).
% 6.92/7.17
% 6.92/7.17 % the_dflt_None_set
% 6.92/7.17 thf(fact_1987_the__dflt__None__set,axiom,
% 6.92/7.17 ! [X: set_int] :
% 6.92/7.17 ( ( the_default_set_int @ bot_bot_set_int @ ( dflt_None_set_int @ X ) )
% 6.92/7.17 = X ) ).
% 6.92/7.17
% 6.92/7.17 % the_dflt_None_set
% 6.92/7.17 thf(fact_1988_bot_Oordering__top__axioms,axiom,
% 6.92/7.17 ( orderi2172309028950807442at_nat
% 6.92/7.17 @ ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ Y4 @ X4 )
% 6.92/7.17 @ ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( ord_le7866589430770878221at_nat @ Y4 @ X4 )
% 6.92/7.17 @ bot_bo2099793752762293965at_nat ) ).
% 6.92/7.17
% 6.92/7.17 % bot.ordering_top_axioms
% 6.92/7.17 thf(fact_1989_bot_Oordering__top__axioms,axiom,
% 6.92/7.17 ( ordering_top_set_o
% 6.92/7.17 @ ^ [X4: set_o,Y4: set_o] : ( ord_less_eq_set_o @ Y4 @ X4 )
% 6.92/7.17 @ ^ [X4: set_o,Y4: set_o] : ( ord_less_set_o @ Y4 @ X4 )
% 6.92/7.17 @ bot_bot_set_o ) ).
% 6.92/7.17
% 6.92/7.17 % bot.ordering_top_axioms
% 6.92/7.17 thf(fact_1990_bot_Oordering__top__axioms,axiom,
% 6.92/7.17 ( ordering_top_set_nat
% 6.92/7.17 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ Y4 @ X4 )
% 6.92/7.17 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_set_nat @ Y4 @ X4 )
% 6.92/7.17 @ bot_bot_set_nat ) ).
% 6.92/7.17
% 6.92/7.17 % bot.ordering_top_axioms
% 6.92/7.17 thf(fact_1991_bot_Oordering__top__axioms,axiom,
% 6.92/7.17 ( ordering_top_assn
% 6.92/7.17 @ ^ [X4: assn,Y4: assn] : ( ord_less_eq_assn @ Y4 @ X4 )
% 6.92/7.17 @ ^ [X4: assn,Y4: assn] : ( ord_less_assn @ Y4 @ X4 )
% 6.92/7.17 @ bot_bot_assn ) ).
% 6.92/7.17
% 6.92/7.17 % bot.ordering_top_axioms
% 6.92/7.17 thf(fact_1992_bot_Oordering__top__axioms,axiom,
% 6.92/7.17 ( ordering_top_set_int
% 6.92/7.17 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_eq_set_int @ Y4 @ X4 )
% 6.92/7.17 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_set_int @ Y4 @ X4 )
% 6.92/7.17 @ bot_bot_set_int ) ).
% 6.92/7.17
% 6.92/7.17 % bot.ordering_top_axioms
% 6.92/7.17 thf(fact_1993_bot_Oordering__top__axioms,axiom,
% 6.92/7.17 ( ordering_top_nat
% 6.92/7.17 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 6.92/7.17 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 )
% 6.92/7.17 @ bot_bot_nat ) ).
% 6.92/7.17
% 6.92/7.17 % bot.ordering_top_axioms
% 6.92/7.17 thf(fact_1994_false__rule,axiom,
% 6.92/7.17 ! [C2: heap_Time_Heap_a,Q2: a > assn] : ( hoare_hoare_triple_a @ bot_bot_assn @ C2 @ Q2 ) ).
% 6.92/7.17
% 6.92/7.17 % false_rule
% 6.92/7.17 thf(fact_1995_false__rule,axiom,
% 6.92/7.17 ! [C2: heap_Time_Heap_b,Q2: b > assn] : ( hoare_hoare_triple_b @ bot_bot_assn @ C2 @ Q2 ) ).
% 6.92/7.17
% 6.92/7.17 % false_rule
% 6.92/7.17 thf(fact_1996_false__rule,axiom,
% 6.92/7.17 ! [C2: heap_T5738788834812785303t_unit,Q2: product_unit > assn] : ( hoare_8945653483474564448t_unit @ bot_bot_assn @ C2 @ Q2 ) ).
% 6.92/7.17
% 6.92/7.17 % false_rule
% 6.92/7.17 thf(fact_1997_bijective__Empty,axiom,
% 6.92/7.17 bijective_nat_nat @ bot_bo2099793752762293965at_nat ).
% 6.92/7.17
% 6.92/7.17 % bijective_Empty
% 6.92/7.17 thf(fact_1998_set__to__map__empty,axiom,
% 6.92/7.17 ( ( set_to_map_nat_nat @ bot_bo2099793752762293965at_nat )
% 6.92/7.17 = ( ^ [X4: nat] : none_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % set_to_map_empty
% 6.92/7.17 thf(fact_1999_ordering__top_Oextremum,axiom,
% 6.92/7.17 ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 6.92/7.17 ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 6.92/7.17 => ( Less_eq @ A @ Top ) ) ).
% 6.92/7.17
% 6.92/7.17 % ordering_top.extremum
% 6.92/7.17 thf(fact_2000_ordering__top_Oextremum__strict,axiom,
% 6.92/7.17 ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 6.92/7.17 ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 6.92/7.17 => ~ ( Less @ Top @ A ) ) ).
% 6.92/7.17
% 6.92/7.17 % ordering_top.extremum_strict
% 6.92/7.17 thf(fact_2001_ordering__top_Oextremum__unique,axiom,
% 6.92/7.17 ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 6.92/7.17 ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 6.92/7.17 => ( ( Less_eq @ Top @ A )
% 6.92/7.17 = ( A = Top ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % ordering_top.extremum_unique
% 6.92/7.17 thf(fact_2002_ordering__top_Onot__eq__extremum,axiom,
% 6.92/7.17 ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 6.92/7.17 ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 6.92/7.17 => ( ( A != Top )
% 6.92/7.17 = ( Less @ A @ Top ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % ordering_top.not_eq_extremum
% 6.92/7.17 thf(fact_2003_ordering__top_Oextremum__uniqueI,axiom,
% 6.92/7.17 ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 6.92/7.17 ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 6.92/7.17 => ( ( Less_eq @ Top @ A )
% 6.92/7.17 => ( A = Top ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % ordering_top.extremum_uniqueI
% 6.92/7.17 thf(fact_2004_bot__empty__eq2,axiom,
% 6.92/7.17 ( bot_bot_int_int_o
% 6.92/7.17 = ( ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ bot_bo1796632182523588997nt_int ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % bot_empty_eq2
% 6.92/7.17 thf(fact_2005_bot__empty__eq2,axiom,
% 6.92/7.17 ( bot_bo5580076615179976505_nat_o
% 6.92/7.17 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ bot_bo1481135142794719944et_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % bot_empty_eq2
% 6.92/7.17 thf(fact_2006_bot__empty__eq2,axiom,
% 6.92/7.17 ( bot_bo3790638025767943357_nat_o
% 6.92/7.17 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ bot_bo5635537948650799172et_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % bot_empty_eq2
% 6.92/7.17 thf(fact_2007_bot__empty__eq2,axiom,
% 6.92/7.17 ( bot_bo5216386038637673661_nat_o
% 6.92/7.17 = ( ^ [X4: b,Y4: produc6653097349344004940it_nat] : ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Y4 ) @ bot_bo8983147464310796868it_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % bot_empty_eq2
% 6.92/7.17 thf(fact_2008_bot__empty__eq2,axiom,
% 6.92/7.17 ( bot_bo3200480807726169982_nat_o
% 6.92/7.17 = ( ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ bot_bo8480459777671986371it_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % bot_empty_eq2
% 6.92/7.17 thf(fact_2009_bot__empty__eq2,axiom,
% 6.92/7.17 ( bot_bot_nat_nat_o
% 6.92/7.17 = ( ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % bot_empty_eq2
% 6.92/7.17 thf(fact_2010_bot__set__def,axiom,
% 6.92/7.17 ( bot_bot_set_list_nat
% 6.92/7.17 = ( collect_list_nat @ bot_bot_list_nat_o ) ) ).
% 6.92/7.17
% 6.92/7.17 % bot_set_def
% 6.92/7.17 thf(fact_2011_bot__set__def,axiom,
% 6.92/7.17 ( bot_bo1488462491386950373nt_int
% 6.92/7.17 = ( collec5210948495886036740nt_int @ bot_bo2686080419298087992_int_o ) ) ).
% 6.92/7.17
% 6.92/7.17 % bot_set_def
% 6.92/7.17 thf(fact_2012_bot__set__def,axiom,
% 6.92/7.17 ( bot_bot_set_set_nat
% 6.92/7.17 = ( collect_set_nat @ bot_bot_set_nat_o ) ) ).
% 6.92/7.17
% 6.92/7.17 % bot_set_def
% 6.92/7.17 thf(fact_2013_bot__set__def,axiom,
% 6.92/7.17 ( bot_bo2099793752762293965at_nat
% 6.92/7.17 = ( collec3392354462482085612at_nat @ bot_bo482883023278783056_nat_o ) ) ).
% 6.92/7.17
% 6.92/7.17 % bot_set_def
% 6.92/7.17 thf(fact_2014_bot__set__def,axiom,
% 6.92/7.17 ( bot_bot_set_o
% 6.92/7.17 = ( collect_o @ bot_bot_o_o ) ) ).
% 6.92/7.17
% 6.92/7.17 % bot_set_def
% 6.92/7.17 thf(fact_2015_bot__set__def,axiom,
% 6.92/7.17 ( bot_bot_set_nat
% 6.92/7.17 = ( collect_nat @ bot_bot_nat_o ) ) ).
% 6.92/7.17
% 6.92/7.17 % bot_set_def
% 6.92/7.17 thf(fact_2016_bot__set__def,axiom,
% 6.92/7.17 ( bot_bot_set_int
% 6.92/7.17 = ( collect_int @ bot_bot_int_o ) ) ).
% 6.92/7.17
% 6.92/7.17 % bot_set_def
% 6.92/7.17 thf(fact_2017_bot__option__def,axiom,
% 6.92/7.17 bot_bot_option_num = none_num ).
% 6.92/7.17
% 6.92/7.17 % bot_option_def
% 6.92/7.17 thf(fact_2018_mod__false,axiom,
% 6.92/7.17 ! [H: produc3658429121746597890et_nat] :
% 6.92/7.17 ~ ( rep_assn @ bot_bot_assn @ H ) ).
% 6.92/7.17
% 6.92/7.17 % mod_false
% 6.92/7.17 thf(fact_2019_less__by__empty,axiom,
% 6.92/7.17 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.17 ( ( A4 = bot_bo2099793752762293965at_nat )
% 6.92/7.17 => ( ord_le3146513528884898305at_nat @ A4 @ B5 ) ) ).
% 6.92/7.17
% 6.92/7.17 % less_by_empty
% 6.92/7.17 thf(fact_2020_raise__rule,axiom,
% 6.92/7.17 ! [S2: list_char,Q2: a > assn] : ( hoare_hoare_triple_a @ bot_bot_assn @ ( heap_Time_raise_a @ S2 ) @ Q2 ) ).
% 6.92/7.17
% 6.92/7.17 % raise_rule
% 6.92/7.17 thf(fact_2021_raise__rule,axiom,
% 6.92/7.17 ! [S2: list_char,Q2: b > assn] : ( hoare_hoare_triple_b @ bot_bot_assn @ ( heap_Time_raise_b @ S2 ) @ Q2 ) ).
% 6.92/7.17
% 6.92/7.17 % raise_rule
% 6.92/7.17 thf(fact_2022_raise__rule,axiom,
% 6.92/7.17 ! [S2: list_char,Q2: product_unit > assn] : ( hoare_8945653483474564448t_unit @ bot_bot_assn @ ( heap_T2927564422264180874t_unit @ S2 ) @ Q2 ) ).
% 6.92/7.17
% 6.92/7.17 % raise_rule
% 6.92/7.17 thf(fact_2023_raise__iff,axiom,
% 6.92/7.17 ! [P2: assn,S2: list_char,Q2: a > assn] :
% 6.92/7.17 ( ( hoare_hoare_triple_a @ P2 @ ( heap_Time_raise_a @ S2 ) @ Q2 )
% 6.92/7.17 = ( P2 = bot_bot_assn ) ) ).
% 6.92/7.17
% 6.92/7.17 % raise_iff
% 6.92/7.17 thf(fact_2024_raise__iff,axiom,
% 6.92/7.17 ! [P2: assn,S2: list_char,Q2: b > assn] :
% 6.92/7.17 ( ( hoare_hoare_triple_b @ P2 @ ( heap_Time_raise_b @ S2 ) @ Q2 )
% 6.92/7.17 = ( P2 = bot_bot_assn ) ) ).
% 6.92/7.17
% 6.92/7.17 % raise_iff
% 6.92/7.17 thf(fact_2025_raise__iff,axiom,
% 6.92/7.17 ! [P2: assn,S2: list_char,Q2: product_unit > assn] :
% 6.92/7.17 ( ( hoare_8945653483474564448t_unit @ P2 @ ( heap_T2927564422264180874t_unit @ S2 ) @ Q2 )
% 6.92/7.17 = ( P2 = bot_bot_assn ) ) ).
% 6.92/7.17
% 6.92/7.17 % raise_iff
% 6.92/7.17 thf(fact_2026_set__to__map__empty__iff_I1_J,axiom,
% 6.92/7.17 ! [S: set_Pr1261947904930325089at_nat] :
% 6.92/7.17 ( ( ( set_to_map_nat_nat @ S )
% 6.92/7.17 = ( ^ [X4: nat] : none_nat ) )
% 6.92/7.17 = ( S = bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % set_to_map_empty_iff(1)
% 6.92/7.17 thf(fact_2027_set__to__map__empty__iff_I2_J,axiom,
% 6.92/7.17 ! [S: set_Pr1261947904930325089at_nat] :
% 6.92/7.17 ( ( ( ^ [X4: nat] : none_nat )
% 6.92/7.17 = ( set_to_map_nat_nat @ S ) )
% 6.92/7.17 = ( S = bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % set_to_map_empty_iff(2)
% 6.92/7.17 thf(fact_2028_dflt__None__set__def,axiom,
% 6.92/7.17 ( dflt_N6592383573632408824at_nat
% 6.92/7.17 = ( ^ [S4: set_Pr1261947904930325089at_nat] : ( if_opt7704869406773131885at_nat @ ( S4 = bot_bo2099793752762293965at_nat ) @ none_s625347054029921090at_nat @ ( some_s147305329494351046at_nat @ S4 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % dflt_None_set_def
% 6.92/7.17 thf(fact_2029_dflt__None__set__def,axiom,
% 6.92/7.17 ( dflt_None_set_o
% 6.92/7.17 = ( ^ [S4: set_o] : ( if_option_set_o @ ( S4 = bot_bot_set_o ) @ none_set_o @ ( some_set_o @ S4 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % dflt_None_set_def
% 6.92/7.17 thf(fact_2030_dflt__None__set__def,axiom,
% 6.92/7.17 ( dflt_None_set_nat
% 6.92/7.17 = ( ^ [S4: set_nat] : ( if_option_set_nat @ ( S4 = bot_bot_set_nat ) @ none_set_nat @ ( some_set_nat @ S4 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % dflt_None_set_def
% 6.92/7.17 thf(fact_2031_dflt__None__set__def,axiom,
% 6.92/7.17 ( dflt_None_set_int
% 6.92/7.17 = ( ^ [S4: set_int] : ( if_option_set_int @ ( S4 = bot_bot_set_int ) @ none_set_int @ ( some_set_int @ S4 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % dflt_None_set_def
% 6.92/7.17 thf(fact_2032_rel__of__empty,axiom,
% 6.92/7.17 ! [P2: product_prod_nat_nat > $o] :
% 6.92/7.17 ( ( rel_of_nat_nat
% 6.92/7.17 @ ^ [X4: nat] : none_nat
% 6.92/7.17 @ P2 )
% 6.92/7.17 = bot_bo2099793752762293965at_nat ) ).
% 6.92/7.17
% 6.92/7.17 % rel_of_empty
% 6.92/7.17 thf(fact_2033_discrete,axiom,
% 6.92/7.17 ( ord_le6747313008572928689nteger
% 6.92/7.17 = ( ^ [A5: code_integer] : ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A5 @ one_one_Code_integer ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % discrete
% 6.92/7.17 thf(fact_2034_discrete,axiom,
% 6.92/7.17 ( ord_less_nat
% 6.92/7.17 = ( ^ [A5: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A5 @ one_one_nat ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % discrete
% 6.92/7.17 thf(fact_2035_discrete,axiom,
% 6.92/7.17 ( ord_less_int
% 6.92/7.17 = ( ^ [A5: int] : ( ord_less_eq_int @ ( plus_plus_int @ A5 @ one_one_int ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % discrete
% 6.92/7.17 thf(fact_2036_tap__def,axiom,
% 6.92/7.17 ( heap_Time_tap_b
% 6.92/7.17 = ( ^ [F3: heap_e7401611519738050253t_unit > b] :
% 6.92/7.17 ( heap_Time_Heap_b2
% 6.92/7.17 @ ^ [H6: heap_e7401611519738050253t_unit] : ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ ( F3 @ H6 ) @ ( produc584006145561248582it_nat @ H6 @ one_one_nat ) ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % tap_def
% 6.92/7.17 thf(fact_2037_tap__def,axiom,
% 6.92/7.17 ( heap_Time_tap_a
% 6.92/7.17 = ( ^ [F3: heap_e7401611519738050253t_unit > a] :
% 6.92/7.17 ( heap_Time_Heap_a2
% 6.92/7.17 @ ^ [H6: heap_e7401611519738050253t_unit] : ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ ( F3 @ H6 ) @ ( produc584006145561248582it_nat @ H6 @ one_one_nat ) ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % tap_def
% 6.92/7.17 thf(fact_2038_tap__def,axiom,
% 6.92/7.17 ( heap_T560649228465745139t_unit
% 6.92/7.17 = ( ^ [F3: heap_e7401611519738050253t_unit > product_unit] :
% 6.92/7.17 ( heap_T6183433275982383450t_unit
% 6.92/7.17 @ ^ [H6: heap_e7401611519738050253t_unit] : ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ ( F3 @ H6 ) @ ( produc584006145561248582it_nat @ H6 @ one_one_nat ) ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % tap_def
% 6.92/7.17 thf(fact_2039_execute__tap,axiom,
% 6.92/7.17 ! [F: heap_e7401611519738050253t_unit > product_unit,H: heap_e7401611519738050253t_unit] :
% 6.92/7.17 ( ( heap_T875086893843062177t_unit @ ( heap_T560649228465745139t_unit @ F ) @ H )
% 6.92/7.17 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ ( F @ H ) @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_tap
% 6.92/7.17 thf(fact_2040_execute__tap,axiom,
% 6.92/7.17 ! [F: heap_e7401611519738050253t_unit > b,H: heap_e7401611519738050253t_unit] :
% 6.92/7.17 ( ( heap_Time_execute_b @ ( heap_Time_tap_b @ F ) @ H )
% 6.92/7.17 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ ( F @ H ) @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_tap
% 6.92/7.17 thf(fact_2041_execute__tap,axiom,
% 6.92/7.17 ! [F: heap_e7401611519738050253t_unit > a,H: heap_e7401611519738050253t_unit] :
% 6.92/7.17 ( ( heap_Time_execute_a @ ( heap_Time_tap_a @ F ) @ H )
% 6.92/7.17 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ ( F @ H ) @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_tap
% 6.92/7.17 thf(fact_2042_add__mono1,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ A @ B )
% 6.92/7.17 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ B @ one_one_Code_integer ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_mono1
% 6.92/7.17 thf(fact_2043_add__mono1,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_rat @ A @ B )
% 6.92/7.17 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_mono1
% 6.92/7.17 thf(fact_2044_add__mono1,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_nat @ A @ B )
% 6.92/7.17 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_mono1
% 6.92/7.17 thf(fact_2045_add__mono1,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_int @ A @ B )
% 6.92/7.17 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_mono1
% 6.92/7.17 thf(fact_2046_less__add__one,axiom,
% 6.92/7.17 ! [A: code_integer] : ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) ) ).
% 6.92/7.17
% 6.92/7.17 % less_add_one
% 6.92/7.17 thf(fact_2047_less__add__one,axiom,
% 6.92/7.17 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 6.92/7.17
% 6.92/7.17 % less_add_one
% 6.92/7.17 thf(fact_2048_less__add__one,axiom,
% 6.92/7.17 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % less_add_one
% 6.92/7.17 thf(fact_2049_less__add__one,axiom,
% 6.92/7.17 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 6.92/7.17
% 6.92/7.17 % less_add_one
% 6.92/7.17 thf(fact_2050_assn__basic__inequalities_I3_J,axiom,
% 6.92/7.17 bot_bot_assn != one_one_assn ).
% 6.92/7.17
% 6.92/7.17 % assn_basic_inequalities(3)
% 6.92/7.17 thf(fact_2051_return__wp__rule,axiom,
% 6.92/7.17 ! [Q2: a > assn,X: a] : ( hoare_hoare_triple_a @ ( Q2 @ X ) @ ( heap_Time_return_a @ X ) @ Q2 ) ).
% 6.92/7.17
% 6.92/7.17 % return_wp_rule
% 6.92/7.17 thf(fact_2052_return__wp__rule,axiom,
% 6.92/7.17 ! [Q2: b > assn,X: b] : ( hoare_hoare_triple_b @ ( Q2 @ X ) @ ( heap_Time_return_b @ X ) @ Q2 ) ).
% 6.92/7.17
% 6.92/7.17 % return_wp_rule
% 6.92/7.17 thf(fact_2053_return__wp__rule,axiom,
% 6.92/7.17 ! [Q2: product_unit > assn,X: product_unit] : ( hoare_8945653483474564448t_unit @ ( Q2 @ X ) @ ( heap_T7507251653302230130t_unit @ X ) @ Q2 ) ).
% 6.92/7.17
% 6.92/7.17 % return_wp_rule
% 6.92/7.17 thf(fact_2054_wait__rule,axiom,
% 6.92/7.17 ! [N2: nat] :
% 6.92/7.17 ( hoare_8945653483474564448t_unit @ one_one_assn @ ( heap_Time_wait @ N2 )
% 6.92/7.17 @ ^ [Uu2: product_unit] : one_one_assn ) ).
% 6.92/7.17
% 6.92/7.17 % wait_rule
% 6.92/7.17 thf(fact_2055_linorder__neqE__linordered__idom,axiom,
% 6.92/7.17 ! [X: rat,Y: rat] :
% 6.92/7.17 ( ( X != Y )
% 6.92/7.17 => ( ~ ( ord_less_rat @ X @ Y )
% 6.92/7.17 => ( ord_less_rat @ Y @ X ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % linorder_neqE_linordered_idom
% 6.92/7.17 thf(fact_2056_linorder__neqE__linordered__idom,axiom,
% 6.92/7.17 ! [X: int,Y: int] :
% 6.92/7.17 ( ( X != Y )
% 6.92/7.17 => ( ~ ( ord_less_int @ X @ Y )
% 6.92/7.17 => ( ord_less_int @ Y @ X ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % linorder_neqE_linordered_idom
% 6.92/7.17 thf(fact_2057_bounded__Max__nat,axiom,
% 6.92/7.17 ! [P2: nat > $o,X: nat,M6: nat] :
% 6.92/7.17 ( ( P2 @ X )
% 6.92/7.17 => ( ! [X3: nat] :
% 6.92/7.17 ( ( P2 @ X3 )
% 6.92/7.17 => ( ord_less_eq_nat @ X3 @ M6 ) )
% 6.92/7.17 => ~ ! [M5: nat] :
% 6.92/7.17 ( ( P2 @ M5 )
% 6.92/7.17 => ~ ! [X6: nat] :
% 6.92/7.17 ( ( P2 @ X6 )
% 6.92/7.17 => ( ord_less_eq_nat @ X6 @ M5 ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % bounded_Max_nat
% 6.92/7.17 thf(fact_2058_mod__emp__simp,axiom,
% 6.92/7.17 ! [H: heap_e7401611519738050253t_unit] : ( rep_assn @ one_one_assn @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % mod_emp_simp
% 6.92/7.17 thf(fact_2059_return__def,axiom,
% 6.92/7.17 ( heap_Time_return_b
% 6.92/7.17 = ( ^ [X4: b] :
% 6.92/7.17 ( heap_Time_heap_b
% 6.92/7.17 @ ^ [H6: heap_e7401611519738050253t_unit] : ( produc4082563078715348724it_nat @ X4 @ ( produc584006145561248582it_nat @ H6 @ one_one_nat ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % return_def
% 6.92/7.17 thf(fact_2060_return__def,axiom,
% 6.92/7.17 ( heap_Time_return_a
% 6.92/7.17 = ( ^ [X4: a] :
% 6.92/7.17 ( heap_Time_heap_a
% 6.92/7.17 @ ^ [H6: heap_e7401611519738050253t_unit] : ( produc9178034014595674355it_nat @ X4 @ ( produc584006145561248582it_nat @ H6 @ one_one_nat ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % return_def
% 6.92/7.17 thf(fact_2061_execute__lookup,axiom,
% 6.92/7.17 ! [R2: ref_Product_unit,H: heap_e7401611519738050253t_unit] :
% 6.92/7.17 ( ( heap_T875086893843062177t_unit @ ( ref_lo7930775386976318366t_unit @ R2 ) @ H )
% 6.92/7.17 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ ( ref_get_Product_unit @ H @ R2 ) @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_lookup
% 6.92/7.17 thf(fact_2062_execute__return,axiom,
% 6.92/7.17 ! [X: product_unit] :
% 6.92/7.17 ( ( heap_T875086893843062177t_unit @ ( heap_T7507251653302230130t_unit @ X ) )
% 6.92/7.17 = ( comp_P3118722334806803912t_unit @ some_P1914260805536162275it_nat
% 6.92/7.17 @ ^ [H6: heap_e7401611519738050253t_unit] : ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H6 @ one_one_nat ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_return
% 6.92/7.17 thf(fact_2063_execute__return,axiom,
% 6.92/7.17 ! [X: b] :
% 6.92/7.17 ( ( heap_Time_execute_b @ ( heap_Time_return_b @ X ) )
% 6.92/7.17 = ( comp_P6401406225962756324t_unit @ some_P2818173045054083285it_nat
% 6.92/7.17 @ ^ [H6: heap_e7401611519738050253t_unit] : ( produc4082563078715348724it_nat @ X @ ( produc584006145561248582it_nat @ H6 @ one_one_nat ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_return
% 6.92/7.17 thf(fact_2064_execute__return,axiom,
% 6.92/7.17 ! [X: a] :
% 6.92/7.17 ( ( heap_Time_execute_a @ ( heap_Time_return_a @ X ) )
% 6.92/7.17 = ( comp_P8552900652980440422t_unit @ some_P7913643980934408916it_nat
% 6.92/7.17 @ ^ [H6: heap_e7401611519738050253t_unit] : ( produc9178034014595674355it_nat @ X @ ( produc584006145561248582it_nat @ H6 @ one_one_nat ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_return
% 6.92/7.17 thf(fact_2065_less__numeral__extra_I4_J,axiom,
% 6.92/7.17 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 6.92/7.17
% 6.92/7.17 % less_numeral_extra(4)
% 6.92/7.17 thf(fact_2066_less__numeral__extra_I4_J,axiom,
% 6.92/7.17 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 6.92/7.17
% 6.92/7.17 % less_numeral_extra(4)
% 6.92/7.17 thf(fact_2067_less__numeral__extra_I4_J,axiom,
% 6.92/7.17 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 6.92/7.17
% 6.92/7.17 % less_numeral_extra(4)
% 6.92/7.17 thf(fact_2068_less__numeral__extra_I4_J,axiom,
% 6.92/7.17 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 6.92/7.17
% 6.92/7.17 % less_numeral_extra(4)
% 6.92/7.17 thf(fact_2069_le__numeral__extra_I4_J,axiom,
% 6.92/7.17 ord_le3102999989581377725nteger @ one_one_Code_integer @ one_one_Code_integer ).
% 6.92/7.17
% 6.92/7.17 % le_numeral_extra(4)
% 6.92/7.17 thf(fact_2070_le__numeral__extra_I4_J,axiom,
% 6.92/7.17 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 6.92/7.17
% 6.92/7.17 % le_numeral_extra(4)
% 6.92/7.17 thf(fact_2071_le__numeral__extra_I4_J,axiom,
% 6.92/7.17 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 6.92/7.17
% 6.92/7.17 % le_numeral_extra(4)
% 6.92/7.17 thf(fact_2072_le__numeral__extra_I4_J,axiom,
% 6.92/7.17 ord_less_eq_int @ one_one_int @ one_one_int ).
% 6.92/7.17
% 6.92/7.17 % le_numeral_extra(4)
% 6.92/7.17 thf(fact_2073_map__to__set__empty,axiom,
% 6.92/7.17 ( ( map_to_set_nat_nat
% 6.92/7.17 @ ^ [X4: nat] : none_nat )
% 6.92/7.17 = bot_bo2099793752762293965at_nat ) ).
% 6.92/7.17
% 6.92/7.17 % map_to_set_empty
% 6.92/7.17 thf(fact_2074_type__copy__map__cong0,axiom,
% 6.92/7.17 ! [M6: code_integer > code_integer,G: code_integer > code_integer,X: code_integer,N7: code_integer > code_integer,H: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 6.92/7.17 ( ( ( M6 @ ( G @ X ) )
% 6.92/7.17 = ( N7 @ ( H @ X ) ) )
% 6.92/7.17 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M6 ) @ G @ X )
% 6.92/7.17 = ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ N7 ) @ H @ X ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % type_copy_map_cong0
% 6.92/7.17 thf(fact_2075_type__copy__map__cong0,axiom,
% 6.92/7.17 ! [M6: code_integer > code_integer,G: code_integer > code_integer,X: code_integer,N7: ( code_integer > code_integer ) > code_integer,H: code_integer > code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 6.92/7.17 ( ( ( M6 @ ( G @ X ) )
% 6.92/7.17 = ( N7 @ ( H @ X ) ) )
% 6.92/7.17 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M6 ) @ G @ X )
% 6.92/7.17 = ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ F @ N7 ) @ H @ X ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % type_copy_map_cong0
% 6.92/7.17 thf(fact_2076_type__copy__map__cong0,axiom,
% 6.92/7.17 ! [M6: code_integer > code_integer > code_integer,G: code_integer > code_integer,X: code_integer,N7: code_integer > code_integer > code_integer,H: code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 6.92/7.17 ( ( ( M6 @ ( G @ X ) )
% 6.92/7.17 = ( N7 @ ( H @ X ) ) )
% 6.92/7.17 => ( ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ M6 ) @ G @ X )
% 6.92/7.17 = ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ N7 ) @ H @ X ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % type_copy_map_cong0
% 6.92/7.17 thf(fact_2077_type__copy__map__cong0,axiom,
% 6.92/7.17 ! [M6: code_integer > code_integer > code_integer,G: code_integer > code_integer,X: code_integer,N7: ( code_integer > code_integer ) > code_integer > code_integer,H: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 6.92/7.17 ( ( ( M6 @ ( G @ X ) )
% 6.92/7.17 = ( N7 @ ( H @ X ) ) )
% 6.92/7.17 => ( ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ M6 ) @ G @ X )
% 6.92/7.17 = ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ F @ N7 ) @ H @ X ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % type_copy_map_cong0
% 6.92/7.17 thf(fact_2078_type__copy__map__cong0,axiom,
% 6.92/7.17 ! [M6: ( code_integer > code_integer ) > code_integer,G: code_integer > code_integer > code_integer,X: code_integer,N7: code_integer > code_integer,H: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 6.92/7.17 ( ( ( M6 @ ( G @ X ) )
% 6.92/7.17 = ( N7 @ ( H @ X ) ) )
% 6.92/7.17 => ( ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ F @ M6 ) @ G @ X )
% 6.92/7.17 = ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ N7 ) @ H @ X ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % type_copy_map_cong0
% 6.92/7.17 thf(fact_2079_type__copy__map__cong0,axiom,
% 6.92/7.17 ! [M6: ( code_integer > code_integer ) > code_integer > code_integer,G: code_integer > code_integer > code_integer,X: code_integer,N7: code_integer > code_integer > code_integer,H: code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 6.92/7.17 ( ( ( M6 @ ( G @ X ) )
% 6.92/7.17 = ( N7 @ ( H @ X ) ) )
% 6.92/7.17 => ( ( comp_C8797469213163452608nteger @ ( comp_C3983183376822107068nteger @ F @ M6 ) @ G @ X )
% 6.92/7.17 = ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ N7 ) @ H @ X ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % type_copy_map_cong0
% 6.92/7.17 thf(fact_2080_type__copy__map__cong0,axiom,
% 6.92/7.17 ! [M6: int > int,G: int > int,X: int,N7: int > int,H: int > int,F: int > nat] :
% 6.92/7.17 ( ( ( M6 @ ( G @ X ) )
% 6.92/7.17 = ( N7 @ ( H @ X ) ) )
% 6.92/7.17 => ( ( comp_int_nat_int @ ( comp_int_nat_int @ F @ M6 ) @ G @ X )
% 6.92/7.17 = ( comp_int_nat_int @ ( comp_int_nat_int @ F @ N7 ) @ H @ X ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % type_copy_map_cong0
% 6.92/7.17 thf(fact_2081_comp__cong__left,axiom,
% 6.92/7.17 ! [X: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,Y: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer] :
% 6.92/7.17 ( ( X = Y )
% 6.92/7.17 => ( ( comp_C1593894019821074884nteger @ X @ F )
% 6.92/7.17 = ( comp_C1593894019821074884nteger @ Y @ F ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % comp_cong_left
% 6.92/7.17 thf(fact_2082_comp__cong__left,axiom,
% 6.92/7.17 ! [X: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,Y: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer] :
% 6.92/7.17 ( ( X = Y )
% 6.92/7.17 => ( ( comp_C8797469213163452608nteger @ X @ F )
% 6.92/7.17 = ( comp_C8797469213163452608nteger @ Y @ F ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % comp_cong_left
% 6.92/7.17 thf(fact_2083_comp__cong__left,axiom,
% 6.92/7.17 ! [X: int > nat,Y: int > nat,F: int > int] :
% 6.92/7.17 ( ( X = Y )
% 6.92/7.17 => ( ( comp_int_nat_int @ X @ F )
% 6.92/7.17 = ( comp_int_nat_int @ Y @ F ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % comp_cong_left
% 6.92/7.17 thf(fact_2084_comp__cong__right,axiom,
% 6.92/7.17 ! [X: code_integer > code_integer,Y: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 6.92/7.17 ( ( X = Y )
% 6.92/7.17 => ( ( comp_C1593894019821074884nteger @ F @ X )
% 6.92/7.17 = ( comp_C1593894019821074884nteger @ F @ Y ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % comp_cong_right
% 6.92/7.17 thf(fact_2085_comp__cong__right,axiom,
% 6.92/7.17 ! [X: code_integer > code_integer > code_integer,Y: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 6.92/7.17 ( ( X = Y )
% 6.92/7.17 => ( ( comp_C8797469213163452608nteger @ F @ X )
% 6.92/7.17 = ( comp_C8797469213163452608nteger @ F @ Y ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % comp_cong_right
% 6.92/7.17 thf(fact_2086_comp__cong__right,axiom,
% 6.92/7.17 ! [X: int > int,Y: int > int,F: int > nat] :
% 6.92/7.17 ( ( X = Y )
% 6.92/7.17 => ( ( comp_int_nat_int @ F @ X )
% 6.92/7.17 = ( comp_int_nat_int @ F @ Y ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % comp_cong_right
% 6.92/7.17 thf(fact_2087_fun__comp__eq__conv,axiom,
% 6.92/7.17 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,Fg: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 6.92/7.17 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 6.92/7.17 = Fg )
% 6.92/7.17 = ( ! [X4: code_integer] :
% 6.92/7.17 ( ( F @ ( G @ X4 ) )
% 6.92/7.17 = ( Fg @ X4 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % fun_comp_eq_conv
% 6.92/7.17 thf(fact_2088_fun__comp__eq__conv,axiom,
% 6.92/7.17 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,Fg: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 6.92/7.17 ( ( ( comp_C8797469213163452608nteger @ F @ G )
% 6.92/7.17 = Fg )
% 6.92/7.17 = ( ! [X4: code_integer] :
% 6.92/7.17 ( ( F @ ( G @ X4 ) )
% 6.92/7.17 = ( Fg @ X4 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % fun_comp_eq_conv
% 6.92/7.17 thf(fact_2089_fun__comp__eq__conv,axiom,
% 6.92/7.17 ! [F: int > nat,G: int > int,Fg: int > nat] :
% 6.92/7.17 ( ( ( comp_int_nat_int @ F @ G )
% 6.92/7.17 = Fg )
% 6.92/7.17 = ( ! [X4: int] :
% 6.92/7.17 ( ( F @ ( G @ X4 ) )
% 6.92/7.17 = ( Fg @ X4 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % fun_comp_eq_conv
% 6.92/7.17 thf(fact_2090_comp__cong,axiom,
% 6.92/7.17 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: code_integer,F4: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer,X10: code_integer] :
% 6.92/7.17 ( ( ( F @ ( G @ X ) )
% 6.92/7.17 = ( F4 @ ( G2 @ X10 ) ) )
% 6.92/7.17 => ( ( comp_C1593894019821074884nteger @ F @ G @ X )
% 6.92/7.17 = ( comp_C1593894019821074884nteger @ F4 @ G2 @ X10 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % comp_cong
% 6.92/7.17 thf(fact_2091_comp__cong,axiom,
% 6.92/7.17 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: code_integer,F4: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer > code_integer,X10: code_integer] :
% 6.92/7.17 ( ( ( F @ ( G @ X ) )
% 6.92/7.17 = ( F4 @ ( G2 @ X10 ) ) )
% 6.92/7.17 => ( ( comp_C1593894019821074884nteger @ F @ G @ X )
% 6.92/7.17 = ( comp_C8797469213163452608nteger @ F4 @ G2 @ X10 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % comp_cong
% 6.92/7.17 thf(fact_2092_comp__cong,axiom,
% 6.92/7.17 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: code_integer,F4: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer,X10: code_integer] :
% 6.92/7.17 ( ( ( F @ ( G @ X ) )
% 6.92/7.17 = ( F4 @ ( G2 @ X10 ) ) )
% 6.92/7.17 => ( ( comp_C8797469213163452608nteger @ F @ G @ X )
% 6.92/7.17 = ( comp_C1593894019821074884nteger @ F4 @ G2 @ X10 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % comp_cong
% 6.92/7.17 thf(fact_2093_comp__cong,axiom,
% 6.92/7.17 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: code_integer,F4: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer > code_integer,X10: code_integer] :
% 6.92/7.17 ( ( ( F @ ( G @ X ) )
% 6.92/7.17 = ( F4 @ ( G2 @ X10 ) ) )
% 6.92/7.17 => ( ( comp_C8797469213163452608nteger @ F @ G @ X )
% 6.92/7.17 = ( comp_C8797469213163452608nteger @ F4 @ G2 @ X10 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % comp_cong
% 6.92/7.17 thf(fact_2094_comp__cong,axiom,
% 6.92/7.17 ! [F: int > nat,G: int > int,X: int,F4: int > nat,G2: int > int,X10: int] :
% 6.92/7.17 ( ( ( F @ ( G @ X ) )
% 6.92/7.17 = ( F4 @ ( G2 @ X10 ) ) )
% 6.92/7.17 => ( ( comp_int_nat_int @ F @ G @ X )
% 6.92/7.17 = ( comp_int_nat_int @ F4 @ G2 @ X10 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % comp_cong
% 6.92/7.17 thf(fact_2095_execute__heap,axiom,
% 6.92/7.17 ! [F: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] :
% 6.92/7.17 ( ( heap_T875086893843062177t_unit @ ( heap_T6927113302350381334t_unit @ F ) )
% 6.92/7.17 = ( comp_P3118722334806803912t_unit @ some_P1914260805536162275it_nat @ F ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_heap
% 6.92/7.17 thf(fact_2096_execute__heap,axiom,
% 6.92/7.17 ! [F: heap_e7401611519738050253t_unit > produc7388388658123137530it_nat] :
% 6.92/7.17 ( ( heap_Time_execute_b @ ( heap_Time_heap_b @ F ) )
% 6.92/7.17 = ( comp_P6401406225962756324t_unit @ some_P2818173045054083285it_nat @ F ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_heap
% 6.92/7.17 thf(fact_2097_execute__heap,axiom,
% 6.92/7.17 ! [F: heap_e7401611519738050253t_unit > produc3260487557148687353it_nat] :
% 6.92/7.17 ( ( heap_Time_execute_a @ ( heap_Time_heap_a @ F ) )
% 6.92/7.17 = ( comp_P8552900652980440422t_unit @ some_P7913643980934408916it_nat @ F ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_heap
% 6.92/7.17 thf(fact_2098_heap__def,axiom,
% 6.92/7.17 ( heap_Time_heap_b
% 6.92/7.17 = ( ^ [F3: heap_e7401611519738050253t_unit > produc7388388658123137530it_nat] : ( heap_Time_Heap_b2 @ ( comp_P6401406225962756324t_unit @ some_P2818173045054083285it_nat @ F3 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % heap_def
% 6.92/7.17 thf(fact_2099_heap__def,axiom,
% 6.92/7.17 ( heap_Time_heap_a
% 6.92/7.17 = ( ^ [F3: heap_e7401611519738050253t_unit > produc3260487557148687353it_nat] : ( heap_Time_Heap_a2 @ ( comp_P8552900652980440422t_unit @ some_P7913643980934408916it_nat @ F3 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % heap_def
% 6.92/7.17 thf(fact_2100_heap__def,axiom,
% 6.92/7.17 ( heap_T6927113302350381334t_unit
% 6.92/7.17 = ( ^ [F3: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] : ( heap_T6183433275982383450t_unit @ ( comp_P3118722334806803912t_unit @ some_P1914260805536162275it_nat @ F3 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % heap_def
% 6.92/7.17 thf(fact_2101_is__num__normalize_I1_J,axiom,
% 6.92/7.17 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.17 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 6.92/7.17 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % is_num_normalize(1)
% 6.92/7.17 thf(fact_2102_is__num__normalize_I1_J,axiom,
% 6.92/7.17 ! [A: int,B: int,C2: int] :
% 6.92/7.17 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 6.92/7.17 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % is_num_normalize(1)
% 6.92/7.17 thf(fact_2103_map__to__set__empty__iff_I2_J,axiom,
% 6.92/7.17 ! [M: nat > option_nat] :
% 6.92/7.17 ( ( bot_bo2099793752762293965at_nat
% 6.92/7.17 = ( map_to_set_nat_nat @ M ) )
% 6.92/7.17 = ( M
% 6.92/7.17 = ( ^ [X4: nat] : none_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % map_to_set_empty_iff(2)
% 6.92/7.17 thf(fact_2104_map__to__set__empty__iff_I1_J,axiom,
% 6.92/7.17 ! [M: nat > option_nat] :
% 6.92/7.17 ( ( ( map_to_set_nat_nat @ M )
% 6.92/7.17 = bot_bo2099793752762293965at_nat )
% 6.92/7.17 = ( M
% 6.92/7.17 = ( ^ [X4: nat] : none_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % map_to_set_empty_iff(1)
% 6.92/7.17 thf(fact_2105_fold__atLeastAtMost__nat_Opsimps,axiom,
% 6.92/7.17 ! [F: nat > nat > nat,A: nat,B: nat,Acc: nat] :
% 6.92/7.17 ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ F @ ( produc487386426758144856at_nat @ A @ ( product_Pair_nat_nat @ B @ Acc ) ) ) )
% 6.92/7.17 => ( ( ( ord_less_nat @ B @ A )
% 6.92/7.17 => ( ( set_fo2584398358068434914at_nat @ F @ A @ B @ Acc )
% 6.92/7.17 = Acc ) )
% 6.92/7.17 & ( ~ ( ord_less_nat @ B @ A )
% 6.92/7.17 => ( ( set_fo2584398358068434914at_nat @ F @ A @ B @ Acc )
% 6.92/7.17 = ( set_fo2584398358068434914at_nat @ F @ ( plus_plus_nat @ A @ one_one_nat ) @ B @ ( F @ A @ Acc ) ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % fold_atLeastAtMost_nat.psimps
% 6.92/7.17 thf(fact_2106_fold__atLeastAtMost__nat_Opelims,axiom,
% 6.92/7.17 ! [X: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 6.92/7.17 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa @ Xb @ Xc )
% 6.92/7.17 = Y )
% 6.92/7.17 => ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) )
% 6.92/7.17 => ~ ( ( ( ( ord_less_nat @ Xb @ Xa )
% 6.92/7.17 => ( Y = Xc ) )
% 6.92/7.17 & ( ~ ( ord_less_nat @ Xb @ Xa )
% 6.92/7.17 => ( Y
% 6.92/7.17 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X @ Xa @ Xc ) ) ) ) )
% 6.92/7.17 => ~ ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % fold_atLeastAtMost_nat.pelims
% 6.92/7.17 thf(fact_2107_Set_Ois__empty__def,axiom,
% 6.92/7.17 ( is_emp1662574758705540307at_nat
% 6.92/7.17 = ( ^ [A6: set_Pr1261947904930325089at_nat] : ( A6 = bot_bo2099793752762293965at_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % Set.is_empty_def
% 6.92/7.17 thf(fact_2108_Set_Ois__empty__def,axiom,
% 6.92/7.17 ( is_empty_o
% 6.92/7.17 = ( ^ [A6: set_o] : ( A6 = bot_bot_set_o ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % Set.is_empty_def
% 6.92/7.17 thf(fact_2109_Set_Ois__empty__def,axiom,
% 6.92/7.17 ( is_empty_nat
% 6.92/7.17 = ( ^ [A6: set_nat] : ( A6 = bot_bot_set_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % Set.is_empty_def
% 6.92/7.17 thf(fact_2110_Set_Ois__empty__def,axiom,
% 6.92/7.17 ( is_empty_int
% 6.92/7.17 = ( ^ [A6: set_int] : ( A6 = bot_bot_set_int ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % Set.is_empty_def
% 6.92/7.17 thf(fact_2111_Heap__lub__empty,axiom,
% 6.92/7.17 ( ( heap_T4436805183663264329t_unit @ bot_bo8105976889876132193t_unit )
% 6.92/7.17 = ( heap_T6183433275982383450t_unit
% 6.92/7.17 @ ^ [X4: heap_e7401611519738050253t_unit] : none_P9117596204409417319it_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % Heap_lub_empty
% 6.92/7.17 thf(fact_2112_fold__atLeastAtMost__nat_Osimps,axiom,
% 6.92/7.17 ( set_fo2584398358068434914at_nat
% 6.92/7.17 = ( ^ [F3: nat > nat > nat,A5: nat,B4: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B4 @ A5 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A5 @ one_one_nat ) @ B4 @ ( F3 @ A5 @ Acc2 ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % fold_atLeastAtMost_nat.simps
% 6.92/7.17 thf(fact_2113_fold__atLeastAtMost__nat_Oelims,axiom,
% 6.92/7.17 ! [X: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 6.92/7.17 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa @ Xb @ Xc )
% 6.92/7.17 = Y )
% 6.92/7.17 => ( ( ( ord_less_nat @ Xb @ Xa )
% 6.92/7.17 => ( Y = Xc ) )
% 6.92/7.17 & ( ~ ( ord_less_nat @ Xb @ Xa )
% 6.92/7.17 => ( Y
% 6.92/7.17 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X @ Xa @ Xc ) ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % fold_atLeastAtMost_nat.elims
% 6.92/7.17 thf(fact_2114_mod__h__bot__iff_I1_J,axiom,
% 6.92/7.17 ! [B: $o,H: heap_e7401611519738050253t_unit] :
% 6.92/7.17 ( ( rep_assn @ ( pure_assn @ B ) @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 6.92/7.17 = B ) ).
% 6.92/7.17
% 6.92/7.17 % mod_h_bot_iff(1)
% 6.92/7.17 thf(fact_2115_pure__assn__eq__conv,axiom,
% 6.92/7.17 ! [P2: $o,Q2: $o] :
% 6.92/7.17 ( ( ( pure_assn @ P2 )
% 6.92/7.17 = ( pure_assn @ Q2 ) )
% 6.92/7.17 = ( P2 = Q2 ) ) ).
% 6.92/7.17
% 6.92/7.17 % pure_assn_eq_conv
% 6.92/7.17 thf(fact_2116_merge__pure__or,axiom,
% 6.92/7.17 ! [A: $o,B: $o] :
% 6.92/7.17 ( ( sup_sup_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 6.92/7.17 = ( pure_assn
% 6.92/7.17 @ ( A
% 6.92/7.17 | B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % merge_pure_or
% 6.92/7.17 thf(fact_2117_pure__assn__eq__emp__iff,axiom,
% 6.92/7.17 ! [P2: $o] :
% 6.92/7.17 ( ( ( pure_assn @ P2 )
% 6.92/7.17 = one_one_assn )
% 6.92/7.17 = P2 ) ).
% 6.92/7.17
% 6.92/7.17 % pure_assn_eq_emp_iff
% 6.92/7.17 thf(fact_2118_pure__true,axiom,
% 6.92/7.17 ( ( pure_assn @ $true )
% 6.92/7.17 = one_one_assn ) ).
% 6.92/7.17
% 6.92/7.17 % pure_true
% 6.92/7.17 thf(fact_2119_pure__assn__eq__false__iff,axiom,
% 6.92/7.17 ! [P2: $o] :
% 6.92/7.17 ( ( ( pure_assn @ P2 )
% 6.92/7.17 = bot_bot_assn )
% 6.92/7.17 = ~ P2 ) ).
% 6.92/7.17
% 6.92/7.17 % pure_assn_eq_false_iff
% 6.92/7.17 thf(fact_2120_pure__false,axiom,
% 6.92/7.17 ( ( pure_assn @ $false )
% 6.92/7.17 = bot_bot_assn ) ).
% 6.92/7.17
% 6.92/7.17 % pure_false
% 6.92/7.17 thf(fact_2121_norm__pre__pure__iff__sng,axiom,
% 6.92/7.17 ! [B: $o,F: heap_Time_Heap_a,Q2: a > assn] :
% 6.92/7.17 ( ( hoare_hoare_triple_a @ ( pure_assn @ B ) @ F @ Q2 )
% 6.92/7.17 = ( B
% 6.92/7.17 => ( hoare_hoare_triple_a @ one_one_assn @ F @ Q2 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % norm_pre_pure_iff_sng
% 6.92/7.17 thf(fact_2122_norm__pre__pure__iff__sng,axiom,
% 6.92/7.17 ! [B: $o,F: heap_Time_Heap_b,Q2: b > assn] :
% 6.92/7.17 ( ( hoare_hoare_triple_b @ ( pure_assn @ B ) @ F @ Q2 )
% 6.92/7.17 = ( B
% 6.92/7.17 => ( hoare_hoare_triple_b @ one_one_assn @ F @ Q2 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % norm_pre_pure_iff_sng
% 6.92/7.17 thf(fact_2123_norm__pre__pure__iff__sng,axiom,
% 6.92/7.17 ! [B: $o,F: heap_T5738788834812785303t_unit,Q2: product_unit > assn] :
% 6.92/7.17 ( ( hoare_8945653483474564448t_unit @ ( pure_assn @ B ) @ F @ Q2 )
% 6.92/7.17 = ( B
% 6.92/7.17 => ( hoare_8945653483474564448t_unit @ one_one_assn @ F @ Q2 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % norm_pre_pure_iff_sng
% 6.92/7.17 thf(fact_2124_norm__pre__pure__rule2,axiom,
% 6.92/7.17 ! [B: $o,F: heap_Time_Heap_a,Q2: a > assn] :
% 6.92/7.17 ( ( B
% 6.92/7.17 => ( hoare_hoare_triple_a @ one_one_assn @ F @ Q2 ) )
% 6.92/7.17 => ( hoare_hoare_triple_a @ ( pure_assn @ B ) @ F @ Q2 ) ) ).
% 6.92/7.17
% 6.92/7.17 % norm_pre_pure_rule2
% 6.92/7.17 thf(fact_2125_norm__pre__pure__rule2,axiom,
% 6.92/7.17 ! [B: $o,F: heap_Time_Heap_b,Q2: b > assn] :
% 6.92/7.17 ( ( B
% 6.92/7.17 => ( hoare_hoare_triple_b @ one_one_assn @ F @ Q2 ) )
% 6.92/7.17 => ( hoare_hoare_triple_b @ ( pure_assn @ B ) @ F @ Q2 ) ) ).
% 6.92/7.17
% 6.92/7.17 % norm_pre_pure_rule2
% 6.92/7.17 thf(fact_2126_norm__pre__pure__rule2,axiom,
% 6.92/7.17 ! [B: $o,F: heap_T5738788834812785303t_unit,Q2: product_unit > assn] :
% 6.92/7.17 ( ( B
% 6.92/7.17 => ( hoare_8945653483474564448t_unit @ one_one_assn @ F @ Q2 ) )
% 6.92/7.17 => ( hoare_8945653483474564448t_unit @ ( pure_assn @ B ) @ F @ Q2 ) ) ).
% 6.92/7.17
% 6.92/7.17 % norm_pre_pure_rule2
% 6.92/7.17 thf(fact_2127_lookup__rule,axiom,
% 6.92/7.17 ! [P3: ref_Product_unit,X: product_unit] :
% 6.92/7.17 ( hoare_8945653483474564448t_unit @ ( sngr_a5825115052027484668t_unit @ P3 @ X ) @ ( ref_lo7930775386976318366t_unit @ P3 )
% 6.92/7.17 @ ^ [R5: product_unit] : ( times_times_assn @ ( sngr_a5825115052027484668t_unit @ P3 @ X ) @ ( pure_assn @ ( R5 = X ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % lookup_rule
% 6.92/7.17 thf(fact_2128_K__record__comp,axiom,
% 6.92/7.17 ! [C2: produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer] :
% 6.92/7.17 ( ( comp_C1593894019821074884nteger
% 6.92/7.17 @ ^ [X4: code_integer] : C2
% 6.92/7.17 @ F )
% 6.92/7.17 = ( ^ [X4: code_integer] : C2 ) ) ).
% 6.92/7.17
% 6.92/7.17 % K_record_comp
% 6.92/7.17 thf(fact_2129_K__record__comp,axiom,
% 6.92/7.17 ! [C2: produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer] :
% 6.92/7.17 ( ( comp_C8797469213163452608nteger
% 6.92/7.17 @ ^ [X4: code_integer > code_integer] : C2
% 6.92/7.17 @ F )
% 6.92/7.17 = ( ^ [X4: code_integer] : C2 ) ) ).
% 6.92/7.17
% 6.92/7.17 % K_record_comp
% 6.92/7.17 thf(fact_2130_K__record__comp,axiom,
% 6.92/7.17 ! [C2: nat,F: int > int] :
% 6.92/7.17 ( ( comp_int_nat_int
% 6.92/7.17 @ ^ [X4: int] : C2
% 6.92/7.17 @ F )
% 6.92/7.17 = ( ^ [X4: int] : C2 ) ) ).
% 6.92/7.17
% 6.92/7.17 % K_record_comp
% 6.92/7.17 thf(fact_2131_execute__ureturn,axiom,
% 6.92/7.17 ! [X: product_unit] :
% 6.92/7.17 ( ( heap_T875086893843062177t_unit @ ( heap_T4284346855313245393t_unit @ X ) )
% 6.92/7.17 = ( comp_P3118722334806803912t_unit @ some_P1914260805536162275it_nat
% 6.92/7.17 @ ^ [H6: heap_e7401611519738050253t_unit] : ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H6 @ zero_zero_nat ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_ureturn
% 6.92/7.17 thf(fact_2132_execute__ureturn,axiom,
% 6.92/7.17 ! [X: b] :
% 6.92/7.17 ( ( heap_Time_execute_b @ ( heap_Time_ureturn_b @ X ) )
% 6.92/7.17 = ( comp_P6401406225962756324t_unit @ some_P2818173045054083285it_nat
% 6.92/7.17 @ ^ [H6: heap_e7401611519738050253t_unit] : ( produc4082563078715348724it_nat @ X @ ( produc584006145561248582it_nat @ H6 @ zero_zero_nat ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_ureturn
% 6.92/7.17 thf(fact_2133_execute__ureturn,axiom,
% 6.92/7.17 ! [X: a] :
% 6.92/7.17 ( ( heap_Time_execute_a @ ( heap_Time_ureturn_a @ X ) )
% 6.92/7.17 = ( comp_P8552900652980440422t_unit @ some_P7913643980934408916it_nat
% 6.92/7.17 @ ^ [H6: heap_e7401611519738050253t_unit] : ( produc9178034014595674355it_nat @ X @ ( produc584006145561248582it_nat @ H6 @ zero_zero_nat ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % execute_ureturn
% 6.92/7.17 thf(fact_2134_mlex__leq,axiom,
% 6.92/7.17 ! [F: int > nat,X: int,Y: int,R3: set_Pr958786334691620121nt_int] :
% 6.92/7.17 ( ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) )
% 6.92/7.17 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R3 )
% 6.92/7.17 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( mlex_prod_int @ F @ R3 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mlex_leq
% 6.92/7.17 thf(fact_2135_mlex__iff,axiom,
% 6.92/7.17 ! [X: int,Y: int,F: int > nat,R3: set_Pr958786334691620121nt_int] :
% 6.92/7.17 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( mlex_prod_int @ F @ R3 ) )
% 6.92/7.17 = ( ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) )
% 6.92/7.17 | ( ( ( F @ X )
% 6.92/7.17 = ( F @ Y ) )
% 6.92/7.17 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R3 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mlex_iff
% 6.92/7.17 thf(fact_2136_mlex__less,axiom,
% 6.92/7.17 ! [F: int > nat,X: int,Y: int,R3: set_Pr958786334691620121nt_int] :
% 6.92/7.17 ( ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) )
% 6.92/7.17 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( mlex_prod_int @ F @ R3 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mlex_less
% 6.92/7.17 thf(fact_2137_ent__pure__post__iff__sng,axiom,
% 6.92/7.17 ! [P2: assn,B: $o] :
% 6.92/7.17 ( ( entails @ P2 @ ( pure_assn @ B ) )
% 6.92/7.17 = ( ! [H6: produc3658429121746597890et_nat] :
% 6.92/7.17 ( ( rep_assn @ P2 @ H6 )
% 6.92/7.17 => B )
% 6.92/7.17 & ( entails @ P2 @ one_one_assn ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % ent_pure_post_iff_sng
% 6.92/7.17 thf(fact_2138_pure__assn__raw_Osimps,axiom,
% 6.92/7.17 ! [B: $o,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.17 ( ( pure_a825153325127701367it_nat @ B @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.17 = ( ( As = bot_bot_set_nat )
% 6.92/7.17 & B ) ) ).
% 6.92/7.17
% 6.92/7.17 % pure_assn_raw.simps
% 6.92/7.17 thf(fact_2139_pure__assn__raw_Oelims_I1_J,axiom,
% 6.92/7.17 ! [X: $o,Xa: produc3658429121746597890et_nat,Y: $o] :
% 6.92/7.17 ( ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 6.92/7.17 = Y )
% 6.92/7.17 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.17 ( ( Xa
% 6.92/7.17 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.17 => ( Y
% 6.92/7.17 = ( ~ ( ( As2 = bot_bot_set_nat )
% 6.92/7.17 & X ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % pure_assn_raw.elims(1)
% 6.92/7.17 thf(fact_2140_pure__assn__raw_Oelims_I2_J,axiom,
% 6.92/7.17 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 6.92/7.17 ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 6.92/7.17 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.17 ( ( Xa
% 6.92/7.17 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.17 => ~ ( ( As2 = bot_bot_set_nat )
% 6.92/7.17 & X ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % pure_assn_raw.elims(2)
% 6.92/7.17 thf(fact_2141_le__zero__eq,axiom,
% 6.92/7.17 ! [N2: nat] :
% 6.92/7.17 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 6.92/7.17 = ( N2 = zero_zero_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % le_zero_eq
% 6.92/7.17 thf(fact_2142_not__gr__zero,axiom,
% 6.92/7.17 ! [N2: nat] :
% 6.92/7.17 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.17 = ( N2 = zero_zero_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % not_gr_zero
% 6.92/7.17 thf(fact_2143_add__0,axiom,
% 6.92/7.17 ! [A: code_integer] :
% 6.92/7.17 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 = A ) ).
% 6.92/7.17
% 6.92/7.17 % add_0
% 6.92/7.17 thf(fact_2144_add__0,axiom,
% 6.92/7.17 ! [A: multis2468970476368604999at_nat] :
% 6.92/7.17 ( ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat @ A )
% 6.92/7.17 = A ) ).
% 6.92/7.17
% 6.92/7.17 % add_0
% 6.92/7.17 thf(fact_2145_add__0,axiom,
% 6.92/7.17 ! [A: rat] :
% 6.92/7.17 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 6.92/7.17 = A ) ).
% 6.92/7.17
% 6.92/7.17 % add_0
% 6.92/7.17 thf(fact_2146_add__0,axiom,
% 6.92/7.17 ! [A: nat] :
% 6.92/7.17 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 6.92/7.17 = A ) ).
% 6.92/7.17
% 6.92/7.17 % add_0
% 6.92/7.17 thf(fact_2147_add__0,axiom,
% 6.92/7.17 ! [A: int] :
% 6.92/7.17 ( ( plus_plus_int @ zero_zero_int @ A )
% 6.92/7.17 = A ) ).
% 6.92/7.17
% 6.92/7.17 % add_0
% 6.92/7.17 thf(fact_2148_zero__eq__add__iff__both__eq__0,axiom,
% 6.92/7.17 ! [X: nat,Y: nat] :
% 6.92/7.17 ( ( zero_zero_nat
% 6.92/7.17 = ( plus_plus_nat @ X @ Y ) )
% 6.92/7.17 = ( ( X = zero_zero_nat )
% 6.92/7.17 & ( Y = zero_zero_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_eq_add_iff_both_eq_0
% 6.92/7.17 thf(fact_2149_add__eq__0__iff__both__eq__0,axiom,
% 6.92/7.17 ! [X: nat,Y: nat] :
% 6.92/7.17 ( ( ( plus_plus_nat @ X @ Y )
% 6.92/7.17 = zero_zero_nat )
% 6.92/7.17 = ( ( X = zero_zero_nat )
% 6.92/7.17 & ( Y = zero_zero_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_eq_0_iff_both_eq_0
% 6.92/7.17 thf(fact_2150_add__cancel__right__right,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( A
% 6.92/7.17 = ( plus_p5714425477246183910nteger @ A @ B ) )
% 6.92/7.17 = ( B = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_right_right
% 6.92/7.17 thf(fact_2151_add__cancel__right__right,axiom,
% 6.92/7.17 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 6.92/7.17 ( ( A
% 6.92/7.17 = ( plus_p7104986032573967614at_nat @ A @ B ) )
% 6.92/7.17 = ( B = zero_z1048942125864253310at_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_right_right
% 6.92/7.17 thf(fact_2152_add__cancel__right__right,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( A
% 6.92/7.17 = ( plus_plus_rat @ A @ B ) )
% 6.92/7.17 = ( B = zero_zero_rat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_right_right
% 6.92/7.17 thf(fact_2153_add__cancel__right__right,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( A
% 6.92/7.17 = ( plus_plus_nat @ A @ B ) )
% 6.92/7.17 = ( B = zero_zero_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_right_right
% 6.92/7.17 thf(fact_2154_add__cancel__right__right,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( A
% 6.92/7.17 = ( plus_plus_int @ A @ B ) )
% 6.92/7.17 = ( B = zero_zero_int ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_right_right
% 6.92/7.17 thf(fact_2155_add__cancel__right__left,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( A
% 6.92/7.17 = ( plus_p5714425477246183910nteger @ B @ A ) )
% 6.92/7.17 = ( B = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_right_left
% 6.92/7.17 thf(fact_2156_add__cancel__right__left,axiom,
% 6.92/7.17 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 6.92/7.17 ( ( A
% 6.92/7.17 = ( plus_p7104986032573967614at_nat @ B @ A ) )
% 6.92/7.17 = ( B = zero_z1048942125864253310at_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_right_left
% 6.92/7.17 thf(fact_2157_add__cancel__right__left,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( A
% 6.92/7.17 = ( plus_plus_rat @ B @ A ) )
% 6.92/7.17 = ( B = zero_zero_rat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_right_left
% 6.92/7.17 thf(fact_2158_add__cancel__right__left,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( A
% 6.92/7.17 = ( plus_plus_nat @ B @ A ) )
% 6.92/7.17 = ( B = zero_zero_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_right_left
% 6.92/7.17 thf(fact_2159_add__cancel__right__left,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( A
% 6.92/7.17 = ( plus_plus_int @ B @ A ) )
% 6.92/7.17 = ( B = zero_zero_int ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_right_left
% 6.92/7.17 thf(fact_2160_add__cancel__left__right,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 6.92/7.17 = A )
% 6.92/7.17 = ( B = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_left_right
% 6.92/7.17 thf(fact_2161_add__cancel__left__right,axiom,
% 6.92/7.17 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 6.92/7.17 ( ( ( plus_p7104986032573967614at_nat @ A @ B )
% 6.92/7.17 = A )
% 6.92/7.17 = ( B = zero_z1048942125864253310at_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_left_right
% 6.92/7.17 thf(fact_2162_add__cancel__left__right,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ( plus_plus_rat @ A @ B )
% 6.92/7.17 = A )
% 6.92/7.17 = ( B = zero_zero_rat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_left_right
% 6.92/7.17 thf(fact_2163_add__cancel__left__right,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ( plus_plus_nat @ A @ B )
% 6.92/7.17 = A )
% 6.92/7.17 = ( B = zero_zero_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_left_right
% 6.92/7.17 thf(fact_2164_add__cancel__left__right,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ( plus_plus_int @ A @ B )
% 6.92/7.17 = A )
% 6.92/7.17 = ( B = zero_zero_int ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_left_right
% 6.92/7.17 thf(fact_2165_add__cancel__left__left,axiom,
% 6.92/7.17 ! [B: code_integer,A: code_integer] :
% 6.92/7.17 ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 6.92/7.17 = A )
% 6.92/7.17 = ( B = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_left_left
% 6.92/7.17 thf(fact_2166_add__cancel__left__left,axiom,
% 6.92/7.17 ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat] :
% 6.92/7.17 ( ( ( plus_p7104986032573967614at_nat @ B @ A )
% 6.92/7.17 = A )
% 6.92/7.17 = ( B = zero_z1048942125864253310at_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_left_left
% 6.92/7.17 thf(fact_2167_add__cancel__left__left,axiom,
% 6.92/7.17 ! [B: rat,A: rat] :
% 6.92/7.17 ( ( ( plus_plus_rat @ B @ A )
% 6.92/7.17 = A )
% 6.92/7.17 = ( B = zero_zero_rat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_left_left
% 6.92/7.17 thf(fact_2168_add__cancel__left__left,axiom,
% 6.92/7.17 ! [B: nat,A: nat] :
% 6.92/7.17 ( ( ( plus_plus_nat @ B @ A )
% 6.92/7.17 = A )
% 6.92/7.17 = ( B = zero_zero_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_left_left
% 6.92/7.17 thf(fact_2169_add__cancel__left__left,axiom,
% 6.92/7.17 ! [B: int,A: int] :
% 6.92/7.17 ( ( ( plus_plus_int @ B @ A )
% 6.92/7.17 = A )
% 6.92/7.17 = ( B = zero_zero_int ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_cancel_left_left
% 6.92/7.17 thf(fact_2170_double__zero__sym,axiom,
% 6.92/7.17 ! [A: code_integer] :
% 6.92/7.17 ( ( zero_z3403309356797280102nteger
% 6.92/7.17 = ( plus_p5714425477246183910nteger @ A @ A ) )
% 6.92/7.17 = ( A = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.17
% 6.92/7.17 % double_zero_sym
% 6.92/7.17 thf(fact_2171_double__zero__sym,axiom,
% 6.92/7.17 ! [A: rat] :
% 6.92/7.17 ( ( zero_zero_rat
% 6.92/7.17 = ( plus_plus_rat @ A @ A ) )
% 6.92/7.17 = ( A = zero_zero_rat ) ) ).
% 6.92/7.17
% 6.92/7.17 % double_zero_sym
% 6.92/7.17 thf(fact_2172_double__zero__sym,axiom,
% 6.92/7.17 ! [A: int] :
% 6.92/7.17 ( ( zero_zero_int
% 6.92/7.17 = ( plus_plus_int @ A @ A ) )
% 6.92/7.17 = ( A = zero_zero_int ) ) ).
% 6.92/7.17
% 6.92/7.17 % double_zero_sym
% 6.92/7.17 thf(fact_2173_add_Oright__neutral,axiom,
% 6.92/7.17 ! [A: code_integer] :
% 6.92/7.17 ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.17 = A ) ).
% 6.92/7.17
% 6.92/7.17 % add.right_neutral
% 6.92/7.17 thf(fact_2174_add_Oright__neutral,axiom,
% 6.92/7.17 ! [A: multis2468970476368604999at_nat] :
% 6.92/7.17 ( ( plus_p7104986032573967614at_nat @ A @ zero_z1048942125864253310at_nat )
% 6.92/7.17 = A ) ).
% 6.92/7.17
% 6.92/7.17 % add.right_neutral
% 6.92/7.17 thf(fact_2175_add_Oright__neutral,axiom,
% 6.92/7.17 ! [A: rat] :
% 6.92/7.17 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 6.92/7.17 = A ) ).
% 6.92/7.17
% 6.92/7.17 % add.right_neutral
% 6.92/7.17 thf(fact_2176_add_Oright__neutral,axiom,
% 6.92/7.17 ! [A: nat] :
% 6.92/7.17 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 6.92/7.17 = A ) ).
% 6.92/7.17
% 6.92/7.17 % add.right_neutral
% 6.92/7.17 thf(fact_2177_add_Oright__neutral,axiom,
% 6.92/7.17 ! [A: int] :
% 6.92/7.17 ( ( plus_plus_int @ A @ zero_zero_int )
% 6.92/7.17 = A ) ).
% 6.92/7.17
% 6.92/7.17 % add.right_neutral
% 6.92/7.17 thf(fact_2178_less__nat__zero__code,axiom,
% 6.92/7.17 ! [N2: nat] :
% 6.92/7.17 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 6.92/7.17
% 6.92/7.17 % less_nat_zero_code
% 6.92/7.17 thf(fact_2179_neq0__conv,axiom,
% 6.92/7.17 ! [N2: nat] :
% 6.92/7.17 ( ( N2 != zero_zero_nat )
% 6.92/7.17 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 6.92/7.17
% 6.92/7.17 % neq0_conv
% 6.92/7.17 thf(fact_2180_bot__nat__0_Onot__eq__extremum,axiom,
% 6.92/7.17 ! [A: nat] :
% 6.92/7.17 ( ( A != zero_zero_nat )
% 6.92/7.17 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 6.92/7.17
% 6.92/7.17 % bot_nat_0.not_eq_extremum
% 6.92/7.17 thf(fact_2181_le0,axiom,
% 6.92/7.17 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 6.92/7.17
% 6.92/7.17 % le0
% 6.92/7.17 thf(fact_2182_bot__nat__0_Oextremum,axiom,
% 6.92/7.17 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 6.92/7.17
% 6.92/7.17 % bot_nat_0.extremum
% 6.92/7.17 thf(fact_2183_add__is__0,axiom,
% 6.92/7.17 ! [M: nat,N2: nat] :
% 6.92/7.17 ( ( ( plus_plus_nat @ M @ N2 )
% 6.92/7.17 = zero_zero_nat )
% 6.92/7.17 = ( ( M = zero_zero_nat )
% 6.92/7.17 & ( N2 = zero_zero_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_is_0
% 6.92/7.17 thf(fact_2184_Nat_Oadd__0__right,axiom,
% 6.92/7.17 ! [M: nat] :
% 6.92/7.17 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 6.92/7.17 = M ) ).
% 6.92/7.17
% 6.92/7.17 % Nat.add_0_right
% 6.92/7.17 thf(fact_2185_merge__pure__star,axiom,
% 6.92/7.17 ! [A: $o,B: $o] :
% 6.92/7.17 ( ( times_times_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 6.92/7.17 = ( pure_assn
% 6.92/7.17 @ ( A
% 6.92/7.17 & B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % merge_pure_star
% 6.92/7.17 thf(fact_2186_star__false__left,axiom,
% 6.92/7.17 ! [P2: assn] :
% 6.92/7.17 ( ( times_times_assn @ bot_bot_assn @ P2 )
% 6.92/7.17 = bot_bot_assn ) ).
% 6.92/7.17
% 6.92/7.17 % star_false_left
% 6.92/7.17 thf(fact_2187_star__false__right,axiom,
% 6.92/7.17 ! [P2: assn] :
% 6.92/7.17 ( ( times_times_assn @ P2 @ bot_bot_assn )
% 6.92/7.17 = bot_bot_assn ) ).
% 6.92/7.17
% 6.92/7.17 % star_false_right
% 6.92/7.17 thf(fact_2188_add__le__same__cancel1,axiom,
% 6.92/7.17 ! [B: code_integer,A: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 6.92/7.17 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_le_same_cancel1
% 6.92/7.17 thf(fact_2189_add__le__same__cancel1,axiom,
% 6.92/7.17 ! [B: rat,A: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 6.92/7.17 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_le_same_cancel1
% 6.92/7.17 thf(fact_2190_add__le__same__cancel1,axiom,
% 6.92/7.17 ! [B: nat,A: nat] :
% 6.92/7.17 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 6.92/7.17 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_le_same_cancel1
% 6.92/7.17 thf(fact_2191_add__le__same__cancel1,axiom,
% 6.92/7.17 ! [B: int,A: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 6.92/7.17 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_le_same_cancel1
% 6.92/7.17 thf(fact_2192_add__le__same__cancel2,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 6.92/7.17 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_le_same_cancel2
% 6.92/7.17 thf(fact_2193_add__le__same__cancel2,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 6.92/7.17 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_le_same_cancel2
% 6.92/7.17 thf(fact_2194_add__le__same__cancel2,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 6.92/7.17 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_le_same_cancel2
% 6.92/7.17 thf(fact_2195_add__le__same__cancel2,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 6.92/7.17 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_le_same_cancel2
% 6.92/7.17 thf(fact_2196_le__add__same__cancel1,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 6.92/7.17 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % le_add_same_cancel1
% 6.92/7.17 thf(fact_2197_le__add__same__cancel1,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 6.92/7.17 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % le_add_same_cancel1
% 6.92/7.17 thf(fact_2198_le__add__same__cancel1,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 6.92/7.17 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % le_add_same_cancel1
% 6.92/7.17 thf(fact_2199_le__add__same__cancel1,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 6.92/7.17 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % le_add_same_cancel1
% 6.92/7.17 thf(fact_2200_le__add__same__cancel2,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 6.92/7.17 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % le_add_same_cancel2
% 6.92/7.17 thf(fact_2201_le__add__same__cancel2,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 6.92/7.17 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % le_add_same_cancel2
% 6.92/7.17 thf(fact_2202_le__add__same__cancel2,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 6.92/7.17 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % le_add_same_cancel2
% 6.92/7.17 thf(fact_2203_le__add__same__cancel2,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 6.92/7.17 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % le_add_same_cancel2
% 6.92/7.17 thf(fact_2204_double__add__le__zero__iff__single__add__le__zero,axiom,
% 6.92/7.17 ! [A: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 6.92/7.17 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.17
% 6.92/7.17 % double_add_le_zero_iff_single_add_le_zero
% 6.92/7.17 thf(fact_2205_double__add__le__zero__iff__single__add__le__zero,axiom,
% 6.92/7.17 ! [A: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 6.92/7.17 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 6.92/7.17
% 6.92/7.17 % double_add_le_zero_iff_single_add_le_zero
% 6.92/7.17 thf(fact_2206_double__add__le__zero__iff__single__add__le__zero,axiom,
% 6.92/7.17 ! [A: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 6.92/7.17 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 6.92/7.17
% 6.92/7.17 % double_add_le_zero_iff_single_add_le_zero
% 6.92/7.17 thf(fact_2207_zero__le__double__add__iff__zero__le__single__add,axiom,
% 6.92/7.17 ! [A: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 6.92/7.17 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_le_double_add_iff_zero_le_single_add
% 6.92/7.17 thf(fact_2208_zero__le__double__add__iff__zero__le__single__add,axiom,
% 6.92/7.17 ! [A: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 6.92/7.17 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_le_double_add_iff_zero_le_single_add
% 6.92/7.17 thf(fact_2209_zero__le__double__add__iff__zero__le__single__add,axiom,
% 6.92/7.17 ! [A: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 6.92/7.17 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_le_double_add_iff_zero_le_single_add
% 6.92/7.17 thf(fact_2210_zero__less__double__add__iff__zero__less__single__add,axiom,
% 6.92/7.17 ! [A: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 6.92/7.17 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_less_double_add_iff_zero_less_single_add
% 6.92/7.17 thf(fact_2211_zero__less__double__add__iff__zero__less__single__add,axiom,
% 6.92/7.17 ! [A: rat] :
% 6.92/7.17 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 6.92/7.17 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_less_double_add_iff_zero_less_single_add
% 6.92/7.17 thf(fact_2212_zero__less__double__add__iff__zero__less__single__add,axiom,
% 6.92/7.17 ! [A: int] :
% 6.92/7.17 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 6.92/7.17 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_less_double_add_iff_zero_less_single_add
% 6.92/7.17 thf(fact_2213_double__add__less__zero__iff__single__add__less__zero,axiom,
% 6.92/7.17 ! [A: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 6.92/7.17 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.17
% 6.92/7.17 % double_add_less_zero_iff_single_add_less_zero
% 6.92/7.17 thf(fact_2214_double__add__less__zero__iff__single__add__less__zero,axiom,
% 6.92/7.17 ! [A: rat] :
% 6.92/7.17 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 6.92/7.17 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 6.92/7.17
% 6.92/7.17 % double_add_less_zero_iff_single_add_less_zero
% 6.92/7.17 thf(fact_2215_double__add__less__zero__iff__single__add__less__zero,axiom,
% 6.92/7.17 ! [A: int] :
% 6.92/7.17 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 6.92/7.17 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 6.92/7.17
% 6.92/7.17 % double_add_less_zero_iff_single_add_less_zero
% 6.92/7.17 thf(fact_2216_less__add__same__cancel2,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 6.92/7.17 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % less_add_same_cancel2
% 6.92/7.17 thf(fact_2217_less__add__same__cancel2,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 6.92/7.17 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % less_add_same_cancel2
% 6.92/7.17 thf(fact_2218_less__add__same__cancel2,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 6.92/7.17 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % less_add_same_cancel2
% 6.92/7.17 thf(fact_2219_less__add__same__cancel2,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 6.92/7.17 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % less_add_same_cancel2
% 6.92/7.17 thf(fact_2220_less__add__same__cancel1,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 6.92/7.17 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % less_add_same_cancel1
% 6.92/7.17 thf(fact_2221_less__add__same__cancel1,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 6.92/7.17 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % less_add_same_cancel1
% 6.92/7.17 thf(fact_2222_less__add__same__cancel1,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 6.92/7.17 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % less_add_same_cancel1
% 6.92/7.17 thf(fact_2223_less__add__same__cancel1,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 6.92/7.17 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 6.92/7.17
% 6.92/7.17 % less_add_same_cancel1
% 6.92/7.17 thf(fact_2224_add__less__same__cancel2,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 6.92/7.17 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_less_same_cancel2
% 6.92/7.17 thf(fact_2225_add__less__same__cancel2,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 6.92/7.17 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_less_same_cancel2
% 6.92/7.17 thf(fact_2226_add__less__same__cancel2,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 6.92/7.17 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_less_same_cancel2
% 6.92/7.17 thf(fact_2227_add__less__same__cancel2,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 6.92/7.17 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_less_same_cancel2
% 6.92/7.17 thf(fact_2228_add__less__same__cancel1,axiom,
% 6.92/7.17 ! [B: code_integer,A: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 6.92/7.17 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_less_same_cancel1
% 6.92/7.17 thf(fact_2229_add__less__same__cancel1,axiom,
% 6.92/7.17 ! [B: rat,A: rat] :
% 6.92/7.17 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 6.92/7.17 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_less_same_cancel1
% 6.92/7.17 thf(fact_2230_add__less__same__cancel1,axiom,
% 6.92/7.17 ! [B: nat,A: nat] :
% 6.92/7.17 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 6.92/7.17 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_less_same_cancel1
% 6.92/7.17 thf(fact_2231_add__less__same__cancel1,axiom,
% 6.92/7.17 ! [B: int,A: int] :
% 6.92/7.17 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 6.92/7.17 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_less_same_cancel1
% 6.92/7.17 thf(fact_2232_add__gr__0,axiom,
% 6.92/7.17 ! [M: nat,N2: nat] :
% 6.92/7.17 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.17 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.17 | ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % add_gr_0
% 6.92/7.17 thf(fact_2233_less__one,axiom,
% 6.92/7.17 ! [N2: nat] :
% 6.92/7.17 ( ( ord_less_nat @ N2 @ one_one_nat )
% 6.92/7.17 = ( N2 = zero_zero_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % less_one
% 6.92/7.17 thf(fact_2234_mod__pure__star__dist,axiom,
% 6.92/7.17 ! [P2: assn,B: $o,H: produc3658429121746597890et_nat] :
% 6.92/7.17 ( ( rep_assn @ ( times_times_assn @ P2 @ ( pure_assn @ B ) ) @ H )
% 6.92/7.17 = ( ( rep_assn @ P2 @ H )
% 6.92/7.17 & B ) ) ).
% 6.92/7.17
% 6.92/7.17 % mod_pure_star_dist
% 6.92/7.17 thf(fact_2235_ent__pure__pre__iff,axiom,
% 6.92/7.17 ! [P2: assn,B: $o,Q2: assn] :
% 6.92/7.17 ( ( entails @ ( times_times_assn @ P2 @ ( pure_assn @ B ) ) @ Q2 )
% 6.92/7.17 = ( B
% 6.92/7.17 => ( entails @ P2 @ Q2 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % ent_pure_pre_iff
% 6.92/7.17 thf(fact_2236_norm__pre__pure__iff,axiom,
% 6.92/7.17 ! [P2: assn,B: $o,F: heap_Time_Heap_a,Q2: a > assn] :
% 6.92/7.17 ( ( hoare_hoare_triple_a @ ( times_times_assn @ P2 @ ( pure_assn @ B ) ) @ F @ Q2 )
% 6.92/7.17 = ( B
% 6.92/7.17 => ( hoare_hoare_triple_a @ P2 @ F @ Q2 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % norm_pre_pure_iff
% 6.92/7.17 thf(fact_2237_norm__pre__pure__iff,axiom,
% 6.92/7.17 ! [P2: assn,B: $o,F: heap_Time_Heap_b,Q2: b > assn] :
% 6.92/7.17 ( ( hoare_hoare_triple_b @ ( times_times_assn @ P2 @ ( pure_assn @ B ) ) @ F @ Q2 )
% 6.92/7.17 = ( B
% 6.92/7.17 => ( hoare_hoare_triple_b @ P2 @ F @ Q2 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % norm_pre_pure_iff
% 6.92/7.17 thf(fact_2238_norm__pre__pure__iff,axiom,
% 6.92/7.17 ! [P2: assn,B: $o,F: heap_T5738788834812785303t_unit,Q2: product_unit > assn] :
% 6.92/7.17 ( ( hoare_8945653483474564448t_unit @ ( times_times_assn @ P2 @ ( pure_assn @ B ) ) @ F @ Q2 )
% 6.92/7.17 = ( B
% 6.92/7.17 => ( hoare_8945653483474564448t_unit @ P2 @ F @ Q2 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % norm_pre_pure_iff
% 6.92/7.17 thf(fact_2239_ent__false__iff,axiom,
% 6.92/7.17 ! [P2: assn] :
% 6.92/7.17 ( ( entails @ P2 @ bot_bot_assn )
% 6.92/7.17 = ( ! [H6: produc3658429121746597890et_nat] :
% 6.92/7.17 ~ ( rep_assn @ P2 @ H6 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % ent_false_iff
% 6.92/7.17 thf(fact_2240_ent__pure__pre__iff__sng,axiom,
% 6.92/7.17 ! [B: $o,Q2: assn] :
% 6.92/7.17 ( ( entails @ ( pure_assn @ B ) @ Q2 )
% 6.92/7.17 = ( B
% 6.92/7.17 => ( entails @ one_one_assn @ Q2 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % ent_pure_pre_iff_sng
% 6.92/7.17 thf(fact_2241_mod__h__bot__iff_I5_J,axiom,
% 6.92/7.17 ! [P2: assn,Q2: assn,H: heap_e7401611519738050253t_unit] :
% 6.92/7.17 ( ( rep_assn @ ( times_times_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 6.92/7.17 = ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 6.92/7.17 & ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mod_h_bot_iff(5)
% 6.92/7.17 thf(fact_2242_ent__pure__post__iff,axiom,
% 6.92/7.17 ! [P2: assn,Q2: assn,B: $o] :
% 6.92/7.17 ( ( entails @ P2 @ ( times_times_assn @ Q2 @ ( pure_assn @ B ) ) )
% 6.92/7.17 = ( ! [H6: produc3658429121746597890et_nat] :
% 6.92/7.17 ( ( rep_assn @ P2 @ H6 )
% 6.92/7.17 => B )
% 6.92/7.17 & ( entails @ P2 @ Q2 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % ent_pure_post_iff
% 6.92/7.17 thf(fact_2243_bot__nat__def,axiom,
% 6.92/7.17 bot_bot_nat = zero_zero_nat ).
% 6.92/7.17
% 6.92/7.17 % bot_nat_def
% 6.92/7.17 thf(fact_2244_lambda__zero,axiom,
% 6.92/7.17 ( ( ^ [H6: code_integer] : zero_z3403309356797280102nteger )
% 6.92/7.17 = ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.17
% 6.92/7.17 % lambda_zero
% 6.92/7.17 thf(fact_2245_lambda__zero,axiom,
% 6.92/7.17 ( ( ^ [H6: rat] : zero_zero_rat )
% 6.92/7.17 = ( times_times_rat @ zero_zero_rat ) ) ).
% 6.92/7.17
% 6.92/7.17 % lambda_zero
% 6.92/7.17 thf(fact_2246_lambda__zero,axiom,
% 6.92/7.17 ( ( ^ [H6: nat] : zero_zero_nat )
% 6.92/7.17 = ( times_times_nat @ zero_zero_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % lambda_zero
% 6.92/7.17 thf(fact_2247_lambda__zero,axiom,
% 6.92/7.17 ( ( ^ [H6: int] : zero_zero_int )
% 6.92/7.17 = ( times_times_int @ zero_zero_int ) ) ).
% 6.92/7.17
% 6.92/7.17 % lambda_zero
% 6.92/7.17 thf(fact_2248_mult__mono,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer,C2: code_integer,D2: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ A @ B )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ C2 @ D2 )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.17 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_mono
% 6.92/7.17 thf(fact_2249_mult__mono,axiom,
% 6.92/7.17 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.17 => ( ( ord_less_eq_rat @ C2 @ D2 )
% 6.92/7.17 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.17 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.17 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_mono
% 6.92/7.17 thf(fact_2250_mult__mono,axiom,
% 6.92/7.17 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.17 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.17 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 6.92/7.17 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 6.92/7.17 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 6.92/7.17 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_mono
% 6.92/7.17 thf(fact_2251_mult__mono,axiom,
% 6.92/7.17 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.17 => ( ( ord_less_eq_int @ C2 @ D2 )
% 6.92/7.17 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 6.92/7.17 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.17 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_mono
% 6.92/7.17 thf(fact_2252_mult__mono_H,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer,C2: code_integer,D2: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ A @ B )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ C2 @ D2 )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.17 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_mono'
% 6.92/7.17 thf(fact_2253_mult__mono_H,axiom,
% 6.92/7.17 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.17 => ( ( ord_less_eq_rat @ C2 @ D2 )
% 6.92/7.17 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.17 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.17 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_mono'
% 6.92/7.17 thf(fact_2254_mult__mono_H,axiom,
% 6.92/7.17 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.17 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.17 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 6.92/7.17 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.17 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 6.92/7.17 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_mono'
% 6.92/7.17 thf(fact_2255_mult__mono_H,axiom,
% 6.92/7.17 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.17 => ( ( ord_less_eq_int @ C2 @ D2 )
% 6.92/7.17 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.17 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.17 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_mono'
% 6.92/7.17 thf(fact_2256_zero__le__square,axiom,
% 6.92/7.17 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ A ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_le_square
% 6.92/7.17 thf(fact_2257_zero__le__square,axiom,
% 6.92/7.17 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_le_square
% 6.92/7.17 thf(fact_2258_zero__le__square,axiom,
% 6.92/7.17 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_le_square
% 6.92/7.17 thf(fact_2259_split__mult__pos__le,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 6.92/7.17 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.17 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 6.92/7.17 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % split_mult_pos_le
% 6.92/7.17 thf(fact_2260_split__mult__pos__le,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.17 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 6.92/7.17 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 6.92/7.17 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 6.92/7.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % split_mult_pos_le
% 6.92/7.17 thf(fact_2261_split__mult__pos__le,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.17 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 6.92/7.17 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 6.92/7.17 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 6.92/7.17 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % split_mult_pos_le
% 6.92/7.17 thf(fact_2262_mult__left__mono__neg,axiom,
% 6.92/7.17 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ B @ A )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.17 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ ( times_3573771949741848930nteger @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_left_mono_neg
% 6.92/7.17 thf(fact_2263_mult__left__mono__neg,axiom,
% 6.92/7.17 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.17 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 6.92/7.17 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_left_mono_neg
% 6.92/7.17 thf(fact_2264_mult__left__mono__neg,axiom,
% 6.92/7.17 ! [B: int,A: int,C2: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ B @ A )
% 6.92/7.17 => ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 6.92/7.17 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_left_mono_neg
% 6.92/7.17 thf(fact_2265_mult__nonpos__nonpos,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 6.92/7.17 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonpos_nonpos
% 6.92/7.17 thf(fact_2266_mult__nonpos__nonpos,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 6.92/7.17 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 6.92/7.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonpos_nonpos
% 6.92/7.17 thf(fact_2267_mult__nonpos__nonpos,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 6.92/7.17 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 6.92/7.17 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonpos_nonpos
% 6.92/7.17 thf(fact_2268_mult__left__mono,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ A @ B )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.17 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ ( times_3573771949741848930nteger @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_left_mono
% 6.92/7.17 thf(fact_2269_mult__left__mono,axiom,
% 6.92/7.17 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.17 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.17 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_left_mono
% 6.92/7.17 thf(fact_2270_mult__left__mono,axiom,
% 6.92/7.17 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.17 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.17 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 6.92/7.17 => ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_left_mono
% 6.92/7.17 thf(fact_2271_mult__left__mono,axiom,
% 6.92/7.17 ! [A: int,B: int,C2: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.17 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.17 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_left_mono
% 6.92/7.17 thf(fact_2272_mult__right__mono__neg,axiom,
% 6.92/7.17 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ B @ A )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.17 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ ( times_3573771949741848930nteger @ B @ C2 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_right_mono_neg
% 6.92/7.17 thf(fact_2273_mult__right__mono__neg,axiom,
% 6.92/7.17 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.17 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 6.92/7.17 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_right_mono_neg
% 6.92/7.17 thf(fact_2274_mult__right__mono__neg,axiom,
% 6.92/7.17 ! [B: int,A: int,C2: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ B @ A )
% 6.92/7.17 => ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 6.92/7.17 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_right_mono_neg
% 6.92/7.17 thf(fact_2275_mult__right__mono,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ A @ B )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.17 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ ( times_3573771949741848930nteger @ B @ C2 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_right_mono
% 6.92/7.17 thf(fact_2276_mult__right__mono,axiom,
% 6.92/7.17 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.17 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.17 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_right_mono
% 6.92/7.17 thf(fact_2277_mult__right__mono,axiom,
% 6.92/7.17 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.17 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.17 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 6.92/7.17 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_right_mono
% 6.92/7.17 thf(fact_2278_mult__right__mono,axiom,
% 6.92/7.17 ! [A: int,B: int,C2: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.17 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.17 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_right_mono
% 6.92/7.17 thf(fact_2279_mult__le__0__iff,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 6.92/7.17 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 6.92/7.17 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.17 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_le_0_iff
% 6.92/7.17 thf(fact_2280_mult__le__0__iff,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 6.92/7.17 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.17 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 6.92/7.17 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 6.92/7.17 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_le_0_iff
% 6.92/7.17 thf(fact_2281_mult__le__0__iff,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 6.92/7.17 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.17 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 6.92/7.17 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 6.92/7.17 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_le_0_iff
% 6.92/7.17 thf(fact_2282_split__mult__neg__le,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 6.92/7.17 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.17 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) )
% 6.92/7.17 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.17
% 6.92/7.17 % split_mult_neg_le
% 6.92/7.17 thf(fact_2283_split__mult__neg__le,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.17 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 6.92/7.17 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 6.92/7.17 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 6.92/7.17 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 6.92/7.17
% 6.92/7.17 % split_mult_neg_le
% 6.92/7.17 thf(fact_2284_split__mult__neg__le,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.17 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 6.92/7.17 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 6.92/7.17 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 6.92/7.17 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 6.92/7.17
% 6.92/7.17 % split_mult_neg_le
% 6.92/7.17 thf(fact_2285_split__mult__neg__le,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.17 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 6.92/7.17 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 6.92/7.17 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 6.92/7.17 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 6.92/7.17
% 6.92/7.17 % split_mult_neg_le
% 6.92/7.17 thf(fact_2286_mult__nonneg__nonneg,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.17 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonneg_nonneg
% 6.92/7.17 thf(fact_2287_mult__nonneg__nonneg,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.17 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.17 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonneg_nonneg
% 6.92/7.17 thf(fact_2288_mult__nonneg__nonneg,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.17 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 6.92/7.17 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonneg_nonneg
% 6.92/7.17 thf(fact_2289_mult__nonneg__nonneg,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.17 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 6.92/7.17 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonneg_nonneg
% 6.92/7.17 thf(fact_2290_mult__nonneg__nonpos,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 6.92/7.17 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonneg_nonpos
% 6.92/7.17 thf(fact_2291_mult__nonneg__nonpos,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.17 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 6.92/7.17 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonneg_nonpos
% 6.92/7.17 thf(fact_2292_mult__nonneg__nonpos,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.17 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 6.92/7.17 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonneg_nonpos
% 6.92/7.17 thf(fact_2293_mult__nonneg__nonpos,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.17 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 6.92/7.17 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonneg_nonpos
% 6.92/7.17 thf(fact_2294_mult__nonpos__nonneg,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.17 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonpos_nonneg
% 6.92/7.17 thf(fact_2295_mult__nonpos__nonneg,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 6.92/7.17 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.17 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonpos_nonneg
% 6.92/7.17 thf(fact_2296_mult__nonpos__nonneg,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 6.92/7.17 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 6.92/7.17 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonpos_nonneg
% 6.92/7.17 thf(fact_2297_mult__nonpos__nonneg,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 6.92/7.17 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 6.92/7.17 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonpos_nonneg
% 6.92/7.17 thf(fact_2298_mult__nonneg__nonpos2,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 6.92/7.17 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonneg_nonpos2
% 6.92/7.17 thf(fact_2299_mult__nonneg__nonpos2,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.17 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 6.92/7.17 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonneg_nonpos2
% 6.92/7.17 thf(fact_2300_mult__nonneg__nonpos2,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.17 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 6.92/7.17 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonneg_nonpos2
% 6.92/7.17 thf(fact_2301_mult__nonneg__nonpos2,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.17 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 6.92/7.17 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_nonneg_nonpos2
% 6.92/7.17 thf(fact_2302_zero__le__mult__iff,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 6.92/7.17 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 6.92/7.17 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.17 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_le_mult_iff
% 6.92/7.17 thf(fact_2303_zero__le__mult__iff,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 6.92/7.17 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.17 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 6.92/7.17 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 6.92/7.17 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_le_mult_iff
% 6.92/7.17 thf(fact_2304_zero__le__mult__iff,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 6.92/7.17 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.17 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 6.92/7.17 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 6.92/7.17 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_le_mult_iff
% 6.92/7.17 thf(fact_2305_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 6.92/7.17 ( ( ord_le3102999989581377725nteger @ A @ B )
% 6.92/7.17 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.17 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ ( times_3573771949741848930nteger @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % ordered_comm_semiring_class.comm_mult_left_mono
% 6.92/7.17 thf(fact_2306_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 6.92/7.17 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.17 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.17 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.17 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % ordered_comm_semiring_class.comm_mult_left_mono
% 6.92/7.17 thf(fact_2307_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 6.92/7.17 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.17 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.17 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 6.92/7.17 => ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % ordered_comm_semiring_class.comm_mult_left_mono
% 6.92/7.17 thf(fact_2308_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 6.92/7.17 ! [A: int,B: int,C2: int] :
% 6.92/7.17 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.17 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.17 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % ordered_comm_semiring_class.comm_mult_left_mono
% 6.92/7.17 thf(fact_2309_ent__iffI,axiom,
% 6.92/7.17 ! [A4: assn,B5: assn] :
% 6.92/7.17 ( ( entails @ A4 @ B5 )
% 6.92/7.17 => ( ( entails @ B5 @ A4 )
% 6.92/7.17 => ( A4 = B5 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % ent_iffI
% 6.92/7.17 thf(fact_2310_ent__refl,axiom,
% 6.92/7.17 ! [P2: assn] : ( entails @ P2 @ P2 ) ).
% 6.92/7.17
% 6.92/7.17 % ent_refl
% 6.92/7.17 thf(fact_2311_ent__trans,axiom,
% 6.92/7.17 ! [P2: assn,Q2: assn,R3: assn] :
% 6.92/7.17 ( ( entails @ P2 @ Q2 )
% 6.92/7.17 => ( ( entails @ Q2 @ R3 )
% 6.92/7.17 => ( entails @ P2 @ R3 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % ent_trans
% 6.92/7.17 thf(fact_2312_ent__star__mono,axiom,
% 6.92/7.17 ! [P2: assn,P6: assn,Q2: assn,Q4: assn] :
% 6.92/7.17 ( ( entails @ P2 @ P6 )
% 6.92/7.17 => ( ( entails @ Q2 @ Q4 )
% 6.92/7.17 => ( entails @ ( times_times_assn @ P2 @ Q2 ) @ ( times_times_assn @ P6 @ Q4 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % ent_star_mono
% 6.92/7.17 thf(fact_2313_assn__times__comm,axiom,
% 6.92/7.17 ( times_times_assn
% 6.92/7.17 = ( ^ [P5: assn,Q3: assn] : ( times_times_assn @ Q3 @ P5 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % assn_times_comm
% 6.92/7.17 thf(fact_2314_assn__times__assoc,axiom,
% 6.92/7.17 ! [P2: assn,Q2: assn,R3: assn] :
% 6.92/7.17 ( ( times_times_assn @ ( times_times_assn @ P2 @ Q2 ) @ R3 )
% 6.92/7.17 = ( times_times_assn @ P2 @ ( times_times_assn @ Q2 @ R3 ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % assn_times_assoc
% 6.92/7.17 thf(fact_2315_mult__neg__neg,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.17 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 6.92/7.17 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_neg_neg
% 6.92/7.17 thf(fact_2316_mult__neg__neg,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.17 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 6.92/7.17 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_neg_neg
% 6.92/7.17 thf(fact_2317_mult__neg__neg,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_int @ A @ zero_zero_int )
% 6.92/7.17 => ( ( ord_less_int @ B @ zero_zero_int )
% 6.92/7.17 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_neg_neg
% 6.92/7.17 thf(fact_2318_not__square__less__zero,axiom,
% 6.92/7.17 ! [A: code_integer] :
% 6.92/7.17 ~ ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ A ) @ zero_z3403309356797280102nteger ) ).
% 6.92/7.17
% 6.92/7.17 % not_square_less_zero
% 6.92/7.17 thf(fact_2319_not__square__less__zero,axiom,
% 6.92/7.17 ! [A: rat] :
% 6.92/7.17 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 6.92/7.17
% 6.92/7.17 % not_square_less_zero
% 6.92/7.17 thf(fact_2320_not__square__less__zero,axiom,
% 6.92/7.17 ! [A: int] :
% 6.92/7.17 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 6.92/7.17
% 6.92/7.17 % not_square_less_zero
% 6.92/7.17 thf(fact_2321_mult__less__0__iff,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 6.92/7.17 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) )
% 6.92/7.17 | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.17 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_less_0_iff
% 6.92/7.17 thf(fact_2322_mult__less__0__iff,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 6.92/7.17 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.17 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 6.92/7.17 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.17 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_less_0_iff
% 6.92/7.17 thf(fact_2323_mult__less__0__iff,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 6.92/7.17 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.17 & ( ord_less_int @ B @ zero_zero_int ) )
% 6.92/7.17 | ( ( ord_less_int @ A @ zero_zero_int )
% 6.92/7.17 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_less_0_iff
% 6.92/7.17 thf(fact_2324_mult__neg__pos,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.17 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.17 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_neg_pos
% 6.92/7.17 thf(fact_2325_mult__neg__pos,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.17 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 6.92/7.17 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_neg_pos
% 6.92/7.17 thf(fact_2326_mult__neg__pos,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_nat @ A @ zero_zero_nat )
% 6.92/7.17 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 6.92/7.17 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_neg_pos
% 6.92/7.17 thf(fact_2327_mult__neg__pos,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_int @ A @ zero_zero_int )
% 6.92/7.17 => ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.17 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_neg_pos
% 6.92/7.17 thf(fact_2328_mult__pos__neg,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 6.92/7.17 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_pos_neg
% 6.92/7.17 thf(fact_2329_mult__pos__neg,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.17 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 6.92/7.17 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_pos_neg
% 6.92/7.17 thf(fact_2330_mult__pos__neg,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_nat @ zero_zero_nat @ A )
% 6.92/7.17 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 6.92/7.17 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_pos_neg
% 6.92/7.17 thf(fact_2331_mult__pos__neg,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.17 => ( ( ord_less_int @ B @ zero_zero_int )
% 6.92/7.17 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_pos_neg
% 6.92/7.17 thf(fact_2332_mult__pos__pos,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.17 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_pos_pos
% 6.92/7.17 thf(fact_2333_mult__pos__pos,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.17 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 6.92/7.17 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_pos_pos
% 6.92/7.17 thf(fact_2334_mult__pos__pos,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_nat @ zero_zero_nat @ A )
% 6.92/7.17 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 6.92/7.17 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_pos_pos
% 6.92/7.17 thf(fact_2335_mult__pos__pos,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.17 => ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.17 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_pos_pos
% 6.92/7.17 thf(fact_2336_mult__pos__neg2,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 6.92/7.17 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_pos_neg2
% 6.92/7.17 thf(fact_2337_mult__pos__neg2,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.17 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 6.92/7.17 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_pos_neg2
% 6.92/7.17 thf(fact_2338_mult__pos__neg2,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_nat @ zero_zero_nat @ A )
% 6.92/7.17 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 6.92/7.17 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_pos_neg2
% 6.92/7.17 thf(fact_2339_mult__pos__neg2,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.17 => ( ( ord_less_int @ B @ zero_zero_int )
% 6.92/7.17 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_pos_neg2
% 6.92/7.17 thf(fact_2340_zero__less__mult__iff,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 6.92/7.17 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) )
% 6.92/7.17 | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.17 & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_less_mult_iff
% 6.92/7.17 thf(fact_2341_zero__less__mult__iff,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 6.92/7.17 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.17 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 6.92/7.17 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.17 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_less_mult_iff
% 6.92/7.17 thf(fact_2342_zero__less__mult__iff,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 6.92/7.17 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.17 & ( ord_less_int @ zero_zero_int @ B ) )
% 6.92/7.17 | ( ( ord_less_int @ A @ zero_zero_int )
% 6.92/7.17 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_less_mult_iff
% 6.92/7.17 thf(fact_2343_zero__less__mult__pos,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 6.92/7.17 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_less_mult_pos
% 6.92/7.17 thf(fact_2344_zero__less__mult__pos,axiom,
% 6.92/7.17 ! [A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 6.92/7.17 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.17 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_less_mult_pos
% 6.92/7.17 thf(fact_2345_zero__less__mult__pos,axiom,
% 6.92/7.17 ! [A: nat,B: nat] :
% 6.92/7.17 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 6.92/7.17 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 6.92/7.17 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_less_mult_pos
% 6.92/7.17 thf(fact_2346_zero__less__mult__pos,axiom,
% 6.92/7.17 ! [A: int,B: int] :
% 6.92/7.17 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 6.92/7.17 => ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.17 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_less_mult_pos
% 6.92/7.17 thf(fact_2347_zero__less__mult__pos2,axiom,
% 6.92/7.17 ! [B: code_integer,A: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ B @ A ) )
% 6.92/7.17 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.17 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_less_mult_pos2
% 6.92/7.17 thf(fact_2348_zero__less__mult__pos2,axiom,
% 6.92/7.17 ! [B: rat,A: rat] :
% 6.92/7.17 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 6.92/7.17 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.17 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_less_mult_pos2
% 6.92/7.17 thf(fact_2349_zero__less__mult__pos2,axiom,
% 6.92/7.17 ! [B: nat,A: nat] :
% 6.92/7.17 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 6.92/7.17 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 6.92/7.17 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_less_mult_pos2
% 6.92/7.17 thf(fact_2350_zero__less__mult__pos2,axiom,
% 6.92/7.17 ! [B: int,A: int] :
% 6.92/7.17 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 6.92/7.17 => ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.17 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % zero_less_mult_pos2
% 6.92/7.17 thf(fact_2351_mult__less__cancel__left__neg,axiom,
% 6.92/7.17 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.17 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 6.92/7.17 = ( ord_le6747313008572928689nteger @ B @ A ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_less_cancel_left_neg
% 6.92/7.17 thf(fact_2352_mult__less__cancel__left__neg,axiom,
% 6.92/7.17 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.17 => ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 6.92/7.17 = ( ord_less_rat @ B @ A ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_less_cancel_left_neg
% 6.92/7.17 thf(fact_2353_mult__less__cancel__left__neg,axiom,
% 6.92/7.17 ! [C2: int,A: int,B: int] :
% 6.92/7.17 ( ( ord_less_int @ C2 @ zero_zero_int )
% 6.92/7.17 => ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 6.92/7.17 = ( ord_less_int @ B @ A ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_less_cancel_left_neg
% 6.92/7.17 thf(fact_2354_mult__less__cancel__left__pos,axiom,
% 6.92/7.17 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.17 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 6.92/7.17 = ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_less_cancel_left_pos
% 6.92/7.17 thf(fact_2355_mult__less__cancel__left__pos,axiom,
% 6.92/7.17 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.17 => ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 6.92/7.17 = ( ord_less_rat @ A @ B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_less_cancel_left_pos
% 6.92/7.17 thf(fact_2356_mult__less__cancel__left__pos,axiom,
% 6.92/7.17 ! [C2: int,A: int,B: int] :
% 6.92/7.17 ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.17 => ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 6.92/7.17 = ( ord_less_int @ A @ B ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_less_cancel_left_pos
% 6.92/7.17 thf(fact_2357_mult__strict__left__mono__neg,axiom,
% 6.92/7.17 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ B @ A )
% 6.92/7.17 => ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.17 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ ( times_3573771949741848930nteger @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_strict_left_mono_neg
% 6.92/7.17 thf(fact_2358_mult__strict__left__mono__neg,axiom,
% 6.92/7.17 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.17 ( ( ord_less_rat @ B @ A )
% 6.92/7.17 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.17 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_strict_left_mono_neg
% 6.92/7.17 thf(fact_2359_mult__strict__left__mono__neg,axiom,
% 6.92/7.17 ! [B: int,A: int,C2: int] :
% 6.92/7.17 ( ( ord_less_int @ B @ A )
% 6.92/7.17 => ( ( ord_less_int @ C2 @ zero_zero_int )
% 6.92/7.17 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_strict_left_mono_neg
% 6.92/7.17 thf(fact_2360_mult__strict__left__mono,axiom,
% 6.92/7.17 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ A @ B )
% 6.92/7.17 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.17 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ ( times_3573771949741848930nteger @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_strict_left_mono
% 6.92/7.17 thf(fact_2361_mult__strict__left__mono,axiom,
% 6.92/7.17 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.17 ( ( ord_less_rat @ A @ B )
% 6.92/7.17 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.17 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_strict_left_mono
% 6.92/7.17 thf(fact_2362_mult__strict__left__mono,axiom,
% 6.92/7.17 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.17 ( ( ord_less_nat @ A @ B )
% 6.92/7.17 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 6.92/7.17 => ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_strict_left_mono
% 6.92/7.17 thf(fact_2363_mult__strict__left__mono,axiom,
% 6.92/7.17 ! [A: int,B: int,C2: int] :
% 6.92/7.17 ( ( ord_less_int @ A @ B )
% 6.92/7.17 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.17 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_strict_left_mono
% 6.92/7.17 thf(fact_2364_mult__less__cancel__left__disj,axiom,
% 6.92/7.17 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 6.92/7.17 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.17 & ( ord_le6747313008572928689nteger @ A @ B ) )
% 6.92/7.17 | ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.17 & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_less_cancel_left_disj
% 6.92/7.17 thf(fact_2365_mult__less__cancel__left__disj,axiom,
% 6.92/7.17 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.17 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 6.92/7.17 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.17 & ( ord_less_rat @ A @ B ) )
% 6.92/7.17 | ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.17 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_less_cancel_left_disj
% 6.92/7.17 thf(fact_2366_mult__less__cancel__left__disj,axiom,
% 6.92/7.17 ! [C2: int,A: int,B: int] :
% 6.92/7.17 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 6.92/7.17 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.17 & ( ord_less_int @ A @ B ) )
% 6.92/7.17 | ( ( ord_less_int @ C2 @ zero_zero_int )
% 6.92/7.17 & ( ord_less_int @ B @ A ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_less_cancel_left_disj
% 6.92/7.17 thf(fact_2367_mult__strict__right__mono__neg,axiom,
% 6.92/7.17 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 6.92/7.17 ( ( ord_le6747313008572928689nteger @ B @ A )
% 6.92/7.17 => ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.17 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ ( times_3573771949741848930nteger @ B @ C2 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_strict_right_mono_neg
% 6.92/7.17 thf(fact_2368_mult__strict__right__mono__neg,axiom,
% 6.92/7.17 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.17 ( ( ord_less_rat @ B @ A )
% 6.92/7.17 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.17 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 6.92/7.17
% 6.92/7.17 % mult_strict_right_mono_neg
% 6.92/7.17 thf(fact_2369_mult__strict__right__mono__neg,axiom,
% 6.92/7.17 ! [B: int,A: int,C2: int] :
% 6.92/7.18 ( ( ord_less_int @ B @ A )
% 6.92/7.18 => ( ( ord_less_int @ C2 @ zero_zero_int )
% 6.92/7.18 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_strict_right_mono_neg
% 6.92/7.18 thf(fact_2370_mult__strict__right__mono,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ A @ B )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ ( times_3573771949741848930nteger @ B @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_strict_right_mono
% 6.92/7.18 thf(fact_2371_mult__strict__right__mono,axiom,
% 6.92/7.18 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.18 ( ( ord_less_rat @ A @ B )
% 6.92/7.18 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_strict_right_mono
% 6.92/7.18 thf(fact_2372_mult__strict__right__mono,axiom,
% 6.92/7.18 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ A @ B )
% 6.92/7.18 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 6.92/7.18 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_strict_right_mono
% 6.92/7.18 thf(fact_2373_mult__strict__right__mono,axiom,
% 6.92/7.18 ! [A: int,B: int,C2: int] :
% 6.92/7.18 ( ( ord_less_int @ A @ B )
% 6.92/7.18 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_strict_right_mono
% 6.92/7.18 thf(fact_2374_mult__less__cancel__right__disj,axiom,
% 6.92/7.18 ! [A: code_integer,C2: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 6.92/7.18 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 & ( ord_le6747313008572928689nteger @ A @ B ) )
% 6.92/7.18 | ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.18 & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_right_disj
% 6.92/7.18 thf(fact_2375_mult__less__cancel__right__disj,axiom,
% 6.92/7.18 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 6.92/7.18 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 & ( ord_less_rat @ A @ B ) )
% 6.92/7.18 | ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.18 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_right_disj
% 6.92/7.18 thf(fact_2376_mult__less__cancel__right__disj,axiom,
% 6.92/7.18 ! [A: int,C2: int,B: int] :
% 6.92/7.18 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 6.92/7.18 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.18 & ( ord_less_int @ A @ B ) )
% 6.92/7.18 | ( ( ord_less_int @ C2 @ zero_zero_int )
% 6.92/7.18 & ( ord_less_int @ B @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_right_disj
% 6.92/7.18 thf(fact_2377_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ A @ B )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ ( times_3573771949741848930nteger @ C2 @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 6.92/7.18 thf(fact_2378_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 6.92/7.18 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.18 ( ( ord_less_rat @ A @ B )
% 6.92/7.18 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 6.92/7.18 thf(fact_2379_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 6.92/7.18 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ A @ B )
% 6.92/7.18 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 6.92/7.18 => ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 6.92/7.18 thf(fact_2380_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 6.92/7.18 ! [A: int,B: int,C2: int] :
% 6.92/7.18 ( ( ord_less_int @ A @ B )
% 6.92/7.18 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 6.92/7.18 thf(fact_2381_mult__le__cancel__left,axiom,
% 6.92/7.18 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 6.92/7.18 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ A @ B ) )
% 6.92/7.18 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_left
% 6.92/7.18 thf(fact_2382_mult__le__cancel__left,axiom,
% 6.92/7.18 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 6.92/7.18 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_eq_rat @ A @ B ) )
% 6.92/7.18 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_left
% 6.92/7.18 thf(fact_2383_mult__le__cancel__left,axiom,
% 6.92/7.18 ! [C2: int,A: int,B: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 6.92/7.18 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_eq_int @ A @ B ) )
% 6.92/7.18 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 6.92/7.18 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_left
% 6.92/7.18 thf(fact_2384_mult__le__cancel__right,axiom,
% 6.92/7.18 ! [A: code_integer,C2: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 6.92/7.18 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ A @ B ) )
% 6.92/7.18 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_right
% 6.92/7.18 thf(fact_2385_mult__le__cancel__right,axiom,
% 6.92/7.18 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 6.92/7.18 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_eq_rat @ A @ B ) )
% 6.92/7.18 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_right
% 6.92/7.18 thf(fact_2386_mult__le__cancel__right,axiom,
% 6.92/7.18 ! [A: int,C2: int,B: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 6.92/7.18 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_eq_int @ A @ B ) )
% 6.92/7.18 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 6.92/7.18 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_right
% 6.92/7.18 thf(fact_2387_mult__left__less__imp__less,axiom,
% 6.92/7.18 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_left_less_imp_less
% 6.92/7.18 thf(fact_2388_mult__left__less__imp__less,axiom,
% 6.92/7.18 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_rat @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_left_less_imp_less
% 6.92/7.18 thf(fact_2389_mult__left__less__imp__less,axiom,
% 6.92/7.18 ! [C2: nat,A: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 6.92/7.18 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 6.92/7.18 => ( ord_less_nat @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_left_less_imp_less
% 6.92/7.18 thf(fact_2390_mult__left__less__imp__less,axiom,
% 6.92/7.18 ! [C2: int,A: int,B: int] :
% 6.92/7.18 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_int @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_left_less_imp_less
% 6.92/7.18 thf(fact_2391_mult__strict__mono,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer,C2: code_integer,D2: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ A @ B )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_strict_mono
% 6.92/7.18 thf(fact_2392_mult__strict__mono,axiom,
% 6.92/7.18 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.18 ( ( ord_less_rat @ A @ B )
% 6.92/7.18 => ( ( ord_less_rat @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_strict_mono
% 6.92/7.18 thf(fact_2393_mult__strict__mono,axiom,
% 6.92/7.18 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ A @ B )
% 6.92/7.18 => ( ( ord_less_nat @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 6.92/7.18 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 6.92/7.18 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_strict_mono
% 6.92/7.18 thf(fact_2394_mult__strict__mono,axiom,
% 6.92/7.18 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.18 ( ( ord_less_int @ A @ B )
% 6.92/7.18 => ( ( ord_less_int @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_strict_mono
% 6.92/7.18 thf(fact_2395_mult__less__cancel__left,axiom,
% 6.92/7.18 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 6.92/7.18 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ A @ B ) )
% 6.92/7.18 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_left
% 6.92/7.18 thf(fact_2396_mult__less__cancel__left,axiom,
% 6.92/7.18 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 6.92/7.18 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_rat @ A @ B ) )
% 6.92/7.18 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_left
% 6.92/7.18 thf(fact_2397_mult__less__cancel__left,axiom,
% 6.92/7.18 ! [C2: int,A: int,B: int] :
% 6.92/7.18 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 6.92/7.18 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_int @ A @ B ) )
% 6.92/7.18 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 6.92/7.18 => ( ord_less_int @ B @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_left
% 6.92/7.18 thf(fact_2398_mult__right__less__imp__less,axiom,
% 6.92/7.18 ! [A: code_integer,C2: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_right_less_imp_less
% 6.92/7.18 thf(fact_2399_mult__right__less__imp__less,axiom,
% 6.92/7.18 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_rat @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_right_less_imp_less
% 6.92/7.18 thf(fact_2400_mult__right__less__imp__less,axiom,
% 6.92/7.18 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 6.92/7.18 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 6.92/7.18 => ( ord_less_nat @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_right_less_imp_less
% 6.92/7.18 thf(fact_2401_mult__right__less__imp__less,axiom,
% 6.92/7.18 ! [A: int,C2: int,B: int] :
% 6.92/7.18 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_int @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_right_less_imp_less
% 6.92/7.18 thf(fact_2402_mult__strict__mono_H,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer,C2: code_integer,D2: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ A @ B )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_strict_mono'
% 6.92/7.18 thf(fact_2403_mult__strict__mono_H,axiom,
% 6.92/7.18 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.18 ( ( ord_less_rat @ A @ B )
% 6.92/7.18 => ( ( ord_less_rat @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_strict_mono'
% 6.92/7.18 thf(fact_2404_mult__strict__mono_H,axiom,
% 6.92/7.18 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ A @ B )
% 6.92/7.18 => ( ( ord_less_nat @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.18 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 6.92/7.18 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_strict_mono'
% 6.92/7.18 thf(fact_2405_mult__strict__mono_H,axiom,
% 6.92/7.18 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.18 ( ( ord_less_int @ A @ B )
% 6.92/7.18 => ( ( ord_less_int @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_strict_mono'
% 6.92/7.18 thf(fact_2406_mult__less__cancel__right,axiom,
% 6.92/7.18 ! [A: code_integer,C2: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 6.92/7.18 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ A @ B ) )
% 6.92/7.18 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_right
% 6.92/7.18 thf(fact_2407_mult__less__cancel__right,axiom,
% 6.92/7.18 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 6.92/7.18 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_rat @ A @ B ) )
% 6.92/7.18 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_right
% 6.92/7.18 thf(fact_2408_mult__less__cancel__right,axiom,
% 6.92/7.18 ! [A: int,C2: int,B: int] :
% 6.92/7.18 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 6.92/7.18 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_int @ A @ B ) )
% 6.92/7.18 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 6.92/7.18 => ( ord_less_int @ B @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_right
% 6.92/7.18 thf(fact_2409_mult__le__cancel__left__neg,axiom,
% 6.92/7.18 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 6.92/7.18 = ( ord_le3102999989581377725nteger @ B @ A ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_left_neg
% 6.92/7.18 thf(fact_2410_mult__le__cancel__left__neg,axiom,
% 6.92/7.18 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.18 => ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 6.92/7.18 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_left_neg
% 6.92/7.18 thf(fact_2411_mult__le__cancel__left__neg,axiom,
% 6.92/7.18 ! [C2: int,A: int,B: int] :
% 6.92/7.18 ( ( ord_less_int @ C2 @ zero_zero_int )
% 6.92/7.18 => ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 6.92/7.18 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_left_neg
% 6.92/7.18 thf(fact_2412_mult__le__cancel__left__pos,axiom,
% 6.92/7.18 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 6.92/7.18 = ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_left_pos
% 6.92/7.18 thf(fact_2413_mult__le__cancel__left__pos,axiom,
% 6.92/7.18 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 6.92/7.18 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_left_pos
% 6.92/7.18 thf(fact_2414_mult__le__cancel__left__pos,axiom,
% 6.92/7.18 ! [C2: int,A: int,B: int] :
% 6.92/7.18 ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 6.92/7.18 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_left_pos
% 6.92/7.18 thf(fact_2415_mult__left__le__imp__le,axiom,
% 6.92/7.18 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_left_le_imp_le
% 6.92/7.18 thf(fact_2416_mult__left__le__imp__le,axiom,
% 6.92/7.18 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 6.92/7.18 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_left_le_imp_le
% 6.92/7.18 thf(fact_2417_mult__left__le__imp__le,axiom,
% 6.92/7.18 ! [C2: nat,A: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 6.92/7.18 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 6.92/7.18 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_left_le_imp_le
% 6.92/7.18 thf(fact_2418_mult__left__le__imp__le,axiom,
% 6.92/7.18 ! [C2: int,A: int,B: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 6.92/7.18 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_left_le_imp_le
% 6.92/7.18 thf(fact_2419_mult__right__le__imp__le,axiom,
% 6.92/7.18 ! [A: code_integer,C2: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_right_le_imp_le
% 6.92/7.18 thf(fact_2420_mult__right__le__imp__le,axiom,
% 6.92/7.18 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 6.92/7.18 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_right_le_imp_le
% 6.92/7.18 thf(fact_2421_mult__right__le__imp__le,axiom,
% 6.92/7.18 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 6.92/7.18 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 6.92/7.18 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_right_le_imp_le
% 6.92/7.18 thf(fact_2422_mult__right__le__imp__le,axiom,
% 6.92/7.18 ! [A: int,C2: int,B: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 6.92/7.18 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_right_le_imp_le
% 6.92/7.18 thf(fact_2423_mult__le__less__imp__less,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer,C2: code_integer,D2: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ A @ B )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_less_imp_less
% 6.92/7.18 thf(fact_2424_mult__le__less__imp__less,axiom,
% 6.92/7.18 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.18 => ( ( ord_less_rat @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_less_imp_less
% 6.92/7.18 thf(fact_2425_mult__le__less__imp__less,axiom,
% 6.92/7.18 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.18 => ( ( ord_less_nat @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 6.92/7.18 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 6.92/7.18 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_less_imp_less
% 6.92/7.18 thf(fact_2426_mult__le__less__imp__less,axiom,
% 6.92/7.18 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.18 => ( ( ord_less_int @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_less_imp_less
% 6.92/7.18 thf(fact_2427_mult__less__le__imp__less,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer,C2: code_integer,D2: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ A @ B )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_le_imp_less
% 6.92/7.18 thf(fact_2428_mult__less__le__imp__less,axiom,
% 6.92/7.18 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.18 ( ( ord_less_rat @ A @ B )
% 6.92/7.18 => ( ( ord_less_eq_rat @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.18 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_le_imp_less
% 6.92/7.18 thf(fact_2429_mult__less__le__imp__less,axiom,
% 6.92/7.18 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ A @ B )
% 6.92/7.18 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.18 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 6.92/7.18 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_le_imp_less
% 6.92/7.18 thf(fact_2430_mult__less__le__imp__less,axiom,
% 6.92/7.18 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.18 ( ( ord_less_int @ A @ B )
% 6.92/7.18 => ( ( ord_less_eq_int @ C2 @ D2 )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.18 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_le_imp_less
% 6.92/7.18 thf(fact_2431_sum__squares__ge__zero,axiom,
% 6.92/7.18 ! [X: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % sum_squares_ge_zero
% 6.92/7.18 thf(fact_2432_sum__squares__ge__zero,axiom,
% 6.92/7.18 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % sum_squares_ge_zero
% 6.92/7.18 thf(fact_2433_sum__squares__ge__zero,axiom,
% 6.92/7.18 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % sum_squares_ge_zero
% 6.92/7.18 thf(fact_2434_mult__left__le,axiom,
% 6.92/7.18 ! [C2: code_integer,A: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ C2 @ one_one_Code_integer )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ A ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_left_le
% 6.92/7.18 thf(fact_2435_mult__left__le,axiom,
% 6.92/7.18 ! [C2: rat,A: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ C2 @ one_one_rat )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.18 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ A ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_left_le
% 6.92/7.18 thf(fact_2436_mult__left__le,axiom,
% 6.92/7.18 ! [C2: nat,A: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ C2 @ one_one_nat )
% 6.92/7.18 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.18 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ A ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_left_le
% 6.92/7.18 thf(fact_2437_mult__left__le,axiom,
% 6.92/7.18 ! [C2: int,A: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ C2 @ one_one_int )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.18 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ A ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_left_le
% 6.92/7.18 thf(fact_2438_mult__le__one,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_one
% 6.92/7.18 thf(fact_2439_mult__le__one,axiom,
% 6.92/7.18 ! [A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.18 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 6.92/7.18 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_one
% 6.92/7.18 thf(fact_2440_mult__le__one,axiom,
% 6.92/7.18 ! [A: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 6.92/7.18 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 6.92/7.18 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 6.92/7.18 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_one
% 6.92/7.18 thf(fact_2441_mult__le__one,axiom,
% 6.92/7.18 ! [A: int,B: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ A @ one_one_int )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 6.92/7.18 => ( ( ord_less_eq_int @ B @ one_one_int )
% 6.92/7.18 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_one
% 6.92/7.18 thf(fact_2442_mult__right__le__one__le,axiom,
% 6.92/7.18 ! [X: code_integer,Y: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ X ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_right_le_one_le
% 6.92/7.18 thf(fact_2443_mult__right__le__one__le,axiom,
% 6.92/7.18 ! [X: rat,Y: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 6.92/7.18 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 6.92/7.18 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_right_le_one_le
% 6.92/7.18 thf(fact_2444_mult__right__le__one__le,axiom,
% 6.92/7.18 ! [X: int,Y: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.18 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 6.92/7.18 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_right_le_one_le
% 6.92/7.18 thf(fact_2445_mult__left__le__one__le,axiom,
% 6.92/7.18 ! [X: code_integer,Y: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Y @ X ) @ X ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_left_le_one_le
% 6.92/7.18 thf(fact_2446_mult__left__le__one__le,axiom,
% 6.92/7.18 ! [X: rat,Y: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 6.92/7.18 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 6.92/7.18 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_left_le_one_le
% 6.92/7.18 thf(fact_2447_mult__left__le__one__le,axiom,
% 6.92/7.18 ! [X: int,Y: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.18 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 6.92/7.18 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_left_le_one_le
% 6.92/7.18 thf(fact_2448_not__sum__squares__lt__zero,axiom,
% 6.92/7.18 ! [X: code_integer,Y: code_integer] :
% 6.92/7.18 ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger ) ).
% 6.92/7.18
% 6.92/7.18 % not_sum_squares_lt_zero
% 6.92/7.18 thf(fact_2449_not__sum__squares__lt__zero,axiom,
% 6.92/7.18 ! [X: rat,Y: rat] :
% 6.92/7.18 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 6.92/7.18
% 6.92/7.18 % not_sum_squares_lt_zero
% 6.92/7.18 thf(fact_2450_not__sum__squares__lt__zero,axiom,
% 6.92/7.18 ! [X: int,Y: int] :
% 6.92/7.18 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 6.92/7.18
% 6.92/7.18 % not_sum_squares_lt_zero
% 6.92/7.18 thf(fact_2451_combine__common__factor,axiom,
% 6.92/7.18 ! [A: rat,E: rat,B: rat,C2: rat] :
% 6.92/7.18 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C2 ) )
% 6.92/7.18 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C2 ) ) ).
% 6.92/7.18
% 6.92/7.18 % combine_common_factor
% 6.92/7.18 thf(fact_2452_combine__common__factor,axiom,
% 6.92/7.18 ! [A: nat,E: nat,B: nat,C2: nat] :
% 6.92/7.18 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C2 ) )
% 6.92/7.18 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C2 ) ) ).
% 6.92/7.18
% 6.92/7.18 % combine_common_factor
% 6.92/7.18 thf(fact_2453_combine__common__factor,axiom,
% 6.92/7.18 ! [A: int,E: int,B: int,C2: int] :
% 6.92/7.18 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C2 ) )
% 6.92/7.18 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C2 ) ) ).
% 6.92/7.18
% 6.92/7.18 % combine_common_factor
% 6.92/7.18 thf(fact_2454_distrib__right,axiom,
% 6.92/7.18 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.18 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 6.92/7.18 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % distrib_right
% 6.92/7.18 thf(fact_2455_distrib__right,axiom,
% 6.92/7.18 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.18 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 6.92/7.18 = ( plus_plus_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % distrib_right
% 6.92/7.18 thf(fact_2456_distrib__right,axiom,
% 6.92/7.18 ! [A: int,B: int,C2: int] :
% 6.92/7.18 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 6.92/7.18 = ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % distrib_right
% 6.92/7.18 thf(fact_2457_distrib__left,axiom,
% 6.92/7.18 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.18 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 6.92/7.18 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % distrib_left
% 6.92/7.18 thf(fact_2458_distrib__left,axiom,
% 6.92/7.18 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.18 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C2 ) )
% 6.92/7.18 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % distrib_left
% 6.92/7.18 thf(fact_2459_distrib__left,axiom,
% 6.92/7.18 ! [A: int,B: int,C2: int] :
% 6.92/7.18 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 6.92/7.18 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % distrib_left
% 6.92/7.18 thf(fact_2460_comm__semiring__class_Odistrib,axiom,
% 6.92/7.18 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.18 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 6.92/7.18 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % comm_semiring_class.distrib
% 6.92/7.18 thf(fact_2461_comm__semiring__class_Odistrib,axiom,
% 6.92/7.18 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.18 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 6.92/7.18 = ( plus_plus_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % comm_semiring_class.distrib
% 6.92/7.18 thf(fact_2462_comm__semiring__class_Odistrib,axiom,
% 6.92/7.18 ! [A: int,B: int,C2: int] :
% 6.92/7.18 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 6.92/7.18 = ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % comm_semiring_class.distrib
% 6.92/7.18 thf(fact_2463_ring__class_Oring__distribs_I1_J,axiom,
% 6.92/7.18 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.18 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 6.92/7.18 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % ring_class.ring_distribs(1)
% 6.92/7.18 thf(fact_2464_ring__class_Oring__distribs_I1_J,axiom,
% 6.92/7.18 ! [A: int,B: int,C2: int] :
% 6.92/7.18 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 6.92/7.18 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % ring_class.ring_distribs(1)
% 6.92/7.18 thf(fact_2465_ring__class_Oring__distribs_I2_J,axiom,
% 6.92/7.18 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.18 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 6.92/7.18 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % ring_class.ring_distribs(2)
% 6.92/7.18 thf(fact_2466_ring__class_Oring__distribs_I2_J,axiom,
% 6.92/7.18 ! [A: int,B: int,C2: int] :
% 6.92/7.18 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 6.92/7.18 = ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % ring_class.ring_distribs(2)
% 6.92/7.18 thf(fact_2467_le__numeral__extra_I3_J,axiom,
% 6.92/7.18 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 6.92/7.18
% 6.92/7.18 % le_numeral_extra(3)
% 6.92/7.18 thf(fact_2468_le__numeral__extra_I3_J,axiom,
% 6.92/7.18 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 6.92/7.18
% 6.92/7.18 % le_numeral_extra(3)
% 6.92/7.18 thf(fact_2469_le__numeral__extra_I3_J,axiom,
% 6.92/7.18 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 6.92/7.18
% 6.92/7.18 % le_numeral_extra(3)
% 6.92/7.18 thf(fact_2470_le__numeral__extra_I3_J,axiom,
% 6.92/7.18 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 6.92/7.18
% 6.92/7.18 % le_numeral_extra(3)
% 6.92/7.18 thf(fact_2471_zero__le,axiom,
% 6.92/7.18 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 6.92/7.18
% 6.92/7.18 % zero_le
% 6.92/7.18 thf(fact_2472_less__numeral__extra_I3_J,axiom,
% 6.92/7.18 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 6.92/7.18
% 6.92/7.18 % less_numeral_extra(3)
% 6.92/7.18 thf(fact_2473_less__numeral__extra_I3_J,axiom,
% 6.92/7.18 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 6.92/7.18
% 6.92/7.18 % less_numeral_extra(3)
% 6.92/7.18 thf(fact_2474_less__numeral__extra_I3_J,axiom,
% 6.92/7.18 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 6.92/7.18
% 6.92/7.18 % less_numeral_extra(3)
% 6.92/7.18 thf(fact_2475_less__numeral__extra_I3_J,axiom,
% 6.92/7.18 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 6.92/7.18
% 6.92/7.18 % less_numeral_extra(3)
% 6.92/7.18 thf(fact_2476_zero__less__iff__neq__zero,axiom,
% 6.92/7.18 ! [N2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.18 = ( N2 != zero_zero_nat ) ) ).
% 6.92/7.18
% 6.92/7.18 % zero_less_iff_neq_zero
% 6.92/7.18 thf(fact_2477_gr__implies__not__zero,axiom,
% 6.92/7.18 ! [M: nat,N2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.18 => ( N2 != zero_zero_nat ) ) ).
% 6.92/7.18
% 6.92/7.18 % gr_implies_not_zero
% 6.92/7.18 thf(fact_2478_not__less__zero,axiom,
% 6.92/7.18 ! [N2: nat] :
% 6.92/7.18 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 6.92/7.18
% 6.92/7.18 % not_less_zero
% 6.92/7.18 thf(fact_2479_gr__zeroI,axiom,
% 6.92/7.18 ! [N2: nat] :
% 6.92/7.18 ( ( N2 != zero_zero_nat )
% 6.92/7.18 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 6.92/7.18
% 6.92/7.18 % gr_zeroI
% 6.92/7.18 thf(fact_2480_add_Ogroup__left__neutral,axiom,
% 6.92/7.18 ! [A: code_integer] :
% 6.92/7.18 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % add.group_left_neutral
% 6.92/7.18 thf(fact_2481_add_Ogroup__left__neutral,axiom,
% 6.92/7.18 ! [A: rat] :
% 6.92/7.18 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % add.group_left_neutral
% 6.92/7.18 thf(fact_2482_add_Ogroup__left__neutral,axiom,
% 6.92/7.18 ! [A: int] :
% 6.92/7.18 ( ( plus_plus_int @ zero_zero_int @ A )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % add.group_left_neutral
% 6.92/7.18 thf(fact_2483_add_Ocomm__neutral,axiom,
% 6.92/7.18 ! [A: code_integer] :
% 6.92/7.18 ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % add.comm_neutral
% 6.92/7.18 thf(fact_2484_add_Ocomm__neutral,axiom,
% 6.92/7.18 ! [A: multis2468970476368604999at_nat] :
% 6.92/7.18 ( ( plus_p7104986032573967614at_nat @ A @ zero_z1048942125864253310at_nat )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % add.comm_neutral
% 6.92/7.18 thf(fact_2485_add_Ocomm__neutral,axiom,
% 6.92/7.18 ! [A: rat] :
% 6.92/7.18 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % add.comm_neutral
% 6.92/7.18 thf(fact_2486_add_Ocomm__neutral,axiom,
% 6.92/7.18 ! [A: nat] :
% 6.92/7.18 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % add.comm_neutral
% 6.92/7.18 thf(fact_2487_add_Ocomm__neutral,axiom,
% 6.92/7.18 ! [A: int] :
% 6.92/7.18 ( ( plus_plus_int @ A @ zero_zero_int )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % add.comm_neutral
% 6.92/7.18 thf(fact_2488_comm__monoid__add__class_Oadd__0,axiom,
% 6.92/7.18 ! [A: code_integer] :
% 6.92/7.18 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % comm_monoid_add_class.add_0
% 6.92/7.18 thf(fact_2489_comm__monoid__add__class_Oadd__0,axiom,
% 6.92/7.18 ! [A: multis2468970476368604999at_nat] :
% 6.92/7.18 ( ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat @ A )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % comm_monoid_add_class.add_0
% 6.92/7.18 thf(fact_2490_comm__monoid__add__class_Oadd__0,axiom,
% 6.92/7.18 ! [A: rat] :
% 6.92/7.18 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % comm_monoid_add_class.add_0
% 6.92/7.18 thf(fact_2491_comm__monoid__add__class_Oadd__0,axiom,
% 6.92/7.18 ! [A: nat] :
% 6.92/7.18 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % comm_monoid_add_class.add_0
% 6.92/7.18 thf(fact_2492_comm__monoid__add__class_Oadd__0,axiom,
% 6.92/7.18 ! [A: int] :
% 6.92/7.18 ( ( plus_plus_int @ zero_zero_int @ A )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % comm_monoid_add_class.add_0
% 6.92/7.18 thf(fact_2493_verit__sum__simplify,axiom,
% 6.92/7.18 ! [A: code_integer] :
% 6.92/7.18 ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % verit_sum_simplify
% 6.92/7.18 thf(fact_2494_verit__sum__simplify,axiom,
% 6.92/7.18 ! [A: multis2468970476368604999at_nat] :
% 6.92/7.18 ( ( plus_p7104986032573967614at_nat @ A @ zero_z1048942125864253310at_nat )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % verit_sum_simplify
% 6.92/7.18 thf(fact_2495_verit__sum__simplify,axiom,
% 6.92/7.18 ! [A: rat] :
% 6.92/7.18 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % verit_sum_simplify
% 6.92/7.18 thf(fact_2496_verit__sum__simplify,axiom,
% 6.92/7.18 ! [A: nat] :
% 6.92/7.18 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % verit_sum_simplify
% 6.92/7.18 thf(fact_2497_verit__sum__simplify,axiom,
% 6.92/7.18 ! [A: int] :
% 6.92/7.18 ( ( plus_plus_int @ A @ zero_zero_int )
% 6.92/7.18 = A ) ).
% 6.92/7.18
% 6.92/7.18 % verit_sum_simplify
% 6.92/7.18 thf(fact_2498_ent__fwd,axiom,
% 6.92/7.18 ! [P2: assn,H: produc3658429121746597890et_nat,Q2: assn] :
% 6.92/7.18 ( ( rep_assn @ P2 @ H )
% 6.92/7.18 => ( ( entails @ P2 @ Q2 )
% 6.92/7.18 => ( rep_assn @ Q2 @ H ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % ent_fwd
% 6.92/7.18 thf(fact_2499_entailsD,axiom,
% 6.92/7.18 ! [P2: assn,Q2: assn,H: produc3658429121746597890et_nat] :
% 6.92/7.18 ( ( entails @ P2 @ Q2 )
% 6.92/7.18 => ( ( rep_assn @ P2 @ H )
% 6.92/7.18 => ( rep_assn @ Q2 @ H ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % entailsD
% 6.92/7.18 thf(fact_2500_entailsI,axiom,
% 6.92/7.18 ! [P2: assn,Q2: assn] :
% 6.92/7.18 ( ! [H2: produc3658429121746597890et_nat] :
% 6.92/7.18 ( ( rep_assn @ P2 @ H2 )
% 6.92/7.18 => ( rep_assn @ Q2 @ H2 ) )
% 6.92/7.18 => ( entails @ P2 @ Q2 ) ) ).
% 6.92/7.18
% 6.92/7.18 % entailsI
% 6.92/7.18 thf(fact_2501_entails__def,axiom,
% 6.92/7.18 ( entails
% 6.92/7.18 = ( ^ [P5: assn,Q3: assn] :
% 6.92/7.18 ! [H6: produc3658429121746597890et_nat] :
% 6.92/7.18 ( ( rep_assn @ P5 @ H6 )
% 6.92/7.18 => ( rep_assn @ Q3 @ H6 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % entails_def
% 6.92/7.18 thf(fact_2502_mod__starD,axiom,
% 6.92/7.18 ! [A4: assn,B5: assn,H: produc3658429121746597890et_nat] :
% 6.92/7.18 ( ( rep_assn @ ( times_times_assn @ A4 @ B5 ) @ H )
% 6.92/7.18 => ? [H12: produc3658429121746597890et_nat,H23: produc3658429121746597890et_nat] :
% 6.92/7.18 ( ( rep_assn @ A4 @ H12 )
% 6.92/7.18 & ( rep_assn @ B5 @ H23 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mod_starD
% 6.92/7.18 thf(fact_2503_mod__starE,axiom,
% 6.92/7.18 ! [A: assn,B: assn,H: produc3658429121746597890et_nat] :
% 6.92/7.18 ( ( rep_assn @ ( times_times_assn @ A @ B ) @ H )
% 6.92/7.18 => ~ ( ? [X_1: produc3658429121746597890et_nat] : ( rep_assn @ A @ X_1 )
% 6.92/7.18 => ! [H_2: produc3658429121746597890et_nat] :
% 6.92/7.18 ~ ( rep_assn @ B @ H_2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mod_starE
% 6.92/7.18 thf(fact_2504_infinite__descent0,axiom,
% 6.92/7.18 ! [P2: nat > $o,N2: nat] :
% 6.92/7.18 ( ( P2 @ zero_zero_nat )
% 6.92/7.18 => ( ! [N5: nat] :
% 6.92/7.18 ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 6.92/7.18 => ( ~ ( P2 @ N5 )
% 6.92/7.18 => ? [M4: nat] :
% 6.92/7.18 ( ( ord_less_nat @ M4 @ N5 )
% 6.92/7.18 & ~ ( P2 @ M4 ) ) ) )
% 6.92/7.18 => ( P2 @ N2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % infinite_descent0
% 6.92/7.18 thf(fact_2505_gr__implies__not0,axiom,
% 6.92/7.18 ! [M: nat,N2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.18 => ( N2 != zero_zero_nat ) ) ).
% 6.92/7.18
% 6.92/7.18 % gr_implies_not0
% 6.92/7.18 thf(fact_2506_less__zeroE,axiom,
% 6.92/7.18 ! [N2: nat] :
% 6.92/7.18 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 6.92/7.18
% 6.92/7.18 % less_zeroE
% 6.92/7.18 thf(fact_2507_not__less0,axiom,
% 6.92/7.18 ! [N2: nat] :
% 6.92/7.18 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 6.92/7.18
% 6.92/7.18 % not_less0
% 6.92/7.18 thf(fact_2508_not__gr0,axiom,
% 6.92/7.18 ! [N2: nat] :
% 6.92/7.18 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.18 = ( N2 = zero_zero_nat ) ) ).
% 6.92/7.18
% 6.92/7.18 % not_gr0
% 6.92/7.18 thf(fact_2509_gr0I,axiom,
% 6.92/7.18 ! [N2: nat] :
% 6.92/7.18 ( ( N2 != zero_zero_nat )
% 6.92/7.18 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 6.92/7.18
% 6.92/7.18 % gr0I
% 6.92/7.18 thf(fact_2510_bot__nat__0_Oextremum__strict,axiom,
% 6.92/7.18 ! [A: nat] :
% 6.92/7.18 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 6.92/7.18
% 6.92/7.18 % bot_nat_0.extremum_strict
% 6.92/7.18 thf(fact_2511_le__0__eq,axiom,
% 6.92/7.18 ! [N2: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 6.92/7.18 = ( N2 = zero_zero_nat ) ) ).
% 6.92/7.18
% 6.92/7.18 % le_0_eq
% 6.92/7.18 thf(fact_2512_bot__nat__0_Oextremum__uniqueI,axiom,
% 6.92/7.18 ! [A: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 6.92/7.18 => ( A = zero_zero_nat ) ) ).
% 6.92/7.18
% 6.92/7.18 % bot_nat_0.extremum_uniqueI
% 6.92/7.18 thf(fact_2513_bot__nat__0_Oextremum__unique,axiom,
% 6.92/7.18 ! [A: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 6.92/7.18 = ( A = zero_zero_nat ) ) ).
% 6.92/7.18
% 6.92/7.18 % bot_nat_0.extremum_unique
% 6.92/7.18 thf(fact_2514_less__eq__nat_Osimps_I1_J,axiom,
% 6.92/7.18 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 6.92/7.18
% 6.92/7.18 % less_eq_nat.simps(1)
% 6.92/7.18 thf(fact_2515_plus__nat_Oadd__0,axiom,
% 6.92/7.18 ! [N2: nat] :
% 6.92/7.18 ( ( plus_plus_nat @ zero_zero_nat @ N2 )
% 6.92/7.18 = N2 ) ).
% 6.92/7.18
% 6.92/7.18 % plus_nat.add_0
% 6.92/7.18 thf(fact_2516_add__eq__self__zero,axiom,
% 6.92/7.18 ! [M: nat,N2: nat] :
% 6.92/7.18 ( ( ( plus_plus_nat @ M @ N2 )
% 6.92/7.18 = M )
% 6.92/7.18 => ( N2 = zero_zero_nat ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_eq_self_zero
% 6.92/7.18 thf(fact_2517_cons__post__rule,axiom,
% 6.92/7.18 ! [P2: assn,C2: heap_Time_Heap_a,Q2: a > assn,Q4: a > assn] :
% 6.92/7.18 ( ( hoare_hoare_triple_a @ P2 @ C2 @ Q2 )
% 6.92/7.18 => ( ! [X3: a] : ( entails @ ( Q2 @ X3 ) @ ( Q4 @ X3 ) )
% 6.92/7.18 => ( hoare_hoare_triple_a @ P2 @ C2 @ Q4 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % cons_post_rule
% 6.92/7.18 thf(fact_2518_cons__post__rule,axiom,
% 6.92/7.18 ! [P2: assn,C2: heap_Time_Heap_b,Q2: b > assn,Q4: b > assn] :
% 6.92/7.18 ( ( hoare_hoare_triple_b @ P2 @ C2 @ Q2 )
% 6.92/7.18 => ( ! [X3: b] : ( entails @ ( Q2 @ X3 ) @ ( Q4 @ X3 ) )
% 6.92/7.18 => ( hoare_hoare_triple_b @ P2 @ C2 @ Q4 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % cons_post_rule
% 6.92/7.18 thf(fact_2519_cons__post__rule,axiom,
% 6.92/7.18 ! [P2: assn,C2: heap_T5738788834812785303t_unit,Q2: product_unit > assn,Q4: product_unit > assn] :
% 6.92/7.18 ( ( hoare_8945653483474564448t_unit @ P2 @ C2 @ Q2 )
% 6.92/7.18 => ( ! [X3: product_unit] : ( entails @ ( Q2 @ X3 ) @ ( Q4 @ X3 ) )
% 6.92/7.18 => ( hoare_8945653483474564448t_unit @ P2 @ C2 @ Q4 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % cons_post_rule
% 6.92/7.18 thf(fact_2520_cons__rule,axiom,
% 6.92/7.18 ! [P2: assn,P6: assn,Q2: a > assn,Q4: a > assn,C2: heap_Time_Heap_a] :
% 6.92/7.18 ( ( entails @ P2 @ P6 )
% 6.92/7.18 => ( ! [X3: a] : ( entails @ ( Q2 @ X3 ) @ ( Q4 @ X3 ) )
% 6.92/7.18 => ( ( hoare_hoare_triple_a @ P6 @ C2 @ Q2 )
% 6.92/7.18 => ( hoare_hoare_triple_a @ P2 @ C2 @ Q4 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % cons_rule
% 6.92/7.18 thf(fact_2521_cons__rule,axiom,
% 6.92/7.18 ! [P2: assn,P6: assn,Q2: b > assn,Q4: b > assn,C2: heap_Time_Heap_b] :
% 6.92/7.18 ( ( entails @ P2 @ P6 )
% 6.92/7.18 => ( ! [X3: b] : ( entails @ ( Q2 @ X3 ) @ ( Q4 @ X3 ) )
% 6.92/7.18 => ( ( hoare_hoare_triple_b @ P6 @ C2 @ Q2 )
% 6.92/7.18 => ( hoare_hoare_triple_b @ P2 @ C2 @ Q4 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % cons_rule
% 6.92/7.18 thf(fact_2522_cons__rule,axiom,
% 6.92/7.18 ! [P2: assn,P6: assn,Q2: product_unit > assn,Q4: product_unit > assn,C2: heap_T5738788834812785303t_unit] :
% 6.92/7.18 ( ( entails @ P2 @ P6 )
% 6.92/7.18 => ( ! [X3: product_unit] : ( entails @ ( Q2 @ X3 ) @ ( Q4 @ X3 ) )
% 6.92/7.18 => ( ( hoare_8945653483474564448t_unit @ P6 @ C2 @ Q2 )
% 6.92/7.18 => ( hoare_8945653483474564448t_unit @ P2 @ C2 @ Q4 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % cons_rule
% 6.92/7.18 thf(fact_2523_ent__disjE,axiom,
% 6.92/7.18 ! [A4: assn,C4: assn,B5: assn] :
% 6.92/7.18 ( ( entails @ A4 @ C4 )
% 6.92/7.18 => ( ( entails @ B5 @ C4 )
% 6.92/7.18 => ( entails @ ( sup_sup_assn @ A4 @ B5 ) @ C4 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % ent_disjE
% 6.92/7.18 thf(fact_2524_ent__disjI1,axiom,
% 6.92/7.18 ! [P2: assn,Q2: assn,R3: assn] :
% 6.92/7.18 ( ( entails @ ( sup_sup_assn @ P2 @ Q2 ) @ R3 )
% 6.92/7.18 => ( entails @ P2 @ R3 ) ) ).
% 6.92/7.18
% 6.92/7.18 % ent_disjI1
% 6.92/7.18 thf(fact_2525_ent__disjI2,axiom,
% 6.92/7.18 ! [P2: assn,Q2: assn,R3: assn] :
% 6.92/7.18 ( ( entails @ ( sup_sup_assn @ P2 @ Q2 ) @ R3 )
% 6.92/7.18 => ( entails @ Q2 @ R3 ) ) ).
% 6.92/7.18
% 6.92/7.18 % ent_disjI2
% 6.92/7.18 thf(fact_2526_ent__disjI1_H,axiom,
% 6.92/7.18 ! [A4: assn,B5: assn,C4: assn] :
% 6.92/7.18 ( ( entails @ A4 @ B5 )
% 6.92/7.18 => ( entails @ A4 @ ( sup_sup_assn @ B5 @ C4 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % ent_disjI1'
% 6.92/7.18 thf(fact_2527_ent__disjI2_H,axiom,
% 6.92/7.18 ! [A4: assn,C4: assn,B5: assn] :
% 6.92/7.18 ( ( entails @ A4 @ C4 )
% 6.92/7.18 => ( entails @ A4 @ ( sup_sup_assn @ B5 @ C4 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % ent_disjI2'
% 6.92/7.18 thf(fact_2528_ent__disjI1__direct,axiom,
% 6.92/7.18 ! [A4: assn,B5: assn] : ( entails @ A4 @ ( sup_sup_assn @ A4 @ B5 ) ) ).
% 6.92/7.18
% 6.92/7.18 % ent_disjI1_direct
% 6.92/7.18 thf(fact_2529_ent__disjI2__direct,axiom,
% 6.92/7.18 ! [B5: assn,A4: assn] : ( entails @ B5 @ ( sup_sup_assn @ A4 @ B5 ) ) ).
% 6.92/7.18
% 6.92/7.18 % ent_disjI2_direct
% 6.92/7.18 thf(fact_2530_star__or__dist1,axiom,
% 6.92/7.18 ! [A4: assn,B5: assn,C4: assn] :
% 6.92/7.18 ( ( times_times_assn @ ( sup_sup_assn @ A4 @ B5 ) @ C4 )
% 6.92/7.18 = ( sup_sup_assn @ ( times_times_assn @ A4 @ C4 ) @ ( times_times_assn @ B5 @ C4 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % star_or_dist1
% 6.92/7.18 thf(fact_2531_star__or__dist2,axiom,
% 6.92/7.18 ! [C4: assn,A4: assn,B5: assn] :
% 6.92/7.18 ( ( times_times_assn @ C4 @ ( sup_sup_assn @ A4 @ B5 ) )
% 6.92/7.18 = ( sup_sup_assn @ ( times_times_assn @ C4 @ A4 ) @ ( times_times_assn @ C4 @ B5 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % star_or_dist2
% 6.92/7.18 thf(fact_2532_assn__one__left,axiom,
% 6.92/7.18 ! [P2: assn] :
% 6.92/7.18 ( ( times_times_assn @ one_one_assn @ P2 )
% 6.92/7.18 = P2 ) ).
% 6.92/7.18
% 6.92/7.18 % assn_one_left
% 6.92/7.18 thf(fact_2533_ent__false,axiom,
% 6.92/7.18 ! [P2: assn] : ( entails @ bot_bot_assn @ P2 ) ).
% 6.92/7.18
% 6.92/7.18 % ent_false
% 6.92/7.18 thf(fact_2534_mult__le__cancel__left1,axiom,
% 6.92/7.18 ! [C2: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ C2 @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 6.92/7.18 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 6.92/7.18 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_left1
% 6.92/7.18 thf(fact_2535_mult__le__cancel__left1,axiom,
% 6.92/7.18 ! [C2: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ C2 @ ( times_times_rat @ C2 @ B ) )
% 6.92/7.18 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 6.92/7.18 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_left1
% 6.92/7.18 thf(fact_2536_mult__le__cancel__left1,axiom,
% 6.92/7.18 ! [C2: int,B: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ C2 @ ( times_times_int @ C2 @ B ) )
% 6.92/7.18 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_eq_int @ one_one_int @ B ) )
% 6.92/7.18 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 6.92/7.18 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_left1
% 6.92/7.18 thf(fact_2537_mult__le__cancel__left2,axiom,
% 6.92/7.18 ! [C2: code_integer,A: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ C2 )
% 6.92/7.18 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 6.92/7.18 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_left2
% 6.92/7.18 thf(fact_2538_mult__le__cancel__left2,axiom,
% 6.92/7.18 ! [C2: rat,A: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ C2 )
% 6.92/7.18 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 6.92/7.18 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_left2
% 6.92/7.18 thf(fact_2539_mult__le__cancel__left2,axiom,
% 6.92/7.18 ! [C2: int,A: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ C2 )
% 6.92/7.18 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_eq_int @ A @ one_one_int ) )
% 6.92/7.18 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 6.92/7.18 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_left2
% 6.92/7.18 thf(fact_2540_mult__le__cancel__right1,axiom,
% 6.92/7.18 ! [C2: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ C2 @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 6.92/7.18 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 6.92/7.18 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_right1
% 6.92/7.18 thf(fact_2541_mult__le__cancel__right1,axiom,
% 6.92/7.18 ! [C2: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ C2 @ ( times_times_rat @ B @ C2 ) )
% 6.92/7.18 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 6.92/7.18 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_right1
% 6.92/7.18 thf(fact_2542_mult__le__cancel__right1,axiom,
% 6.92/7.18 ! [C2: int,B: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ C2 @ ( times_times_int @ B @ C2 ) )
% 6.92/7.18 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_eq_int @ one_one_int @ B ) )
% 6.92/7.18 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 6.92/7.18 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_right1
% 6.92/7.18 thf(fact_2543_mult__le__cancel__right2,axiom,
% 6.92/7.18 ! [A: code_integer,C2: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ C2 )
% 6.92/7.18 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 6.92/7.18 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_right2
% 6.92/7.18 thf(fact_2544_mult__le__cancel__right2,axiom,
% 6.92/7.18 ! [A: rat,C2: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ C2 )
% 6.92/7.18 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 6.92/7.18 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_right2
% 6.92/7.18 thf(fact_2545_mult__le__cancel__right2,axiom,
% 6.92/7.18 ! [A: int,C2: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ C2 )
% 6.92/7.18 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_eq_int @ A @ one_one_int ) )
% 6.92/7.18 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 6.92/7.18 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_right2
% 6.92/7.18 thf(fact_2546_mult__less__cancel__left1,axiom,
% 6.92/7.18 ! [C2: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ C2 @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 6.92/7.18 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 6.92/7.18 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_left1
% 6.92/7.18 thf(fact_2547_mult__less__cancel__left1,axiom,
% 6.92/7.18 ! [C2: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_rat @ C2 @ ( times_times_rat @ C2 @ B ) )
% 6.92/7.18 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_rat @ one_one_rat @ B ) )
% 6.92/7.18 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_left1
% 6.92/7.18 thf(fact_2548_mult__less__cancel__left1,axiom,
% 6.92/7.18 ! [C2: int,B: int] :
% 6.92/7.18 ( ( ord_less_int @ C2 @ ( times_times_int @ C2 @ B ) )
% 6.92/7.18 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_int @ one_one_int @ B ) )
% 6.92/7.18 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 6.92/7.18 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_left1
% 6.92/7.18 thf(fact_2549_mult__less__cancel__left2,axiom,
% 6.92/7.18 ! [C2: code_integer,A: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ C2 )
% 6.92/7.18 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 6.92/7.18 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_left2
% 6.92/7.18 thf(fact_2550_mult__less__cancel__left2,axiom,
% 6.92/7.18 ! [C2: rat,A: rat] :
% 6.92/7.18 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ C2 )
% 6.92/7.18 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_rat @ A @ one_one_rat ) )
% 6.92/7.18 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_left2
% 6.92/7.18 thf(fact_2551_mult__less__cancel__left2,axiom,
% 6.92/7.18 ! [C2: int,A: int] :
% 6.92/7.18 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ C2 )
% 6.92/7.18 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_int @ A @ one_one_int ) )
% 6.92/7.18 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 6.92/7.18 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_left2
% 6.92/7.18 thf(fact_2552_mult__less__cancel__right1,axiom,
% 6.92/7.18 ! [C2: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ C2 @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 6.92/7.18 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 6.92/7.18 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_right1
% 6.92/7.18 thf(fact_2553_mult__less__cancel__right1,axiom,
% 6.92/7.18 ! [C2: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_rat @ C2 @ ( times_times_rat @ B @ C2 ) )
% 6.92/7.18 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_rat @ one_one_rat @ B ) )
% 6.92/7.18 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_right1
% 6.92/7.18 thf(fact_2554_mult__less__cancel__right1,axiom,
% 6.92/7.18 ! [C2: int,B: int] :
% 6.92/7.18 ( ( ord_less_int @ C2 @ ( times_times_int @ B @ C2 ) )
% 6.92/7.18 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_int @ one_one_int @ B ) )
% 6.92/7.18 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 6.92/7.18 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_right1
% 6.92/7.18 thf(fact_2555_mult__less__cancel__right2,axiom,
% 6.92/7.18 ! [A: code_integer,C2: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ C2 )
% 6.92/7.18 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 6.92/7.18 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_right2
% 6.92/7.18 thf(fact_2556_mult__less__cancel__right2,axiom,
% 6.92/7.18 ! [A: rat,C2: rat] :
% 6.92/7.18 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ C2 )
% 6.92/7.18 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ord_less_rat @ A @ one_one_rat ) )
% 6.92/7.18 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_right2
% 6.92/7.18 thf(fact_2557_mult__less__cancel__right2,axiom,
% 6.92/7.18 ! [A: int,C2: int] :
% 6.92/7.18 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ C2 )
% 6.92/7.18 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ord_less_int @ A @ one_one_int ) )
% 6.92/7.18 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 6.92/7.18 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel_right2
% 6.92/7.18 thf(fact_2558_convex__bound__le,axiom,
% 6.92/7.18 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ X @ A )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ Y @ A )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 6.92/7.18 => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 6.92/7.18 = one_one_Code_integer )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % convex_bound_le
% 6.92/7.18 thf(fact_2559_convex__bound__le,axiom,
% 6.92/7.18 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ X @ A )
% 6.92/7.18 => ( ( ord_less_eq_rat @ Y @ A )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 6.92/7.18 => ( ( ( plus_plus_rat @ U @ V )
% 6.92/7.18 = one_one_rat )
% 6.92/7.18 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % convex_bound_le
% 6.92/7.18 thf(fact_2560_convex__bound__le,axiom,
% 6.92/7.18 ! [X: int,A: int,Y: int,U: int,V: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ X @ A )
% 6.92/7.18 => ( ( ord_less_eq_int @ Y @ A )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 6.92/7.18 => ( ( ( plus_plus_int @ U @ V )
% 6.92/7.18 = one_one_int )
% 6.92/7.18 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % convex_bound_le
% 6.92/7.18 thf(fact_2561_lambda__one,axiom,
% 6.92/7.18 ( ( ^ [X4: code_integer] : X4 )
% 6.92/7.18 = ( times_3573771949741848930nteger @ one_one_Code_integer ) ) ).
% 6.92/7.18
% 6.92/7.18 % lambda_one
% 6.92/7.18 thf(fact_2562_lambda__one,axiom,
% 6.92/7.18 ( ( ^ [X4: assn] : X4 )
% 6.92/7.18 = ( times_times_assn @ one_one_assn ) ) ).
% 6.92/7.18
% 6.92/7.18 % lambda_one
% 6.92/7.18 thf(fact_2563_lambda__one,axiom,
% 6.92/7.18 ( ( ^ [X4: rat] : X4 )
% 6.92/7.18 = ( times_times_rat @ one_one_rat ) ) ).
% 6.92/7.18
% 6.92/7.18 % lambda_one
% 6.92/7.18 thf(fact_2564_lambda__one,axiom,
% 6.92/7.18 ( ( ^ [X4: nat] : X4 )
% 6.92/7.18 = ( times_times_nat @ one_one_nat ) ) ).
% 6.92/7.18
% 6.92/7.18 % lambda_one
% 6.92/7.18 thf(fact_2565_lambda__one,axiom,
% 6.92/7.18 ( ( ^ [X4: int] : X4 )
% 6.92/7.18 = ( times_times_int @ one_one_int ) ) ).
% 6.92/7.18
% 6.92/7.18 % lambda_one
% 6.92/7.18 thf(fact_2566_cons__pre__rule,axiom,
% 6.92/7.18 ! [P2: assn,P6: assn,C2: heap_Time_Heap_a,Q2: a > assn] :
% 6.92/7.18 ( ( entails @ P2 @ P6 )
% 6.92/7.18 => ( ( hoare_hoare_triple_a @ P6 @ C2 @ Q2 )
% 6.92/7.18 => ( hoare_hoare_triple_a @ P2 @ C2 @ Q2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % cons_pre_rule
% 6.92/7.18 thf(fact_2567_cons__pre__rule,axiom,
% 6.92/7.18 ! [P2: assn,P6: assn,C2: heap_Time_Heap_b,Q2: b > assn] :
% 6.92/7.18 ( ( entails @ P2 @ P6 )
% 6.92/7.18 => ( ( hoare_hoare_triple_b @ P6 @ C2 @ Q2 )
% 6.92/7.18 => ( hoare_hoare_triple_b @ P2 @ C2 @ Q2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % cons_pre_rule
% 6.92/7.18 thf(fact_2568_cons__pre__rule,axiom,
% 6.92/7.18 ! [P2: assn,P6: assn,C2: heap_T5738788834812785303t_unit,Q2: product_unit > assn] :
% 6.92/7.18 ( ( entails @ P2 @ P6 )
% 6.92/7.18 => ( ( hoare_8945653483474564448t_unit @ P6 @ C2 @ Q2 )
% 6.92/7.18 => ( hoare_8945653483474564448t_unit @ P2 @ C2 @ Q2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % cons_pre_rule
% 6.92/7.18 thf(fact_2569_frame__rule,axiom,
% 6.92/7.18 ! [P2: assn,C2: heap_Time_Heap_a,Q2: a > assn,R3: assn] :
% 6.92/7.18 ( ( hoare_hoare_triple_a @ P2 @ C2 @ Q2 )
% 6.92/7.18 => ( hoare_hoare_triple_a @ ( times_times_assn @ P2 @ R3 ) @ C2
% 6.92/7.18 @ ^ [X4: a] : ( times_times_assn @ ( Q2 @ X4 ) @ R3 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % frame_rule
% 6.92/7.18 thf(fact_2570_frame__rule,axiom,
% 6.92/7.18 ! [P2: assn,C2: heap_Time_Heap_b,Q2: b > assn,R3: assn] :
% 6.92/7.18 ( ( hoare_hoare_triple_b @ P2 @ C2 @ Q2 )
% 6.92/7.18 => ( hoare_hoare_triple_b @ ( times_times_assn @ P2 @ R3 ) @ C2
% 6.92/7.18 @ ^ [X4: b] : ( times_times_assn @ ( Q2 @ X4 ) @ R3 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % frame_rule
% 6.92/7.18 thf(fact_2571_frame__rule,axiom,
% 6.92/7.18 ! [P2: assn,C2: heap_T5738788834812785303t_unit,Q2: product_unit > assn,R3: assn] :
% 6.92/7.18 ( ( hoare_8945653483474564448t_unit @ P2 @ C2 @ Q2 )
% 6.92/7.18 => ( hoare_8945653483474564448t_unit @ ( times_times_assn @ P2 @ R3 ) @ C2
% 6.92/7.18 @ ^ [X4: product_unit] : ( times_times_assn @ ( Q2 @ X4 ) @ R3 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % frame_rule
% 6.92/7.18 thf(fact_2572_convex__bound__lt,axiom,
% 6.92/7.18 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ X @ A )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ Y @ A )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 6.92/7.18 => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 6.92/7.18 = one_one_Code_integer )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % convex_bound_lt
% 6.92/7.18 thf(fact_2573_convex__bound__lt,axiom,
% 6.92/7.18 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 6.92/7.18 ( ( ord_less_rat @ X @ A )
% 6.92/7.18 => ( ( ord_less_rat @ Y @ A )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 6.92/7.18 => ( ( ( plus_plus_rat @ U @ V )
% 6.92/7.18 = one_one_rat )
% 6.92/7.18 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % convex_bound_lt
% 6.92/7.18 thf(fact_2574_convex__bound__lt,axiom,
% 6.92/7.18 ! [X: int,A: int,Y: int,U: int,V: int] :
% 6.92/7.18 ( ( ord_less_int @ X @ A )
% 6.92/7.18 => ( ( ord_less_int @ Y @ A )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 6.92/7.18 => ( ( ( plus_plus_int @ U @ V )
% 6.92/7.18 = one_one_int )
% 6.92/7.18 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % convex_bound_lt
% 6.92/7.18 thf(fact_2575_less__1__mult,axiom,
% 6.92/7.18 ! [M: code_integer,N2: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ M )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ N2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ M @ N2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % less_1_mult
% 6.92/7.18 thf(fact_2576_less__1__mult,axiom,
% 6.92/7.18 ! [M: rat,N2: rat] :
% 6.92/7.18 ( ( ord_less_rat @ one_one_rat @ M )
% 6.92/7.18 => ( ( ord_less_rat @ one_one_rat @ N2 )
% 6.92/7.18 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % less_1_mult
% 6.92/7.18 thf(fact_2577_less__1__mult,axiom,
% 6.92/7.18 ! [M: nat,N2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ one_one_nat @ M )
% 6.92/7.18 => ( ( ord_less_nat @ one_one_nat @ N2 )
% 6.92/7.18 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % less_1_mult
% 6.92/7.18 thf(fact_2578_less__1__mult,axiom,
% 6.92/7.18 ! [M: int,N2: int] :
% 6.92/7.18 ( ( ord_less_int @ one_one_int @ M )
% 6.92/7.18 => ( ( ord_less_int @ one_one_int @ N2 )
% 6.92/7.18 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % less_1_mult
% 6.92/7.18 thf(fact_2579_add__decreasing,axiom,
% 6.92/7.18 ! [A: code_integer,C2: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ C2 @ B )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C2 ) @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_decreasing
% 6.92/7.18 thf(fact_2580_add__decreasing,axiom,
% 6.92/7.18 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 6.92/7.18 => ( ( ord_less_eq_rat @ C2 @ B )
% 6.92/7.18 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_decreasing
% 6.92/7.18 thf(fact_2581_add__decreasing,axiom,
% 6.92/7.18 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 6.92/7.18 => ( ( ord_less_eq_nat @ C2 @ B )
% 6.92/7.18 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_decreasing
% 6.92/7.18 thf(fact_2582_add__decreasing,axiom,
% 6.92/7.18 ! [A: int,C2: int,B: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 6.92/7.18 => ( ( ord_less_eq_int @ C2 @ B )
% 6.92/7.18 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_decreasing
% 6.92/7.18 thf(fact_2583_add__increasing,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ B @ C2 )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_increasing
% 6.92/7.18 thf(fact_2584_add__increasing,axiom,
% 6.92/7.18 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.18 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.18 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_increasing
% 6.92/7.18 thf(fact_2585_add__increasing,axiom,
% 6.92/7.18 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.18 => ( ( ord_less_eq_nat @ B @ C2 )
% 6.92/7.18 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_increasing
% 6.92/7.18 thf(fact_2586_add__increasing,axiom,
% 6.92/7.18 ! [A: int,B: int,C2: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.18 => ( ( ord_less_eq_int @ B @ C2 )
% 6.92/7.18 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_increasing
% 6.92/7.18 thf(fact_2587_add__decreasing2,axiom,
% 6.92/7.18 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ A @ B )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C2 ) @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_decreasing2
% 6.92/7.18 thf(fact_2588_add__decreasing2,axiom,
% 6.92/7.18 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 6.92/7.18 => ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.18 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_decreasing2
% 6.92/7.18 thf(fact_2589_add__decreasing2,axiom,
% 6.92/7.18 ! [C2: nat,A: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ C2 @ zero_zero_nat )
% 6.92/7.18 => ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.18 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_decreasing2
% 6.92/7.18 thf(fact_2590_add__decreasing2,axiom,
% 6.92/7.18 ! [C2: int,A: int,B: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 6.92/7.18 => ( ( ord_less_eq_int @ A @ B )
% 6.92/7.18 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_decreasing2
% 6.92/7.18 thf(fact_2591_add__increasing2,axiom,
% 6.92/7.18 ! [C2: code_integer,B: code_integer,A: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ B @ A )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_increasing2
% 6.92/7.18 thf(fact_2592_add__increasing2,axiom,
% 6.92/7.18 ! [C2: rat,B: rat,A: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.18 => ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.18 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_increasing2
% 6.92/7.18 thf(fact_2593_add__increasing2,axiom,
% 6.92/7.18 ! [C2: nat,B: nat,A: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 6.92/7.18 => ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.18 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_increasing2
% 6.92/7.18 thf(fact_2594_add__increasing2,axiom,
% 6.92/7.18 ! [C2: int,B: int,A: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.18 => ( ( ord_less_eq_int @ B @ A )
% 6.92/7.18 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_increasing2
% 6.92/7.18 thf(fact_2595_add__nonneg__nonneg,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonneg_nonneg
% 6.92/7.18 thf(fact_2596_add__nonneg__nonneg,axiom,
% 6.92/7.18 ! [A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.18 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonneg_nonneg
% 6.92/7.18 thf(fact_2597_add__nonneg__nonneg,axiom,
% 6.92/7.18 ! [A: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.18 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 6.92/7.18 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonneg_nonneg
% 6.92/7.18 thf(fact_2598_add__nonneg__nonneg,axiom,
% 6.92/7.18 ! [A: int,B: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 6.92/7.18 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonneg_nonneg
% 6.92/7.18 thf(fact_2599_add__nonpos__nonpos,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonpos_nonpos
% 6.92/7.18 thf(fact_2600_add__nonpos__nonpos,axiom,
% 6.92/7.18 ! [A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 6.92/7.18 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonpos_nonpos
% 6.92/7.18 thf(fact_2601_add__nonpos__nonpos,axiom,
% 6.92/7.18 ! [A: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 6.92/7.18 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 6.92/7.18 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonpos_nonpos
% 6.92/7.18 thf(fact_2602_add__nonpos__nonpos,axiom,
% 6.92/7.18 ! [A: int,B: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 6.92/7.18 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 6.92/7.18 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonpos_nonpos
% 6.92/7.18 thf(fact_2603_add__nonneg__eq__0__iff,axiom,
% 6.92/7.18 ! [X: code_integer,Y: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 6.92/7.18 => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 6.92/7.18 = zero_z3403309356797280102nteger )
% 6.92/7.18 = ( ( X = zero_z3403309356797280102nteger )
% 6.92/7.18 & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonneg_eq_0_iff
% 6.92/7.18 thf(fact_2604_add__nonneg__eq__0__iff,axiom,
% 6.92/7.18 ! [X: rat,Y: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 6.92/7.18 => ( ( ( plus_plus_rat @ X @ Y )
% 6.92/7.18 = zero_zero_rat )
% 6.92/7.18 = ( ( X = zero_zero_rat )
% 6.92/7.18 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonneg_eq_0_iff
% 6.92/7.18 thf(fact_2605_add__nonneg__eq__0__iff,axiom,
% 6.92/7.18 ! [X: nat,Y: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 6.92/7.18 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 6.92/7.18 => ( ( ( plus_plus_nat @ X @ Y )
% 6.92/7.18 = zero_zero_nat )
% 6.92/7.18 = ( ( X = zero_zero_nat )
% 6.92/7.18 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonneg_eq_0_iff
% 6.92/7.18 thf(fact_2606_add__nonneg__eq__0__iff,axiom,
% 6.92/7.18 ! [X: int,Y: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.18 => ( ( ( plus_plus_int @ X @ Y )
% 6.92/7.18 = zero_zero_int )
% 6.92/7.18 = ( ( X = zero_zero_int )
% 6.92/7.18 & ( Y = zero_zero_int ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonneg_eq_0_iff
% 6.92/7.18 thf(fact_2607_add__nonpos__eq__0__iff,axiom,
% 6.92/7.18 ! [X: code_integer,Y: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ X @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ Y @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 6.92/7.18 = zero_z3403309356797280102nteger )
% 6.92/7.18 = ( ( X = zero_z3403309356797280102nteger )
% 6.92/7.18 & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonpos_eq_0_iff
% 6.92/7.18 thf(fact_2608_add__nonpos__eq__0__iff,axiom,
% 6.92/7.18 ! [X: rat,Y: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 6.92/7.18 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 6.92/7.18 => ( ( ( plus_plus_rat @ X @ Y )
% 6.92/7.18 = zero_zero_rat )
% 6.92/7.18 = ( ( X = zero_zero_rat )
% 6.92/7.18 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonpos_eq_0_iff
% 6.92/7.18 thf(fact_2609_add__nonpos__eq__0__iff,axiom,
% 6.92/7.18 ! [X: nat,Y: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 6.92/7.18 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 6.92/7.18 => ( ( ( plus_plus_nat @ X @ Y )
% 6.92/7.18 = zero_zero_nat )
% 6.92/7.18 = ( ( X = zero_zero_nat )
% 6.92/7.18 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonpos_eq_0_iff
% 6.92/7.18 thf(fact_2610_add__nonpos__eq__0__iff,axiom,
% 6.92/7.18 ! [X: int,Y: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 6.92/7.18 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 6.92/7.18 => ( ( ( plus_plus_int @ X @ Y )
% 6.92/7.18 = zero_zero_int )
% 6.92/7.18 = ( ( X = zero_zero_int )
% 6.92/7.18 & ( Y = zero_zero_int ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonpos_eq_0_iff
% 6.92/7.18 thf(fact_2611_not__one__le__zero,axiom,
% 6.92/7.18 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 6.92/7.18
% 6.92/7.18 % not_one_le_zero
% 6.92/7.18 thf(fact_2612_not__one__le__zero,axiom,
% 6.92/7.18 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 6.92/7.18
% 6.92/7.18 % not_one_le_zero
% 6.92/7.18 thf(fact_2613_not__one__le__zero,axiom,
% 6.92/7.18 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 6.92/7.18
% 6.92/7.18 % not_one_le_zero
% 6.92/7.18 thf(fact_2614_not__one__le__zero,axiom,
% 6.92/7.18 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 6.92/7.18
% 6.92/7.18 % not_one_le_zero
% 6.92/7.18 thf(fact_2615_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 6.92/7.18 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 6.92/7.18
% 6.92/7.18 % linordered_nonzero_semiring_class.zero_le_one
% 6.92/7.18 thf(fact_2616_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 6.92/7.18 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 6.92/7.18
% 6.92/7.18 % linordered_nonzero_semiring_class.zero_le_one
% 6.92/7.18 thf(fact_2617_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 6.92/7.18 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 6.92/7.18
% 6.92/7.18 % linordered_nonzero_semiring_class.zero_le_one
% 6.92/7.18 thf(fact_2618_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 6.92/7.18 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 6.92/7.18
% 6.92/7.18 % linordered_nonzero_semiring_class.zero_le_one
% 6.92/7.18 thf(fact_2619_zero__less__one__class_Ozero__le__one,axiom,
% 6.92/7.18 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 6.92/7.18
% 6.92/7.18 % zero_less_one_class.zero_le_one
% 6.92/7.18 thf(fact_2620_zero__less__one__class_Ozero__le__one,axiom,
% 6.92/7.18 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 6.92/7.18
% 6.92/7.18 % zero_less_one_class.zero_le_one
% 6.92/7.18 thf(fact_2621_zero__less__one__class_Ozero__le__one,axiom,
% 6.92/7.18 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 6.92/7.18
% 6.92/7.18 % zero_less_one_class.zero_le_one
% 6.92/7.18 thf(fact_2622_zero__less__one__class_Ozero__le__one,axiom,
% 6.92/7.18 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 6.92/7.18
% 6.92/7.18 % zero_less_one_class.zero_le_one
% 6.92/7.18 thf(fact_2623_pos__add__strict,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ B @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % pos_add_strict
% 6.92/7.18 thf(fact_2624_pos__add__strict,axiom,
% 6.92/7.18 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.18 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.18 => ( ( ord_less_rat @ B @ C2 )
% 6.92/7.18 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % pos_add_strict
% 6.92/7.18 thf(fact_2625_pos__add__strict,axiom,
% 6.92/7.18 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ zero_zero_nat @ A )
% 6.92/7.18 => ( ( ord_less_nat @ B @ C2 )
% 6.92/7.18 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % pos_add_strict
% 6.92/7.18 thf(fact_2626_pos__add__strict,axiom,
% 6.92/7.18 ! [A: int,B: int,C2: int] :
% 6.92/7.18 ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.18 => ( ( ord_less_int @ B @ C2 )
% 6.92/7.18 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % pos_add_strict
% 6.92/7.18 thf(fact_2627_canonically__ordered__monoid__add__class_OlessE,axiom,
% 6.92/7.18 ! [A: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_nat @ A @ B )
% 6.92/7.18 => ~ ! [C: nat] :
% 6.92/7.18 ( ( B
% 6.92/7.18 = ( plus_plus_nat @ A @ C ) )
% 6.92/7.18 => ( C = zero_zero_nat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % canonically_ordered_monoid_add_class.lessE
% 6.92/7.18 thf(fact_2628_add__pos__pos,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_pos_pos
% 6.92/7.18 thf(fact_2629_add__pos__pos,axiom,
% 6.92/7.18 ! [A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.18 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 6.92/7.18 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_pos_pos
% 6.92/7.18 thf(fact_2630_add__pos__pos,axiom,
% 6.92/7.18 ! [A: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_nat @ zero_zero_nat @ A )
% 6.92/7.18 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 6.92/7.18 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_pos_pos
% 6.92/7.18 thf(fact_2631_add__pos__pos,axiom,
% 6.92/7.18 ! [A: int,B: int] :
% 6.92/7.18 ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.18 => ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.18 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_pos_pos
% 6.92/7.18 thf(fact_2632_add__neg__neg,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_neg_neg
% 6.92/7.18 thf(fact_2633_add__neg__neg,axiom,
% 6.92/7.18 ! [A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.18 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_neg_neg
% 6.92/7.18 thf(fact_2634_add__neg__neg,axiom,
% 6.92/7.18 ! [A: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_nat @ A @ zero_zero_nat )
% 6.92/7.18 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 6.92/7.18 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_neg_neg
% 6.92/7.18 thf(fact_2635_add__neg__neg,axiom,
% 6.92/7.18 ! [A: int,B: int] :
% 6.92/7.18 ( ( ord_less_int @ A @ zero_zero_int )
% 6.92/7.18 => ( ( ord_less_int @ B @ zero_zero_int )
% 6.92/7.18 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_neg_neg
% 6.92/7.18 thf(fact_2636_add__less__zeroD,axiom,
% 6.92/7.18 ! [X: code_integer,Y: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ X @ zero_z3403309356797280102nteger )
% 6.92/7.18 | ( ord_le6747313008572928689nteger @ Y @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_less_zeroD
% 6.92/7.18 thf(fact_2637_add__less__zeroD,axiom,
% 6.92/7.18 ! [X: rat,Y: rat] :
% 6.92/7.18 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 6.92/7.18 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 6.92/7.18 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_less_zeroD
% 6.92/7.18 thf(fact_2638_add__less__zeroD,axiom,
% 6.92/7.18 ! [X: int,Y: int] :
% 6.92/7.18 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 6.92/7.18 => ( ( ord_less_int @ X @ zero_zero_int )
% 6.92/7.18 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_less_zeroD
% 6.92/7.18 thf(fact_2639_less__numeral__extra_I1_J,axiom,
% 6.92/7.18 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 6.92/7.18
% 6.92/7.18 % less_numeral_extra(1)
% 6.92/7.18 thf(fact_2640_less__numeral__extra_I1_J,axiom,
% 6.92/7.18 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 6.92/7.18
% 6.92/7.18 % less_numeral_extra(1)
% 6.92/7.18 thf(fact_2641_less__numeral__extra_I1_J,axiom,
% 6.92/7.18 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 6.92/7.18
% 6.92/7.18 % less_numeral_extra(1)
% 6.92/7.18 thf(fact_2642_less__numeral__extra_I1_J,axiom,
% 6.92/7.18 ord_less_int @ zero_zero_int @ one_one_int ).
% 6.92/7.18
% 6.92/7.18 % less_numeral_extra(1)
% 6.92/7.18 thf(fact_2643_not__one__less__zero,axiom,
% 6.92/7.18 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 6.92/7.18
% 6.92/7.18 % not_one_less_zero
% 6.92/7.18 thf(fact_2644_not__one__less__zero,axiom,
% 6.92/7.18 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 6.92/7.18
% 6.92/7.18 % not_one_less_zero
% 6.92/7.18 thf(fact_2645_not__one__less__zero,axiom,
% 6.92/7.18 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 6.92/7.18
% 6.92/7.18 % not_one_less_zero
% 6.92/7.18 thf(fact_2646_not__one__less__zero,axiom,
% 6.92/7.18 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 6.92/7.18
% 6.92/7.18 % not_one_less_zero
% 6.92/7.18 thf(fact_2647_zero__less__one,axiom,
% 6.92/7.18 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 6.92/7.18
% 6.92/7.18 % zero_less_one
% 6.92/7.18 thf(fact_2648_zero__less__one,axiom,
% 6.92/7.18 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 6.92/7.18
% 6.92/7.18 % zero_less_one
% 6.92/7.18 thf(fact_2649_zero__less__one,axiom,
% 6.92/7.18 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 6.92/7.18
% 6.92/7.18 % zero_less_one
% 6.92/7.18 thf(fact_2650_zero__less__one,axiom,
% 6.92/7.18 ord_less_int @ zero_zero_int @ one_one_int ).
% 6.92/7.18
% 6.92/7.18 % zero_less_one
% 6.92/7.18 thf(fact_2651_ex__least__nat__le,axiom,
% 6.92/7.18 ! [P2: nat > $o,N2: nat] :
% 6.92/7.18 ( ( P2 @ N2 )
% 6.92/7.18 => ( ~ ( P2 @ zero_zero_nat )
% 6.92/7.18 => ? [K: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ K @ N2 )
% 6.92/7.18 & ! [I4: nat] :
% 6.92/7.18 ( ( ord_less_nat @ I4 @ K )
% 6.92/7.18 => ~ ( P2 @ I4 ) )
% 6.92/7.18 & ( P2 @ K ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % ex_least_nat_le
% 6.92/7.18 thf(fact_2652_less__imp__add__positive,axiom,
% 6.92/7.18 ! [I2: nat,J2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.18 => ? [K: nat] :
% 6.92/7.18 ( ( ord_less_nat @ zero_zero_nat @ K )
% 6.92/7.18 & ( ( plus_plus_nat @ I2 @ K )
% 6.92/7.18 = J2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % less_imp_add_positive
% 6.92/7.18 thf(fact_2653_nat__geq__1__eq__neqz,axiom,
% 6.92/7.18 ! [X: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ one_one_nat @ X )
% 6.92/7.18 = ( X != zero_zero_nat ) ) ).
% 6.92/7.18
% 6.92/7.18 % nat_geq_1_eq_neqz
% 6.92/7.18 thf(fact_2654_norm__pre__pure__rule1,axiom,
% 6.92/7.18 ! [B: $o,P2: assn,F: heap_Time_Heap_a,Q2: a > assn] :
% 6.92/7.18 ( ( B
% 6.92/7.18 => ( hoare_hoare_triple_a @ P2 @ F @ Q2 ) )
% 6.92/7.18 => ( hoare_hoare_triple_a @ ( times_times_assn @ P2 @ ( pure_assn @ B ) ) @ F @ Q2 ) ) ).
% 6.92/7.18
% 6.92/7.18 % norm_pre_pure_rule1
% 6.92/7.18 thf(fact_2655_norm__pre__pure__rule1,axiom,
% 6.92/7.18 ! [B: $o,P2: assn,F: heap_Time_Heap_b,Q2: b > assn] :
% 6.92/7.18 ( ( B
% 6.92/7.18 => ( hoare_hoare_triple_b @ P2 @ F @ Q2 ) )
% 6.92/7.18 => ( hoare_hoare_triple_b @ ( times_times_assn @ P2 @ ( pure_assn @ B ) ) @ F @ Q2 ) ) ).
% 6.92/7.18
% 6.92/7.18 % norm_pre_pure_rule1
% 6.92/7.18 thf(fact_2656_norm__pre__pure__rule1,axiom,
% 6.92/7.18 ! [B: $o,P2: assn,F: heap_T5738788834812785303t_unit,Q2: product_unit > assn] :
% 6.92/7.18 ( ( B
% 6.92/7.18 => ( hoare_8945653483474564448t_unit @ P2 @ F @ Q2 ) )
% 6.92/7.18 => ( hoare_8945653483474564448t_unit @ ( times_times_assn @ P2 @ ( pure_assn @ B ) ) @ F @ Q2 ) ) ).
% 6.92/7.18
% 6.92/7.18 % norm_pre_pure_rule1
% 6.92/7.18 thf(fact_2657_bot__nat__0_Oordering__top__axioms,axiom,
% 6.92/7.18 ( ordering_top_nat
% 6.92/7.18 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 6.92/7.18 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 )
% 6.92/7.18 @ zero_zero_nat ) ).
% 6.92/7.18
% 6.92/7.18 % bot_nat_0.ordering_top_axioms
% 6.92/7.18 thf(fact_2658_ureturn__def,axiom,
% 6.92/7.18 ( heap_Time_ureturn_b
% 6.92/7.18 = ( ^ [X4: b] :
% 6.92/7.18 ( heap_Time_heap_b
% 6.92/7.18 @ ^ [H6: heap_e7401611519738050253t_unit] : ( produc4082563078715348724it_nat @ X4 @ ( produc584006145561248582it_nat @ H6 @ zero_zero_nat ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % ureturn_def
% 6.92/7.18 thf(fact_2659_ureturn__def,axiom,
% 6.92/7.18 ( heap_Time_ureturn_a
% 6.92/7.18 = ( ^ [X4: a] :
% 6.92/7.18 ( heap_Time_heap_a
% 6.92/7.18 @ ^ [H6: heap_e7401611519738050253t_unit] : ( produc9178034014595674355it_nat @ X4 @ ( produc584006145561248582it_nat @ H6 @ zero_zero_nat ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % ureturn_def
% 6.92/7.18 thf(fact_2660_add__neg__nonpos,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_neg_nonpos
% 6.92/7.18 thf(fact_2661_add__neg__nonpos,axiom,
% 6.92/7.18 ! [A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.18 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_neg_nonpos
% 6.92/7.18 thf(fact_2662_add__neg__nonpos,axiom,
% 6.92/7.18 ! [A: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_nat @ A @ zero_zero_nat )
% 6.92/7.18 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 6.92/7.18 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_neg_nonpos
% 6.92/7.18 thf(fact_2663_add__neg__nonpos,axiom,
% 6.92/7.18 ! [A: int,B: int] :
% 6.92/7.18 ( ( ord_less_int @ A @ zero_zero_int )
% 6.92/7.18 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 6.92/7.18 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_neg_nonpos
% 6.92/7.18 thf(fact_2664_add__nonneg__pos,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonneg_pos
% 6.92/7.18 thf(fact_2665_add__nonneg__pos,axiom,
% 6.92/7.18 ! [A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.18 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 6.92/7.18 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonneg_pos
% 6.92/7.18 thf(fact_2666_add__nonneg__pos,axiom,
% 6.92/7.18 ! [A: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.18 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 6.92/7.18 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonneg_pos
% 6.92/7.18 thf(fact_2667_add__nonneg__pos,axiom,
% 6.92/7.18 ! [A: int,B: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.18 => ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.18 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonneg_pos
% 6.92/7.18 thf(fact_2668_add__nonpos__neg,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonpos_neg
% 6.92/7.18 thf(fact_2669_add__nonpos__neg,axiom,
% 6.92/7.18 ! [A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 6.92/7.18 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 6.92/7.18 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonpos_neg
% 6.92/7.18 thf(fact_2670_add__nonpos__neg,axiom,
% 6.92/7.18 ! [A: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 6.92/7.18 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 6.92/7.18 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonpos_neg
% 6.92/7.18 thf(fact_2671_add__nonpos__neg,axiom,
% 6.92/7.18 ! [A: int,B: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 6.92/7.18 => ( ( ord_less_int @ B @ zero_zero_int )
% 6.92/7.18 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_nonpos_neg
% 6.92/7.18 thf(fact_2672_add__pos__nonneg,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_pos_nonneg
% 6.92/7.18 thf(fact_2673_add__pos__nonneg,axiom,
% 6.92/7.18 ! [A: rat,B: rat] :
% 6.92/7.18 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.18 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.18 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_pos_nonneg
% 6.92/7.18 thf(fact_2674_add__pos__nonneg,axiom,
% 6.92/7.18 ! [A: nat,B: nat] :
% 6.92/7.18 ( ( ord_less_nat @ zero_zero_nat @ A )
% 6.92/7.18 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 6.92/7.18 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_pos_nonneg
% 6.92/7.18 thf(fact_2675_add__pos__nonneg,axiom,
% 6.92/7.18 ! [A: int,B: int] :
% 6.92/7.18 ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.18 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 6.92/7.18 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_pos_nonneg
% 6.92/7.18 thf(fact_2676_add__strict__increasing,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ B @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_strict_increasing
% 6.92/7.18 thf(fact_2677_add__strict__increasing,axiom,
% 6.92/7.18 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.18 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.18 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.18 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_strict_increasing
% 6.92/7.18 thf(fact_2678_add__strict__increasing,axiom,
% 6.92/7.18 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ zero_zero_nat @ A )
% 6.92/7.18 => ( ( ord_less_eq_nat @ B @ C2 )
% 6.92/7.18 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_strict_increasing
% 6.92/7.18 thf(fact_2679_add__strict__increasing,axiom,
% 6.92/7.18 ! [A: int,B: int,C2: int] :
% 6.92/7.18 ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.18 => ( ( ord_less_eq_int @ B @ C2 )
% 6.92/7.18 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_strict_increasing
% 6.92/7.18 thf(fact_2680_add__strict__increasing2,axiom,
% 6.92/7.18 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ B @ C2 )
% 6.92/7.18 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_strict_increasing2
% 6.92/7.18 thf(fact_2681_add__strict__increasing2,axiom,
% 6.92/7.18 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.18 => ( ( ord_less_rat @ B @ C2 )
% 6.92/7.18 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_strict_increasing2
% 6.92/7.18 thf(fact_2682_add__strict__increasing2,axiom,
% 6.92/7.18 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.18 => ( ( ord_less_nat @ B @ C2 )
% 6.92/7.18 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_strict_increasing2
% 6.92/7.18 thf(fact_2683_add__strict__increasing2,axiom,
% 6.92/7.18 ! [A: int,B: int,C2: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.18 => ( ( ord_less_int @ B @ C2 )
% 6.92/7.18 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_strict_increasing2
% 6.92/7.18 thf(fact_2684_zero__less__two,axiom,
% 6.92/7.18 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 6.92/7.18
% 6.92/7.18 % zero_less_two
% 6.92/7.18 thf(fact_2685_zero__less__two,axiom,
% 6.92/7.18 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 6.92/7.18
% 6.92/7.18 % zero_less_two
% 6.92/7.18 thf(fact_2686_zero__less__two,axiom,
% 6.92/7.18 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 6.92/7.18
% 6.92/7.18 % zero_less_two
% 6.92/7.18 thf(fact_2687_zero__less__two,axiom,
% 6.92/7.18 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 6.92/7.18
% 6.92/7.18 % zero_less_two
% 6.92/7.18 thf(fact_2688_return__sp__rule,axiom,
% 6.92/7.18 ! [P2: assn,X: a] :
% 6.92/7.18 ( hoare_hoare_triple_a @ P2 @ ( heap_Time_return_a @ X )
% 6.92/7.18 @ ^ [R5: a] : ( times_times_assn @ P2 @ ( pure_assn @ ( R5 = X ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % return_sp_rule
% 6.92/7.18 thf(fact_2689_return__sp__rule,axiom,
% 6.92/7.18 ! [P2: assn,X: b] :
% 6.92/7.18 ( hoare_hoare_triple_b @ P2 @ ( heap_Time_return_b @ X )
% 6.92/7.18 @ ^ [R5: b] : ( times_times_assn @ P2 @ ( pure_assn @ ( R5 = X ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % return_sp_rule
% 6.92/7.18 thf(fact_2690_return__sp__rule,axiom,
% 6.92/7.18 ! [P2: assn,X: product_unit] :
% 6.92/7.18 ( hoare_8945653483474564448t_unit @ P2 @ ( heap_T7507251653302230130t_unit @ X )
% 6.92/7.18 @ ^ [R5: product_unit] : ( times_times_assn @ P2 @ ( pure_assn @ ( R5 = X ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % return_sp_rule
% 6.92/7.18 thf(fact_2691_pure__assn__raw_Oelims_I3_J,axiom,
% 6.92/7.18 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 6.92/7.18 ( ~ ( pure_a825153325127701367it_nat @ X @ Xa )
% 6.92/7.18 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.18 ( ( Xa
% 6.92/7.18 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.18 => ( ( As2 = bot_bot_set_nat )
% 6.92/7.18 & X ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % pure_assn_raw.elims(3)
% 6.92/7.18 thf(fact_2692_field__le__mult__one__interval,axiom,
% 6.92/7.18 ! [X: rat,Y: rat] :
% 6.92/7.18 ( ! [Z2: rat] :
% 6.92/7.18 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 6.92/7.18 => ( ( ord_less_rat @ Z2 @ one_one_rat )
% 6.92/7.18 => ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X ) @ Y ) ) )
% 6.92/7.18 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 6.92/7.18
% 6.92/7.18 % field_le_mult_one_interval
% 6.92/7.18 thf(fact_2693_double__eq__0__iff,axiom,
% 6.92/7.18 ! [A: code_integer] :
% 6.92/7.18 ( ( ( plus_p5714425477246183910nteger @ A @ A )
% 6.92/7.18 = zero_z3403309356797280102nteger )
% 6.92/7.18 = ( A = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.18
% 6.92/7.18 % double_eq_0_iff
% 6.92/7.18 thf(fact_2694_double__eq__0__iff,axiom,
% 6.92/7.18 ! [A: rat] :
% 6.92/7.18 ( ( ( plus_plus_rat @ A @ A )
% 6.92/7.18 = zero_zero_rat )
% 6.92/7.18 = ( A = zero_zero_rat ) ) ).
% 6.92/7.18
% 6.92/7.18 % double_eq_0_iff
% 6.92/7.18 thf(fact_2695_double__eq__0__iff,axiom,
% 6.92/7.18 ! [A: int] :
% 6.92/7.18 ( ( ( plus_plus_int @ A @ A )
% 6.92/7.18 = zero_zero_int )
% 6.92/7.18 = ( A = zero_zero_int ) ) ).
% 6.92/7.18
% 6.92/7.18 % double_eq_0_iff
% 6.92/7.18 thf(fact_2696_sum__squares__gt__zero__iff,axiom,
% 6.92/7.18 ! [X: code_integer,Y: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) )
% 6.92/7.18 = ( ( X != zero_z3403309356797280102nteger )
% 6.92/7.18 | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % sum_squares_gt_zero_iff
% 6.92/7.18 thf(fact_2697_sum__squares__gt__zero__iff,axiom,
% 6.92/7.18 ! [X: rat,Y: rat] :
% 6.92/7.18 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 6.92/7.18 = ( ( X != zero_zero_rat )
% 6.92/7.18 | ( Y != zero_zero_rat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % sum_squares_gt_zero_iff
% 6.92/7.18 thf(fact_2698_sum__squares__gt__zero__iff,axiom,
% 6.92/7.18 ! [X: int,Y: int] :
% 6.92/7.18 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 6.92/7.18 = ( ( X != zero_zero_int )
% 6.92/7.18 | ( Y != zero_zero_int ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % sum_squares_gt_zero_iff
% 6.92/7.18 thf(fact_2699_sum__squares__le__zero__iff,axiom,
% 6.92/7.18 ! [X: code_integer,Y: code_integer] :
% 6.92/7.18 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger )
% 6.92/7.18 = ( ( X = zero_z3403309356797280102nteger )
% 6.92/7.18 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % sum_squares_le_zero_iff
% 6.92/7.18 thf(fact_2700_sum__squares__le__zero__iff,axiom,
% 6.92/7.18 ! [X: rat,Y: rat] :
% 6.92/7.18 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 6.92/7.18 = ( ( X = zero_zero_rat )
% 6.92/7.18 & ( Y = zero_zero_rat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % sum_squares_le_zero_iff
% 6.92/7.18 thf(fact_2701_sum__squares__le__zero__iff,axiom,
% 6.92/7.18 ! [X: int,Y: int] :
% 6.92/7.18 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 6.92/7.18 = ( ( X = zero_zero_int )
% 6.92/7.18 & ( Y = zero_zero_int ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % sum_squares_le_zero_iff
% 6.92/7.18 thf(fact_2702_mult__le__cancel__iff1,axiom,
% 6.92/7.18 ! [Z3: code_integer,X: code_integer,Y: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z3 )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Z3 ) @ ( times_3573771949741848930nteger @ Y @ Z3 ) )
% 6.92/7.18 = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_iff1
% 6.92/7.18 thf(fact_2703_mult__le__cancel__iff1,axiom,
% 6.92/7.18 ! [Z3: rat,X: rat,Y: rat] :
% 6.92/7.18 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 6.92/7.18 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ Y @ Z3 ) )
% 6.92/7.18 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_iff1
% 6.92/7.18 thf(fact_2704_mult__le__cancel__iff1,axiom,
% 6.92/7.18 ! [Z3: int,X: int,Y: int] :
% 6.92/7.18 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 6.92/7.18 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z3 ) @ ( times_times_int @ Y @ Z3 ) )
% 6.92/7.18 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_iff1
% 6.92/7.18 thf(fact_2705_mult__le__cancel__iff2,axiom,
% 6.92/7.18 ! [Z3: code_integer,X: code_integer,Y: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z3 )
% 6.92/7.18 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Z3 @ X ) @ ( times_3573771949741848930nteger @ Z3 @ Y ) )
% 6.92/7.18 = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_iff2
% 6.92/7.18 thf(fact_2706_mult__le__cancel__iff2,axiom,
% 6.92/7.18 ! [Z3: rat,X: rat,Y: rat] :
% 6.92/7.18 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 6.92/7.18 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X ) @ ( times_times_rat @ Z3 @ Y ) )
% 6.92/7.18 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_iff2
% 6.92/7.18 thf(fact_2707_mult__le__cancel__iff2,axiom,
% 6.92/7.18 ! [Z3: int,X: int,Y: int] :
% 6.92/7.18 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 6.92/7.18 => ( ( ord_less_eq_int @ ( times_times_int @ Z3 @ X ) @ ( times_times_int @ Z3 @ Y ) )
% 6.92/7.18 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel_iff2
% 6.92/7.18 thf(fact_2708_field__le__epsilon,axiom,
% 6.92/7.18 ! [X: rat,Y: rat] :
% 6.92/7.18 ( ! [E2: rat] :
% 6.92/7.18 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 6.92/7.18 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E2 ) ) )
% 6.92/7.18 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 6.92/7.18
% 6.92/7.18 % field_le_epsilon
% 6.92/7.18 thf(fact_2709_divides__aux__eq,axiom,
% 6.92/7.18 ! [Q6: code_integer,R2: code_integer] :
% 6.92/7.18 ( ( unique5706413561485394159nteger @ ( produc1086072967326762835nteger @ Q6 @ R2 ) )
% 6.92/7.18 = ( R2 = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.18
% 6.92/7.18 % divides_aux_eq
% 6.92/7.18 thf(fact_2710_divides__aux__eq,axiom,
% 6.92/7.18 ! [Q6: nat,R2: nat] :
% 6.92/7.18 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q6 @ R2 ) )
% 6.92/7.18 = ( R2 = zero_zero_nat ) ) ).
% 6.92/7.18
% 6.92/7.18 % divides_aux_eq
% 6.92/7.18 thf(fact_2711_divides__aux__eq,axiom,
% 6.92/7.18 ! [Q6: int,R2: int] :
% 6.92/7.18 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 6.92/7.18 = ( R2 = zero_zero_int ) ) ).
% 6.92/7.18
% 6.92/7.18 % divides_aux_eq
% 6.92/7.18 thf(fact_2712_pure__assn__raw_Opelims_I3_J,axiom,
% 6.92/7.18 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 6.92/7.18 ( ~ ( pure_a825153325127701367it_nat @ X @ Xa )
% 6.92/7.18 => ( ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ Xa ) )
% 6.92/7.18 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.18 ( ( Xa
% 6.92/7.18 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.18 => ( ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) )
% 6.92/7.18 => ( ( As2 = bot_bot_set_nat )
% 6.92/7.18 & X ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % pure_assn_raw.pelims(3)
% 6.92/7.18 thf(fact_2713_pure__assn__raw_Opelims_I2_J,axiom,
% 6.92/7.18 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 6.92/7.18 ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 6.92/7.18 => ( ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ Xa ) )
% 6.92/7.18 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.18 ( ( Xa
% 6.92/7.18 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.18 => ( ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) )
% 6.92/7.18 => ~ ( ( As2 = bot_bot_set_nat )
% 6.92/7.18 & X ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % pure_assn_raw.pelims(2)
% 6.92/7.18 thf(fact_2714_mult__cancel2,axiom,
% 6.92/7.18 ! [M: nat,K2: nat,N2: nat] :
% 6.92/7.18 ( ( ( times_times_nat @ M @ K2 )
% 6.92/7.18 = ( times_times_nat @ N2 @ K2 ) )
% 6.92/7.18 = ( ( M = N2 )
% 6.92/7.18 | ( K2 = zero_zero_nat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_cancel2
% 6.92/7.18 thf(fact_2715_mult__cancel1,axiom,
% 6.92/7.18 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.18 ( ( ( times_times_nat @ K2 @ M )
% 6.92/7.18 = ( times_times_nat @ K2 @ N2 ) )
% 6.92/7.18 = ( ( M = N2 )
% 6.92/7.18 | ( K2 = zero_zero_nat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_cancel1
% 6.92/7.18 thf(fact_2716_mult__0__right,axiom,
% 6.92/7.18 ! [M: nat] :
% 6.92/7.18 ( ( times_times_nat @ M @ zero_zero_nat )
% 6.92/7.18 = zero_zero_nat ) ).
% 6.92/7.18
% 6.92/7.18 % mult_0_right
% 6.92/7.18 thf(fact_2717_mult__is__0,axiom,
% 6.92/7.18 ! [M: nat,N2: nat] :
% 6.92/7.18 ( ( ( times_times_nat @ M @ N2 )
% 6.92/7.18 = zero_zero_nat )
% 6.92/7.18 = ( ( M = zero_zero_nat )
% 6.92/7.18 | ( N2 = zero_zero_nat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_is_0
% 6.92/7.18 thf(fact_2718_nat__mult__eq__1__iff,axiom,
% 6.92/7.18 ! [M: nat,N2: nat] :
% 6.92/7.18 ( ( ( times_times_nat @ M @ N2 )
% 6.92/7.18 = one_one_nat )
% 6.92/7.18 = ( ( M = one_one_nat )
% 6.92/7.18 & ( N2 = one_one_nat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % nat_mult_eq_1_iff
% 6.92/7.18 thf(fact_2719_nat__1__eq__mult__iff,axiom,
% 6.92/7.18 ! [M: nat,N2: nat] :
% 6.92/7.18 ( ( one_one_nat
% 6.92/7.18 = ( times_times_nat @ M @ N2 ) )
% 6.92/7.18 = ( ( M = one_one_nat )
% 6.92/7.18 & ( N2 = one_one_nat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % nat_1_eq_mult_iff
% 6.92/7.18 thf(fact_2720_nat__0__less__mult__iff,axiom,
% 6.92/7.18 ! [M: nat,N2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N2 ) )
% 6.92/7.18 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.18 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % nat_0_less_mult_iff
% 6.92/7.18 thf(fact_2721_mult__less__cancel2,axiom,
% 6.92/7.18 ! [M: nat,K2: nat,N2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ ( times_times_nat @ M @ K2 ) @ ( times_times_nat @ N2 @ K2 ) )
% 6.92/7.18 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.18 & ( ord_less_nat @ M @ N2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_cancel2
% 6.92/7.18 thf(fact_2722_mult__le__cancel2,axiom,
% 6.92/7.18 ! [M: nat,K2: nat,N2: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K2 ) @ ( times_times_nat @ N2 @ K2 ) )
% 6.92/7.18 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.18 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_cancel2
% 6.92/7.18 thf(fact_2723_mult__0,axiom,
% 6.92/7.18 ! [N2: nat] :
% 6.92/7.18 ( ( times_times_nat @ zero_zero_nat @ N2 )
% 6.92/7.18 = zero_zero_nat ) ).
% 6.92/7.18
% 6.92/7.18 % mult_0
% 6.92/7.18 thf(fact_2724_le__cube,axiom,
% 6.92/7.18 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % le_cube
% 6.92/7.18 thf(fact_2725_le__square,axiom,
% 6.92/7.18 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 6.92/7.18
% 6.92/7.18 % le_square
% 6.92/7.18 thf(fact_2726_mult__le__mono,axiom,
% 6.92/7.18 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.18 => ( ( ord_less_eq_nat @ K2 @ L )
% 6.92/7.18 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K2 ) @ ( times_times_nat @ J2 @ L ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_mono
% 6.92/7.18 thf(fact_2727_mult__le__mono1,axiom,
% 6.92/7.18 ! [I2: nat,J2: nat,K2: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.18 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K2 ) @ ( times_times_nat @ J2 @ K2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_mono1
% 6.92/7.18 thf(fact_2728_mult__le__mono2,axiom,
% 6.92/7.18 ! [I2: nat,J2: nat,K2: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.18 => ( ord_less_eq_nat @ ( times_times_nat @ K2 @ I2 ) @ ( times_times_nat @ K2 @ J2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_le_mono2
% 6.92/7.18 thf(fact_2729_add__mult__distrib2,axiom,
% 6.92/7.18 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.18 ( ( times_times_nat @ K2 @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.18 = ( plus_plus_nat @ ( times_times_nat @ K2 @ M ) @ ( times_times_nat @ K2 @ N2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_mult_distrib2
% 6.92/7.18 thf(fact_2730_add__mult__distrib,axiom,
% 6.92/7.18 ! [M: nat,N2: nat,K2: nat] :
% 6.92/7.18 ( ( times_times_nat @ ( plus_plus_nat @ M @ N2 ) @ K2 )
% 6.92/7.18 = ( plus_plus_nat @ ( times_times_nat @ M @ K2 ) @ ( times_times_nat @ N2 @ K2 ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % add_mult_distrib
% 6.92/7.18 thf(fact_2731_nat__mult__1__right,axiom,
% 6.92/7.18 ! [N2: nat] :
% 6.92/7.18 ( ( times_times_nat @ N2 @ one_one_nat )
% 6.92/7.18 = N2 ) ).
% 6.92/7.18
% 6.92/7.18 % nat_mult_1_right
% 6.92/7.18 thf(fact_2732_nat__mult__1,axiom,
% 6.92/7.18 ! [N2: nat] :
% 6.92/7.18 ( ( times_times_nat @ one_one_nat @ N2 )
% 6.92/7.18 = N2 ) ).
% 6.92/7.18
% 6.92/7.18 % nat_mult_1
% 6.92/7.18 thf(fact_2733_mult__less__mono2,axiom,
% 6.92/7.18 ! [I2: nat,J2: nat,K2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.18 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.18 => ( ord_less_nat @ ( times_times_nat @ K2 @ I2 ) @ ( times_times_nat @ K2 @ J2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_mono2
% 6.92/7.18 thf(fact_2734_mult__less__mono1,axiom,
% 6.92/7.18 ! [I2: nat,J2: nat,K2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.18 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.18 => ( ord_less_nat @ ( times_times_nat @ I2 @ K2 ) @ ( times_times_nat @ J2 @ K2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_mono1
% 6.92/7.18 thf(fact_2735_mlex__snd__decrI,axiom,
% 6.92/7.18 ! [A: nat,A2: nat,B: nat,B2: nat,N7: nat] :
% 6.92/7.18 ( ( A = A2 )
% 6.92/7.18 => ( ( ord_less_nat @ B @ B2 )
% 6.92/7.18 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N7 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N7 ) @ B2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mlex_snd_decrI
% 6.92/7.18 thf(fact_2736_mlex__fst__decrI,axiom,
% 6.92/7.18 ! [A: nat,A2: nat,B: nat,N7: nat,B2: nat] :
% 6.92/7.18 ( ( ord_less_nat @ A @ A2 )
% 6.92/7.18 => ( ( ord_less_nat @ B @ N7 )
% 6.92/7.18 => ( ( ord_less_nat @ B2 @ N7 )
% 6.92/7.18 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N7 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N7 ) @ B2 ) ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mlex_fst_decrI
% 6.92/7.18 thf(fact_2737_mlex__bound,axiom,
% 6.92/7.18 ! [A: nat,A4: nat,B: nat,N7: nat] :
% 6.92/7.18 ( ( ord_less_nat @ A @ A4 )
% 6.92/7.18 => ( ( ord_less_nat @ B @ N7 )
% 6.92/7.18 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N7 ) @ B ) @ ( times_times_nat @ A4 @ N7 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mlex_bound
% 6.92/7.18 thf(fact_2738_mlex__leI,axiom,
% 6.92/7.18 ! [A: nat,A2: nat,B: nat,B2: nat,N7: nat] :
% 6.92/7.18 ( ( ord_less_eq_nat @ A @ A2 )
% 6.92/7.18 => ( ( ord_less_eq_nat @ B @ B2 )
% 6.92/7.18 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N7 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N7 ) @ B2 ) ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mlex_leI
% 6.92/7.18 thf(fact_2739_mult__eq__self__implies__10,axiom,
% 6.92/7.18 ! [M: nat,N2: nat] :
% 6.92/7.18 ( ( M
% 6.92/7.18 = ( times_times_nat @ M @ N2 ) )
% 6.92/7.18 => ( ( N2 = one_one_nat )
% 6.92/7.18 | ( M = zero_zero_nat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_eq_self_implies_10
% 6.92/7.18 thf(fact_2740_linordered__field__no__lb,axiom,
% 6.92/7.18 ! [X6: rat] :
% 6.92/7.18 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X6 ) ).
% 6.92/7.18
% 6.92/7.18 % linordered_field_no_lb
% 6.92/7.18 thf(fact_2741_linordered__field__no__ub,axiom,
% 6.92/7.18 ! [X6: rat] :
% 6.92/7.18 ? [X_1: rat] : ( ord_less_rat @ X6 @ X_1 ) ).
% 6.92/7.18
% 6.92/7.18 % linordered_field_no_ub
% 6.92/7.18 thf(fact_2742_mult__less__iff1,axiom,
% 6.92/7.18 ! [Z3: code_integer,X: code_integer,Y: code_integer] :
% 6.92/7.18 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z3 )
% 6.92/7.18 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ X @ Z3 ) @ ( times_3573771949741848930nteger @ Y @ Z3 ) )
% 6.92/7.18 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_iff1
% 6.92/7.18 thf(fact_2743_mult__less__iff1,axiom,
% 6.92/7.18 ! [Z3: rat,X: rat,Y: rat] :
% 6.92/7.18 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 6.92/7.18 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ Y @ Z3 ) )
% 6.92/7.18 = ( ord_less_rat @ X @ Y ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_iff1
% 6.92/7.18 thf(fact_2744_mult__less__iff1,axiom,
% 6.92/7.18 ! [Z3: int,X: int,Y: int] :
% 6.92/7.18 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 6.92/7.18 => ( ( ord_less_int @ ( times_times_int @ X @ Z3 ) @ ( times_times_int @ Y @ Z3 ) )
% 6.92/7.18 = ( ord_less_int @ X @ Y ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % mult_less_iff1
% 6.92/7.18 thf(fact_2745_sum__squares__eq__zero__iff,axiom,
% 6.92/7.18 ! [X: code_integer,Y: code_integer] :
% 6.92/7.18 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 6.92/7.18 = zero_z3403309356797280102nteger )
% 6.92/7.18 = ( ( X = zero_z3403309356797280102nteger )
% 6.92/7.18 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % sum_squares_eq_zero_iff
% 6.92/7.18 thf(fact_2746_sum__squares__eq__zero__iff,axiom,
% 6.92/7.18 ! [X: rat,Y: rat] :
% 6.92/7.18 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 6.92/7.18 = zero_zero_rat )
% 6.92/7.18 = ( ( X = zero_zero_rat )
% 6.92/7.18 & ( Y = zero_zero_rat ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % sum_squares_eq_zero_iff
% 6.92/7.18 thf(fact_2747_sum__squares__eq__zero__iff,axiom,
% 6.92/7.18 ! [X: int,Y: int] :
% 6.92/7.18 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 6.92/7.18 = zero_zero_int )
% 6.92/7.18 = ( ( X = zero_zero_int )
% 6.92/7.18 & ( Y = zero_zero_int ) ) ) ).
% 6.92/7.18
% 6.92/7.18 % sum_squares_eq_zero_iff
% 6.92/7.18 thf(fact_2748_pure__assn__raw_Opelims_I1_J,axiom,
% 6.92/7.18 ! [X: $o,Xa: produc3658429121746597890et_nat,Y: $o] :
% 6.92/7.18 ( ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 6.92/7.18 = Y )
% 6.92/7.18 => ( ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ Xa ) )
% 6.92/7.18 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.18 ( ( Xa
% 6.92/7.18 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.19 => ( ( Y
% 6.92/7.19 = ( ( As2 = bot_bot_set_nat )
% 6.92/7.19 & X ) )
% 6.92/7.19 => ~ ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % pure_assn_raw.pelims(1)
% 6.92/7.19 thf(fact_2749_nat__mult__le__cancel__disj,axiom,
% 6.92/7.19 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ ( times_times_nat @ K2 @ M ) @ ( times_times_nat @ K2 @ N2 ) )
% 6.92/7.19 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.19 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % nat_mult_le_cancel_disj
% 6.92/7.19 thf(fact_2750_nat__mult__less__cancel__disj,axiom,
% 6.92/7.19 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_nat @ ( times_times_nat @ K2 @ M ) @ ( times_times_nat @ K2 @ N2 ) )
% 6.92/7.19 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.19 & ( ord_less_nat @ M @ N2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % nat_mult_less_cancel_disj
% 6.92/7.19 thf(fact_2751_nat__mult__le__cancel1,axiom,
% 6.92/7.19 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.19 => ( ( ord_less_eq_nat @ ( times_times_nat @ K2 @ M ) @ ( times_times_nat @ K2 @ N2 ) )
% 6.92/7.19 = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % nat_mult_le_cancel1
% 6.92/7.19 thf(fact_2752_add__scale__eq__noteq,axiom,
% 6.92/7.19 ! [R2: code_integer,A: code_integer,B: code_integer,C2: code_integer,D2: code_integer] :
% 6.92/7.19 ( ( R2 != zero_z3403309356797280102nteger )
% 6.92/7.19 => ( ( ( A = B )
% 6.92/7.19 & ( C2 != D2 ) )
% 6.92/7.19 => ( ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ R2 @ C2 ) )
% 6.92/7.19 != ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ R2 @ D2 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % add_scale_eq_noteq
% 6.92/7.19 thf(fact_2753_add__scale__eq__noteq,axiom,
% 6.92/7.19 ! [R2: rat,A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.19 ( ( R2 != zero_zero_rat )
% 6.92/7.19 => ( ( ( A = B )
% 6.92/7.19 & ( C2 != D2 ) )
% 6.92/7.19 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C2 ) )
% 6.92/7.19 != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D2 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % add_scale_eq_noteq
% 6.92/7.19 thf(fact_2754_add__scale__eq__noteq,axiom,
% 6.92/7.19 ! [R2: nat,A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.19 ( ( R2 != zero_zero_nat )
% 6.92/7.19 => ( ( ( A = B )
% 6.92/7.19 & ( C2 != D2 ) )
% 6.92/7.19 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C2 ) )
% 6.92/7.19 != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D2 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % add_scale_eq_noteq
% 6.92/7.19 thf(fact_2755_add__scale__eq__noteq,axiom,
% 6.92/7.19 ! [R2: int,A: int,B: int,C2: int,D2: int] :
% 6.92/7.19 ( ( R2 != zero_zero_int )
% 6.92/7.19 => ( ( ( A = B )
% 6.92/7.19 & ( C2 != D2 ) )
% 6.92/7.19 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C2 ) )
% 6.92/7.19 != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D2 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % add_scale_eq_noteq
% 6.92/7.19 thf(fact_2756_Euclid__induct,axiom,
% 6.92/7.19 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 6.92/7.19 ( ! [A3: nat,B3: nat] :
% 6.92/7.19 ( ( P2 @ A3 @ B3 )
% 6.92/7.19 = ( P2 @ B3 @ A3 ) )
% 6.92/7.19 => ( ! [A3: nat] : ( P2 @ A3 @ zero_zero_nat )
% 6.92/7.19 => ( ! [A3: nat,B3: nat] :
% 6.92/7.19 ( ( P2 @ A3 @ B3 )
% 6.92/7.19 => ( P2 @ A3 @ ( plus_plus_nat @ A3 @ B3 ) ) )
% 6.92/7.19 => ( P2 @ A @ B ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Euclid_induct
% 6.92/7.19 thf(fact_2757_nat__mult__eq__cancel1,axiom,
% 6.92/7.19 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.19 => ( ( ( times_times_nat @ K2 @ M )
% 6.92/7.19 = ( times_times_nat @ K2 @ N2 ) )
% 6.92/7.19 = ( M = N2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % nat_mult_eq_cancel1
% 6.92/7.19 thf(fact_2758_left__add__mult__distrib,axiom,
% 6.92/7.19 ! [I2: nat,U: nat,J2: nat,K2: nat] :
% 6.92/7.19 ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ K2 ) )
% 6.92/7.19 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J2 ) @ U ) @ K2 ) ) ).
% 6.92/7.19
% 6.92/7.19 % left_add_mult_distrib
% 6.92/7.19 thf(fact_2759_add__0__iff,axiom,
% 6.92/7.19 ! [B: code_integer,A: code_integer] :
% 6.92/7.19 ( ( B
% 6.92/7.19 = ( plus_p5714425477246183910nteger @ B @ A ) )
% 6.92/7.19 = ( A = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.19
% 6.92/7.19 % add_0_iff
% 6.92/7.19 thf(fact_2760_add__0__iff,axiom,
% 6.92/7.19 ! [B: rat,A: rat] :
% 6.92/7.19 ( ( B
% 6.92/7.19 = ( plus_plus_rat @ B @ A ) )
% 6.92/7.19 = ( A = zero_zero_rat ) ) ).
% 6.92/7.19
% 6.92/7.19 % add_0_iff
% 6.92/7.19 thf(fact_2761_add__0__iff,axiom,
% 6.92/7.19 ! [B: nat,A: nat] :
% 6.92/7.19 ( ( B
% 6.92/7.19 = ( plus_plus_nat @ B @ A ) )
% 6.92/7.19 = ( A = zero_zero_nat ) ) ).
% 6.92/7.19
% 6.92/7.19 % add_0_iff
% 6.92/7.19 thf(fact_2762_add__0__iff,axiom,
% 6.92/7.19 ! [B: int,A: int] :
% 6.92/7.19 ( ( B
% 6.92/7.19 = ( plus_plus_int @ B @ A ) )
% 6.92/7.19 = ( A = zero_zero_int ) ) ).
% 6.92/7.19
% 6.92/7.19 % add_0_iff
% 6.92/7.19 thf(fact_2763_crossproduct__noteq,axiom,
% 6.92/7.19 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.19 ( ( ( A != B )
% 6.92/7.19 & ( C2 != D2 ) )
% 6.92/7.19 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D2 ) )
% 6.92/7.19 != ( plus_plus_rat @ ( times_times_rat @ A @ D2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % crossproduct_noteq
% 6.92/7.19 thf(fact_2764_crossproduct__noteq,axiom,
% 6.92/7.19 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.19 ( ( ( A != B )
% 6.92/7.19 & ( C2 != D2 ) )
% 6.92/7.19 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D2 ) )
% 6.92/7.19 != ( plus_plus_nat @ ( times_times_nat @ A @ D2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % crossproduct_noteq
% 6.92/7.19 thf(fact_2765_crossproduct__noteq,axiom,
% 6.92/7.19 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.19 ( ( ( A != B )
% 6.92/7.19 & ( C2 != D2 ) )
% 6.92/7.19 = ( ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D2 ) )
% 6.92/7.19 != ( plus_plus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % crossproduct_noteq
% 6.92/7.19 thf(fact_2766_crossproduct__eq,axiom,
% 6.92/7.19 ! [W2: rat,Y: rat,X: rat,Z3: rat] :
% 6.92/7.19 ( ( ( plus_plus_rat @ ( times_times_rat @ W2 @ Y ) @ ( times_times_rat @ X @ Z3 ) )
% 6.92/7.19 = ( plus_plus_rat @ ( times_times_rat @ W2 @ Z3 ) @ ( times_times_rat @ X @ Y ) ) )
% 6.92/7.19 = ( ( W2 = X )
% 6.92/7.19 | ( Y = Z3 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % crossproduct_eq
% 6.92/7.19 thf(fact_2767_crossproduct__eq,axiom,
% 6.92/7.19 ! [W2: nat,Y: nat,X: nat,Z3: nat] :
% 6.92/7.19 ( ( ( plus_plus_nat @ ( times_times_nat @ W2 @ Y ) @ ( times_times_nat @ X @ Z3 ) )
% 6.92/7.19 = ( plus_plus_nat @ ( times_times_nat @ W2 @ Z3 ) @ ( times_times_nat @ X @ Y ) ) )
% 6.92/7.19 = ( ( W2 = X )
% 6.92/7.19 | ( Y = Z3 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % crossproduct_eq
% 6.92/7.19 thf(fact_2768_crossproduct__eq,axiom,
% 6.92/7.19 ! [W2: int,Y: int,X: int,Z3: int] :
% 6.92/7.19 ( ( ( plus_plus_int @ ( times_times_int @ W2 @ Y ) @ ( times_times_int @ X @ Z3 ) )
% 6.92/7.19 = ( plus_plus_int @ ( times_times_int @ W2 @ Z3 ) @ ( times_times_int @ X @ Y ) ) )
% 6.92/7.19 = ( ( W2 = X )
% 6.92/7.19 | ( Y = Z3 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % crossproduct_eq
% 6.92/7.19 thf(fact_2769_nat__mult__less__cancel1,axiom,
% 6.92/7.19 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.19 => ( ( ord_less_nat @ ( times_times_nat @ K2 @ M ) @ ( times_times_nat @ K2 @ N2 ) )
% 6.92/7.19 = ( ord_less_nat @ M @ N2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % nat_mult_less_cancel1
% 6.92/7.19 thf(fact_2770_ent__mp,axiom,
% 6.92/7.19 ! [P2: assn,Q2: assn] : ( entails @ ( times_times_assn @ P2 @ ( wand_assn @ P2 @ Q2 ) ) @ Q2 ) ).
% 6.92/7.19
% 6.92/7.19 % ent_mp
% 6.92/7.19 thf(fact_2771_ent__wandI,axiom,
% 6.92/7.19 ! [Q2: assn,P2: assn,R3: assn] :
% 6.92/7.19 ( ( entails @ ( times_times_assn @ Q2 @ P2 ) @ R3 )
% 6.92/7.19 => ( entails @ P2 @ ( wand_assn @ Q2 @ R3 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % ent_wandI
% 6.92/7.19 thf(fact_2772_power__decreasing__iff,axiom,
% 6.92/7.19 ! [B: code_integer,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.19 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 6.92/7.19 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ M ) @ ( power_8256067586552552935nteger @ B @ N2 ) )
% 6.92/7.19 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_decreasing_iff
% 6.92/7.19 thf(fact_2773_power__decreasing__iff,axiom,
% 6.92/7.19 ! [B: rat,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_rat @ zero_zero_rat @ B )
% 6.92/7.19 => ( ( ord_less_rat @ B @ one_one_rat )
% 6.92/7.19 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 6.92/7.19 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_decreasing_iff
% 6.92/7.19 thf(fact_2774_power__decreasing__iff,axiom,
% 6.92/7.19 ! [B: nat,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_nat @ zero_zero_nat @ B )
% 6.92/7.19 => ( ( ord_less_nat @ B @ one_one_nat )
% 6.92/7.19 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 6.92/7.19 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_decreasing_iff
% 6.92/7.19 thf(fact_2775_power__decreasing__iff,axiom,
% 6.92/7.19 ! [B: int,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.19 => ( ( ord_less_int @ B @ one_one_int )
% 6.92/7.19 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 6.92/7.19 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_decreasing_iff
% 6.92/7.19 thf(fact_2776_mod__star__conv,axiom,
% 6.92/7.19 ! [A4: assn,B5: assn,H: produc3658429121746597890et_nat] :
% 6.92/7.19 ( ( rep_assn @ ( times_times_assn @ A4 @ B5 ) @ H )
% 6.92/7.19 = ( ? [Hr: heap_e7401611519738050253t_unit,As1: set_nat,As22: set_nat] :
% 6.92/7.19 ( ( H
% 6.92/7.19 = ( produc7507926704131184380et_nat @ Hr @ ( sup_sup_set_nat @ As1 @ As22 ) ) )
% 6.92/7.19 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 6.92/7.19 = bot_bot_set_nat )
% 6.92/7.19 & ( rep_assn @ A4 @ ( produc7507926704131184380et_nat @ Hr @ As1 ) )
% 6.92/7.19 & ( rep_assn @ B5 @ ( produc7507926704131184380et_nat @ Hr @ As22 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % mod_star_conv
% 6.92/7.19 thf(fact_2777_star__assnI,axiom,
% 6.92/7.19 ! [P2: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q2: assn,As5: set_nat] :
% 6.92/7.19 ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.19 => ( ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H @ As5 ) )
% 6.92/7.19 => ( ( ( inf_inf_set_nat @ As @ As5 )
% 6.92/7.19 = bot_bot_set_nat )
% 6.92/7.19 => ( rep_assn @ ( times_times_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H @ ( sup_sup_set_nat @ As @ As5 ) ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % star_assnI
% 6.92/7.19 thf(fact_2778_power__strict__mono,axiom,
% 6.92/7.19 ! [A: code_integer,B: code_integer,N2: nat] :
% 6.92/7.19 ( ( ord_le6747313008572928689nteger @ A @ B )
% 6.92/7.19 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.19 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.19 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_strict_mono
% 6.92/7.19 thf(fact_2779_power__strict__mono,axiom,
% 6.92/7.19 ! [A: rat,B: rat,N2: nat] :
% 6.92/7.19 ( ( ord_less_rat @ A @ B )
% 6.92/7.19 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.19 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.19 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_strict_mono
% 6.92/7.19 thf(fact_2780_power__strict__mono,axiom,
% 6.92/7.19 ! [A: nat,B: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_nat @ A @ B )
% 6.92/7.19 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.19 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.19 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_strict_mono
% 6.92/7.19 thf(fact_2781_power__strict__mono,axiom,
% 6.92/7.19 ! [A: int,B: int,N2: nat] :
% 6.92/7.19 ( ( ord_less_int @ A @ B )
% 6.92/7.19 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.19 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.19 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_strict_mono
% 6.92/7.19 thf(fact_2782_power__increasing__iff,axiom,
% 6.92/7.19 ! [B: code_integer,X: nat,Y: nat] :
% 6.92/7.19 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 6.92/7.19 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 6.92/7.19 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_increasing_iff
% 6.92/7.19 thf(fact_2783_power__increasing__iff,axiom,
% 6.92/7.19 ! [B: rat,X: nat,Y: nat] :
% 6.92/7.19 ( ( ord_less_rat @ one_one_rat @ B )
% 6.92/7.19 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 6.92/7.19 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_increasing_iff
% 6.92/7.19 thf(fact_2784_power__increasing__iff,axiom,
% 6.92/7.19 ! [B: nat,X: nat,Y: nat] :
% 6.92/7.19 ( ( ord_less_nat @ one_one_nat @ B )
% 6.92/7.19 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 6.92/7.19 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_increasing_iff
% 6.92/7.19 thf(fact_2785_power__increasing__iff,axiom,
% 6.92/7.19 ! [B: int,X: nat,Y: nat] :
% 6.92/7.19 ( ( ord_less_int @ one_one_int @ B )
% 6.92/7.19 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 6.92/7.19 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_increasing_iff
% 6.92/7.19 thf(fact_2786_divide__le__eq__1__neg,axiom,
% 6.92/7.19 ! [A: rat,B: rat] :
% 6.92/7.19 ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.19 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 6.92/7.19 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % divide_le_eq_1_neg
% 6.92/7.19 thf(fact_2787_divide__le__eq__1__pos,axiom,
% 6.92/7.19 ! [A: rat,B: rat] :
% 6.92/7.19 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.19 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 6.92/7.19 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % divide_le_eq_1_pos
% 6.92/7.19 thf(fact_2788_Int__iff,axiom,
% 6.92/7.19 ! [C2: $o,A4: set_o,B5: set_o] :
% 6.92/7.19 ( ( member_o @ C2 @ ( inf_inf_set_o @ A4 @ B5 ) )
% 6.92/7.19 = ( ( member_o @ C2 @ A4 )
% 6.92/7.19 & ( member_o @ C2 @ B5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_iff
% 6.92/7.19 thf(fact_2789_Int__iff,axiom,
% 6.92/7.19 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.19 ( ( member2340774599025711042nt_int @ C2 @ ( inf_in8396524679539076455nt_int @ A4 @ B5 ) )
% 6.92/7.19 = ( ( member2340774599025711042nt_int @ C2 @ A4 )
% 6.92/7.19 & ( member2340774599025711042nt_int @ C2 @ B5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_iff
% 6.92/7.19 thf(fact_2790_Int__iff,axiom,
% 6.92/7.19 ! [C2: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.19 ( ( member_set_nat @ C2 @ ( inf_inf_set_set_nat @ A4 @ B5 ) )
% 6.92/7.19 = ( ( member_set_nat @ C2 @ A4 )
% 6.92/7.19 & ( member_set_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_iff
% 6.92/7.19 thf(fact_2791_Int__iff,axiom,
% 6.92/7.19 ! [C2: int,A4: set_int,B5: set_int] :
% 6.92/7.19 ( ( member_int @ C2 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.92/7.19 = ( ( member_int @ C2 @ A4 )
% 6.92/7.19 & ( member_int @ C2 @ B5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_iff
% 6.92/7.19 thf(fact_2792_Int__iff,axiom,
% 6.92/7.19 ! [C2: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( member8440522571783428010at_nat @ C2 @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) )
% 6.92/7.19 = ( ( member8440522571783428010at_nat @ C2 @ A4 )
% 6.92/7.19 & ( member8440522571783428010at_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_iff
% 6.92/7.19 thf(fact_2793_Int__iff,axiom,
% 6.92/7.19 ! [C2: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.19 ( ( member_nat @ C2 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 6.92/7.19 = ( ( member_nat @ C2 @ A4 )
% 6.92/7.19 & ( member_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_iff
% 6.92/7.19 thf(fact_2794_IntI,axiom,
% 6.92/7.19 ! [C2: $o,A4: set_o,B5: set_o] :
% 6.92/7.19 ( ( member_o @ C2 @ A4 )
% 6.92/7.19 => ( ( member_o @ C2 @ B5 )
% 6.92/7.19 => ( member_o @ C2 @ ( inf_inf_set_o @ A4 @ B5 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntI
% 6.92/7.19 thf(fact_2795_IntI,axiom,
% 6.92/7.19 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.19 ( ( member2340774599025711042nt_int @ C2 @ A4 )
% 6.92/7.19 => ( ( member2340774599025711042nt_int @ C2 @ B5 )
% 6.92/7.19 => ( member2340774599025711042nt_int @ C2 @ ( inf_in8396524679539076455nt_int @ A4 @ B5 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntI
% 6.92/7.19 thf(fact_2796_IntI,axiom,
% 6.92/7.19 ! [C2: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.19 ( ( member_set_nat @ C2 @ A4 )
% 6.92/7.19 => ( ( member_set_nat @ C2 @ B5 )
% 6.92/7.19 => ( member_set_nat @ C2 @ ( inf_inf_set_set_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntI
% 6.92/7.19 thf(fact_2797_IntI,axiom,
% 6.92/7.19 ! [C2: int,A4: set_int,B5: set_int] :
% 6.92/7.19 ( ( member_int @ C2 @ A4 )
% 6.92/7.19 => ( ( member_int @ C2 @ B5 )
% 6.92/7.19 => ( member_int @ C2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntI
% 6.92/7.19 thf(fact_2798_IntI,axiom,
% 6.92/7.19 ! [C2: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( member8440522571783428010at_nat @ C2 @ A4 )
% 6.92/7.19 => ( ( member8440522571783428010at_nat @ C2 @ B5 )
% 6.92/7.19 => ( member8440522571783428010at_nat @ C2 @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntI
% 6.92/7.19 thf(fact_2799_IntI,axiom,
% 6.92/7.19 ! [C2: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.19 ( ( member_nat @ C2 @ A4 )
% 6.92/7.19 => ( ( member_nat @ C2 @ B5 )
% 6.92/7.19 => ( member_nat @ C2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntI
% 6.92/7.19 thf(fact_2800_le__inf__iff,axiom,
% 6.92/7.19 ! [X: assn,Y: assn,Z3: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ X @ ( inf_inf_assn @ Y @ Z3 ) )
% 6.92/7.19 = ( ( ord_less_eq_assn @ X @ Y )
% 6.92/7.19 & ( ord_less_eq_assn @ X @ Z3 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_inf_iff
% 6.92/7.19 thf(fact_2801_le__inf__iff,axiom,
% 6.92/7.19 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) )
% 6.92/7.19 = ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 6.92/7.19 & ( ord_le3146513528884898305at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_inf_iff
% 6.92/7.19 thf(fact_2802_le__inf__iff,axiom,
% 6.92/7.19 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z3 ) )
% 6.92/7.19 = ( ( ord_less_eq_set_nat @ X @ Y )
% 6.92/7.19 & ( ord_less_eq_set_nat @ X @ Z3 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_inf_iff
% 6.92/7.19 thf(fact_2803_le__inf__iff,axiom,
% 6.92/7.19 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z3 ) )
% 6.92/7.19 = ( ( ord_le8369615600986905444_int_o @ X @ Y )
% 6.92/7.19 & ( ord_le8369615600986905444_int_o @ X @ Z3 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_inf_iff
% 6.92/7.19 thf(fact_2804_le__inf__iff,axiom,
% 6.92/7.19 ! [X: set_int,Y: set_int,Z3: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ X @ ( inf_inf_set_int @ Y @ Z3 ) )
% 6.92/7.19 = ( ( ord_less_eq_set_int @ X @ Y )
% 6.92/7.19 & ( ord_less_eq_set_int @ X @ Z3 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_inf_iff
% 6.92/7.19 thf(fact_2805_le__inf__iff,axiom,
% 6.92/7.19 ! [X: rat,Y: rat,Z3: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z3 ) )
% 6.92/7.19 = ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.19 & ( ord_less_eq_rat @ X @ Z3 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_inf_iff
% 6.92/7.19 thf(fact_2806_le__inf__iff,axiom,
% 6.92/7.19 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z3 ) )
% 6.92/7.19 = ( ( ord_less_eq_nat @ X @ Y )
% 6.92/7.19 & ( ord_less_eq_nat @ X @ Z3 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_inf_iff
% 6.92/7.19 thf(fact_2807_le__inf__iff,axiom,
% 6.92/7.19 ! [X: int,Y: int,Z3: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z3 ) )
% 6.92/7.19 = ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.19 & ( ord_less_eq_int @ X @ Z3 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_inf_iff
% 6.92/7.19 thf(fact_2808_inf_Obounded__iff,axiom,
% 6.92/7.19 ! [A: assn,B: assn,C2: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ A @ ( inf_inf_assn @ B @ C2 ) )
% 6.92/7.19 = ( ( ord_less_eq_assn @ A @ B )
% 6.92/7.19 & ( ord_less_eq_assn @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.bounded_iff
% 6.92/7.19 thf(fact_2809_inf_Obounded__iff,axiom,
% 6.92/7.19 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) )
% 6.92/7.19 = ( ( ord_le3146513528884898305at_nat @ A @ B )
% 6.92/7.19 & ( ord_le3146513528884898305at_nat @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.bounded_iff
% 6.92/7.19 thf(fact_2810_inf_Obounded__iff,axiom,
% 6.92/7.19 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) )
% 6.92/7.19 = ( ( ord_less_eq_set_nat @ A @ B )
% 6.92/7.19 & ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.bounded_iff
% 6.92/7.19 thf(fact_2811_inf_Obounded__iff,axiom,
% 6.92/7.19 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C2: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C2 ) )
% 6.92/7.19 = ( ( ord_le8369615600986905444_int_o @ A @ B )
% 6.92/7.19 & ( ord_le8369615600986905444_int_o @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.bounded_iff
% 6.92/7.19 thf(fact_2812_inf_Obounded__iff,axiom,
% 6.92/7.19 ! [A: set_int,B: set_int,C2: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ A @ ( inf_inf_set_int @ B @ C2 ) )
% 6.92/7.19 = ( ( ord_less_eq_set_int @ A @ B )
% 6.92/7.19 & ( ord_less_eq_set_int @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.bounded_iff
% 6.92/7.19 thf(fact_2813_inf_Obounded__iff,axiom,
% 6.92/7.19 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C2 ) )
% 6.92/7.19 = ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.19 & ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.bounded_iff
% 6.92/7.19 thf(fact_2814_inf_Obounded__iff,axiom,
% 6.92/7.19 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C2 ) )
% 6.92/7.19 = ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.19 & ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.bounded_iff
% 6.92/7.19 thf(fact_2815_inf_Obounded__iff,axiom,
% 6.92/7.19 ! [A: int,B: int,C2: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C2 ) )
% 6.92/7.19 = ( ( ord_less_eq_int @ A @ B )
% 6.92/7.19 & ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.bounded_iff
% 6.92/7.19 thf(fact_2816_nat__zero__less__power__iff,axiom,
% 6.92/7.19 ! [X: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N2 ) )
% 6.92/7.19 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 6.92/7.19 | ( N2 = zero_zero_nat ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % nat_zero_less_power_iff
% 6.92/7.19 thf(fact_2817_inf__sup__absorb,axiom,
% 6.92/7.19 ! [X: assn,Y: assn] :
% 6.92/7.19 ( ( inf_inf_assn @ X @ ( sup_sup_assn @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_absorb
% 6.92/7.19 thf(fact_2818_inf__sup__absorb,axiom,
% 6.92/7.19 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_absorb
% 6.92/7.19 thf(fact_2819_inf__sup__absorb,axiom,
% 6.92/7.19 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 6.92/7.19 ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_absorb
% 6.92/7.19 thf(fact_2820_inf__sup__absorb,axiom,
% 6.92/7.19 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 6.92/7.19 ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_absorb
% 6.92/7.19 thf(fact_2821_inf__sup__absorb,axiom,
% 6.92/7.19 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 6.92/7.19 ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_absorb
% 6.92/7.19 thf(fact_2822_inf__sup__absorb,axiom,
% 6.92/7.19 ! [X: set_nat,Y: set_nat] :
% 6.92/7.19 ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_absorb
% 6.92/7.19 thf(fact_2823_inf__sup__absorb,axiom,
% 6.92/7.19 ! [X: nat,Y: nat] :
% 6.92/7.19 ( ( inf_inf_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_absorb
% 6.92/7.19 thf(fact_2824_inf__sup__absorb,axiom,
% 6.92/7.19 ! [X: int,Y: int] :
% 6.92/7.19 ( ( inf_inf_int @ X @ ( sup_sup_int @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_absorb
% 6.92/7.19 thf(fact_2825_sup__inf__absorb,axiom,
% 6.92/7.19 ! [X: assn,Y: assn] :
% 6.92/7.19 ( ( sup_sup_assn @ X @ ( inf_inf_assn @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % sup_inf_absorb
% 6.92/7.19 thf(fact_2826_sup__inf__absorb,axiom,
% 6.92/7.19 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % sup_inf_absorb
% 6.92/7.19 thf(fact_2827_sup__inf__absorb,axiom,
% 6.92/7.19 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 6.92/7.19 ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % sup_inf_absorb
% 6.92/7.19 thf(fact_2828_sup__inf__absorb,axiom,
% 6.92/7.19 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 6.92/7.19 ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % sup_inf_absorb
% 6.92/7.19 thf(fact_2829_sup__inf__absorb,axiom,
% 6.92/7.19 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 6.92/7.19 ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % sup_inf_absorb
% 6.92/7.19 thf(fact_2830_sup__inf__absorb,axiom,
% 6.92/7.19 ! [X: set_nat,Y: set_nat] :
% 6.92/7.19 ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % sup_inf_absorb
% 6.92/7.19 thf(fact_2831_sup__inf__absorb,axiom,
% 6.92/7.19 ! [X: nat,Y: nat] :
% 6.92/7.19 ( ( sup_sup_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % sup_inf_absorb
% 6.92/7.19 thf(fact_2832_sup__inf__absorb,axiom,
% 6.92/7.19 ! [X: int,Y: int] :
% 6.92/7.19 ( ( sup_sup_int @ X @ ( inf_inf_int @ X @ Y ) )
% 6.92/7.19 = X ) ).
% 6.92/7.19
% 6.92/7.19 % sup_inf_absorb
% 6.92/7.19 thf(fact_2833_Int__subset__iff,axiom,
% 6.92/7.19 ! [C4: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ C4 @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) )
% 6.92/7.19 = ( ( ord_le3146513528884898305at_nat @ C4 @ A4 )
% 6.92/7.19 & ( ord_le3146513528884898305at_nat @ C4 @ B5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_subset_iff
% 6.92/7.19 thf(fact_2834_Int__subset__iff,axiom,
% 6.92/7.19 ! [C4: set_nat,A4: set_nat,B5: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ C4 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 6.92/7.19 = ( ( ord_less_eq_set_nat @ C4 @ A4 )
% 6.92/7.19 & ( ord_less_eq_set_nat @ C4 @ B5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_subset_iff
% 6.92/7.19 thf(fact_2835_Int__subset__iff,axiom,
% 6.92/7.19 ! [C4: set_int,A4: set_int,B5: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ C4 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.92/7.19 = ( ( ord_less_eq_set_int @ C4 @ A4 )
% 6.92/7.19 & ( ord_less_eq_set_int @ C4 @ B5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_subset_iff
% 6.92/7.19 thf(fact_2836_inf__Some,axiom,
% 6.92/7.19 ! [X: assn,Y: assn] :
% 6.92/7.19 ( ( inf_inf_option_assn @ ( some_assn @ X ) @ ( some_assn @ Y ) )
% 6.92/7.19 = ( some_assn @ ( inf_inf_assn @ X @ Y ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_Some
% 6.92/7.19 thf(fact_2837_inf__Some,axiom,
% 6.92/7.19 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( inf_in777885744494410645at_nat @ ( some_s147305329494351046at_nat @ X ) @ ( some_s147305329494351046at_nat @ Y ) )
% 6.92/7.19 = ( some_s147305329494351046at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_Some
% 6.92/7.19 thf(fact_2838_inf__Some,axiom,
% 6.92/7.19 ! [X: set_nat,Y: set_nat] :
% 6.92/7.19 ( ( inf_in7812914138253463912et_nat @ ( some_set_nat @ X ) @ ( some_set_nat @ Y ) )
% 6.92/7.19 = ( some_set_nat @ ( inf_inf_set_nat @ X @ Y ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_Some
% 6.92/7.19 thf(fact_2839_inf__Some,axiom,
% 6.92/7.19 ! [X: nat,Y: nat] :
% 6.92/7.19 ( ( inf_inf_option_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 6.92/7.19 = ( some_nat @ ( inf_inf_nat @ X @ Y ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_Some
% 6.92/7.19 thf(fact_2840_inf__Some,axiom,
% 6.92/7.19 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 6.92/7.19 ( ( inf_in7104746047340619750_int_o @ ( some_P180497116919641311_int_o @ X ) @ ( some_P180497116919641311_int_o @ Y ) )
% 6.92/7.19 = ( some_P180497116919641311_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_Some
% 6.92/7.19 thf(fact_2841_Int__Un__eq_I4_J,axiom,
% 6.92/7.19 ! [T7: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( sup_su6327502436637775413at_nat @ T7 @ ( inf_in2572325071724192079at_nat @ S @ T7 ) )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(4)
% 6.92/7.19 thf(fact_2842_Int__Un__eq_I4_J,axiom,
% 6.92/7.19 ! [T7: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 6.92/7.19 ( ( sup_su3035147773818789531at_nat @ T7 @ ( inf_in1697001100524423349at_nat @ S @ T7 ) )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(4)
% 6.92/7.19 thf(fact_2843_Int__Un__eq_I4_J,axiom,
% 6.92/7.19 ! [T7: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 6.92/7.19 ( ( sup_su5525570899277871387at_nat @ T7 @ ( inf_in7913087082777306421at_nat @ S @ T7 ) )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(4)
% 6.92/7.19 thf(fact_2844_Int__Un__eq_I4_J,axiom,
% 6.92/7.19 ! [T7: set_nat,S: set_nat] :
% 6.92/7.19 ( ( sup_sup_set_nat @ T7 @ ( inf_inf_set_nat @ S @ T7 ) )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(4)
% 6.92/7.19 thf(fact_2845_Int__Un__eq_I3_J,axiom,
% 6.92/7.19 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( sup_su6327502436637775413at_nat @ S @ ( inf_in2572325071724192079at_nat @ S @ T7 ) )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(3)
% 6.92/7.19 thf(fact_2846_Int__Un__eq_I3_J,axiom,
% 6.92/7.19 ! [S: set_Pr8551490117392284871at_nat,T7: set_Pr8551490117392284871at_nat] :
% 6.92/7.19 ( ( sup_su3035147773818789531at_nat @ S @ ( inf_in1697001100524423349at_nat @ S @ T7 ) )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(3)
% 6.92/7.19 thf(fact_2847_Int__Un__eq_I3_J,axiom,
% 6.92/7.19 ! [S: set_Pr4329608150637261639at_nat,T7: set_Pr4329608150637261639at_nat] :
% 6.92/7.19 ( ( sup_su5525570899277871387at_nat @ S @ ( inf_in7913087082777306421at_nat @ S @ T7 ) )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(3)
% 6.92/7.19 thf(fact_2848_Int__Un__eq_I3_J,axiom,
% 6.92/7.19 ! [S: set_nat,T7: set_nat] :
% 6.92/7.19 ( ( sup_sup_set_nat @ S @ ( inf_inf_set_nat @ S @ T7 ) )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(3)
% 6.92/7.19 thf(fact_2849_Int__Un__eq_I2_J,axiom,
% 6.92/7.19 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ S @ T7 ) @ T7 )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(2)
% 6.92/7.19 thf(fact_2850_Int__Un__eq_I2_J,axiom,
% 6.92/7.19 ! [S: set_Pr8551490117392284871at_nat,T7: set_Pr8551490117392284871at_nat] :
% 6.92/7.19 ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ S @ T7 ) @ T7 )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(2)
% 6.92/7.19 thf(fact_2851_Int__Un__eq_I2_J,axiom,
% 6.92/7.19 ! [S: set_Pr4329608150637261639at_nat,T7: set_Pr4329608150637261639at_nat] :
% 6.92/7.19 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ S @ T7 ) @ T7 )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(2)
% 6.92/7.19 thf(fact_2852_Int__Un__eq_I2_J,axiom,
% 6.92/7.19 ! [S: set_nat,T7: set_nat] :
% 6.92/7.19 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T7 ) @ T7 )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(2)
% 6.92/7.19 thf(fact_2853_Int__Un__eq_I1_J,axiom,
% 6.92/7.19 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ S @ T7 ) @ S )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(1)
% 6.92/7.19 thf(fact_2854_Int__Un__eq_I1_J,axiom,
% 6.92/7.19 ! [S: set_Pr8551490117392284871at_nat,T7: set_Pr8551490117392284871at_nat] :
% 6.92/7.19 ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ S @ T7 ) @ S )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(1)
% 6.92/7.19 thf(fact_2855_Int__Un__eq_I1_J,axiom,
% 6.92/7.19 ! [S: set_Pr4329608150637261639at_nat,T7: set_Pr4329608150637261639at_nat] :
% 6.92/7.19 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ S @ T7 ) @ S )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(1)
% 6.92/7.19 thf(fact_2856_Int__Un__eq_I1_J,axiom,
% 6.92/7.19 ! [S: set_nat,T7: set_nat] :
% 6.92/7.19 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T7 ) @ S )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Un_eq(1)
% 6.92/7.19 thf(fact_2857_Un__Int__eq_I4_J,axiom,
% 6.92/7.19 ! [T7: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( inf_in2572325071724192079at_nat @ T7 @ ( sup_su6327502436637775413at_nat @ S @ T7 ) )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(4)
% 6.92/7.19 thf(fact_2858_Un__Int__eq_I4_J,axiom,
% 6.92/7.19 ! [T7: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 6.92/7.19 ( ( inf_in1697001100524423349at_nat @ T7 @ ( sup_su3035147773818789531at_nat @ S @ T7 ) )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(4)
% 6.92/7.19 thf(fact_2859_Un__Int__eq_I4_J,axiom,
% 6.92/7.19 ! [T7: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 6.92/7.19 ( ( inf_in7913087082777306421at_nat @ T7 @ ( sup_su5525570899277871387at_nat @ S @ T7 ) )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(4)
% 6.92/7.19 thf(fact_2860_Un__Int__eq_I4_J,axiom,
% 6.92/7.19 ! [T7: set_nat,S: set_nat] :
% 6.92/7.19 ( ( inf_inf_set_nat @ T7 @ ( sup_sup_set_nat @ S @ T7 ) )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(4)
% 6.92/7.19 thf(fact_2861_Un__Int__eq_I3_J,axiom,
% 6.92/7.19 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( inf_in2572325071724192079at_nat @ S @ ( sup_su6327502436637775413at_nat @ S @ T7 ) )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(3)
% 6.92/7.19 thf(fact_2862_Un__Int__eq_I3_J,axiom,
% 6.92/7.19 ! [S: set_Pr8551490117392284871at_nat,T7: set_Pr8551490117392284871at_nat] :
% 6.92/7.19 ( ( inf_in1697001100524423349at_nat @ S @ ( sup_su3035147773818789531at_nat @ S @ T7 ) )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(3)
% 6.92/7.19 thf(fact_2863_Un__Int__eq_I3_J,axiom,
% 6.92/7.19 ! [S: set_Pr4329608150637261639at_nat,T7: set_Pr4329608150637261639at_nat] :
% 6.92/7.19 ( ( inf_in7913087082777306421at_nat @ S @ ( sup_su5525570899277871387at_nat @ S @ T7 ) )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(3)
% 6.92/7.19 thf(fact_2864_Un__Int__eq_I3_J,axiom,
% 6.92/7.19 ! [S: set_nat,T7: set_nat] :
% 6.92/7.19 ( ( inf_inf_set_nat @ S @ ( sup_sup_set_nat @ S @ T7 ) )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(3)
% 6.92/7.19 thf(fact_2865_Un__Int__eq_I2_J,axiom,
% 6.92/7.19 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ S @ T7 ) @ T7 )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(2)
% 6.92/7.19 thf(fact_2866_Un__Int__eq_I2_J,axiom,
% 6.92/7.19 ! [S: set_Pr8551490117392284871at_nat,T7: set_Pr8551490117392284871at_nat] :
% 6.92/7.19 ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ S @ T7 ) @ T7 )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(2)
% 6.92/7.19 thf(fact_2867_Un__Int__eq_I2_J,axiom,
% 6.92/7.19 ! [S: set_Pr4329608150637261639at_nat,T7: set_Pr4329608150637261639at_nat] :
% 6.92/7.19 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ S @ T7 ) @ T7 )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(2)
% 6.92/7.19 thf(fact_2868_Un__Int__eq_I2_J,axiom,
% 6.92/7.19 ! [S: set_nat,T7: set_nat] :
% 6.92/7.19 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T7 ) @ T7 )
% 6.92/7.19 = T7 ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(2)
% 6.92/7.19 thf(fact_2869_Un__Int__eq_I1_J,axiom,
% 6.92/7.19 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ S @ T7 ) @ S )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(1)
% 6.92/7.19 thf(fact_2870_Un__Int__eq_I1_J,axiom,
% 6.92/7.19 ! [S: set_Pr8551490117392284871at_nat,T7: set_Pr8551490117392284871at_nat] :
% 6.92/7.19 ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ S @ T7 ) @ S )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(1)
% 6.92/7.19 thf(fact_2871_Un__Int__eq_I1_J,axiom,
% 6.92/7.19 ! [S: set_Pr4329608150637261639at_nat,T7: set_Pr4329608150637261639at_nat] :
% 6.92/7.19 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ S @ T7 ) @ S )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(1)
% 6.92/7.19 thf(fact_2872_Un__Int__eq_I1_J,axiom,
% 6.92/7.19 ! [S: set_nat,T7: set_nat] :
% 6.92/7.19 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T7 ) @ S )
% 6.92/7.19 = S ) ).
% 6.92/7.19
% 6.92/7.19 % Un_Int_eq(1)
% 6.92/7.19 thf(fact_2873_power__inject__exp,axiom,
% 6.92/7.19 ! [A: code_integer,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 6.92/7.19 => ( ( ( power_8256067586552552935nteger @ A @ M )
% 6.92/7.19 = ( power_8256067586552552935nteger @ A @ N2 ) )
% 6.92/7.19 = ( M = N2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_inject_exp
% 6.92/7.19 thf(fact_2874_power__inject__exp,axiom,
% 6.92/7.19 ! [A: rat,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_rat @ one_one_rat @ A )
% 6.92/7.19 => ( ( ( power_power_rat @ A @ M )
% 6.92/7.19 = ( power_power_rat @ A @ N2 ) )
% 6.92/7.19 = ( M = N2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_inject_exp
% 6.92/7.19 thf(fact_2875_power__inject__exp,axiom,
% 6.92/7.19 ! [A: nat,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_nat @ one_one_nat @ A )
% 6.92/7.19 => ( ( ( power_power_nat @ A @ M )
% 6.92/7.19 = ( power_power_nat @ A @ N2 ) )
% 6.92/7.19 = ( M = N2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_inject_exp
% 6.92/7.19 thf(fact_2876_power__inject__exp,axiom,
% 6.92/7.19 ! [A: int,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_int @ one_one_int @ A )
% 6.92/7.19 => ( ( ( power_power_int @ A @ M )
% 6.92/7.19 = ( power_power_int @ A @ N2 ) )
% 6.92/7.19 = ( M = N2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_inject_exp
% 6.92/7.19 thf(fact_2877_divide__le__0__1__iff,axiom,
% 6.92/7.19 ! [A: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 6.92/7.19 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 6.92/7.19
% 6.92/7.19 % divide_le_0_1_iff
% 6.92/7.19 thf(fact_2878_zero__le__divide__1__iff,axiom,
% 6.92/7.19 ! [A: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 6.92/7.19 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 6.92/7.19
% 6.92/7.19 % zero_le_divide_1_iff
% 6.92/7.19 thf(fact_2879_divide__less__0__1__iff,axiom,
% 6.92/7.19 ! [A: rat] :
% 6.92/7.19 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 6.92/7.19 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 6.92/7.19
% 6.92/7.19 % divide_less_0_1_iff
% 6.92/7.19 thf(fact_2880_divide__less__eq__1__neg,axiom,
% 6.92/7.19 ! [A: rat,B: rat] :
% 6.92/7.19 ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.19 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 6.92/7.19 = ( ord_less_rat @ A @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % divide_less_eq_1_neg
% 6.92/7.19 thf(fact_2881_divide__less__eq__1__pos,axiom,
% 6.92/7.19 ! [A: rat,B: rat] :
% 6.92/7.19 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.19 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 6.92/7.19 = ( ord_less_rat @ B @ A ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % divide_less_eq_1_pos
% 6.92/7.19 thf(fact_2882_less__divide__eq__1__neg,axiom,
% 6.92/7.19 ! [A: rat,B: rat] :
% 6.92/7.19 ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.19 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 6.92/7.19 = ( ord_less_rat @ B @ A ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % less_divide_eq_1_neg
% 6.92/7.19 thf(fact_2883_less__divide__eq__1__pos,axiom,
% 6.92/7.19 ! [A: rat,B: rat] :
% 6.92/7.19 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.19 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 6.92/7.19 = ( ord_less_rat @ A @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % less_divide_eq_1_pos
% 6.92/7.19 thf(fact_2884_zero__less__divide__1__iff,axiom,
% 6.92/7.19 ! [A: rat] :
% 6.92/7.19 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 6.92/7.19 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 6.92/7.19
% 6.92/7.19 % zero_less_divide_1_iff
% 6.92/7.19 thf(fact_2885_power__strict__increasing__iff,axiom,
% 6.92/7.19 ! [B: code_integer,X: nat,Y: nat] :
% 6.92/7.19 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 6.92/7.19 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 6.92/7.19 = ( ord_less_nat @ X @ Y ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_strict_increasing_iff
% 6.92/7.19 thf(fact_2886_power__strict__increasing__iff,axiom,
% 6.92/7.19 ! [B: rat,X: nat,Y: nat] :
% 6.92/7.19 ( ( ord_less_rat @ one_one_rat @ B )
% 6.92/7.19 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 6.92/7.19 = ( ord_less_nat @ X @ Y ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_strict_increasing_iff
% 6.92/7.19 thf(fact_2887_power__strict__increasing__iff,axiom,
% 6.92/7.19 ! [B: nat,X: nat,Y: nat] :
% 6.92/7.19 ( ( ord_less_nat @ one_one_nat @ B )
% 6.92/7.19 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 6.92/7.19 = ( ord_less_nat @ X @ Y ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_strict_increasing_iff
% 6.92/7.19 thf(fact_2888_power__strict__increasing__iff,axiom,
% 6.92/7.19 ! [B: int,X: nat,Y: nat] :
% 6.92/7.19 ( ( ord_less_int @ one_one_int @ B )
% 6.92/7.19 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 6.92/7.19 = ( ord_less_nat @ X @ Y ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_strict_increasing_iff
% 6.92/7.19 thf(fact_2889_power__eq__0__iff,axiom,
% 6.92/7.19 ! [A: code_integer,N2: nat] :
% 6.92/7.19 ( ( ( power_8256067586552552935nteger @ A @ N2 )
% 6.92/7.19 = zero_z3403309356797280102nteger )
% 6.92/7.19 = ( ( A = zero_z3403309356797280102nteger )
% 6.92/7.19 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_eq_0_iff
% 6.92/7.19 thf(fact_2890_power__eq__0__iff,axiom,
% 6.92/7.19 ! [A: rat,N2: nat] :
% 6.92/7.19 ( ( ( power_power_rat @ A @ N2 )
% 6.92/7.19 = zero_zero_rat )
% 6.92/7.19 = ( ( A = zero_zero_rat )
% 6.92/7.19 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_eq_0_iff
% 6.92/7.19 thf(fact_2891_power__eq__0__iff,axiom,
% 6.92/7.19 ! [A: nat,N2: nat] :
% 6.92/7.19 ( ( ( power_power_nat @ A @ N2 )
% 6.92/7.19 = zero_zero_nat )
% 6.92/7.19 = ( ( A = zero_zero_nat )
% 6.92/7.19 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_eq_0_iff
% 6.92/7.19 thf(fact_2892_power__eq__0__iff,axiom,
% 6.92/7.19 ! [A: int,N2: nat] :
% 6.92/7.19 ( ( ( power_power_int @ A @ N2 )
% 6.92/7.19 = zero_zero_int )
% 6.92/7.19 = ( ( A = zero_zero_int )
% 6.92/7.19 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_eq_0_iff
% 6.92/7.19 thf(fact_2893_le__divide__eq__1__pos,axiom,
% 6.92/7.19 ! [A: rat,B: rat] :
% 6.92/7.19 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.19 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 6.92/7.19 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_divide_eq_1_pos
% 6.92/7.19 thf(fact_2894_le__divide__eq__1__neg,axiom,
% 6.92/7.19 ! [A: rat,B: rat] :
% 6.92/7.19 ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.19 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 6.92/7.19 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_divide_eq_1_neg
% 6.92/7.19 thf(fact_2895_power__strict__decreasing__iff,axiom,
% 6.92/7.19 ! [B: code_integer,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.19 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 6.92/7.19 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ M ) @ ( power_8256067586552552935nteger @ B @ N2 ) )
% 6.92/7.19 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_strict_decreasing_iff
% 6.92/7.19 thf(fact_2896_power__strict__decreasing__iff,axiom,
% 6.92/7.19 ! [B: rat,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_rat @ zero_zero_rat @ B )
% 6.92/7.19 => ( ( ord_less_rat @ B @ one_one_rat )
% 6.92/7.19 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 6.92/7.19 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_strict_decreasing_iff
% 6.92/7.19 thf(fact_2897_power__strict__decreasing__iff,axiom,
% 6.92/7.19 ! [B: nat,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_nat @ zero_zero_nat @ B )
% 6.92/7.19 => ( ( ord_less_nat @ B @ one_one_nat )
% 6.92/7.19 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 6.92/7.19 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_strict_decreasing_iff
% 6.92/7.19 thf(fact_2898_power__strict__decreasing__iff,axiom,
% 6.92/7.19 ! [B: int,M: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.19 => ( ( ord_less_int @ B @ one_one_int )
% 6.92/7.19 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 6.92/7.19 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_strict_decreasing_iff
% 6.92/7.19 thf(fact_2899_power__mono__iff,axiom,
% 6.92/7.19 ! [A: code_integer,B: code_integer,N2: nat] :
% 6.92/7.19 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.19 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.19 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.19 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) )
% 6.92/7.19 = ( ord_le3102999989581377725nteger @ A @ B ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_mono_iff
% 6.92/7.19 thf(fact_2900_power__mono__iff,axiom,
% 6.92/7.19 ! [A: rat,B: rat,N2: nat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.19 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.19 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.19 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 6.92/7.19 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_mono_iff
% 6.92/7.19 thf(fact_2901_power__mono__iff,axiom,
% 6.92/7.19 ! [A: nat,B: nat,N2: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.19 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 6.92/7.19 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.19 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 6.92/7.19 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_mono_iff
% 6.92/7.19 thf(fact_2902_power__mono__iff,axiom,
% 6.92/7.19 ! [A: int,B: int,N2: nat] :
% 6.92/7.19 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.19 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 6.92/7.19 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.19 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 6.92/7.19 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % power_mono_iff
% 6.92/7.19 thf(fact_2903_Int__left__commute,axiom,
% 6.92/7.19 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( inf_in2572325071724192079at_nat @ A4 @ ( inf_in2572325071724192079at_nat @ B5 @ C4 ) )
% 6.92/7.19 = ( inf_in2572325071724192079at_nat @ B5 @ ( inf_in2572325071724192079at_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_left_commute
% 6.92/7.19 thf(fact_2904_Int__left__commute,axiom,
% 6.92/7.19 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.19 ( ( inf_inf_set_nat @ A4 @ ( inf_inf_set_nat @ B5 @ C4 ) )
% 6.92/7.19 = ( inf_inf_set_nat @ B5 @ ( inf_inf_set_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_left_commute
% 6.92/7.19 thf(fact_2905_Int__left__absorb,axiom,
% 6.92/7.19 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( inf_in2572325071724192079at_nat @ A4 @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) )
% 6.92/7.19 = ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_left_absorb
% 6.92/7.19 thf(fact_2906_Int__left__absorb,axiom,
% 6.92/7.19 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.19 ( ( inf_inf_set_nat @ A4 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 6.92/7.19 = ( inf_inf_set_nat @ A4 @ B5 ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_left_absorb
% 6.92/7.19 thf(fact_2907_Int__commute,axiom,
% 6.92/7.19 ( inf_in2572325071724192079at_nat
% 6.92/7.19 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B6 @ A6 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_commute
% 6.92/7.19 thf(fact_2908_Int__commute,axiom,
% 6.92/7.19 ( inf_inf_set_nat
% 6.92/7.19 = ( ^ [A6: set_nat,B6: set_nat] : ( inf_inf_set_nat @ B6 @ A6 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_commute
% 6.92/7.19 thf(fact_2909_Int__absorb,axiom,
% 6.92/7.19 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( inf_in2572325071724192079at_nat @ A4 @ A4 )
% 6.92/7.19 = A4 ) ).
% 6.92/7.19
% 6.92/7.19 % Int_absorb
% 6.92/7.19 thf(fact_2910_Int__absorb,axiom,
% 6.92/7.19 ! [A4: set_nat] :
% 6.92/7.19 ( ( inf_inf_set_nat @ A4 @ A4 )
% 6.92/7.19 = A4 ) ).
% 6.92/7.19
% 6.92/7.19 % Int_absorb
% 6.92/7.19 thf(fact_2911_Int__assoc,axiom,
% 6.92/7.19 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.19 = ( inf_in2572325071724192079at_nat @ A4 @ ( inf_in2572325071724192079at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_assoc
% 6.92/7.19 thf(fact_2912_Int__assoc,axiom,
% 6.92/7.19 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.19 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.19 = ( inf_inf_set_nat @ A4 @ ( inf_inf_set_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_assoc
% 6.92/7.19 thf(fact_2913_IntD2,axiom,
% 6.92/7.19 ! [C2: $o,A4: set_o,B5: set_o] :
% 6.92/7.19 ( ( member_o @ C2 @ ( inf_inf_set_o @ A4 @ B5 ) )
% 6.92/7.19 => ( member_o @ C2 @ B5 ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntD2
% 6.92/7.19 thf(fact_2914_IntD2,axiom,
% 6.92/7.19 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.19 ( ( member2340774599025711042nt_int @ C2 @ ( inf_in8396524679539076455nt_int @ A4 @ B5 ) )
% 6.92/7.19 => ( member2340774599025711042nt_int @ C2 @ B5 ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntD2
% 6.92/7.19 thf(fact_2915_IntD2,axiom,
% 6.92/7.19 ! [C2: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.19 ( ( member_set_nat @ C2 @ ( inf_inf_set_set_nat @ A4 @ B5 ) )
% 6.92/7.19 => ( member_set_nat @ C2 @ B5 ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntD2
% 6.92/7.19 thf(fact_2916_IntD2,axiom,
% 6.92/7.19 ! [C2: int,A4: set_int,B5: set_int] :
% 6.92/7.19 ( ( member_int @ C2 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.92/7.19 => ( member_int @ C2 @ B5 ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntD2
% 6.92/7.19 thf(fact_2917_IntD2,axiom,
% 6.92/7.19 ! [C2: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( member8440522571783428010at_nat @ C2 @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) )
% 6.92/7.19 => ( member8440522571783428010at_nat @ C2 @ B5 ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntD2
% 6.92/7.19 thf(fact_2918_IntD2,axiom,
% 6.92/7.19 ! [C2: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.19 ( ( member_nat @ C2 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 6.92/7.19 => ( member_nat @ C2 @ B5 ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntD2
% 6.92/7.19 thf(fact_2919_IntD1,axiom,
% 6.92/7.19 ! [C2: $o,A4: set_o,B5: set_o] :
% 6.92/7.19 ( ( member_o @ C2 @ ( inf_inf_set_o @ A4 @ B5 ) )
% 6.92/7.19 => ( member_o @ C2 @ A4 ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntD1
% 6.92/7.19 thf(fact_2920_IntD1,axiom,
% 6.92/7.19 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.19 ( ( member2340774599025711042nt_int @ C2 @ ( inf_in8396524679539076455nt_int @ A4 @ B5 ) )
% 6.92/7.19 => ( member2340774599025711042nt_int @ C2 @ A4 ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntD1
% 6.92/7.19 thf(fact_2921_IntD1,axiom,
% 6.92/7.19 ! [C2: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.19 ( ( member_set_nat @ C2 @ ( inf_inf_set_set_nat @ A4 @ B5 ) )
% 6.92/7.19 => ( member_set_nat @ C2 @ A4 ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntD1
% 6.92/7.19 thf(fact_2922_IntD1,axiom,
% 6.92/7.19 ! [C2: int,A4: set_int,B5: set_int] :
% 6.92/7.19 ( ( member_int @ C2 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.92/7.19 => ( member_int @ C2 @ A4 ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntD1
% 6.92/7.19 thf(fact_2923_IntD1,axiom,
% 6.92/7.19 ! [C2: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( member8440522571783428010at_nat @ C2 @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) )
% 6.92/7.19 => ( member8440522571783428010at_nat @ C2 @ A4 ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntD1
% 6.92/7.19 thf(fact_2924_IntD1,axiom,
% 6.92/7.19 ! [C2: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.19 ( ( member_nat @ C2 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 6.92/7.19 => ( member_nat @ C2 @ A4 ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntD1
% 6.92/7.19 thf(fact_2925_IntE,axiom,
% 6.92/7.19 ! [C2: $o,A4: set_o,B5: set_o] :
% 6.92/7.19 ( ( member_o @ C2 @ ( inf_inf_set_o @ A4 @ B5 ) )
% 6.92/7.19 => ~ ( ( member_o @ C2 @ A4 )
% 6.92/7.19 => ~ ( member_o @ C2 @ B5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntE
% 6.92/7.19 thf(fact_2926_IntE,axiom,
% 6.92/7.19 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.19 ( ( member2340774599025711042nt_int @ C2 @ ( inf_in8396524679539076455nt_int @ A4 @ B5 ) )
% 6.92/7.19 => ~ ( ( member2340774599025711042nt_int @ C2 @ A4 )
% 6.92/7.19 => ~ ( member2340774599025711042nt_int @ C2 @ B5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntE
% 6.92/7.19 thf(fact_2927_IntE,axiom,
% 6.92/7.19 ! [C2: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.19 ( ( member_set_nat @ C2 @ ( inf_inf_set_set_nat @ A4 @ B5 ) )
% 6.92/7.19 => ~ ( ( member_set_nat @ C2 @ A4 )
% 6.92/7.19 => ~ ( member_set_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntE
% 6.92/7.19 thf(fact_2928_IntE,axiom,
% 6.92/7.19 ! [C2: int,A4: set_int,B5: set_int] :
% 6.92/7.19 ( ( member_int @ C2 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.92/7.19 => ~ ( ( member_int @ C2 @ A4 )
% 6.92/7.19 => ~ ( member_int @ C2 @ B5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntE
% 6.92/7.19 thf(fact_2929_IntE,axiom,
% 6.92/7.19 ! [C2: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( member8440522571783428010at_nat @ C2 @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) )
% 6.92/7.19 => ~ ( ( member8440522571783428010at_nat @ C2 @ A4 )
% 6.92/7.19 => ~ ( member8440522571783428010at_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntE
% 6.92/7.19 thf(fact_2930_IntE,axiom,
% 6.92/7.19 ! [C2: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.19 ( ( member_nat @ C2 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 6.92/7.19 => ~ ( ( member_nat @ C2 @ A4 )
% 6.92/7.19 => ~ ( member_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % IntE
% 6.92/7.19 thf(fact_2931_Int__def,axiom,
% 6.92/7.19 ( inf_inf_set_o
% 6.92/7.19 = ( ^ [A6: set_o,B6: set_o] :
% 6.92/7.19 ( collect_o
% 6.92/7.19 @ ^ [X4: $o] :
% 6.92/7.19 ( ( member_o @ X4 @ A6 )
% 6.92/7.19 & ( member_o @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_def
% 6.92/7.19 thf(fact_2932_Int__def,axiom,
% 6.92/7.19 ( inf_inf_set_list_nat
% 6.92/7.19 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 6.92/7.19 ( collect_list_nat
% 6.92/7.19 @ ^ [X4: list_nat] :
% 6.92/7.19 ( ( member_list_nat @ X4 @ A6 )
% 6.92/7.19 & ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_def
% 6.92/7.19 thf(fact_2933_Int__def,axiom,
% 6.92/7.19 ( inf_in8396524679539076455nt_int
% 6.92/7.19 = ( ^ [A6: set_se6260736226359567993nt_int,B6: set_se6260736226359567993nt_int] :
% 6.92/7.19 ( collec5210948495886036740nt_int
% 6.92/7.19 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.19 ( ( member2340774599025711042nt_int @ X4 @ A6 )
% 6.92/7.19 & ( member2340774599025711042nt_int @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_def
% 6.92/7.19 thf(fact_2934_Int__def,axiom,
% 6.92/7.19 ( inf_inf_set_set_nat
% 6.92/7.19 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 6.92/7.19 ( collect_set_nat
% 6.92/7.19 @ ^ [X4: set_nat] :
% 6.92/7.19 ( ( member_set_nat @ X4 @ A6 )
% 6.92/7.19 & ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_def
% 6.92/7.19 thf(fact_2935_Int__def,axiom,
% 6.92/7.19 ( inf_inf_set_int
% 6.92/7.19 = ( ^ [A6: set_int,B6: set_int] :
% 6.92/7.19 ( collect_int
% 6.92/7.19 @ ^ [X4: int] :
% 6.92/7.19 ( ( member_int @ X4 @ A6 )
% 6.92/7.19 & ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_def
% 6.92/7.19 thf(fact_2936_Int__def,axiom,
% 6.92/7.19 ( inf_in2572325071724192079at_nat
% 6.92/7.19 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( collec3392354462482085612at_nat
% 6.92/7.19 @ ^ [X4: product_prod_nat_nat] :
% 6.92/7.19 ( ( member8440522571783428010at_nat @ X4 @ A6 )
% 6.92/7.19 & ( member8440522571783428010at_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_def
% 6.92/7.19 thf(fact_2937_Int__def,axiom,
% 6.92/7.19 ( inf_inf_set_nat
% 6.92/7.19 = ( ^ [A6: set_nat,B6: set_nat] :
% 6.92/7.19 ( collect_nat
% 6.92/7.19 @ ^ [X4: nat] :
% 6.92/7.19 ( ( member_nat @ X4 @ A6 )
% 6.92/7.19 & ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_def
% 6.92/7.19 thf(fact_2938_Int__Collect,axiom,
% 6.92/7.19 ! [X: $o,A4: set_o,P2: $o > $o] :
% 6.92/7.19 ( ( member_o @ X @ ( inf_inf_set_o @ A4 @ ( collect_o @ P2 ) ) )
% 6.92/7.19 = ( ( member_o @ X @ A4 )
% 6.92/7.19 & ( P2 @ X ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Collect
% 6.92/7.19 thf(fact_2939_Int__Collect,axiom,
% 6.92/7.19 ! [X: list_nat,A4: set_list_nat,P2: list_nat > $o] :
% 6.92/7.19 ( ( member_list_nat @ X @ ( inf_inf_set_list_nat @ A4 @ ( collect_list_nat @ P2 ) ) )
% 6.92/7.19 = ( ( member_list_nat @ X @ A4 )
% 6.92/7.19 & ( P2 @ X ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Collect
% 6.92/7.19 thf(fact_2940_Int__Collect,axiom,
% 6.92/7.19 ! [X: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,P2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.19 ( ( member2340774599025711042nt_int @ X @ ( inf_in8396524679539076455nt_int @ A4 @ ( collec5210948495886036740nt_int @ P2 ) ) )
% 6.92/7.19 = ( ( member2340774599025711042nt_int @ X @ A4 )
% 6.92/7.19 & ( P2 @ X ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Collect
% 6.92/7.19 thf(fact_2941_Int__Collect,axiom,
% 6.92/7.19 ! [X: set_nat,A4: set_set_nat,P2: set_nat > $o] :
% 6.92/7.19 ( ( member_set_nat @ X @ ( inf_inf_set_set_nat @ A4 @ ( collect_set_nat @ P2 ) ) )
% 6.92/7.19 = ( ( member_set_nat @ X @ A4 )
% 6.92/7.19 & ( P2 @ X ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Collect
% 6.92/7.19 thf(fact_2942_Int__Collect,axiom,
% 6.92/7.19 ! [X: int,A4: set_int,P2: int > $o] :
% 6.92/7.19 ( ( member_int @ X @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) )
% 6.92/7.19 = ( ( member_int @ X @ A4 )
% 6.92/7.19 & ( P2 @ X ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Collect
% 6.92/7.19 thf(fact_2943_Int__Collect,axiom,
% 6.92/7.19 ! [X: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,P2: product_prod_nat_nat > $o] :
% 6.92/7.19 ( ( member8440522571783428010at_nat @ X @ ( inf_in2572325071724192079at_nat @ A4 @ ( collec3392354462482085612at_nat @ P2 ) ) )
% 6.92/7.19 = ( ( member8440522571783428010at_nat @ X @ A4 )
% 6.92/7.19 & ( P2 @ X ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Collect
% 6.92/7.19 thf(fact_2944_Int__Collect,axiom,
% 6.92/7.19 ! [X: nat,A4: set_nat,P2: nat > $o] :
% 6.92/7.19 ( ( member_nat @ X @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) )
% 6.92/7.19 = ( ( member_nat @ X @ A4 )
% 6.92/7.19 & ( P2 @ X ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Int_Collect
% 6.92/7.19 thf(fact_2945_Collect__conj__eq,axiom,
% 6.92/7.19 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 6.92/7.19 ( ( collect_list_nat
% 6.92/7.19 @ ^ [X4: list_nat] :
% 6.92/7.19 ( ( P2 @ X4 )
% 6.92/7.19 & ( Q2 @ X4 ) ) )
% 6.92/7.19 = ( inf_inf_set_list_nat @ ( collect_list_nat @ P2 ) @ ( collect_list_nat @ Q2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Collect_conj_eq
% 6.92/7.19 thf(fact_2946_Collect__conj__eq,axiom,
% 6.92/7.19 ! [P2: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.19 ( ( collec5210948495886036740nt_int
% 6.92/7.19 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.19 ( ( P2 @ X4 )
% 6.92/7.19 & ( Q2 @ X4 ) ) )
% 6.92/7.19 = ( inf_in8396524679539076455nt_int @ ( collec5210948495886036740nt_int @ P2 ) @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Collect_conj_eq
% 6.92/7.19 thf(fact_2947_Collect__conj__eq,axiom,
% 6.92/7.19 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 6.92/7.19 ( ( collect_set_nat
% 6.92/7.19 @ ^ [X4: set_nat] :
% 6.92/7.19 ( ( P2 @ X4 )
% 6.92/7.19 & ( Q2 @ X4 ) ) )
% 6.92/7.19 = ( inf_inf_set_set_nat @ ( collect_set_nat @ P2 ) @ ( collect_set_nat @ Q2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Collect_conj_eq
% 6.92/7.19 thf(fact_2948_Collect__conj__eq,axiom,
% 6.92/7.19 ! [P2: int > $o,Q2: int > $o] :
% 6.92/7.19 ( ( collect_int
% 6.92/7.19 @ ^ [X4: int] :
% 6.92/7.19 ( ( P2 @ X4 )
% 6.92/7.19 & ( Q2 @ X4 ) ) )
% 6.92/7.19 = ( inf_inf_set_int @ ( collect_int @ P2 ) @ ( collect_int @ Q2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Collect_conj_eq
% 6.92/7.19 thf(fact_2949_Collect__conj__eq,axiom,
% 6.92/7.19 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 6.92/7.19 ( ( collec3392354462482085612at_nat
% 6.92/7.19 @ ^ [X4: product_prod_nat_nat] :
% 6.92/7.19 ( ( P2 @ X4 )
% 6.92/7.19 & ( Q2 @ X4 ) ) )
% 6.92/7.19 = ( inf_in2572325071724192079at_nat @ ( collec3392354462482085612at_nat @ P2 ) @ ( collec3392354462482085612at_nat @ Q2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Collect_conj_eq
% 6.92/7.19 thf(fact_2950_Collect__conj__eq,axiom,
% 6.92/7.19 ! [P2: nat > $o,Q2: nat > $o] :
% 6.92/7.19 ( ( collect_nat
% 6.92/7.19 @ ^ [X4: nat] :
% 6.92/7.19 ( ( P2 @ X4 )
% 6.92/7.19 & ( Q2 @ X4 ) ) )
% 6.92/7.19 = ( inf_inf_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % Collect_conj_eq
% 6.92/7.19 thf(fact_2951_inf__sup__ord_I2_J,axiom,
% 6.92/7.19 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(2)
% 6.92/7.19 thf(fact_2952_inf__sup__ord_I2_J,axiom,
% 6.92/7.19 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(2)
% 6.92/7.19 thf(fact_2953_inf__sup__ord_I2_J,axiom,
% 6.92/7.19 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(2)
% 6.92/7.19 thf(fact_2954_inf__sup__ord_I2_J,axiom,
% 6.92/7.19 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(2)
% 6.92/7.19 thf(fact_2955_inf__sup__ord_I2_J,axiom,
% 6.92/7.19 ! [X: set_int,Y: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(2)
% 6.92/7.19 thf(fact_2956_inf__sup__ord_I2_J,axiom,
% 6.92/7.19 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(2)
% 6.92/7.19 thf(fact_2957_inf__sup__ord_I2_J,axiom,
% 6.92/7.19 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(2)
% 6.92/7.19 thf(fact_2958_inf__sup__ord_I2_J,axiom,
% 6.92/7.19 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(2)
% 6.92/7.19 thf(fact_2959_inf__sup__ord_I1_J,axiom,
% 6.92/7.19 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(1)
% 6.92/7.19 thf(fact_2960_inf__sup__ord_I1_J,axiom,
% 6.92/7.19 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(1)
% 6.92/7.19 thf(fact_2961_inf__sup__ord_I1_J,axiom,
% 6.92/7.19 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(1)
% 6.92/7.19 thf(fact_2962_inf__sup__ord_I1_J,axiom,
% 6.92/7.19 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(1)
% 6.92/7.19 thf(fact_2963_inf__sup__ord_I1_J,axiom,
% 6.92/7.19 ! [X: set_int,Y: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(1)
% 6.92/7.19 thf(fact_2964_inf__sup__ord_I1_J,axiom,
% 6.92/7.19 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(1)
% 6.92/7.19 thf(fact_2965_inf__sup__ord_I1_J,axiom,
% 6.92/7.19 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(1)
% 6.92/7.19 thf(fact_2966_inf__sup__ord_I1_J,axiom,
% 6.92/7.19 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_sup_ord(1)
% 6.92/7.19 thf(fact_2967_inf__le1,axiom,
% 6.92/7.19 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le1
% 6.92/7.19 thf(fact_2968_inf__le1,axiom,
% 6.92/7.19 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le1
% 6.92/7.19 thf(fact_2969_inf__le1,axiom,
% 6.92/7.19 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le1
% 6.92/7.19 thf(fact_2970_inf__le1,axiom,
% 6.92/7.19 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le1
% 6.92/7.19 thf(fact_2971_inf__le1,axiom,
% 6.92/7.19 ! [X: set_int,Y: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le1
% 6.92/7.19 thf(fact_2972_inf__le1,axiom,
% 6.92/7.19 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le1
% 6.92/7.19 thf(fact_2973_inf__le1,axiom,
% 6.92/7.19 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le1
% 6.92/7.19 thf(fact_2974_inf__le1,axiom,
% 6.92/7.19 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le1
% 6.92/7.19 thf(fact_2975_inf__le2,axiom,
% 6.92/7.19 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le2
% 6.92/7.19 thf(fact_2976_inf__le2,axiom,
% 6.92/7.19 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le2
% 6.92/7.19 thf(fact_2977_inf__le2,axiom,
% 6.92/7.19 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le2
% 6.92/7.19 thf(fact_2978_inf__le2,axiom,
% 6.92/7.19 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le2
% 6.92/7.19 thf(fact_2979_inf__le2,axiom,
% 6.92/7.19 ! [X: set_int,Y: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le2
% 6.92/7.19 thf(fact_2980_inf__le2,axiom,
% 6.92/7.19 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le2
% 6.92/7.19 thf(fact_2981_inf__le2,axiom,
% 6.92/7.19 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le2
% 6.92/7.19 thf(fact_2982_inf__le2,axiom,
% 6.92/7.19 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 6.92/7.19
% 6.92/7.19 % inf_le2
% 6.92/7.19 thf(fact_2983_le__infE,axiom,
% 6.92/7.19 ! [X: assn,A: assn,B: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ X @ ( inf_inf_assn @ A @ B ) )
% 6.92/7.19 => ~ ( ( ord_less_eq_assn @ X @ A )
% 6.92/7.19 => ~ ( ord_less_eq_assn @ X @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infE
% 6.92/7.19 thf(fact_2984_le__infE,axiom,
% 6.92/7.19 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 6.92/7.19 => ~ ( ( ord_le3146513528884898305at_nat @ X @ A )
% 6.92/7.19 => ~ ( ord_le3146513528884898305at_nat @ X @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infE
% 6.92/7.19 thf(fact_2985_le__infE,axiom,
% 6.92/7.19 ! [X: set_nat,A: set_nat,B: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) )
% 6.92/7.19 => ~ ( ( ord_less_eq_set_nat @ X @ A )
% 6.92/7.19 => ~ ( ord_less_eq_set_nat @ X @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infE
% 6.92/7.19 thf(fact_2986_le__infE,axiom,
% 6.92/7.19 ! [X: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ A @ B ) )
% 6.92/7.19 => ~ ( ( ord_le8369615600986905444_int_o @ X @ A )
% 6.92/7.19 => ~ ( ord_le8369615600986905444_int_o @ X @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infE
% 6.92/7.19 thf(fact_2987_le__infE,axiom,
% 6.92/7.19 ! [X: set_int,A: set_int,B: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ X @ ( inf_inf_set_int @ A @ B ) )
% 6.92/7.19 => ~ ( ( ord_less_eq_set_int @ X @ A )
% 6.92/7.19 => ~ ( ord_less_eq_set_int @ X @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infE
% 6.92/7.19 thf(fact_2988_le__infE,axiom,
% 6.92/7.19 ! [X: rat,A: rat,B: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) )
% 6.92/7.19 => ~ ( ( ord_less_eq_rat @ X @ A )
% 6.92/7.19 => ~ ( ord_less_eq_rat @ X @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infE
% 6.92/7.19 thf(fact_2989_le__infE,axiom,
% 6.92/7.19 ! [X: nat,A: nat,B: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) )
% 6.92/7.19 => ~ ( ( ord_less_eq_nat @ X @ A )
% 6.92/7.19 => ~ ( ord_less_eq_nat @ X @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infE
% 6.92/7.19 thf(fact_2990_le__infE,axiom,
% 6.92/7.19 ! [X: int,A: int,B: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) )
% 6.92/7.19 => ~ ( ( ord_less_eq_int @ X @ A )
% 6.92/7.19 => ~ ( ord_less_eq_int @ X @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infE
% 6.92/7.19 thf(fact_2991_le__infI,axiom,
% 6.92/7.19 ! [X: assn,A: assn,B: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ X @ A )
% 6.92/7.19 => ( ( ord_less_eq_assn @ X @ B )
% 6.92/7.19 => ( ord_less_eq_assn @ X @ ( inf_inf_assn @ A @ B ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI
% 6.92/7.19 thf(fact_2992_le__infI,axiom,
% 6.92/7.19 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ X @ A )
% 6.92/7.19 => ( ( ord_le3146513528884898305at_nat @ X @ B )
% 6.92/7.19 => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI
% 6.92/7.19 thf(fact_2993_le__infI,axiom,
% 6.92/7.19 ! [X: set_nat,A: set_nat,B: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ X @ A )
% 6.92/7.19 => ( ( ord_less_eq_set_nat @ X @ B )
% 6.92/7.19 => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI
% 6.92/7.19 thf(fact_2994_le__infI,axiom,
% 6.92/7.19 ! [X: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ X @ A )
% 6.92/7.19 => ( ( ord_le8369615600986905444_int_o @ X @ B )
% 6.92/7.19 => ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ A @ B ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI
% 6.92/7.19 thf(fact_2995_le__infI,axiom,
% 6.92/7.19 ! [X: set_int,A: set_int,B: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ X @ A )
% 6.92/7.19 => ( ( ord_less_eq_set_int @ X @ B )
% 6.92/7.19 => ( ord_less_eq_set_int @ X @ ( inf_inf_set_int @ A @ B ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI
% 6.92/7.19 thf(fact_2996_le__infI,axiom,
% 6.92/7.19 ! [X: rat,A: rat,B: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ X @ A )
% 6.92/7.19 => ( ( ord_less_eq_rat @ X @ B )
% 6.92/7.19 => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI
% 6.92/7.19 thf(fact_2997_le__infI,axiom,
% 6.92/7.19 ! [X: nat,A: nat,B: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ X @ A )
% 6.92/7.19 => ( ( ord_less_eq_nat @ X @ B )
% 6.92/7.19 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI
% 6.92/7.19 thf(fact_2998_le__infI,axiom,
% 6.92/7.19 ! [X: int,A: int,B: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ X @ A )
% 6.92/7.19 => ( ( ord_less_eq_int @ X @ B )
% 6.92/7.19 => ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI
% 6.92/7.19 thf(fact_2999_inf__mono,axiom,
% 6.92/7.19 ! [A: assn,C2: assn,B: assn,D2: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ A @ C2 )
% 6.92/7.19 => ( ( ord_less_eq_assn @ B @ D2 )
% 6.92/7.19 => ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ ( inf_inf_assn @ C2 @ D2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_mono
% 6.92/7.19 thf(fact_3000_inf__mono,axiom,
% 6.92/7.19 ! [A: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,D2: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ A @ C2 )
% 6.92/7.19 => ( ( ord_le3146513528884898305at_nat @ B @ D2 )
% 6.92/7.19 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ ( inf_in2572325071724192079at_nat @ C2 @ D2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_mono
% 6.92/7.19 thf(fact_3001_inf__mono,axiom,
% 6.92/7.19 ! [A: set_nat,C2: set_nat,B: set_nat,D2: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ A @ C2 )
% 6.92/7.19 => ( ( ord_less_eq_set_nat @ B @ D2 )
% 6.92/7.19 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ ( inf_inf_set_nat @ C2 @ D2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_mono
% 6.92/7.19 thf(fact_3002_inf__mono,axiom,
% 6.92/7.19 ! [A: product_prod_int_int > $o,C2: product_prod_int_int > $o,B: product_prod_int_int > $o,D2: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ A @ C2 )
% 6.92/7.19 => ( ( ord_le8369615600986905444_int_o @ B @ D2 )
% 6.92/7.19 => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ ( inf_in3604695632404883862_int_o @ C2 @ D2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_mono
% 6.92/7.19 thf(fact_3003_inf__mono,axiom,
% 6.92/7.19 ! [A: set_int,C2: set_int,B: set_int,D2: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ A @ C2 )
% 6.92/7.19 => ( ( ord_less_eq_set_int @ B @ D2 )
% 6.92/7.19 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ B ) @ ( inf_inf_set_int @ C2 @ D2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_mono
% 6.92/7.19 thf(fact_3004_inf__mono,axiom,
% 6.92/7.19 ! [A: rat,C2: rat,B: rat,D2: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ A @ C2 )
% 6.92/7.19 => ( ( ord_less_eq_rat @ B @ D2 )
% 6.92/7.19 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ ( inf_inf_rat @ C2 @ D2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_mono
% 6.92/7.19 thf(fact_3005_inf__mono,axiom,
% 6.92/7.19 ! [A: nat,C2: nat,B: nat,D2: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ A @ C2 )
% 6.92/7.19 => ( ( ord_less_eq_nat @ B @ D2 )
% 6.92/7.19 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ ( inf_inf_nat @ C2 @ D2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_mono
% 6.92/7.19 thf(fact_3006_inf__mono,axiom,
% 6.92/7.19 ! [A: int,C2: int,B: int,D2: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ A @ C2 )
% 6.92/7.19 => ( ( ord_less_eq_int @ B @ D2 )
% 6.92/7.19 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ ( inf_inf_int @ C2 @ D2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_mono
% 6.92/7.19 thf(fact_3007_le__infI1,axiom,
% 6.92/7.19 ! [A: assn,X: assn,B: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ A @ X )
% 6.92/7.19 => ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI1
% 6.92/7.19 thf(fact_3008_le__infI1,axiom,
% 6.92/7.19 ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ A @ X )
% 6.92/7.19 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI1
% 6.92/7.19 thf(fact_3009_le__infI1,axiom,
% 6.92/7.19 ! [A: set_nat,X: set_nat,B: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ A @ X )
% 6.92/7.19 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI1
% 6.92/7.19 thf(fact_3010_le__infI1,axiom,
% 6.92/7.19 ! [A: product_prod_int_int > $o,X: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ A @ X )
% 6.92/7.19 => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI1
% 6.92/7.19 thf(fact_3011_le__infI1,axiom,
% 6.92/7.19 ! [A: set_int,X: set_int,B: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ A @ X )
% 6.92/7.19 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI1
% 6.92/7.19 thf(fact_3012_le__infI1,axiom,
% 6.92/7.19 ! [A: rat,X: rat,B: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ A @ X )
% 6.92/7.19 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI1
% 6.92/7.19 thf(fact_3013_le__infI1,axiom,
% 6.92/7.19 ! [A: nat,X: nat,B: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ A @ X )
% 6.92/7.19 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI1
% 6.92/7.19 thf(fact_3014_le__infI1,axiom,
% 6.92/7.19 ! [A: int,X: int,B: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ A @ X )
% 6.92/7.19 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI1
% 6.92/7.19 thf(fact_3015_le__infI2,axiom,
% 6.92/7.19 ! [B: assn,X: assn,A: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ B @ X )
% 6.92/7.19 => ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI2
% 6.92/7.19 thf(fact_3016_le__infI2,axiom,
% 6.92/7.19 ! [B: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ B @ X )
% 6.92/7.19 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI2
% 6.92/7.19 thf(fact_3017_le__infI2,axiom,
% 6.92/7.19 ! [B: set_nat,X: set_nat,A: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ B @ X )
% 6.92/7.19 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI2
% 6.92/7.19 thf(fact_3018_le__infI2,axiom,
% 6.92/7.19 ! [B: product_prod_int_int > $o,X: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ B @ X )
% 6.92/7.19 => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI2
% 6.92/7.19 thf(fact_3019_le__infI2,axiom,
% 6.92/7.19 ! [B: set_int,X: set_int,A: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ B @ X )
% 6.92/7.19 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI2
% 6.92/7.19 thf(fact_3020_le__infI2,axiom,
% 6.92/7.19 ! [B: rat,X: rat,A: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ B @ X )
% 6.92/7.19 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI2
% 6.92/7.19 thf(fact_3021_le__infI2,axiom,
% 6.92/7.19 ! [B: nat,X: nat,A: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ B @ X )
% 6.92/7.19 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI2
% 6.92/7.19 thf(fact_3022_le__infI2,axiom,
% 6.92/7.19 ! [B: int,X: int,A: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ B @ X )
% 6.92/7.19 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_infI2
% 6.92/7.19 thf(fact_3023_inf_OorderE,axiom,
% 6.92/7.19 ! [A: assn,B: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ A @ B )
% 6.92/7.19 => ( A
% 6.92/7.19 = ( inf_inf_assn @ A @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderE
% 6.92/7.19 thf(fact_3024_inf_OorderE,axiom,
% 6.92/7.19 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 6.92/7.19 => ( A
% 6.92/7.19 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderE
% 6.92/7.19 thf(fact_3025_inf_OorderE,axiom,
% 6.92/7.19 ! [A: set_nat,B: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ A @ B )
% 6.92/7.19 => ( A
% 6.92/7.19 = ( inf_inf_set_nat @ A @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderE
% 6.92/7.19 thf(fact_3026_inf_OorderE,axiom,
% 6.92/7.19 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ A @ B )
% 6.92/7.19 => ( A
% 6.92/7.19 = ( inf_in3604695632404883862_int_o @ A @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderE
% 6.92/7.19 thf(fact_3027_inf_OorderE,axiom,
% 6.92/7.19 ! [A: set_int,B: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ A @ B )
% 6.92/7.19 => ( A
% 6.92/7.19 = ( inf_inf_set_int @ A @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderE
% 6.92/7.19 thf(fact_3028_inf_OorderE,axiom,
% 6.92/7.19 ! [A: rat,B: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.19 => ( A
% 6.92/7.19 = ( inf_inf_rat @ A @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderE
% 6.92/7.19 thf(fact_3029_inf_OorderE,axiom,
% 6.92/7.19 ! [A: nat,B: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.19 => ( A
% 6.92/7.19 = ( inf_inf_nat @ A @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderE
% 6.92/7.19 thf(fact_3030_inf_OorderE,axiom,
% 6.92/7.19 ! [A: int,B: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.19 => ( A
% 6.92/7.19 = ( inf_inf_int @ A @ B ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderE
% 6.92/7.19 thf(fact_3031_inf_OorderI,axiom,
% 6.92/7.19 ! [A: assn,B: assn] :
% 6.92/7.19 ( ( A
% 6.92/7.19 = ( inf_inf_assn @ A @ B ) )
% 6.92/7.19 => ( ord_less_eq_assn @ A @ B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderI
% 6.92/7.19 thf(fact_3032_inf_OorderI,axiom,
% 6.92/7.19 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( A
% 6.92/7.19 = ( inf_in2572325071724192079at_nat @ A @ B ) )
% 6.92/7.19 => ( ord_le3146513528884898305at_nat @ A @ B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderI
% 6.92/7.19 thf(fact_3033_inf_OorderI,axiom,
% 6.92/7.19 ! [A: set_nat,B: set_nat] :
% 6.92/7.19 ( ( A
% 6.92/7.19 = ( inf_inf_set_nat @ A @ B ) )
% 6.92/7.19 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderI
% 6.92/7.19 thf(fact_3034_inf_OorderI,axiom,
% 6.92/7.19 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 6.92/7.19 ( ( A
% 6.92/7.19 = ( inf_in3604695632404883862_int_o @ A @ B ) )
% 6.92/7.19 => ( ord_le8369615600986905444_int_o @ A @ B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderI
% 6.92/7.19 thf(fact_3035_inf_OorderI,axiom,
% 6.92/7.19 ! [A: set_int,B: set_int] :
% 6.92/7.19 ( ( A
% 6.92/7.19 = ( inf_inf_set_int @ A @ B ) )
% 6.92/7.19 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderI
% 6.92/7.19 thf(fact_3036_inf_OorderI,axiom,
% 6.92/7.19 ! [A: rat,B: rat] :
% 6.92/7.19 ( ( A
% 6.92/7.19 = ( inf_inf_rat @ A @ B ) )
% 6.92/7.19 => ( ord_less_eq_rat @ A @ B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderI
% 6.92/7.19 thf(fact_3037_inf_OorderI,axiom,
% 6.92/7.19 ! [A: nat,B: nat] :
% 6.92/7.19 ( ( A
% 6.92/7.19 = ( inf_inf_nat @ A @ B ) )
% 6.92/7.19 => ( ord_less_eq_nat @ A @ B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderI
% 6.92/7.19 thf(fact_3038_inf_OorderI,axiom,
% 6.92/7.19 ! [A: int,B: int] :
% 6.92/7.19 ( ( A
% 6.92/7.19 = ( inf_inf_int @ A @ B ) )
% 6.92/7.19 => ( ord_less_eq_int @ A @ B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.orderI
% 6.92/7.19 thf(fact_3039_inf__unique,axiom,
% 6.92/7.19 ! [F: assn > assn > assn,X: assn,Y: assn] :
% 6.92/7.19 ( ! [X3: assn,Y3: assn] : ( ord_less_eq_assn @ ( F @ X3 @ Y3 ) @ X3 )
% 6.92/7.19 => ( ! [X3: assn,Y3: assn] : ( ord_less_eq_assn @ ( F @ X3 @ Y3 ) @ Y3 )
% 6.92/7.19 => ( ! [X3: assn,Y3: assn,Z2: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ X3 @ Y3 )
% 6.92/7.19 => ( ( ord_less_eq_assn @ X3 @ Z2 )
% 6.92/7.19 => ( ord_less_eq_assn @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 6.92/7.19 => ( ( inf_inf_assn @ X @ Y )
% 6.92/7.19 = ( F @ X @ Y ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_unique
% 6.92/7.19 thf(fact_3040_inf__unique,axiom,
% 6.92/7.19 ! [F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F @ X3 @ Y3 ) @ X3 )
% 6.92/7.19 => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F @ X3 @ Y3 ) @ Y3 )
% 6.92/7.19 => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ X3 @ Y3 )
% 6.92/7.19 => ( ( ord_le3146513528884898305at_nat @ X3 @ Z2 )
% 6.92/7.19 => ( ord_le3146513528884898305at_nat @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 6.92/7.19 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 6.92/7.19 = ( F @ X @ Y ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_unique
% 6.92/7.19 thf(fact_3041_inf__unique,axiom,
% 6.92/7.19 ! [F: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 6.92/7.19 ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( F @ X3 @ Y3 ) @ X3 )
% 6.92/7.19 => ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( F @ X3 @ Y3 ) @ Y3 )
% 6.92/7.19 => ( ! [X3: set_nat,Y3: set_nat,Z2: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 6.92/7.19 => ( ( ord_less_eq_set_nat @ X3 @ Z2 )
% 6.92/7.19 => ( ord_less_eq_set_nat @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 6.92/7.19 => ( ( inf_inf_set_nat @ X @ Y )
% 6.92/7.19 = ( F @ X @ Y ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_unique
% 6.92/7.19 thf(fact_3042_inf__unique,axiom,
% 6.92/7.19 ! [F: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o,X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 6.92/7.19 ( ! [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( F @ X3 @ Y3 ) @ X3 )
% 6.92/7.19 => ( ! [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( F @ X3 @ Y3 ) @ Y3 )
% 6.92/7.19 => ( ! [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o,Z2: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ X3 @ Y3 )
% 6.92/7.19 => ( ( ord_le8369615600986905444_int_o @ X3 @ Z2 )
% 6.92/7.19 => ( ord_le8369615600986905444_int_o @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 6.92/7.19 => ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 6.92/7.19 = ( F @ X @ Y ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_unique
% 6.92/7.19 thf(fact_3043_inf__unique,axiom,
% 6.92/7.19 ! [F: set_int > set_int > set_int,X: set_int,Y: set_int] :
% 6.92/7.19 ( ! [X3: set_int,Y3: set_int] : ( ord_less_eq_set_int @ ( F @ X3 @ Y3 ) @ X3 )
% 6.92/7.19 => ( ! [X3: set_int,Y3: set_int] : ( ord_less_eq_set_int @ ( F @ X3 @ Y3 ) @ Y3 )
% 6.92/7.19 => ( ! [X3: set_int,Y3: set_int,Z2: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ X3 @ Y3 )
% 6.92/7.19 => ( ( ord_less_eq_set_int @ X3 @ Z2 )
% 6.92/7.19 => ( ord_less_eq_set_int @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 6.92/7.19 => ( ( inf_inf_set_int @ X @ Y )
% 6.92/7.19 = ( F @ X @ Y ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_unique
% 6.92/7.19 thf(fact_3044_inf__unique,axiom,
% 6.92/7.19 ! [F: rat > rat > rat,X: rat,Y: rat] :
% 6.92/7.19 ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ ( F @ X3 @ Y3 ) @ X3 )
% 6.92/7.19 => ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ ( F @ X3 @ Y3 ) @ Y3 )
% 6.92/7.19 => ( ! [X3: rat,Y3: rat,Z2: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 6.92/7.19 => ( ( ord_less_eq_rat @ X3 @ Z2 )
% 6.92/7.19 => ( ord_less_eq_rat @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 6.92/7.19 => ( ( inf_inf_rat @ X @ Y )
% 6.92/7.19 = ( F @ X @ Y ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_unique
% 6.92/7.19 thf(fact_3045_inf__unique,axiom,
% 6.92/7.19 ! [F: nat > nat > nat,X: nat,Y: nat] :
% 6.92/7.19 ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ ( F @ X3 @ Y3 ) @ X3 )
% 6.92/7.19 => ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ ( F @ X3 @ Y3 ) @ Y3 )
% 6.92/7.19 => ( ! [X3: nat,Y3: nat,Z2: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 6.92/7.19 => ( ( ord_less_eq_nat @ X3 @ Z2 )
% 6.92/7.19 => ( ord_less_eq_nat @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 6.92/7.19 => ( ( inf_inf_nat @ X @ Y )
% 6.92/7.19 = ( F @ X @ Y ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_unique
% 6.92/7.19 thf(fact_3046_inf__unique,axiom,
% 6.92/7.19 ! [F: int > int > int,X: int,Y: int] :
% 6.92/7.19 ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ ( F @ X3 @ Y3 ) @ X3 )
% 6.92/7.19 => ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ ( F @ X3 @ Y3 ) @ Y3 )
% 6.92/7.19 => ( ! [X3: int,Y3: int,Z2: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ X3 @ Y3 )
% 6.92/7.19 => ( ( ord_less_eq_int @ X3 @ Z2 )
% 6.92/7.19 => ( ord_less_eq_int @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 6.92/7.19 => ( ( inf_inf_int @ X @ Y )
% 6.92/7.19 = ( F @ X @ Y ) ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_unique
% 6.92/7.19 thf(fact_3047_le__iff__inf,axiom,
% 6.92/7.19 ( ord_less_eq_assn
% 6.92/7.19 = ( ^ [X4: assn,Y4: assn] :
% 6.92/7.19 ( ( inf_inf_assn @ X4 @ Y4 )
% 6.92/7.19 = X4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_iff_inf
% 6.92/7.19 thf(fact_3048_le__iff__inf,axiom,
% 6.92/7.19 ( ord_le3146513528884898305at_nat
% 6.92/7.19 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( inf_in2572325071724192079at_nat @ X4 @ Y4 )
% 6.92/7.19 = X4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_iff_inf
% 6.92/7.19 thf(fact_3049_le__iff__inf,axiom,
% 6.92/7.19 ( ord_less_eq_set_nat
% 6.92/7.19 = ( ^ [X4: set_nat,Y4: set_nat] :
% 6.92/7.19 ( ( inf_inf_set_nat @ X4 @ Y4 )
% 6.92/7.19 = X4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_iff_inf
% 6.92/7.19 thf(fact_3050_le__iff__inf,axiom,
% 6.92/7.19 ( ord_le8369615600986905444_int_o
% 6.92/7.19 = ( ^ [X4: product_prod_int_int > $o,Y4: product_prod_int_int > $o] :
% 6.92/7.19 ( ( inf_in3604695632404883862_int_o @ X4 @ Y4 )
% 6.92/7.19 = X4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_iff_inf
% 6.92/7.19 thf(fact_3051_le__iff__inf,axiom,
% 6.92/7.19 ( ord_less_eq_set_int
% 6.92/7.19 = ( ^ [X4: set_int,Y4: set_int] :
% 6.92/7.19 ( ( inf_inf_set_int @ X4 @ Y4 )
% 6.92/7.19 = X4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_iff_inf
% 6.92/7.19 thf(fact_3052_le__iff__inf,axiom,
% 6.92/7.19 ( ord_less_eq_rat
% 6.92/7.19 = ( ^ [X4: rat,Y4: rat] :
% 6.92/7.19 ( ( inf_inf_rat @ X4 @ Y4 )
% 6.92/7.19 = X4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_iff_inf
% 6.92/7.19 thf(fact_3053_le__iff__inf,axiom,
% 6.92/7.19 ( ord_less_eq_nat
% 6.92/7.19 = ( ^ [X4: nat,Y4: nat] :
% 6.92/7.19 ( ( inf_inf_nat @ X4 @ Y4 )
% 6.92/7.19 = X4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_iff_inf
% 6.92/7.19 thf(fact_3054_le__iff__inf,axiom,
% 6.92/7.19 ( ord_less_eq_int
% 6.92/7.19 = ( ^ [X4: int,Y4: int] :
% 6.92/7.19 ( ( inf_inf_int @ X4 @ Y4 )
% 6.92/7.19 = X4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % le_iff_inf
% 6.92/7.19 thf(fact_3055_inf_Oabsorb1,axiom,
% 6.92/7.19 ! [A: assn,B: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ A @ B )
% 6.92/7.19 => ( ( inf_inf_assn @ A @ B )
% 6.92/7.19 = A ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb1
% 6.92/7.19 thf(fact_3056_inf_Oabsorb1,axiom,
% 6.92/7.19 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 6.92/7.19 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 6.92/7.19 = A ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb1
% 6.92/7.19 thf(fact_3057_inf_Oabsorb1,axiom,
% 6.92/7.19 ! [A: set_nat,B: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ A @ B )
% 6.92/7.19 => ( ( inf_inf_set_nat @ A @ B )
% 6.92/7.19 = A ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb1
% 6.92/7.19 thf(fact_3058_inf_Oabsorb1,axiom,
% 6.92/7.19 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ A @ B )
% 6.92/7.19 => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 6.92/7.19 = A ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb1
% 6.92/7.19 thf(fact_3059_inf_Oabsorb1,axiom,
% 6.92/7.19 ! [A: set_int,B: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ A @ B )
% 6.92/7.19 => ( ( inf_inf_set_int @ A @ B )
% 6.92/7.19 = A ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb1
% 6.92/7.19 thf(fact_3060_inf_Oabsorb1,axiom,
% 6.92/7.19 ! [A: rat,B: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.19 => ( ( inf_inf_rat @ A @ B )
% 6.92/7.19 = A ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb1
% 6.92/7.19 thf(fact_3061_inf_Oabsorb1,axiom,
% 6.92/7.19 ! [A: nat,B: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.19 => ( ( inf_inf_nat @ A @ B )
% 6.92/7.19 = A ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb1
% 6.92/7.19 thf(fact_3062_inf_Oabsorb1,axiom,
% 6.92/7.19 ! [A: int,B: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.19 => ( ( inf_inf_int @ A @ B )
% 6.92/7.19 = A ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb1
% 6.92/7.19 thf(fact_3063_inf_Oabsorb2,axiom,
% 6.92/7.19 ! [B: assn,A: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ B @ A )
% 6.92/7.19 => ( ( inf_inf_assn @ A @ B )
% 6.92/7.19 = B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb2
% 6.92/7.19 thf(fact_3064_inf_Oabsorb2,axiom,
% 6.92/7.19 ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ B @ A )
% 6.92/7.19 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 6.92/7.19 = B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb2
% 6.92/7.19 thf(fact_3065_inf_Oabsorb2,axiom,
% 6.92/7.19 ! [B: set_nat,A: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ B @ A )
% 6.92/7.19 => ( ( inf_inf_set_nat @ A @ B )
% 6.92/7.19 = B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb2
% 6.92/7.19 thf(fact_3066_inf_Oabsorb2,axiom,
% 6.92/7.19 ! [B: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ B @ A )
% 6.92/7.19 => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 6.92/7.19 = B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb2
% 6.92/7.19 thf(fact_3067_inf_Oabsorb2,axiom,
% 6.92/7.19 ! [B: set_int,A: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ B @ A )
% 6.92/7.19 => ( ( inf_inf_set_int @ A @ B )
% 6.92/7.19 = B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb2
% 6.92/7.19 thf(fact_3068_inf_Oabsorb2,axiom,
% 6.92/7.19 ! [B: rat,A: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.19 => ( ( inf_inf_rat @ A @ B )
% 6.92/7.19 = B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb2
% 6.92/7.19 thf(fact_3069_inf_Oabsorb2,axiom,
% 6.92/7.19 ! [B: nat,A: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.19 => ( ( inf_inf_nat @ A @ B )
% 6.92/7.19 = B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb2
% 6.92/7.19 thf(fact_3070_inf_Oabsorb2,axiom,
% 6.92/7.19 ! [B: int,A: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ B @ A )
% 6.92/7.19 => ( ( inf_inf_int @ A @ B )
% 6.92/7.19 = B ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb2
% 6.92/7.19 thf(fact_3071_inf__absorb1,axiom,
% 6.92/7.19 ! [X: assn,Y: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ X @ Y )
% 6.92/7.19 => ( ( inf_inf_assn @ X @ Y )
% 6.92/7.19 = X ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb1
% 6.92/7.19 thf(fact_3072_inf__absorb1,axiom,
% 6.92/7.19 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 6.92/7.19 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 6.92/7.19 = X ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb1
% 6.92/7.19 thf(fact_3073_inf__absorb1,axiom,
% 6.92/7.19 ! [X: set_nat,Y: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ X @ Y )
% 6.92/7.19 => ( ( inf_inf_set_nat @ X @ Y )
% 6.92/7.19 = X ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb1
% 6.92/7.19 thf(fact_3074_inf__absorb1,axiom,
% 6.92/7.19 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ X @ Y )
% 6.92/7.19 => ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 6.92/7.19 = X ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb1
% 6.92/7.19 thf(fact_3075_inf__absorb1,axiom,
% 6.92/7.19 ! [X: set_int,Y: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ X @ Y )
% 6.92/7.19 => ( ( inf_inf_set_int @ X @ Y )
% 6.92/7.19 = X ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb1
% 6.92/7.19 thf(fact_3076_inf__absorb1,axiom,
% 6.92/7.19 ! [X: rat,Y: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.19 => ( ( inf_inf_rat @ X @ Y )
% 6.92/7.19 = X ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb1
% 6.92/7.19 thf(fact_3077_inf__absorb1,axiom,
% 6.92/7.19 ! [X: nat,Y: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ X @ Y )
% 6.92/7.19 => ( ( inf_inf_nat @ X @ Y )
% 6.92/7.19 = X ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb1
% 6.92/7.19 thf(fact_3078_inf__absorb1,axiom,
% 6.92/7.19 ! [X: int,Y: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.19 => ( ( inf_inf_int @ X @ Y )
% 6.92/7.19 = X ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb1
% 6.92/7.19 thf(fact_3079_inf__absorb2,axiom,
% 6.92/7.19 ! [Y: assn,X: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ Y @ X )
% 6.92/7.19 => ( ( inf_inf_assn @ X @ Y )
% 6.92/7.19 = Y ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb2
% 6.92/7.19 thf(fact_3080_inf__absorb2,axiom,
% 6.92/7.19 ! [Y: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ Y @ X )
% 6.92/7.19 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 6.92/7.19 = Y ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb2
% 6.92/7.19 thf(fact_3081_inf__absorb2,axiom,
% 6.92/7.19 ! [Y: set_nat,X: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ Y @ X )
% 6.92/7.19 => ( ( inf_inf_set_nat @ X @ Y )
% 6.92/7.19 = Y ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb2
% 6.92/7.19 thf(fact_3082_inf__absorb2,axiom,
% 6.92/7.19 ! [Y: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ Y @ X )
% 6.92/7.19 => ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 6.92/7.19 = Y ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb2
% 6.92/7.19 thf(fact_3083_inf__absorb2,axiom,
% 6.92/7.19 ! [Y: set_int,X: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ Y @ X )
% 6.92/7.19 => ( ( inf_inf_set_int @ X @ Y )
% 6.92/7.19 = Y ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb2
% 6.92/7.19 thf(fact_3084_inf__absorb2,axiom,
% 6.92/7.19 ! [Y: rat,X: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ Y @ X )
% 6.92/7.19 => ( ( inf_inf_rat @ X @ Y )
% 6.92/7.19 = Y ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb2
% 6.92/7.19 thf(fact_3085_inf__absorb2,axiom,
% 6.92/7.19 ! [Y: nat,X: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ Y @ X )
% 6.92/7.19 => ( ( inf_inf_nat @ X @ Y )
% 6.92/7.19 = Y ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb2
% 6.92/7.19 thf(fact_3086_inf__absorb2,axiom,
% 6.92/7.19 ! [Y: int,X: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ Y @ X )
% 6.92/7.19 => ( ( inf_inf_int @ X @ Y )
% 6.92/7.19 = Y ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_absorb2
% 6.92/7.19 thf(fact_3087_inf_OboundedE,axiom,
% 6.92/7.19 ! [A: assn,B: assn,C2: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ A @ ( inf_inf_assn @ B @ C2 ) )
% 6.92/7.19 => ~ ( ( ord_less_eq_assn @ A @ B )
% 6.92/7.19 => ~ ( ord_less_eq_assn @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedE
% 6.92/7.19 thf(fact_3088_inf_OboundedE,axiom,
% 6.92/7.19 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) )
% 6.92/7.19 => ~ ( ( ord_le3146513528884898305at_nat @ A @ B )
% 6.92/7.19 => ~ ( ord_le3146513528884898305at_nat @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedE
% 6.92/7.19 thf(fact_3089_inf_OboundedE,axiom,
% 6.92/7.19 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) )
% 6.92/7.19 => ~ ( ( ord_less_eq_set_nat @ A @ B )
% 6.92/7.19 => ~ ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedE
% 6.92/7.19 thf(fact_3090_inf_OboundedE,axiom,
% 6.92/7.19 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C2: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C2 ) )
% 6.92/7.19 => ~ ( ( ord_le8369615600986905444_int_o @ A @ B )
% 6.92/7.19 => ~ ( ord_le8369615600986905444_int_o @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedE
% 6.92/7.19 thf(fact_3091_inf_OboundedE,axiom,
% 6.92/7.19 ! [A: set_int,B: set_int,C2: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ A @ ( inf_inf_set_int @ B @ C2 ) )
% 6.92/7.19 => ~ ( ( ord_less_eq_set_int @ A @ B )
% 6.92/7.19 => ~ ( ord_less_eq_set_int @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedE
% 6.92/7.19 thf(fact_3092_inf_OboundedE,axiom,
% 6.92/7.19 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C2 ) )
% 6.92/7.19 => ~ ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.19 => ~ ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedE
% 6.92/7.19 thf(fact_3093_inf_OboundedE,axiom,
% 6.92/7.19 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C2 ) )
% 6.92/7.19 => ~ ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.19 => ~ ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedE
% 6.92/7.19 thf(fact_3094_inf_OboundedE,axiom,
% 6.92/7.19 ! [A: int,B: int,C2: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C2 ) )
% 6.92/7.19 => ~ ( ( ord_less_eq_int @ A @ B )
% 6.92/7.19 => ~ ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedE
% 6.92/7.19 thf(fact_3095_inf_OboundedI,axiom,
% 6.92/7.19 ! [A: assn,B: assn,C2: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ A @ B )
% 6.92/7.19 => ( ( ord_less_eq_assn @ A @ C2 )
% 6.92/7.19 => ( ord_less_eq_assn @ A @ ( inf_inf_assn @ B @ C2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedI
% 6.92/7.19 thf(fact_3096_inf_OboundedI,axiom,
% 6.92/7.19 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 6.92/7.19 => ( ( ord_le3146513528884898305at_nat @ A @ C2 )
% 6.92/7.19 => ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedI
% 6.92/7.19 thf(fact_3097_inf_OboundedI,axiom,
% 6.92/7.19 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ A @ B )
% 6.92/7.19 => ( ( ord_less_eq_set_nat @ A @ C2 )
% 6.92/7.19 => ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedI
% 6.92/7.19 thf(fact_3098_inf_OboundedI,axiom,
% 6.92/7.19 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C2: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ A @ B )
% 6.92/7.19 => ( ( ord_le8369615600986905444_int_o @ A @ C2 )
% 6.92/7.19 => ( ord_le8369615600986905444_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedI
% 6.92/7.19 thf(fact_3099_inf_OboundedI,axiom,
% 6.92/7.19 ! [A: set_int,B: set_int,C2: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ A @ B )
% 6.92/7.19 => ( ( ord_less_eq_set_int @ A @ C2 )
% 6.92/7.19 => ( ord_less_eq_set_int @ A @ ( inf_inf_set_int @ B @ C2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedI
% 6.92/7.19 thf(fact_3100_inf_OboundedI,axiom,
% 6.92/7.19 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.19 => ( ( ord_less_eq_rat @ A @ C2 )
% 6.92/7.19 => ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedI
% 6.92/7.19 thf(fact_3101_inf_OboundedI,axiom,
% 6.92/7.19 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.19 => ( ( ord_less_eq_nat @ A @ C2 )
% 6.92/7.19 => ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedI
% 6.92/7.19 thf(fact_3102_inf_OboundedI,axiom,
% 6.92/7.19 ! [A: int,B: int,C2: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.19 => ( ( ord_less_eq_int @ A @ C2 )
% 6.92/7.19 => ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C2 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.boundedI
% 6.92/7.19 thf(fact_3103_inf__greatest,axiom,
% 6.92/7.19 ! [X: assn,Y: assn,Z3: assn] :
% 6.92/7.19 ( ( ord_less_eq_assn @ X @ Y )
% 6.92/7.19 => ( ( ord_less_eq_assn @ X @ Z3 )
% 6.92/7.19 => ( ord_less_eq_assn @ X @ ( inf_inf_assn @ Y @ Z3 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_greatest
% 6.92/7.19 thf(fact_3104_inf__greatest,axiom,
% 6.92/7.19 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 6.92/7.19 => ( ( ord_le3146513528884898305at_nat @ X @ Z3 )
% 6.92/7.19 => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_greatest
% 6.92/7.19 thf(fact_3105_inf__greatest,axiom,
% 6.92/7.19 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 6.92/7.19 ( ( ord_less_eq_set_nat @ X @ Y )
% 6.92/7.19 => ( ( ord_less_eq_set_nat @ X @ Z3 )
% 6.92/7.19 => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z3 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_greatest
% 6.92/7.19 thf(fact_3106_inf__greatest,axiom,
% 6.92/7.19 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o] :
% 6.92/7.19 ( ( ord_le8369615600986905444_int_o @ X @ Y )
% 6.92/7.19 => ( ( ord_le8369615600986905444_int_o @ X @ Z3 )
% 6.92/7.19 => ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z3 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_greatest
% 6.92/7.19 thf(fact_3107_inf__greatest,axiom,
% 6.92/7.19 ! [X: set_int,Y: set_int,Z3: set_int] :
% 6.92/7.19 ( ( ord_less_eq_set_int @ X @ Y )
% 6.92/7.19 => ( ( ord_less_eq_set_int @ X @ Z3 )
% 6.92/7.19 => ( ord_less_eq_set_int @ X @ ( inf_inf_set_int @ Y @ Z3 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_greatest
% 6.92/7.19 thf(fact_3108_inf__greatest,axiom,
% 6.92/7.19 ! [X: rat,Y: rat,Z3: rat] :
% 6.92/7.19 ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.19 => ( ( ord_less_eq_rat @ X @ Z3 )
% 6.92/7.19 => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z3 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_greatest
% 6.92/7.19 thf(fact_3109_inf__greatest,axiom,
% 6.92/7.19 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.19 ( ( ord_less_eq_nat @ X @ Y )
% 6.92/7.19 => ( ( ord_less_eq_nat @ X @ Z3 )
% 6.92/7.19 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z3 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_greatest
% 6.92/7.19 thf(fact_3110_inf__greatest,axiom,
% 6.92/7.19 ! [X: int,Y: int,Z3: int] :
% 6.92/7.19 ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.19 => ( ( ord_less_eq_int @ X @ Z3 )
% 6.92/7.19 => ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z3 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf_greatest
% 6.92/7.19 thf(fact_3111_inf_Oorder__iff,axiom,
% 6.92/7.19 ( ord_less_eq_assn
% 6.92/7.19 = ( ^ [A5: assn,B4: assn] :
% 6.92/7.19 ( A5
% 6.92/7.19 = ( inf_inf_assn @ A5 @ B4 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.order_iff
% 6.92/7.19 thf(fact_3112_inf_Oorder__iff,axiom,
% 6.92/7.19 ( ord_le3146513528884898305at_nat
% 6.92/7.19 = ( ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( A5
% 6.92/7.19 = ( inf_in2572325071724192079at_nat @ A5 @ B4 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.order_iff
% 6.92/7.19 thf(fact_3113_inf_Oorder__iff,axiom,
% 6.92/7.19 ( ord_less_eq_set_nat
% 6.92/7.19 = ( ^ [A5: set_nat,B4: set_nat] :
% 6.92/7.19 ( A5
% 6.92/7.19 = ( inf_inf_set_nat @ A5 @ B4 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.order_iff
% 6.92/7.19 thf(fact_3114_inf_Oorder__iff,axiom,
% 6.92/7.19 ( ord_le8369615600986905444_int_o
% 6.92/7.19 = ( ^ [A5: product_prod_int_int > $o,B4: product_prod_int_int > $o] :
% 6.92/7.19 ( A5
% 6.92/7.19 = ( inf_in3604695632404883862_int_o @ A5 @ B4 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.order_iff
% 6.92/7.19 thf(fact_3115_inf_Oorder__iff,axiom,
% 6.92/7.19 ( ord_less_eq_set_int
% 6.92/7.19 = ( ^ [A5: set_int,B4: set_int] :
% 6.92/7.19 ( A5
% 6.92/7.19 = ( inf_inf_set_int @ A5 @ B4 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.order_iff
% 6.92/7.19 thf(fact_3116_inf_Oorder__iff,axiom,
% 6.92/7.19 ( ord_less_eq_rat
% 6.92/7.19 = ( ^ [A5: rat,B4: rat] :
% 6.92/7.19 ( A5
% 6.92/7.19 = ( inf_inf_rat @ A5 @ B4 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.order_iff
% 6.92/7.19 thf(fact_3117_inf_Oorder__iff,axiom,
% 6.92/7.19 ( ord_less_eq_nat
% 6.92/7.19 = ( ^ [A5: nat,B4: nat] :
% 6.92/7.19 ( A5
% 6.92/7.19 = ( inf_inf_nat @ A5 @ B4 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.order_iff
% 6.92/7.19 thf(fact_3118_inf_Oorder__iff,axiom,
% 6.92/7.19 ( ord_less_eq_int
% 6.92/7.19 = ( ^ [A5: int,B4: int] :
% 6.92/7.19 ( A5
% 6.92/7.19 = ( inf_inf_int @ A5 @ B4 ) ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.order_iff
% 6.92/7.19 thf(fact_3119_inf_Ocobounded1,axiom,
% 6.92/7.19 ! [A: assn,B: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ A ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded1
% 6.92/7.19 thf(fact_3120_inf_Ocobounded1,axiom,
% 6.92/7.19 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ A ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded1
% 6.92/7.19 thf(fact_3121_inf_Ocobounded1,axiom,
% 6.92/7.19 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ A ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded1
% 6.92/7.19 thf(fact_3122_inf_Ocobounded1,axiom,
% 6.92/7.19 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ A ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded1
% 6.92/7.19 thf(fact_3123_inf_Ocobounded1,axiom,
% 6.92/7.19 ! [A: set_int,B: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ B ) @ A ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded1
% 6.92/7.19 thf(fact_3124_inf_Ocobounded1,axiom,
% 6.92/7.19 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ A ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded1
% 6.92/7.19 thf(fact_3125_inf_Ocobounded1,axiom,
% 6.92/7.19 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ A ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded1
% 6.92/7.19 thf(fact_3126_inf_Ocobounded1,axiom,
% 6.92/7.19 ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ A ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded1
% 6.92/7.19 thf(fact_3127_inf_Ocobounded2,axiom,
% 6.92/7.19 ! [A: assn,B: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ B ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded2
% 6.92/7.19 thf(fact_3128_inf_Ocobounded2,axiom,
% 6.92/7.19 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ B ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded2
% 6.92/7.19 thf(fact_3129_inf_Ocobounded2,axiom,
% 6.92/7.19 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ B ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded2
% 6.92/7.19 thf(fact_3130_inf_Ocobounded2,axiom,
% 6.92/7.19 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ B ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded2
% 6.92/7.19 thf(fact_3131_inf_Ocobounded2,axiom,
% 6.92/7.19 ! [A: set_int,B: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ B ) @ B ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded2
% 6.92/7.19 thf(fact_3132_inf_Ocobounded2,axiom,
% 6.92/7.19 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ B ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded2
% 6.92/7.19 thf(fact_3133_inf_Ocobounded2,axiom,
% 6.92/7.19 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ B ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded2
% 6.92/7.19 thf(fact_3134_inf_Ocobounded2,axiom,
% 6.92/7.19 ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ B ) ).
% 6.92/7.19
% 6.92/7.19 % inf.cobounded2
% 6.92/7.19 thf(fact_3135_inf_Oabsorb__iff1,axiom,
% 6.92/7.19 ( ord_less_eq_assn
% 6.92/7.19 = ( ^ [A5: assn,B4: assn] :
% 6.92/7.19 ( ( inf_inf_assn @ A5 @ B4 )
% 6.92/7.19 = A5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb_iff1
% 6.92/7.19 thf(fact_3136_inf_Oabsorb__iff1,axiom,
% 6.92/7.19 ( ord_le3146513528884898305at_nat
% 6.92/7.19 = ( ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( inf_in2572325071724192079at_nat @ A5 @ B4 )
% 6.92/7.19 = A5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb_iff1
% 6.92/7.19 thf(fact_3137_inf_Oabsorb__iff1,axiom,
% 6.92/7.19 ( ord_less_eq_set_nat
% 6.92/7.19 = ( ^ [A5: set_nat,B4: set_nat] :
% 6.92/7.19 ( ( inf_inf_set_nat @ A5 @ B4 )
% 6.92/7.19 = A5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb_iff1
% 6.92/7.19 thf(fact_3138_inf_Oabsorb__iff1,axiom,
% 6.92/7.19 ( ord_le8369615600986905444_int_o
% 6.92/7.19 = ( ^ [A5: product_prod_int_int > $o,B4: product_prod_int_int > $o] :
% 6.92/7.19 ( ( inf_in3604695632404883862_int_o @ A5 @ B4 )
% 6.92/7.19 = A5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb_iff1
% 6.92/7.19 thf(fact_3139_inf_Oabsorb__iff1,axiom,
% 6.92/7.19 ( ord_less_eq_set_int
% 6.92/7.19 = ( ^ [A5: set_int,B4: set_int] :
% 6.92/7.19 ( ( inf_inf_set_int @ A5 @ B4 )
% 6.92/7.19 = A5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb_iff1
% 6.92/7.19 thf(fact_3140_inf_Oabsorb__iff1,axiom,
% 6.92/7.19 ( ord_less_eq_rat
% 6.92/7.19 = ( ^ [A5: rat,B4: rat] :
% 6.92/7.19 ( ( inf_inf_rat @ A5 @ B4 )
% 6.92/7.19 = A5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb_iff1
% 6.92/7.19 thf(fact_3141_inf_Oabsorb__iff1,axiom,
% 6.92/7.19 ( ord_less_eq_nat
% 6.92/7.19 = ( ^ [A5: nat,B4: nat] :
% 6.92/7.19 ( ( inf_inf_nat @ A5 @ B4 )
% 6.92/7.19 = A5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb_iff1
% 6.92/7.19 thf(fact_3142_inf_Oabsorb__iff1,axiom,
% 6.92/7.19 ( ord_less_eq_int
% 6.92/7.19 = ( ^ [A5: int,B4: int] :
% 6.92/7.19 ( ( inf_inf_int @ A5 @ B4 )
% 6.92/7.19 = A5 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb_iff1
% 6.92/7.19 thf(fact_3143_inf_Oabsorb__iff2,axiom,
% 6.92/7.19 ( ord_less_eq_assn
% 6.92/7.19 = ( ^ [B4: assn,A5: assn] :
% 6.92/7.19 ( ( inf_inf_assn @ A5 @ B4 )
% 6.92/7.19 = B4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb_iff2
% 6.92/7.19 thf(fact_3144_inf_Oabsorb__iff2,axiom,
% 6.92/7.19 ( ord_le3146513528884898305at_nat
% 6.92/7.19 = ( ^ [B4: set_Pr1261947904930325089at_nat,A5: set_Pr1261947904930325089at_nat] :
% 6.92/7.19 ( ( inf_in2572325071724192079at_nat @ A5 @ B4 )
% 6.92/7.19 = B4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb_iff2
% 6.92/7.19 thf(fact_3145_inf_Oabsorb__iff2,axiom,
% 6.92/7.19 ( ord_less_eq_set_nat
% 6.92/7.19 = ( ^ [B4: set_nat,A5: set_nat] :
% 6.92/7.19 ( ( inf_inf_set_nat @ A5 @ B4 )
% 6.92/7.19 = B4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb_iff2
% 6.92/7.19 thf(fact_3146_inf_Oabsorb__iff2,axiom,
% 6.92/7.19 ( ord_le8369615600986905444_int_o
% 6.92/7.19 = ( ^ [B4: product_prod_int_int > $o,A5: product_prod_int_int > $o] :
% 6.92/7.19 ( ( inf_in3604695632404883862_int_o @ A5 @ B4 )
% 6.92/7.19 = B4 ) ) ) ).
% 6.92/7.19
% 6.92/7.19 % inf.absorb_iff2
% 6.92/7.19 thf(fact_3147_inf_Oabsorb__iff2,axiom,
% 6.92/7.19 ( ord_less_eq_set_int
% 6.92/7.19 = ( ^ [B4: set_int,A5: set_int] :
% 6.92/7.19 ( ( inf_inf_set_int @ A5 @ B4 )
% 6.92/7.20 = B4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb_iff2
% 6.92/7.20 thf(fact_3148_inf_Oabsorb__iff2,axiom,
% 6.92/7.20 ( ord_less_eq_rat
% 6.92/7.20 = ( ^ [B4: rat,A5: rat] :
% 6.92/7.20 ( ( inf_inf_rat @ A5 @ B4 )
% 6.92/7.20 = B4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb_iff2
% 6.92/7.20 thf(fact_3149_inf_Oabsorb__iff2,axiom,
% 6.92/7.20 ( ord_less_eq_nat
% 6.92/7.20 = ( ^ [B4: nat,A5: nat] :
% 6.92/7.20 ( ( inf_inf_nat @ A5 @ B4 )
% 6.92/7.20 = B4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb_iff2
% 6.92/7.20 thf(fact_3150_inf_Oabsorb__iff2,axiom,
% 6.92/7.20 ( ord_less_eq_int
% 6.92/7.20 = ( ^ [B4: int,A5: int] :
% 6.92/7.20 ( ( inf_inf_int @ A5 @ B4 )
% 6.92/7.20 = B4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb_iff2
% 6.92/7.20 thf(fact_3151_inf_OcoboundedI1,axiom,
% 6.92/7.20 ! [A: assn,C2: assn,B: assn] :
% 6.92/7.20 ( ( ord_less_eq_assn @ A @ C2 )
% 6.92/7.20 => ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI1
% 6.92/7.20 thf(fact_3152_inf_OcoboundedI1,axiom,
% 6.92/7.20 ! [A: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ord_le3146513528884898305at_nat @ A @ C2 )
% 6.92/7.20 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI1
% 6.92/7.20 thf(fact_3153_inf_OcoboundedI1,axiom,
% 6.92/7.20 ! [A: set_nat,C2: set_nat,B: set_nat] :
% 6.92/7.20 ( ( ord_less_eq_set_nat @ A @ C2 )
% 6.92/7.20 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI1
% 6.92/7.20 thf(fact_3154_inf_OcoboundedI1,axiom,
% 6.92/7.20 ! [A: product_prod_int_int > $o,C2: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 6.92/7.20 ( ( ord_le8369615600986905444_int_o @ A @ C2 )
% 6.92/7.20 => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI1
% 6.92/7.20 thf(fact_3155_inf_OcoboundedI1,axiom,
% 6.92/7.20 ! [A: set_int,C2: set_int,B: set_int] :
% 6.92/7.20 ( ( ord_less_eq_set_int @ A @ C2 )
% 6.92/7.20 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI1
% 6.92/7.20 thf(fact_3156_inf_OcoboundedI1,axiom,
% 6.92/7.20 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ A @ C2 )
% 6.92/7.20 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI1
% 6.92/7.20 thf(fact_3157_inf_OcoboundedI1,axiom,
% 6.92/7.20 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.20 ( ( ord_less_eq_nat @ A @ C2 )
% 6.92/7.20 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI1
% 6.92/7.20 thf(fact_3158_inf_OcoboundedI1,axiom,
% 6.92/7.20 ! [A: int,C2: int,B: int] :
% 6.92/7.20 ( ( ord_less_eq_int @ A @ C2 )
% 6.92/7.20 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI1
% 6.92/7.20 thf(fact_3159_inf_OcoboundedI2,axiom,
% 6.92/7.20 ! [B: assn,C2: assn,A: assn] :
% 6.92/7.20 ( ( ord_less_eq_assn @ B @ C2 )
% 6.92/7.20 => ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI2
% 6.92/7.20 thf(fact_3160_inf_OcoboundedI2,axiom,
% 6.92/7.20 ! [B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ord_le3146513528884898305at_nat @ B @ C2 )
% 6.92/7.20 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI2
% 6.92/7.20 thf(fact_3161_inf_OcoboundedI2,axiom,
% 6.92/7.20 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 6.92/7.20 ( ( ord_less_eq_set_nat @ B @ C2 )
% 6.92/7.20 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI2
% 6.92/7.20 thf(fact_3162_inf_OcoboundedI2,axiom,
% 6.92/7.20 ! [B: product_prod_int_int > $o,C2: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 6.92/7.20 ( ( ord_le8369615600986905444_int_o @ B @ C2 )
% 6.92/7.20 => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI2
% 6.92/7.20 thf(fact_3163_inf_OcoboundedI2,axiom,
% 6.92/7.20 ! [B: set_int,C2: set_int,A: set_int] :
% 6.92/7.20 ( ( ord_less_eq_set_int @ B @ C2 )
% 6.92/7.20 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI2
% 6.92/7.20 thf(fact_3164_inf_OcoboundedI2,axiom,
% 6.92/7.20 ! [B: rat,C2: rat,A: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.20 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI2
% 6.92/7.20 thf(fact_3165_inf_OcoboundedI2,axiom,
% 6.92/7.20 ! [B: nat,C2: nat,A: nat] :
% 6.92/7.20 ( ( ord_less_eq_nat @ B @ C2 )
% 6.92/7.20 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI2
% 6.92/7.20 thf(fact_3166_inf_OcoboundedI2,axiom,
% 6.92/7.20 ! [B: int,C2: int,A: int] :
% 6.92/7.20 ( ( ord_less_eq_int @ B @ C2 )
% 6.92/7.20 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.coboundedI2
% 6.92/7.20 thf(fact_3167_less__infI1,axiom,
% 6.92/7.20 ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ord_le7866589430770878221at_nat @ A @ X )
% 6.92/7.20 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_infI1
% 6.92/7.20 thf(fact_3168_less__infI1,axiom,
% 6.92/7.20 ! [A: set_nat,X: set_nat,B: set_nat] :
% 6.92/7.20 ( ( ord_less_set_nat @ A @ X )
% 6.92/7.20 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_infI1
% 6.92/7.20 thf(fact_3169_less__infI1,axiom,
% 6.92/7.20 ! [A: product_prod_int_int > $o,X: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 6.92/7.20 ( ( ord_le8213806771718485336_int_o @ A @ X )
% 6.92/7.20 => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_infI1
% 6.92/7.20 thf(fact_3170_less__infI1,axiom,
% 6.92/7.20 ! [A: assn,X: assn,B: assn] :
% 6.92/7.20 ( ( ord_less_assn @ A @ X )
% 6.92/7.20 => ( ord_less_assn @ ( inf_inf_assn @ A @ B ) @ X ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_infI1
% 6.92/7.20 thf(fact_3171_less__infI1,axiom,
% 6.92/7.20 ! [A: rat,X: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_rat @ A @ X )
% 6.92/7.20 => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_infI1
% 6.92/7.20 thf(fact_3172_less__infI1,axiom,
% 6.92/7.20 ! [A: nat,X: nat,B: nat] :
% 6.92/7.20 ( ( ord_less_nat @ A @ X )
% 6.92/7.20 => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_infI1
% 6.92/7.20 thf(fact_3173_less__infI1,axiom,
% 6.92/7.20 ! [A: int,X: int,B: int] :
% 6.92/7.20 ( ( ord_less_int @ A @ X )
% 6.92/7.20 => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_infI1
% 6.92/7.20 thf(fact_3174_less__infI2,axiom,
% 6.92/7.20 ! [B: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ord_le7866589430770878221at_nat @ B @ X )
% 6.92/7.20 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_infI2
% 6.92/7.20 thf(fact_3175_less__infI2,axiom,
% 6.92/7.20 ! [B: set_nat,X: set_nat,A: set_nat] :
% 6.92/7.20 ( ( ord_less_set_nat @ B @ X )
% 6.92/7.20 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_infI2
% 6.92/7.20 thf(fact_3176_less__infI2,axiom,
% 6.92/7.20 ! [B: product_prod_int_int > $o,X: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 6.92/7.20 ( ( ord_le8213806771718485336_int_o @ B @ X )
% 6.92/7.20 => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_infI2
% 6.92/7.20 thf(fact_3177_less__infI2,axiom,
% 6.92/7.20 ! [B: assn,X: assn,A: assn] :
% 6.92/7.20 ( ( ord_less_assn @ B @ X )
% 6.92/7.20 => ( ord_less_assn @ ( inf_inf_assn @ A @ B ) @ X ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_infI2
% 6.92/7.20 thf(fact_3178_less__infI2,axiom,
% 6.92/7.20 ! [B: rat,X: rat,A: rat] :
% 6.92/7.20 ( ( ord_less_rat @ B @ X )
% 6.92/7.20 => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_infI2
% 6.92/7.20 thf(fact_3179_less__infI2,axiom,
% 6.92/7.20 ! [B: nat,X: nat,A: nat] :
% 6.92/7.20 ( ( ord_less_nat @ B @ X )
% 6.92/7.20 => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_infI2
% 6.92/7.20 thf(fact_3180_less__infI2,axiom,
% 6.92/7.20 ! [B: int,X: int,A: int] :
% 6.92/7.20 ( ( ord_less_int @ B @ X )
% 6.92/7.20 => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_infI2
% 6.92/7.20 thf(fact_3181_inf_Oabsorb3,axiom,
% 6.92/7.20 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ord_le7866589430770878221at_nat @ A @ B )
% 6.92/7.20 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 6.92/7.20 = A ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb3
% 6.92/7.20 thf(fact_3182_inf_Oabsorb3,axiom,
% 6.92/7.20 ! [A: set_nat,B: set_nat] :
% 6.92/7.20 ( ( ord_less_set_nat @ A @ B )
% 6.92/7.20 => ( ( inf_inf_set_nat @ A @ B )
% 6.92/7.20 = A ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb3
% 6.92/7.20 thf(fact_3183_inf_Oabsorb3,axiom,
% 6.92/7.20 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 6.92/7.20 ( ( ord_le8213806771718485336_int_o @ A @ B )
% 6.92/7.20 => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 6.92/7.20 = A ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb3
% 6.92/7.20 thf(fact_3184_inf_Oabsorb3,axiom,
% 6.92/7.20 ! [A: assn,B: assn] :
% 6.92/7.20 ( ( ord_less_assn @ A @ B )
% 6.92/7.20 => ( ( inf_inf_assn @ A @ B )
% 6.92/7.20 = A ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb3
% 6.92/7.20 thf(fact_3185_inf_Oabsorb3,axiom,
% 6.92/7.20 ! [A: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_rat @ A @ B )
% 6.92/7.20 => ( ( inf_inf_rat @ A @ B )
% 6.92/7.20 = A ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb3
% 6.92/7.20 thf(fact_3186_inf_Oabsorb3,axiom,
% 6.92/7.20 ! [A: nat,B: nat] :
% 6.92/7.20 ( ( ord_less_nat @ A @ B )
% 6.92/7.20 => ( ( inf_inf_nat @ A @ B )
% 6.92/7.20 = A ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb3
% 6.92/7.20 thf(fact_3187_inf_Oabsorb3,axiom,
% 6.92/7.20 ! [A: int,B: int] :
% 6.92/7.20 ( ( ord_less_int @ A @ B )
% 6.92/7.20 => ( ( inf_inf_int @ A @ B )
% 6.92/7.20 = A ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb3
% 6.92/7.20 thf(fact_3188_inf_Oabsorb4,axiom,
% 6.92/7.20 ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ord_le7866589430770878221at_nat @ B @ A )
% 6.92/7.20 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 6.92/7.20 = B ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb4
% 6.92/7.20 thf(fact_3189_inf_Oabsorb4,axiom,
% 6.92/7.20 ! [B: set_nat,A: set_nat] :
% 6.92/7.20 ( ( ord_less_set_nat @ B @ A )
% 6.92/7.20 => ( ( inf_inf_set_nat @ A @ B )
% 6.92/7.20 = B ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb4
% 6.92/7.20 thf(fact_3190_inf_Oabsorb4,axiom,
% 6.92/7.20 ! [B: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 6.92/7.20 ( ( ord_le8213806771718485336_int_o @ B @ A )
% 6.92/7.20 => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 6.92/7.20 = B ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb4
% 6.92/7.20 thf(fact_3191_inf_Oabsorb4,axiom,
% 6.92/7.20 ! [B: assn,A: assn] :
% 6.92/7.20 ( ( ord_less_assn @ B @ A )
% 6.92/7.20 => ( ( inf_inf_assn @ A @ B )
% 6.92/7.20 = B ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb4
% 6.92/7.20 thf(fact_3192_inf_Oabsorb4,axiom,
% 6.92/7.20 ! [B: rat,A: rat] :
% 6.92/7.20 ( ( ord_less_rat @ B @ A )
% 6.92/7.20 => ( ( inf_inf_rat @ A @ B )
% 6.92/7.20 = B ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb4
% 6.92/7.20 thf(fact_3193_inf_Oabsorb4,axiom,
% 6.92/7.20 ! [B: nat,A: nat] :
% 6.92/7.20 ( ( ord_less_nat @ B @ A )
% 6.92/7.20 => ( ( inf_inf_nat @ A @ B )
% 6.92/7.20 = B ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb4
% 6.92/7.20 thf(fact_3194_inf_Oabsorb4,axiom,
% 6.92/7.20 ! [B: int,A: int] :
% 6.92/7.20 ( ( ord_less_int @ B @ A )
% 6.92/7.20 => ( ( inf_inf_int @ A @ B )
% 6.92/7.20 = B ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.absorb4
% 6.92/7.20 thf(fact_3195_inf_Ostrict__boundedE,axiom,
% 6.92/7.20 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ord_le7866589430770878221at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) )
% 6.92/7.20 => ~ ( ( ord_le7866589430770878221at_nat @ A @ B )
% 6.92/7.20 => ~ ( ord_le7866589430770878221at_nat @ A @ C2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_boundedE
% 6.92/7.20 thf(fact_3196_inf_Ostrict__boundedE,axiom,
% 6.92/7.20 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 6.92/7.20 ( ( ord_less_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) )
% 6.92/7.20 => ~ ( ( ord_less_set_nat @ A @ B )
% 6.92/7.20 => ~ ( ord_less_set_nat @ A @ C2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_boundedE
% 6.92/7.20 thf(fact_3197_inf_Ostrict__boundedE,axiom,
% 6.92/7.20 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C2: product_prod_int_int > $o] :
% 6.92/7.20 ( ( ord_le8213806771718485336_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C2 ) )
% 6.92/7.20 => ~ ( ( ord_le8213806771718485336_int_o @ A @ B )
% 6.92/7.20 => ~ ( ord_le8213806771718485336_int_o @ A @ C2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_boundedE
% 6.92/7.20 thf(fact_3198_inf_Ostrict__boundedE,axiom,
% 6.92/7.20 ! [A: assn,B: assn,C2: assn] :
% 6.92/7.20 ( ( ord_less_assn @ A @ ( inf_inf_assn @ B @ C2 ) )
% 6.92/7.20 => ~ ( ( ord_less_assn @ A @ B )
% 6.92/7.20 => ~ ( ord_less_assn @ A @ C2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_boundedE
% 6.92/7.20 thf(fact_3199_inf_Ostrict__boundedE,axiom,
% 6.92/7.20 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.20 ( ( ord_less_rat @ A @ ( inf_inf_rat @ B @ C2 ) )
% 6.92/7.20 => ~ ( ( ord_less_rat @ A @ B )
% 6.92/7.20 => ~ ( ord_less_rat @ A @ C2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_boundedE
% 6.92/7.20 thf(fact_3200_inf_Ostrict__boundedE,axiom,
% 6.92/7.20 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.20 ( ( ord_less_nat @ A @ ( inf_inf_nat @ B @ C2 ) )
% 6.92/7.20 => ~ ( ( ord_less_nat @ A @ B )
% 6.92/7.20 => ~ ( ord_less_nat @ A @ C2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_boundedE
% 6.92/7.20 thf(fact_3201_inf_Ostrict__boundedE,axiom,
% 6.92/7.20 ! [A: int,B: int,C2: int] :
% 6.92/7.20 ( ( ord_less_int @ A @ ( inf_inf_int @ B @ C2 ) )
% 6.92/7.20 => ~ ( ( ord_less_int @ A @ B )
% 6.92/7.20 => ~ ( ord_less_int @ A @ C2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_boundedE
% 6.92/7.20 thf(fact_3202_inf_Ostrict__order__iff,axiom,
% 6.92/7.20 ( ord_le7866589430770878221at_nat
% 6.92/7.20 = ( ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( A5
% 6.92/7.20 = ( inf_in2572325071724192079at_nat @ A5 @ B4 ) )
% 6.92/7.20 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_order_iff
% 6.92/7.20 thf(fact_3203_inf_Ostrict__order__iff,axiom,
% 6.92/7.20 ( ord_less_set_nat
% 6.92/7.20 = ( ^ [A5: set_nat,B4: set_nat] :
% 6.92/7.20 ( ( A5
% 6.92/7.20 = ( inf_inf_set_nat @ A5 @ B4 ) )
% 6.92/7.20 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_order_iff
% 6.92/7.20 thf(fact_3204_inf_Ostrict__order__iff,axiom,
% 6.92/7.20 ( ord_le8213806771718485336_int_o
% 6.92/7.20 = ( ^ [A5: product_prod_int_int > $o,B4: product_prod_int_int > $o] :
% 6.92/7.20 ( ( A5
% 6.92/7.20 = ( inf_in3604695632404883862_int_o @ A5 @ B4 ) )
% 6.92/7.20 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_order_iff
% 6.92/7.20 thf(fact_3205_inf_Ostrict__order__iff,axiom,
% 6.92/7.20 ( ord_less_assn
% 6.92/7.20 = ( ^ [A5: assn,B4: assn] :
% 6.92/7.20 ( ( A5
% 6.92/7.20 = ( inf_inf_assn @ A5 @ B4 ) )
% 6.92/7.20 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_order_iff
% 6.92/7.20 thf(fact_3206_inf_Ostrict__order__iff,axiom,
% 6.92/7.20 ( ord_less_rat
% 6.92/7.20 = ( ^ [A5: rat,B4: rat] :
% 6.92/7.20 ( ( A5
% 6.92/7.20 = ( inf_inf_rat @ A5 @ B4 ) )
% 6.92/7.20 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_order_iff
% 6.92/7.20 thf(fact_3207_inf_Ostrict__order__iff,axiom,
% 6.92/7.20 ( ord_less_nat
% 6.92/7.20 = ( ^ [A5: nat,B4: nat] :
% 6.92/7.20 ( ( A5
% 6.92/7.20 = ( inf_inf_nat @ A5 @ B4 ) )
% 6.92/7.20 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_order_iff
% 6.92/7.20 thf(fact_3208_inf_Ostrict__order__iff,axiom,
% 6.92/7.20 ( ord_less_int
% 6.92/7.20 = ( ^ [A5: int,B4: int] :
% 6.92/7.20 ( ( A5
% 6.92/7.20 = ( inf_inf_int @ A5 @ B4 ) )
% 6.92/7.20 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_order_iff
% 6.92/7.20 thf(fact_3209_inf_Ostrict__coboundedI1,axiom,
% 6.92/7.20 ! [A: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ord_le7866589430770878221at_nat @ A @ C2 )
% 6.92/7.20 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_coboundedI1
% 6.92/7.20 thf(fact_3210_inf_Ostrict__coboundedI1,axiom,
% 6.92/7.20 ! [A: set_nat,C2: set_nat,B: set_nat] :
% 6.92/7.20 ( ( ord_less_set_nat @ A @ C2 )
% 6.92/7.20 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_coboundedI1
% 6.92/7.20 thf(fact_3211_inf_Ostrict__coboundedI1,axiom,
% 6.92/7.20 ! [A: product_prod_int_int > $o,C2: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 6.92/7.20 ( ( ord_le8213806771718485336_int_o @ A @ C2 )
% 6.92/7.20 => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_coboundedI1
% 6.92/7.20 thf(fact_3212_inf_Ostrict__coboundedI1,axiom,
% 6.92/7.20 ! [A: assn,C2: assn,B: assn] :
% 6.92/7.20 ( ( ord_less_assn @ A @ C2 )
% 6.92/7.20 => ( ord_less_assn @ ( inf_inf_assn @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_coboundedI1
% 6.92/7.20 thf(fact_3213_inf_Ostrict__coboundedI1,axiom,
% 6.92/7.20 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_rat @ A @ C2 )
% 6.92/7.20 => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_coboundedI1
% 6.92/7.20 thf(fact_3214_inf_Ostrict__coboundedI1,axiom,
% 6.92/7.20 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.20 ( ( ord_less_nat @ A @ C2 )
% 6.92/7.20 => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_coboundedI1
% 6.92/7.20 thf(fact_3215_inf_Ostrict__coboundedI1,axiom,
% 6.92/7.20 ! [A: int,C2: int,B: int] :
% 6.92/7.20 ( ( ord_less_int @ A @ C2 )
% 6.92/7.20 => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_coboundedI1
% 6.92/7.20 thf(fact_3216_inf_Ostrict__coboundedI2,axiom,
% 6.92/7.20 ! [B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ord_le7866589430770878221at_nat @ B @ C2 )
% 6.92/7.20 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_coboundedI2
% 6.92/7.20 thf(fact_3217_inf_Ostrict__coboundedI2,axiom,
% 6.92/7.20 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 6.92/7.20 ( ( ord_less_set_nat @ B @ C2 )
% 6.92/7.20 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_coboundedI2
% 6.92/7.20 thf(fact_3218_inf_Ostrict__coboundedI2,axiom,
% 6.92/7.20 ! [B: product_prod_int_int > $o,C2: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 6.92/7.20 ( ( ord_le8213806771718485336_int_o @ B @ C2 )
% 6.92/7.20 => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_coboundedI2
% 6.92/7.20 thf(fact_3219_inf_Ostrict__coboundedI2,axiom,
% 6.92/7.20 ! [B: assn,C2: assn,A: assn] :
% 6.92/7.20 ( ( ord_less_assn @ B @ C2 )
% 6.92/7.20 => ( ord_less_assn @ ( inf_inf_assn @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_coboundedI2
% 6.92/7.20 thf(fact_3220_inf_Ostrict__coboundedI2,axiom,
% 6.92/7.20 ! [B: rat,C2: rat,A: rat] :
% 6.92/7.20 ( ( ord_less_rat @ B @ C2 )
% 6.92/7.20 => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_coboundedI2
% 6.92/7.20 thf(fact_3221_inf_Ostrict__coboundedI2,axiom,
% 6.92/7.20 ! [B: nat,C2: nat,A: nat] :
% 6.92/7.20 ( ( ord_less_nat @ B @ C2 )
% 6.92/7.20 => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_coboundedI2
% 6.92/7.20 thf(fact_3222_inf_Ostrict__coboundedI2,axiom,
% 6.92/7.20 ! [B: int,C2: int,A: int] :
% 6.92/7.20 ( ( ord_less_int @ B @ C2 )
% 6.92/7.20 => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ C2 ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf.strict_coboundedI2
% 6.92/7.20 thf(fact_3223_distrib__imp1,axiom,
% 6.92/7.20 ! [X: assn,Y: assn,Z3: assn] :
% 6.92/7.20 ( ! [X3: assn,Y3: assn,Z2: assn] :
% 6.92/7.20 ( ( inf_inf_assn @ X3 @ ( sup_sup_assn @ Y3 @ Z2 ) )
% 6.92/7.20 = ( sup_sup_assn @ ( inf_inf_assn @ X3 @ Y3 ) @ ( inf_inf_assn @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( sup_sup_assn @ X @ ( inf_inf_assn @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_inf_assn @ ( sup_sup_assn @ X @ Y ) @ ( sup_sup_assn @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp1
% 6.92/7.20 thf(fact_3224_distrib__imp1,axiom,
% 6.92/7.20 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( inf_in2572325071724192079at_nat @ X3 @ ( sup_su6327502436637775413at_nat @ Y3 @ Z2 ) )
% 6.92/7.20 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X3 @ Y3 ) @ ( inf_in2572325071724192079at_nat @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp1
% 6.92/7.20 thf(fact_3225_distrib__imp1,axiom,
% 6.92/7.20 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o] :
% 6.92/7.20 ( ! [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o,Z2: product_prod_int_int > $o] :
% 6.92/7.20 ( ( inf_in3604695632404883862_int_o @ X3 @ ( sup_su8463660629351352368_int_o @ Y3 @ Z2 ) )
% 6.92/7.20 = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X3 @ Y3 ) @ ( inf_in3604695632404883862_int_o @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp1
% 6.92/7.20 thf(fact_3226_distrib__imp1,axiom,
% 6.92/7.20 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ! [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat,Z2: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( inf_in1697001100524423349at_nat @ X3 @ ( sup_su3035147773818789531at_nat @ Y3 @ Z2 ) )
% 6.92/7.20 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X3 @ Y3 ) @ ( inf_in1697001100524423349at_nat @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp1
% 6.92/7.20 thf(fact_3227_distrib__imp1,axiom,
% 6.92/7.20 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ! [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( inf_in7913087082777306421at_nat @ X3 @ ( sup_su5525570899277871387at_nat @ Y3 @ Z2 ) )
% 6.92/7.20 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X3 @ Y3 ) @ ( inf_in7913087082777306421at_nat @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp1
% 6.92/7.20 thf(fact_3228_distrib__imp1,axiom,
% 6.92/7.20 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 6.92/7.20 ( ! [X3: set_nat,Y3: set_nat,Z2: set_nat] :
% 6.92/7.20 ( ( inf_inf_set_nat @ X3 @ ( sup_sup_set_nat @ Y3 @ Z2 ) )
% 6.92/7.20 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X3 @ Y3 ) @ ( inf_inf_set_nat @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp1
% 6.92/7.20 thf(fact_3229_distrib__imp1,axiom,
% 6.92/7.20 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.20 ( ! [X3: nat,Y3: nat,Z2: nat] :
% 6.92/7.20 ( ( inf_inf_nat @ X3 @ ( sup_sup_nat @ Y3 @ Z2 ) )
% 6.92/7.20 = ( sup_sup_nat @ ( inf_inf_nat @ X3 @ Y3 ) @ ( inf_inf_nat @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp1
% 6.92/7.20 thf(fact_3230_distrib__imp1,axiom,
% 6.92/7.20 ! [X: int,Y: int,Z3: int] :
% 6.92/7.20 ( ! [X3: int,Y3: int,Z2: int] :
% 6.92/7.20 ( ( inf_inf_int @ X3 @ ( sup_sup_int @ Y3 @ Z2 ) )
% 6.92/7.20 = ( sup_sup_int @ ( inf_inf_int @ X3 @ Y3 ) @ ( inf_inf_int @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( sup_sup_int @ X @ ( inf_inf_int @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_inf_int @ ( sup_sup_int @ X @ Y ) @ ( sup_sup_int @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp1
% 6.92/7.20 thf(fact_3231_distrib__imp2,axiom,
% 6.92/7.20 ! [X: assn,Y: assn,Z3: assn] :
% 6.92/7.20 ( ! [X3: assn,Y3: assn,Z2: assn] :
% 6.92/7.20 ( ( sup_sup_assn @ X3 @ ( inf_inf_assn @ Y3 @ Z2 ) )
% 6.92/7.20 = ( inf_inf_assn @ ( sup_sup_assn @ X3 @ Y3 ) @ ( sup_sup_assn @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( inf_inf_assn @ X @ ( sup_sup_assn @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_sup_assn @ ( inf_inf_assn @ X @ Y ) @ ( inf_inf_assn @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp2
% 6.92/7.20 thf(fact_3232_distrib__imp2,axiom,
% 6.92/7.20 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( sup_su6327502436637775413at_nat @ X3 @ ( inf_in2572325071724192079at_nat @ Y3 @ Z2 ) )
% 6.92/7.20 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X3 @ Y3 ) @ ( sup_su6327502436637775413at_nat @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp2
% 6.92/7.20 thf(fact_3233_distrib__imp2,axiom,
% 6.92/7.20 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o] :
% 6.92/7.20 ( ! [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o,Z2: product_prod_int_int > $o] :
% 6.92/7.20 ( ( sup_su8463660629351352368_int_o @ X3 @ ( inf_in3604695632404883862_int_o @ Y3 @ Z2 ) )
% 6.92/7.20 = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X3 @ Y3 ) @ ( sup_su8463660629351352368_int_o @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp2
% 6.92/7.20 thf(fact_3234_distrib__imp2,axiom,
% 6.92/7.20 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ! [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat,Z2: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( sup_su3035147773818789531at_nat @ X3 @ ( inf_in1697001100524423349at_nat @ Y3 @ Z2 ) )
% 6.92/7.20 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X3 @ Y3 ) @ ( sup_su3035147773818789531at_nat @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp2
% 6.92/7.20 thf(fact_3235_distrib__imp2,axiom,
% 6.92/7.20 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ! [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( sup_su5525570899277871387at_nat @ X3 @ ( inf_in7913087082777306421at_nat @ Y3 @ Z2 ) )
% 6.92/7.20 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X3 @ Y3 ) @ ( sup_su5525570899277871387at_nat @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp2
% 6.92/7.20 thf(fact_3236_distrib__imp2,axiom,
% 6.92/7.20 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 6.92/7.20 ( ! [X3: set_nat,Y3: set_nat,Z2: set_nat] :
% 6.92/7.20 ( ( sup_sup_set_nat @ X3 @ ( inf_inf_set_nat @ Y3 @ Z2 ) )
% 6.92/7.20 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X3 @ Y3 ) @ ( sup_sup_set_nat @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp2
% 6.92/7.20 thf(fact_3237_distrib__imp2,axiom,
% 6.92/7.20 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.20 ( ! [X3: nat,Y3: nat,Z2: nat] :
% 6.92/7.20 ( ( sup_sup_nat @ X3 @ ( inf_inf_nat @ Y3 @ Z2 ) )
% 6.92/7.20 = ( inf_inf_nat @ ( sup_sup_nat @ X3 @ Y3 ) @ ( sup_sup_nat @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp2
% 6.92/7.20 thf(fact_3238_distrib__imp2,axiom,
% 6.92/7.20 ! [X: int,Y: int,Z3: int] :
% 6.92/7.20 ( ! [X3: int,Y3: int,Z2: int] :
% 6.92/7.20 ( ( sup_sup_int @ X3 @ ( inf_inf_int @ Y3 @ Z2 ) )
% 6.92/7.20 = ( inf_inf_int @ ( sup_sup_int @ X3 @ Y3 ) @ ( sup_sup_int @ X3 @ Z2 ) ) )
% 6.92/7.20 => ( ( inf_inf_int @ X @ ( sup_sup_int @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_sup_int @ ( inf_inf_int @ X @ Y ) @ ( inf_inf_int @ X @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_imp2
% 6.92/7.20 thf(fact_3239_inf__sup__distrib1,axiom,
% 6.92/7.20 ! [X: assn,Y: assn,Z3: assn] :
% 6.92/7.20 ( ( inf_inf_assn @ X @ ( sup_sup_assn @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_sup_assn @ ( inf_inf_assn @ X @ Y ) @ ( inf_inf_assn @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib1
% 6.92/7.20 thf(fact_3240_inf__sup__distrib1,axiom,
% 6.92/7.20 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib1
% 6.92/7.20 thf(fact_3241_inf__sup__distrib1,axiom,
% 6.92/7.20 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o] :
% 6.92/7.20 ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib1
% 6.92/7.20 thf(fact_3242_inf__sup__distrib1,axiom,
% 6.92/7.20 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib1
% 6.92/7.20 thf(fact_3243_inf__sup__distrib1,axiom,
% 6.92/7.20 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib1
% 6.92/7.20 thf(fact_3244_inf__sup__distrib1,axiom,
% 6.92/7.20 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 6.92/7.20 ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib1
% 6.92/7.20 thf(fact_3245_inf__sup__distrib1,axiom,
% 6.92/7.20 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.20 ( ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib1
% 6.92/7.20 thf(fact_3246_inf__sup__distrib1,axiom,
% 6.92/7.20 ! [X: int,Y: int,Z3: int] :
% 6.92/7.20 ( ( inf_inf_int @ X @ ( sup_sup_int @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_sup_int @ ( inf_inf_int @ X @ Y ) @ ( inf_inf_int @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib1
% 6.92/7.20 thf(fact_3247_inf__sup__distrib2,axiom,
% 6.92/7.20 ! [Y: assn,Z3: assn,X: assn] :
% 6.92/7.20 ( ( inf_inf_assn @ ( sup_sup_assn @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( sup_sup_assn @ ( inf_inf_assn @ Y @ X ) @ ( inf_inf_assn @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib2
% 6.92/7.20 thf(fact_3248_inf__sup__distrib2,axiom,
% 6.92/7.20 ! [Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ X ) @ ( inf_in2572325071724192079at_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib2
% 6.92/7.20 thf(fact_3249_inf__sup__distrib2,axiom,
% 6.92/7.20 ! [Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 6.92/7.20 ( ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ X ) @ ( inf_in3604695632404883862_int_o @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib2
% 6.92/7.20 thf(fact_3250_inf__sup__distrib2,axiom,
% 6.92/7.20 ! [Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ X ) @ ( inf_in1697001100524423349at_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib2
% 6.92/7.20 thf(fact_3251_inf__sup__distrib2,axiom,
% 6.92/7.20 ! [Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ X ) @ ( inf_in7913087082777306421at_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib2
% 6.92/7.20 thf(fact_3252_inf__sup__distrib2,axiom,
% 6.92/7.20 ! [Y: set_nat,Z3: set_nat,X: set_nat] :
% 6.92/7.20 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ X ) @ ( inf_inf_set_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib2
% 6.92/7.20 thf(fact_3253_inf__sup__distrib2,axiom,
% 6.92/7.20 ! [Y: nat,Z3: nat,X: nat] :
% 6.92/7.20 ( ( inf_inf_nat @ ( sup_sup_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( sup_sup_nat @ ( inf_inf_nat @ Y @ X ) @ ( inf_inf_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib2
% 6.92/7.20 thf(fact_3254_inf__sup__distrib2,axiom,
% 6.92/7.20 ! [Y: int,Z3: int,X: int] :
% 6.92/7.20 ( ( inf_inf_int @ ( sup_sup_int @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( sup_sup_int @ ( inf_inf_int @ Y @ X ) @ ( inf_inf_int @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_sup_distrib2
% 6.92/7.20 thf(fact_3255_sup__inf__distrib1,axiom,
% 6.92/7.20 ! [X: assn,Y: assn,Z3: assn] :
% 6.92/7.20 ( ( sup_sup_assn @ X @ ( inf_inf_assn @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_inf_assn @ ( sup_sup_assn @ X @ Y ) @ ( sup_sup_assn @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib1
% 6.92/7.20 thf(fact_3256_sup__inf__distrib1,axiom,
% 6.92/7.20 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib1
% 6.92/7.20 thf(fact_3257_sup__inf__distrib1,axiom,
% 6.92/7.20 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o] :
% 6.92/7.20 ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib1
% 6.92/7.20 thf(fact_3258_sup__inf__distrib1,axiom,
% 6.92/7.20 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib1
% 6.92/7.20 thf(fact_3259_sup__inf__distrib1,axiom,
% 6.92/7.20 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib1
% 6.92/7.20 thf(fact_3260_sup__inf__distrib1,axiom,
% 6.92/7.20 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 6.92/7.20 ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib1
% 6.92/7.20 thf(fact_3261_sup__inf__distrib1,axiom,
% 6.92/7.20 ! [X: nat,Y: nat,Z3: nat] :
% 6.92/7.20 ( ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib1
% 6.92/7.20 thf(fact_3262_sup__inf__distrib1,axiom,
% 6.92/7.20 ! [X: int,Y: int,Z3: int] :
% 6.92/7.20 ( ( sup_sup_int @ X @ ( inf_inf_int @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_inf_int @ ( sup_sup_int @ X @ Y ) @ ( sup_sup_int @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib1
% 6.92/7.20 thf(fact_3263_sup__inf__distrib2,axiom,
% 6.92/7.20 ! [Y: assn,Z3: assn,X: assn] :
% 6.92/7.20 ( ( sup_sup_assn @ ( inf_inf_assn @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( inf_inf_assn @ ( sup_sup_assn @ Y @ X ) @ ( sup_sup_assn @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib2
% 6.92/7.20 thf(fact_3264_sup__inf__distrib2,axiom,
% 6.92/7.20 ! [Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ X ) @ ( sup_su6327502436637775413at_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib2
% 6.92/7.20 thf(fact_3265_sup__inf__distrib2,axiom,
% 6.92/7.20 ! [Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 6.92/7.20 ( ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ X ) @ ( sup_su8463660629351352368_int_o @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib2
% 6.92/7.20 thf(fact_3266_sup__inf__distrib2,axiom,
% 6.92/7.20 ! [Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ X ) @ ( sup_su3035147773818789531at_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib2
% 6.92/7.20 thf(fact_3267_sup__inf__distrib2,axiom,
% 6.92/7.20 ! [Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ X ) @ ( sup_su5525570899277871387at_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib2
% 6.92/7.20 thf(fact_3268_sup__inf__distrib2,axiom,
% 6.92/7.20 ! [Y: set_nat,Z3: set_nat,X: set_nat] :
% 6.92/7.20 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ X ) @ ( sup_sup_set_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib2
% 6.92/7.20 thf(fact_3269_sup__inf__distrib2,axiom,
% 6.92/7.20 ! [Y: nat,Z3: nat,X: nat] :
% 6.92/7.20 ( ( sup_sup_nat @ ( inf_inf_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( inf_inf_nat @ ( sup_sup_nat @ Y @ X ) @ ( sup_sup_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib2
% 6.92/7.20 thf(fact_3270_sup__inf__distrib2,axiom,
% 6.92/7.20 ! [Y: int,Z3: int,X: int] :
% 6.92/7.20 ( ( sup_sup_int @ ( inf_inf_int @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( inf_inf_int @ ( sup_sup_int @ Y @ X ) @ ( sup_sup_int @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % sup_inf_distrib2
% 6.92/7.20 thf(fact_3271_boolean__algebra_Oconj__disj__distrib,axiom,
% 6.92/7.20 ! [X: assn,Y: assn,Z3: assn] :
% 6.92/7.20 ( ( inf_inf_assn @ X @ ( sup_sup_assn @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_sup_assn @ ( inf_inf_assn @ X @ Y ) @ ( inf_inf_assn @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.conj_disj_distrib
% 6.92/7.20 thf(fact_3272_boolean__algebra_Oconj__disj__distrib,axiom,
% 6.92/7.20 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.conj_disj_distrib
% 6.92/7.20 thf(fact_3273_boolean__algebra_Oconj__disj__distrib,axiom,
% 6.92/7.20 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o] :
% 6.92/7.20 ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.conj_disj_distrib
% 6.92/7.20 thf(fact_3274_boolean__algebra_Oconj__disj__distrib,axiom,
% 6.92/7.20 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.conj_disj_distrib
% 6.92/7.20 thf(fact_3275_boolean__algebra_Oconj__disj__distrib,axiom,
% 6.92/7.20 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.conj_disj_distrib
% 6.92/7.20 thf(fact_3276_boolean__algebra_Oconj__disj__distrib,axiom,
% 6.92/7.20 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 6.92/7.20 ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.conj_disj_distrib
% 6.92/7.20 thf(fact_3277_boolean__algebra_Odisj__conj__distrib,axiom,
% 6.92/7.20 ! [X: assn,Y: assn,Z3: assn] :
% 6.92/7.20 ( ( sup_sup_assn @ X @ ( inf_inf_assn @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_inf_assn @ ( sup_sup_assn @ X @ Y ) @ ( sup_sup_assn @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.disj_conj_distrib
% 6.92/7.20 thf(fact_3278_boolean__algebra_Odisj__conj__distrib,axiom,
% 6.92/7.20 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.disj_conj_distrib
% 6.92/7.20 thf(fact_3279_boolean__algebra_Odisj__conj__distrib,axiom,
% 6.92/7.20 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o] :
% 6.92/7.20 ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.disj_conj_distrib
% 6.92/7.20 thf(fact_3280_boolean__algebra_Odisj__conj__distrib,axiom,
% 6.92/7.20 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.disj_conj_distrib
% 6.92/7.20 thf(fact_3281_boolean__algebra_Odisj__conj__distrib,axiom,
% 6.92/7.20 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.disj_conj_distrib
% 6.92/7.20 thf(fact_3282_boolean__algebra_Odisj__conj__distrib,axiom,
% 6.92/7.20 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 6.92/7.20 ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z3 ) )
% 6.92/7.20 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.disj_conj_distrib
% 6.92/7.20 thf(fact_3283_boolean__algebra_Oconj__disj__distrib2,axiom,
% 6.92/7.20 ! [Y: assn,Z3: assn,X: assn] :
% 6.92/7.20 ( ( inf_inf_assn @ ( sup_sup_assn @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( sup_sup_assn @ ( inf_inf_assn @ Y @ X ) @ ( inf_inf_assn @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.conj_disj_distrib2
% 6.92/7.20 thf(fact_3284_boolean__algebra_Oconj__disj__distrib2,axiom,
% 6.92/7.20 ! [Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ X ) @ ( inf_in2572325071724192079at_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.conj_disj_distrib2
% 6.92/7.20 thf(fact_3285_boolean__algebra_Oconj__disj__distrib2,axiom,
% 6.92/7.20 ! [Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 6.92/7.20 ( ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ X ) @ ( inf_in3604695632404883862_int_o @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.conj_disj_distrib2
% 6.92/7.20 thf(fact_3286_boolean__algebra_Oconj__disj__distrib2,axiom,
% 6.92/7.20 ! [Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ X ) @ ( inf_in1697001100524423349at_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.conj_disj_distrib2
% 6.92/7.20 thf(fact_3287_boolean__algebra_Oconj__disj__distrib2,axiom,
% 6.92/7.20 ! [Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ X ) @ ( inf_in7913087082777306421at_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.conj_disj_distrib2
% 6.92/7.20 thf(fact_3288_boolean__algebra_Oconj__disj__distrib2,axiom,
% 6.92/7.20 ! [Y: set_nat,Z3: set_nat,X: set_nat] :
% 6.92/7.20 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ X ) @ ( inf_inf_set_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.conj_disj_distrib2
% 6.92/7.20 thf(fact_3289_boolean__algebra_Odisj__conj__distrib2,axiom,
% 6.92/7.20 ! [Y: assn,Z3: assn,X: assn] :
% 6.92/7.20 ( ( sup_sup_assn @ ( inf_inf_assn @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( inf_inf_assn @ ( sup_sup_assn @ Y @ X ) @ ( sup_sup_assn @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.disj_conj_distrib2
% 6.92/7.20 thf(fact_3290_boolean__algebra_Odisj__conj__distrib2,axiom,
% 6.92/7.20 ! [Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ X ) @ ( sup_su6327502436637775413at_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.disj_conj_distrib2
% 6.92/7.20 thf(fact_3291_boolean__algebra_Odisj__conj__distrib2,axiom,
% 6.92/7.20 ! [Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 6.92/7.20 ( ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ X ) @ ( sup_su8463660629351352368_int_o @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.disj_conj_distrib2
% 6.92/7.20 thf(fact_3292_boolean__algebra_Odisj__conj__distrib2,axiom,
% 6.92/7.20 ! [Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ X ) @ ( sup_su3035147773818789531at_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.disj_conj_distrib2
% 6.92/7.20 thf(fact_3293_boolean__algebra_Odisj__conj__distrib2,axiom,
% 6.92/7.20 ! [Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ X ) @ ( sup_su5525570899277871387at_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.disj_conj_distrib2
% 6.92/7.20 thf(fact_3294_boolean__algebra_Odisj__conj__distrib2,axiom,
% 6.92/7.20 ! [Y: set_nat,Z3: set_nat,X: set_nat] :
% 6.92/7.20 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ Z3 ) @ X )
% 6.92/7.20 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ X ) @ ( sup_sup_set_nat @ Z3 @ X ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % boolean_algebra.disj_conj_distrib2
% 6.92/7.20 thf(fact_3295_add__divide__distrib,axiom,
% 6.92/7.20 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.20 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 6.92/7.20 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % add_divide_distrib
% 6.92/7.20 thf(fact_3296_disjointI,axiom,
% 6.92/7.20 ! [A: set_se6260736226359567993nt_int,B: set_se6260736226359567993nt_int] :
% 6.92/7.20 ( ! [X3: set_Pr958786334691620121nt_int] :
% 6.92/7.20 ( ( member2340774599025711042nt_int @ X3 @ A )
% 6.92/7.20 => ~ ( member2340774599025711042nt_int @ X3 @ B ) )
% 6.92/7.20 => ( ( inf_in8396524679539076455nt_int @ A @ B )
% 6.92/7.20 = bot_bo1488462491386950373nt_int ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjointI
% 6.92/7.20 thf(fact_3297_disjointI,axiom,
% 6.92/7.20 ! [A: set_set_nat,B: set_set_nat] :
% 6.92/7.20 ( ! [X3: set_nat] :
% 6.92/7.20 ( ( member_set_nat @ X3 @ A )
% 6.92/7.20 => ~ ( member_set_nat @ X3 @ B ) )
% 6.92/7.20 => ( ( inf_inf_set_set_nat @ A @ B )
% 6.92/7.20 = bot_bot_set_set_nat ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjointI
% 6.92/7.20 thf(fact_3298_disjointI,axiom,
% 6.92/7.20 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ! [X3: product_prod_nat_nat] :
% 6.92/7.20 ( ( member8440522571783428010at_nat @ X3 @ A )
% 6.92/7.20 => ~ ( member8440522571783428010at_nat @ X3 @ B ) )
% 6.92/7.20 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 6.92/7.20 = bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjointI
% 6.92/7.20 thf(fact_3299_disjointI,axiom,
% 6.92/7.20 ! [A: set_o,B: set_o] :
% 6.92/7.20 ( ! [X3: $o] :
% 6.92/7.20 ( ( member_o @ X3 @ A )
% 6.92/7.20 => ~ ( member_o @ X3 @ B ) )
% 6.92/7.20 => ( ( inf_inf_set_o @ A @ B )
% 6.92/7.20 = bot_bot_set_o ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjointI
% 6.92/7.20 thf(fact_3300_disjointI,axiom,
% 6.92/7.20 ! [A: set_nat,B: set_nat] :
% 6.92/7.20 ( ! [X3: nat] :
% 6.92/7.20 ( ( member_nat @ X3 @ A )
% 6.92/7.20 => ~ ( member_nat @ X3 @ B ) )
% 6.92/7.20 => ( ( inf_inf_set_nat @ A @ B )
% 6.92/7.20 = bot_bot_set_nat ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjointI
% 6.92/7.20 thf(fact_3301_disjointI,axiom,
% 6.92/7.20 ! [A: set_int,B: set_int] :
% 6.92/7.20 ( ! [X3: int] :
% 6.92/7.20 ( ( member_int @ X3 @ A )
% 6.92/7.20 => ~ ( member_int @ X3 @ B ) )
% 6.92/7.20 => ( ( inf_inf_set_int @ A @ B )
% 6.92/7.20 = bot_bot_set_int ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjointI
% 6.92/7.20 thf(fact_3302_disjoint__iff__not__equal,axiom,
% 6.92/7.20 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ( inf_in2572325071724192079at_nat @ A4 @ B5 )
% 6.92/7.20 = bot_bo2099793752762293965at_nat )
% 6.92/7.20 = ( ! [X4: product_prod_nat_nat] :
% 6.92/7.20 ( ( member8440522571783428010at_nat @ X4 @ A4 )
% 6.92/7.20 => ! [Y4: product_prod_nat_nat] :
% 6.92/7.20 ( ( member8440522571783428010at_nat @ Y4 @ B5 )
% 6.92/7.20 => ( X4 != Y4 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjoint_iff_not_equal
% 6.92/7.20 thf(fact_3303_disjoint__iff__not__equal,axiom,
% 6.92/7.20 ! [A4: set_o,B5: set_o] :
% 6.92/7.20 ( ( ( inf_inf_set_o @ A4 @ B5 )
% 6.92/7.20 = bot_bot_set_o )
% 6.92/7.20 = ( ! [X4: $o] :
% 6.92/7.20 ( ( member_o @ X4 @ A4 )
% 6.92/7.20 => ! [Y4: $o] :
% 6.92/7.20 ( ( member_o @ Y4 @ B5 )
% 6.92/7.20 => ( X4 = ~ Y4 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjoint_iff_not_equal
% 6.92/7.20 thf(fact_3304_disjoint__iff__not__equal,axiom,
% 6.92/7.20 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.20 ( ( ( inf_inf_set_nat @ A4 @ B5 )
% 6.92/7.20 = bot_bot_set_nat )
% 6.92/7.20 = ( ! [X4: nat] :
% 6.92/7.20 ( ( member_nat @ X4 @ A4 )
% 6.92/7.20 => ! [Y4: nat] :
% 6.92/7.20 ( ( member_nat @ Y4 @ B5 )
% 6.92/7.20 => ( X4 != Y4 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjoint_iff_not_equal
% 6.92/7.20 thf(fact_3305_disjoint__iff__not__equal,axiom,
% 6.92/7.20 ! [A4: set_int,B5: set_int] :
% 6.92/7.20 ( ( ( inf_inf_set_int @ A4 @ B5 )
% 6.92/7.20 = bot_bot_set_int )
% 6.92/7.20 = ( ! [X4: int] :
% 6.92/7.20 ( ( member_int @ X4 @ A4 )
% 6.92/7.20 => ! [Y4: int] :
% 6.92/7.20 ( ( member_int @ Y4 @ B5 )
% 6.92/7.20 => ( X4 != Y4 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjoint_iff_not_equal
% 6.92/7.20 thf(fact_3306_Int__empty__right,axiom,
% 6.92/7.20 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( inf_in2572325071724192079at_nat @ A4 @ bot_bo2099793752762293965at_nat )
% 6.92/7.20 = bot_bo2099793752762293965at_nat ) ).
% 6.92/7.20
% 6.92/7.20 % Int_empty_right
% 6.92/7.20 thf(fact_3307_Int__empty__right,axiom,
% 6.92/7.20 ! [A4: set_o] :
% 6.92/7.20 ( ( inf_inf_set_o @ A4 @ bot_bot_set_o )
% 6.92/7.20 = bot_bot_set_o ) ).
% 6.92/7.20
% 6.92/7.20 % Int_empty_right
% 6.92/7.20 thf(fact_3308_Int__empty__right,axiom,
% 6.92/7.20 ! [A4: set_nat] :
% 6.92/7.20 ( ( inf_inf_set_nat @ A4 @ bot_bot_set_nat )
% 6.92/7.20 = bot_bot_set_nat ) ).
% 6.92/7.20
% 6.92/7.20 % Int_empty_right
% 6.92/7.20 thf(fact_3309_Int__empty__right,axiom,
% 6.92/7.20 ! [A4: set_int] :
% 6.92/7.20 ( ( inf_inf_set_int @ A4 @ bot_bot_set_int )
% 6.92/7.20 = bot_bot_set_int ) ).
% 6.92/7.20
% 6.92/7.20 % Int_empty_right
% 6.92/7.20 thf(fact_3310_Int__empty__left,axiom,
% 6.92/7.20 ! [B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ B5 )
% 6.92/7.20 = bot_bo2099793752762293965at_nat ) ).
% 6.92/7.20
% 6.92/7.20 % Int_empty_left
% 6.92/7.20 thf(fact_3311_Int__empty__left,axiom,
% 6.92/7.20 ! [B5: set_o] :
% 6.92/7.20 ( ( inf_inf_set_o @ bot_bot_set_o @ B5 )
% 6.92/7.20 = bot_bot_set_o ) ).
% 6.92/7.20
% 6.92/7.20 % Int_empty_left
% 6.92/7.20 thf(fact_3312_Int__empty__left,axiom,
% 6.92/7.20 ! [B5: set_nat] :
% 6.92/7.20 ( ( inf_inf_set_nat @ bot_bot_set_nat @ B5 )
% 6.92/7.20 = bot_bot_set_nat ) ).
% 6.92/7.20
% 6.92/7.20 % Int_empty_left
% 6.92/7.20 thf(fact_3313_Int__empty__left,axiom,
% 6.92/7.20 ! [B5: set_int] :
% 6.92/7.20 ( ( inf_inf_set_int @ bot_bot_set_int @ B5 )
% 6.92/7.20 = bot_bot_set_int ) ).
% 6.92/7.20
% 6.92/7.20 % Int_empty_left
% 6.92/7.20 thf(fact_3314_disjoint__iff,axiom,
% 6.92/7.20 ! [A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.20 ( ( ( inf_in8396524679539076455nt_int @ A4 @ B5 )
% 6.92/7.20 = bot_bo1488462491386950373nt_int )
% 6.92/7.20 = ( ! [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.20 ( ( member2340774599025711042nt_int @ X4 @ A4 )
% 6.92/7.20 => ~ ( member2340774599025711042nt_int @ X4 @ B5 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjoint_iff
% 6.92/7.20 thf(fact_3315_disjoint__iff,axiom,
% 6.92/7.20 ! [A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.20 ( ( ( inf_inf_set_set_nat @ A4 @ B5 )
% 6.92/7.20 = bot_bot_set_set_nat )
% 6.92/7.20 = ( ! [X4: set_nat] :
% 6.92/7.20 ( ( member_set_nat @ X4 @ A4 )
% 6.92/7.20 => ~ ( member_set_nat @ X4 @ B5 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjoint_iff
% 6.92/7.20 thf(fact_3316_disjoint__iff,axiom,
% 6.92/7.20 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ( inf_in2572325071724192079at_nat @ A4 @ B5 )
% 6.92/7.20 = bot_bo2099793752762293965at_nat )
% 6.92/7.20 = ( ! [X4: product_prod_nat_nat] :
% 6.92/7.20 ( ( member8440522571783428010at_nat @ X4 @ A4 )
% 6.92/7.20 => ~ ( member8440522571783428010at_nat @ X4 @ B5 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjoint_iff
% 6.92/7.20 thf(fact_3317_disjoint__iff,axiom,
% 6.92/7.20 ! [A4: set_o,B5: set_o] :
% 6.92/7.20 ( ( ( inf_inf_set_o @ A4 @ B5 )
% 6.92/7.20 = bot_bot_set_o )
% 6.92/7.20 = ( ! [X4: $o] :
% 6.92/7.20 ( ( member_o @ X4 @ A4 )
% 6.92/7.20 => ~ ( member_o @ X4 @ B5 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjoint_iff
% 6.92/7.20 thf(fact_3318_disjoint__iff,axiom,
% 6.92/7.20 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.20 ( ( ( inf_inf_set_nat @ A4 @ B5 )
% 6.92/7.20 = bot_bot_set_nat )
% 6.92/7.20 = ( ! [X4: nat] :
% 6.92/7.20 ( ( member_nat @ X4 @ A4 )
% 6.92/7.20 => ~ ( member_nat @ X4 @ B5 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjoint_iff
% 6.92/7.20 thf(fact_3319_disjoint__iff,axiom,
% 6.92/7.20 ! [A4: set_int,B5: set_int] :
% 6.92/7.20 ( ( ( inf_inf_set_int @ A4 @ B5 )
% 6.92/7.20 = bot_bot_set_int )
% 6.92/7.20 = ( ! [X4: int] :
% 6.92/7.20 ( ( member_int @ X4 @ A4 )
% 6.92/7.20 => ~ ( member_int @ X4 @ B5 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjoint_iff
% 6.92/7.20 thf(fact_3320_Int__emptyI,axiom,
% 6.92/7.20 ! [A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.20 ( ! [X3: set_Pr958786334691620121nt_int] :
% 6.92/7.20 ( ( member2340774599025711042nt_int @ X3 @ A4 )
% 6.92/7.20 => ~ ( member2340774599025711042nt_int @ X3 @ B5 ) )
% 6.92/7.20 => ( ( inf_in8396524679539076455nt_int @ A4 @ B5 )
% 6.92/7.20 = bot_bo1488462491386950373nt_int ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_emptyI
% 6.92/7.20 thf(fact_3321_Int__emptyI,axiom,
% 6.92/7.20 ! [A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.20 ( ! [X3: set_nat] :
% 6.92/7.20 ( ( member_set_nat @ X3 @ A4 )
% 6.92/7.20 => ~ ( member_set_nat @ X3 @ B5 ) )
% 6.92/7.20 => ( ( inf_inf_set_set_nat @ A4 @ B5 )
% 6.92/7.20 = bot_bot_set_set_nat ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_emptyI
% 6.92/7.20 thf(fact_3322_Int__emptyI,axiom,
% 6.92/7.20 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ! [X3: product_prod_nat_nat] :
% 6.92/7.20 ( ( member8440522571783428010at_nat @ X3 @ A4 )
% 6.92/7.20 => ~ ( member8440522571783428010at_nat @ X3 @ B5 ) )
% 6.92/7.20 => ( ( inf_in2572325071724192079at_nat @ A4 @ B5 )
% 6.92/7.20 = bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_emptyI
% 6.92/7.20 thf(fact_3323_Int__emptyI,axiom,
% 6.92/7.20 ! [A4: set_o,B5: set_o] :
% 6.92/7.20 ( ! [X3: $o] :
% 6.92/7.20 ( ( member_o @ X3 @ A4 )
% 6.92/7.20 => ~ ( member_o @ X3 @ B5 ) )
% 6.92/7.20 => ( ( inf_inf_set_o @ A4 @ B5 )
% 6.92/7.20 = bot_bot_set_o ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_emptyI
% 6.92/7.20 thf(fact_3324_Int__emptyI,axiom,
% 6.92/7.20 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.20 ( ! [X3: nat] :
% 6.92/7.20 ( ( member_nat @ X3 @ A4 )
% 6.92/7.20 => ~ ( member_nat @ X3 @ B5 ) )
% 6.92/7.20 => ( ( inf_inf_set_nat @ A4 @ B5 )
% 6.92/7.20 = bot_bot_set_nat ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_emptyI
% 6.92/7.20 thf(fact_3325_Int__emptyI,axiom,
% 6.92/7.20 ! [A4: set_int,B5: set_int] :
% 6.92/7.20 ( ! [X3: int] :
% 6.92/7.20 ( ( member_int @ X3 @ A4 )
% 6.92/7.20 => ~ ( member_int @ X3 @ B5 ) )
% 6.92/7.20 => ( ( inf_inf_set_int @ A4 @ B5 )
% 6.92/7.20 = bot_bot_set_int ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_emptyI
% 6.92/7.20 thf(fact_3326_Int__mono,axiom,
% 6.92/7.20 ! [A4: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,D4: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ord_le3146513528884898305at_nat @ A4 @ C4 )
% 6.92/7.20 => ( ( ord_le3146513528884898305at_nat @ B5 @ D4 )
% 6.92/7.20 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) @ ( inf_in2572325071724192079at_nat @ C4 @ D4 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_mono
% 6.92/7.20 thf(fact_3327_Int__mono,axiom,
% 6.92/7.20 ! [A4: set_nat,C4: set_nat,B5: set_nat,D4: set_nat] :
% 6.92/7.20 ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.92/7.20 => ( ( ord_less_eq_set_nat @ B5 @ D4 )
% 6.92/7.20 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A4 @ B5 ) @ ( inf_inf_set_nat @ C4 @ D4 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_mono
% 6.92/7.20 thf(fact_3328_Int__mono,axiom,
% 6.92/7.20 ! [A4: set_int,C4: set_int,B5: set_int,D4: set_int] :
% 6.92/7.20 ( ( ord_less_eq_set_int @ A4 @ C4 )
% 6.92/7.20 => ( ( ord_less_eq_set_int @ B5 @ D4 )
% 6.92/7.20 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A4 @ B5 ) @ ( inf_inf_set_int @ C4 @ D4 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_mono
% 6.92/7.20 thf(fact_3329_Int__lower1,axiom,
% 6.92/7.20 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) @ A4 ) ).
% 6.92/7.20
% 6.92/7.20 % Int_lower1
% 6.92/7.20 thf(fact_3330_Int__lower1,axiom,
% 6.92/7.20 ! [A4: set_nat,B5: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A4 @ B5 ) @ A4 ) ).
% 6.92/7.20
% 6.92/7.20 % Int_lower1
% 6.92/7.20 thf(fact_3331_Int__lower1,axiom,
% 6.92/7.20 ! [A4: set_int,B5: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ A4 @ B5 ) @ A4 ) ).
% 6.92/7.20
% 6.92/7.20 % Int_lower1
% 6.92/7.20 thf(fact_3332_Int__lower2,axiom,
% 6.92/7.20 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) @ B5 ) ).
% 6.92/7.20
% 6.92/7.20 % Int_lower2
% 6.92/7.20 thf(fact_3333_Int__lower2,axiom,
% 6.92/7.20 ! [A4: set_nat,B5: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A4 @ B5 ) @ B5 ) ).
% 6.92/7.20
% 6.92/7.20 % Int_lower2
% 6.92/7.20 thf(fact_3334_Int__lower2,axiom,
% 6.92/7.20 ! [A4: set_int,B5: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ A4 @ B5 ) @ B5 ) ).
% 6.92/7.20
% 6.92/7.20 % Int_lower2
% 6.92/7.20 thf(fact_3335_Int__absorb1,axiom,
% 6.92/7.20 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ord_le3146513528884898305at_nat @ B5 @ A4 )
% 6.92/7.20 => ( ( inf_in2572325071724192079at_nat @ A4 @ B5 )
% 6.92/7.20 = B5 ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_absorb1
% 6.92/7.20 thf(fact_3336_Int__absorb1,axiom,
% 6.92/7.20 ! [B5: set_nat,A4: set_nat] :
% 6.92/7.20 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 6.92/7.20 => ( ( inf_inf_set_nat @ A4 @ B5 )
% 6.92/7.20 = B5 ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_absorb1
% 6.92/7.20 thf(fact_3337_Int__absorb1,axiom,
% 6.92/7.20 ! [B5: set_int,A4: set_int] :
% 6.92/7.20 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 6.92/7.20 => ( ( inf_inf_set_int @ A4 @ B5 )
% 6.92/7.20 = B5 ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_absorb1
% 6.92/7.20 thf(fact_3338_Int__absorb2,axiom,
% 6.92/7.20 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 6.92/7.20 => ( ( inf_in2572325071724192079at_nat @ A4 @ B5 )
% 6.92/7.20 = A4 ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_absorb2
% 6.92/7.20 thf(fact_3339_Int__absorb2,axiom,
% 6.92/7.20 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.20 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.92/7.20 => ( ( inf_inf_set_nat @ A4 @ B5 )
% 6.92/7.20 = A4 ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_absorb2
% 6.92/7.20 thf(fact_3340_Int__absorb2,axiom,
% 6.92/7.20 ! [A4: set_int,B5: set_int] :
% 6.92/7.20 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.20 => ( ( inf_inf_set_int @ A4 @ B5 )
% 6.92/7.20 = A4 ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_absorb2
% 6.92/7.20 thf(fact_3341_Int__greatest,axiom,
% 6.92/7.20 ! [C4: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ord_le3146513528884898305at_nat @ C4 @ A4 )
% 6.92/7.20 => ( ( ord_le3146513528884898305at_nat @ C4 @ B5 )
% 6.92/7.20 => ( ord_le3146513528884898305at_nat @ C4 @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_greatest
% 6.92/7.20 thf(fact_3342_Int__greatest,axiom,
% 6.92/7.20 ! [C4: set_nat,A4: set_nat,B5: set_nat] :
% 6.92/7.20 ( ( ord_less_eq_set_nat @ C4 @ A4 )
% 6.92/7.20 => ( ( ord_less_eq_set_nat @ C4 @ B5 )
% 6.92/7.20 => ( ord_less_eq_set_nat @ C4 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_greatest
% 6.92/7.20 thf(fact_3343_Int__greatest,axiom,
% 6.92/7.20 ! [C4: set_int,A4: set_int,B5: set_int] :
% 6.92/7.20 ( ( ord_less_eq_set_int @ C4 @ A4 )
% 6.92/7.20 => ( ( ord_less_eq_set_int @ C4 @ B5 )
% 6.92/7.20 => ( ord_less_eq_set_int @ C4 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_greatest
% 6.92/7.20 thf(fact_3344_Int__Collect__mono,axiom,
% 6.92/7.20 ! [A4: set_o,B5: set_o,P2: $o > $o,Q2: $o > $o] :
% 6.92/7.20 ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.92/7.20 => ( ! [X3: $o] :
% 6.92/7.20 ( ( member_o @ X3 @ A4 )
% 6.92/7.20 => ( ( P2 @ X3 )
% 6.92/7.20 => ( Q2 @ X3 ) ) )
% 6.92/7.20 => ( ord_less_eq_set_o @ ( inf_inf_set_o @ A4 @ ( collect_o @ P2 ) ) @ ( inf_inf_set_o @ B5 @ ( collect_o @ Q2 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_Collect_mono
% 6.92/7.20 thf(fact_3345_Int__Collect__mono,axiom,
% 6.92/7.20 ! [A4: set_list_nat,B5: set_list_nat,P2: list_nat > $o,Q2: list_nat > $o] :
% 6.92/7.20 ( ( ord_le6045566169113846134st_nat @ A4 @ B5 )
% 6.92/7.20 => ( ! [X3: list_nat] :
% 6.92/7.20 ( ( member_list_nat @ X3 @ A4 )
% 6.92/7.20 => ( ( P2 @ X3 )
% 6.92/7.20 => ( Q2 @ X3 ) ) )
% 6.92/7.20 => ( ord_le6045566169113846134st_nat @ ( inf_inf_set_list_nat @ A4 @ ( collect_list_nat @ P2 ) ) @ ( inf_inf_set_list_nat @ B5 @ ( collect_list_nat @ Q2 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_Collect_mono
% 6.92/7.20 thf(fact_3346_Int__Collect__mono,axiom,
% 6.92/7.20 ! [A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int,P2: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.20 ( ( ord_le483042692224249369nt_int @ A4 @ B5 )
% 6.92/7.20 => ( ! [X3: set_Pr958786334691620121nt_int] :
% 6.92/7.20 ( ( member2340774599025711042nt_int @ X3 @ A4 )
% 6.92/7.20 => ( ( P2 @ X3 )
% 6.92/7.20 => ( Q2 @ X3 ) ) )
% 6.92/7.20 => ( ord_le483042692224249369nt_int @ ( inf_in8396524679539076455nt_int @ A4 @ ( collec5210948495886036740nt_int @ P2 ) ) @ ( inf_in8396524679539076455nt_int @ B5 @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_Collect_mono
% 6.92/7.20 thf(fact_3347_Int__Collect__mono,axiom,
% 6.92/7.20 ! [A4: set_set_nat,B5: set_set_nat,P2: set_nat > $o,Q2: set_nat > $o] :
% 6.92/7.20 ( ( ord_le6893508408891458716et_nat @ A4 @ B5 )
% 6.92/7.20 => ( ! [X3: set_nat] :
% 6.92/7.20 ( ( member_set_nat @ X3 @ A4 )
% 6.92/7.20 => ( ( P2 @ X3 )
% 6.92/7.20 => ( Q2 @ X3 ) ) )
% 6.92/7.20 => ( ord_le6893508408891458716et_nat @ ( inf_inf_set_set_nat @ A4 @ ( collect_set_nat @ P2 ) ) @ ( inf_inf_set_set_nat @ B5 @ ( collect_set_nat @ Q2 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_Collect_mono
% 6.92/7.20 thf(fact_3348_Int__Collect__mono,axiom,
% 6.92/7.20 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 6.92/7.20 ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 6.92/7.20 => ( ! [X3: product_prod_nat_nat] :
% 6.92/7.20 ( ( member8440522571783428010at_nat @ X3 @ A4 )
% 6.92/7.20 => ( ( P2 @ X3 )
% 6.92/7.20 => ( Q2 @ X3 ) ) )
% 6.92/7.20 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ ( collec3392354462482085612at_nat @ P2 ) ) @ ( inf_in2572325071724192079at_nat @ B5 @ ( collec3392354462482085612at_nat @ Q2 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_Collect_mono
% 6.92/7.20 thf(fact_3349_Int__Collect__mono,axiom,
% 6.92/7.20 ! [A4: set_nat,B5: set_nat,P2: nat > $o,Q2: nat > $o] :
% 6.92/7.20 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.92/7.20 => ( ! [X3: nat] :
% 6.92/7.20 ( ( member_nat @ X3 @ A4 )
% 6.92/7.20 => ( ( P2 @ X3 )
% 6.92/7.20 => ( Q2 @ X3 ) ) )
% 6.92/7.20 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) @ ( inf_inf_set_nat @ B5 @ ( collect_nat @ Q2 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_Collect_mono
% 6.92/7.20 thf(fact_3350_Int__Collect__mono,axiom,
% 6.92/7.20 ! [A4: set_int,B5: set_int,P2: int > $o,Q2: int > $o] :
% 6.92/7.20 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.20 => ( ! [X3: int] :
% 6.92/7.20 ( ( member_int @ X3 @ A4 )
% 6.92/7.20 => ( ( P2 @ X3 )
% 6.92/7.20 => ( Q2 @ X3 ) ) )
% 6.92/7.20 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) @ ( inf_inf_set_int @ B5 @ ( collect_int @ Q2 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_Collect_mono
% 6.92/7.20 thf(fact_3351_inter__eq__subsetI,axiom,
% 6.92/7.20 ! [S: set_Pr1261947904930325089at_nat,S6: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ord_le3146513528884898305at_nat @ S @ S6 )
% 6.92/7.20 => ( ( ( inf_in2572325071724192079at_nat @ A4 @ S6 )
% 6.92/7.20 = ( inf_in2572325071724192079at_nat @ B5 @ S6 ) )
% 6.92/7.20 => ( ( inf_in2572325071724192079at_nat @ A4 @ S )
% 6.92/7.20 = ( inf_in2572325071724192079at_nat @ B5 @ S ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inter_eq_subsetI
% 6.92/7.20 thf(fact_3352_inter__eq__subsetI,axiom,
% 6.92/7.20 ! [S: set_nat,S6: set_nat,A4: set_nat,B5: set_nat] :
% 6.92/7.20 ( ( ord_less_eq_set_nat @ S @ S6 )
% 6.92/7.20 => ( ( ( inf_inf_set_nat @ A4 @ S6 )
% 6.92/7.20 = ( inf_inf_set_nat @ B5 @ S6 ) )
% 6.92/7.20 => ( ( inf_inf_set_nat @ A4 @ S )
% 6.92/7.20 = ( inf_inf_set_nat @ B5 @ S ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inter_eq_subsetI
% 6.92/7.20 thf(fact_3353_inter__eq__subsetI,axiom,
% 6.92/7.20 ! [S: set_int,S6: set_int,A4: set_int,B5: set_int] :
% 6.92/7.20 ( ( ord_less_eq_set_int @ S @ S6 )
% 6.92/7.20 => ( ( ( inf_inf_set_int @ A4 @ S6 )
% 6.92/7.20 = ( inf_inf_set_int @ B5 @ S6 ) )
% 6.92/7.20 => ( ( inf_inf_set_int @ A4 @ S )
% 6.92/7.20 = ( inf_inf_set_int @ B5 @ S ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inter_eq_subsetI
% 6.92/7.20 thf(fact_3354_Un__Int__crazy,axiom,
% 6.92/7.20 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( sup_su6327502436637775413at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) @ ( inf_in2572325071724192079at_nat @ B5 @ C4 ) ) @ ( inf_in2572325071724192079at_nat @ C4 @ A4 ) )
% 6.92/7.20 = ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) @ ( sup_su6327502436637775413at_nat @ B5 @ C4 ) ) @ ( sup_su6327502436637775413at_nat @ C4 @ A4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_crazy
% 6.92/7.20 thf(fact_3355_Un__Int__crazy,axiom,
% 6.92/7.20 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A4 @ B5 ) @ ( inf_in1697001100524423349at_nat @ B5 @ C4 ) ) @ ( inf_in1697001100524423349at_nat @ C4 @ A4 ) )
% 6.92/7.20 = ( inf_in1697001100524423349at_nat @ ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) @ ( sup_su3035147773818789531at_nat @ B5 @ C4 ) ) @ ( sup_su3035147773818789531at_nat @ C4 @ A4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_crazy
% 6.92/7.20 thf(fact_3356_Un__Int__crazy,axiom,
% 6.92/7.20 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A4 @ B5 ) @ ( inf_in7913087082777306421at_nat @ B5 @ C4 ) ) @ ( inf_in7913087082777306421at_nat @ C4 @ A4 ) )
% 6.92/7.20 = ( inf_in7913087082777306421at_nat @ ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) @ ( sup_su5525570899277871387at_nat @ B5 @ C4 ) ) @ ( sup_su5525570899277871387at_nat @ C4 @ A4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_crazy
% 6.92/7.20 thf(fact_3357_Un__Int__crazy,axiom,
% 6.92/7.20 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.20 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ A4 @ B5 ) @ ( inf_inf_set_nat @ B5 @ C4 ) ) @ ( inf_inf_set_nat @ C4 @ A4 ) )
% 6.92/7.20 = ( inf_inf_set_nat @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ A4 @ B5 ) @ ( sup_sup_set_nat @ B5 @ C4 ) ) @ ( sup_sup_set_nat @ C4 @ A4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_crazy
% 6.92/7.20 thf(fact_3358_Int__Un__distrib,axiom,
% 6.92/7.20 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( inf_in2572325071724192079at_nat @ A4 @ ( sup_su6327502436637775413at_nat @ B5 @ C4 ) )
% 6.92/7.20 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) @ ( inf_in2572325071724192079at_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_Un_distrib
% 6.92/7.20 thf(fact_3359_Int__Un__distrib,axiom,
% 6.92/7.20 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( inf_in1697001100524423349at_nat @ A4 @ ( sup_su3035147773818789531at_nat @ B5 @ C4 ) )
% 6.92/7.20 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A4 @ B5 ) @ ( inf_in1697001100524423349at_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_Un_distrib
% 6.92/7.20 thf(fact_3360_Int__Un__distrib,axiom,
% 6.92/7.20 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( inf_in7913087082777306421at_nat @ A4 @ ( sup_su5525570899277871387at_nat @ B5 @ C4 ) )
% 6.92/7.20 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A4 @ B5 ) @ ( inf_in7913087082777306421at_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_Un_distrib
% 6.92/7.20 thf(fact_3361_Int__Un__distrib,axiom,
% 6.92/7.20 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.20 ( ( inf_inf_set_nat @ A4 @ ( sup_sup_set_nat @ B5 @ C4 ) )
% 6.92/7.20 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ A4 @ B5 ) @ ( inf_inf_set_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_Un_distrib
% 6.92/7.20 thf(fact_3362_Un__Int__distrib,axiom,
% 6.92/7.20 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( sup_su6327502436637775413at_nat @ A4 @ ( inf_in2572325071724192079at_nat @ B5 @ C4 ) )
% 6.92/7.20 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) @ ( sup_su6327502436637775413at_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_distrib
% 6.92/7.20 thf(fact_3363_Un__Int__distrib,axiom,
% 6.92/7.20 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( sup_su3035147773818789531at_nat @ A4 @ ( inf_in1697001100524423349at_nat @ B5 @ C4 ) )
% 6.92/7.20 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) @ ( sup_su3035147773818789531at_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_distrib
% 6.92/7.20 thf(fact_3364_Un__Int__distrib,axiom,
% 6.92/7.20 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( sup_su5525570899277871387at_nat @ A4 @ ( inf_in7913087082777306421at_nat @ B5 @ C4 ) )
% 6.92/7.20 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) @ ( sup_su5525570899277871387at_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_distrib
% 6.92/7.20 thf(fact_3365_Un__Int__distrib,axiom,
% 6.92/7.20 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.20 ( ( sup_sup_set_nat @ A4 @ ( inf_inf_set_nat @ B5 @ C4 ) )
% 6.92/7.20 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ A4 @ B5 ) @ ( sup_sup_set_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_distrib
% 6.92/7.20 thf(fact_3366_Int__Un__distrib2,axiom,
% 6.92/7.20 ! [B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ B5 @ C4 ) @ A4 )
% 6.92/7.20 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ B5 @ A4 ) @ ( inf_in2572325071724192079at_nat @ C4 @ A4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_Un_distrib2
% 6.92/7.20 thf(fact_3367_Int__Un__distrib2,axiom,
% 6.92/7.20 ! [B5: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat,A4: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ B5 @ C4 ) @ A4 )
% 6.92/7.20 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ B5 @ A4 ) @ ( inf_in1697001100524423349at_nat @ C4 @ A4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_Un_distrib2
% 6.92/7.20 thf(fact_3368_Int__Un__distrib2,axiom,
% 6.92/7.20 ! [B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ B5 @ C4 ) @ A4 )
% 6.92/7.20 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ B5 @ A4 ) @ ( inf_in7913087082777306421at_nat @ C4 @ A4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_Un_distrib2
% 6.92/7.20 thf(fact_3369_Int__Un__distrib2,axiom,
% 6.92/7.20 ! [B5: set_nat,C4: set_nat,A4: set_nat] :
% 6.92/7.20 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ B5 @ C4 ) @ A4 )
% 6.92/7.20 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ B5 @ A4 ) @ ( inf_inf_set_nat @ C4 @ A4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Int_Un_distrib2
% 6.92/7.20 thf(fact_3370_Un__Int__distrib2,axiom,
% 6.92/7.20 ! [B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ B5 @ C4 ) @ A4 )
% 6.92/7.20 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ B5 @ A4 ) @ ( sup_su6327502436637775413at_nat @ C4 @ A4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_distrib2
% 6.92/7.20 thf(fact_3371_Un__Int__distrib2,axiom,
% 6.92/7.20 ! [B5: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat,A4: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ B5 @ C4 ) @ A4 )
% 6.92/7.20 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ B5 @ A4 ) @ ( sup_su3035147773818789531at_nat @ C4 @ A4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_distrib2
% 6.92/7.20 thf(fact_3372_Un__Int__distrib2,axiom,
% 6.92/7.20 ! [B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ B5 @ C4 ) @ A4 )
% 6.92/7.20 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ B5 @ A4 ) @ ( sup_su5525570899277871387at_nat @ C4 @ A4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_distrib2
% 6.92/7.20 thf(fact_3373_Un__Int__distrib2,axiom,
% 6.92/7.20 ! [B5: set_nat,C4: set_nat,A4: set_nat] :
% 6.92/7.20 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ B5 @ C4 ) @ A4 )
% 6.92/7.20 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ B5 @ A4 ) @ ( sup_sup_set_nat @ C4 @ A4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_distrib2
% 6.92/7.20 thf(fact_3374_inf__option__def,axiom,
% 6.92/7.20 ( inf_inf_option_assn
% 6.92/7.20 = ( ^ [X4: option_assn,Y4: option_assn] :
% 6.92/7.20 ( case_o4484465799723439917n_assn @ none_assn
% 6.92/7.20 @ ^ [Z: assn] :
% 6.92/7.20 ( case_o4484465799723439917n_assn @ none_assn
% 6.92/7.20 @ ^ [Aa: assn] : ( some_assn @ ( inf_inf_assn @ Z @ Aa ) )
% 6.92/7.20 @ Y4 )
% 6.92/7.20 @ X4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_option_def
% 6.92/7.20 thf(fact_3375_inf__option__def,axiom,
% 6.92/7.20 ( inf_in777885744494410645at_nat
% 6.92/7.20 = ( ^ [X4: option8963830502488799655at_nat,Y4: option8963830502488799655at_nat] :
% 6.92/7.20 ( case_o311359030874850053at_nat @ none_s625347054029921090at_nat
% 6.92/7.20 @ ^ [Z: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( case_o311359030874850053at_nat @ none_s625347054029921090at_nat
% 6.92/7.20 @ ^ [Aa: set_Pr1261947904930325089at_nat] : ( some_s147305329494351046at_nat @ ( inf_in2572325071724192079at_nat @ Z @ Aa ) )
% 6.92/7.20 @ Y4 )
% 6.92/7.20 @ X4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_option_def
% 6.92/7.20 thf(fact_3376_inf__option__def,axiom,
% 6.92/7.20 ( inf_in7812914138253463912et_nat
% 6.92/7.20 = ( ^ [X4: option_set_nat,Y4: option_set_nat] :
% 6.92/7.20 ( case_o4054078431260844265et_nat @ none_set_nat
% 6.92/7.20 @ ^ [Z: set_nat] :
% 6.92/7.20 ( case_o4054078431260844265et_nat @ none_set_nat
% 6.92/7.20 @ ^ [Aa: set_nat] : ( some_set_nat @ ( inf_inf_set_nat @ Z @ Aa ) )
% 6.92/7.20 @ Y4 )
% 6.92/7.20 @ X4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_option_def
% 6.92/7.20 thf(fact_3377_inf__option__def,axiom,
% 6.92/7.20 ( inf_inf_option_nat
% 6.92/7.20 = ( ^ [X4: option_nat,Y4: option_nat] :
% 6.92/7.20 ( case_o7429725398727453821at_nat @ none_nat
% 6.92/7.20 @ ^ [Z: nat] :
% 6.92/7.20 ( case_o7429725398727453821at_nat @ none_nat
% 6.92/7.20 @ ^ [Aa: nat] : ( some_nat @ ( inf_inf_nat @ Z @ Aa ) )
% 6.92/7.20 @ Y4 )
% 6.92/7.20 @ X4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_option_def
% 6.92/7.20 thf(fact_3378_inf__option__def,axiom,
% 6.92/7.20 ( inf_in7104746047340619750_int_o
% 6.92/7.20 = ( ^ [X4: option1893999432384633940_int_o,Y4: option1893999432384633940_int_o] :
% 6.92/7.20 ( case_o670596351732880613_int_o @ none_P2320557853698873699_int_o
% 6.92/7.20 @ ^ [Z: product_prod_int_int > $o] :
% 6.92/7.20 ( case_o670596351732880613_int_o @ none_P2320557853698873699_int_o
% 6.92/7.20 @ ^ [Aa: product_prod_int_int > $o] : ( some_P180497116919641311_int_o @ ( inf_in3604695632404883862_int_o @ Z @ Aa ) )
% 6.92/7.20 @ Y4 )
% 6.92/7.20 @ X4 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % inf_option_def
% 6.92/7.20 thf(fact_3379_distrib__sup__le,axiom,
% 6.92/7.20 ! [X: assn,Y: assn,Z3: assn] : ( ord_less_eq_assn @ ( sup_sup_assn @ X @ ( inf_inf_assn @ Y @ Z3 ) ) @ ( inf_inf_assn @ ( sup_sup_assn @ X @ Y ) @ ( sup_sup_assn @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_sup_le
% 6.92/7.20 thf(fact_3380_distrib__sup__le,axiom,
% 6.92/7.20 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) ) @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_sup_le
% 6.92/7.20 thf(fact_3381_distrib__sup__le,axiom,
% 6.92/7.20 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z3 ) ) @ ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_sup_le
% 6.92/7.20 thf(fact_3382_distrib__sup__le,axiom,
% 6.92/7.20 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z3 ) ) @ ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_sup_le
% 6.92/7.20 thf(fact_3383_distrib__sup__le,axiom,
% 6.92/7.20 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z3 ) ) @ ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_sup_le
% 6.92/7.20 thf(fact_3384_distrib__sup__le,axiom,
% 6.92/7.20 ! [X: set_nat,Y: set_nat,Z3: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z3 ) ) @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_sup_le
% 6.92/7.20 thf(fact_3385_distrib__sup__le,axiom,
% 6.92/7.20 ! [X: set_int,Y: set_int,Z3: set_int] : ( ord_less_eq_set_int @ ( sup_sup_set_int @ X @ ( inf_inf_set_int @ Y @ Z3 ) ) @ ( inf_inf_set_int @ ( sup_sup_set_int @ X @ Y ) @ ( sup_sup_set_int @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_sup_le
% 6.92/7.20 thf(fact_3386_distrib__sup__le,axiom,
% 6.92/7.20 ! [X: rat,Y: rat,Z3: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ X @ ( inf_inf_rat @ Y @ Z3 ) ) @ ( inf_inf_rat @ ( sup_sup_rat @ X @ Y ) @ ( sup_sup_rat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_sup_le
% 6.92/7.20 thf(fact_3387_distrib__sup__le,axiom,
% 6.92/7.20 ! [X: nat,Y: nat,Z3: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z3 ) ) @ ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_sup_le
% 6.92/7.20 thf(fact_3388_distrib__sup__le,axiom,
% 6.92/7.20 ! [X: int,Y: int,Z3: int] : ( ord_less_eq_int @ ( sup_sup_int @ X @ ( inf_inf_int @ Y @ Z3 ) ) @ ( inf_inf_int @ ( sup_sup_int @ X @ Y ) @ ( sup_sup_int @ X @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_sup_le
% 6.92/7.20 thf(fact_3389_distrib__inf__le,axiom,
% 6.92/7.20 ! [X: assn,Y: assn,Z3: assn] : ( ord_less_eq_assn @ ( sup_sup_assn @ ( inf_inf_assn @ X @ Y ) @ ( inf_inf_assn @ X @ Z3 ) ) @ ( inf_inf_assn @ X @ ( sup_sup_assn @ Y @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_inf_le
% 6.92/7.20 thf(fact_3390_distrib__inf__le,axiom,
% 6.92/7.20 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z3 ) ) @ ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_inf_le
% 6.92/7.20 thf(fact_3391_distrib__inf__le,axiom,
% 6.92/7.20 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z3 ) ) @ ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_inf_le
% 6.92/7.20 thf(fact_3392_distrib__inf__le,axiom,
% 6.92/7.20 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z3 ) ) @ ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_inf_le
% 6.92/7.20 thf(fact_3393_distrib__inf__le,axiom,
% 6.92/7.20 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z3 ) ) @ ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_inf_le
% 6.92/7.20 thf(fact_3394_distrib__inf__le,axiom,
% 6.92/7.20 ! [X: set_nat,Y: set_nat,Z3: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z3 ) ) @ ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_inf_le
% 6.92/7.20 thf(fact_3395_distrib__inf__le,axiom,
% 6.92/7.20 ! [X: set_int,Y: set_int,Z3: set_int] : ( ord_less_eq_set_int @ ( sup_sup_set_int @ ( inf_inf_set_int @ X @ Y ) @ ( inf_inf_set_int @ X @ Z3 ) ) @ ( inf_inf_set_int @ X @ ( sup_sup_set_int @ Y @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_inf_le
% 6.92/7.20 thf(fact_3396_distrib__inf__le,axiom,
% 6.92/7.20 ! [X: rat,Y: rat,Z3: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ ( inf_inf_rat @ X @ Y ) @ ( inf_inf_rat @ X @ Z3 ) ) @ ( inf_inf_rat @ X @ ( sup_sup_rat @ Y @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_inf_le
% 6.92/7.20 thf(fact_3397_distrib__inf__le,axiom,
% 6.92/7.20 ! [X: nat,Y: nat,Z3: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z3 ) ) @ ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_inf_le
% 6.92/7.20 thf(fact_3398_distrib__inf__le,axiom,
% 6.92/7.20 ! [X: int,Y: int,Z3: int] : ( ord_less_eq_int @ ( sup_sup_int @ ( inf_inf_int @ X @ Y ) @ ( inf_inf_int @ X @ Z3 ) ) @ ( inf_inf_int @ X @ ( sup_sup_int @ Y @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % distrib_inf_le
% 6.92/7.20 thf(fact_3399_power__mono,axiom,
% 6.92/7.20 ! [A: code_integer,B: code_integer,N2: nat] :
% 6.92/7.20 ( ( ord_le3102999989581377725nteger @ A @ B )
% 6.92/7.20 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.20 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_mono
% 6.92/7.20 thf(fact_3400_power__mono,axiom,
% 6.92/7.20 ! [A: rat,B: rat,N2: nat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.20 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.20 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_mono
% 6.92/7.20 thf(fact_3401_power__mono,axiom,
% 6.92/7.20 ! [A: nat,B: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.20 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.20 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_mono
% 6.92/7.20 thf(fact_3402_power__mono,axiom,
% 6.92/7.20 ! [A: int,B: int,N2: nat] :
% 6.92/7.20 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.20 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.20 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_mono
% 6.92/7.20 thf(fact_3403_zero__le__power,axiom,
% 6.92/7.20 ! [A: code_integer,N2: nat] :
% 6.92/7.20 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.20 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % zero_le_power
% 6.92/7.20 thf(fact_3404_zero__le__power,axiom,
% 6.92/7.20 ! [A: rat,N2: nat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.20 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % zero_le_power
% 6.92/7.20 thf(fact_3405_zero__le__power,axiom,
% 6.92/7.20 ! [A: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.20 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % zero_le_power
% 6.92/7.20 thf(fact_3406_zero__le__power,axiom,
% 6.92/7.20 ! [A: int,N2: nat] :
% 6.92/7.20 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.20 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % zero_le_power
% 6.92/7.20 thf(fact_3407_zero__less__power,axiom,
% 6.92/7.20 ! [A: code_integer,N2: nat] :
% 6.92/7.20 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.20 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % zero_less_power
% 6.92/7.20 thf(fact_3408_zero__less__power,axiom,
% 6.92/7.20 ! [A: rat,N2: nat] :
% 6.92/7.20 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.20 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % zero_less_power
% 6.92/7.20 thf(fact_3409_zero__less__power,axiom,
% 6.92/7.20 ! [A: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_nat @ zero_zero_nat @ A )
% 6.92/7.20 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % zero_less_power
% 6.92/7.20 thf(fact_3410_zero__less__power,axiom,
% 6.92/7.20 ! [A: int,N2: nat] :
% 6.92/7.20 ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.20 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % zero_less_power
% 6.92/7.20 thf(fact_3411_one__le__power,axiom,
% 6.92/7.20 ! [A: code_integer,N2: nat] :
% 6.92/7.20 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 6.92/7.20 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % one_le_power
% 6.92/7.20 thf(fact_3412_one__le__power,axiom,
% 6.92/7.20 ! [A: rat,N2: nat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 6.92/7.20 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % one_le_power
% 6.92/7.20 thf(fact_3413_one__le__power,axiom,
% 6.92/7.20 ! [A: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 6.92/7.20 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % one_le_power
% 6.92/7.20 thf(fact_3414_one__le__power,axiom,
% 6.92/7.20 ! [A: int,N2: nat] :
% 6.92/7.20 ( ( ord_less_eq_int @ one_one_int @ A )
% 6.92/7.20 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % one_le_power
% 6.92/7.20 thf(fact_3415_divide__le__0__iff,axiom,
% 6.92/7.20 ! [A: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 6.92/7.20 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.20 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 6.92/7.20 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 6.92/7.20 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_le_0_iff
% 6.92/7.20 thf(fact_3416_divide__right__mono,axiom,
% 6.92/7.20 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.20 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_right_mono
% 6.92/7.20 thf(fact_3417_zero__le__divide__iff,axiom,
% 6.92/7.20 ! [A: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 6.92/7.20 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.20 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 6.92/7.20 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 6.92/7.20 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % zero_le_divide_iff
% 6.92/7.20 thf(fact_3418_divide__nonneg__nonneg,axiom,
% 6.92/7.20 ! [X: rat,Y: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 6.92/7.20 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 6.92/7.20 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_nonneg_nonneg
% 6.92/7.20 thf(fact_3419_divide__nonneg__nonpos,axiom,
% 6.92/7.20 ! [X: rat,Y: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 6.92/7.20 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_nonneg_nonpos
% 6.92/7.20 thf(fact_3420_divide__nonpos__nonneg,axiom,
% 6.92/7.20 ! [X: rat,Y: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 6.92/7.20 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 6.92/7.20 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_nonpos_nonneg
% 6.92/7.20 thf(fact_3421_divide__nonpos__nonpos,axiom,
% 6.92/7.20 ! [X: rat,Y: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 6.92/7.20 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_nonpos_nonpos
% 6.92/7.20 thf(fact_3422_divide__right__mono__neg,axiom,
% 6.92/7.20 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.20 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ ( divide_divide_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_right_mono_neg
% 6.92/7.20 thf(fact_3423_divide__neg__neg,axiom,
% 6.92/7.20 ! [X: rat,Y: rat] :
% 6.92/7.20 ( ( ord_less_rat @ X @ zero_zero_rat )
% 6.92/7.20 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_neg_neg
% 6.92/7.20 thf(fact_3424_divide__neg__pos,axiom,
% 6.92/7.20 ! [X: rat,Y: rat] :
% 6.92/7.20 ( ( ord_less_rat @ X @ zero_zero_rat )
% 6.92/7.20 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 6.92/7.20 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_neg_pos
% 6.92/7.20 thf(fact_3425_divide__pos__neg,axiom,
% 6.92/7.20 ! [X: rat,Y: rat] :
% 6.92/7.20 ( ( ord_less_rat @ zero_zero_rat @ X )
% 6.92/7.20 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_pos_neg
% 6.92/7.20 thf(fact_3426_divide__pos__pos,axiom,
% 6.92/7.20 ! [X: rat,Y: rat] :
% 6.92/7.20 ( ( ord_less_rat @ zero_zero_rat @ X )
% 6.92/7.20 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 6.92/7.20 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_pos_pos
% 6.92/7.20 thf(fact_3427_divide__less__0__iff,axiom,
% 6.92/7.20 ! [A: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 6.92/7.20 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.20 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 6.92/7.20 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.20 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_less_0_iff
% 6.92/7.20 thf(fact_3428_divide__less__cancel,axiom,
% 6.92/7.20 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 6.92/7.20 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ord_less_rat @ A @ B ) )
% 6.92/7.20 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_rat @ B @ A ) )
% 6.92/7.20 & ( C2 != zero_zero_rat ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_less_cancel
% 6.92/7.20 thf(fact_3429_zero__less__divide__iff,axiom,
% 6.92/7.20 ! [A: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 6.92/7.20 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.20 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 6.92/7.20 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.20 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % zero_less_divide_iff
% 6.92/7.20 thf(fact_3430_divide__strict__right__mono,axiom,
% 6.92/7.20 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.20 ( ( ord_less_rat @ A @ B )
% 6.92/7.20 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ord_less_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_strict_right_mono
% 6.92/7.20 thf(fact_3431_divide__strict__right__mono__neg,axiom,
% 6.92/7.20 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.20 ( ( ord_less_rat @ B @ A )
% 6.92/7.20 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_strict_right_mono_neg
% 6.92/7.20 thf(fact_3432_power__add,axiom,
% 6.92/7.20 ! [A: assn,M: nat,N2: nat] :
% 6.92/7.20 ( ( power_power_assn @ A @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.20 = ( times_times_assn @ ( power_power_assn @ A @ M ) @ ( power_power_assn @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_add
% 6.92/7.20 thf(fact_3433_power__add,axiom,
% 6.92/7.20 ! [A: rat,M: nat,N2: nat] :
% 6.92/7.20 ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.20 = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_add
% 6.92/7.20 thf(fact_3434_power__add,axiom,
% 6.92/7.20 ! [A: nat,M: nat,N2: nat] :
% 6.92/7.20 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.20 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_add
% 6.92/7.20 thf(fact_3435_power__add,axiom,
% 6.92/7.20 ! [A: int,M: nat,N2: nat] :
% 6.92/7.20 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.20 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_add
% 6.92/7.20 thf(fact_3436_nat__power__less__imp__less,axiom,
% 6.92/7.20 ! [I2: nat,M: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 6.92/7.20 => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N2 ) )
% 6.92/7.20 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % nat_power_less_imp_less
% 6.92/7.20 thf(fact_3437_disjoint__mono,axiom,
% 6.92/7.20 ! [A: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ord_le3146513528884898305at_nat @ A @ A2 )
% 6.92/7.20 => ( ( ord_le3146513528884898305at_nat @ B @ B2 )
% 6.92/7.20 => ( ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 6.92/7.20 = bot_bo2099793752762293965at_nat )
% 6.92/7.20 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 6.92/7.20 = bot_bo2099793752762293965at_nat ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjoint_mono
% 6.92/7.20 thf(fact_3438_disjoint__mono,axiom,
% 6.92/7.20 ! [A: set_o,A2: set_o,B: set_o,B2: set_o] :
% 6.92/7.20 ( ( ord_less_eq_set_o @ A @ A2 )
% 6.92/7.20 => ( ( ord_less_eq_set_o @ B @ B2 )
% 6.92/7.20 => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 6.92/7.20 = bot_bot_set_o )
% 6.92/7.20 => ( ( inf_inf_set_o @ A @ B )
% 6.92/7.20 = bot_bot_set_o ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjoint_mono
% 6.92/7.20 thf(fact_3439_disjoint__mono,axiom,
% 6.92/7.20 ! [A: set_nat,A2: set_nat,B: set_nat,B2: set_nat] :
% 6.92/7.20 ( ( ord_less_eq_set_nat @ A @ A2 )
% 6.92/7.20 => ( ( ord_less_eq_set_nat @ B @ B2 )
% 6.92/7.20 => ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 6.92/7.20 = bot_bot_set_nat )
% 6.92/7.20 => ( ( inf_inf_set_nat @ A @ B )
% 6.92/7.20 = bot_bot_set_nat ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjoint_mono
% 6.92/7.20 thf(fact_3440_disjoint__mono,axiom,
% 6.92/7.20 ! [A: set_int,A2: set_int,B: set_int,B2: set_int] :
% 6.92/7.20 ( ( ord_less_eq_set_int @ A @ A2 )
% 6.92/7.20 => ( ( ord_less_eq_set_int @ B @ B2 )
% 6.92/7.20 => ( ( ( inf_inf_set_int @ A2 @ B2 )
% 6.92/7.20 = bot_bot_set_int )
% 6.92/7.20 => ( ( inf_inf_set_int @ A @ B )
% 6.92/7.20 = bot_bot_set_int ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % disjoint_mono
% 6.92/7.20 thf(fact_3441_Un__Int__assoc__eq,axiom,
% 6.92/7.20 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.20 ( ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.20 = ( inf_in2572325071724192079at_nat @ A4 @ ( sup_su6327502436637775413at_nat @ B5 @ C4 ) ) )
% 6.92/7.20 = ( ord_le3146513528884898305at_nat @ C4 @ A4 ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_assoc_eq
% 6.92/7.20 thf(fact_3442_Un__Int__assoc__eq,axiom,
% 6.92/7.20 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat] :
% 6.92/7.20 ( ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.20 = ( inf_in1697001100524423349at_nat @ A4 @ ( sup_su3035147773818789531at_nat @ B5 @ C4 ) ) )
% 6.92/7.20 = ( ord_le8081472938463900775at_nat @ C4 @ A4 ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_assoc_eq
% 6.92/7.20 thf(fact_3443_Un__Int__assoc__eq,axiom,
% 6.92/7.20 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] :
% 6.92/7.20 ( ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.20 = ( inf_in7913087082777306421at_nat @ A4 @ ( sup_su5525570899277871387at_nat @ B5 @ C4 ) ) )
% 6.92/7.20 = ( ord_le1268244103169919719at_nat @ C4 @ A4 ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_assoc_eq
% 6.92/7.20 thf(fact_3444_Un__Int__assoc__eq,axiom,
% 6.92/7.20 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.20 ( ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.20 = ( inf_inf_set_nat @ A4 @ ( sup_sup_set_nat @ B5 @ C4 ) ) )
% 6.92/7.20 = ( ord_less_eq_set_nat @ C4 @ A4 ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_assoc_eq
% 6.92/7.20 thf(fact_3445_Un__Int__assoc__eq,axiom,
% 6.92/7.20 ! [A4: set_int,B5: set_int,C4: set_int] :
% 6.92/7.20 ( ( ( sup_sup_set_int @ ( inf_inf_set_int @ A4 @ B5 ) @ C4 )
% 6.92/7.20 = ( inf_inf_set_int @ A4 @ ( sup_sup_set_int @ B5 @ C4 ) ) )
% 6.92/7.20 = ( ord_less_eq_set_int @ C4 @ A4 ) ) ).
% 6.92/7.20
% 6.92/7.20 % Un_Int_assoc_eq
% 6.92/7.20 thf(fact_3446_power__less__imp__less__base,axiom,
% 6.92/7.20 ! [A: code_integer,N2: nat,B: code_integer] :
% 6.92/7.20 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) )
% 6.92/7.20 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.20 => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_less_imp_less_base
% 6.92/7.20 thf(fact_3447_power__less__imp__less__base,axiom,
% 6.92/7.20 ! [A: rat,N2: nat,B: rat] :
% 6.92/7.20 ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 6.92/7.20 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.20 => ( ord_less_rat @ A @ B ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_less_imp_less_base
% 6.92/7.20 thf(fact_3448_power__less__imp__less__base,axiom,
% 6.92/7.20 ! [A: nat,N2: nat,B: nat] :
% 6.92/7.20 ( ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 6.92/7.20 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 6.92/7.20 => ( ord_less_nat @ A @ B ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_less_imp_less_base
% 6.92/7.20 thf(fact_3449_power__less__imp__less__base,axiom,
% 6.92/7.20 ! [A: int,N2: nat,B: int] :
% 6.92/7.20 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 6.92/7.20 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 6.92/7.20 => ( ord_less_int @ A @ B ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_less_imp_less_base
% 6.92/7.20 thf(fact_3450_power__le__one,axiom,
% 6.92/7.20 ! [A: code_integer,N2: nat] :
% 6.92/7.20 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.20 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 6.92/7.20 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ one_one_Code_integer ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_le_one
% 6.92/7.20 thf(fact_3451_power__le__one,axiom,
% 6.92/7.20 ! [A: rat,N2: nat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.20 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 6.92/7.20 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ one_one_rat ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_le_one
% 6.92/7.20 thf(fact_3452_power__le__one,axiom,
% 6.92/7.20 ! [A: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.20 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 6.92/7.20 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_le_one
% 6.92/7.20 thf(fact_3453_power__le__one,axiom,
% 6.92/7.20 ! [A: int,N2: nat] :
% 6.92/7.20 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.20 => ( ( ord_less_eq_int @ A @ one_one_int )
% 6.92/7.20 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ one_one_int ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_le_one
% 6.92/7.20 thf(fact_3454_divide__nonpos__pos,axiom,
% 6.92/7.20 ! [X: rat,Y: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 6.92/7.20 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 6.92/7.20 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_nonpos_pos
% 6.92/7.20 thf(fact_3455_divide__nonpos__neg,axiom,
% 6.92/7.20 ! [X: rat,Y: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 6.92/7.20 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_nonpos_neg
% 6.92/7.20 thf(fact_3456_divide__nonneg__pos,axiom,
% 6.92/7.20 ! [X: rat,Y: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 6.92/7.20 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 6.92/7.20 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_nonneg_pos
% 6.92/7.20 thf(fact_3457_divide__nonneg__neg,axiom,
% 6.92/7.20 ! [X: rat,Y: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 6.92/7.20 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_nonneg_neg
% 6.92/7.20 thf(fact_3458_divide__le__cancel,axiom,
% 6.92/7.20 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 6.92/7.20 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ord_less_eq_rat @ A @ B ) )
% 6.92/7.20 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_le_cancel
% 6.92/7.20 thf(fact_3459_frac__less2,axiom,
% 6.92/7.20 ! [X: rat,Y: rat,W2: rat,Z3: rat] :
% 6.92/7.20 ( ( ord_less_rat @ zero_zero_rat @ X )
% 6.92/7.20 => ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.20 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 6.92/7.20 => ( ( ord_less_rat @ W2 @ Z3 )
% 6.92/7.20 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z3 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % frac_less2
% 6.92/7.20 thf(fact_3460_frac__less,axiom,
% 6.92/7.20 ! [X: rat,Y: rat,W2: rat,Z3: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 6.92/7.20 => ( ( ord_less_rat @ X @ Y )
% 6.92/7.20 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 6.92/7.20 => ( ( ord_less_eq_rat @ W2 @ Z3 )
% 6.92/7.20 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z3 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % frac_less
% 6.92/7.20 thf(fact_3461_frac__le,axiom,
% 6.92/7.20 ! [Y: rat,X: rat,W2: rat,Z3: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 6.92/7.20 => ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.20 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 6.92/7.20 => ( ( ord_less_eq_rat @ W2 @ Z3 )
% 6.92/7.20 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z3 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % frac_le
% 6.92/7.20 thf(fact_3462_div__positive,axiom,
% 6.92/7.20 ! [B: code_integer,A: code_integer] :
% 6.92/7.20 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.20 => ( ( ord_le3102999989581377725nteger @ B @ A )
% 6.92/7.20 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % div_positive
% 6.92/7.20 thf(fact_3463_div__positive,axiom,
% 6.92/7.20 ! [B: nat,A: nat] :
% 6.92/7.20 ( ( ord_less_nat @ zero_zero_nat @ B )
% 6.92/7.20 => ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.20 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % div_positive
% 6.92/7.20 thf(fact_3464_div__positive,axiom,
% 6.92/7.20 ! [B: int,A: int] :
% 6.92/7.20 ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.20 => ( ( ord_less_eq_int @ B @ A )
% 6.92/7.20 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % div_positive
% 6.92/7.20 thf(fact_3465_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 6.92/7.20 ! [A: code_integer,B: code_integer] :
% 6.92/7.20 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.20 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 6.92/7.20 => ( ( divide6298287555418463151nteger @ A @ B )
% 6.92/7.20 = zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % unique_euclidean_semiring_numeral_class.div_less
% 6.92/7.20 thf(fact_3466_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 6.92/7.20 ! [A: nat,B: nat] :
% 6.92/7.20 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.20 => ( ( ord_less_nat @ A @ B )
% 6.92/7.20 => ( ( divide_divide_nat @ A @ B )
% 6.92/7.20 = zero_zero_nat ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % unique_euclidean_semiring_numeral_class.div_less
% 6.92/7.20 thf(fact_3467_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 6.92/7.20 ! [A: int,B: int] :
% 6.92/7.20 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.20 => ( ( ord_less_int @ A @ B )
% 6.92/7.20 => ( ( divide_divide_int @ A @ B )
% 6.92/7.20 = zero_zero_int ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % unique_euclidean_semiring_numeral_class.div_less
% 6.92/7.20 thf(fact_3468_power__gt1__lemma,axiom,
% 6.92/7.20 ! [A: code_integer,N2: nat] :
% 6.92/7.20 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 6.92/7.20 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_gt1_lemma
% 6.92/7.20 thf(fact_3469_power__gt1__lemma,axiom,
% 6.92/7.20 ! [A: rat,N2: nat] :
% 6.92/7.20 ( ( ord_less_rat @ one_one_rat @ A )
% 6.92/7.20 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_gt1_lemma
% 6.92/7.20 thf(fact_3470_power__gt1__lemma,axiom,
% 6.92/7.20 ! [A: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_nat @ one_one_nat @ A )
% 6.92/7.20 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_gt1_lemma
% 6.92/7.20 thf(fact_3471_power__gt1__lemma,axiom,
% 6.92/7.20 ! [A: int,N2: nat] :
% 6.92/7.20 ( ( ord_less_int @ one_one_int @ A )
% 6.92/7.20 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_gt1_lemma
% 6.92/7.20 thf(fact_3472_power__less__power__Suc,axiom,
% 6.92/7.20 ! [A: code_integer,N2: nat] :
% 6.92/7.20 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 6.92/7.20 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_less_power_Suc
% 6.92/7.20 thf(fact_3473_power__less__power__Suc,axiom,
% 6.92/7.20 ! [A: rat,N2: nat] :
% 6.92/7.20 ( ( ord_less_rat @ one_one_rat @ A )
% 6.92/7.20 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_less_power_Suc
% 6.92/7.20 thf(fact_3474_power__less__power__Suc,axiom,
% 6.92/7.20 ! [A: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_nat @ one_one_nat @ A )
% 6.92/7.20 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_less_power_Suc
% 6.92/7.20 thf(fact_3475_power__less__power__Suc,axiom,
% 6.92/7.20 ! [A: int,N2: nat] :
% 6.92/7.20 ( ( ord_less_int @ one_one_int @ A )
% 6.92/7.20 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_less_power_Suc
% 6.92/7.20 thf(fact_3476_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 6.92/7.20 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 6.92/7.20 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.20 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 6.92/7.20 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 6.92/7.20 thf(fact_3477_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 6.92/7.20 ! [C2: nat,A: nat,B: nat] :
% 6.92/7.20 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 6.92/7.20 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 6.92/7.20 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 6.92/7.20 thf(fact_3478_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 6.92/7.20 ! [C2: int,A: int,B: int] :
% 6.92/7.20 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.20 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 6.92/7.20 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 6.92/7.20 thf(fact_3479_divide__less__eq,axiom,
% 6.92/7.20 ! [B: rat,C2: rat,A: rat] :
% 6.92/7.20 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 6.92/7.20 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 6.92/7.20 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 6.92/7.20 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_less_eq
% 6.92/7.20 thf(fact_3480_less__divide__eq,axiom,
% 6.92/7.20 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.20 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 6.92/7.20 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 6.92/7.20 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 6.92/7.20 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_divide_eq
% 6.92/7.20 thf(fact_3481_neg__divide__less__eq,axiom,
% 6.92/7.20 ! [C2: rat,B: rat,A: rat] :
% 6.92/7.20 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 6.92/7.20 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % neg_divide_less_eq
% 6.92/7.20 thf(fact_3482_neg__less__divide__eq,axiom,
% 6.92/7.20 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 6.92/7.20 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % neg_less_divide_eq
% 6.92/7.20 thf(fact_3483_pos__divide__less__eq,axiom,
% 6.92/7.20 ! [C2: rat,B: rat,A: rat] :
% 6.92/7.20 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 6.92/7.20 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % pos_divide_less_eq
% 6.92/7.20 thf(fact_3484_pos__less__divide__eq,axiom,
% 6.92/7.20 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 6.92/7.20 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % pos_less_divide_eq
% 6.92/7.20 thf(fact_3485_mult__imp__div__pos__less,axiom,
% 6.92/7.20 ! [Y: rat,X: rat,Z3: rat] :
% 6.92/7.20 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 6.92/7.20 => ( ( ord_less_rat @ X @ ( times_times_rat @ Z3 @ Y ) )
% 6.92/7.20 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % mult_imp_div_pos_less
% 6.92/7.20 thf(fact_3486_mult__imp__less__div__pos,axiom,
% 6.92/7.20 ! [Y: rat,Z3: rat,X: rat] :
% 6.92/7.20 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 6.92/7.20 => ( ( ord_less_rat @ ( times_times_rat @ Z3 @ Y ) @ X )
% 6.92/7.20 => ( ord_less_rat @ Z3 @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % mult_imp_less_div_pos
% 6.92/7.20 thf(fact_3487_divide__strict__left__mono,axiom,
% 6.92/7.20 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.20 ( ( ord_less_rat @ B @ A )
% 6.92/7.20 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 6.92/7.20 => ( ord_less_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_strict_left_mono
% 6.92/7.20 thf(fact_3488_divide__strict__left__mono__neg,axiom,
% 6.92/7.20 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.20 ( ( ord_less_rat @ A @ B )
% 6.92/7.20 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 6.92/7.20 => ( ord_less_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_strict_left_mono_neg
% 6.92/7.20 thf(fact_3489_divide__less__eq__1,axiom,
% 6.92/7.20 ! [B: rat,A: rat] :
% 6.92/7.20 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 6.92/7.20 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.20 & ( ord_less_rat @ B @ A ) )
% 6.92/7.20 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.20 & ( ord_less_rat @ A @ B ) )
% 6.92/7.20 | ( A = zero_zero_rat ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_less_eq_1
% 6.92/7.20 thf(fact_3490_less__divide__eq__1,axiom,
% 6.92/7.20 ! [B: rat,A: rat] :
% 6.92/7.20 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 6.92/7.20 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.20 & ( ord_less_rat @ A @ B ) )
% 6.92/7.20 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.20 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_divide_eq_1
% 6.92/7.20 thf(fact_3491_add__divide__eq__if__simps_I2_J,axiom,
% 6.92/7.20 ! [Z3: rat,A: rat,B: rat] :
% 6.92/7.20 ( ( ( Z3 = zero_zero_rat )
% 6.92/7.20 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z3 ) @ B )
% 6.92/7.20 = B ) )
% 6.92/7.20 & ( ( Z3 != zero_zero_rat )
% 6.92/7.20 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z3 ) @ B )
% 6.92/7.20 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % add_divide_eq_if_simps(2)
% 6.92/7.20 thf(fact_3492_add__divide__eq__if__simps_I1_J,axiom,
% 6.92/7.20 ! [Z3: rat,A: rat,B: rat] :
% 6.92/7.20 ( ( ( Z3 = zero_zero_rat )
% 6.92/7.20 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z3 ) )
% 6.92/7.20 = A ) )
% 6.92/7.20 & ( ( Z3 != zero_zero_rat )
% 6.92/7.20 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z3 ) )
% 6.92/7.20 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % add_divide_eq_if_simps(1)
% 6.92/7.20 thf(fact_3493_add__frac__eq,axiom,
% 6.92/7.20 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 6.92/7.20 ( ( Y != zero_zero_rat )
% 6.92/7.20 => ( ( Z3 != zero_zero_rat )
% 6.92/7.20 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z3 ) )
% 6.92/7.20 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z3 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % add_frac_eq
% 6.92/7.20 thf(fact_3494_add__frac__num,axiom,
% 6.92/7.20 ! [Y: rat,X: rat,Z3: rat] :
% 6.92/7.20 ( ( Y != zero_zero_rat )
% 6.92/7.20 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z3 )
% 6.92/7.20 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z3 @ Y ) ) @ Y ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % add_frac_num
% 6.92/7.20 thf(fact_3495_add__num__frac,axiom,
% 6.92/7.20 ! [Y: rat,Z3: rat,X: rat] :
% 6.92/7.20 ( ( Y != zero_zero_rat )
% 6.92/7.20 => ( ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ X @ Y ) )
% 6.92/7.20 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z3 @ Y ) ) @ Y ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % add_num_frac
% 6.92/7.20 thf(fact_3496_add__divide__eq__iff,axiom,
% 6.92/7.20 ! [Z3: rat,X: rat,Y: rat] :
% 6.92/7.20 ( ( Z3 != zero_zero_rat )
% 6.92/7.20 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z3 ) )
% 6.92/7.20 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % add_divide_eq_iff
% 6.92/7.20 thf(fact_3497_divide__add__eq__iff,axiom,
% 6.92/7.20 ! [Z3: rat,X: rat,Y: rat] :
% 6.92/7.20 ( ( Z3 != zero_zero_rat )
% 6.92/7.20 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z3 ) @ Y )
% 6.92/7.20 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_add_eq_iff
% 6.92/7.20 thf(fact_3498_power__less__imp__less__exp,axiom,
% 6.92/7.20 ! [A: code_integer,M: nat,N2: nat] :
% 6.92/7.20 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 6.92/7.20 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 6.92/7.20 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_less_imp_less_exp
% 6.92/7.20 thf(fact_3499_power__less__imp__less__exp,axiom,
% 6.92/7.20 ! [A: rat,M: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_rat @ one_one_rat @ A )
% 6.92/7.20 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 6.92/7.20 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_less_imp_less_exp
% 6.92/7.20 thf(fact_3500_power__less__imp__less__exp,axiom,
% 6.92/7.20 ! [A: nat,M: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_nat @ one_one_nat @ A )
% 6.92/7.20 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 6.92/7.20 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_less_imp_less_exp
% 6.92/7.20 thf(fact_3501_power__less__imp__less__exp,axiom,
% 6.92/7.20 ! [A: int,M: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_int @ one_one_int @ A )
% 6.92/7.20 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 6.92/7.20 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_less_imp_less_exp
% 6.92/7.20 thf(fact_3502_power__strict__increasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: code_integer] :
% 6.92/7.20 ( ( ord_less_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 6.92/7.20 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ A @ N7 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_strict_increasing
% 6.92/7.20 thf(fact_3503_power__strict__increasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: rat] :
% 6.92/7.20 ( ( ord_less_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_less_rat @ one_one_rat @ A )
% 6.92/7.20 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N7 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_strict_increasing
% 6.92/7.20 thf(fact_3504_power__strict__increasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: nat] :
% 6.92/7.20 ( ( ord_less_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_less_nat @ one_one_nat @ A )
% 6.92/7.20 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N7 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_strict_increasing
% 6.92/7.20 thf(fact_3505_power__strict__increasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: int] :
% 6.92/7.20 ( ( ord_less_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_less_int @ one_one_int @ A )
% 6.92/7.20 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N7 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_strict_increasing
% 6.92/7.20 thf(fact_3506_power__increasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: code_integer] :
% 6.92/7.20 ( ( ord_less_eq_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 6.92/7.20 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ A @ N7 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_increasing
% 6.92/7.20 thf(fact_3507_power__increasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: rat] :
% 6.92/7.20 ( ( ord_less_eq_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 6.92/7.20 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N7 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_increasing
% 6.92/7.20 thf(fact_3508_power__increasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: nat] :
% 6.92/7.20 ( ( ord_less_eq_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 6.92/7.20 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N7 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_increasing
% 6.92/7.20 thf(fact_3509_power__increasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: int] :
% 6.92/7.20 ( ( ord_less_eq_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_less_eq_int @ one_one_int @ A )
% 6.92/7.20 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N7 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_increasing
% 6.92/7.20 thf(fact_3510_zero__power,axiom,
% 6.92/7.20 ! [N2: nat] :
% 6.92/7.20 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N2 )
% 6.92/7.20 = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.20
% 6.92/7.20 % zero_power
% 6.92/7.20 thf(fact_3511_zero__power,axiom,
% 6.92/7.20 ! [N2: nat] :
% 6.92/7.20 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 6.92/7.20 = zero_zero_rat ) ) ).
% 6.92/7.20
% 6.92/7.20 % zero_power
% 6.92/7.20 thf(fact_3512_zero__power,axiom,
% 6.92/7.20 ! [N2: nat] :
% 6.92/7.20 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 = zero_zero_nat ) ) ).
% 6.92/7.20
% 6.92/7.20 % zero_power
% 6.92/7.20 thf(fact_3513_zero__power,axiom,
% 6.92/7.20 ! [N2: nat] :
% 6.92/7.20 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 => ( ( power_power_int @ zero_zero_int @ N2 )
% 6.92/7.20 = zero_zero_int ) ) ).
% 6.92/7.20
% 6.92/7.20 % zero_power
% 6.92/7.20 thf(fact_3514_gt__half__sum,axiom,
% 6.92/7.20 ! [A: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_rat @ A @ B )
% 6.92/7.20 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 6.92/7.20
% 6.92/7.20 % gt_half_sum
% 6.92/7.20 thf(fact_3515_less__half__sum,axiom,
% 6.92/7.20 ! [A: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_rat @ A @ B )
% 6.92/7.20 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % less_half_sum
% 6.92/7.20 thf(fact_3516_nat__mult__div__cancel1,axiom,
% 6.92/7.20 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.20 => ( ( divide_divide_nat @ ( times_times_nat @ K2 @ M ) @ ( times_times_nat @ K2 @ N2 ) )
% 6.92/7.20 = ( divide_divide_nat @ M @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % nat_mult_div_cancel1
% 6.92/7.20 thf(fact_3517_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.20 lattic6529551498584149819at_nat @ inf_in2572325071724192079at_nat @ ord_le3146513528884898305at_nat @ ord_le7866589430770878221at_nat ).
% 6.92/7.20
% 6.92/7.20 % Inf_fin.semilattice_order_set_axioms
% 6.92/7.20 thf(fact_3518_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.20 lattic3109210760196336428et_nat @ inf_inf_set_nat @ ord_less_eq_set_nat @ ord_less_set_nat ).
% 6.92/7.20
% 6.92/7.20 % Inf_fin.semilattice_order_set_axioms
% 6.92/7.20 thf(fact_3519_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.20 lattic8660852769118194346_int_o @ inf_in3604695632404883862_int_o @ ord_le8369615600986905444_int_o @ ord_le8213806771718485336_int_o ).
% 6.92/7.20
% 6.92/7.20 % Inf_fin.semilattice_order_set_axioms
% 6.92/7.20 thf(fact_3520_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.20 lattic5623431474481994958t_assn @ inf_inf_assn @ ord_less_eq_assn @ ord_less_assn ).
% 6.92/7.20
% 6.92/7.20 % Inf_fin.semilattice_order_set_axioms
% 6.92/7.20 thf(fact_3521_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.20 lattic8154731777541915528et_int @ inf_inf_set_int @ ord_less_eq_set_int @ ord_less_set_int ).
% 6.92/7.20
% 6.92/7.20 % Inf_fin.semilattice_order_set_axioms
% 6.92/7.20 thf(fact_3522_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.20 lattic5374021519246970238et_rat @ inf_inf_rat @ ord_less_eq_rat @ ord_less_rat ).
% 6.92/7.20
% 6.92/7.20 % Inf_fin.semilattice_order_set_axioms
% 6.92/7.20 thf(fact_3523_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.20 lattic6009151579333465974et_nat @ inf_inf_nat @ ord_less_eq_nat @ ord_less_nat ).
% 6.92/7.20
% 6.92/7.20 % Inf_fin.semilattice_order_set_axioms
% 6.92/7.20 thf(fact_3524_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 6.92/7.20 lattic6006661108824415698et_int @ inf_inf_int @ ord_less_eq_int @ ord_less_int ).
% 6.92/7.20
% 6.92/7.20 % Inf_fin.semilattice_order_set_axioms
% 6.92/7.20 thf(fact_3525_power__Suc__less,axiom,
% 6.92/7.20 ! [A: code_integer,N2: nat] :
% 6.92/7.20 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.20 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 6.92/7.20 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_Suc_less
% 6.92/7.20 thf(fact_3526_power__Suc__less,axiom,
% 6.92/7.20 ! [A: rat,N2: nat] :
% 6.92/7.20 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.20 => ( ( ord_less_rat @ A @ one_one_rat )
% 6.92/7.20 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_Suc_less
% 6.92/7.20 thf(fact_3527_power__Suc__less,axiom,
% 6.92/7.20 ! [A: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_nat @ zero_zero_nat @ A )
% 6.92/7.20 => ( ( ord_less_nat @ A @ one_one_nat )
% 6.92/7.20 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_Suc_less
% 6.92/7.20 thf(fact_3528_power__Suc__less,axiom,
% 6.92/7.20 ! [A: int,N2: nat] :
% 6.92/7.20 ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.20 => ( ( ord_less_int @ A @ one_one_int )
% 6.92/7.20 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_Suc_less
% 6.92/7.20 thf(fact_3529_divide__left__mono__neg,axiom,
% 6.92/7.20 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.20 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 6.92/7.20 => ( ord_less_eq_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_left_mono_neg
% 6.92/7.20 thf(fact_3530_mult__imp__le__div__pos,axiom,
% 6.92/7.20 ! [Y: rat,Z3: rat,X: rat] :
% 6.92/7.20 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 6.92/7.20 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ Y ) @ X )
% 6.92/7.20 => ( ord_less_eq_rat @ Z3 @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % mult_imp_le_div_pos
% 6.92/7.20 thf(fact_3531_mult__imp__div__pos__le,axiom,
% 6.92/7.20 ! [Y: rat,X: rat,Z3: rat] :
% 6.92/7.20 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 6.92/7.20 => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z3 @ Y ) )
% 6.92/7.20 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z3 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % mult_imp_div_pos_le
% 6.92/7.20 thf(fact_3532_pos__le__divide__eq,axiom,
% 6.92/7.20 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 6.92/7.20 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % pos_le_divide_eq
% 6.92/7.20 thf(fact_3533_pos__divide__le__eq,axiom,
% 6.92/7.20 ! [C2: rat,B: rat,A: rat] :
% 6.92/7.20 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 6.92/7.20 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % pos_divide_le_eq
% 6.92/7.20 thf(fact_3534_neg__le__divide__eq,axiom,
% 6.92/7.20 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 6.92/7.20 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % neg_le_divide_eq
% 6.92/7.20 thf(fact_3535_neg__divide__le__eq,axiom,
% 6.92/7.20 ! [C2: rat,B: rat,A: rat] :
% 6.92/7.20 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 6.92/7.20 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % neg_divide_le_eq
% 6.92/7.20 thf(fact_3536_divide__left__mono,axiom,
% 6.92/7.20 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.20 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 6.92/7.20 => ( ord_less_eq_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_left_mono
% 6.92/7.20 thf(fact_3537_le__divide__eq,axiom,
% 6.92/7.20 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 6.92/7.20 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 6.92/7.20 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 6.92/7.20 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % le_divide_eq
% 6.92/7.20 thf(fact_3538_divide__le__eq,axiom,
% 6.92/7.20 ! [B: rat,C2: rat,A: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 6.92/7.20 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 6.92/7.20 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.20 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 6.92/7.20 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.20 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_le_eq
% 6.92/7.20 thf(fact_3539_le__divide__eq__1,axiom,
% 6.92/7.20 ! [B: rat,A: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 6.92/7.20 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.20 & ( ord_less_eq_rat @ A @ B ) )
% 6.92/7.20 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.20 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % le_divide_eq_1
% 6.92/7.20 thf(fact_3540_divide__le__eq__1,axiom,
% 6.92/7.20 ! [B: rat,A: rat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 6.92/7.20 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.20 & ( ord_less_eq_rat @ B @ A ) )
% 6.92/7.20 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.20 & ( ord_less_eq_rat @ A @ B ) )
% 6.92/7.20 | ( A = zero_zero_rat ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % divide_le_eq_1
% 6.92/7.20 thf(fact_3541_power__strict__decreasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: code_integer] :
% 6.92/7.20 ( ( ord_less_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.20 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 6.92/7.20 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N7 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_strict_decreasing
% 6.92/7.20 thf(fact_3542_power__strict__decreasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: rat] :
% 6.92/7.20 ( ( ord_less_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.20 => ( ( ord_less_rat @ A @ one_one_rat )
% 6.92/7.20 => ( ord_less_rat @ ( power_power_rat @ A @ N7 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_strict_decreasing
% 6.92/7.20 thf(fact_3543_power__strict__decreasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: nat] :
% 6.92/7.20 ( ( ord_less_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 6.92/7.20 => ( ( ord_less_nat @ A @ one_one_nat )
% 6.92/7.20 => ( ord_less_nat @ ( power_power_nat @ A @ N7 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_strict_decreasing
% 6.92/7.20 thf(fact_3544_power__strict__decreasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: int] :
% 6.92/7.20 ( ( ord_less_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.20 => ( ( ord_less_int @ A @ one_one_int )
% 6.92/7.20 => ( ord_less_int @ ( power_power_int @ A @ N7 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_strict_decreasing
% 6.92/7.20 thf(fact_3545_power__decreasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: code_integer] :
% 6.92/7.20 ( ( ord_less_eq_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.20 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 6.92/7.20 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N7 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_decreasing
% 6.92/7.20 thf(fact_3546_power__decreasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: rat] :
% 6.92/7.20 ( ( ord_less_eq_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.20 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 6.92/7.20 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N7 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_decreasing
% 6.92/7.20 thf(fact_3547_power__decreasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: nat] :
% 6.92/7.20 ( ( ord_less_eq_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.20 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 6.92/7.20 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N7 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_decreasing
% 6.92/7.20 thf(fact_3548_power__decreasing,axiom,
% 6.92/7.20 ! [N2: nat,N7: nat,A: int] :
% 6.92/7.20 ( ( ord_less_eq_nat @ N2 @ N7 )
% 6.92/7.20 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.20 => ( ( ord_less_eq_int @ A @ one_one_int )
% 6.92/7.20 => ( ord_less_eq_int @ ( power_power_int @ A @ N7 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_decreasing
% 6.92/7.20 thf(fact_3549_power__eq__iff__eq__base,axiom,
% 6.92/7.20 ! [N2: nat,A: code_integer,B: code_integer] :
% 6.92/7.20 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.20 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.20 => ( ( ( power_8256067586552552935nteger @ A @ N2 )
% 6.92/7.20 = ( power_8256067586552552935nteger @ B @ N2 ) )
% 6.92/7.20 = ( A = B ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_eq_iff_eq_base
% 6.92/7.20 thf(fact_3550_power__eq__iff__eq__base,axiom,
% 6.92/7.20 ! [N2: nat,A: rat,B: rat] :
% 6.92/7.20 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.20 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.20 => ( ( ( power_power_rat @ A @ N2 )
% 6.92/7.20 = ( power_power_rat @ B @ N2 ) )
% 6.92/7.20 = ( A = B ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_eq_iff_eq_base
% 6.92/7.20 thf(fact_3551_power__eq__iff__eq__base,axiom,
% 6.92/7.20 ! [N2: nat,A: nat,B: nat] :
% 6.92/7.20 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.20 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 6.92/7.20 => ( ( ( power_power_nat @ A @ N2 )
% 6.92/7.20 = ( power_power_nat @ B @ N2 ) )
% 6.92/7.20 = ( A = B ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_eq_iff_eq_base
% 6.92/7.20 thf(fact_3552_power__eq__iff__eq__base,axiom,
% 6.92/7.20 ! [N2: nat,A: int,B: int] :
% 6.92/7.20 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.20 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 6.92/7.20 => ( ( ( power_power_int @ A @ N2 )
% 6.92/7.20 = ( power_power_int @ B @ N2 ) )
% 6.92/7.20 = ( A = B ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_eq_iff_eq_base
% 6.92/7.20 thf(fact_3553_power__eq__imp__eq__base,axiom,
% 6.92/7.20 ! [A: code_integer,N2: nat,B: code_integer] :
% 6.92/7.20 ( ( ( power_8256067586552552935nteger @ A @ N2 )
% 6.92/7.20 = ( power_8256067586552552935nteger @ B @ N2 ) )
% 6.92/7.20 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.20 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.20 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 => ( A = B ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_eq_imp_eq_base
% 6.92/7.20 thf(fact_3554_power__eq__imp__eq__base,axiom,
% 6.92/7.20 ! [A: rat,N2: nat,B: rat] :
% 6.92/7.20 ( ( ( power_power_rat @ A @ N2 )
% 6.92/7.20 = ( power_power_rat @ B @ N2 ) )
% 6.92/7.20 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.20 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.20 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 => ( A = B ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_eq_imp_eq_base
% 6.92/7.20 thf(fact_3555_power__eq__imp__eq__base,axiom,
% 6.92/7.20 ! [A: nat,N2: nat,B: nat] :
% 6.92/7.20 ( ( ( power_power_nat @ A @ N2 )
% 6.92/7.20 = ( power_power_nat @ B @ N2 ) )
% 6.92/7.20 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.20 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 6.92/7.20 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 => ( A = B ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_eq_imp_eq_base
% 6.92/7.20 thf(fact_3556_power__eq__imp__eq__base,axiom,
% 6.92/7.20 ! [A: int,N2: nat,B: int] :
% 6.92/7.20 ( ( ( power_power_int @ A @ N2 )
% 6.92/7.20 = ( power_power_int @ B @ N2 ) )
% 6.92/7.20 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.20 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 6.92/7.20 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 => ( A = B ) ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_eq_imp_eq_base
% 6.92/7.20 thf(fact_3557_power__le__imp__le__exp,axiom,
% 6.92/7.20 ! [A: code_integer,M: nat,N2: nat] :
% 6.92/7.20 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 6.92/7.20 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 6.92/7.20 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_le_imp_le_exp
% 6.92/7.20 thf(fact_3558_power__le__imp__le__exp,axiom,
% 6.92/7.20 ! [A: rat,M: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_rat @ one_one_rat @ A )
% 6.92/7.20 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 6.92/7.20 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_le_imp_le_exp
% 6.92/7.20 thf(fact_3559_power__le__imp__le__exp,axiom,
% 6.92/7.20 ! [A: nat,M: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_nat @ one_one_nat @ A )
% 6.92/7.20 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 6.92/7.20 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_le_imp_le_exp
% 6.92/7.20 thf(fact_3560_power__le__imp__le__exp,axiom,
% 6.92/7.20 ! [A: int,M: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_int @ one_one_int @ A )
% 6.92/7.20 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 6.92/7.20 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % power_le_imp_le_exp
% 6.92/7.20 thf(fact_3561_self__le__power,axiom,
% 6.92/7.20 ! [A: code_integer,N2: nat] :
% 6.92/7.20 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 6.92/7.20 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 => ( ord_le3102999989581377725nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % self_le_power
% 6.92/7.20 thf(fact_3562_self__le__power,axiom,
% 6.92/7.20 ! [A: rat,N2: nat] :
% 6.92/7.20 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 6.92/7.20 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 6.92/7.20
% 6.92/7.20 % self_le_power
% 6.92/7.20 thf(fact_3563_self__le__power,axiom,
% 6.92/7.20 ! [A: nat,N2: nat] :
% 6.92/7.20 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 6.92/7.20 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.20 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % self_le_power
% 6.92/7.21 thf(fact_3564_self__le__power,axiom,
% 6.92/7.21 ! [A: int,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_int @ one_one_int @ A )
% 6.92/7.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % self_le_power
% 6.92/7.21 thf(fact_3565_one__less__power,axiom,
% 6.92/7.21 ! [A: code_integer,N2: nat] :
% 6.92/7.21 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 6.92/7.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % one_less_power
% 6.92/7.21 thf(fact_3566_one__less__power,axiom,
% 6.92/7.21 ! [A: rat,N2: nat] :
% 6.92/7.21 ( ( ord_less_rat @ one_one_rat @ A )
% 6.92/7.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % one_less_power
% 6.92/7.21 thf(fact_3567_one__less__power,axiom,
% 6.92/7.21 ! [A: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ one_one_nat @ A )
% 6.92/7.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % one_less_power
% 6.92/7.21 thf(fact_3568_one__less__power,axiom,
% 6.92/7.21 ! [A: int,N2: nat] :
% 6.92/7.21 ( ( ord_less_int @ one_one_int @ A )
% 6.92/7.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % one_less_power
% 6.92/7.21 thf(fact_3569_div__mult__self1,axiom,
% 6.92/7.21 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 6.92/7.21 ( ( B != zero_z3403309356797280102nteger )
% 6.92/7.21 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C2 @ B ) ) @ B )
% 6.92/7.21 = ( plus_p5714425477246183910nteger @ C2 @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self1
% 6.92/7.21 thf(fact_3570_div__mult__self1,axiom,
% 6.92/7.21 ! [B: nat,A: nat,C2: nat] :
% 6.92/7.21 ( ( B != zero_zero_nat )
% 6.92/7.21 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C2 @ B ) ) @ B )
% 6.92/7.21 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self1
% 6.92/7.21 thf(fact_3571_div__mult__self1,axiom,
% 6.92/7.21 ! [B: int,A: int,C2: int] :
% 6.92/7.21 ( ( B != zero_zero_int )
% 6.92/7.21 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C2 @ B ) ) @ B )
% 6.92/7.21 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self1
% 6.92/7.21 thf(fact_3572_div__mult__self1,axiom,
% 6.92/7.21 ! [B: code_natural,A: code_natural,C2: code_natural] :
% 6.92/7.21 ( ( B != zero_z2226904508553997617atural )
% 6.92/7.21 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C2 @ B ) ) @ B )
% 6.92/7.21 = ( plus_p4538020629002901425atural @ C2 @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self1
% 6.92/7.21 thf(fact_3573_div__mult__self2,axiom,
% 6.92/7.21 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 6.92/7.21 ( ( B != zero_z3403309356797280102nteger )
% 6.92/7.21 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C2 ) ) @ B )
% 6.92/7.21 = ( plus_p5714425477246183910nteger @ C2 @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self2
% 6.92/7.21 thf(fact_3574_div__mult__self2,axiom,
% 6.92/7.21 ! [B: nat,A: nat,C2: nat] :
% 6.92/7.21 ( ( B != zero_zero_nat )
% 6.92/7.21 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C2 ) ) @ B )
% 6.92/7.21 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self2
% 6.92/7.21 thf(fact_3575_div__mult__self2,axiom,
% 6.92/7.21 ! [B: int,A: int,C2: int] :
% 6.92/7.21 ( ( B != zero_zero_int )
% 6.92/7.21 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C2 ) ) @ B )
% 6.92/7.21 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self2
% 6.92/7.21 thf(fact_3576_div__mult__self2,axiom,
% 6.92/7.21 ! [B: code_natural,A: code_natural,C2: code_natural] :
% 6.92/7.21 ( ( B != zero_z2226904508553997617atural )
% 6.92/7.21 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C2 ) ) @ B )
% 6.92/7.21 = ( plus_p4538020629002901425atural @ C2 @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self2
% 6.92/7.21 thf(fact_3577_div__mult__self3,axiom,
% 6.92/7.21 ! [B: code_integer,C2: code_integer,A: code_integer] :
% 6.92/7.21 ( ( B != zero_z3403309356797280102nteger )
% 6.92/7.21 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C2 @ B ) @ A ) @ B )
% 6.92/7.21 = ( plus_p5714425477246183910nteger @ C2 @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self3
% 6.92/7.21 thf(fact_3578_div__mult__self3,axiom,
% 6.92/7.21 ! [B: nat,C2: nat,A: nat] :
% 6.92/7.21 ( ( B != zero_zero_nat )
% 6.92/7.21 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C2 @ B ) @ A ) @ B )
% 6.92/7.21 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self3
% 6.92/7.21 thf(fact_3579_div__mult__self3,axiom,
% 6.92/7.21 ! [B: int,C2: int,A: int] :
% 6.92/7.21 ( ( B != zero_zero_int )
% 6.92/7.21 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C2 @ B ) @ A ) @ B )
% 6.92/7.21 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self3
% 6.92/7.21 thf(fact_3580_div__mult__self3,axiom,
% 6.92/7.21 ! [B: code_natural,C2: code_natural,A: code_natural] :
% 6.92/7.21 ( ( B != zero_z2226904508553997617atural )
% 6.92/7.21 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C2 @ B ) @ A ) @ B )
% 6.92/7.21 = ( plus_p4538020629002901425atural @ C2 @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self3
% 6.92/7.21 thf(fact_3581_div__mult__self4,axiom,
% 6.92/7.21 ! [B: code_integer,C2: code_integer,A: code_integer] :
% 6.92/7.21 ( ( B != zero_z3403309356797280102nteger )
% 6.92/7.21 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C2 ) @ A ) @ B )
% 6.92/7.21 = ( plus_p5714425477246183910nteger @ C2 @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self4
% 6.92/7.21 thf(fact_3582_div__mult__self4,axiom,
% 6.92/7.21 ! [B: nat,C2: nat,A: nat] :
% 6.92/7.21 ( ( B != zero_zero_nat )
% 6.92/7.21 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C2 ) @ A ) @ B )
% 6.92/7.21 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self4
% 6.92/7.21 thf(fact_3583_div__mult__self4,axiom,
% 6.92/7.21 ! [B: int,C2: int,A: int] :
% 6.92/7.21 ( ( B != zero_zero_int )
% 6.92/7.21 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C2 ) @ A ) @ B )
% 6.92/7.21 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self4
% 6.92/7.21 thf(fact_3584_div__mult__self4,axiom,
% 6.92/7.21 ! [B: code_natural,C2: code_natural,A: code_natural] :
% 6.92/7.21 ( ( B != zero_z2226904508553997617atural )
% 6.92/7.21 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C2 ) @ A ) @ B )
% 6.92/7.21 = ( plus_p4538020629002901425atural @ C2 @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self4
% 6.92/7.21 thf(fact_3585_div__mult__self__is__m,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N2 ) @ N2 )
% 6.92/7.21 = M ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self_is_m
% 6.92/7.21 thf(fact_3586_div__mult__self1__is__m,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ( divide_divide_nat @ ( times_times_nat @ N2 @ M ) @ N2 )
% 6.92/7.21 = M ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_self1_is_m
% 6.92/7.21 thf(fact_3587_div__less,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.21 => ( ( divide_divide_nat @ M @ N2 )
% 6.92/7.21 = zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_less
% 6.92/7.21 thf(fact_3588_dividend__less__times__div,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % dividend_less_times_div
% 6.92/7.21 thf(fact_3589_dividend__less__div__times,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % dividend_less_div_times
% 6.92/7.21 thf(fact_3590_merge__pure__and,axiom,
% 6.92/7.21 ! [A: $o,B: $o] :
% 6.92/7.21 ( ( inf_inf_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 6.92/7.21 = ( pure_assn
% 6.92/7.21 @ ( A
% 6.92/7.21 & B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % merge_pure_and
% 6.92/7.21 thf(fact_3591_mod__h__bot__iff_I6_J,axiom,
% 6.92/7.21 ! [P2: assn,Q2: assn,H: heap_e7401611519738050253t_unit] :
% 6.92/7.21 ( ( rep_assn @ ( inf_inf_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 6.92/7.21 = ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 6.92/7.21 & ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_h_bot_iff(6)
% 6.92/7.21 thf(fact_3592_inf__Int__eq2,axiom,
% 6.92/7.21 ! [R3: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
% 6.92/7.21 ( ( inf_inf_int_int_o
% 6.92/7.21 @ ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R3 )
% 6.92/7.21 @ ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ S ) )
% 6.92/7.21 = ( ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ ( inf_in2269163501485487111nt_int @ R3 @ S ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_Int_eq2
% 6.92/7.21 thf(fact_3593_inf__Int__eq2,axiom,
% 6.92/7.21 ! [R3: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 6.92/7.21 ( ( inf_in3295504058751909687_nat_o
% 6.92/7.21 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R3 )
% 6.92/7.21 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ S ) )
% 6.92/7.21 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ ( inf_in1768905781608824518et_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_Int_eq2
% 6.92/7.21 thf(fact_3594_inf__Int__eq2,axiom,
% 6.92/7.21 ! [R3: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 6.92/7.21 ( ( inf_in2641120393918057659_nat_o
% 6.92/7.21 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R3 )
% 6.92/7.21 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ S ) )
% 6.92/7.21 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ ( inf_in3088352823822785602et_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_Int_eq2
% 6.92/7.21 thf(fact_3595_inf__Int__eq2,axiom,
% 6.92/7.21 ! [R3: set_Pr7600907837789447088it_nat,S: set_Pr7600907837789447088it_nat] :
% 6.92/7.21 ( ( inf_in844129575377303227_nat_o
% 6.92/7.21 @ ^ [X4: b,Y4: produc6653097349344004940it_nat] : ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Y4 ) @ R3 )
% 6.92/7.21 @ ^ [X4: b,Y4: produc6653097349344004940it_nat] : ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Y4 ) @ S ) )
% 6.92/7.21 = ( ^ [X4: b,Y4: produc6653097349344004940it_nat] : ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Y4 ) @ ( inf_in3995795194662975554it_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_Int_eq2
% 6.92/7.21 thf(fact_3596_inf__Int__eq2,axiom,
% 6.92/7.21 ! [R3: set_Pr7098220151150636591it_nat,S: set_Pr7098220151150636591it_nat] :
% 6.92/7.21 ( ( inf_in8051596381320575356_nat_o
% 6.92/7.21 @ ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ R3 )
% 6.92/7.21 @ ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ S ) )
% 6.92/7.21 = ( ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ ( inf_in3493107508024165057it_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_Int_eq2
% 6.92/7.21 thf(fact_3597_inf__Int__eq2,axiom,
% 6.92/7.21 ! [R3: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 6.92/7.21 ( ( inf_inf_nat_nat_o
% 6.92/7.21 @ ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R3 )
% 6.92/7.21 @ ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ S ) )
% 6.92/7.21 = ( ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ ( inf_in2572325071724192079at_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_Int_eq2
% 6.92/7.21 thf(fact_3598_mod__and__dist,axiom,
% 6.92/7.21 ! [P2: assn,Q2: assn,H: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ( rep_assn @ ( inf_inf_assn @ P2 @ Q2 ) @ H )
% 6.92/7.21 = ( ( rep_assn @ P2 @ H )
% 6.92/7.21 & ( rep_assn @ Q2 @ H ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_and_dist
% 6.92/7.21 thf(fact_3599_ent__conjI,axiom,
% 6.92/7.21 ! [A4: assn,B5: assn,C4: assn] :
% 6.92/7.21 ( ( entails @ A4 @ B5 )
% 6.92/7.21 => ( ( entails @ A4 @ C4 )
% 6.92/7.21 => ( entails @ A4 @ ( inf_inf_assn @ B5 @ C4 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % ent_conjI
% 6.92/7.21 thf(fact_3600_ent__conjE1,axiom,
% 6.92/7.21 ! [A4: assn,C4: assn,B5: assn] :
% 6.92/7.21 ( ( entails @ A4 @ C4 )
% 6.92/7.21 => ( entails @ ( inf_inf_assn @ A4 @ B5 ) @ C4 ) ) ).
% 6.92/7.21
% 6.92/7.21 % ent_conjE1
% 6.92/7.21 thf(fact_3601_ent__conjE2,axiom,
% 6.92/7.21 ! [B5: assn,C4: assn,A4: assn] :
% 6.92/7.21 ( ( entails @ B5 @ C4 )
% 6.92/7.21 => ( entails @ ( inf_inf_assn @ A4 @ B5 ) @ C4 ) ) ).
% 6.92/7.21
% 6.92/7.21 % ent_conjE2
% 6.92/7.21 thf(fact_3602_inf__Int__eq,axiom,
% 6.92/7.21 ! [R3: set_o,S: set_o] :
% 6.92/7.21 ( ( inf_inf_o_o
% 6.92/7.21 @ ^ [X4: $o] : ( member_o @ X4 @ R3 )
% 6.92/7.21 @ ^ [X4: $o] : ( member_o @ X4 @ S ) )
% 6.92/7.21 = ( ^ [X4: $o] : ( member_o @ X4 @ ( inf_inf_set_o @ R3 @ S ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_Int_eq
% 6.92/7.21 thf(fact_3603_inf__Int__eq,axiom,
% 6.92/7.21 ! [R3: set_se6260736226359567993nt_int,S: set_se6260736226359567993nt_int] :
% 6.92/7.21 ( ( inf_in5102985939729578038_int_o
% 6.92/7.21 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ R3 )
% 6.92/7.21 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ S ) )
% 6.92/7.21 = ( ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ ( inf_in8396524679539076455nt_int @ R3 @ S ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_Int_eq
% 6.92/7.21 thf(fact_3604_inf__Int__eq,axiom,
% 6.92/7.21 ! [R3: set_set_nat,S: set_set_nat] :
% 6.92/7.21 ( ( inf_inf_set_nat_o
% 6.92/7.21 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ R3 )
% 6.92/7.21 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ S ) )
% 6.92/7.21 = ( ^ [X4: set_nat] : ( member_set_nat @ X4 @ ( inf_inf_set_set_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_Int_eq
% 6.92/7.21 thf(fact_3605_inf__Int__eq,axiom,
% 6.92/7.21 ! [R3: set_int,S: set_int] :
% 6.92/7.21 ( ( inf_inf_int_o
% 6.92/7.21 @ ^ [X4: int] : ( member_int @ X4 @ R3 )
% 6.92/7.21 @ ^ [X4: int] : ( member_int @ X4 @ S ) )
% 6.92/7.21 = ( ^ [X4: int] : ( member_int @ X4 @ ( inf_inf_set_int @ R3 @ S ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_Int_eq
% 6.92/7.21 thf(fact_3606_inf__Int__eq,axiom,
% 6.92/7.21 ! [R3: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 6.92/7.21 ( ( inf_in5163264567034779214_nat_o
% 6.92/7.21 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ R3 )
% 6.92/7.21 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ S ) )
% 6.92/7.21 = ( ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ ( inf_in2572325071724192079at_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_Int_eq
% 6.92/7.21 thf(fact_3607_inf__Int__eq,axiom,
% 6.92/7.21 ! [R3: set_nat,S: set_nat] :
% 6.92/7.21 ( ( inf_inf_nat_o
% 6.92/7.21 @ ^ [X4: nat] : ( member_nat @ X4 @ R3 )
% 6.92/7.21 @ ^ [X4: nat] : ( member_nat @ X4 @ S ) )
% 6.92/7.21 = ( ^ [X4: nat] : ( member_nat @ X4 @ ( inf_inf_set_nat @ R3 @ S ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_Int_eq
% 6.92/7.21 thf(fact_3608_inf__Int__eq,axiom,
% 6.92/7.21 ! [R3: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
% 6.92/7.21 ( ( inf_in3604695632404883862_int_o
% 6.92/7.21 @ ^ [X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ R3 )
% 6.92/7.21 @ ^ [X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ S ) )
% 6.92/7.21 = ( ^ [X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ ( inf_in2269163501485487111nt_int @ R3 @ S ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_Int_eq
% 6.92/7.21 thf(fact_3609_inf__set__def,axiom,
% 6.92/7.21 ( inf_inf_set_o
% 6.92/7.21 = ( ^ [A6: set_o,B6: set_o] :
% 6.92/7.21 ( collect_o
% 6.92/7.21 @ ( inf_inf_o_o
% 6.92/7.21 @ ^ [X4: $o] : ( member_o @ X4 @ A6 )
% 6.92/7.21 @ ^ [X4: $o] : ( member_o @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_set_def
% 6.92/7.21 thf(fact_3610_inf__set__def,axiom,
% 6.92/7.21 ( inf_inf_set_list_nat
% 6.92/7.21 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 6.92/7.21 ( collect_list_nat
% 6.92/7.21 @ ( inf_inf_list_nat_o
% 6.92/7.21 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A6 )
% 6.92/7.21 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_set_def
% 6.92/7.21 thf(fact_3611_inf__set__def,axiom,
% 6.92/7.21 ( inf_in8396524679539076455nt_int
% 6.92/7.21 = ( ^ [A6: set_se6260736226359567993nt_int,B6: set_se6260736226359567993nt_int] :
% 6.92/7.21 ( collec5210948495886036740nt_int
% 6.92/7.21 @ ( inf_in5102985939729578038_int_o
% 6.92/7.21 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ A6 )
% 6.92/7.21 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_set_def
% 6.92/7.21 thf(fact_3612_inf__set__def,axiom,
% 6.92/7.21 ( inf_inf_set_set_nat
% 6.92/7.21 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 6.92/7.21 ( collect_set_nat
% 6.92/7.21 @ ( inf_inf_set_nat_o
% 6.92/7.21 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 6.92/7.21 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_set_def
% 6.92/7.21 thf(fact_3613_inf__set__def,axiom,
% 6.92/7.21 ( inf_inf_set_int
% 6.92/7.21 = ( ^ [A6: set_int,B6: set_int] :
% 6.92/7.21 ( collect_int
% 6.92/7.21 @ ( inf_inf_int_o
% 6.92/7.21 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 6.92/7.21 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_set_def
% 6.92/7.21 thf(fact_3614_inf__set__def,axiom,
% 6.92/7.21 ( inf_in2269163501485487111nt_int
% 6.92/7.21 = ( ^ [A6: set_Pr958786334691620121nt_int,B6: set_Pr958786334691620121nt_int] :
% 6.92/7.21 ( collec213857154873943460nt_int
% 6.92/7.21 @ ( inf_in3604695632404883862_int_o
% 6.92/7.21 @ ^ [X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ A6 )
% 6.92/7.21 @ ^ [X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_set_def
% 6.92/7.21 thf(fact_3615_inf__set__def,axiom,
% 6.92/7.21 ( inf_in2572325071724192079at_nat
% 6.92/7.21 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 6.92/7.21 ( collec3392354462482085612at_nat
% 6.92/7.21 @ ( inf_in5163264567034779214_nat_o
% 6.92/7.21 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ A6 )
% 6.92/7.21 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_set_def
% 6.92/7.21 thf(fact_3616_inf__set__def,axiom,
% 6.92/7.21 ( inf_inf_set_nat
% 6.92/7.21 = ( ^ [A6: set_nat,B6: set_nat] :
% 6.92/7.21 ( collect_nat
% 6.92/7.21 @ ( inf_inf_nat_o
% 6.92/7.21 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 6.92/7.21 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_set_def
% 6.92/7.21 thf(fact_3617_div__le__dividend,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ).
% 6.92/7.21
% 6.92/7.21 % div_le_dividend
% 6.92/7.21 thf(fact_3618_div__le__mono,axiom,
% 6.92/7.21 ! [M: nat,N2: nat,K2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.21 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K2 ) @ ( divide_divide_nat @ N2 @ K2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_le_mono
% 6.92/7.21 thf(fact_3619_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ( divide_divide_nat @ M @ N2 )
% 6.92/7.21 = zero_zero_nat )
% 6.92/7.21 = ( ( ord_less_nat @ M @ N2 )
% 6.92/7.21 | ( N2 = zero_zero_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % Euclidean_Division.div_eq_0_iff
% 6.92/7.21 thf(fact_3620_less__mult__imp__div__less,axiom,
% 6.92/7.21 ! [M: nat,I2: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N2 ) )
% 6.92/7.21 => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ I2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_mult_imp_div_less
% 6.92/7.21 thf(fact_3621_div__times__less__eq__dividend,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) @ M ) ).
% 6.92/7.21
% 6.92/7.21 % div_times_less_eq_dividend
% 6.92/7.21 thf(fact_3622_times__div__less__eq__dividend,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) @ M ) ).
% 6.92/7.21
% 6.92/7.21 % times_div_less_eq_dividend
% 6.92/7.21 thf(fact_3623_div__le__mono2,axiom,
% 6.92/7.21 ! [M: nat,N2: nat,K2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.21 => ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.21 => ( ord_less_eq_nat @ ( divide_divide_nat @ K2 @ N2 ) @ ( divide_divide_nat @ K2 @ M ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_le_mono2
% 6.92/7.21 thf(fact_3624_div__greater__zero__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N2 ) )
% 6.92/7.21 = ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.21 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_greater_zero_iff
% 6.92/7.21 thf(fact_3625_div__less__iff__less__mult,axiom,
% 6.92/7.21 ! [Q6: nat,M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ Q6 )
% 6.92/7.21 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q6 ) @ N2 )
% 6.92/7.21 = ( ord_less_nat @ M @ ( times_times_nat @ N2 @ Q6 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_less_iff_less_mult
% 6.92/7.21 thf(fact_3626_div__eq__dividend__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.21 => ( ( ( divide_divide_nat @ M @ N2 )
% 6.92/7.21 = M )
% 6.92/7.21 = ( N2 = one_one_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_eq_dividend_iff
% 6.92/7.21 thf(fact_3627_div__less__dividend,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] :
% 6.92/7.21 ( ( ord_less_nat @ one_one_nat @ N2 )
% 6.92/7.21 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.21 => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_less_dividend
% 6.92/7.21 thf(fact_3628_div__add__self2,axiom,
% 6.92/7.21 ! [B: code_integer,A: code_integer] :
% 6.92/7.21 ( ( B != zero_z3403309356797280102nteger )
% 6.92/7.21 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 6.92/7.21 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_add_self2
% 6.92/7.21 thf(fact_3629_div__add__self2,axiom,
% 6.92/7.21 ! [B: nat,A: nat] :
% 6.92/7.21 ( ( B != zero_zero_nat )
% 6.92/7.21 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 6.92/7.21 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_add_self2
% 6.92/7.21 thf(fact_3630_div__add__self2,axiom,
% 6.92/7.21 ! [B: int,A: int] :
% 6.92/7.21 ( ( B != zero_zero_int )
% 6.92/7.21 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 6.92/7.21 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_add_self2
% 6.92/7.21 thf(fact_3631_div__add__self2,axiom,
% 6.92/7.21 ! [B: code_natural,A: code_natural] :
% 6.92/7.21 ( ( B != zero_z2226904508553997617atural )
% 6.92/7.21 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 6.92/7.21 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_add_self2
% 6.92/7.21 thf(fact_3632_div__add__self1,axiom,
% 6.92/7.21 ! [B: code_integer,A: code_integer] :
% 6.92/7.21 ( ( B != zero_z3403309356797280102nteger )
% 6.92/7.21 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 6.92/7.21 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_add_self1
% 6.92/7.21 thf(fact_3633_div__add__self1,axiom,
% 6.92/7.21 ! [B: nat,A: nat] :
% 6.92/7.21 ( ( B != zero_zero_nat )
% 6.92/7.21 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 6.92/7.21 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_add_self1
% 6.92/7.21 thf(fact_3634_div__add__self1,axiom,
% 6.92/7.21 ! [B: int,A: int] :
% 6.92/7.21 ( ( B != zero_zero_int )
% 6.92/7.21 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 6.92/7.21 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_add_self1
% 6.92/7.21 thf(fact_3635_div__add__self1,axiom,
% 6.92/7.21 ! [B: code_natural,A: code_natural] :
% 6.92/7.21 ( ( B != zero_z2226904508553997617atural )
% 6.92/7.21 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 6.92/7.21 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_add_self1
% 6.92/7.21 thf(fact_3636_less__eq__div__iff__mult__less__eq,axiom,
% 6.92/7.21 ! [Q6: nat,M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ Q6 )
% 6.92/7.21 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N2 @ Q6 ) )
% 6.92/7.21 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q6 ) @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_eq_div_iff_mult_less_eq
% 6.92/7.21 thf(fact_3637_split__div,axiom,
% 6.92/7.21 ! [P2: nat > $o,M: nat,N2: nat] :
% 6.92/7.21 ( ( P2 @ ( divide_divide_nat @ M @ N2 ) )
% 6.92/7.21 = ( ( ( N2 = zero_zero_nat )
% 6.92/7.21 => ( P2 @ zero_zero_nat ) )
% 6.92/7.21 & ( ( N2 != zero_zero_nat )
% 6.92/7.21 => ! [I: nat,J: nat] :
% 6.92/7.21 ( ( ord_less_nat @ J @ N2 )
% 6.92/7.21 => ( ( M
% 6.92/7.21 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I ) @ J ) )
% 6.92/7.21 => ( P2 @ I ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % split_div
% 6.92/7.21 thf(fact_3638_wand__assnI,axiom,
% 6.92/7.21 ! [H: heap_e7401611519738050253t_unit,As: set_nat,Q2: assn,R3: assn] :
% 6.92/7.21 ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.21 => ( ! [H4: heap_e7401611519738050253t_unit,As6: set_nat] :
% 6.92/7.21 ( ( ( inf_inf_set_nat @ As @ As6 )
% 6.92/7.21 = bot_bot_set_nat )
% 6.92/7.21 => ( ( relH @ As @ H @ H4 )
% 6.92/7.21 => ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) )
% 6.92/7.21 => ( ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H4 @ As6 ) )
% 6.92/7.21 => ( rep_assn @ R3 @ ( produc7507926704131184380et_nat @ H4 @ ( sup_sup_set_nat @ As @ As6 ) ) ) ) ) ) )
% 6.92/7.21 => ( rep_assn @ ( wand_assn @ Q2 @ R3 ) @ ( produc7507926704131184380et_nat @ H @ As ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % wand_assnI
% 6.92/7.21 thf(fact_3639_times__assn__raw_Oelims_I3_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( Xb
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ? [As12: set_nat,As23: set_nat] :
% 6.92/7.21 ( ( As2
% 6.92/7.21 = ( sup_sup_set_nat @ As12 @ As23 ) )
% 6.92/7.21 & ( ( inf_inf_set_nat @ As12 @ As23 )
% 6.92/7.21 = bot_bot_set_nat )
% 6.92/7.21 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As12 ) )
% 6.92/7.21 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As23 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % times_assn_raw.elims(3)
% 6.92/7.21 thf(fact_3640_times__assn__raw_Oelims_I2_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ( times_assn_raw @ X @ Xa @ Xb )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( Xb
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ~ ? [As13: set_nat,As24: set_nat] :
% 6.92/7.21 ( ( As2
% 6.92/7.21 = ( sup_sup_set_nat @ As13 @ As24 ) )
% 6.92/7.21 & ( ( inf_inf_set_nat @ As13 @ As24 )
% 6.92/7.21 = bot_bot_set_nat )
% 6.92/7.21 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As13 ) )
% 6.92/7.21 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As24 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % times_assn_raw.elims(2)
% 6.92/7.21 thf(fact_3641_times__assn__raw_Oelims_I1_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 6.92/7.21 ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 6.92/7.21 = Y )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( Xb
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ( Y
% 6.92/7.21 = ( ~ ? [As1: set_nat,As22: set_nat] :
% 6.92/7.21 ( ( As2
% 6.92/7.21 = ( sup_sup_set_nat @ As1 @ As22 ) )
% 6.92/7.21 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 6.92/7.21 = bot_bot_set_nat )
% 6.92/7.21 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As1 ) )
% 6.92/7.21 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As22 ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % times_assn_raw.elims(1)
% 6.92/7.21 thf(fact_3642_times__assn__raw_Osimps,axiom,
% 6.92/7.21 ! [P2: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.21 ( ( times_assn_raw @ P2 @ Q2 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.21 = ( ? [As1: set_nat,As22: set_nat] :
% 6.92/7.21 ( ( As
% 6.92/7.21 = ( sup_sup_set_nat @ As1 @ As22 ) )
% 6.92/7.21 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 6.92/7.21 = bot_bot_set_nat )
% 6.92/7.21 & ( P2 @ ( produc7507926704131184380et_nat @ H @ As1 ) )
% 6.92/7.21 & ( Q2 @ ( produc7507926704131184380et_nat @ H @ As22 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % times_assn_raw.simps
% 6.92/7.21 thf(fact_3643_times__assn__raw_Opelims_I3_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 6.92/7.21 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( Xb
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) )
% 6.92/7.21 => ? [As12: set_nat,As23: set_nat] :
% 6.92/7.21 ( ( As2
% 6.92/7.21 = ( sup_sup_set_nat @ As12 @ As23 ) )
% 6.92/7.21 & ( ( inf_inf_set_nat @ As12 @ As23 )
% 6.92/7.21 = bot_bot_set_nat )
% 6.92/7.21 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As12 ) )
% 6.92/7.21 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As23 ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % times_assn_raw.pelims(3)
% 6.92/7.21 thf(fact_3644_times__assn__raw_Opelims_I2_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ( times_assn_raw @ X @ Xa @ Xb )
% 6.92/7.21 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( Xb
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) )
% 6.92/7.21 => ~ ? [As13: set_nat,As24: set_nat] :
% 6.92/7.21 ( ( As2
% 6.92/7.21 = ( sup_sup_set_nat @ As13 @ As24 ) )
% 6.92/7.21 & ( ( inf_inf_set_nat @ As13 @ As24 )
% 6.92/7.21 = bot_bot_set_nat )
% 6.92/7.21 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As13 ) )
% 6.92/7.21 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As24 ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % times_assn_raw.pelims(2)
% 6.92/7.21 thf(fact_3645_times__assn__raw_Opelims_I1_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 6.92/7.21 ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 6.92/7.21 = Y )
% 6.92/7.21 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( Xb
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ( ( Y
% 6.92/7.21 = ( ? [As1: set_nat,As22: set_nat] :
% 6.92/7.21 ( ( As2
% 6.92/7.21 = ( sup_sup_set_nat @ As1 @ As22 ) )
% 6.92/7.21 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 6.92/7.21 = bot_bot_set_nat )
% 6.92/7.21 & ( X @ ( produc7507926704131184380et_nat @ H2 @ As1 ) )
% 6.92/7.21 & ( Xa @ ( produc7507926704131184380et_nat @ H2 @ As22 ) ) ) ) )
% 6.92/7.21 => ~ ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % times_assn_raw.pelims(1)
% 6.92/7.21 thf(fact_3646_in__range__empty,axiom,
% 6.92/7.21 ! [H: heap_e7401611519738050253t_unit] : ( in_range @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % in_range_empty
% 6.92/7.21 thf(fact_3647_in__range__dist__union,axiom,
% 6.92/7.21 ! [H: heap_e7401611519738050253t_unit,As: set_nat,As5: set_nat] :
% 6.92/7.21 ( ( in_range @ ( produc7507926704131184380et_nat @ H @ ( sup_sup_set_nat @ As @ As5 ) ) )
% 6.92/7.21 = ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.21 & ( in_range @ ( produc7507926704131184380et_nat @ H @ As5 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % in_range_dist_union
% 6.92/7.21 thf(fact_3648_inf__unit__def,axiom,
% 6.92/7.21 ( inf_inf_Product_unit
% 6.92/7.21 = ( ^ [Uu3: product_unit,Uv: product_unit] : product_Unity ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_unit_def
% 6.92/7.21 thf(fact_3649_less__eq__assn__def,axiom,
% 6.92/7.21 ( ord_less_eq_assn
% 6.92/7.21 = ( ^ [A5: assn,B4: assn] :
% 6.92/7.21 ( A5
% 6.92/7.21 = ( inf_inf_assn @ A5 @ B4 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_eq_assn_def
% 6.92/7.21 thf(fact_3650_old_Ounit_Oexhaust,axiom,
% 6.92/7.21 ! [Y: product_unit] : ( Y = product_Unity ) ).
% 6.92/7.21
% 6.92/7.21 % old.unit.exhaust
% 6.92/7.21 thf(fact_3651_sup__unit__def,axiom,
% 6.92/7.21 ( sup_sup_Product_unit
% 6.92/7.21 = ( ^ [Uu3: product_unit,Uv: product_unit] : product_Unity ) ) ).
% 6.92/7.21
% 6.92/7.21 % sup_unit_def
% 6.92/7.21 thf(fact_3652_bot__unit__def,axiom,
% 6.92/7.21 bot_bot_Product_unit = product_Unity ).
% 6.92/7.21
% 6.92/7.21 % bot_unit_def
% 6.92/7.21 thf(fact_3653_models__in__range,axiom,
% 6.92/7.21 ! [P2: assn,H: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ( rep_assn @ P2 @ H )
% 6.92/7.21 => ( in_range @ H ) ) ).
% 6.92/7.21
% 6.92/7.21 % models_in_range
% 6.92/7.21 thf(fact_3654_relH__in__rangeI_I2_J,axiom,
% 6.92/7.21 ! [As: set_nat,H: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 6.92/7.21 ( ( relH @ As @ H @ H5 )
% 6.92/7.21 => ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % relH_in_rangeI(2)
% 6.92/7.21 thf(fact_3655_relH__in__rangeI_I1_J,axiom,
% 6.92/7.21 ! [As: set_nat,H: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 6.92/7.21 ( ( relH @ As @ H @ H5 )
% 6.92/7.21 => ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % relH_in_rangeI(1)
% 6.92/7.21 thf(fact_3656_relH__refl,axiom,
% 6.92/7.21 ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.21 ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.21 => ( relH @ As @ H @ H ) ) ).
% 6.92/7.21
% 6.92/7.21 % relH_refl
% 6.92/7.21 thf(fact_3657_in__range__subset,axiom,
% 6.92/7.21 ! [As: set_nat,As5: set_nat,H: heap_e7401611519738050253t_unit] :
% 6.92/7.21 ( ( ord_less_eq_set_nat @ As @ As5 )
% 6.92/7.21 => ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As5 ) )
% 6.92/7.21 => ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % in_range_subset
% 6.92/7.21 thf(fact_3658_wait__def,axiom,
% 6.92/7.21 ( heap_Time_wait
% 6.92/7.21 = ( ^ [N: nat] :
% 6.92/7.21 ( heap_T6183433275982383450t_unit
% 6.92/7.21 @ ^ [H6: heap_e7401611519738050253t_unit] : ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ product_Unity @ ( produc584006145561248582it_nat @ H6 @ N ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % wait_def
% 6.92/7.21 thf(fact_3659_in__range_Osimps,axiom,
% 6.92/7.21 ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.21 ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.21 = ( ! [X4: nat] :
% 6.92/7.21 ( ( member_nat @ X4 @ As )
% 6.92/7.21 => ( ord_less_nat @ X4 @ ( lim_Product_unit @ H ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % in_range.simps
% 6.92/7.21 thf(fact_3660_in__range_Oelims_I1_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 6.92/7.21 ( ( ( in_range @ X )
% 6.92/7.21 = Y )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( X
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ( Y
% 6.92/7.21 = ( ~ ! [X4: nat] :
% 6.92/7.21 ( ( member_nat @ X4 @ As2 )
% 6.92/7.21 => ( ord_less_nat @ X4 @ ( lim_Product_unit @ H2 ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % in_range.elims(1)
% 6.92/7.21 thf(fact_3661_in__range_Oelims_I2_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ( in_range @ X )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( X
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ~ ! [X6: nat] :
% 6.92/7.21 ( ( member_nat @ X6 @ As2 )
% 6.92/7.21 => ( ord_less_nat @ X6 @ ( lim_Product_unit @ H2 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % in_range.elims(2)
% 6.92/7.21 thf(fact_3662_in__range_Oelims_I3_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ~ ( in_range @ X )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( X
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ! [X3: nat] :
% 6.92/7.21 ( ( member_nat @ X3 @ As2 )
% 6.92/7.21 => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H2 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % in_range.elims(3)
% 6.92/7.21 thf(fact_3663_wand__raw_Osimps,axiom,
% 6.92/7.21 ! [P2: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.21 ( ( wand_raw @ P2 @ Q2 @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.21 = ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.92/7.21 & ! [H7: heap_e7401611519738050253t_unit,As7: set_nat] :
% 6.92/7.21 ( ( ( ( inf_inf_set_nat @ As @ As7 )
% 6.92/7.21 = bot_bot_set_nat )
% 6.92/7.21 & ( relH @ As @ H @ H7 )
% 6.92/7.21 & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As ) )
% 6.92/7.21 & ( P2 @ ( produc7507926704131184380et_nat @ H7 @ As7 ) ) )
% 6.92/7.21 => ( Q2 @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As @ As7 ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % wand_raw.simps
% 6.92/7.21 thf(fact_3664_wand__raw_Oelims_I1_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 6.92/7.21 ( ( ( wand_raw @ X @ Xa @ Xb )
% 6.92/7.21 = Y )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( Xb
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ( Y
% 6.92/7.21 = ( ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 & ! [H7: heap_e7401611519738050253t_unit,As7: set_nat] :
% 6.92/7.21 ( ( ( ( inf_inf_set_nat @ As2 @ As7 )
% 6.92/7.21 = bot_bot_set_nat )
% 6.92/7.21 & ( relH @ As2 @ H2 @ H7 )
% 6.92/7.21 & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As2 ) )
% 6.92/7.21 & ( X @ ( produc7507926704131184380et_nat @ H7 @ As7 ) ) )
% 6.92/7.21 => ( Xa @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As2 @ As7 ) ) ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % wand_raw.elims(1)
% 6.92/7.21 thf(fact_3665_wand__raw_Oelims_I2_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ( wand_raw @ X @ Xa @ Xb )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( Xb
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 & ! [H8: heap_e7401611519738050253t_unit,As8: set_nat] :
% 6.92/7.21 ( ( ( ( inf_inf_set_nat @ As2 @ As8 )
% 6.92/7.21 = bot_bot_set_nat )
% 6.92/7.21 & ( relH @ As2 @ H2 @ H8 )
% 6.92/7.21 & ( in_range @ ( produc7507926704131184380et_nat @ H8 @ As2 ) )
% 6.92/7.21 & ( X @ ( produc7507926704131184380et_nat @ H8 @ As8 ) ) )
% 6.92/7.21 => ( Xa @ ( produc7507926704131184380et_nat @ H8 @ ( sup_sup_set_nat @ As2 @ As8 ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % wand_raw.elims(2)
% 6.92/7.21 thf(fact_3666_wand__raw_Oelims_I3_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ~ ( wand_raw @ X @ Xa @ Xb )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( Xb
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 & ! [H4: heap_e7401611519738050253t_unit,As6: set_nat] :
% 6.92/7.21 ( ( ( ( inf_inf_set_nat @ As2 @ As6 )
% 6.92/7.21 = bot_bot_set_nat )
% 6.92/7.21 & ( relH @ As2 @ H2 @ H4 )
% 6.92/7.21 & ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As2 ) )
% 6.92/7.21 & ( X @ ( produc7507926704131184380et_nat @ H4 @ As6 ) ) )
% 6.92/7.21 => ( Xa @ ( produc7507926704131184380et_nat @ H4 @ ( sup_sup_set_nat @ As2 @ As6 ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % wand_raw.elims(3)
% 6.92/7.21 thf(fact_3667_wand__raw_Opelims_I1_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 6.92/7.21 ( ( ( wand_raw @ X @ Xa @ Xb )
% 6.92/7.21 = Y )
% 6.92/7.21 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( Xb
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ( ( Y
% 6.92/7.21 = ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 & ! [H7: heap_e7401611519738050253t_unit,As7: set_nat] :
% 6.92/7.21 ( ( ( ( inf_inf_set_nat @ As2 @ As7 )
% 6.92/7.21 = bot_bot_set_nat )
% 6.92/7.21 & ( relH @ As2 @ H2 @ H7 )
% 6.92/7.21 & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As2 ) )
% 6.92/7.21 & ( X @ ( produc7507926704131184380et_nat @ H7 @ As7 ) ) )
% 6.92/7.21 => ( Xa @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As2 @ As7 ) ) ) ) ) )
% 6.92/7.21 => ~ ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % wand_raw.pelims(1)
% 6.92/7.21 thf(fact_3668_wand__raw_Opelims_I2_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ( wand_raw @ X @ Xa @ Xb )
% 6.92/7.21 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( Xb
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) )
% 6.92/7.21 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 & ! [H8: heap_e7401611519738050253t_unit,As8: set_nat] :
% 6.92/7.21 ( ( ( ( inf_inf_set_nat @ As2 @ As8 )
% 6.92/7.21 = bot_bot_set_nat )
% 6.92/7.21 & ( relH @ As2 @ H2 @ H8 )
% 6.92/7.21 & ( in_range @ ( produc7507926704131184380et_nat @ H8 @ As2 ) )
% 6.92/7.21 & ( X @ ( produc7507926704131184380et_nat @ H8 @ As8 ) ) )
% 6.92/7.21 => ( Xa @ ( produc7507926704131184380et_nat @ H8 @ ( sup_sup_set_nat @ As2 @ As8 ) ) ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % wand_raw.pelims(2)
% 6.92/7.21 thf(fact_3669_wand__raw_Opelims_I3_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ~ ( wand_raw @ X @ Xa @ Xb )
% 6.92/7.21 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( Xb
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) )
% 6.92/7.21 => ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 & ! [H4: heap_e7401611519738050253t_unit,As6: set_nat] :
% 6.92/7.21 ( ( ( ( inf_inf_set_nat @ As2 @ As6 )
% 6.92/7.21 = bot_bot_set_nat )
% 6.92/7.21 & ( relH @ As2 @ H2 @ H4 )
% 6.92/7.21 & ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As2 ) )
% 6.92/7.21 & ( X @ ( produc7507926704131184380et_nat @ H4 @ As6 ) ) )
% 6.92/7.21 => ( Xa @ ( produc7507926704131184380et_nat @ H4 @ ( sup_sup_set_nat @ As2 @ As6 ) ) ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % wand_raw.pelims(3)
% 6.92/7.21 thf(fact_3670_in__range_Opelims_I1_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 6.92/7.21 ( ( ( in_range @ X )
% 6.92/7.21 = Y )
% 6.92/7.21 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( X
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ( ( Y
% 6.92/7.21 = ( ! [X4: nat] :
% 6.92/7.21 ( ( member_nat @ X4 @ As2 )
% 6.92/7.21 => ( ord_less_nat @ X4 @ ( lim_Product_unit @ H2 ) ) ) ) )
% 6.92/7.21 => ~ ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % in_range.pelims(1)
% 6.92/7.21 thf(fact_3671_less__assn__def,axiom,
% 6.92/7.21 ( ord_less_assn
% 6.92/7.21 = ( ^ [A5: assn,B4: assn] :
% 6.92/7.21 ( ( ord_less_eq_assn @ A5 @ B4 )
% 6.92/7.21 & ( A5 != B4 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_assn_def
% 6.92/7.21 thf(fact_3672_in__range_Opelims_I3_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ~ ( in_range @ X )
% 6.92/7.21 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( X
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ! [X3: nat] :
% 6.92/7.21 ( ( member_nat @ X3 @ As2 )
% 6.92/7.21 => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H2 ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % in_range.pelims(3)
% 6.92/7.21 thf(fact_3673_in__range_Opelims_I2_J,axiom,
% 6.92/7.21 ! [X: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ( in_range @ X )
% 6.92/7.21 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 6.92/7.21 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.21 ( ( X
% 6.92/7.21 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.92/7.21 => ~ ! [X6: nat] :
% 6.92/7.21 ( ( member_nat @ X6 @ As2 )
% 6.92/7.21 => ( ord_less_nat @ X6 @ ( lim_Product_unit @ H2 ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % in_range.pelims(2)
% 6.92/7.21 thf(fact_3674_default__unit__def,axiom,
% 6.92/7.21 defaul566961228789861419t_unit = product_Unity ).
% 6.92/7.21
% 6.92/7.21 % default_unit_def
% 6.92/7.21 thf(fact_3675_verit__le__mono__div,axiom,
% 6.92/7.21 ! [A4: nat,B5: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ A4 @ B5 )
% 6.92/7.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ord_less_eq_nat
% 6.92/7.21 @ ( plus_plus_nat @ ( divide_divide_nat @ A4 @ N2 )
% 6.92/7.21 @ ( if_nat
% 6.92/7.21 @ ( ( modulo_modulo_nat @ B5 @ N2 )
% 6.92/7.21 = zero_zero_nat )
% 6.92/7.21 @ one_one_nat
% 6.92/7.21 @ zero_zero_nat ) )
% 6.92/7.21 @ ( divide_divide_nat @ B5 @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % verit_le_mono_div
% 6.92/7.21 thf(fact_3676_of__nat__zero__less__power__iff,axiom,
% 6.92/7.21 ! [X: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N2 ) )
% 6.92/7.21 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 6.92/7.21 | ( N2 = zero_zero_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_zero_less_power_iff
% 6.92/7.21 thf(fact_3677_of__nat__zero__less__power__iff,axiom,
% 6.92/7.21 ! [X: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N2 ) )
% 6.92/7.21 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 6.92/7.21 | ( N2 = zero_zero_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_zero_less_power_iff
% 6.92/7.21 thf(fact_3678_of__nat__zero__less__power__iff,axiom,
% 6.92/7.21 ! [X: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N2 ) )
% 6.92/7.21 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 6.92/7.21 | ( N2 = zero_zero_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_zero_less_power_iff
% 6.92/7.21 thf(fact_3679_of__nat__zero__less__power__iff,axiom,
% 6.92/7.21 ! [X: nat,N2: nat] :
% 6.92/7.21 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ X ) @ N2 ) )
% 6.92/7.21 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 6.92/7.21 | ( N2 = zero_zero_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_zero_less_power_iff
% 6.92/7.21 thf(fact_3680_wand__assn__def,axiom,
% 6.92/7.21 ( wand_assn
% 6.92/7.21 = ( ^ [P5: assn,Q3: assn] : ( abs_assn @ ( wand_raw @ ( rep_assn @ P5 ) @ ( rep_assn @ Q3 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % wand_assn_def
% 6.92/7.21 thf(fact_3681_distrib__left__NO__MATCH,axiom,
% 6.92/7.21 ! [X: nat,Y: nat,A: rat,B: rat,C2: rat] :
% 6.92/7.21 ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ A )
% 6.92/7.21 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 6.92/7.21 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_left_NO_MATCH
% 6.92/7.21 thf(fact_3682_distrib__left__NO__MATCH,axiom,
% 6.92/7.21 ! [X: nat,Y: nat,A: nat,B: nat,C2: nat] :
% 6.92/7.21 ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ A )
% 6.92/7.21 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C2 ) )
% 6.92/7.21 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_left_NO_MATCH
% 6.92/7.21 thf(fact_3683_distrib__left__NO__MATCH,axiom,
% 6.92/7.21 ! [X: nat,Y: nat,A: int,B: int,C2: int] :
% 6.92/7.21 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ A )
% 6.92/7.21 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_left_NO_MATCH
% 6.92/7.21 thf(fact_3684_distrib__left__NO__MATCH,axiom,
% 6.92/7.21 ! [X: int,Y: int,A: rat,B: rat,C2: rat] :
% 6.92/7.21 ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ A )
% 6.92/7.21 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 6.92/7.21 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_left_NO_MATCH
% 6.92/7.21 thf(fact_3685_distrib__left__NO__MATCH,axiom,
% 6.92/7.21 ! [X: int,Y: int,A: nat,B: nat,C2: nat] :
% 6.92/7.21 ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ A )
% 6.92/7.21 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C2 ) )
% 6.92/7.21 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_left_NO_MATCH
% 6.92/7.21 thf(fact_3686_distrib__left__NO__MATCH,axiom,
% 6.92/7.21 ! [X: int,Y: int,A: int,B: int,C2: int] :
% 6.92/7.21 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ A )
% 6.92/7.21 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_left_NO_MATCH
% 6.92/7.21 thf(fact_3687_distrib__left__NO__MATCH,axiom,
% 6.92/7.21 ! [X: code_natural,Y: code_natural,A: rat,B: rat,C2: rat] :
% 6.92/7.21 ( ( nO_MAT3836730678284324717al_rat @ ( divide5121882707175180666atural @ X @ Y ) @ A )
% 6.92/7.21 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 6.92/7.21 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_left_NO_MATCH
% 6.92/7.21 thf(fact_3688_distrib__left__NO__MATCH,axiom,
% 6.92/7.21 ! [X: code_natural,Y: code_natural,A: nat,B: nat,C2: nat] :
% 6.92/7.21 ( ( nO_MAT4471860738370820453al_nat @ ( divide5121882707175180666atural @ X @ Y ) @ A )
% 6.92/7.21 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C2 ) )
% 6.92/7.21 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_left_NO_MATCH
% 6.92/7.21 thf(fact_3689_distrib__left__NO__MATCH,axiom,
% 6.92/7.21 ! [X: code_natural,Y: code_natural,A: int,B: int,C2: int] :
% 6.92/7.21 ( ( nO_MAT4469370267861770177al_int @ ( divide5121882707175180666atural @ X @ Y ) @ A )
% 6.92/7.21 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_left_NO_MATCH
% 6.92/7.21 thf(fact_3690_distrib__left__NO__MATCH,axiom,
% 6.92/7.21 ! [X: rat,Y: rat,A: rat,B: rat,C2: rat] :
% 6.92/7.21 ( ( nO_MATCH_rat_rat @ ( divide_divide_rat @ X @ Y ) @ A )
% 6.92/7.21 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 6.92/7.21 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_left_NO_MATCH
% 6.92/7.21 thf(fact_3691_of__nat__eq__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ( semiri1314217659103216013at_int @ M )
% 6.92/7.21 = ( semiri1314217659103216013at_int @ N2 ) )
% 6.92/7.21 = ( M = N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_eq_iff
% 6.92/7.21 thf(fact_3692_of__nat__eq__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ( semiri1316708129612266289at_nat @ M )
% 6.92/7.21 = ( semiri1316708129612266289at_nat @ N2 ) )
% 6.92/7.21 = ( M = N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_eq_iff
% 6.92/7.21 thf(fact_3693_of__nat__eq__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ( semiri4939895301339042750nteger @ M )
% 6.92/7.21 = ( semiri4939895301339042750nteger @ N2 ) )
% 6.92/7.21 = ( M = N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_eq_iff
% 6.92/7.21 thf(fact_3694_mod__add__self1,axiom,
% 6.92/7.21 ! [B: nat,A: nat] :
% 6.92/7.21 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 6.92/7.21 = ( modulo_modulo_nat @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_self1
% 6.92/7.21 thf(fact_3695_mod__add__self1,axiom,
% 6.92/7.21 ! [B: int,A: int] :
% 6.92/7.21 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 6.92/7.21 = ( modulo_modulo_int @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_self1
% 6.92/7.21 thf(fact_3696_mod__add__self1,axiom,
% 6.92/7.21 ! [B: code_natural,A: code_natural] :
% 6.92/7.21 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 6.92/7.21 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_self1
% 6.92/7.21 thf(fact_3697_mod__add__self2,axiom,
% 6.92/7.21 ! [A: nat,B: nat] :
% 6.92/7.21 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 6.92/7.21 = ( modulo_modulo_nat @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_self2
% 6.92/7.21 thf(fact_3698_mod__add__self2,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 6.92/7.21 = ( modulo_modulo_int @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_self2
% 6.92/7.21 thf(fact_3699_mod__add__self2,axiom,
% 6.92/7.21 ! [A: code_natural,B: code_natural] :
% 6.92/7.21 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 6.92/7.21 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_self2
% 6.92/7.21 thf(fact_3700_mod__less,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.21 => ( ( modulo_modulo_nat @ M @ N2 )
% 6.92/7.21 = M ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_less
% 6.92/7.21 thf(fact_3701_Rep__assn__inverse,axiom,
% 6.92/7.21 ! [X: assn] :
% 6.92/7.21 ( ( abs_assn @ ( rep_assn @ X ) )
% 6.92/7.21 = X ) ).
% 6.92/7.21
% 6.92/7.21 % Rep_assn_inverse
% 6.92/7.21 thf(fact_3702_of__nat__0,axiom,
% 6.92/7.21 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 6.92/7.21 = zero_zero_rat ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0
% 6.92/7.21 thf(fact_3703_of__nat__0,axiom,
% 6.92/7.21 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 6.92/7.21 = zero_zero_int ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0
% 6.92/7.21 thf(fact_3704_of__nat__0,axiom,
% 6.92/7.21 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 6.92/7.21 = zero_zero_nat ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0
% 6.92/7.21 thf(fact_3705_of__nat__0,axiom,
% 6.92/7.21 ( ( semiri4939895301339042750nteger @ zero_zero_nat )
% 6.92/7.21 = zero_z3403309356797280102nteger ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0
% 6.92/7.21 thf(fact_3706_of__nat__eq__0__iff,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ( ( ( semiri681578069525770553at_rat @ M )
% 6.92/7.21 = zero_zero_rat )
% 6.92/7.21 = ( M = zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_eq_0_iff
% 6.92/7.21 thf(fact_3707_of__nat__eq__0__iff,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ( ( ( semiri1314217659103216013at_int @ M )
% 6.92/7.21 = zero_zero_int )
% 6.92/7.21 = ( M = zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_eq_0_iff
% 6.92/7.21 thf(fact_3708_of__nat__eq__0__iff,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ( ( ( semiri1316708129612266289at_nat @ M )
% 6.92/7.21 = zero_zero_nat )
% 6.92/7.21 = ( M = zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_eq_0_iff
% 6.92/7.21 thf(fact_3709_of__nat__eq__0__iff,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ( ( ( semiri4939895301339042750nteger @ M )
% 6.92/7.21 = zero_z3403309356797280102nteger )
% 6.92/7.21 = ( M = zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_eq_0_iff
% 6.92/7.21 thf(fact_3710_of__nat__0__eq__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( zero_zero_rat
% 6.92/7.21 = ( semiri681578069525770553at_rat @ N2 ) )
% 6.92/7.21 = ( zero_zero_nat = N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0_eq_iff
% 6.92/7.21 thf(fact_3711_of__nat__0__eq__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( zero_zero_int
% 6.92/7.21 = ( semiri1314217659103216013at_int @ N2 ) )
% 6.92/7.21 = ( zero_zero_nat = N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0_eq_iff
% 6.92/7.21 thf(fact_3712_of__nat__0__eq__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( zero_zero_nat
% 6.92/7.21 = ( semiri1316708129612266289at_nat @ N2 ) )
% 6.92/7.21 = ( zero_zero_nat = N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0_eq_iff
% 6.92/7.21 thf(fact_3713_of__nat__0__eq__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( zero_z3403309356797280102nteger
% 6.92/7.21 = ( semiri4939895301339042750nteger @ N2 ) )
% 6.92/7.21 = ( zero_zero_nat = N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0_eq_iff
% 6.92/7.21 thf(fact_3714_mod__mult__self1,axiom,
% 6.92/7.21 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.21 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C2 @ B ) ) @ B )
% 6.92/7.21 = ( modulo_modulo_nat @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult_self1
% 6.92/7.21 thf(fact_3715_mod__mult__self1,axiom,
% 6.92/7.21 ! [A: int,C2: int,B: int] :
% 6.92/7.21 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C2 @ B ) ) @ B )
% 6.92/7.21 = ( modulo_modulo_int @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult_self1
% 6.92/7.21 thf(fact_3716_mod__mult__self1,axiom,
% 6.92/7.21 ! [A: code_natural,C2: code_natural,B: code_natural] :
% 6.92/7.21 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C2 @ B ) ) @ B )
% 6.92/7.21 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult_self1
% 6.92/7.21 thf(fact_3717_mod__mult__self2,axiom,
% 6.92/7.21 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.21 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C2 ) ) @ B )
% 6.92/7.21 = ( modulo_modulo_nat @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult_self2
% 6.92/7.21 thf(fact_3718_mod__mult__self2,axiom,
% 6.92/7.21 ! [A: int,B: int,C2: int] :
% 6.92/7.21 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C2 ) ) @ B )
% 6.92/7.21 = ( modulo_modulo_int @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult_self2
% 6.92/7.21 thf(fact_3719_mod__mult__self2,axiom,
% 6.92/7.21 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 6.92/7.21 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C2 ) ) @ B )
% 6.92/7.21 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult_self2
% 6.92/7.21 thf(fact_3720_mod__mult__self3,axiom,
% 6.92/7.21 ! [C2: nat,B: nat,A: nat] :
% 6.92/7.21 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C2 @ B ) @ A ) @ B )
% 6.92/7.21 = ( modulo_modulo_nat @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult_self3
% 6.92/7.21 thf(fact_3721_mod__mult__self3,axiom,
% 6.92/7.21 ! [C2: int,B: int,A: int] :
% 6.92/7.21 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C2 @ B ) @ A ) @ B )
% 6.92/7.21 = ( modulo_modulo_int @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult_self3
% 6.92/7.21 thf(fact_3722_mod__mult__self3,axiom,
% 6.92/7.21 ! [C2: code_natural,B: code_natural,A: code_natural] :
% 6.92/7.21 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C2 @ B ) @ A ) @ B )
% 6.92/7.21 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult_self3
% 6.92/7.21 thf(fact_3723_mod__mult__self4,axiom,
% 6.92/7.21 ! [B: nat,C2: nat,A: nat] :
% 6.92/7.21 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C2 ) @ A ) @ B )
% 6.92/7.21 = ( modulo_modulo_nat @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult_self4
% 6.92/7.21 thf(fact_3724_mod__mult__self4,axiom,
% 6.92/7.21 ! [B: int,C2: int,A: int] :
% 6.92/7.21 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C2 ) @ A ) @ B )
% 6.92/7.21 = ( modulo_modulo_int @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult_self4
% 6.92/7.21 thf(fact_3725_mod__mult__self4,axiom,
% 6.92/7.21 ! [B: code_natural,C2: code_natural,A: code_natural] :
% 6.92/7.21 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C2 ) @ A ) @ B )
% 6.92/7.21 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult_self4
% 6.92/7.21 thf(fact_3726_of__nat__less__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 6.92/7.21 = ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_iff
% 6.92/7.21 thf(fact_3727_of__nat__less__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 6.92/7.21 = ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_iff
% 6.92/7.21 thf(fact_3728_of__nat__less__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 6.92/7.21 = ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_iff
% 6.92/7.21 thf(fact_3729_of__nat__less__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 6.92/7.21 = ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_iff
% 6.92/7.21 thf(fact_3730_of__nat__le__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 6.92/7.21 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_le_iff
% 6.92/7.21 thf(fact_3731_of__nat__le__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 6.92/7.21 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_le_iff
% 6.92/7.21 thf(fact_3732_of__nat__le__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 6.92/7.21 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_le_iff
% 6.92/7.21 thf(fact_3733_of__nat__le__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 6.92/7.21 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_le_iff
% 6.92/7.21 thf(fact_3734_of__nat__add,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.21 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_add
% 6.92/7.21 thf(fact_3735_of__nat__add,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.21 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_add
% 6.92/7.21 thf(fact_3736_of__nat__add,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.21 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_add
% 6.92/7.21 thf(fact_3737_of__nat__add,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( semiri4939895301339042750nteger @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.21 = ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_add
% 6.92/7.21 thf(fact_3738_of__nat__mult,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N2 ) )
% 6.92/7.21 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_mult
% 6.92/7.21 thf(fact_3739_of__nat__mult,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N2 ) )
% 6.92/7.21 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_mult
% 6.92/7.21 thf(fact_3740_of__nat__mult,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N2 ) )
% 6.92/7.21 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_mult
% 6.92/7.21 thf(fact_3741_of__nat__mult,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( semiri4939895301339042750nteger @ ( times_times_nat @ M @ N2 ) )
% 6.92/7.21 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_mult
% 6.92/7.21 thf(fact_3742_of__nat__eq__1__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( ( semiri681578069525770553at_rat @ N2 )
% 6.92/7.21 = one_one_rat )
% 6.92/7.21 = ( N2 = one_one_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_eq_1_iff
% 6.92/7.21 thf(fact_3743_of__nat__eq__1__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( ( semiri1314217659103216013at_int @ N2 )
% 6.92/7.21 = one_one_int )
% 6.92/7.21 = ( N2 = one_one_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_eq_1_iff
% 6.92/7.21 thf(fact_3744_of__nat__eq__1__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( ( semiri1316708129612266289at_nat @ N2 )
% 6.92/7.21 = one_one_nat )
% 6.92/7.21 = ( N2 = one_one_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_eq_1_iff
% 6.92/7.21 thf(fact_3745_of__nat__eq__1__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( ( semiri4939895301339042750nteger @ N2 )
% 6.92/7.21 = one_one_Code_integer )
% 6.92/7.21 = ( N2 = one_one_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_eq_1_iff
% 6.92/7.21 thf(fact_3746_of__nat__1__eq__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( one_one_rat
% 6.92/7.21 = ( semiri681578069525770553at_rat @ N2 ) )
% 6.92/7.21 = ( N2 = one_one_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_1_eq_iff
% 6.92/7.21 thf(fact_3747_of__nat__1__eq__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( one_one_int
% 6.92/7.21 = ( semiri1314217659103216013at_int @ N2 ) )
% 6.92/7.21 = ( N2 = one_one_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_1_eq_iff
% 6.92/7.21 thf(fact_3748_of__nat__1__eq__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( one_one_nat
% 6.92/7.21 = ( semiri1316708129612266289at_nat @ N2 ) )
% 6.92/7.21 = ( N2 = one_one_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_1_eq_iff
% 6.92/7.21 thf(fact_3749_of__nat__1__eq__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( one_one_Code_integer
% 6.92/7.21 = ( semiri4939895301339042750nteger @ N2 ) )
% 6.92/7.21 = ( N2 = one_one_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_1_eq_iff
% 6.92/7.21 thf(fact_3750_of__nat__1,axiom,
% 6.92/7.21 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 6.92/7.21 = one_one_rat ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_1
% 6.92/7.21 thf(fact_3751_of__nat__1,axiom,
% 6.92/7.21 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 6.92/7.21 = one_one_int ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_1
% 6.92/7.21 thf(fact_3752_of__nat__1,axiom,
% 6.92/7.21 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 6.92/7.21 = one_one_nat ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_1
% 6.92/7.21 thf(fact_3753_of__nat__1,axiom,
% 6.92/7.21 ( ( semiri4939895301339042750nteger @ one_one_nat )
% 6.92/7.21 = one_one_Code_integer ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_1
% 6.92/7.21 thf(fact_3754_of__nat__le__0__iff,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger )
% 6.92/7.21 = ( M = zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_le_0_iff
% 6.92/7.21 thf(fact_3755_of__nat__le__0__iff,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 6.92/7.21 = ( M = zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_le_0_iff
% 6.92/7.21 thf(fact_3756_of__nat__le__0__iff,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 6.92/7.21 = ( M = zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_le_0_iff
% 6.92/7.21 thf(fact_3757_of__nat__le__0__iff,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 6.92/7.21 = ( M = zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_le_0_iff
% 6.92/7.21 thf(fact_3758_of__nat__0__less__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 6.92/7.21 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0_less_iff
% 6.92/7.21 thf(fact_3759_of__nat__0__less__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 6.92/7.21 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0_less_iff
% 6.92/7.21 thf(fact_3760_of__nat__0__less__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) )
% 6.92/7.21 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0_less_iff
% 6.92/7.21 thf(fact_3761_of__nat__0__less__iff,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N2 ) )
% 6.92/7.21 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0_less_iff
% 6.92/7.21 thf(fact_3762_of__nat__less__of__nat__power__cancel__iff,axiom,
% 6.92/7.21 ! [B: nat,W2: nat,X: nat] :
% 6.92/7.21 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 6.92/7.21 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_of_nat_power_cancel_iff
% 6.92/7.21 thf(fact_3763_of__nat__less__of__nat__power__cancel__iff,axiom,
% 6.92/7.21 ! [B: nat,W2: nat,X: nat] :
% 6.92/7.21 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 6.92/7.21 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_of_nat_power_cancel_iff
% 6.92/7.21 thf(fact_3764_of__nat__less__of__nat__power__cancel__iff,axiom,
% 6.92/7.21 ! [B: nat,W2: nat,X: nat] :
% 6.92/7.21 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 6.92/7.21 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_of_nat_power_cancel_iff
% 6.92/7.21 thf(fact_3765_of__nat__less__of__nat__power__cancel__iff,axiom,
% 6.92/7.21 ! [B: nat,W2: nat,X: nat] :
% 6.92/7.21 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 6.92/7.21 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_of_nat_power_cancel_iff
% 6.92/7.21 thf(fact_3766_of__nat__power__less__of__nat__cancel__iff,axiom,
% 6.92/7.21 ! [X: nat,B: nat,W2: nat] :
% 6.92/7.21 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 6.92/7.21 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_power_less_of_nat_cancel_iff
% 6.92/7.21 thf(fact_3767_of__nat__power__less__of__nat__cancel__iff,axiom,
% 6.92/7.21 ! [X: nat,B: nat,W2: nat] :
% 6.92/7.21 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 6.92/7.21 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_power_less_of_nat_cancel_iff
% 6.92/7.21 thf(fact_3768_of__nat__power__less__of__nat__cancel__iff,axiom,
% 6.92/7.21 ! [X: nat,B: nat,W2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 6.92/7.21 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_power_less_of_nat_cancel_iff
% 6.92/7.21 thf(fact_3769_of__nat__power__less__of__nat__cancel__iff,axiom,
% 6.92/7.21 ! [X: nat,B: nat,W2: nat] :
% 6.92/7.21 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) )
% 6.92/7.21 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_power_less_of_nat_cancel_iff
% 6.92/7.21 thf(fact_3770_of__nat__power__le__of__nat__cancel__iff,axiom,
% 6.92/7.21 ! [X: nat,B: nat,W2: nat] :
% 6.92/7.21 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) )
% 6.92/7.21 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_power_le_of_nat_cancel_iff
% 6.92/7.21 thf(fact_3771_of__nat__power__le__of__nat__cancel__iff,axiom,
% 6.92/7.21 ! [X: nat,B: nat,W2: nat] :
% 6.92/7.21 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 6.92/7.21 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_power_le_of_nat_cancel_iff
% 6.92/7.21 thf(fact_3772_of__nat__power__le__of__nat__cancel__iff,axiom,
% 6.92/7.21 ! [X: nat,B: nat,W2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 6.92/7.21 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_power_le_of_nat_cancel_iff
% 6.92/7.21 thf(fact_3773_of__nat__power__le__of__nat__cancel__iff,axiom,
% 6.92/7.21 ! [X: nat,B: nat,W2: nat] :
% 6.92/7.21 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 6.92/7.21 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_power_le_of_nat_cancel_iff
% 6.92/7.21 thf(fact_3774_of__nat__le__of__nat__power__cancel__iff,axiom,
% 6.92/7.21 ! [B: nat,W2: nat,X: nat] :
% 6.92/7.21 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 6.92/7.21 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_le_of_nat_power_cancel_iff
% 6.92/7.21 thf(fact_3775_of__nat__le__of__nat__power__cancel__iff,axiom,
% 6.92/7.21 ! [B: nat,W2: nat,X: nat] :
% 6.92/7.21 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 6.92/7.21 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_le_of_nat_power_cancel_iff
% 6.92/7.21 thf(fact_3776_of__nat__le__of__nat__power__cancel__iff,axiom,
% 6.92/7.21 ! [B: nat,W2: nat,X: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 6.92/7.21 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_le_of_nat_power_cancel_iff
% 6.92/7.21 thf(fact_3777_of__nat__le__of__nat__power__cancel__iff,axiom,
% 6.92/7.21 ! [B: nat,W2: nat,X: nat] :
% 6.92/7.21 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 6.92/7.21 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_le_of_nat_power_cancel_iff
% 6.92/7.21 thf(fact_3778_mod__add__right__eq,axiom,
% 6.92/7.21 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.21 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C2 ) ) @ C2 )
% 6.92/7.21 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_right_eq
% 6.92/7.21 thf(fact_3779_mod__add__right__eq,axiom,
% 6.92/7.21 ! [A: int,B: int,C2: int] :
% 6.92/7.21 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C2 ) ) @ C2 )
% 6.92/7.21 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_right_eq
% 6.92/7.21 thf(fact_3780_mod__add__right__eq,axiom,
% 6.92/7.21 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 6.92/7.21 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( modulo8411746178871703098atural @ B @ C2 ) ) @ C2 )
% 6.92/7.21 = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_right_eq
% 6.92/7.21 thf(fact_3781_mod__add__left__eq,axiom,
% 6.92/7.21 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.21 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C2 ) @ B ) @ C2 )
% 6.92/7.21 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_left_eq
% 6.92/7.21 thf(fact_3782_mod__add__left__eq,axiom,
% 6.92/7.21 ! [A: int,C2: int,B: int] :
% 6.92/7.21 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C2 ) @ B ) @ C2 )
% 6.92/7.21 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_left_eq
% 6.92/7.21 thf(fact_3783_mod__add__left__eq,axiom,
% 6.92/7.21 ! [A: code_natural,C2: code_natural,B: code_natural] :
% 6.92/7.21 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C2 ) @ B ) @ C2 )
% 6.92/7.21 = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_left_eq
% 6.92/7.21 thf(fact_3784_mod__add__cong,axiom,
% 6.92/7.21 ! [A: nat,C2: nat,A2: nat,B: nat,B2: nat] :
% 6.92/7.21 ( ( ( modulo_modulo_nat @ A @ C2 )
% 6.92/7.21 = ( modulo_modulo_nat @ A2 @ C2 ) )
% 6.92/7.21 => ( ( ( modulo_modulo_nat @ B @ C2 )
% 6.92/7.21 = ( modulo_modulo_nat @ B2 @ C2 ) )
% 6.92/7.21 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 6.92/7.21 = ( modulo_modulo_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_cong
% 6.92/7.21 thf(fact_3785_mod__add__cong,axiom,
% 6.92/7.21 ! [A: int,C2: int,A2: int,B: int,B2: int] :
% 6.92/7.21 ( ( ( modulo_modulo_int @ A @ C2 )
% 6.92/7.21 = ( modulo_modulo_int @ A2 @ C2 ) )
% 6.92/7.21 => ( ( ( modulo_modulo_int @ B @ C2 )
% 6.92/7.21 = ( modulo_modulo_int @ B2 @ C2 ) )
% 6.92/7.21 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 6.92/7.21 = ( modulo_modulo_int @ ( plus_plus_int @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_cong
% 6.92/7.21 thf(fact_3786_mod__add__cong,axiom,
% 6.92/7.21 ! [A: code_natural,C2: code_natural,A2: code_natural,B: code_natural,B2: code_natural] :
% 6.92/7.21 ( ( ( modulo8411746178871703098atural @ A @ C2 )
% 6.92/7.21 = ( modulo8411746178871703098atural @ A2 @ C2 ) )
% 6.92/7.21 => ( ( ( modulo8411746178871703098atural @ B @ C2 )
% 6.92/7.21 = ( modulo8411746178871703098atural @ B2 @ C2 ) )
% 6.92/7.21 => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C2 )
% 6.92/7.21 = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_cong
% 6.92/7.21 thf(fact_3787_mod__add__eq,axiom,
% 6.92/7.21 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.21 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C2 ) @ ( modulo_modulo_nat @ B @ C2 ) ) @ C2 )
% 6.92/7.21 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_eq
% 6.92/7.21 thf(fact_3788_mod__add__eq,axiom,
% 6.92/7.21 ! [A: int,C2: int,B: int] :
% 6.92/7.21 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C2 ) @ ( modulo_modulo_int @ B @ C2 ) ) @ C2 )
% 6.92/7.21 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_eq
% 6.92/7.21 thf(fact_3789_mod__add__eq,axiom,
% 6.92/7.21 ! [A: code_natural,C2: code_natural,B: code_natural] :
% 6.92/7.21 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C2 ) @ ( modulo8411746178871703098atural @ B @ C2 ) ) @ C2 )
% 6.92/7.21 = ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_add_eq
% 6.92/7.21 thf(fact_3790_mult__of__nat__commute,axiom,
% 6.92/7.21 ! [X: nat,Y: rat] :
% 6.92/7.21 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y )
% 6.92/7.21 = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mult_of_nat_commute
% 6.92/7.21 thf(fact_3791_mult__of__nat__commute,axiom,
% 6.92/7.21 ! [X: nat,Y: int] :
% 6.92/7.21 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 6.92/7.21 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mult_of_nat_commute
% 6.92/7.21 thf(fact_3792_mult__of__nat__commute,axiom,
% 6.92/7.21 ! [X: nat,Y: nat] :
% 6.92/7.21 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 6.92/7.21 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mult_of_nat_commute
% 6.92/7.21 thf(fact_3793_mult__of__nat__commute,axiom,
% 6.92/7.21 ! [X: nat,Y: code_integer] :
% 6.92/7.21 ( ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ X ) @ Y )
% 6.92/7.21 = ( times_3573771949741848930nteger @ Y @ ( semiri4939895301339042750nteger @ X ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mult_of_nat_commute
% 6.92/7.21 thf(fact_3794_mod__less__eq__dividend,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ M ) ).
% 6.92/7.21
% 6.92/7.21 % mod_less_eq_dividend
% 6.92/7.21 thf(fact_3795_int__ops_I1_J,axiom,
% 6.92/7.21 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 6.92/7.21 = zero_zero_int ) ).
% 6.92/7.21
% 6.92/7.21 % int_ops(1)
% 6.92/7.21 thf(fact_3796_nat__int__comparison_I2_J,axiom,
% 6.92/7.21 ( ord_less_nat
% 6.92/7.21 = ( ^ [A5: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_int_comparison(2)
% 6.92/7.21 thf(fact_3797_zle__int,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 6.92/7.21 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % zle_int
% 6.92/7.21 thf(fact_3798_nat__int__comparison_I3_J,axiom,
% 6.92/7.21 ( ord_less_eq_nat
% 6.92/7.21 = ( ^ [A5: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_int_comparison(3)
% 6.92/7.21 thf(fact_3799_zadd__int__left,axiom,
% 6.92/7.21 ! [M: nat,N2: nat,Z3: int] :
% 6.92/7.21 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ Z3 ) )
% 6.92/7.21 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) ) @ Z3 ) ) ).
% 6.92/7.21
% 6.92/7.21 % zadd_int_left
% 6.92/7.21 thf(fact_3800_int__ops_I5_J,axiom,
% 6.92/7.21 ! [A: nat,B: nat] :
% 6.92/7.21 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 6.92/7.21 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_ops(5)
% 6.92/7.21 thf(fact_3801_int__plus,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] :
% 6.92/7.21 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N2 @ M ) )
% 6.92/7.21 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_plus
% 6.92/7.21 thf(fact_3802_int__ops_I7_J,axiom,
% 6.92/7.21 ! [A: nat,B: nat] :
% 6.92/7.21 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 6.92/7.21 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_ops(7)
% 6.92/7.21 thf(fact_3803_int__ops_I2_J,axiom,
% 6.92/7.21 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 6.92/7.21 = one_one_int ) ).
% 6.92/7.21
% 6.92/7.21 % int_ops(2)
% 6.92/7.21 thf(fact_3804_mod__mult2__eq_H,axiom,
% 6.92/7.21 ! [A: code_natural,M: nat,N2: nat] :
% 6.92/7.21 ( ( modulo8411746178871703098atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N2 ) ) )
% 6.92/7.21 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M ) ) @ ( semiri3763490453095760265atural @ N2 ) ) ) @ ( modulo8411746178871703098atural @ A @ ( semiri3763490453095760265atural @ M ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult2_eq'
% 6.92/7.21 thf(fact_3805_mod__mult2__eq_H,axiom,
% 6.92/7.21 ! [A: int,M: nat,N2: nat] :
% 6.92/7.21 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 6.92/7.21 = ( 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 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult2_eq'
% 6.92/7.21 thf(fact_3806_mod__mult2__eq_H,axiom,
% 6.92/7.21 ! [A: nat,M: nat,N2: nat] :
% 6.92/7.21 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 6.92/7.21 = ( 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 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult2_eq'
% 6.92/7.21 thf(fact_3807_mod__mult2__eq_H,axiom,
% 6.92/7.21 ! [A: code_integer,M: nat,N2: nat] :
% 6.92/7.21 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 6.92/7.21 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult2_eq'
% 6.92/7.21 thf(fact_3808_nat__less__as__int,axiom,
% 6.92/7.21 ( ord_less_nat
% 6.92/7.21 = ( ^ [A5: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_less_as_int
% 6.92/7.21 thf(fact_3809_nat__leq__as__int,axiom,
% 6.92/7.21 ( ord_less_eq_nat
% 6.92/7.21 = ( ^ [A5: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_leq_as_int
% 6.92/7.21 thf(fact_3810_Abs__assn__eqI_I1_J,axiom,
% 6.92/7.21 ! [P2: produc3658429121746597890et_nat > $o,Pr: assn] :
% 6.92/7.21 ( ! [H2: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ( P2 @ H2 )
% 6.92/7.21 = ( rep_assn @ Pr @ H2 ) )
% 6.92/7.21 => ( ( abs_assn @ P2 )
% 6.92/7.21 = Pr ) ) ).
% 6.92/7.21
% 6.92/7.21 % Abs_assn_eqI(1)
% 6.92/7.21 thf(fact_3811_Abs__assn__eqI_I2_J,axiom,
% 6.92/7.21 ! [P2: produc3658429121746597890et_nat > $o,Pr: assn] :
% 6.92/7.21 ( ! [H2: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ( P2 @ H2 )
% 6.92/7.21 = ( rep_assn @ Pr @ H2 ) )
% 6.92/7.21 => ( Pr
% 6.92/7.21 = ( abs_assn @ P2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % Abs_assn_eqI(2)
% 6.92/7.21 thf(fact_3812_pure__assn__def,axiom,
% 6.92/7.21 ( pure_assn
% 6.92/7.21 = ( ^ [B4: $o] : ( abs_assn @ ( pure_a825153325127701367it_nat @ B4 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % pure_assn_def
% 6.92/7.21 thf(fact_3813_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 6.92/7.21 ! [A: code_integer,B: code_integer] :
% 6.92/7.21 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.21 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 6.92/7.21 thf(fact_3814_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 6.92/7.21 ! [A: nat,B: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.21 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 6.92/7.21 thf(fact_3815_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.21 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 6.92/7.21 thf(fact_3816_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 6.92/7.21 ! [B: code_integer,A: code_integer] :
% 6.92/7.21 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.21 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 6.92/7.21 thf(fact_3817_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 6.92/7.21 ! [B: nat,A: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ B )
% 6.92/7.21 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 6.92/7.21 thf(fact_3818_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 6.92/7.21 ! [B: int,A: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.21 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 6.92/7.21 thf(fact_3819_of__nat__0__le__iff,axiom,
% 6.92/7.21 ! [N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0_le_iff
% 6.92/7.21 thf(fact_3820_of__nat__0__le__iff,axiom,
% 6.92/7.21 ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0_le_iff
% 6.92/7.21 thf(fact_3821_of__nat__0__le__iff,axiom,
% 6.92/7.21 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0_le_iff
% 6.92/7.21 thf(fact_3822_of__nat__0__le__iff,axiom,
% 6.92/7.21 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_0_le_iff
% 6.92/7.21 thf(fact_3823_of__nat__less__0__iff,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_0_iff
% 6.92/7.21 thf(fact_3824_of__nat__less__0__iff,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_0_iff
% 6.92/7.21 thf(fact_3825_of__nat__less__0__iff,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_0_iff
% 6.92/7.21 thf(fact_3826_of__nat__less__0__iff,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ~ ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_0_iff
% 6.92/7.21 thf(fact_3827_mod__eqE,axiom,
% 6.92/7.21 ! [A: int,C2: int,B: int] :
% 6.92/7.21 ( ( ( modulo_modulo_int @ A @ C2 )
% 6.92/7.21 = ( modulo_modulo_int @ B @ C2 ) )
% 6.92/7.21 => ~ ! [D: int] :
% 6.92/7.21 ( B
% 6.92/7.21 != ( plus_plus_int @ A @ ( times_times_int @ C2 @ D ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_eqE
% 6.92/7.21 thf(fact_3828_div__add1__eq,axiom,
% 6.92/7.21 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.21 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C2 ) @ ( divide_divide_nat @ B @ C2 ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C2 ) @ ( modulo_modulo_nat @ B @ C2 ) ) @ C2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_add1_eq
% 6.92/7.21 thf(fact_3829_div__add1__eq,axiom,
% 6.92/7.21 ! [A: int,B: int,C2: int] :
% 6.92/7.21 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A @ C2 ) @ ( divide_divide_int @ B @ C2 ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C2 ) @ ( modulo_modulo_int @ B @ C2 ) ) @ C2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_add1_eq
% 6.92/7.21 thf(fact_3830_div__add1__eq,axiom,
% 6.92/7.21 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 6.92/7.21 ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ C2 ) @ ( divide5121882707175180666atural @ B @ C2 ) ) @ ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ C2 ) @ ( modulo8411746178871703098atural @ B @ C2 ) ) @ C2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_add1_eq
% 6.92/7.21 thf(fact_3831_less__imp__of__nat__less,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.21 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_imp_of_nat_less
% 6.92/7.21 thf(fact_3832_less__imp__of__nat__less,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.21 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_imp_of_nat_less
% 6.92/7.21 thf(fact_3833_less__imp__of__nat__less,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.21 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_imp_of_nat_less
% 6.92/7.21 thf(fact_3834_less__imp__of__nat__less,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.21 => ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_imp_of_nat_less
% 6.92/7.21 thf(fact_3835_of__nat__less__imp__less,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 6.92/7.21 => ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_imp_less
% 6.92/7.21 thf(fact_3836_of__nat__less__imp__less,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 6.92/7.21 => ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_imp_less
% 6.92/7.21 thf(fact_3837_of__nat__less__imp__less,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 6.92/7.21 => ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_imp_less
% 6.92/7.21 thf(fact_3838_of__nat__less__imp__less,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 6.92/7.21 => ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_less_imp_less
% 6.92/7.21 thf(fact_3839_of__nat__mono,axiom,
% 6.92/7.21 ! [I2: nat,J2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.21 => ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ I2 ) @ ( semiri4939895301339042750nteger @ J2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_mono
% 6.92/7.21 thf(fact_3840_of__nat__mono,axiom,
% 6.92/7.21 ! [I2: nat,J2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.21 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I2 ) @ ( semiri681578069525770553at_rat @ J2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_mono
% 6.92/7.21 thf(fact_3841_of__nat__mono,axiom,
% 6.92/7.21 ! [I2: nat,J2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.21 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ ( semiri1316708129612266289at_nat @ J2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_mono
% 6.92/7.21 thf(fact_3842_of__nat__mono,axiom,
% 6.92/7.21 ! [I2: nat,J2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.21 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_mono
% 6.92/7.21 thf(fact_3843_gcd__nat__induct,axiom,
% 6.92/7.21 ! [P2: nat > nat > $o,M: nat,N2: nat] :
% 6.92/7.21 ( ! [M5: nat] : ( P2 @ M5 @ zero_zero_nat )
% 6.92/7.21 => ( ! [M5: nat,N5: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 6.92/7.21 => ( ( P2 @ N5 @ ( modulo_modulo_nat @ M5 @ N5 ) )
% 6.92/7.21 => ( P2 @ M5 @ N5 ) ) )
% 6.92/7.21 => ( P2 @ M @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % gcd_nat_induct
% 6.92/7.21 thf(fact_3844_mod__less__divisor,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_less_divisor
% 6.92/7.21 thf(fact_3845_zmult__zless__mono2__lemma,axiom,
% 6.92/7.21 ! [I2: int,J2: int,K2: nat] :
% 6.92/7.21 ( ( ord_less_int @ I2 @ J2 )
% 6.92/7.21 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.21 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K2 ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K2 ) @ J2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zmult_zless_mono2_lemma
% 6.92/7.21 thf(fact_3846_pos__int__cases,axiom,
% 6.92/7.21 ! [K2: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ K2 )
% 6.92/7.21 => ~ ! [N5: nat] :
% 6.92/7.21 ( ( K2
% 6.92/7.21 = ( semiri1314217659103216013at_int @ N5 ) )
% 6.92/7.21 => ~ ( ord_less_nat @ zero_zero_nat @ N5 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % pos_int_cases
% 6.92/7.21 thf(fact_3847_zero__less__imp__eq__int,axiom,
% 6.92/7.21 ! [K2: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ K2 )
% 6.92/7.21 => ? [N5: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 6.92/7.21 & ( K2
% 6.92/7.21 = ( semiri1314217659103216013at_int @ N5 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zero_less_imp_eq_int
% 6.92/7.21 thf(fact_3848_nat__mod__eq__iff,axiom,
% 6.92/7.21 ! [X: nat,N2: nat,Y: nat] :
% 6.92/7.21 ( ( ( modulo_modulo_nat @ X @ N2 )
% 6.92/7.21 = ( modulo_modulo_nat @ Y @ N2 ) )
% 6.92/7.21 = ( ? [Q1: nat,Q22: nat] :
% 6.92/7.21 ( ( plus_plus_nat @ X @ ( times_times_nat @ N2 @ Q1 ) )
% 6.92/7.21 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_mod_eq_iff
% 6.92/7.21 thf(fact_3849_bot__assn__def,axiom,
% 6.92/7.21 ( bot_bot_assn
% 6.92/7.21 = ( abs_assn
% 6.92/7.21 @ ^ [Uu2: produc3658429121746597890et_nat] : $false ) ) ).
% 6.92/7.21
% 6.92/7.21 % bot_assn_def
% 6.92/7.21 thf(fact_3850_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 6.92/7.21 ! [B: code_integer,A: code_integer] :
% 6.92/7.21 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.21 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 6.92/7.21 thf(fact_3851_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 6.92/7.21 ! [B: nat,A: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ B )
% 6.92/7.21 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 6.92/7.21 thf(fact_3852_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 6.92/7.21 ! [B: int,A: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.21 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 6.92/7.21 thf(fact_3853_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 6.92/7.21 ! [A: code_integer,B: code_integer] :
% 6.92/7.21 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.21 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 6.92/7.21 => ( ( modulo364778990260209775nteger @ A @ B )
% 6.92/7.21 = A ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_euclidean_semiring_numeral_class.mod_less
% 6.92/7.21 thf(fact_3854_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 6.92/7.21 ! [A: nat,B: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.21 => ( ( ord_less_nat @ A @ B )
% 6.92/7.21 => ( ( modulo_modulo_nat @ A @ B )
% 6.92/7.21 = A ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_euclidean_semiring_numeral_class.mod_less
% 6.92/7.21 thf(fact_3855_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.21 => ( ( ord_less_int @ A @ B )
% 6.92/7.21 => ( ( modulo_modulo_int @ A @ B )
% 6.92/7.21 = A ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_euclidean_semiring_numeral_class.mod_less
% 6.92/7.21 thf(fact_3856_mult__div__mod__eq,axiom,
% 6.92/7.21 ! [B: nat,A: nat] :
% 6.92/7.21 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % mult_div_mod_eq
% 6.92/7.21 thf(fact_3857_mult__div__mod__eq,axiom,
% 6.92/7.21 ! [B: int,A: int] :
% 6.92/7.21 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % mult_div_mod_eq
% 6.92/7.21 thf(fact_3858_mult__div__mod__eq,axiom,
% 6.92/7.21 ! [B: code_natural,A: code_natural] :
% 6.92/7.21 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % mult_div_mod_eq
% 6.92/7.21 thf(fact_3859_mod__mult__div__eq,axiom,
% 6.92/7.21 ! [A: nat,B: nat] :
% 6.92/7.21 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult_div_eq
% 6.92/7.21 thf(fact_3860_mod__mult__div__eq,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult_div_eq
% 6.92/7.21 thf(fact_3861_mod__mult__div__eq,axiom,
% 6.92/7.21 ! [A: code_natural,B: code_natural] :
% 6.92/7.21 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult_div_eq
% 6.92/7.21 thf(fact_3862_mod__div__mult__eq,axiom,
% 6.92/7.21 ! [A: nat,B: nat] :
% 6.92/7.21 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % mod_div_mult_eq
% 6.92/7.21 thf(fact_3863_mod__div__mult__eq,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % mod_div_mult_eq
% 6.92/7.21 thf(fact_3864_mod__div__mult__eq,axiom,
% 6.92/7.21 ! [A: code_natural,B: code_natural] :
% 6.92/7.21 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % mod_div_mult_eq
% 6.92/7.21 thf(fact_3865_div__mult__mod__eq,axiom,
% 6.92/7.21 ! [A: nat,B: nat] :
% 6.92/7.21 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_mod_eq
% 6.92/7.21 thf(fact_3866_div__mult__mod__eq,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_mod_eq
% 6.92/7.21 thf(fact_3867_div__mult__mod__eq,axiom,
% 6.92/7.21 ! [A: code_natural,B: code_natural] :
% 6.92/7.21 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult_mod_eq
% 6.92/7.21 thf(fact_3868_mod__div__decomp,axiom,
% 6.92/7.21 ! [A: nat,B: nat] :
% 6.92/7.21 ( A
% 6.92/7.21 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_div_decomp
% 6.92/7.21 thf(fact_3869_mod__div__decomp,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( A
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_div_decomp
% 6.92/7.21 thf(fact_3870_mod__div__decomp,axiom,
% 6.92/7.21 ! [A: code_natural,B: code_natural] :
% 6.92/7.21 ( A
% 6.92/7.21 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_div_decomp
% 6.92/7.21 thf(fact_3871_cancel__div__mod__rules_I1_J,axiom,
% 6.92/7.21 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.21 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C2 )
% 6.92/7.21 = ( plus_plus_nat @ A @ C2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % cancel_div_mod_rules(1)
% 6.92/7.21 thf(fact_3872_cancel__div__mod__rules_I1_J,axiom,
% 6.92/7.21 ! [A: int,B: int,C2: int] :
% 6.92/7.21 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C2 )
% 6.92/7.21 = ( plus_plus_int @ A @ C2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % cancel_div_mod_rules(1)
% 6.92/7.21 thf(fact_3873_cancel__div__mod__rules_I1_J,axiom,
% 6.92/7.21 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 6.92/7.21 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C2 )
% 6.92/7.21 = ( plus_p4538020629002901425atural @ A @ C2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % cancel_div_mod_rules(1)
% 6.92/7.21 thf(fact_3874_cancel__div__mod__rules_I2_J,axiom,
% 6.92/7.21 ! [B: nat,A: nat,C2: nat] :
% 6.92/7.21 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C2 )
% 6.92/7.21 = ( plus_plus_nat @ A @ C2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % cancel_div_mod_rules(2)
% 6.92/7.21 thf(fact_3875_cancel__div__mod__rules_I2_J,axiom,
% 6.92/7.21 ! [B: int,A: int,C2: int] :
% 6.92/7.21 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C2 )
% 6.92/7.21 = ( plus_plus_int @ A @ C2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % cancel_div_mod_rules(2)
% 6.92/7.21 thf(fact_3876_cancel__div__mod__rules_I2_J,axiom,
% 6.92/7.21 ! [B: code_natural,A: code_natural,C2: code_natural] :
% 6.92/7.21 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C2 )
% 6.92/7.21 = ( plus_p4538020629002901425atural @ A @ C2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % cancel_div_mod_rules(2)
% 6.92/7.21 thf(fact_3877_div__mult1__eq,axiom,
% 6.92/7.21 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.21 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C2 ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C2 ) ) @ C2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult1_eq
% 6.92/7.21 thf(fact_3878_div__mult1__eq,axiom,
% 6.92/7.21 ! [A: int,B: int,C2: int] :
% 6.92/7.21 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C2 ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C2 ) ) @ C2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult1_eq
% 6.92/7.21 thf(fact_3879_div__mult1__eq,axiom,
% 6.92/7.21 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 6.92/7.21 ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C2 ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C2 ) ) @ C2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mult1_eq
% 6.92/7.21 thf(fact_3880_mod__le__divisor,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_le_divisor
% 6.92/7.21 thf(fact_3881_nat__mod__eq__lemma,axiom,
% 6.92/7.21 ! [X: nat,N2: nat,Y: nat] :
% 6.92/7.21 ( ( ( modulo_modulo_nat @ X @ N2 )
% 6.92/7.21 = ( modulo_modulo_nat @ Y @ N2 ) )
% 6.92/7.21 => ( ( ord_less_eq_nat @ Y @ X )
% 6.92/7.21 => ? [Q5: nat] :
% 6.92/7.21 ( X
% 6.92/7.21 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q5 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_mod_eq_lemma
% 6.92/7.21 thf(fact_3882_mod__eq__nat2E,axiom,
% 6.92/7.21 ! [M: nat,Q6: nat,N2: nat] :
% 6.92/7.21 ( ( ( modulo_modulo_nat @ M @ Q6 )
% 6.92/7.21 = ( modulo_modulo_nat @ N2 @ Q6 ) )
% 6.92/7.21 => ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.21 => ~ ! [S7: nat] :
% 6.92/7.21 ( N2
% 6.92/7.21 != ( plus_plus_nat @ M @ ( times_times_nat @ Q6 @ S7 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_eq_nat2E
% 6.92/7.21 thf(fact_3883_mod__eq__nat1E,axiom,
% 6.92/7.21 ! [M: nat,Q6: nat,N2: nat] :
% 6.92/7.21 ( ( ( modulo_modulo_nat @ M @ Q6 )
% 6.92/7.21 = ( modulo_modulo_nat @ N2 @ Q6 ) )
% 6.92/7.21 => ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.21 => ~ ! [S7: nat] :
% 6.92/7.21 ( M
% 6.92/7.21 != ( plus_plus_nat @ N2 @ ( times_times_nat @ Q6 @ S7 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_eq_nat1E
% 6.92/7.21 thf(fact_3884_div__less__mono,axiom,
% 6.92/7.21 ! [A4: nat,B5: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ A4 @ B5 )
% 6.92/7.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ( ( modulo_modulo_nat @ A4 @ N2 )
% 6.92/7.21 = zero_zero_nat )
% 6.92/7.21 => ( ( ( modulo_modulo_nat @ B5 @ N2 )
% 6.92/7.21 = zero_zero_nat )
% 6.92/7.21 => ( ord_less_nat @ ( divide_divide_nat @ A4 @ N2 ) @ ( divide_divide_nat @ B5 @ N2 ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_less_mono
% 6.92/7.21 thf(fact_3885_div__mod__decomp,axiom,
% 6.92/7.21 ! [A4: nat,N2: nat] :
% 6.92/7.21 ( A4
% 6.92/7.21 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A4 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A4 @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mod_decomp
% 6.92/7.21 thf(fact_3886_mod__mult2__eq,axiom,
% 6.92/7.21 ! [M: nat,N2: nat,Q6: nat] :
% 6.92/7.21 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N2 @ Q6 ) )
% 6.92/7.21 = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N2 ) @ Q6 ) ) @ ( modulo_modulo_nat @ M @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_mult2_eq
% 6.92/7.21 thf(fact_3887_sup__assn__def,axiom,
% 6.92/7.21 ( sup_sup_assn
% 6.92/7.21 = ( ^ [P5: assn,Q3: assn] :
% 6.92/7.21 ( abs_assn
% 6.92/7.21 @ ^ [H6: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ( rep_assn @ P5 @ H6 )
% 6.92/7.21 | ( rep_assn @ Q3 @ H6 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % sup_assn_def
% 6.92/7.21 thf(fact_3888_inf__assn__def,axiom,
% 6.92/7.21 ( inf_inf_assn
% 6.92/7.21 = ( ^ [P5: assn,Q3: assn] :
% 6.92/7.21 ( abs_assn
% 6.92/7.21 @ ^ [H6: produc3658429121746597890et_nat] :
% 6.92/7.21 ( ( rep_assn @ P5 @ H6 )
% 6.92/7.21 & ( rep_assn @ Q3 @ H6 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inf_assn_def
% 6.92/7.21 thf(fact_3889_split__mod,axiom,
% 6.92/7.21 ! [P2: nat > $o,M: nat,N2: nat] :
% 6.92/7.21 ( ( P2 @ ( modulo_modulo_nat @ M @ N2 ) )
% 6.92/7.21 = ( ( ( N2 = zero_zero_nat )
% 6.92/7.21 => ( P2 @ M ) )
% 6.92/7.21 & ( ( N2 != zero_zero_nat )
% 6.92/7.21 => ! [I: nat,J: nat] :
% 6.92/7.21 ( ( ord_less_nat @ J @ N2 )
% 6.92/7.21 => ( ( M
% 6.92/7.21 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I ) @ J ) )
% 6.92/7.21 => ( P2 @ J ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % split_mod
% 6.92/7.21 thf(fact_3890_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 6.92/7.21 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 6.92/7.21 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 6.92/7.21 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 6.92/7.21 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C2 ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 6.92/7.21 thf(fact_3891_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 6.92/7.21 ! [C2: nat,A: nat,B: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 6.92/7.21 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 6.92/7.21 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 6.92/7.21 thf(fact_3892_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 6.92/7.21 ! [C2: int,A: int,B: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.21 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C2 ) )
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 6.92/7.21 thf(fact_3893_times__assn__def,axiom,
% 6.92/7.21 ( times_times_assn
% 6.92/7.21 = ( ^ [P5: assn,Q3: assn] : ( abs_assn @ ( times_assn_raw @ ( rep_assn @ P5 ) @ ( rep_assn @ Q3 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % times_assn_def
% 6.92/7.21 thf(fact_3894_distrib__right__NO__MATCH,axiom,
% 6.92/7.21 ! [X: nat,Y: nat,C2: rat,A: rat,B: rat] :
% 6.92/7.21 ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ C2 )
% 6.92/7.21 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_right_NO_MATCH
% 6.92/7.21 thf(fact_3895_distrib__right__NO__MATCH,axiom,
% 6.92/7.21 ! [X: nat,Y: nat,C2: nat,A: nat,B: nat] :
% 6.92/7.21 ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ C2 )
% 6.92/7.21 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_plus_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_right_NO_MATCH
% 6.92/7.21 thf(fact_3896_distrib__right__NO__MATCH,axiom,
% 6.92/7.21 ! [X: nat,Y: nat,C2: int,A: int,B: int] :
% 6.92/7.21 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ C2 )
% 6.92/7.21 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_right_NO_MATCH
% 6.92/7.21 thf(fact_3897_distrib__right__NO__MATCH,axiom,
% 6.92/7.21 ! [X: int,Y: int,C2: rat,A: rat,B: rat] :
% 6.92/7.21 ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ C2 )
% 6.92/7.21 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_right_NO_MATCH
% 6.92/7.21 thf(fact_3898_distrib__right__NO__MATCH,axiom,
% 6.92/7.21 ! [X: int,Y: int,C2: nat,A: nat,B: nat] :
% 6.92/7.21 ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ C2 )
% 6.92/7.21 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_plus_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_right_NO_MATCH
% 6.92/7.21 thf(fact_3899_distrib__right__NO__MATCH,axiom,
% 6.92/7.21 ! [X: int,Y: int,C2: int,A: int,B: int] :
% 6.92/7.21 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ C2 )
% 6.92/7.21 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_right_NO_MATCH
% 6.92/7.21 thf(fact_3900_distrib__right__NO__MATCH,axiom,
% 6.92/7.21 ! [X: code_natural,Y: code_natural,C2: rat,A: rat,B: rat] :
% 6.92/7.21 ( ( nO_MAT3836730678284324717al_rat @ ( divide5121882707175180666atural @ X @ Y ) @ C2 )
% 6.92/7.21 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_right_NO_MATCH
% 6.92/7.21 thf(fact_3901_distrib__right__NO__MATCH,axiom,
% 6.92/7.21 ! [X: code_natural,Y: code_natural,C2: nat,A: nat,B: nat] :
% 6.92/7.21 ( ( nO_MAT4471860738370820453al_nat @ ( divide5121882707175180666atural @ X @ Y ) @ C2 )
% 6.92/7.21 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_plus_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_right_NO_MATCH
% 6.92/7.21 thf(fact_3902_distrib__right__NO__MATCH,axiom,
% 6.92/7.21 ! [X: code_natural,Y: code_natural,C2: int,A: int,B: int] :
% 6.92/7.21 ( ( nO_MAT4469370267861770177al_int @ ( divide5121882707175180666atural @ X @ Y ) @ C2 )
% 6.92/7.21 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_right_NO_MATCH
% 6.92/7.21 thf(fact_3903_distrib__right__NO__MATCH,axiom,
% 6.92/7.21 ! [X: rat,Y: rat,C2: rat,A: rat,B: rat] :
% 6.92/7.21 ( ( nO_MATCH_rat_rat @ ( divide_divide_rat @ X @ Y ) @ C2 )
% 6.92/7.21 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 6.92/7.21 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % distrib_right_NO_MATCH
% 6.92/7.21 thf(fact_3904_ex__less__of__nat__mult,axiom,
% 6.92/7.21 ! [X: rat,Y: rat] :
% 6.92/7.21 ( ( ord_less_rat @ zero_zero_rat @ X )
% 6.92/7.21 => ? [N5: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N5 ) @ X ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % ex_less_of_nat_mult
% 6.92/7.21 thf(fact_3905_of__nat__code,axiom,
% 6.92/7.21 ( semiri681578069525770553at_rat
% 6.92/7.21 = ( ^ [N: nat] :
% 6.92/7.21 ( semiri7787848453975740701ux_rat
% 6.92/7.21 @ ^ [I: rat] : ( plus_plus_rat @ I @ one_one_rat )
% 6.92/7.21 @ N
% 6.92/7.21 @ zero_zero_rat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_code
% 6.92/7.21 thf(fact_3906_of__nat__code,axiom,
% 6.92/7.21 ( semiri1314217659103216013at_int
% 6.92/7.21 = ( ^ [N: nat] :
% 6.92/7.21 ( semiri8420488043553186161ux_int
% 6.92/7.21 @ ^ [I: int] : ( plus_plus_int @ I @ one_one_int )
% 6.92/7.21 @ N
% 6.92/7.21 @ zero_zero_int ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_code
% 6.92/7.21 thf(fact_3907_of__nat__code,axiom,
% 6.92/7.21 ( semiri1316708129612266289at_nat
% 6.92/7.21 = ( ^ [N: nat] :
% 6.92/7.21 ( semiri8422978514062236437ux_nat
% 6.92/7.21 @ ^ [I: nat] : ( plus_plus_nat @ I @ one_one_nat )
% 6.92/7.21 @ N
% 6.92/7.21 @ zero_zero_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_code
% 6.92/7.21 thf(fact_3908_of__nat__code,axiom,
% 6.92/7.21 ( semiri4939895301339042750nteger
% 6.92/7.21 = ( ^ [N: nat] :
% 6.92/7.21 ( semiri4055485073559036834nteger
% 6.92/7.21 @ ^ [I: code_integer] : ( plus_p5714425477246183910nteger @ I @ one_one_Code_integer )
% 6.92/7.21 @ N
% 6.92/7.21 @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_code
% 6.92/7.21 thf(fact_3909_reals__Archimedean2,axiom,
% 6.92/7.21 ! [X: rat] :
% 6.92/7.21 ? [N5: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N5 ) ) ).
% 6.92/7.21
% 6.92/7.21 % reals_Archimedean2
% 6.92/7.21 thf(fact_3910_real__arch__simple,axiom,
% 6.92/7.21 ! [X: rat] :
% 6.92/7.21 ? [N5: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N5 ) ) ).
% 6.92/7.21
% 6.92/7.21 % real_arch_simple
% 6.92/7.21 thf(fact_3911_Suc__times__mod__eq,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 6.92/7.21 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N2 ) ) @ M )
% 6.92/7.21 = one_one_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_times_mod_eq
% 6.92/7.21 thf(fact_3912_nat_Oinject,axiom,
% 6.92/7.21 ! [X2: nat,Y2: nat] :
% 6.92/7.21 ( ( ( suc @ X2 )
% 6.92/7.21 = ( suc @ Y2 ) )
% 6.92/7.21 = ( X2 = Y2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat.inject
% 6.92/7.21 thf(fact_3913_old_Onat_Oinject,axiom,
% 6.92/7.21 ! [Nat: nat,Nat2: nat] :
% 6.92/7.21 ( ( ( suc @ Nat )
% 6.92/7.21 = ( suc @ Nat2 ) )
% 6.92/7.21 = ( Nat = Nat2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % old.nat.inject
% 6.92/7.21 thf(fact_3914_Suc__less__eq,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 6.92/7.21 = ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_less_eq
% 6.92/7.21 thf(fact_3915_Suc__mono,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.21 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_mono
% 6.92/7.21 thf(fact_3916_lessI,axiom,
% 6.92/7.21 ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % lessI
% 6.92/7.21 thf(fact_3917_Suc__le__mono,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( suc @ M ) )
% 6.92/7.21 = ( ord_less_eq_nat @ N2 @ M ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_le_mono
% 6.92/7.21 thf(fact_3918_add__Suc__right,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( plus_plus_nat @ M @ ( suc @ N2 ) )
% 6.92/7.21 = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % add_Suc_right
% 6.92/7.21 thf(fact_3919_less__Suc0,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 6.92/7.21 = ( N2 = zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_Suc0
% 6.92/7.21 thf(fact_3920_zero__less__Suc,axiom,
% 6.92/7.21 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % zero_less_Suc
% 6.92/7.21 thf(fact_3921_mult__eq__1__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ( times_times_nat @ M @ N2 )
% 6.92/7.21 = ( suc @ zero_zero_nat ) )
% 6.92/7.21 = ( ( M
% 6.92/7.21 = ( suc @ zero_zero_nat ) )
% 6.92/7.21 & ( N2
% 6.92/7.21 = ( suc @ zero_zero_nat ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mult_eq_1_iff
% 6.92/7.21 thf(fact_3922_one__eq__mult__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ( suc @ zero_zero_nat )
% 6.92/7.21 = ( times_times_nat @ M @ N2 ) )
% 6.92/7.21 = ( ( M
% 6.92/7.21 = ( suc @ zero_zero_nat ) )
% 6.92/7.21 & ( N2
% 6.92/7.21 = ( suc @ zero_zero_nat ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % one_eq_mult_iff
% 6.92/7.21 thf(fact_3923_mult__Suc__right,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( times_times_nat @ M @ ( suc @ N2 ) )
% 6.92/7.21 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mult_Suc_right
% 6.92/7.21 thf(fact_3924_mod__neg__neg__trivial,axiom,
% 6.92/7.21 ! [K2: int,L: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ K2 @ zero_zero_int )
% 6.92/7.21 => ( ( ord_less_int @ L @ K2 )
% 6.92/7.21 => ( ( modulo_modulo_int @ K2 @ L )
% 6.92/7.21 = K2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_neg_neg_trivial
% 6.92/7.21 thf(fact_3925_mod__pos__pos__trivial,axiom,
% 6.92/7.21 ! [K2: int,L: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.21 => ( ( ord_less_int @ K2 @ L )
% 6.92/7.21 => ( ( modulo_modulo_int @ K2 @ L )
% 6.92/7.21 = K2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_pos_pos_trivial
% 6.92/7.21 thf(fact_3926_div__pos__pos__trivial,axiom,
% 6.92/7.21 ! [K2: int,L: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.21 => ( ( ord_less_int @ K2 @ L )
% 6.92/7.21 => ( ( divide_divide_int @ K2 @ L )
% 6.92/7.21 = zero_zero_int ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_pos_pos_trivial
% 6.92/7.21 thf(fact_3927_div__neg__neg__trivial,axiom,
% 6.92/7.21 ! [K2: int,L: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ K2 @ zero_zero_int )
% 6.92/7.21 => ( ( ord_less_int @ L @ K2 )
% 6.92/7.21 => ( ( divide_divide_int @ K2 @ L )
% 6.92/7.21 = zero_zero_int ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_neg_neg_trivial
% 6.92/7.21 thf(fact_3928_of__nat__Suc,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 6.92/7.21 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_Suc
% 6.92/7.21 thf(fact_3929_of__nat__Suc,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 6.92/7.21 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_Suc
% 6.92/7.21 thf(fact_3930_of__nat__Suc,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 6.92/7.21 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_Suc
% 6.92/7.21 thf(fact_3931_of__nat__Suc,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ( ( semiri4939895301339042750nteger @ ( suc @ M ) )
% 6.92/7.21 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_Suc
% 6.92/7.21 thf(fact_3932_one__le__mult__iff,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) )
% 6.92/7.21 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 6.92/7.21 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % one_le_mult_iff
% 6.92/7.21 thf(fact_3933_Suc__mod__mult__self4,axiom,
% 6.92/7.21 ! [N2: nat,K2: nat,M: nat] :
% 6.92/7.21 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N2 @ K2 ) @ M ) ) @ N2 )
% 6.92/7.21 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_mod_mult_self4
% 6.92/7.21 thf(fact_3934_Suc__mod__mult__self3,axiom,
% 6.92/7.21 ! [K2: nat,N2: nat,M: nat] :
% 6.92/7.21 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K2 @ N2 ) @ M ) ) @ N2 )
% 6.92/7.21 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_mod_mult_self3
% 6.92/7.21 thf(fact_3935_Suc__mod__mult__self2,axiom,
% 6.92/7.21 ! [M: nat,N2: nat,K2: nat] :
% 6.92/7.21 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N2 @ K2 ) ) ) @ N2 )
% 6.92/7.21 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_mod_mult_self2
% 6.92/7.21 thf(fact_3936_Suc__mod__mult__self1,axiom,
% 6.92/7.21 ! [M: nat,K2: nat,N2: nat] :
% 6.92/7.21 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K2 @ N2 ) ) ) @ N2 )
% 6.92/7.21 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_mod_mult_self1
% 6.92/7.21 thf(fact_3937_zle__add1__eq__le,axiom,
% 6.92/7.21 ! [W2: int,Z3: int] :
% 6.92/7.21 ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z3 @ one_one_int ) )
% 6.92/7.21 = ( ord_less_eq_int @ W2 @ Z3 ) ) ).
% 6.92/7.21
% 6.92/7.21 % zle_add1_eq_le
% 6.92/7.21 thf(fact_3938_neg__mod__conj,axiom,
% 6.92/7.21 ! [B: int,A: int] :
% 6.92/7.21 ( ( ord_less_int @ B @ zero_zero_int )
% 6.92/7.21 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 6.92/7.21 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % neg_mod_conj
% 6.92/7.21 thf(fact_3939_pos__mod__conj,axiom,
% 6.92/7.21 ! [B: int,A: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.21 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 6.92/7.21 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % pos_mod_conj
% 6.92/7.21 thf(fact_3940_zmod__trivial__iff,axiom,
% 6.92/7.21 ! [I2: int,K2: int] :
% 6.92/7.21 ( ( ( modulo_modulo_int @ I2 @ K2 )
% 6.92/7.21 = I2 )
% 6.92/7.21 = ( ( K2 = zero_zero_int )
% 6.92/7.21 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 6.92/7.21 & ( ord_less_int @ I2 @ K2 ) )
% 6.92/7.21 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 6.92/7.21 & ( ord_less_int @ K2 @ I2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zmod_trivial_iff
% 6.92/7.21 thf(fact_3941_zmod__le__nonneg__dividend,axiom,
% 6.92/7.21 ! [M: int,K2: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 6.92/7.21 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K2 ) @ M ) ) ).
% 6.92/7.21
% 6.92/7.21 % zmod_le_nonneg_dividend
% 6.92/7.21 thf(fact_3942_zero__le__imp__eq__int,axiom,
% 6.92/7.21 ! [K2: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.21 => ? [N5: nat] :
% 6.92/7.21 ( K2
% 6.92/7.21 = ( semiri1314217659103216013at_int @ N5 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zero_le_imp_eq_int
% 6.92/7.21 thf(fact_3943_nonneg__int__cases,axiom,
% 6.92/7.21 ! [K2: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.21 => ~ ! [N5: nat] :
% 6.92/7.21 ( K2
% 6.92/7.21 != ( semiri1314217659103216013at_int @ N5 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nonneg_int_cases
% 6.92/7.21 thf(fact_3944_le__imp__0__less,axiom,
% 6.92/7.21 ! [Z3: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.21 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z3 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % le_imp_0_less
% 6.92/7.21 thf(fact_3945_int__one__le__iff__zero__less,axiom,
% 6.92/7.21 ! [Z3: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ one_one_int @ Z3 )
% 6.92/7.21 = ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_one_le_iff_zero_less
% 6.92/7.21 thf(fact_3946_zless__imp__add1__zle,axiom,
% 6.92/7.21 ! [W2: int,Z3: int] :
% 6.92/7.21 ( ( ord_less_int @ W2 @ Z3 )
% 6.92/7.21 => ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z3 ) ) ).
% 6.92/7.21
% 6.92/7.21 % zless_imp_add1_zle
% 6.92/7.21 thf(fact_3947_add1__zle__eq,axiom,
% 6.92/7.21 ! [W2: int,Z3: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z3 )
% 6.92/7.21 = ( ord_less_int @ W2 @ Z3 ) ) ).
% 6.92/7.21
% 6.92/7.21 % add1_zle_eq
% 6.92/7.21 thf(fact_3948_zle__iff__zadd,axiom,
% 6.92/7.21 ( ord_less_eq_int
% 6.92/7.21 = ( ^ [W3: int,Z: int] :
% 6.92/7.21 ? [N: nat] :
% 6.92/7.21 ( Z
% 6.92/7.21 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zle_iff_zadd
% 6.92/7.21 thf(fact_3949_incr__mult__lemma,axiom,
% 6.92/7.21 ! [D2: int,P2: int > $o,K2: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ D2 )
% 6.92/7.21 => ( ! [X3: int] :
% 6.92/7.21 ( ( P2 @ X3 )
% 6.92/7.21 => ( P2 @ ( plus_plus_int @ X3 @ D2 ) ) )
% 6.92/7.21 => ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.21 => ! [X6: int] :
% 6.92/7.21 ( ( P2 @ X6 )
% 6.92/7.21 => ( P2 @ ( plus_plus_int @ X6 @ ( times_times_int @ K2 @ D2 ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % incr_mult_lemma
% 6.92/7.21 thf(fact_3950_unique__quotient__lemma__neg,axiom,
% 6.92/7.21 ! [B: int,Q7: int,R7: int,Q6: int,R2: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q7 ) @ R7 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R2 ) )
% 6.92/7.21 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 6.92/7.21 => ( ( ord_less_int @ B @ R2 )
% 6.92/7.21 => ( ( ord_less_int @ B @ R7 )
% 6.92/7.21 => ( ord_less_eq_int @ Q6 @ Q7 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_quotient_lemma_neg
% 6.92/7.21 thf(fact_3951_unique__quotient__lemma,axiom,
% 6.92/7.21 ! [B: int,Q7: int,R7: int,Q6: int,R2: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q7 ) @ R7 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R2 ) )
% 6.92/7.21 => ( ( ord_less_eq_int @ zero_zero_int @ R7 )
% 6.92/7.21 => ( ( ord_less_int @ R7 @ B )
% 6.92/7.21 => ( ( ord_less_int @ R2 @ B )
% 6.92/7.21 => ( ord_less_eq_int @ Q7 @ Q6 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % unique_quotient_lemma
% 6.92/7.21 thf(fact_3952_zdiv__mono2__neg__lemma,axiom,
% 6.92/7.21 ! [B: int,Q6: int,R2: int,B2: int,Q7: int,R7: int] :
% 6.92/7.21 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R2 )
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ B2 @ Q7 ) @ R7 ) )
% 6.92/7.21 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q7 ) @ R7 ) @ zero_zero_int )
% 6.92/7.21 => ( ( ord_less_int @ R2 @ B )
% 6.92/7.21 => ( ( ord_less_eq_int @ zero_zero_int @ R7 )
% 6.92/7.21 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 6.92/7.21 => ( ( ord_less_eq_int @ B2 @ B )
% 6.92/7.21 => ( ord_less_eq_int @ Q7 @ Q6 ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zdiv_mono2_neg_lemma
% 6.92/7.21 thf(fact_3953_zdiv__mono2__lemma,axiom,
% 6.92/7.21 ! [B: int,Q6: int,R2: int,B2: int,Q7: int,R7: int] :
% 6.92/7.21 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R2 )
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ B2 @ Q7 ) @ R7 ) )
% 6.92/7.21 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q7 ) @ R7 ) )
% 6.92/7.21 => ( ( ord_less_int @ R7 @ B2 )
% 6.92/7.21 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 6.92/7.21 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 6.92/7.21 => ( ( ord_less_eq_int @ B2 @ B )
% 6.92/7.21 => ( ord_less_eq_int @ Q6 @ Q7 ) ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zdiv_mono2_lemma
% 6.92/7.21 thf(fact_3954_int__mod__pos__eq,axiom,
% 6.92/7.21 ! [A: int,B: int,Q6: int,R2: int] :
% 6.92/7.21 ( ( A
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R2 ) )
% 6.92/7.21 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 6.92/7.21 => ( ( ord_less_int @ R2 @ B )
% 6.92/7.21 => ( ( modulo_modulo_int @ A @ B )
% 6.92/7.21 = R2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_mod_pos_eq
% 6.92/7.21 thf(fact_3955_int__mod__neg__eq,axiom,
% 6.92/7.21 ! [A: int,B: int,Q6: int,R2: int] :
% 6.92/7.21 ( ( A
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R2 ) )
% 6.92/7.21 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 6.92/7.21 => ( ( ord_less_int @ B @ R2 )
% 6.92/7.21 => ( ( modulo_modulo_int @ A @ B )
% 6.92/7.21 = R2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_mod_neg_eq
% 6.92/7.21 thf(fact_3956_q__pos__lemma,axiom,
% 6.92/7.21 ! [B2: int,Q7: int,R7: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q7 ) @ R7 ) )
% 6.92/7.21 => ( ( ord_less_int @ R7 @ B2 )
% 6.92/7.21 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 6.92/7.21 => ( ord_less_eq_int @ zero_zero_int @ Q7 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % q_pos_lemma
% 6.92/7.21 thf(fact_3957_split__zmod,axiom,
% 6.92/7.21 ! [P2: int > $o,N2: int,K2: int] :
% 6.92/7.21 ( ( P2 @ ( modulo_modulo_int @ N2 @ K2 ) )
% 6.92/7.21 = ( ( ( K2 = zero_zero_int )
% 6.92/7.21 => ( P2 @ N2 ) )
% 6.92/7.21 & ( ( ord_less_int @ zero_zero_int @ K2 )
% 6.92/7.21 => ! [I: int,J: int] :
% 6.92/7.21 ( ( ( ord_less_eq_int @ zero_zero_int @ J )
% 6.92/7.21 & ( ord_less_int @ J @ K2 )
% 6.92/7.21 & ( N2
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 6.92/7.21 => ( P2 @ J ) ) )
% 6.92/7.21 & ( ( ord_less_int @ K2 @ zero_zero_int )
% 6.92/7.21 => ! [I: int,J: int] :
% 6.92/7.21 ( ( ( ord_less_int @ K2 @ J )
% 6.92/7.21 & ( ord_less_eq_int @ J @ zero_zero_int )
% 6.92/7.21 & ( N2
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 6.92/7.21 => ( P2 @ J ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % split_zmod
% 6.92/7.21 thf(fact_3958_neg__mod__sign,axiom,
% 6.92/7.21 ! [L: int,K2: int] :
% 6.92/7.21 ( ( ord_less_int @ L @ zero_zero_int )
% 6.92/7.21 => ( ord_less_eq_int @ ( modulo_modulo_int @ K2 @ L ) @ zero_zero_int ) ) ).
% 6.92/7.21
% 6.92/7.21 % neg_mod_sign
% 6.92/7.21 thf(fact_3959_Euclidean__Division_Opos__mod__sign,axiom,
% 6.92/7.21 ! [L: int,K2: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ L )
% 6.92/7.21 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K2 @ L ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % Euclidean_Division.pos_mod_sign
% 6.92/7.21 thf(fact_3960_mod__pos__neg__trivial,axiom,
% 6.92/7.21 ! [K2: int,L: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ K2 )
% 6.92/7.21 => ( ( ord_less_eq_int @ ( plus_plus_int @ K2 @ L ) @ zero_zero_int )
% 6.92/7.21 => ( ( modulo_modulo_int @ K2 @ L )
% 6.92/7.21 = ( plus_plus_int @ K2 @ L ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_pos_neg_trivial
% 6.92/7.21 thf(fact_3961_zdiv__mono1,axiom,
% 6.92/7.21 ! [A: int,A2: int,B: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ A @ A2 )
% 6.92/7.21 => ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.21 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A2 @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zdiv_mono1
% 6.92/7.21 thf(fact_3962_zdiv__mono2,axiom,
% 6.92/7.21 ! [A: int,B2: int,B: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.21 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 6.92/7.21 => ( ( ord_less_eq_int @ B2 @ B )
% 6.92/7.21 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zdiv_mono2
% 6.92/7.21 thf(fact_3963_zdiv__eq__0__iff,axiom,
% 6.92/7.21 ! [I2: int,K2: int] :
% 6.92/7.21 ( ( ( divide_divide_int @ I2 @ K2 )
% 6.92/7.21 = zero_zero_int )
% 6.92/7.21 = ( ( K2 = zero_zero_int )
% 6.92/7.21 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 6.92/7.21 & ( ord_less_int @ I2 @ K2 ) )
% 6.92/7.21 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 6.92/7.21 & ( ord_less_int @ K2 @ I2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zdiv_eq_0_iff
% 6.92/7.21 thf(fact_3964_zdiv__mono1__neg,axiom,
% 6.92/7.21 ! [A: int,A2: int,B: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ A @ A2 )
% 6.92/7.21 => ( ( ord_less_int @ B @ zero_zero_int )
% 6.92/7.21 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zdiv_mono1_neg
% 6.92/7.21 thf(fact_3965_zdiv__mono2__neg,axiom,
% 6.92/7.21 ! [A: int,B2: int,B: int] :
% 6.92/7.21 ( ( ord_less_int @ A @ zero_zero_int )
% 6.92/7.21 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 6.92/7.21 => ( ( ord_less_eq_int @ B2 @ B )
% 6.92/7.21 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zdiv_mono2_neg
% 6.92/7.21 thf(fact_3966_div__int__pos__iff,axiom,
% 6.92/7.21 ! [K2: int,L: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K2 @ L ) )
% 6.92/7.21 = ( ( K2 = zero_zero_int )
% 6.92/7.21 | ( L = zero_zero_int )
% 6.92/7.21 | ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.21 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 6.92/7.21 | ( ( ord_less_int @ K2 @ zero_zero_int )
% 6.92/7.21 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_int_pos_iff
% 6.92/7.21 thf(fact_3967_div__positive__int,axiom,
% 6.92/7.21 ! [L: int,K2: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ L @ K2 )
% 6.92/7.21 => ( ( ord_less_int @ zero_zero_int @ L )
% 6.92/7.21 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K2 @ L ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_positive_int
% 6.92/7.21 thf(fact_3968_div__nonneg__neg__le0,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.21 => ( ( ord_less_int @ B @ zero_zero_int )
% 6.92/7.21 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_nonneg_neg_le0
% 6.92/7.21 thf(fact_3969_div__nonpos__pos__le0,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 6.92/7.21 => ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.21 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_nonpos_pos_le0
% 6.92/7.21 thf(fact_3970_pos__imp__zdiv__pos__iff,axiom,
% 6.92/7.21 ! [K2: int,I2: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ K2 )
% 6.92/7.21 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K2 ) )
% 6.92/7.21 = ( ord_less_eq_int @ K2 @ I2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % pos_imp_zdiv_pos_iff
% 6.92/7.21 thf(fact_3971_neg__imp__zdiv__nonneg__iff,axiom,
% 6.92/7.21 ! [B: int,A: int] :
% 6.92/7.21 ( ( ord_less_int @ B @ zero_zero_int )
% 6.92/7.21 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 6.92/7.21 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % neg_imp_zdiv_nonneg_iff
% 6.92/7.21 thf(fact_3972_pos__imp__zdiv__nonneg__iff,axiom,
% 6.92/7.21 ! [B: int,A: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.21 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 6.92/7.21 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % pos_imp_zdiv_nonneg_iff
% 6.92/7.21 thf(fact_3973_nonneg1__imp__zdiv__pos__iff,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.21 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 6.92/7.21 = ( ( ord_less_eq_int @ B @ A )
% 6.92/7.21 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nonneg1_imp_zdiv_pos_iff
% 6.92/7.21 thf(fact_3974_verit__le__mono__div__int,axiom,
% 6.92/7.21 ! [A4: int,B5: int,N2: int] :
% 6.92/7.21 ( ( ord_less_int @ A4 @ B5 )
% 6.92/7.21 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 6.92/7.21 => ( ord_less_eq_int
% 6.92/7.21 @ ( plus_plus_int @ ( divide_divide_int @ A4 @ N2 )
% 6.92/7.21 @ ( if_int
% 6.92/7.21 @ ( ( modulo_modulo_int @ B5 @ N2 )
% 6.92/7.21 = zero_zero_int )
% 6.92/7.21 @ one_one_int
% 6.92/7.21 @ zero_zero_int ) )
% 6.92/7.21 @ ( divide_divide_int @ B5 @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % verit_le_mono_div_int
% 6.92/7.21 thf(fact_3975_zmod__zmult2__eq,axiom,
% 6.92/7.21 ! [C2: int,A: int,B: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.21 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C2 ) )
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zmod_zmult2_eq
% 6.92/7.21 thf(fact_3976_split__pos__lemma,axiom,
% 6.92/7.21 ! [K2: int,P2: int > int > $o,N2: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ K2 )
% 6.92/7.21 => ( ( P2 @ ( divide_divide_int @ N2 @ K2 ) @ ( modulo_modulo_int @ N2 @ K2 ) )
% 6.92/7.21 = ( ! [I: int,J: int] :
% 6.92/7.21 ( ( ( ord_less_eq_int @ zero_zero_int @ J )
% 6.92/7.21 & ( ord_less_int @ J @ K2 )
% 6.92/7.21 & ( N2
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 6.92/7.21 => ( P2 @ I @ J ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % split_pos_lemma
% 6.92/7.21 thf(fact_3977_split__neg__lemma,axiom,
% 6.92/7.21 ! [K2: int,P2: int > int > $o,N2: int] :
% 6.92/7.21 ( ( ord_less_int @ K2 @ zero_zero_int )
% 6.92/7.21 => ( ( P2 @ ( divide_divide_int @ N2 @ K2 ) @ ( modulo_modulo_int @ N2 @ K2 ) )
% 6.92/7.21 = ( ! [I: int,J: int] :
% 6.92/7.21 ( ( ( ord_less_int @ K2 @ J )
% 6.92/7.21 & ( ord_less_eq_int @ J @ zero_zero_int )
% 6.92/7.21 & ( N2
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 6.92/7.21 => ( P2 @ I @ J ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % split_neg_lemma
% 6.92/7.21 thf(fact_3978_int__div__pos__eq,axiom,
% 6.92/7.21 ! [A: int,B: int,Q6: int,R2: int] :
% 6.92/7.21 ( ( A
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R2 ) )
% 6.92/7.21 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 6.92/7.21 => ( ( ord_less_int @ R2 @ B )
% 6.92/7.21 => ( ( divide_divide_int @ A @ B )
% 6.92/7.21 = Q6 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_div_pos_eq
% 6.92/7.21 thf(fact_3979_int__div__neg__eq,axiom,
% 6.92/7.21 ! [A: int,B: int,Q6: int,R2: int] :
% 6.92/7.21 ( ( A
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R2 ) )
% 6.92/7.21 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 6.92/7.21 => ( ( ord_less_int @ B @ R2 )
% 6.92/7.21 => ( ( divide_divide_int @ A @ B )
% 6.92/7.21 = Q6 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_div_neg_eq
% 6.92/7.21 thf(fact_3980_split__zdiv,axiom,
% 6.92/7.21 ! [P2: int > $o,N2: int,K2: int] :
% 6.92/7.21 ( ( P2 @ ( divide_divide_int @ N2 @ K2 ) )
% 6.92/7.21 = ( ( ( K2 = zero_zero_int )
% 6.92/7.21 => ( P2 @ zero_zero_int ) )
% 6.92/7.21 & ( ( ord_less_int @ zero_zero_int @ K2 )
% 6.92/7.21 => ! [I: int,J: int] :
% 6.92/7.21 ( ( ( ord_less_eq_int @ zero_zero_int @ J )
% 6.92/7.21 & ( ord_less_int @ J @ K2 )
% 6.92/7.21 & ( N2
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 6.92/7.21 => ( P2 @ I ) ) )
% 6.92/7.21 & ( ( ord_less_int @ K2 @ zero_zero_int )
% 6.92/7.21 => ! [I: int,J: int] :
% 6.92/7.21 ( ( ( ord_less_int @ K2 @ J )
% 6.92/7.21 & ( ord_less_eq_int @ J @ zero_zero_int )
% 6.92/7.21 & ( N2
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 6.92/7.21 => ( P2 @ I ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % split_zdiv
% 6.92/7.21 thf(fact_3981_div__mod__decomp__int,axiom,
% 6.92/7.21 ! [A4: int,N2: int] :
% 6.92/7.21 ( A4
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A4 @ N2 ) @ N2 ) @ ( modulo_modulo_int @ A4 @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_mod_decomp_int
% 6.92/7.21 thf(fact_3982_int__div__less__self,axiom,
% 6.92/7.21 ! [X: int,K2: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ X )
% 6.92/7.21 => ( ( ord_less_int @ one_one_int @ K2 )
% 6.92/7.21 => ( ord_less_int @ ( divide_divide_int @ X @ K2 ) @ X ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_div_less_self
% 6.92/7.21 thf(fact_3983_zdiv__mono__strict,axiom,
% 6.92/7.21 ! [A4: int,B5: int,N2: int] :
% 6.92/7.21 ( ( ord_less_int @ A4 @ B5 )
% 6.92/7.21 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 6.92/7.21 => ( ( ( modulo_modulo_int @ A4 @ N2 )
% 6.92/7.21 = zero_zero_int )
% 6.92/7.21 => ( ( ( modulo_modulo_int @ B5 @ N2 )
% 6.92/7.21 = zero_zero_int )
% 6.92/7.21 => ( ord_less_int @ ( divide_divide_int @ A4 @ N2 ) @ ( divide_divide_int @ B5 @ N2 ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zdiv_mono_strict
% 6.92/7.21 thf(fact_3984_pos__imp__zdiv__neg__iff,axiom,
% 6.92/7.21 ! [B: int,A: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.21 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 6.92/7.21 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % pos_imp_zdiv_neg_iff
% 6.92/7.21 thf(fact_3985_neg__imp__zdiv__neg__iff,axiom,
% 6.92/7.21 ! [B: int,A: int] :
% 6.92/7.21 ( ( ord_less_int @ B @ zero_zero_int )
% 6.92/7.21 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 6.92/7.21 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % neg_imp_zdiv_neg_iff
% 6.92/7.21 thf(fact_3986_div__neg__pos__less0,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( ord_less_int @ A @ zero_zero_int )
% 6.92/7.21 => ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.21 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_neg_pos_less0
% 6.92/7.21 thf(fact_3987_Euclidean__Division_Opos__mod__bound,axiom,
% 6.92/7.21 ! [L: int,K2: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ L )
% 6.92/7.21 => ( ord_less_int @ ( modulo_modulo_int @ K2 @ L ) @ L ) ) ).
% 6.92/7.21
% 6.92/7.21 % Euclidean_Division.pos_mod_bound
% 6.92/7.21 thf(fact_3988_neg__mod__bound,axiom,
% 6.92/7.21 ! [L: int,K2: int] :
% 6.92/7.21 ( ( ord_less_int @ L @ zero_zero_int )
% 6.92/7.21 => ( ord_less_int @ L @ ( modulo_modulo_int @ K2 @ L ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % neg_mod_bound
% 6.92/7.21 thf(fact_3989_zmult__zless__mono2,axiom,
% 6.92/7.21 ! [I2: int,J2: int,K2: int] :
% 6.92/7.21 ( ( ord_less_int @ I2 @ J2 )
% 6.92/7.21 => ( ( ord_less_int @ zero_zero_int @ K2 )
% 6.92/7.21 => ( ord_less_int @ ( times_times_int @ K2 @ I2 ) @ ( times_times_int @ K2 @ J2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zmult_zless_mono2
% 6.92/7.21 thf(fact_3990_pos__zmult__eq__1__iff,axiom,
% 6.92/7.21 ! [M: int,N2: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ M )
% 6.92/7.21 => ( ( ( times_times_int @ M @ N2 )
% 6.92/7.21 = one_one_int )
% 6.92/7.21 = ( ( M = one_one_int )
% 6.92/7.21 & ( N2 = one_one_int ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % pos_zmult_eq_1_iff
% 6.92/7.21 thf(fact_3991_int__Suc,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 6.92/7.21 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_Suc
% 6.92/7.21 thf(fact_3992_int__ops_I4_J,axiom,
% 6.92/7.21 ! [A: nat] :
% 6.92/7.21 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 6.92/7.21 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_ops(4)
% 6.92/7.21 thf(fact_3993_int__if,axiom,
% 6.92/7.21 ! [P2: $o,A: nat,B: nat] :
% 6.92/7.21 ( ( P2
% 6.92/7.21 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P2 @ A @ B ) )
% 6.92/7.21 = ( semiri1314217659103216013at_int @ A ) ) )
% 6.92/7.21 & ( ~ P2
% 6.92/7.21 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P2 @ A @ B ) )
% 6.92/7.21 = ( semiri1314217659103216013at_int @ B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_if
% 6.92/7.21 thf(fact_3994_nat__int__comparison_I1_J,axiom,
% 6.92/7.21 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 6.92/7.21 = ( ^ [A5: nat,B4: nat] :
% 6.92/7.21 ( ( semiri1314217659103216013at_int @ A5 )
% 6.92/7.21 = ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_int_comparison(1)
% 6.92/7.21 thf(fact_3995_zless__iff__Suc__zadd,axiom,
% 6.92/7.21 ( ord_less_int
% 6.92/7.21 = ( ^ [W3: int,Z: int] :
% 6.92/7.21 ? [N: nat] :
% 6.92/7.21 ( Z
% 6.92/7.21 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zless_iff_Suc_zadd
% 6.92/7.21 thf(fact_3996_int__gr__induct,axiom,
% 6.92/7.21 ! [K2: int,I2: int,P2: int > $o] :
% 6.92/7.21 ( ( ord_less_int @ K2 @ I2 )
% 6.92/7.21 => ( ( P2 @ ( plus_plus_int @ K2 @ one_one_int ) )
% 6.92/7.21 => ( ! [I3: int] :
% 6.92/7.21 ( ( ord_less_int @ K2 @ I3 )
% 6.92/7.21 => ( ( P2 @ I3 )
% 6.92/7.21 => ( P2 @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 6.92/7.21 => ( P2 @ I2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_gr_induct
% 6.92/7.21 thf(fact_3997_zless__add1__eq,axiom,
% 6.92/7.21 ! [W2: int,Z3: int] :
% 6.92/7.21 ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z3 @ one_one_int ) )
% 6.92/7.21 = ( ( ord_less_int @ W2 @ Z3 )
% 6.92/7.21 | ( W2 = Z3 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zless_add1_eq
% 6.92/7.21 thf(fact_3998_odd__less__0__iff,axiom,
% 6.92/7.21 ! [Z3: int] :
% 6.92/7.21 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z3 ) @ Z3 ) @ zero_zero_int )
% 6.92/7.21 = ( ord_less_int @ Z3 @ zero_zero_int ) ) ).
% 6.92/7.21
% 6.92/7.21 % odd_less_0_iff
% 6.92/7.21 thf(fact_3999_less__int__code_I1_J,axiom,
% 6.92/7.21 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 6.92/7.21
% 6.92/7.21 % less_int_code(1)
% 6.92/7.21 thf(fact_4000_plus__int__code_I1_J,axiom,
% 6.92/7.21 ! [K2: int] :
% 6.92/7.21 ( ( plus_plus_int @ K2 @ zero_zero_int )
% 6.92/7.21 = K2 ) ).
% 6.92/7.21
% 6.92/7.21 % plus_int_code(1)
% 6.92/7.21 thf(fact_4001_plus__int__code_I2_J,axiom,
% 6.92/7.21 ! [L: int] :
% 6.92/7.21 ( ( plus_plus_int @ zero_zero_int @ L )
% 6.92/7.21 = L ) ).
% 6.92/7.21
% 6.92/7.21 % plus_int_code(2)
% 6.92/7.21 thf(fact_4002_odd__nonzero,axiom,
% 6.92/7.21 ! [Z3: int] :
% 6.92/7.21 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z3 ) @ Z3 )
% 6.92/7.21 != zero_zero_int ) ).
% 6.92/7.21
% 6.92/7.21 % odd_nonzero
% 6.92/7.21 thf(fact_4003_Suc__inject,axiom,
% 6.92/7.21 ! [X: nat,Y: nat] :
% 6.92/7.21 ( ( ( suc @ X )
% 6.92/7.21 = ( suc @ Y ) )
% 6.92/7.21 => ( X = Y ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_inject
% 6.92/7.21 thf(fact_4004_n__not__Suc__n,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( N2
% 6.92/7.21 != ( suc @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % n_not_Suc_n
% 6.92/7.21 thf(fact_4005_int__distrib_I2_J,axiom,
% 6.92/7.21 ! [W2: int,Z1: int,Z22: int] :
% 6.92/7.21 ( ( times_times_int @ W2 @ ( plus_plus_int @ Z1 @ Z22 ) )
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_distrib(2)
% 6.92/7.21 thf(fact_4006_int__distrib_I1_J,axiom,
% 6.92/7.21 ! [Z1: int,Z22: int,W2: int] :
% 6.92/7.21 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W2 )
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_distrib(1)
% 6.92/7.21 thf(fact_4007_zdiv__zmult2__eq,axiom,
% 6.92/7.21 ! [C2: int,A: int,B: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 6.92/7.21 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 6.92/7.21 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zdiv_zmult2_eq
% 6.92/7.21 thf(fact_4008_verit__la__generic,axiom,
% 6.92/7.21 ! [A: int,X: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ A @ X )
% 6.92/7.21 | ( A = X )
% 6.92/7.21 | ( ord_less_eq_int @ X @ A ) ) ).
% 6.92/7.21
% 6.92/7.21 % verit_la_generic
% 6.92/7.21 thf(fact_4009_int__ge__induct,axiom,
% 6.92/7.21 ! [K2: int,I2: int,P2: int > $o] :
% 6.92/7.21 ( ( ord_less_eq_int @ K2 @ I2 )
% 6.92/7.21 => ( ( P2 @ K2 )
% 6.92/7.21 => ( ! [I3: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ K2 @ I3 )
% 6.92/7.21 => ( ( P2 @ I3 )
% 6.92/7.21 => ( P2 @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 6.92/7.21 => ( P2 @ I2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_ge_induct
% 6.92/7.21 thf(fact_4010_less__eq__int__code_I1_J,axiom,
% 6.92/7.21 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 6.92/7.21
% 6.92/7.21 % less_eq_int_code(1)
% 6.92/7.21 thf(fact_4011_imp__le__cong,axiom,
% 6.92/7.21 ! [X: int,X10: int,P2: $o,P6: $o] :
% 6.92/7.21 ( ( X = X10 )
% 6.92/7.21 => ( ( ( ord_less_eq_int @ zero_zero_int @ X10 )
% 6.92/7.21 => ( P2 = P6 ) )
% 6.92/7.21 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.21 => P2 )
% 6.92/7.21 = ( ( ord_less_eq_int @ zero_zero_int @ X10 )
% 6.92/7.21 => P6 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % imp_le_cong
% 6.92/7.21 thf(fact_4012_conj__le__cong,axiom,
% 6.92/7.21 ! [X: int,X10: int,P2: $o,P6: $o] :
% 6.92/7.21 ( ( X = X10 )
% 6.92/7.21 => ( ( ( ord_less_eq_int @ zero_zero_int @ X10 )
% 6.92/7.21 => ( P2 = P6 ) )
% 6.92/7.21 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.21 & P2 )
% 6.92/7.21 = ( ( ord_less_eq_int @ zero_zero_int @ X10 )
% 6.92/7.21 & P6 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % conj_le_cong
% 6.92/7.21 thf(fact_4013_nat_Odistinct_I1_J,axiom,
% 6.92/7.21 ! [X2: nat] :
% 6.92/7.21 ( zero_zero_nat
% 6.92/7.21 != ( suc @ X2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat.distinct(1)
% 6.92/7.21 thf(fact_4014_old_Onat_Odistinct_I2_J,axiom,
% 6.92/7.21 ! [Nat2: nat] :
% 6.92/7.21 ( ( suc @ Nat2 )
% 6.92/7.21 != zero_zero_nat ) ).
% 6.92/7.21
% 6.92/7.21 % old.nat.distinct(2)
% 6.92/7.21 thf(fact_4015_old_Onat_Odistinct_I1_J,axiom,
% 6.92/7.21 ! [Nat2: nat] :
% 6.92/7.21 ( zero_zero_nat
% 6.92/7.21 != ( suc @ Nat2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % old.nat.distinct(1)
% 6.92/7.21 thf(fact_4016_nat_OdiscI,axiom,
% 6.92/7.21 ! [Nat: nat,X2: nat] :
% 6.92/7.21 ( ( Nat
% 6.92/7.21 = ( suc @ X2 ) )
% 6.92/7.21 => ( Nat != zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat.discI
% 6.92/7.21 thf(fact_4017_old_Onat_Oexhaust,axiom,
% 6.92/7.21 ! [Y: nat] :
% 6.92/7.21 ( ( Y != zero_zero_nat )
% 6.92/7.21 => ~ ! [Nat3: nat] :
% 6.92/7.21 ( Y
% 6.92/7.21 != ( suc @ Nat3 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % old.nat.exhaust
% 6.92/7.21 thf(fact_4018_nat__induct,axiom,
% 6.92/7.21 ! [P2: nat > $o,N2: nat] :
% 6.92/7.21 ( ( P2 @ zero_zero_nat )
% 6.92/7.21 => ( ! [N5: nat] :
% 6.92/7.21 ( ( P2 @ N5 )
% 6.92/7.21 => ( P2 @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( P2 @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_induct
% 6.92/7.21 thf(fact_4019_diff__induct,axiom,
% 6.92/7.21 ! [P2: nat > nat > $o,M: nat,N2: nat] :
% 6.92/7.21 ( ! [X3: nat] : ( P2 @ X3 @ zero_zero_nat )
% 6.92/7.21 => ( ! [Y3: nat] : ( P2 @ zero_zero_nat @ ( suc @ Y3 ) )
% 6.92/7.21 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.21 ( ( P2 @ X3 @ Y3 )
% 6.92/7.21 => ( P2 @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 6.92/7.21 => ( P2 @ M @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % diff_induct
% 6.92/7.21 thf(fact_4020_zero__induct,axiom,
% 6.92/7.21 ! [P2: nat > $o,K2: nat] :
% 6.92/7.21 ( ( P2 @ K2 )
% 6.92/7.21 => ( ! [N5: nat] :
% 6.92/7.21 ( ( P2 @ ( suc @ N5 ) )
% 6.92/7.21 => ( P2 @ N5 ) )
% 6.92/7.21 => ( P2 @ zero_zero_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % zero_induct
% 6.92/7.21 thf(fact_4021_Suc__neq__Zero,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ( ( suc @ M )
% 6.92/7.21 != zero_zero_nat ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_neq_Zero
% 6.92/7.21 thf(fact_4022_Zero__neq__Suc,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ( zero_zero_nat
% 6.92/7.21 != ( suc @ M ) ) ).
% 6.92/7.21
% 6.92/7.21 % Zero_neq_Suc
% 6.92/7.21 thf(fact_4023_Zero__not__Suc,axiom,
% 6.92/7.21 ! [M: nat] :
% 6.92/7.21 ( zero_zero_nat
% 6.92/7.21 != ( suc @ M ) ) ).
% 6.92/7.21
% 6.92/7.21 % Zero_not_Suc
% 6.92/7.21 thf(fact_4024_not0__implies__Suc,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( N2 != zero_zero_nat )
% 6.92/7.21 => ? [M5: nat] :
% 6.92/7.21 ( N2
% 6.92/7.21 = ( suc @ M5 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % not0_implies_Suc
% 6.92/7.21 thf(fact_4025_not__less__less__Suc__eq,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] :
% 6.92/7.21 ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.21 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 6.92/7.21 = ( N2 = M ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % not_less_less_Suc_eq
% 6.92/7.21 thf(fact_4026_strict__inc__induct,axiom,
% 6.92/7.21 ! [I2: nat,J2: nat,P2: nat > $o] :
% 6.92/7.21 ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.21 => ( ! [I3: nat] :
% 6.92/7.21 ( ( J2
% 6.92/7.21 = ( suc @ I3 ) )
% 6.92/7.21 => ( P2 @ I3 ) )
% 6.92/7.21 => ( ! [I3: nat] :
% 6.92/7.21 ( ( ord_less_nat @ I3 @ J2 )
% 6.92/7.21 => ( ( P2 @ ( suc @ I3 ) )
% 6.92/7.21 => ( P2 @ I3 ) ) )
% 6.92/7.21 => ( P2 @ I2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % strict_inc_induct
% 6.92/7.21 thf(fact_4027_less__Suc__induct,axiom,
% 6.92/7.21 ! [I2: nat,J2: nat,P2: nat > nat > $o] :
% 6.92/7.21 ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.21 => ( ! [I3: nat] : ( P2 @ I3 @ ( suc @ I3 ) )
% 6.92/7.21 => ( ! [I3: nat,J3: nat,K: nat] :
% 6.92/7.21 ( ( ord_less_nat @ I3 @ J3 )
% 6.92/7.21 => ( ( ord_less_nat @ J3 @ K )
% 6.92/7.21 => ( ( P2 @ I3 @ J3 )
% 6.92/7.21 => ( ( P2 @ J3 @ K )
% 6.92/7.21 => ( P2 @ I3 @ K ) ) ) ) )
% 6.92/7.21 => ( P2 @ I2 @ J2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_Suc_induct
% 6.92/7.21 thf(fact_4028_less__trans__Suc,axiom,
% 6.92/7.21 ! [I2: nat,J2: nat,K2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.21 => ( ( ord_less_nat @ J2 @ K2 )
% 6.92/7.21 => ( ord_less_nat @ ( suc @ I2 ) @ K2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_trans_Suc
% 6.92/7.21 thf(fact_4029_Suc__less__SucD,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 6.92/7.21 => ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_less_SucD
% 6.92/7.21 thf(fact_4030_less__antisym,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] :
% 6.92/7.21 ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.21 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 6.92/7.21 => ( M = N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_antisym
% 6.92/7.21 thf(fact_4031_Suc__less__eq2,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] :
% 6.92/7.21 ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.21 = ( ? [M7: nat] :
% 6.92/7.21 ( ( M
% 6.92/7.21 = ( suc @ M7 ) )
% 6.92/7.21 & ( ord_less_nat @ N2 @ M7 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_less_eq2
% 6.92/7.21 thf(fact_4032_All__less__Suc,axiom,
% 6.92/7.21 ! [N2: nat,P2: nat > $o] :
% 6.92/7.21 ( ( ! [I: nat] :
% 6.92/7.21 ( ( ord_less_nat @ I @ ( suc @ N2 ) )
% 6.92/7.21 => ( P2 @ I ) ) )
% 6.92/7.21 = ( ( P2 @ N2 )
% 6.92/7.21 & ! [I: nat] :
% 6.92/7.21 ( ( ord_less_nat @ I @ N2 )
% 6.92/7.21 => ( P2 @ I ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % All_less_Suc
% 6.92/7.21 thf(fact_4033_not__less__eq,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ~ ( ord_less_nat @ M @ N2 ) )
% 6.92/7.21 = ( ord_less_nat @ N2 @ ( suc @ M ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % not_less_eq
% 6.92/7.21 thf(fact_4034_less__Suc__eq,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 6.92/7.21 = ( ( ord_less_nat @ M @ N2 )
% 6.92/7.21 | ( M = N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_Suc_eq
% 6.92/7.21 thf(fact_4035_Ex__less__Suc,axiom,
% 6.92/7.21 ! [N2: nat,P2: nat > $o] :
% 6.92/7.21 ( ( ? [I: nat] :
% 6.92/7.21 ( ( ord_less_nat @ I @ ( suc @ N2 ) )
% 6.92/7.21 & ( P2 @ I ) ) )
% 6.92/7.21 = ( ( P2 @ N2 )
% 6.92/7.21 | ? [I: nat] :
% 6.92/7.21 ( ( ord_less_nat @ I @ N2 )
% 6.92/7.21 & ( P2 @ I ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % Ex_less_Suc
% 6.92/7.21 thf(fact_4036_less__SucI,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.21 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_SucI
% 6.92/7.21 thf(fact_4037_less__SucE,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 6.92/7.21 => ( ~ ( ord_less_nat @ M @ N2 )
% 6.92/7.21 => ( M = N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_SucE
% 6.92/7.21 thf(fact_4038_Suc__lessI,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.21 => ( ( ( suc @ M )
% 6.92/7.21 != N2 )
% 6.92/7.21 => ( ord_less_nat @ ( suc @ M ) @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_lessI
% 6.92/7.21 thf(fact_4039_Suc__lessE,axiom,
% 6.92/7.21 ! [I2: nat,K2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ ( suc @ I2 ) @ K2 )
% 6.92/7.21 => ~ ! [J3: nat] :
% 6.92/7.21 ( ( ord_less_nat @ I2 @ J3 )
% 6.92/7.21 => ( K2
% 6.92/7.21 != ( suc @ J3 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_lessE
% 6.92/7.21 thf(fact_4040_Suc__lessD,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ ( suc @ M ) @ N2 )
% 6.92/7.21 => ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_lessD
% 6.92/7.21 thf(fact_4041_Nat_OlessE,axiom,
% 6.92/7.21 ! [I2: nat,K2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ I2 @ K2 )
% 6.92/7.21 => ( ( K2
% 6.92/7.21 != ( suc @ I2 ) )
% 6.92/7.21 => ~ ! [J3: nat] :
% 6.92/7.21 ( ( ord_less_nat @ I2 @ J3 )
% 6.92/7.21 => ( K2
% 6.92/7.21 != ( suc @ J3 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % Nat.lessE
% 6.92/7.21 thf(fact_4042_transitive__stepwise__le,axiom,
% 6.92/7.21 ! [M: nat,N2: nat,R3: nat > nat > $o] :
% 6.92/7.21 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.21 => ( ! [X3: nat] : ( R3 @ X3 @ X3 )
% 6.92/7.21 => ( ! [X3: nat,Y3: nat,Z2: nat] :
% 6.92/7.21 ( ( R3 @ X3 @ Y3 )
% 6.92/7.21 => ( ( R3 @ Y3 @ Z2 )
% 6.92/7.21 => ( R3 @ X3 @ Z2 ) ) )
% 6.92/7.21 => ( ! [N5: nat] : ( R3 @ N5 @ ( suc @ N5 ) )
% 6.92/7.21 => ( R3 @ M @ N2 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % transitive_stepwise_le
% 6.92/7.21 thf(fact_4043_nat__induct__at__least,axiom,
% 6.92/7.21 ! [M: nat,N2: nat,P2: nat > $o] :
% 6.92/7.21 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.21 => ( ( P2 @ M )
% 6.92/7.21 => ( ! [N5: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ M @ N5 )
% 6.92/7.21 => ( ( P2 @ N5 )
% 6.92/7.21 => ( P2 @ ( suc @ N5 ) ) ) )
% 6.92/7.21 => ( P2 @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_induct_at_least
% 6.92/7.21 thf(fact_4044_full__nat__induct,axiom,
% 6.92/7.21 ! [P2: nat > $o,N2: nat] :
% 6.92/7.21 ( ! [N5: nat] :
% 6.92/7.21 ( ! [M4: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( suc @ M4 ) @ N5 )
% 6.92/7.21 => ( P2 @ M4 ) )
% 6.92/7.21 => ( P2 @ N5 ) )
% 6.92/7.21 => ( P2 @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % full_nat_induct
% 6.92/7.21 thf(fact_4045_not__less__eq__eq,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ~ ( ord_less_eq_nat @ M @ N2 ) )
% 6.92/7.21 = ( ord_less_eq_nat @ ( suc @ N2 ) @ M ) ) ).
% 6.92/7.21
% 6.92/7.21 % not_less_eq_eq
% 6.92/7.21 thf(fact_4046_Suc__n__not__le__n,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ~ ( ord_less_eq_nat @ ( suc @ N2 ) @ N2 ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_n_not_le_n
% 6.92/7.21 thf(fact_4047_le__Suc__eq,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 6.92/7.21 = ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.21 | ( M
% 6.92/7.21 = ( suc @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % le_Suc_eq
% 6.92/7.21 thf(fact_4048_Suc__le__D,axiom,
% 6.92/7.21 ! [N2: nat,M8: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ M8 )
% 6.92/7.21 => ? [M5: nat] :
% 6.92/7.21 ( M8
% 6.92/7.21 = ( suc @ M5 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_le_D
% 6.92/7.21 thf(fact_4049_le__SucI,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.21 => ( ord_less_eq_nat @ M @ ( suc @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % le_SucI
% 6.92/7.21 thf(fact_4050_le__SucE,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 6.92/7.21 => ( ~ ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.21 => ( M
% 6.92/7.21 = ( suc @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % le_SucE
% 6.92/7.21 thf(fact_4051_Suc__leD,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 6.92/7.21 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_leD
% 6.92/7.21 thf(fact_4052_nat__arith_Osuc1,axiom,
% 6.92/7.21 ! [A4: nat,K2: nat,A: nat] :
% 6.92/7.21 ( ( A4
% 6.92/7.21 = ( plus_plus_nat @ K2 @ A ) )
% 6.92/7.21 => ( ( suc @ A4 )
% 6.92/7.21 = ( plus_plus_nat @ K2 @ ( suc @ A ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_arith.suc1
% 6.92/7.21 thf(fact_4053_add__Suc,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 6.92/7.21 = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % add_Suc
% 6.92/7.21 thf(fact_4054_add__Suc__shift,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 6.92/7.21 = ( plus_plus_nat @ M @ ( suc @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % add_Suc_shift
% 6.92/7.21 thf(fact_4055_Suc__mult__cancel1,axiom,
% 6.92/7.21 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.21 ( ( ( times_times_nat @ ( suc @ K2 ) @ M )
% 6.92/7.21 = ( times_times_nat @ ( suc @ K2 ) @ N2 ) )
% 6.92/7.21 = ( M = N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_mult_cancel1
% 6.92/7.21 thf(fact_4056_lift__Suc__mono__less__iff,axiom,
% 6.92/7.21 ! [F: nat > assn,N2: nat,M: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_assn @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( ( ord_less_assn @ ( F @ N2 ) @ ( F @ M ) )
% 6.92/7.21 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_mono_less_iff
% 6.92/7.21 thf(fact_4057_lift__Suc__mono__less__iff,axiom,
% 6.92/7.21 ! [F: nat > rat,N2: nat,M: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_rat @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( ( ord_less_rat @ ( F @ N2 ) @ ( F @ M ) )
% 6.92/7.21 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_mono_less_iff
% 6.92/7.21 thf(fact_4058_lift__Suc__mono__less__iff,axiom,
% 6.92/7.21 ! [F: nat > num,N2: nat,M: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_num @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( ( ord_less_num @ ( F @ N2 ) @ ( F @ M ) )
% 6.92/7.21 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_mono_less_iff
% 6.92/7.21 thf(fact_4059_lift__Suc__mono__less__iff,axiom,
% 6.92/7.21 ! [F: nat > nat,N2: nat,M: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_nat @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( ( ord_less_nat @ ( F @ N2 ) @ ( F @ M ) )
% 6.92/7.21 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_mono_less_iff
% 6.92/7.21 thf(fact_4060_lift__Suc__mono__less__iff,axiom,
% 6.92/7.21 ! [F: nat > int,N2: nat,M: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_int @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( ( ord_less_int @ ( F @ N2 ) @ ( F @ M ) )
% 6.92/7.21 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_mono_less_iff
% 6.92/7.21 thf(fact_4061_lift__Suc__mono__less,axiom,
% 6.92/7.21 ! [F: nat > assn,N2: nat,N6: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_assn @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( ( ord_less_nat @ N2 @ N6 )
% 6.92/7.21 => ( ord_less_assn @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_mono_less
% 6.92/7.21 thf(fact_4062_lift__Suc__mono__less,axiom,
% 6.92/7.21 ! [F: nat > rat,N2: nat,N6: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_rat @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( ( ord_less_nat @ N2 @ N6 )
% 6.92/7.21 => ( ord_less_rat @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_mono_less
% 6.92/7.21 thf(fact_4063_lift__Suc__mono__less,axiom,
% 6.92/7.21 ! [F: nat > num,N2: nat,N6: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_num @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( ( ord_less_nat @ N2 @ N6 )
% 6.92/7.21 => ( ord_less_num @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_mono_less
% 6.92/7.21 thf(fact_4064_lift__Suc__mono__less,axiom,
% 6.92/7.21 ! [F: nat > nat,N2: nat,N6: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_nat @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( ( ord_less_nat @ N2 @ N6 )
% 6.92/7.21 => ( ord_less_nat @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_mono_less
% 6.92/7.21 thf(fact_4065_lift__Suc__mono__less,axiom,
% 6.92/7.21 ! [F: nat > int,N2: nat,N6: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_int @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( ( ord_less_nat @ N2 @ N6 )
% 6.92/7.21 => ( ord_less_int @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_mono_less
% 6.92/7.21 thf(fact_4066_lift__Suc__antimono__le,axiom,
% 6.92/7.21 ! [F: nat > set_int,N2: nat,N6: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N5 ) ) @ ( F @ N5 ) )
% 6.92/7.21 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 6.92/7.21 => ( ord_less_eq_set_int @ ( F @ N6 ) @ ( F @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_antimono_le
% 6.92/7.21 thf(fact_4067_lift__Suc__antimono__le,axiom,
% 6.92/7.21 ! [F: nat > rat,N2: nat,N6: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N5 ) ) @ ( F @ N5 ) )
% 6.92/7.21 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 6.92/7.21 => ( ord_less_eq_rat @ ( F @ N6 ) @ ( F @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_antimono_le
% 6.92/7.21 thf(fact_4068_lift__Suc__antimono__le,axiom,
% 6.92/7.21 ! [F: nat > num,N2: nat,N6: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N5 ) ) @ ( F @ N5 ) )
% 6.92/7.21 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 6.92/7.21 => ( ord_less_eq_num @ ( F @ N6 ) @ ( F @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_antimono_le
% 6.92/7.21 thf(fact_4069_lift__Suc__antimono__le,axiom,
% 6.92/7.21 ! [F: nat > nat,N2: nat,N6: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N5 ) ) @ ( F @ N5 ) )
% 6.92/7.21 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 6.92/7.21 => ( ord_less_eq_nat @ ( F @ N6 ) @ ( F @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_antimono_le
% 6.92/7.21 thf(fact_4070_lift__Suc__antimono__le,axiom,
% 6.92/7.21 ! [F: nat > int,N2: nat,N6: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N5 ) ) @ ( F @ N5 ) )
% 6.92/7.21 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 6.92/7.21 => ( ord_less_eq_int @ ( F @ N6 ) @ ( F @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_antimono_le
% 6.92/7.21 thf(fact_4071_lift__Suc__mono__le,axiom,
% 6.92/7.21 ! [F: nat > set_int,N2: nat,N6: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_eq_set_int @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 6.92/7.21 => ( ord_less_eq_set_int @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_mono_le
% 6.92/7.21 thf(fact_4072_lift__Suc__mono__le,axiom,
% 6.92/7.21 ! [F: nat > rat,N2: nat,N6: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 6.92/7.21 => ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_mono_le
% 6.92/7.21 thf(fact_4073_lift__Suc__mono__le,axiom,
% 6.92/7.21 ! [F: nat > num,N2: nat,N6: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 6.92/7.21 => ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_mono_le
% 6.92/7.21 thf(fact_4074_lift__Suc__mono__le,axiom,
% 6.92/7.21 ! [F: nat > nat,N2: nat,N6: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 6.92/7.21 => ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_mono_le
% 6.92/7.21 thf(fact_4075_lift__Suc__mono__le,axiom,
% 6.92/7.21 ! [F: nat > int,N2: nat,N6: nat] :
% 6.92/7.21 ( ! [N5: nat] : ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 6.92/7.21 => ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % lift_Suc_mono_le
% 6.92/7.21 thf(fact_4076_of__nat__neq__0,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( semiri681578069525770553at_rat @ ( suc @ N2 ) )
% 6.92/7.21 != zero_zero_rat ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_neq_0
% 6.92/7.21 thf(fact_4077_of__nat__neq__0,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 6.92/7.21 != zero_zero_int ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_neq_0
% 6.92/7.21 thf(fact_4078_of__nat__neq__0,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( semiri1316708129612266289at_nat @ ( suc @ N2 ) )
% 6.92/7.21 != zero_zero_nat ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_neq_0
% 6.92/7.21 thf(fact_4079_of__nat__neq__0,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( semiri4939895301339042750nteger @ ( suc @ N2 ) )
% 6.92/7.21 != zero_z3403309356797280102nteger ) ).
% 6.92/7.21
% 6.92/7.21 % of_nat_neq_0
% 6.92/7.21 thf(fact_4080_Ex__less__Suc2,axiom,
% 6.92/7.21 ! [N2: nat,P2: nat > $o] :
% 6.92/7.21 ( ( ? [I: nat] :
% 6.92/7.21 ( ( ord_less_nat @ I @ ( suc @ N2 ) )
% 6.92/7.21 & ( P2 @ I ) ) )
% 6.92/7.21 = ( ( P2 @ zero_zero_nat )
% 6.92/7.21 | ? [I: nat] :
% 6.92/7.21 ( ( ord_less_nat @ I @ N2 )
% 6.92/7.21 & ( P2 @ ( suc @ I ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % Ex_less_Suc2
% 6.92/7.21 thf(fact_4081_gr0__conv__Suc,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 = ( ? [M3: nat] :
% 6.92/7.21 ( N2
% 6.92/7.21 = ( suc @ M3 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % gr0_conv_Suc
% 6.92/7.21 thf(fact_4082_All__less__Suc2,axiom,
% 6.92/7.21 ! [N2: nat,P2: nat > $o] :
% 6.92/7.21 ( ( ! [I: nat] :
% 6.92/7.21 ( ( ord_less_nat @ I @ ( suc @ N2 ) )
% 6.92/7.21 => ( P2 @ I ) ) )
% 6.92/7.21 = ( ( P2 @ zero_zero_nat )
% 6.92/7.21 & ! [I: nat] :
% 6.92/7.21 ( ( ord_less_nat @ I @ N2 )
% 6.92/7.21 => ( P2 @ ( suc @ I ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % All_less_Suc2
% 6.92/7.21 thf(fact_4083_gr0__implies__Suc,axiom,
% 6.92/7.21 ! [N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ? [M5: nat] :
% 6.92/7.21 ( N2
% 6.92/7.21 = ( suc @ M5 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % gr0_implies_Suc
% 6.92/7.21 thf(fact_4084_less__Suc__eq__0__disj,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 6.92/7.21 = ( ( M = zero_zero_nat )
% 6.92/7.21 | ? [J: nat] :
% 6.92/7.21 ( ( M
% 6.92/7.21 = ( suc @ J ) )
% 6.92/7.21 & ( ord_less_nat @ J @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_Suc_eq_0_disj
% 6.92/7.21 thf(fact_4085_nat__compl__induct,axiom,
% 6.92/7.21 ! [P2: nat > $o,N2: nat] :
% 6.92/7.21 ( ( P2 @ zero_zero_nat )
% 6.92/7.21 => ( ! [N5: nat] :
% 6.92/7.21 ( ! [Nn: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ Nn @ N5 )
% 6.92/7.21 => ( P2 @ Nn ) )
% 6.92/7.21 => ( P2 @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( P2 @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_compl_induct
% 6.92/7.21 thf(fact_4086_nat__compl__induct_H,axiom,
% 6.92/7.21 ! [P2: nat > $o,N2: nat] :
% 6.92/7.21 ( ( P2 @ zero_zero_nat )
% 6.92/7.21 => ( ! [N5: nat] :
% 6.92/7.21 ( ! [Nn: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ Nn @ N5 )
% 6.92/7.21 => ( P2 @ Nn ) )
% 6.92/7.21 => ( P2 @ ( suc @ N5 ) ) )
% 6.92/7.21 => ( P2 @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_compl_induct'
% 6.92/7.21 thf(fact_4087_add__is__1,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ( plus_plus_nat @ M @ N2 )
% 6.92/7.21 = ( suc @ zero_zero_nat ) )
% 6.92/7.21 = ( ( ( M
% 6.92/7.21 = ( suc @ zero_zero_nat ) )
% 6.92/7.21 & ( N2 = zero_zero_nat ) )
% 6.92/7.21 | ( ( M = zero_zero_nat )
% 6.92/7.21 & ( N2
% 6.92/7.21 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % add_is_1
% 6.92/7.21 thf(fact_4088_one__is__add,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ( suc @ zero_zero_nat )
% 6.92/7.21 = ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.21 = ( ( ( M
% 6.92/7.21 = ( suc @ zero_zero_nat ) )
% 6.92/7.21 & ( N2 = zero_zero_nat ) )
% 6.92/7.21 | ( ( M = zero_zero_nat )
% 6.92/7.21 & ( N2
% 6.92/7.21 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % one_is_add
% 6.92/7.21 thf(fact_4089_Suc__leI,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.21 => ( ord_less_eq_nat @ ( suc @ M ) @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_leI
% 6.92/7.21 thf(fact_4090_Suc__le__eq,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 6.92/7.21 = ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_le_eq
% 6.92/7.21 thf(fact_4091_dec__induct,axiom,
% 6.92/7.21 ! [I2: nat,J2: nat,P2: nat > $o] :
% 6.92/7.21 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.21 => ( ( P2 @ I2 )
% 6.92/7.21 => ( ! [N5: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ I2 @ N5 )
% 6.92/7.21 => ( ( ord_less_nat @ N5 @ J2 )
% 6.92/7.21 => ( ( P2 @ N5 )
% 6.92/7.21 => ( P2 @ ( suc @ N5 ) ) ) ) )
% 6.92/7.21 => ( P2 @ J2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % dec_induct
% 6.92/7.21 thf(fact_4092_inc__induct,axiom,
% 6.92/7.21 ! [I2: nat,J2: nat,P2: nat > $o] :
% 6.92/7.21 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.21 => ( ( P2 @ J2 )
% 6.92/7.21 => ( ! [N5: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ I2 @ N5 )
% 6.92/7.21 => ( ( ord_less_nat @ N5 @ J2 )
% 6.92/7.21 => ( ( P2 @ ( suc @ N5 ) )
% 6.92/7.21 => ( P2 @ N5 ) ) ) )
% 6.92/7.21 => ( P2 @ I2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % inc_induct
% 6.92/7.21 thf(fact_4093_Suc__le__lessD,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 6.92/7.21 => ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_le_lessD
% 6.92/7.21 thf(fact_4094_le__less__Suc__eq,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.21 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 6.92/7.21 = ( N2 = M ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % le_less_Suc_eq
% 6.92/7.21 thf(fact_4095_less__Suc__eq__le,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 6.92/7.21 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_Suc_eq_le
% 6.92/7.21 thf(fact_4096_less__eq__Suc__le,axiom,
% 6.92/7.21 ( ord_less_nat
% 6.92/7.21 = ( ^ [N: nat] : ( ord_less_eq_nat @ ( suc @ N ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_eq_Suc_le
% 6.92/7.21 thf(fact_4097_le__imp__less__Suc,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.21 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % le_imp_less_Suc
% 6.92/7.21 thf(fact_4098_nat__in__between__eq_I2_J,axiom,
% 6.92/7.21 ! [A: nat,B: nat] :
% 6.92/7.21 ( ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.21 & ( ord_less_nat @ B @ ( suc @ A ) ) )
% 6.92/7.21 = ( B = A ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_in_between_eq(2)
% 6.92/7.21 thf(fact_4099_nat__in__between__eq_I1_J,axiom,
% 6.92/7.21 ! [A: nat,B: nat] :
% 6.92/7.21 ( ( ( ord_less_nat @ A @ B )
% 6.92/7.21 & ( ord_less_eq_nat @ B @ ( suc @ A ) ) )
% 6.92/7.21 = ( B
% 6.92/7.21 = ( suc @ A ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_in_between_eq(1)
% 6.92/7.21 thf(fact_4100_less__natE,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.21 => ~ ! [Q5: nat] :
% 6.92/7.21 ( N2
% 6.92/7.21 != ( suc @ ( plus_plus_nat @ M @ Q5 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_natE
% 6.92/7.21 thf(fact_4101_less__add__Suc1,axiom,
% 6.92/7.21 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_add_Suc1
% 6.92/7.21 thf(fact_4102_less__add__Suc2,axiom,
% 6.92/7.21 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M @ I2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_add_Suc2
% 6.92/7.21 thf(fact_4103_less__iff__Suc__add,axiom,
% 6.92/7.21 ( ord_less_nat
% 6.92/7.21 = ( ^ [M3: nat,N: nat] :
% 6.92/7.21 ? [K3: nat] :
% 6.92/7.21 ( N
% 6.92/7.21 = ( suc @ ( plus_plus_nat @ M3 @ K3 ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_iff_Suc_add
% 6.92/7.21 thf(fact_4104_less__imp__Suc__add,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.21 => ? [K: nat] :
% 6.92/7.21 ( N2
% 6.92/7.21 = ( suc @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % less_imp_Suc_add
% 6.92/7.21 thf(fact_4105_Suc__mult__less__cancel1,axiom,
% 6.92/7.21 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K2 ) @ M ) @ ( times_times_nat @ ( suc @ K2 ) @ N2 ) )
% 6.92/7.21 = ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_mult_less_cancel1
% 6.92/7.21 thf(fact_4106_One__nat__def,axiom,
% 6.92/7.21 ( one_one_nat
% 6.92/7.21 = ( suc @ zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % One_nat_def
% 6.92/7.21 thf(fact_4107_Suc__mult__le__cancel1,axiom,
% 6.92/7.21 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K2 ) @ M ) @ ( times_times_nat @ ( suc @ K2 ) @ N2 ) )
% 6.92/7.21 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_mult_le_cancel1
% 6.92/7.21 thf(fact_4108_mult__Suc,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] :
% 6.92/7.21 ( ( times_times_nat @ ( suc @ M ) @ N2 )
% 6.92/7.21 = ( plus_plus_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mult_Suc
% 6.92/7.21 thf(fact_4109_Suc__eq__plus1,axiom,
% 6.92/7.21 ( suc
% 6.92/7.21 = ( ^ [N: nat] : ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_eq_plus1
% 6.92/7.21 thf(fact_4110_plus__1__eq__Suc,axiom,
% 6.92/7.21 ( ( plus_plus_nat @ one_one_nat )
% 6.92/7.21 = suc ) ).
% 6.92/7.21
% 6.92/7.21 % plus_1_eq_Suc
% 6.92/7.21 thf(fact_4111_Suc__eq__plus1__left,axiom,
% 6.92/7.21 ( suc
% 6.92/7.21 = ( plus_plus_nat @ one_one_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_eq_plus1_left
% 6.92/7.21 thf(fact_4112_mod__induct,axiom,
% 6.92/7.21 ! [P2: nat > $o,N2: nat,P3: nat,M: nat] :
% 6.92/7.21 ( ( P2 @ N2 )
% 6.92/7.21 => ( ( ord_less_nat @ N2 @ P3 )
% 6.92/7.21 => ( ( ord_less_nat @ M @ P3 )
% 6.92/7.21 => ( ! [N5: nat] :
% 6.92/7.21 ( ( ord_less_nat @ N5 @ P3 )
% 6.92/7.21 => ( ( P2 @ N5 )
% 6.92/7.21 => ( P2 @ ( modulo_modulo_nat @ ( suc @ N5 ) @ P3 ) ) ) )
% 6.92/7.21 => ( P2 @ M ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % mod_induct
% 6.92/7.21 thf(fact_4113_mod__Suc__le__divisor,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N2 ) ) @ N2 ) ).
% 6.92/7.21
% 6.92/7.21 % mod_Suc_le_divisor
% 6.92/7.21 thf(fact_4114_Suc__div__le__mono,axiom,
% 6.92/7.21 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ ( divide_divide_nat @ ( suc @ M ) @ N2 ) ) ).
% 6.92/7.21
% 6.92/7.21 % Suc_div_le_mono
% 6.92/7.21 thf(fact_4115_power__le__imp__le__base,axiom,
% 6.92/7.21 ! [A: code_integer,N2: nat,B: code_integer] :
% 6.92/7.21 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) ) @ ( power_8256067586552552935nteger @ B @ ( suc @ N2 ) ) )
% 6.92/7.21 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.21 => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_le_imp_le_base
% 6.92/7.21 thf(fact_4116_power__le__imp__le__base,axiom,
% 6.92/7.21 ! [A: rat,N2: nat,B: rat] :
% 6.92/7.21 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 6.92/7.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.21 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_le_imp_le_base
% 6.92/7.21 thf(fact_4117_power__le__imp__le__base,axiom,
% 6.92/7.21 ! [A: nat,N2: nat,B: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 6.92/7.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 6.92/7.21 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_le_imp_le_base
% 6.92/7.21 thf(fact_4118_power__le__imp__le__base,axiom,
% 6.92/7.21 ! [A: int,N2: nat,B: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ ( power_power_int @ B @ ( suc @ N2 ) ) )
% 6.92/7.21 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 6.92/7.21 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_le_imp_le_base
% 6.92/7.21 thf(fact_4119_power__inject__base,axiom,
% 6.92/7.21 ! [A: code_integer,N2: nat,B: code_integer] :
% 6.92/7.21 ( ( ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) )
% 6.92/7.21 = ( power_8256067586552552935nteger @ B @ ( suc @ N2 ) ) )
% 6.92/7.21 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.21 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.21 => ( A = B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_inject_base
% 6.92/7.21 thf(fact_4120_power__inject__base,axiom,
% 6.92/7.21 ! [A: rat,N2: nat,B: rat] :
% 6.92/7.21 ( ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 6.92/7.21 = ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 6.92/7.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.21 => ( A = B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_inject_base
% 6.92/7.21 thf(fact_4121_power__inject__base,axiom,
% 6.92/7.21 ! [A: nat,N2: nat,B: nat] :
% 6.92/7.21 ( ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 6.92/7.21 = ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 6.92/7.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 6.92/7.21 => ( A = B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_inject_base
% 6.92/7.21 thf(fact_4122_power__inject__base,axiom,
% 6.92/7.21 ! [A: int,N2: nat,B: int] :
% 6.92/7.21 ( ( ( power_power_int @ A @ ( suc @ N2 ) )
% 6.92/7.21 = ( power_power_int @ B @ ( suc @ N2 ) ) )
% 6.92/7.21 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.21 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 6.92/7.21 => ( A = B ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_inject_base
% 6.92/7.21 thf(fact_4123_power__gt1,axiom,
% 6.92/7.21 ! [A: code_integer,N2: nat] :
% 6.92/7.21 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 6.92/7.21 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_gt1
% 6.92/7.21 thf(fact_4124_power__gt1,axiom,
% 6.92/7.21 ! [A: rat,N2: nat] :
% 6.92/7.21 ( ( ord_less_rat @ one_one_rat @ A )
% 6.92/7.21 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_gt1
% 6.92/7.21 thf(fact_4125_power__gt1,axiom,
% 6.92/7.21 ! [A: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ one_one_nat @ A )
% 6.92/7.21 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_gt1
% 6.92/7.21 thf(fact_4126_power__gt1,axiom,
% 6.92/7.21 ! [A: int,N2: nat] :
% 6.92/7.21 ( ( ord_less_int @ one_one_int @ A )
% 6.92/7.21 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_gt1
% 6.92/7.21 thf(fact_4127_ex__least__nat__less,axiom,
% 6.92/7.21 ! [P2: nat > $o,N2: nat] :
% 6.92/7.21 ( ( P2 @ N2 )
% 6.92/7.21 => ( ~ ( P2 @ zero_zero_nat )
% 6.92/7.21 => ? [K: nat] :
% 6.92/7.21 ( ( ord_less_nat @ K @ N2 )
% 6.92/7.21 & ! [I4: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ I4 @ K )
% 6.92/7.21 => ~ ( P2 @ I4 ) )
% 6.92/7.21 & ( P2 @ ( suc @ K ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % ex_least_nat_less
% 6.92/7.21 thf(fact_4128_n__less__n__mult__m,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 6.92/7.21 => ( ord_less_nat @ N2 @ ( times_times_nat @ N2 @ M ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % n_less_n_mult_m
% 6.92/7.21 thf(fact_4129_n__less__m__mult__n,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 6.92/7.21 => ( ord_less_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % n_less_m_mult_n
% 6.92/7.21 thf(fact_4130_one__less__mult,axiom,
% 6.92/7.21 ! [N2: nat,M: nat] :
% 6.92/7.21 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 6.92/7.21 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 6.92/7.21 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % one_less_mult
% 6.92/7.21 thf(fact_4131_nat__induct__non__zero,axiom,
% 6.92/7.21 ! [N2: nat,P2: nat > $o] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.21 => ( ( P2 @ one_one_nat )
% 6.92/7.21 => ( ! [N5: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 6.92/7.21 => ( ( P2 @ N5 )
% 6.92/7.21 => ( P2 @ ( suc @ N5 ) ) ) )
% 6.92/7.21 => ( P2 @ N2 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_induct_non_zero
% 6.92/7.21 thf(fact_4132_power__gt__expt,axiom,
% 6.92/7.21 ! [N2: nat,K2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 6.92/7.21 => ( ord_less_nat @ K2 @ ( power_power_nat @ N2 @ K2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_gt_expt
% 6.92/7.21 thf(fact_4133_nat__one__le__power,axiom,
% 6.92/7.21 ! [I2: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I2 )
% 6.92/7.21 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I2 @ N2 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_one_le_power
% 6.92/7.21 thf(fact_4134_nat__approx__posE,axiom,
% 6.92/7.21 ! [E: rat] :
% 6.92/7.21 ( ( ord_less_rat @ zero_zero_rat @ E )
% 6.92/7.21 => ~ ! [N5: nat] :
% 6.92/7.21 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N5 ) ) ) @ E ) ) ).
% 6.92/7.21
% 6.92/7.21 % nat_approx_posE
% 6.92/7.21 thf(fact_4135_power__Suc__le__self,axiom,
% 6.92/7.21 ! [A: code_integer,N2: nat] :
% 6.92/7.21 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.21 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 6.92/7.21 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_Suc_le_self
% 6.92/7.21 thf(fact_4136_power__Suc__le__self,axiom,
% 6.92/7.21 ! [A: rat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.21 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 6.92/7.21 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_Suc_le_self
% 6.92/7.21 thf(fact_4137_power__Suc__le__self,axiom,
% 6.92/7.21 ! [A: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.21 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 6.92/7.21 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_Suc_le_self
% 6.92/7.21 thf(fact_4138_power__Suc__le__self,axiom,
% 6.92/7.21 ! [A: int,N2: nat] :
% 6.92/7.21 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.21 => ( ( ord_less_eq_int @ A @ one_one_int )
% 6.92/7.21 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_Suc_le_self
% 6.92/7.21 thf(fact_4139_power__Suc__less__one,axiom,
% 6.92/7.21 ! [A: code_integer,N2: nat] :
% 6.92/7.21 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.21 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 6.92/7.21 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) ) @ one_one_Code_integer ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_Suc_less_one
% 6.92/7.21 thf(fact_4140_power__Suc__less__one,axiom,
% 6.92/7.21 ! [A: rat,N2: nat] :
% 6.92/7.21 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.21 => ( ( ord_less_rat @ A @ one_one_rat )
% 6.92/7.21 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ one_one_rat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_Suc_less_one
% 6.92/7.21 thf(fact_4141_power__Suc__less__one,axiom,
% 6.92/7.21 ! [A: nat,N2: nat] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ A )
% 6.92/7.21 => ( ( ord_less_nat @ A @ one_one_nat )
% 6.92/7.21 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ one_one_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_Suc_less_one
% 6.92/7.21 thf(fact_4142_power__Suc__less__one,axiom,
% 6.92/7.21 ! [A: int,N2: nat] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.21 => ( ( ord_less_int @ A @ one_one_int )
% 6.92/7.21 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ one_one_int ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % power_Suc_less_one
% 6.92/7.21 thf(fact_4143_div__nat__eqI,axiom,
% 6.92/7.21 ! [N2: nat,Q6: nat,M: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q6 ) @ M )
% 6.92/7.21 => ( ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q6 ) ) )
% 6.92/7.21 => ( ( divide_divide_nat @ M @ N2 )
% 6.92/7.21 = Q6 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_nat_eqI
% 6.92/7.21 thf(fact_4144_split__div_H,axiom,
% 6.92/7.21 ! [P2: nat > $o,M: nat,N2: nat] :
% 6.92/7.21 ( ( P2 @ ( divide_divide_nat @ M @ N2 ) )
% 6.92/7.21 = ( ( ( N2 = zero_zero_nat )
% 6.92/7.21 & ( P2 @ zero_zero_nat ) )
% 6.92/7.21 | ? [Q8: nat] :
% 6.92/7.21 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q8 ) @ M )
% 6.92/7.21 & ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q8 ) ) )
% 6.92/7.21 & ( P2 @ Q8 ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % split_div'
% 6.92/7.21 thf(fact_4145_option_Osize__gen_I2_J,axiom,
% 6.92/7.21 ! [X: produc7388388658123137530it_nat > nat,X2: produc7388388658123137530it_nat] :
% 6.92/7.21 ( ( size_o5858930521590659991it_nat @ X @ ( some_P2818173045054083285it_nat @ X2 ) )
% 6.92/7.21 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % option.size_gen(2)
% 6.92/7.21 thf(fact_4146_option_Osize__gen_I2_J,axiom,
% 6.92/7.21 ! [X: produc3260487557148687353it_nat > nat,X2: produc3260487557148687353it_nat] :
% 6.92/7.21 ( ( size_o1731029420616209814it_nat @ X @ ( some_P7913643980934408916it_nat @ X2 ) )
% 6.92/7.21 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % option.size_gen(2)
% 6.92/7.21 thf(fact_4147_option_Osize__gen_I2_J,axiom,
% 6.92/7.21 ! [X: produc8664842809031399944it_nat > nat,X2: produc8664842809031399944it_nat] :
% 6.92/7.21 ( ( size_o29782932136985253it_nat @ X @ ( some_P1914260805536162275it_nat @ X2 ) )
% 6.92/7.21 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % option.size_gen(2)
% 6.92/7.21 thf(fact_4148_option_Osize__gen_I2_J,axiom,
% 6.92/7.21 ! [X: num > nat,X2: num] :
% 6.92/7.21 ( ( size_option_num @ X @ ( some_num @ X2 ) )
% 6.92/7.21 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % option.size_gen(2)
% 6.92/7.21 thf(fact_4149_Heap_Osize__gen,axiom,
% 6.92/7.21 ! [Xa: product_unit > nat,X: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 6.92/7.21 ( ( heap_T4142866422068808505t_unit @ Xa @ ( heap_T6183433275982383450t_unit @ X ) )
% 6.92/7.21 = ( suc @ zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % Heap.size_gen
% 6.92/7.21 thf(fact_4150_option_Osize__gen_I1_J,axiom,
% 6.92/7.21 ! [X: num > nat] :
% 6.92/7.21 ( ( size_option_num @ X @ none_num )
% 6.92/7.21 = ( suc @ zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % option.size_gen(1)
% 6.92/7.21 thf(fact_4151_Heap_Osize_I2_J,axiom,
% 6.92/7.21 ! [X: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 6.92/7.21 ( ( size_s1564113455978345259t_unit @ ( heap_T6183433275982383450t_unit @ X ) )
% 6.92/7.21 = ( suc @ zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % Heap.size(2)
% 6.92/7.21 thf(fact_4152_eucl__rel__int__iff,axiom,
% 6.92/7.21 ! [K2: int,L: int,Q6: int,R2: int] :
% 6.92/7.21 ( ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 6.92/7.21 = ( ( K2
% 6.92/7.21 = ( plus_plus_int @ ( times_times_int @ L @ Q6 ) @ R2 ) )
% 6.92/7.21 & ( ( ord_less_int @ zero_zero_int @ L )
% 6.92/7.21 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 6.92/7.21 & ( ord_less_int @ R2 @ L ) ) )
% 6.92/7.21 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 6.92/7.21 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 6.92/7.21 => ( ( ord_less_int @ L @ R2 )
% 6.92/7.21 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 6.92/7.21 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 6.92/7.21 => ( Q6 = zero_zero_int ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % eucl_rel_int_iff
% 6.92/7.21 thf(fact_4153_size__neq__size__imp__neq,axiom,
% 6.92/7.21 ! [X: list_nat,Y: list_nat] :
% 6.92/7.21 ( ( ( size_size_list_nat @ X )
% 6.92/7.21 != ( size_size_list_nat @ Y ) )
% 6.92/7.21 => ( X != Y ) ) ).
% 6.92/7.21
% 6.92/7.21 % size_neq_size_imp_neq
% 6.92/7.21 thf(fact_4154_size__neq__size__imp__neq,axiom,
% 6.92/7.21 ! [X: num,Y: num] :
% 6.92/7.21 ( ( ( size_size_num @ X )
% 6.92/7.21 != ( size_size_num @ Y ) )
% 6.92/7.21 => ( X != Y ) ) ).
% 6.92/7.21
% 6.92/7.21 % size_neq_size_imp_neq
% 6.92/7.21 thf(fact_4155_size__neq__size__imp__neq,axiom,
% 6.92/7.21 ! [X: list_o,Y: list_o] :
% 6.92/7.21 ( ( ( size_size_list_o @ X )
% 6.92/7.21 != ( size_size_list_o @ Y ) )
% 6.92/7.21 => ( X != Y ) ) ).
% 6.92/7.21
% 6.92/7.21 % size_neq_size_imp_neq
% 6.92/7.21 thf(fact_4156_size__neq__size__imp__neq,axiom,
% 6.92/7.21 ! [X: list_int,Y: list_int] :
% 6.92/7.21 ( ( ( size_size_list_int @ X )
% 6.92/7.21 != ( size_size_list_int @ Y ) )
% 6.92/7.21 => ( X != Y ) ) ).
% 6.92/7.21
% 6.92/7.21 % size_neq_size_imp_neq
% 6.92/7.21 thf(fact_4157_upto_Opinduct,axiom,
% 6.92/7.21 ! [A0: int,A1: int,P2: int > int > $o] :
% 6.92/7.21 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 6.92/7.21 => ( ! [I3: int,J3: int] :
% 6.92/7.21 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J3 ) )
% 6.92/7.21 => ( ( ( ord_less_eq_int @ I3 @ J3 )
% 6.92/7.21 => ( P2 @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) )
% 6.92/7.21 => ( P2 @ I3 @ J3 ) ) )
% 6.92/7.21 => ( P2 @ A0 @ A1 ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % upto.pinduct
% 6.92/7.21 thf(fact_4158_option_Osize_I3_J,axiom,
% 6.92/7.21 ( ( size_size_option_num @ none_num )
% 6.92/7.21 = ( suc @ zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % option.size(3)
% 6.92/7.21 thf(fact_4159_option_Osize_I4_J,axiom,
% 6.92/7.21 ! [X2: produc7388388658123137530it_nat] :
% 6.92/7.21 ( ( size_s2866289034186623454it_nat @ ( some_P2818173045054083285it_nat @ X2 ) )
% 6.92/7.21 = ( suc @ zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % option.size(4)
% 6.92/7.21 thf(fact_4160_option_Osize_I4_J,axiom,
% 6.92/7.21 ! [X2: produc3260487557148687353it_nat] :
% 6.92/7.21 ( ( size_s2363601347547812957it_nat @ ( some_P7913643980934408916it_nat @ X2 ) )
% 6.92/7.21 = ( suc @ zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % option.size(4)
% 6.92/7.21 thf(fact_4161_option_Osize_I4_J,axiom,
% 6.92/7.21 ! [X2: produc8664842809031399944it_nat] :
% 6.92/7.21 ( ( size_s8766407808098229740it_nat @ ( some_P1914260805536162275it_nat @ X2 ) )
% 6.92/7.21 = ( suc @ zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % option.size(4)
% 6.92/7.21 thf(fact_4162_option_Osize_I4_J,axiom,
% 6.92/7.21 ! [X2: num] :
% 6.92/7.21 ( ( size_size_option_num @ ( some_num @ X2 ) )
% 6.92/7.21 = ( suc @ zero_zero_nat ) ) ).
% 6.92/7.21
% 6.92/7.21 % option.size(4)
% 6.92/7.21 thf(fact_4163_div__pos__neg__trivial,axiom,
% 6.92/7.21 ! [K2: int,L: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ K2 )
% 6.92/7.21 => ( ( ord_less_eq_int @ ( plus_plus_int @ K2 @ L ) @ zero_zero_int )
% 6.92/7.21 => ( ( divide_divide_int @ K2 @ L )
% 6.92/7.21 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_pos_neg_trivial
% 6.92/7.21 thf(fact_4164_div__pos__geq,axiom,
% 6.92/7.21 ! [L: int,K2: int] :
% 6.92/7.21 ( ( ord_less_int @ zero_zero_int @ L )
% 6.92/7.21 => ( ( ord_less_eq_int @ L @ K2 )
% 6.92/7.21 => ( ( divide_divide_int @ K2 @ L )
% 6.92/7.21 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K2 @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % div_pos_geq
% 6.92/7.21 thf(fact_4165_int__power__div__base,axiom,
% 6.92/7.21 ! [M: nat,K2: int] :
% 6.92/7.21 ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.21 => ( ( ord_less_int @ zero_zero_int @ K2 )
% 6.92/7.21 => ( ( divide_divide_int @ ( power_power_int @ K2 @ M ) @ K2 )
% 6.92/7.21 = ( power_power_int @ K2 @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % int_power_div_base
% 6.92/7.21 thf(fact_4166_one__less__nat__eq,axiom,
% 6.92/7.21 ! [Z3: int] :
% 6.92/7.21 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z3 ) )
% 6.92/7.21 = ( ord_less_int @ one_one_int @ Z3 ) ) ).
% 6.92/7.21
% 6.92/7.21 % one_less_nat_eq
% 6.92/7.21 thf(fact_4167_verit__minus__simplify_I4_J,axiom,
% 6.92/7.21 ! [B: int] :
% 6.92/7.21 ( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
% 6.92/7.21 = B ) ).
% 6.92/7.21
% 6.92/7.21 % verit_minus_simplify(4)
% 6.92/7.21 thf(fact_4168_verit__minus__simplify_I4_J,axiom,
% 6.92/7.21 ! [B: code_integer] :
% 6.92/7.21 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B ) )
% 6.92/7.21 = B ) ).
% 6.92/7.21
% 6.92/7.21 % verit_minus_simplify(4)
% 6.92/7.21 thf(fact_4169_verit__minus__simplify_I4_J,axiom,
% 6.92/7.21 ! [B: rat] :
% 6.92/7.21 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B ) )
% 6.92/7.21 = B ) ).
% 6.92/7.21
% 6.92/7.21 % verit_minus_simplify(4)
% 6.92/7.21 thf(fact_4170_compl__le__compl__iff,axiom,
% 6.92/7.21 ! [X: assn,Y: assn] :
% 6.92/7.21 ( ( ord_less_eq_assn @ ( uminus_uminus_assn @ X ) @ ( uminus_uminus_assn @ Y ) )
% 6.92/7.21 = ( ord_less_eq_assn @ Y @ X ) ) ).
% 6.92/7.21
% 6.92/7.21 % compl_le_compl_iff
% 6.92/7.21 thf(fact_4171_compl__le__compl__iff,axiom,
% 6.92/7.21 ! [X: product_unit,Y: product_unit] :
% 6.92/7.21 ( ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) )
% 6.92/7.21 = ( ord_le3221252021190050221t_unit @ Y @ X ) ) ).
% 6.92/7.21
% 6.92/7.21 % compl_le_compl_iff
% 6.92/7.21 thf(fact_4172_compl__le__compl__iff,axiom,
% 6.92/7.21 ! [X: set_int,Y: set_int] :
% 6.92/7.21 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( uminus1532241313380277803et_int @ Y ) )
% 6.92/7.21 = ( ord_less_eq_set_int @ Y @ X ) ) ).
% 6.92/7.21
% 6.92/7.21 % compl_le_compl_iff
% 6.92/7.21 thf(fact_4173_neg__le__iff__le,axiom,
% 6.92/7.21 ! [B: code_integer,A: code_integer] :
% 6.92/7.21 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 6.92/7.21 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % neg_le_iff_le
% 6.92/7.21 thf(fact_4174_neg__le__iff__le,axiom,
% 6.92/7.21 ! [B: rat,A: rat] :
% 6.92/7.21 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 6.92/7.21 = ( ord_less_eq_rat @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % neg_le_iff_le
% 6.92/7.21 thf(fact_4175_neg__le__iff__le,axiom,
% 6.92/7.21 ! [B: int,A: int] :
% 6.92/7.21 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 6.92/7.21 = ( ord_less_eq_int @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % neg_le_iff_le
% 6.92/7.21 thf(fact_4176_add__diff__cancel__right_H,axiom,
% 6.92/7.21 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 6.92/7.21 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ A @ B ) @ B )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_right'
% 6.92/7.21 thf(fact_4177_add__diff__cancel__right_H,axiom,
% 6.92/7.21 ! [A: rat,B: rat] :
% 6.92/7.21 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_right'
% 6.92/7.21 thf(fact_4178_add__diff__cancel__right_H,axiom,
% 6.92/7.21 ! [A: nat,B: nat] :
% 6.92/7.21 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_right'
% 6.92/7.21 thf(fact_4179_add__diff__cancel__right_H,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_right'
% 6.92/7.21 thf(fact_4180_add__diff__cancel__right,axiom,
% 6.92/7.21 ! [A: multis2468970476368604999at_nat,C2: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 6.92/7.21 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ A @ C2 ) @ ( plus_p7104986032573967614at_nat @ B @ C2 ) )
% 6.92/7.21 = ( minus_4286766774447292334at_nat @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_right
% 6.92/7.21 thf(fact_4181_add__diff__cancel__right,axiom,
% 6.92/7.21 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.21 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 6.92/7.21 = ( minus_minus_rat @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_right
% 6.92/7.21 thf(fact_4182_add__diff__cancel__right,axiom,
% 6.92/7.21 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.21 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 6.92/7.21 = ( minus_minus_nat @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_right
% 6.92/7.21 thf(fact_4183_add__diff__cancel__right,axiom,
% 6.92/7.21 ! [A: int,C2: int,B: int] :
% 6.92/7.21 ( ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 6.92/7.21 = ( minus_minus_int @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_right
% 6.92/7.21 thf(fact_4184_add__diff__cancel__left_H,axiom,
% 6.92/7.21 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 6.92/7.21 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ A @ B ) @ A )
% 6.92/7.21 = B ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_left'
% 6.92/7.21 thf(fact_4185_add__diff__cancel__left_H,axiom,
% 6.92/7.21 ! [A: rat,B: rat] :
% 6.92/7.21 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 6.92/7.21 = B ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_left'
% 6.92/7.21 thf(fact_4186_add__diff__cancel__left_H,axiom,
% 6.92/7.21 ! [A: nat,B: nat] :
% 6.92/7.21 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 6.92/7.21 = B ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_left'
% 6.92/7.21 thf(fact_4187_add__diff__cancel__left_H,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 6.92/7.21 = B ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_left'
% 6.92/7.21 thf(fact_4188_add__diff__cancel__left,axiom,
% 6.92/7.21 ! [C2: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 6.92/7.21 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ C2 @ A ) @ ( plus_p7104986032573967614at_nat @ C2 @ B ) )
% 6.92/7.21 = ( minus_4286766774447292334at_nat @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_left
% 6.92/7.21 thf(fact_4189_add__diff__cancel__left,axiom,
% 6.92/7.21 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.21 ( ( minus_minus_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 6.92/7.21 = ( minus_minus_rat @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_left
% 6.92/7.21 thf(fact_4190_add__diff__cancel__left,axiom,
% 6.92/7.21 ! [C2: nat,A: nat,B: nat] :
% 6.92/7.21 ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 6.92/7.21 = ( minus_minus_nat @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_left
% 6.92/7.21 thf(fact_4191_add__diff__cancel__left,axiom,
% 6.92/7.21 ! [C2: int,A: int,B: int] :
% 6.92/7.21 ( ( minus_minus_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 6.92/7.21 = ( minus_minus_int @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel_left
% 6.92/7.21 thf(fact_4192_diff__add__cancel,axiom,
% 6.92/7.21 ! [A: rat,B: rat] :
% 6.92/7.21 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % diff_add_cancel
% 6.92/7.21 thf(fact_4193_diff__add__cancel,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % diff_add_cancel
% 6.92/7.21 thf(fact_4194_add__diff__cancel,axiom,
% 6.92/7.21 ! [A: rat,B: rat] :
% 6.92/7.21 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel
% 6.92/7.21 thf(fact_4195_add__diff__cancel,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 6.92/7.21 = A ) ).
% 6.92/7.21
% 6.92/7.21 % add_diff_cancel
% 6.92/7.21 thf(fact_4196_compl__less__compl__iff,axiom,
% 6.92/7.21 ! [X: assn,Y: assn] :
% 6.92/7.21 ( ( ord_less_assn @ ( uminus_uminus_assn @ X ) @ ( uminus_uminus_assn @ Y ) )
% 6.92/7.21 = ( ord_less_assn @ Y @ X ) ) ).
% 6.92/7.21
% 6.92/7.21 % compl_less_compl_iff
% 6.92/7.21 thf(fact_4197_compl__less__compl__iff,axiom,
% 6.92/7.21 ! [X: product_unit,Y: product_unit] :
% 6.92/7.21 ( ( ord_le361264281704409273t_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) )
% 6.92/7.21 = ( ord_le361264281704409273t_unit @ Y @ X ) ) ).
% 6.92/7.21
% 6.92/7.21 % compl_less_compl_iff
% 6.92/7.21 thf(fact_4198_neg__less__iff__less,axiom,
% 6.92/7.21 ! [B: int,A: int] :
% 6.92/7.21 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 6.92/7.21 = ( ord_less_int @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % neg_less_iff_less
% 6.92/7.21 thf(fact_4199_neg__less__iff__less,axiom,
% 6.92/7.21 ! [B: code_integer,A: code_integer] :
% 6.92/7.21 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 6.92/7.21 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % neg_less_iff_less
% 6.92/7.21 thf(fact_4200_neg__less__iff__less,axiom,
% 6.92/7.21 ! [B: rat,A: rat] :
% 6.92/7.21 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 6.92/7.21 = ( ord_less_rat @ A @ B ) ) ).
% 6.92/7.21
% 6.92/7.21 % neg_less_iff_less
% 6.92/7.21 thf(fact_4201_minus__add__distrib,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 6.92/7.21 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % minus_add_distrib
% 6.92/7.21 thf(fact_4202_minus__add__distrib,axiom,
% 6.92/7.21 ! [A: code_integer,B: code_integer] :
% 6.92/7.21 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 6.92/7.21 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % minus_add_distrib
% 6.92/7.21 thf(fact_4203_minus__add__distrib,axiom,
% 6.92/7.21 ! [A: rat,B: rat] :
% 6.92/7.21 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 6.92/7.21 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 6.92/7.21
% 6.92/7.21 % minus_add_distrib
% 6.92/7.21 thf(fact_4204_minus__add__cancel,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 6.92/7.21 = B ) ).
% 6.92/7.21
% 6.92/7.21 % minus_add_cancel
% 6.92/7.21 thf(fact_4205_minus__add__cancel,axiom,
% 6.92/7.21 ! [A: code_integer,B: code_integer] :
% 6.92/7.21 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 6.92/7.21 = B ) ).
% 6.92/7.21
% 6.92/7.21 % minus_add_cancel
% 6.92/7.21 thf(fact_4206_minus__add__cancel,axiom,
% 6.92/7.21 ! [A: rat,B: rat] :
% 6.92/7.21 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 6.92/7.21 = B ) ).
% 6.92/7.21
% 6.92/7.21 % minus_add_cancel
% 6.92/7.21 thf(fact_4207_add__minus__cancel,axiom,
% 6.92/7.21 ! [A: int,B: int] :
% 6.92/7.21 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 6.92/7.21 = B ) ).
% 6.92/7.21
% 6.92/7.21 % add_minus_cancel
% 6.92/7.21 thf(fact_4208_add__minus__cancel,axiom,
% 6.92/7.21 ! [A: code_integer,B: code_integer] :
% 6.92/7.21 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 6.92/7.21 = B ) ).
% 6.92/7.21
% 6.92/7.21 % add_minus_cancel
% 6.92/7.21 thf(fact_4209_add__minus__cancel,axiom,
% 6.92/7.21 ! [A: rat,B: rat] :
% 6.92/7.21 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 6.92/7.21 = B ) ).
% 6.92/7.21
% 6.92/7.21 % add_minus_cancel
% 6.92/7.21 thf(fact_4210_diff__0__eq__0,axiom,
% 6.92/7.22 ! [N2: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 6.92/7.22 = zero_zero_nat ) ).
% 6.92/7.22
% 6.92/7.22 % diff_0_eq_0
% 6.92/7.22 thf(fact_4211_diff__self__eq__0,axiom,
% 6.92/7.22 ! [M: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ M @ M )
% 6.92/7.22 = zero_zero_nat ) ).
% 6.92/7.22
% 6.92/7.22 % diff_self_eq_0
% 6.92/7.22 thf(fact_4212_diff__Suc__Suc,axiom,
% 6.92/7.22 ! [M: nat,N2: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 6.92/7.22 = ( minus_minus_nat @ M @ N2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_Suc_Suc
% 6.92/7.22 thf(fact_4213_Suc__diff__diff,axiom,
% 6.92/7.22 ! [M: nat,N2: nat,K2: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( suc @ K2 ) )
% 6.92/7.22 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N2 ) @ K2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Suc_diff_diff
% 6.92/7.22 thf(fact_4214_diff__diff__cancel,axiom,
% 6.92/7.22 ! [I2: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ I2 @ N2 )
% 6.92/7.22 => ( ( minus_minus_nat @ N2 @ ( minus_minus_nat @ N2 @ I2 ) )
% 6.92/7.22 = I2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_diff_cancel
% 6.92/7.22 thf(fact_4215_diff__diff__left,axiom,
% 6.92/7.22 ! [I2: nat,J2: nat,K2: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J2 ) @ K2 )
% 6.92/7.22 = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J2 @ K2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_diff_left
% 6.92/7.22 thf(fact_4216_diff__ge__0__iff__ge,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 6.92/7.22 = ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_ge_0_iff_ge
% 6.92/7.22 thf(fact_4217_diff__ge__0__iff__ge,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 6.92/7.22 = ( ord_less_eq_rat @ B @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_ge_0_iff_ge
% 6.92/7.22 thf(fact_4218_diff__ge__0__iff__ge,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 6.92/7.22 = ( ord_less_eq_int @ B @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_ge_0_iff_ge
% 6.92/7.22 thf(fact_4219_zero__comp__diff__simps_I1_J,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 6.92/7.22 = ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % zero_comp_diff_simps(1)
% 6.92/7.22 thf(fact_4220_zero__comp__diff__simps_I1_J,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 6.92/7.22 = ( ord_less_eq_rat @ B @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % zero_comp_diff_simps(1)
% 6.92/7.22 thf(fact_4221_zero__comp__diff__simps_I1_J,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 6.92/7.22 = ( ord_less_eq_int @ B @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % zero_comp_diff_simps(1)
% 6.92/7.22 thf(fact_4222_diff__gt__0__iff__gt,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 6.92/7.22 = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_gt_0_iff_gt
% 6.92/7.22 thf(fact_4223_diff__gt__0__iff__gt,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 6.92/7.22 = ( ord_less_rat @ B @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_gt_0_iff_gt
% 6.92/7.22 thf(fact_4224_diff__gt__0__iff__gt,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 6.92/7.22 = ( ord_less_int @ B @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_gt_0_iff_gt
% 6.92/7.22 thf(fact_4225_zero__comp__diff__simps_I2_J,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 6.92/7.22 = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % zero_comp_diff_simps(2)
% 6.92/7.22 thf(fact_4226_zero__comp__diff__simps_I2_J,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 6.92/7.22 = ( ord_less_rat @ B @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % zero_comp_diff_simps(2)
% 6.92/7.22 thf(fact_4227_zero__comp__diff__simps_I2_J,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 6.92/7.22 = ( ord_less_int @ B @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % zero_comp_diff_simps(2)
% 6.92/7.22 thf(fact_4228_neg__less__eq__nonneg,axiom,
% 6.92/7.22 ! [A: code_integer] :
% 6.92/7.22 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 6.92/7.22 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_less_eq_nonneg
% 6.92/7.22 thf(fact_4229_neg__less__eq__nonneg,axiom,
% 6.92/7.22 ! [A: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 6.92/7.22 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_less_eq_nonneg
% 6.92/7.22 thf(fact_4230_neg__less__eq__nonneg,axiom,
% 6.92/7.22 ! [A: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 6.92/7.22 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_less_eq_nonneg
% 6.92/7.22 thf(fact_4231_less__eq__neg__nonpos,axiom,
% 6.92/7.22 ! [A: code_integer] :
% 6.92/7.22 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 6.92/7.22 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_eq_neg_nonpos
% 6.92/7.22 thf(fact_4232_less__eq__neg__nonpos,axiom,
% 6.92/7.22 ! [A: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 6.92/7.22 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_eq_neg_nonpos
% 6.92/7.22 thf(fact_4233_less__eq__neg__nonpos,axiom,
% 6.92/7.22 ! [A: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 6.92/7.22 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_eq_neg_nonpos
% 6.92/7.22 thf(fact_4234_neg__le__0__iff__le,axiom,
% 6.92/7.22 ! [A: code_integer] :
% 6.92/7.22 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 6.92/7.22 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_le_0_iff_le
% 6.92/7.22 thf(fact_4235_neg__le__0__iff__le,axiom,
% 6.92/7.22 ! [A: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 6.92/7.22 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_le_0_iff_le
% 6.92/7.22 thf(fact_4236_neg__le__0__iff__le,axiom,
% 6.92/7.22 ! [A: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 6.92/7.22 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_le_0_iff_le
% 6.92/7.22 thf(fact_4237_neg__0__le__iff__le,axiom,
% 6.92/7.22 ! [A: code_integer] :
% 6.92/7.22 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 6.92/7.22 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_0_le_iff_le
% 6.92/7.22 thf(fact_4238_neg__0__le__iff__le,axiom,
% 6.92/7.22 ! [A: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 6.92/7.22 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_0_le_iff_le
% 6.92/7.22 thf(fact_4239_neg__0__le__iff__le,axiom,
% 6.92/7.22 ! [A: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 6.92/7.22 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_0_le_iff_le
% 6.92/7.22 thf(fact_4240_le__add__diff__inverse,axiom,
% 6.92/7.22 ! [B: rat,A: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.22 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 6.92/7.22 = A ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_add_diff_inverse
% 6.92/7.22 thf(fact_4241_le__add__diff__inverse,axiom,
% 6.92/7.22 ! [B: nat,A: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.22 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 6.92/7.22 = A ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_add_diff_inverse
% 6.92/7.22 thf(fact_4242_le__add__diff__inverse,axiom,
% 6.92/7.22 ! [B: int,A: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ B @ A )
% 6.92/7.22 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 6.92/7.22 = A ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_add_diff_inverse
% 6.92/7.22 thf(fact_4243_le__add__diff__inverse2,axiom,
% 6.92/7.22 ! [B: rat,A: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.22 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 6.92/7.22 = A ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_add_diff_inverse2
% 6.92/7.22 thf(fact_4244_le__add__diff__inverse2,axiom,
% 6.92/7.22 ! [B: nat,A: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.22 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 6.92/7.22 = A ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_add_diff_inverse2
% 6.92/7.22 thf(fact_4245_le__add__diff__inverse2,axiom,
% 6.92/7.22 ! [B: int,A: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ B @ A )
% 6.92/7.22 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 6.92/7.22 = A ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_add_diff_inverse2
% 6.92/7.22 thf(fact_4246_diff__add__zero,axiom,
% 6.92/7.22 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( minus_4286766774447292334at_nat @ A @ ( plus_p7104986032573967614at_nat @ A @ B ) )
% 6.92/7.22 = zero_z1048942125864253310at_nat ) ).
% 6.92/7.22
% 6.92/7.22 % diff_add_zero
% 6.92/7.22 thf(fact_4247_diff__add__zero,axiom,
% 6.92/7.22 ! [A: nat,B: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 6.92/7.22 = zero_zero_nat ) ).
% 6.92/7.22
% 6.92/7.22 % diff_add_zero
% 6.92/7.22 thf(fact_4248_less__neg__neg,axiom,
% 6.92/7.22 ! [A: int] :
% 6.92/7.22 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 6.92/7.22 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_neg_neg
% 6.92/7.22 thf(fact_4249_less__neg__neg,axiom,
% 6.92/7.22 ! [A: code_integer] :
% 6.92/7.22 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 6.92/7.22 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_neg_neg
% 6.92/7.22 thf(fact_4250_less__neg__neg,axiom,
% 6.92/7.22 ! [A: rat] :
% 6.92/7.22 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 6.92/7.22 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_neg_neg
% 6.92/7.22 thf(fact_4251_neg__less__pos,axiom,
% 6.92/7.22 ! [A: int] :
% 6.92/7.22 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 6.92/7.22 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_less_pos
% 6.92/7.22 thf(fact_4252_neg__less__pos,axiom,
% 6.92/7.22 ! [A: code_integer] :
% 6.92/7.22 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 6.92/7.22 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_less_pos
% 6.92/7.22 thf(fact_4253_neg__less__pos,axiom,
% 6.92/7.22 ! [A: rat] :
% 6.92/7.22 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 6.92/7.22 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_less_pos
% 6.92/7.22 thf(fact_4254_neg__0__less__iff__less,axiom,
% 6.92/7.22 ! [A: int] :
% 6.92/7.22 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 6.92/7.22 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_0_less_iff_less
% 6.92/7.22 thf(fact_4255_neg__0__less__iff__less,axiom,
% 6.92/7.22 ! [A: code_integer] :
% 6.92/7.22 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 6.92/7.22 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_0_less_iff_less
% 6.92/7.22 thf(fact_4256_neg__0__less__iff__less,axiom,
% 6.92/7.22 ! [A: rat] :
% 6.92/7.22 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 6.92/7.22 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_0_less_iff_less
% 6.92/7.22 thf(fact_4257_neg__less__0__iff__less,axiom,
% 6.92/7.22 ! [A: int] :
% 6.92/7.22 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 6.92/7.22 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_less_0_iff_less
% 6.92/7.22 thf(fact_4258_neg__less__0__iff__less,axiom,
% 6.92/7.22 ! [A: code_integer] :
% 6.92/7.22 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 6.92/7.22 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_less_0_iff_less
% 6.92/7.22 thf(fact_4259_neg__less__0__iff__less,axiom,
% 6.92/7.22 ! [A: rat] :
% 6.92/7.22 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 6.92/7.22 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_less_0_iff_less
% 6.92/7.22 thf(fact_4260_add_Oright__inverse,axiom,
% 6.92/7.22 ! [A: int] :
% 6.92/7.22 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 6.92/7.22 = zero_zero_int ) ).
% 6.92/7.22
% 6.92/7.22 % add.right_inverse
% 6.92/7.22 thf(fact_4261_add_Oright__inverse,axiom,
% 6.92/7.22 ! [A: code_integer] :
% 6.92/7.22 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 6.92/7.22 = zero_z3403309356797280102nteger ) ).
% 6.92/7.22
% 6.92/7.22 % add.right_inverse
% 6.92/7.22 thf(fact_4262_add_Oright__inverse,axiom,
% 6.92/7.22 ! [A: rat] :
% 6.92/7.22 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 6.92/7.22 = zero_zero_rat ) ).
% 6.92/7.22
% 6.92/7.22 % add.right_inverse
% 6.92/7.22 thf(fact_4263_ab__left__minus,axiom,
% 6.92/7.22 ! [A: int] :
% 6.92/7.22 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 6.92/7.22 = zero_zero_int ) ).
% 6.92/7.22
% 6.92/7.22 % ab_left_minus
% 6.92/7.22 thf(fact_4264_ab__left__minus,axiom,
% 6.92/7.22 ! [A: code_integer] :
% 6.92/7.22 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 6.92/7.22 = zero_z3403309356797280102nteger ) ).
% 6.92/7.22
% 6.92/7.22 % ab_left_minus
% 6.92/7.22 thf(fact_4265_ab__left__minus,axiom,
% 6.92/7.22 ! [A: rat] :
% 6.92/7.22 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 6.92/7.22 = zero_zero_rat ) ).
% 6.92/7.22
% 6.92/7.22 % ab_left_minus
% 6.92/7.22 thf(fact_4266_verit__minus__simplify_I3_J,axiom,
% 6.92/7.22 ! [B: int] :
% 6.92/7.22 ( ( minus_minus_int @ zero_zero_int @ B )
% 6.92/7.22 = ( uminus_uminus_int @ B ) ) ).
% 6.92/7.22
% 6.92/7.22 % verit_minus_simplify(3)
% 6.92/7.22 thf(fact_4267_verit__minus__simplify_I3_J,axiom,
% 6.92/7.22 ! [B: code_integer] :
% 6.92/7.22 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.22 = ( uminus1351360451143612070nteger @ B ) ) ).
% 6.92/7.22
% 6.92/7.22 % verit_minus_simplify(3)
% 6.92/7.22 thf(fact_4268_verit__minus__simplify_I3_J,axiom,
% 6.92/7.22 ! [B: rat] :
% 6.92/7.22 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 6.92/7.22 = ( uminus_uminus_rat @ B ) ) ).
% 6.92/7.22
% 6.92/7.22 % verit_minus_simplify(3)
% 6.92/7.22 thf(fact_4269_diff__minus__eq__add,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 6.92/7.22 = ( plus_plus_int @ A @ B ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_minus_eq_add
% 6.92/7.22 thf(fact_4270_diff__minus__eq__add,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 6.92/7.22 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_minus_eq_add
% 6.92/7.22 thf(fact_4271_diff__minus__eq__add,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 6.92/7.22 = ( plus_plus_rat @ A @ B ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_minus_eq_add
% 6.92/7.22 thf(fact_4272_uminus__add__conv__diff,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 6.92/7.22 = ( minus_minus_int @ B @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % uminus_add_conv_diff
% 6.92/7.22 thf(fact_4273_uminus__add__conv__diff,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 6.92/7.22 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % uminus_add_conv_diff
% 6.92/7.22 thf(fact_4274_uminus__add__conv__diff,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 6.92/7.22 = ( minus_minus_rat @ B @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % uminus_add_conv_diff
% 6.92/7.22 thf(fact_4275_boolean__algebra_Ode__Morgan__disj,axiom,
% 6.92/7.22 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( uminus6524753893492686040at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 6.92/7.22 = ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % boolean_algebra.de_Morgan_disj
% 6.92/7.22 thf(fact_4276_boolean__algebra_Ode__Morgan__disj,axiom,
% 6.92/7.22 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 6.92/7.22 ( ( uminus7117520113953359693_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) )
% 6.92/7.22 = ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ ( uminus7117520113953359693_int_o @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % boolean_algebra.de_Morgan_disj
% 6.92/7.22 thf(fact_4277_boolean__algebra_Ode__Morgan__disj,axiom,
% 6.92/7.22 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( uminus2330091110623919550at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 6.92/7.22 = ( inf_in1697001100524423349at_nat @ ( uminus2330091110623919550at_nat @ X ) @ ( uminus2330091110623919550at_nat @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % boolean_algebra.de_Morgan_disj
% 6.92/7.22 thf(fact_4278_boolean__algebra_Ode__Morgan__disj,axiom,
% 6.92/7.22 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( uminus935396558254630718at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 6.92/7.22 = ( inf_in7913087082777306421at_nat @ ( uminus935396558254630718at_nat @ X ) @ ( uminus935396558254630718at_nat @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % boolean_algebra.de_Morgan_disj
% 6.92/7.22 thf(fact_4279_boolean__algebra_Ode__Morgan__disj,axiom,
% 6.92/7.22 ! [X: set_nat,Y: set_nat] :
% 6.92/7.22 ( ( uminus5710092332889474511et_nat @ ( sup_sup_set_nat @ X @ Y ) )
% 6.92/7.22 = ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % boolean_algebra.de_Morgan_disj
% 6.92/7.22 thf(fact_4280_boolean__algebra_Ode__Morgan__disj,axiom,
% 6.92/7.22 ! [X: assn,Y: assn] :
% 6.92/7.22 ( ( uminus_uminus_assn @ ( sup_sup_assn @ X @ Y ) )
% 6.92/7.22 = ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ ( uminus_uminus_assn @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % boolean_algebra.de_Morgan_disj
% 6.92/7.22 thf(fact_4281_boolean__algebra_Ode__Morgan__disj,axiom,
% 6.92/7.22 ! [X: product_unit,Y: product_unit] :
% 6.92/7.22 ( ( uminus2952777764628376836t_unit @ ( sup_sup_Product_unit @ X @ Y ) )
% 6.92/7.22 = ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % boolean_algebra.de_Morgan_disj
% 6.92/7.22 thf(fact_4282_boolean__algebra_Ode__Morgan__conj,axiom,
% 6.92/7.22 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( uminus6524753893492686040at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 6.92/7.22 = ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ X ) @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % boolean_algebra.de_Morgan_conj
% 6.92/7.22 thf(fact_4283_boolean__algebra_Ode__Morgan__conj,axiom,
% 6.92/7.22 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 6.92/7.22 ( ( uminus7117520113953359693_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 6.92/7.22 = ( sup_su8463660629351352368_int_o @ ( uminus7117520113953359693_int_o @ X ) @ ( uminus7117520113953359693_int_o @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % boolean_algebra.de_Morgan_conj
% 6.92/7.22 thf(fact_4284_boolean__algebra_Ode__Morgan__conj,axiom,
% 6.92/7.22 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( uminus2330091110623919550at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) )
% 6.92/7.22 = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ X ) @ ( uminus2330091110623919550at_nat @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % boolean_algebra.de_Morgan_conj
% 6.92/7.22 thf(fact_4285_boolean__algebra_Ode__Morgan__conj,axiom,
% 6.92/7.22 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( uminus935396558254630718at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) )
% 6.92/7.22 = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ X ) @ ( uminus935396558254630718at_nat @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % boolean_algebra.de_Morgan_conj
% 6.92/7.22 thf(fact_4286_boolean__algebra_Ode__Morgan__conj,axiom,
% 6.92/7.22 ! [X: set_nat,Y: set_nat] :
% 6.92/7.22 ( ( uminus5710092332889474511et_nat @ ( inf_inf_set_nat @ X @ Y ) )
% 6.92/7.22 = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % boolean_algebra.de_Morgan_conj
% 6.92/7.22 thf(fact_4287_boolean__algebra_Ode__Morgan__conj,axiom,
% 6.92/7.22 ! [X: assn,Y: assn] :
% 6.92/7.22 ( ( uminus_uminus_assn @ ( inf_inf_assn @ X @ Y ) )
% 6.92/7.22 = ( sup_sup_assn @ ( uminus_uminus_assn @ X ) @ ( uminus_uminus_assn @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % boolean_algebra.de_Morgan_conj
% 6.92/7.22 thf(fact_4288_boolean__algebra_Ode__Morgan__conj,axiom,
% 6.92/7.22 ! [X: product_unit,Y: product_unit] :
% 6.92/7.22 ( ( uminus2952777764628376836t_unit @ ( inf_inf_Product_unit @ X @ Y ) )
% 6.92/7.22 = ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % boolean_algebra.de_Morgan_conj
% 6.92/7.22 thf(fact_4289_zero__less__diff,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) )
% 6.92/7.22 = ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % zero_less_diff
% 6.92/7.22 thf(fact_4290_diff__is__0__eq_H,axiom,
% 6.92/7.22 ! [M: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.22 => ( ( minus_minus_nat @ M @ N2 )
% 6.92/7.22 = zero_zero_nat ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_is_0_eq'
% 6.92/7.22 thf(fact_4291_diff__is__0__eq,axiom,
% 6.92/7.22 ! [M: nat,N2: nat] :
% 6.92/7.22 ( ( ( minus_minus_nat @ M @ N2 )
% 6.92/7.22 = zero_zero_nat )
% 6.92/7.22 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_is_0_eq
% 6.92/7.22 thf(fact_4292_Nat_Odiff__diff__right,axiom,
% 6.92/7.22 ! [K2: nat,J2: nat,I2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ J2 )
% 6.92/7.22 => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 6.92/7.22 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K2 ) @ J2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Nat.diff_diff_right
% 6.92/7.22 thf(fact_4293_Nat_Oadd__diff__assoc2,axiom,
% 6.92/7.22 ! [K2: nat,J2: nat,I2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ J2 )
% 6.92/7.22 => ( ( plus_plus_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 )
% 6.92/7.22 = ( minus_minus_nat @ ( plus_plus_nat @ J2 @ I2 ) @ K2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Nat.add_diff_assoc2
% 6.92/7.22 thf(fact_4294_Nat_Oadd__diff__assoc,axiom,
% 6.92/7.22 ! [K2: nat,J2: nat,I2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ J2 )
% 6.92/7.22 => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 6.92/7.22 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J2 ) @ K2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Nat.add_diff_assoc
% 6.92/7.22 thf(fact_4295_diff__Suc__1,axiom,
% 6.92/7.22 ! [N2: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 6.92/7.22 = N2 ) ).
% 6.92/7.22
% 6.92/7.22 % diff_Suc_1
% 6.92/7.22 thf(fact_4296_negative__zle,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 6.92/7.22
% 6.92/7.22 % negative_zle
% 6.92/7.22 thf(fact_4297_add__neg__numeral__special_I7_J,axiom,
% 6.92/7.22 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 6.92/7.22 = zero_zero_int ) ).
% 6.92/7.22
% 6.92/7.22 % add_neg_numeral_special(7)
% 6.92/7.22 thf(fact_4298_add__neg__numeral__special_I7_J,axiom,
% 6.92/7.22 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 6.92/7.22 = zero_z3403309356797280102nteger ) ).
% 6.92/7.22
% 6.92/7.22 % add_neg_numeral_special(7)
% 6.92/7.22 thf(fact_4299_add__neg__numeral__special_I7_J,axiom,
% 6.92/7.22 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 6.92/7.22 = zero_zero_rat ) ).
% 6.92/7.22
% 6.92/7.22 % add_neg_numeral_special(7)
% 6.92/7.22 thf(fact_4300_add__neg__numeral__special_I8_J,axiom,
% 6.92/7.22 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 6.92/7.22 = zero_zero_int ) ).
% 6.92/7.22
% 6.92/7.22 % add_neg_numeral_special(8)
% 6.92/7.22 thf(fact_4301_add__neg__numeral__special_I8_J,axiom,
% 6.92/7.22 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 6.92/7.22 = zero_z3403309356797280102nteger ) ).
% 6.92/7.22
% 6.92/7.22 % add_neg_numeral_special(8)
% 6.92/7.22 thf(fact_4302_add__neg__numeral__special_I8_J,axiom,
% 6.92/7.22 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 6.92/7.22 = zero_zero_rat ) ).
% 6.92/7.22
% 6.92/7.22 % add_neg_numeral_special(8)
% 6.92/7.22 thf(fact_4303_Suc__pred,axiom,
% 6.92/7.22 ! [N2: nat] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.22 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 6.92/7.22 = N2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Suc_pred
% 6.92/7.22 thf(fact_4304_diff__Suc__diff__eq1,axiom,
% 6.92/7.22 ! [K2: nat,J2: nat,I2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ J2 )
% 6.92/7.22 => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J2 @ K2 ) ) )
% 6.92/7.22 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( suc @ J2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_Suc_diff_eq1
% 6.92/7.22 thf(fact_4305_diff__Suc__diff__eq2,axiom,
% 6.92/7.22 ! [K2: nat,J2: nat,I2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ J2 )
% 6.92/7.22 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J2 @ K2 ) ) @ I2 )
% 6.92/7.22 = ( minus_minus_nat @ ( suc @ J2 ) @ ( plus_plus_nat @ K2 @ I2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_Suc_diff_eq2
% 6.92/7.22 thf(fact_4306_Suc__diff,axiom,
% 6.92/7.22 ! [M: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.22 => ( ( ord_less_eq_nat @ one_one_nat @ M )
% 6.92/7.22 => ( ( suc @ ( minus_minus_nat @ N2 @ M ) )
% 6.92/7.22 = ( minus_minus_nat @ N2 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Suc_diff
% 6.92/7.22 thf(fact_4307_nat__le__0,axiom,
% 6.92/7.22 ! [Z3: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ Z3 @ zero_zero_int )
% 6.92/7.22 => ( ( nat2 @ Z3 )
% 6.92/7.22 = zero_zero_nat ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_le_0
% 6.92/7.22 thf(fact_4308_nat__0__iff,axiom,
% 6.92/7.22 ! [I2: int] :
% 6.92/7.22 ( ( ( nat2 @ I2 )
% 6.92/7.22 = zero_zero_nat )
% 6.92/7.22 = ( ord_less_eq_int @ I2 @ zero_zero_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_0_iff
% 6.92/7.22 thf(fact_4309_zless__nat__conj,axiom,
% 6.92/7.22 ! [W2: int,Z3: int] :
% 6.92/7.22 ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z3 ) )
% 6.92/7.22 = ( ( ord_less_int @ zero_zero_int @ Z3 )
% 6.92/7.22 & ( ord_less_int @ W2 @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % zless_nat_conj
% 6.92/7.22 thf(fact_4310_negative__zless,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 6.92/7.22
% 6.92/7.22 % negative_zless
% 6.92/7.22 thf(fact_4311_int__nat__eq,axiom,
% 6.92/7.22 ! [Z3: int] :
% 6.92/7.22 ( ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.22 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z3 ) )
% 6.92/7.22 = Z3 ) )
% 6.92/7.22 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.22 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z3 ) )
% 6.92/7.22 = zero_zero_int ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % int_nat_eq
% 6.92/7.22 thf(fact_4312_zle__diff1__eq,axiom,
% 6.92/7.22 ! [W2: int,Z3: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ W2 @ ( minus_minus_int @ Z3 @ one_one_int ) )
% 6.92/7.22 = ( ord_less_int @ W2 @ Z3 ) ) ).
% 6.92/7.22
% 6.92/7.22 % zle_diff1_eq
% 6.92/7.22 thf(fact_4313_Suc__diff__1,axiom,
% 6.92/7.22 ! [N2: nat] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.22 => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 6.92/7.22 = N2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Suc_diff_1
% 6.92/7.22 thf(fact_4314_zero__less__nat__eq,axiom,
% 6.92/7.22 ! [Z3: int] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z3 ) )
% 6.92/7.22 = ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% 6.92/7.22
% 6.92/7.22 % zero_less_nat_eq
% 6.92/7.22 thf(fact_4315_verit__negate__coefficient_I3_J,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( A = B )
% 6.92/7.22 => ( ( uminus_uminus_int @ A )
% 6.92/7.22 = ( uminus_uminus_int @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % verit_negate_coefficient(3)
% 6.92/7.22 thf(fact_4316_verit__negate__coefficient_I3_J,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( A = B )
% 6.92/7.22 => ( ( uminus1351360451143612070nteger @ A )
% 6.92/7.22 = ( uminus1351360451143612070nteger @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % verit_negate_coefficient(3)
% 6.92/7.22 thf(fact_4317_verit__negate__coefficient_I3_J,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( A = B )
% 6.92/7.22 => ( ( uminus_uminus_rat @ A )
% 6.92/7.22 = ( uminus_uminus_rat @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % verit_negate_coefficient(3)
% 6.92/7.22 thf(fact_4318_diff__commute,axiom,
% 6.92/7.22 ! [I2: nat,J2: nat,K2: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J2 ) @ K2 )
% 6.92/7.22 = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K2 ) @ J2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_commute
% 6.92/7.22 thf(fact_4319_nat__diff__distrib_H,axiom,
% 6.92/7.22 ! [X: int,Y: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.22 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.22 => ( ( nat2 @ ( minus_minus_int @ X @ Y ) )
% 6.92/7.22 = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_diff_distrib'
% 6.92/7.22 thf(fact_4320_nat__diff__distrib,axiom,
% 6.92/7.22 ! [Z7: int,Z3: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 6.92/7.22 => ( ( ord_less_eq_int @ Z7 @ Z3 )
% 6.92/7.22 => ( ( nat2 @ ( minus_minus_int @ Z3 @ Z7 ) )
% 6.92/7.22 = ( minus_minus_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_diff_distrib
% 6.92/7.22 thf(fact_4321_group__cancel_Osub2,axiom,
% 6.92/7.22 ! [B5: int,K2: int,B: int,A: int] :
% 6.92/7.22 ( ( B5
% 6.92/7.22 = ( plus_plus_int @ K2 @ B ) )
% 6.92/7.22 => ( ( minus_minus_int @ A @ B5 )
% 6.92/7.22 = ( plus_plus_int @ ( uminus_uminus_int @ K2 ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % group_cancel.sub2
% 6.92/7.22 thf(fact_4322_group__cancel_Osub2,axiom,
% 6.92/7.22 ! [B5: code_integer,K2: code_integer,B: code_integer,A: code_integer] :
% 6.92/7.22 ( ( B5
% 6.92/7.22 = ( plus_p5714425477246183910nteger @ K2 @ B ) )
% 6.92/7.22 => ( ( minus_8373710615458151222nteger @ A @ B5 )
% 6.92/7.22 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K2 ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % group_cancel.sub2
% 6.92/7.22 thf(fact_4323_group__cancel_Osub2,axiom,
% 6.92/7.22 ! [B5: rat,K2: rat,B: rat,A: rat] :
% 6.92/7.22 ( ( B5
% 6.92/7.22 = ( plus_plus_rat @ K2 @ B ) )
% 6.92/7.22 => ( ( minus_minus_rat @ A @ B5 )
% 6.92/7.22 = ( plus_plus_rat @ ( uminus_uminus_rat @ K2 ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % group_cancel.sub2
% 6.92/7.22 thf(fact_4324_diff__conv__add__uminus,axiom,
% 6.92/7.22 ( minus_minus_int
% 6.92/7.22 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ A5 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_conv_add_uminus
% 6.92/7.22 thf(fact_4325_diff__conv__add__uminus,axiom,
% 6.92/7.22 ( minus_8373710615458151222nteger
% 6.92/7.22 = ( ^ [A5: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A5 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_conv_add_uminus
% 6.92/7.22 thf(fact_4326_diff__conv__add__uminus,axiom,
% 6.92/7.22 ( minus_minus_rat
% 6.92/7.22 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ A5 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_conv_add_uminus
% 6.92/7.22 thf(fact_4327_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 6.92/7.22 ( minus_minus_int
% 6.92/7.22 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ A5 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % ab_group_add_class.ab_diff_conv_add_uminus
% 6.92/7.22 thf(fact_4328_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 6.92/7.22 ( minus_8373710615458151222nteger
% 6.92/7.22 = ( ^ [A5: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A5 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % ab_group_add_class.ab_diff_conv_add_uminus
% 6.92/7.22 thf(fact_4329_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 6.92/7.22 ( minus_minus_rat
% 6.92/7.22 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ A5 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % ab_group_add_class.ab_diff_conv_add_uminus
% 6.92/7.22 thf(fact_4330_int__minus,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ M ) )
% 6.92/7.22 = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % int_minus
% 6.92/7.22 thf(fact_4331_nat__minus__as__int,axiom,
% 6.92/7.22 ( minus_minus_nat
% 6.92/7.22 = ( ^ [A5: nat,B4: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_minus_as_int
% 6.92/7.22 thf(fact_4332_of__nat__diff,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N2 ) )
% 6.92/7.22 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % of_nat_diff
% 6.92/7.22 thf(fact_4333_of__nat__diff,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N2 ) )
% 6.92/7.22 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % of_nat_diff
% 6.92/7.22 thf(fact_4334_of__nat__diff,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N2 ) )
% 6.92/7.22 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % of_nat_diff
% 6.92/7.22 thf(fact_4335_of__nat__diff,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( semiri4939895301339042750nteger @ ( minus_minus_nat @ M @ N2 ) )
% 6.92/7.22 = ( minus_8373710615458151222nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % of_nat_diff
% 6.92/7.22 thf(fact_4336_diff__nat__eq__if,axiom,
% 6.92/7.22 ! [Z7: int,Z3: int] :
% 6.92/7.22 ( ( ( ord_less_int @ Z7 @ zero_zero_int )
% 6.92/7.22 => ( ( minus_minus_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z7 ) )
% 6.92/7.22 = ( nat2 @ Z3 ) ) )
% 6.92/7.22 & ( ~ ( ord_less_int @ Z7 @ zero_zero_int )
% 6.92/7.22 => ( ( minus_minus_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z7 ) )
% 6.92/7.22 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z3 @ Z7 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z3 @ Z7 ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_nat_eq_if
% 6.92/7.22 thf(fact_4337_diff__eq__diff__less__eq,axiom,
% 6.92/7.22 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.22 ( ( ( minus_minus_rat @ A @ B )
% 6.92/7.22 = ( minus_minus_rat @ C2 @ D2 ) )
% 6.92/7.22 => ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.22 = ( ord_less_eq_rat @ C2 @ D2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_eq_diff_less_eq
% 6.92/7.22 thf(fact_4338_diff__eq__diff__less__eq,axiom,
% 6.92/7.22 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.22 ( ( ( minus_minus_int @ A @ B )
% 6.92/7.22 = ( minus_minus_int @ C2 @ D2 ) )
% 6.92/7.22 => ( ( ord_less_eq_int @ A @ B )
% 6.92/7.22 = ( ord_less_eq_int @ C2 @ D2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_eq_diff_less_eq
% 6.92/7.22 thf(fact_4339_diff__right__mono,axiom,
% 6.92/7.22 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.22 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ C2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_right_mono
% 6.92/7.22 thf(fact_4340_diff__right__mono,axiom,
% 6.92/7.22 ! [A: int,B: int,C2: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.22 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ C2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_right_mono
% 6.92/7.22 thf(fact_4341_diff__left__mono,axiom,
% 6.92/7.22 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.22 => ( ord_less_eq_rat @ ( minus_minus_rat @ C2 @ A ) @ ( minus_minus_rat @ C2 @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_left_mono
% 6.92/7.22 thf(fact_4342_diff__left__mono,axiom,
% 6.92/7.22 ! [B: int,A: int,C2: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ B @ A )
% 6.92/7.22 => ( ord_less_eq_int @ ( minus_minus_int @ C2 @ A ) @ ( minus_minus_int @ C2 @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_left_mono
% 6.92/7.22 thf(fact_4343_diff__mono,axiom,
% 6.92/7.22 ! [A: rat,B: rat,D2: rat,C2: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.22 => ( ( ord_less_eq_rat @ D2 @ C2 )
% 6.92/7.22 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_mono
% 6.92/7.22 thf(fact_4344_diff__mono,axiom,
% 6.92/7.22 ! [A: int,B: int,D2: int,C2: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.22 => ( ( ord_less_eq_int @ D2 @ C2 )
% 6.92/7.22 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_mono
% 6.92/7.22 thf(fact_4345_diff__strict__right__mono,axiom,
% 6.92/7.22 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.22 ( ( ord_less_rat @ A @ B )
% 6.92/7.22 => ( ord_less_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ C2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_strict_right_mono
% 6.92/7.22 thf(fact_4346_diff__strict__right__mono,axiom,
% 6.92/7.22 ! [A: int,B: int,C2: int] :
% 6.92/7.22 ( ( ord_less_int @ A @ B )
% 6.92/7.22 => ( ord_less_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ C2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_strict_right_mono
% 6.92/7.22 thf(fact_4347_diff__strict__left__mono,axiom,
% 6.92/7.22 ! [B: rat,A: rat,C2: rat] :
% 6.92/7.22 ( ( ord_less_rat @ B @ A )
% 6.92/7.22 => ( ord_less_rat @ ( minus_minus_rat @ C2 @ A ) @ ( minus_minus_rat @ C2 @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_strict_left_mono
% 6.92/7.22 thf(fact_4348_diff__strict__left__mono,axiom,
% 6.92/7.22 ! [B: int,A: int,C2: int] :
% 6.92/7.22 ( ( ord_less_int @ B @ A )
% 6.92/7.22 => ( ord_less_int @ ( minus_minus_int @ C2 @ A ) @ ( minus_minus_int @ C2 @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_strict_left_mono
% 6.92/7.22 thf(fact_4349_diff__eq__diff__less,axiom,
% 6.92/7.22 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.22 ( ( ( minus_minus_rat @ A @ B )
% 6.92/7.22 = ( minus_minus_rat @ C2 @ D2 ) )
% 6.92/7.22 => ( ( ord_less_rat @ A @ B )
% 6.92/7.22 = ( ord_less_rat @ C2 @ D2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_eq_diff_less
% 6.92/7.22 thf(fact_4350_diff__eq__diff__less,axiom,
% 6.92/7.22 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.22 ( ( ( minus_minus_int @ A @ B )
% 6.92/7.22 = ( minus_minus_int @ C2 @ D2 ) )
% 6.92/7.22 => ( ( ord_less_int @ A @ B )
% 6.92/7.22 = ( ord_less_int @ C2 @ D2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_eq_diff_less
% 6.92/7.22 thf(fact_4351_diff__strict__mono,axiom,
% 6.92/7.22 ! [A: rat,B: rat,D2: rat,C2: rat] :
% 6.92/7.22 ( ( ord_less_rat @ A @ B )
% 6.92/7.22 => ( ( ord_less_rat @ D2 @ C2 )
% 6.92/7.22 => ( ord_less_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_strict_mono
% 6.92/7.22 thf(fact_4352_diff__strict__mono,axiom,
% 6.92/7.22 ! [A: int,B: int,D2: int,C2: int] :
% 6.92/7.22 ( ( ord_less_int @ A @ B )
% 6.92/7.22 => ( ( ord_less_int @ D2 @ C2 )
% 6.92/7.22 => ( ord_less_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_strict_mono
% 6.92/7.22 thf(fact_4353_diff__diff__eq,axiom,
% 6.92/7.22 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C2: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( minus_4286766774447292334at_nat @ ( minus_4286766774447292334at_nat @ A @ B ) @ C2 )
% 6.92/7.22 = ( minus_4286766774447292334at_nat @ A @ ( plus_p7104986032573967614at_nat @ B @ C2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_diff_eq
% 6.92/7.22 thf(fact_4354_diff__diff__eq,axiom,
% 6.92/7.22 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.22 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 6.92/7.22 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_diff_eq
% 6.92/7.22 thf(fact_4355_diff__diff__eq,axiom,
% 6.92/7.22 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 )
% 6.92/7.22 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_diff_eq
% 6.92/7.22 thf(fact_4356_diff__diff__eq,axiom,
% 6.92/7.22 ! [A: int,B: int,C2: int] :
% 6.92/7.22 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 6.92/7.22 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_diff_eq
% 6.92/7.22 thf(fact_4357_add__implies__diff,axiom,
% 6.92/7.22 ! [C2: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( ( plus_p7104986032573967614at_nat @ C2 @ B )
% 6.92/7.22 = A )
% 6.92/7.22 => ( C2
% 6.92/7.22 = ( minus_4286766774447292334at_nat @ A @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_implies_diff
% 6.92/7.22 thf(fact_4358_add__implies__diff,axiom,
% 6.92/7.22 ! [C2: rat,B: rat,A: rat] :
% 6.92/7.22 ( ( ( plus_plus_rat @ C2 @ B )
% 6.92/7.22 = A )
% 6.92/7.22 => ( C2
% 6.92/7.22 = ( minus_minus_rat @ A @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_implies_diff
% 6.92/7.22 thf(fact_4359_add__implies__diff,axiom,
% 6.92/7.22 ! [C2: nat,B: nat,A: nat] :
% 6.92/7.22 ( ( ( plus_plus_nat @ C2 @ B )
% 6.92/7.22 = A )
% 6.92/7.22 => ( C2
% 6.92/7.22 = ( minus_minus_nat @ A @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_implies_diff
% 6.92/7.22 thf(fact_4360_add__implies__diff,axiom,
% 6.92/7.22 ! [C2: int,B: int,A: int] :
% 6.92/7.22 ( ( ( plus_plus_int @ C2 @ B )
% 6.92/7.22 = A )
% 6.92/7.22 => ( C2
% 6.92/7.22 = ( minus_minus_int @ A @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_implies_diff
% 6.92/7.22 thf(fact_4361_diff__add__eq__diff__diff__swap,axiom,
% 6.92/7.22 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.22 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 6.92/7.22 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C2 ) @ B ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_add_eq_diff_diff_swap
% 6.92/7.22 thf(fact_4362_diff__add__eq__diff__diff__swap,axiom,
% 6.92/7.22 ! [A: int,B: int,C2: int] :
% 6.92/7.22 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 6.92/7.22 = ( minus_minus_int @ ( minus_minus_int @ A @ C2 ) @ B ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_add_eq_diff_diff_swap
% 6.92/7.22 thf(fact_4363_diff__add__eq,axiom,
% 6.92/7.22 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.22 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 6.92/7.22 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_add_eq
% 6.92/7.22 thf(fact_4364_diff__add__eq,axiom,
% 6.92/7.22 ! [A: int,B: int,C2: int] :
% 6.92/7.22 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 6.92/7.22 = ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_add_eq
% 6.92/7.22 thf(fact_4365_diff__diff__eq2,axiom,
% 6.92/7.22 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.22 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 6.92/7.22 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_diff_eq2
% 6.92/7.22 thf(fact_4366_diff__diff__eq2,axiom,
% 6.92/7.22 ! [A: int,B: int,C2: int] :
% 6.92/7.22 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 6.92/7.22 = ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_diff_eq2
% 6.92/7.22 thf(fact_4367_add__diff__eq,axiom,
% 6.92/7.22 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.22 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 6.92/7.22 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_diff_eq
% 6.92/7.22 thf(fact_4368_add__diff__eq,axiom,
% 6.92/7.22 ! [A: int,B: int,C2: int] :
% 6.92/7.22 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 6.92/7.22 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_diff_eq
% 6.92/7.22 thf(fact_4369_eq__diff__eq,axiom,
% 6.92/7.22 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.22 ( ( A
% 6.92/7.22 = ( minus_minus_rat @ C2 @ B ) )
% 6.92/7.22 = ( ( plus_plus_rat @ A @ B )
% 6.92/7.22 = C2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % eq_diff_eq
% 6.92/7.22 thf(fact_4370_eq__diff__eq,axiom,
% 6.92/7.22 ! [A: int,C2: int,B: int] :
% 6.92/7.22 ( ( A
% 6.92/7.22 = ( minus_minus_int @ C2 @ B ) )
% 6.92/7.22 = ( ( plus_plus_int @ A @ B )
% 6.92/7.22 = C2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % eq_diff_eq
% 6.92/7.22 thf(fact_4371_diff__eq__eq,axiom,
% 6.92/7.22 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.22 ( ( ( minus_minus_rat @ A @ B )
% 6.92/7.22 = C2 )
% 6.92/7.22 = ( A
% 6.92/7.22 = ( plus_plus_rat @ C2 @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_eq_eq
% 6.92/7.22 thf(fact_4372_diff__eq__eq,axiom,
% 6.92/7.22 ! [A: int,B: int,C2: int] :
% 6.92/7.22 ( ( ( minus_minus_int @ A @ B )
% 6.92/7.22 = C2 )
% 6.92/7.22 = ( A
% 6.92/7.22 = ( plus_plus_int @ C2 @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_eq_eq
% 6.92/7.22 thf(fact_4373_group__cancel_Osub1,axiom,
% 6.92/7.22 ! [A4: rat,K2: rat,A: rat,B: rat] :
% 6.92/7.22 ( ( A4
% 6.92/7.22 = ( plus_plus_rat @ K2 @ A ) )
% 6.92/7.22 => ( ( minus_minus_rat @ A4 @ B )
% 6.92/7.22 = ( plus_plus_rat @ K2 @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % group_cancel.sub1
% 6.92/7.22 thf(fact_4374_group__cancel_Osub1,axiom,
% 6.92/7.22 ! [A4: int,K2: int,A: int,B: int] :
% 6.92/7.22 ( ( A4
% 6.92/7.22 = ( plus_plus_int @ K2 @ A ) )
% 6.92/7.22 => ( ( minus_minus_int @ A4 @ B )
% 6.92/7.22 = ( plus_plus_int @ K2 @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % group_cancel.sub1
% 6.92/7.22 thf(fact_4375_inf__period_I2_J,axiom,
% 6.92/7.22 ! [P2: rat > $o,D4: rat,Q2: rat > $o] :
% 6.92/7.22 ( ! [X3: rat,K: rat] :
% 6.92/7.22 ( ( P2 @ X3 )
% 6.92/7.22 = ( P2 @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D4 ) ) ) )
% 6.92/7.22 => ( ! [X3: rat,K: rat] :
% 6.92/7.22 ( ( Q2 @ X3 )
% 6.92/7.22 = ( Q2 @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D4 ) ) ) )
% 6.92/7.22 => ! [X6: rat,K4: rat] :
% 6.92/7.22 ( ( ( P2 @ X6 )
% 6.92/7.22 | ( Q2 @ X6 ) )
% 6.92/7.22 = ( ( P2 @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D4 ) ) )
% 6.92/7.22 | ( Q2 @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % inf_period(2)
% 6.92/7.22 thf(fact_4376_inf__period_I2_J,axiom,
% 6.92/7.22 ! [P2: int > $o,D4: int,Q2: int > $o] :
% 6.92/7.22 ( ! [X3: int,K: int] :
% 6.92/7.22 ( ( P2 @ X3 )
% 6.92/7.22 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D4 ) ) ) )
% 6.92/7.22 => ( ! [X3: int,K: int] :
% 6.92/7.22 ( ( Q2 @ X3 )
% 6.92/7.22 = ( Q2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D4 ) ) ) )
% 6.92/7.22 => ! [X6: int,K4: int] :
% 6.92/7.22 ( ( ( P2 @ X6 )
% 6.92/7.22 | ( Q2 @ X6 ) )
% 6.92/7.22 = ( ( P2 @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D4 ) ) )
% 6.92/7.22 | ( Q2 @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % inf_period(2)
% 6.92/7.22 thf(fact_4377_inf__period_I1_J,axiom,
% 6.92/7.22 ! [P2: rat > $o,D4: rat,Q2: rat > $o] :
% 6.92/7.22 ( ! [X3: rat,K: rat] :
% 6.92/7.22 ( ( P2 @ X3 )
% 6.92/7.22 = ( P2 @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D4 ) ) ) )
% 6.92/7.22 => ( ! [X3: rat,K: rat] :
% 6.92/7.22 ( ( Q2 @ X3 )
% 6.92/7.22 = ( Q2 @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D4 ) ) ) )
% 6.92/7.22 => ! [X6: rat,K4: rat] :
% 6.92/7.22 ( ( ( P2 @ X6 )
% 6.92/7.22 & ( Q2 @ X6 ) )
% 6.92/7.22 = ( ( P2 @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D4 ) ) )
% 6.92/7.22 & ( Q2 @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % inf_period(1)
% 6.92/7.22 thf(fact_4378_inf__period_I1_J,axiom,
% 6.92/7.22 ! [P2: int > $o,D4: int,Q2: int > $o] :
% 6.92/7.22 ( ! [X3: int,K: int] :
% 6.92/7.22 ( ( P2 @ X3 )
% 6.92/7.22 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D4 ) ) ) )
% 6.92/7.22 => ( ! [X3: int,K: int] :
% 6.92/7.22 ( ( Q2 @ X3 )
% 6.92/7.22 = ( Q2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D4 ) ) ) )
% 6.92/7.22 => ! [X6: int,K4: int] :
% 6.92/7.22 ( ( ( P2 @ X6 )
% 6.92/7.22 & ( Q2 @ X6 ) )
% 6.92/7.22 = ( ( P2 @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D4 ) ) )
% 6.92/7.22 & ( Q2 @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % inf_period(1)
% 6.92/7.22 thf(fact_4379_compl__le__swap2,axiom,
% 6.92/7.22 ! [Y: assn,X: assn] :
% 6.92/7.22 ( ( ord_less_eq_assn @ ( uminus_uminus_assn @ Y ) @ X )
% 6.92/7.22 => ( ord_less_eq_assn @ ( uminus_uminus_assn @ X ) @ Y ) ) ).
% 6.92/7.22
% 6.92/7.22 % compl_le_swap2
% 6.92/7.22 thf(fact_4380_compl__le__swap2,axiom,
% 6.92/7.22 ! [Y: product_unit,X: product_unit] :
% 6.92/7.22 ( ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ Y ) @ X )
% 6.92/7.22 => ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) ) ).
% 6.92/7.22
% 6.92/7.22 % compl_le_swap2
% 6.92/7.22 thf(fact_4381_compl__le__swap2,axiom,
% 6.92/7.22 ! [Y: set_int,X: set_int] :
% 6.92/7.22 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X )
% 6.92/7.22 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) ) ).
% 6.92/7.22
% 6.92/7.22 % compl_le_swap2
% 6.92/7.22 thf(fact_4382_compl__le__swap1,axiom,
% 6.92/7.22 ! [Y: assn,X: assn] :
% 6.92/7.22 ( ( ord_less_eq_assn @ Y @ ( uminus_uminus_assn @ X ) )
% 6.92/7.22 => ( ord_less_eq_assn @ X @ ( uminus_uminus_assn @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % compl_le_swap1
% 6.92/7.22 thf(fact_4383_compl__le__swap1,axiom,
% 6.92/7.22 ! [Y: product_unit,X: product_unit] :
% 6.92/7.22 ( ( ord_le3221252021190050221t_unit @ Y @ ( uminus2952777764628376836t_unit @ X ) )
% 6.92/7.22 => ( ord_le3221252021190050221t_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % compl_le_swap1
% 6.92/7.22 thf(fact_4384_compl__le__swap1,axiom,
% 6.92/7.22 ! [Y: set_int,X: set_int] :
% 6.92/7.22 ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X ) )
% 6.92/7.22 => ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % compl_le_swap1
% 6.92/7.22 thf(fact_4385_compl__mono,axiom,
% 6.92/7.22 ! [X: assn,Y: assn] :
% 6.92/7.22 ( ( ord_less_eq_assn @ X @ Y )
% 6.92/7.22 => ( ord_less_eq_assn @ ( uminus_uminus_assn @ Y ) @ ( uminus_uminus_assn @ X ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % compl_mono
% 6.92/7.22 thf(fact_4386_compl__mono,axiom,
% 6.92/7.22 ! [X: product_unit,Y: product_unit] :
% 6.92/7.22 ( ( ord_le3221252021190050221t_unit @ X @ Y )
% 6.92/7.22 => ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ Y ) @ ( uminus2952777764628376836t_unit @ X ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % compl_mono
% 6.92/7.22 thf(fact_4387_compl__mono,axiom,
% 6.92/7.22 ! [X: set_int,Y: set_int] :
% 6.92/7.22 ( ( ord_less_eq_set_int @ X @ Y )
% 6.92/7.22 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % compl_mono
% 6.92/7.22 thf(fact_4388_le__imp__neg__le,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( ord_le3102999989581377725nteger @ A @ B )
% 6.92/7.22 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_imp_neg_le
% 6.92/7.22 thf(fact_4389_le__imp__neg__le,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.22 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_imp_neg_le
% 6.92/7.22 thf(fact_4390_le__imp__neg__le,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.22 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_imp_neg_le
% 6.92/7.22 thf(fact_4391_minus__le__iff,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 6.92/7.22 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % minus_le_iff
% 6.92/7.22 thf(fact_4392_minus__le__iff,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 6.92/7.22 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % minus_le_iff
% 6.92/7.22 thf(fact_4393_minus__le__iff,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 6.92/7.22 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % minus_le_iff
% 6.92/7.22 thf(fact_4394_le__minus__iff,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 6.92/7.22 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_minus_iff
% 6.92/7.22 thf(fact_4395_le__minus__iff,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 6.92/7.22 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_minus_iff
% 6.92/7.22 thf(fact_4396_le__minus__iff,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 6.92/7.22 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_minus_iff
% 6.92/7.22 thf(fact_4397_compl__less__swap2,axiom,
% 6.92/7.22 ! [Y: assn,X: assn] :
% 6.92/7.22 ( ( ord_less_assn @ ( uminus_uminus_assn @ Y ) @ X )
% 6.92/7.22 => ( ord_less_assn @ ( uminus_uminus_assn @ X ) @ Y ) ) ).
% 6.92/7.22
% 6.92/7.22 % compl_less_swap2
% 6.92/7.22 thf(fact_4398_compl__less__swap2,axiom,
% 6.92/7.22 ! [Y: product_unit,X: product_unit] :
% 6.92/7.22 ( ( ord_le361264281704409273t_unit @ ( uminus2952777764628376836t_unit @ Y ) @ X )
% 6.92/7.22 => ( ord_le361264281704409273t_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) ) ).
% 6.92/7.22
% 6.92/7.22 % compl_less_swap2
% 6.92/7.22 thf(fact_4399_compl__less__swap1,axiom,
% 6.92/7.22 ! [Y: assn,X: assn] :
% 6.92/7.22 ( ( ord_less_assn @ Y @ ( uminus_uminus_assn @ X ) )
% 6.92/7.22 => ( ord_less_assn @ X @ ( uminus_uminus_assn @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % compl_less_swap1
% 6.92/7.22 thf(fact_4400_compl__less__swap1,axiom,
% 6.92/7.22 ! [Y: product_unit,X: product_unit] :
% 6.92/7.22 ( ( ord_le361264281704409273t_unit @ Y @ ( uminus2952777764628376836t_unit @ X ) )
% 6.92/7.22 => ( ord_le361264281704409273t_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % compl_less_swap1
% 6.92/7.22 thf(fact_4401_minus__less__iff,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 6.92/7.22 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % minus_less_iff
% 6.92/7.22 thf(fact_4402_minus__less__iff,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 6.92/7.22 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % minus_less_iff
% 6.92/7.22 thf(fact_4403_minus__less__iff,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 6.92/7.22 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 6.92/7.22
% 6.92/7.22 % minus_less_iff
% 6.92/7.22 thf(fact_4404_less__minus__iff,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 6.92/7.22 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_minus_iff
% 6.92/7.22 thf(fact_4405_less__minus__iff,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 6.92/7.22 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_minus_iff
% 6.92/7.22 thf(fact_4406_less__minus__iff,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 6.92/7.22 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_minus_iff
% 6.92/7.22 thf(fact_4407_verit__negate__coefficient_I2_J,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( ord_less_int @ A @ B )
% 6.92/7.22 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % verit_negate_coefficient(2)
% 6.92/7.22 thf(fact_4408_verit__negate__coefficient_I2_J,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( ord_le6747313008572928689nteger @ A @ B )
% 6.92/7.22 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % verit_negate_coefficient(2)
% 6.92/7.22 thf(fact_4409_verit__negate__coefficient_I2_J,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_rat @ A @ B )
% 6.92/7.22 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % verit_negate_coefficient(2)
% 6.92/7.22 thf(fact_4410_is__num__normalize_I8_J,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 6.92/7.22 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % is_num_normalize(8)
% 6.92/7.22 thf(fact_4411_is__num__normalize_I8_J,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 6.92/7.22 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % is_num_normalize(8)
% 6.92/7.22 thf(fact_4412_is__num__normalize_I8_J,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 6.92/7.22 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % is_num_normalize(8)
% 6.92/7.22 thf(fact_4413_add_Oinverse__distrib__swap,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 6.92/7.22 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add.inverse_distrib_swap
% 6.92/7.22 thf(fact_4414_add_Oinverse__distrib__swap,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 6.92/7.22 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add.inverse_distrib_swap
% 6.92/7.22 thf(fact_4415_add_Oinverse__distrib__swap,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 6.92/7.22 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add.inverse_distrib_swap
% 6.92/7.22 thf(fact_4416_group__cancel_Oneg1,axiom,
% 6.92/7.22 ! [A4: int,K2: int,A: int] :
% 6.92/7.22 ( ( A4
% 6.92/7.22 = ( plus_plus_int @ K2 @ A ) )
% 6.92/7.22 => ( ( uminus_uminus_int @ A4 )
% 6.92/7.22 = ( plus_plus_int @ ( uminus_uminus_int @ K2 ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % group_cancel.neg1
% 6.92/7.22 thf(fact_4417_group__cancel_Oneg1,axiom,
% 6.92/7.22 ! [A4: code_integer,K2: code_integer,A: code_integer] :
% 6.92/7.22 ( ( A4
% 6.92/7.22 = ( plus_p5714425477246183910nteger @ K2 @ A ) )
% 6.92/7.22 => ( ( uminus1351360451143612070nteger @ A4 )
% 6.92/7.22 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K2 ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % group_cancel.neg1
% 6.92/7.22 thf(fact_4418_group__cancel_Oneg1,axiom,
% 6.92/7.22 ! [A4: rat,K2: rat,A: rat] :
% 6.92/7.22 ( ( A4
% 6.92/7.22 = ( plus_plus_rat @ K2 @ A ) )
% 6.92/7.22 => ( ( uminus_uminus_rat @ A4 )
% 6.92/7.22 = ( plus_plus_rat @ ( uminus_uminus_rat @ K2 ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % group_cancel.neg1
% 6.92/7.22 thf(fact_4419_length__induct,axiom,
% 6.92/7.22 ! [P2: list_nat > $o,Xs: list_nat] :
% 6.92/7.22 ( ! [Xs2: list_nat] :
% 6.92/7.22 ( ! [Ys: list_nat] :
% 6.92/7.22 ( ( ord_less_nat @ ( size_size_list_nat @ Ys ) @ ( size_size_list_nat @ Xs2 ) )
% 6.92/7.22 => ( P2 @ Ys ) )
% 6.92/7.22 => ( P2 @ Xs2 ) )
% 6.92/7.22 => ( P2 @ Xs ) ) ).
% 6.92/7.22
% 6.92/7.22 % length_induct
% 6.92/7.22 thf(fact_4420_length__induct,axiom,
% 6.92/7.22 ! [P2: list_o > $o,Xs: list_o] :
% 6.92/7.22 ( ! [Xs2: list_o] :
% 6.92/7.22 ( ! [Ys: list_o] :
% 6.92/7.22 ( ( ord_less_nat @ ( size_size_list_o @ Ys ) @ ( size_size_list_o @ Xs2 ) )
% 6.92/7.22 => ( P2 @ Ys ) )
% 6.92/7.22 => ( P2 @ Xs2 ) )
% 6.92/7.22 => ( P2 @ Xs ) ) ).
% 6.92/7.22
% 6.92/7.22 % length_induct
% 6.92/7.22 thf(fact_4421_length__induct,axiom,
% 6.92/7.22 ! [P2: list_int > $o,Xs: list_int] :
% 6.92/7.22 ( ! [Xs2: list_int] :
% 6.92/7.22 ( ! [Ys: list_int] :
% 6.92/7.22 ( ( ord_less_nat @ ( size_size_list_int @ Ys ) @ ( size_size_list_int @ Xs2 ) )
% 6.92/7.22 => ( P2 @ Ys ) )
% 6.92/7.22 => ( P2 @ Xs2 ) )
% 6.92/7.22 => ( P2 @ Xs ) ) ).
% 6.92/7.22
% 6.92/7.22 % length_induct
% 6.92/7.22 thf(fact_4422_minus__nat_Odiff__0,axiom,
% 6.92/7.22 ! [M: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 6.92/7.22 = M ) ).
% 6.92/7.22
% 6.92/7.22 % minus_nat.diff_0
% 6.92/7.22 thf(fact_4423_diffs0__imp__equal,axiom,
% 6.92/7.22 ! [M: nat,N2: nat] :
% 6.92/7.22 ( ( ( minus_minus_nat @ M @ N2 )
% 6.92/7.22 = zero_zero_nat )
% 6.92/7.22 => ( ( ( minus_minus_nat @ N2 @ M )
% 6.92/7.22 = zero_zero_nat )
% 6.92/7.22 => ( M = N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diffs0_imp_equal
% 6.92/7.22 thf(fact_4424_zero__induct__lemma,axiom,
% 6.92/7.22 ! [P2: nat > $o,K2: nat,I2: nat] :
% 6.92/7.22 ( ( P2 @ K2 )
% 6.92/7.22 => ( ! [N5: nat] :
% 6.92/7.22 ( ( P2 @ ( suc @ N5 ) )
% 6.92/7.22 => ( P2 @ N5 ) )
% 6.92/7.22 => ( P2 @ ( minus_minus_nat @ K2 @ I2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % zero_induct_lemma
% 6.92/7.22 thf(fact_4425_less__imp__diff__less,axiom,
% 6.92/7.22 ! [J2: nat,K2: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_nat @ J2 @ K2 )
% 6.92/7.22 => ( ord_less_nat @ ( minus_minus_nat @ J2 @ N2 ) @ K2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_imp_diff_less
% 6.92/7.22 thf(fact_4426_diff__less__mono2,axiom,
% 6.92/7.22 ! [M: nat,N2: nat,L: nat] :
% 6.92/7.22 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.22 => ( ( ord_less_nat @ M @ L )
% 6.92/7.22 => ( ord_less_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_less_mono2
% 6.92/7.22 thf(fact_4427_diff__le__mono2,axiom,
% 6.92/7.22 ! [M: nat,N2: nat,L: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.22 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_le_mono2
% 6.92/7.22 thf(fact_4428_le__diff__iff_H,axiom,
% 6.92/7.22 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ A @ C2 )
% 6.92/7.22 => ( ( ord_less_eq_nat @ B @ C2 )
% 6.92/7.22 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C2 @ A ) @ ( minus_minus_nat @ C2 @ B ) )
% 6.92/7.22 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_diff_iff'
% 6.92/7.22 thf(fact_4429_diff__le__self,axiom,
% 6.92/7.22 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ).
% 6.92/7.22
% 6.92/7.22 % diff_le_self
% 6.92/7.22 thf(fact_4430_diff__le__mono,axiom,
% 6.92/7.22 ! [M: nat,N2: nat,L: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.22 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N2 @ L ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_le_mono
% 6.92/7.22 thf(fact_4431_Nat_Odiff__diff__eq,axiom,
% 6.92/7.22 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ M )
% 6.92/7.22 => ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.22 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K2 ) @ ( minus_minus_nat @ N2 @ K2 ) )
% 6.92/7.22 = ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Nat.diff_diff_eq
% 6.92/7.22 thf(fact_4432_le__diff__iff,axiom,
% 6.92/7.22 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ M )
% 6.92/7.22 => ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.22 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K2 ) @ ( minus_minus_nat @ N2 @ K2 ) )
% 6.92/7.22 = ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_diff_iff
% 6.92/7.22 thf(fact_4433_eq__diff__iff,axiom,
% 6.92/7.22 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ M )
% 6.92/7.22 => ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.22 => ( ( ( minus_minus_nat @ M @ K2 )
% 6.92/7.22 = ( minus_minus_nat @ N2 @ K2 ) )
% 6.92/7.22 = ( M = N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % eq_diff_iff
% 6.92/7.22 thf(fact_4434_Nat_Odiff__cancel,axiom,
% 6.92/7.22 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ ( plus_plus_nat @ K2 @ M ) @ ( plus_plus_nat @ K2 @ N2 ) )
% 6.92/7.22 = ( minus_minus_nat @ M @ N2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Nat.diff_cancel
% 6.92/7.22 thf(fact_4435_diff__cancel2,axiom,
% 6.92/7.22 ! [M: nat,K2: nat,N2: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K2 ) @ ( plus_plus_nat @ N2 @ K2 ) )
% 6.92/7.22 = ( minus_minus_nat @ M @ N2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_cancel2
% 6.92/7.22 thf(fact_4436_diff__add__inverse,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M ) @ N2 )
% 6.92/7.22 = M ) ).
% 6.92/7.22
% 6.92/7.22 % diff_add_inverse
% 6.92/7.22 thf(fact_4437_diff__add__inverse2,axiom,
% 6.92/7.22 ! [M: nat,N2: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ N2 )
% 6.92/7.22 = M ) ).
% 6.92/7.22
% 6.92/7.22 % diff_add_inverse2
% 6.92/7.22 thf(fact_4438_diff__mult__distrib,axiom,
% 6.92/7.22 ! [M: nat,N2: nat,K2: nat] :
% 6.92/7.22 ( ( times_times_nat @ ( minus_minus_nat @ M @ N2 ) @ K2 )
% 6.92/7.22 = ( minus_minus_nat @ ( times_times_nat @ M @ K2 ) @ ( times_times_nat @ N2 @ K2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_mult_distrib
% 6.92/7.22 thf(fact_4439_diff__mult__distrib2,axiom,
% 6.92/7.22 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.22 ( ( times_times_nat @ K2 @ ( minus_minus_nat @ M @ N2 ) )
% 6.92/7.22 = ( minus_minus_nat @ ( times_times_nat @ K2 @ M ) @ ( times_times_nat @ K2 @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_mult_distrib2
% 6.92/7.22 thf(fact_4440_int__ops_I6_J,axiom,
% 6.92/7.22 ! [A: nat,B: nat] :
% 6.92/7.22 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 6.92/7.22 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 6.92/7.22 = zero_zero_int ) )
% 6.92/7.22 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 6.92/7.22 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 6.92/7.22 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % int_ops(6)
% 6.92/7.22 thf(fact_4441_nat__mult__distrib__neg,axiom,
% 6.92/7.22 ! [Z3: int,Z7: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ Z3 @ zero_zero_int )
% 6.92/7.22 => ( ( nat2 @ ( times_times_int @ Z3 @ Z7 ) )
% 6.92/7.22 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z3 ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_mult_distrib_neg
% 6.92/7.22 thf(fact_4442_zdiff__int__split,axiom,
% 6.92/7.22 ! [P2: int > $o,X: nat,Y: nat] :
% 6.92/7.22 ( ( P2 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 6.92/7.22 = ( ( ( ord_less_eq_nat @ Y @ X )
% 6.92/7.22 => ( P2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 6.92/7.22 & ( ( ord_less_nat @ X @ Y )
% 6.92/7.22 => ( P2 @ zero_zero_int ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % zdiff_int_split
% 6.92/7.22 thf(fact_4443_le__iff__diff__le__0,axiom,
% 6.92/7.22 ( ord_le3102999989581377725nteger
% 6.92/7.22 = ( ^ [A5: code_integer,B4: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A5 @ B4 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_iff_diff_le_0
% 6.92/7.22 thf(fact_4444_le__iff__diff__le__0,axiom,
% 6.92/7.22 ( ord_less_eq_rat
% 6.92/7.22 = ( ^ [A5: rat,B4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A5 @ B4 ) @ zero_zero_rat ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_iff_diff_le_0
% 6.92/7.22 thf(fact_4445_le__iff__diff__le__0,axiom,
% 6.92/7.22 ( ord_less_eq_int
% 6.92/7.22 = ( ^ [A5: int,B4: int] : ( ord_less_eq_int @ ( minus_minus_int @ A5 @ B4 ) @ zero_zero_int ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_iff_diff_le_0
% 6.92/7.22 thf(fact_4446_nat__zero__as__int,axiom,
% 6.92/7.22 ( zero_zero_nat
% 6.92/7.22 = ( nat2 @ zero_zero_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_zero_as_int
% 6.92/7.22 thf(fact_4447_less__iff__diff__less__0,axiom,
% 6.92/7.22 ( ord_le6747313008572928689nteger
% 6.92/7.22 = ( ^ [A5: code_integer,B4: code_integer] : ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A5 @ B4 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_iff_diff_less_0
% 6.92/7.22 thf(fact_4448_less__iff__diff__less__0,axiom,
% 6.92/7.22 ( ord_less_rat
% 6.92/7.22 = ( ^ [A5: rat,B4: rat] : ( ord_less_rat @ ( minus_minus_rat @ A5 @ B4 ) @ zero_zero_rat ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_iff_diff_less_0
% 6.92/7.22 thf(fact_4449_less__iff__diff__less__0,axiom,
% 6.92/7.22 ( ord_less_int
% 6.92/7.22 = ( ^ [A5: int,B4: int] : ( ord_less_int @ ( minus_minus_int @ A5 @ B4 ) @ zero_zero_int ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_iff_diff_less_0
% 6.92/7.22 thf(fact_4450_diff__le__eq,axiom,
% 6.92/7.22 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 6.92/7.22 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_le_eq
% 6.92/7.22 thf(fact_4451_diff__le__eq,axiom,
% 6.92/7.22 ! [A: int,B: int,C2: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 6.92/7.22 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_le_eq
% 6.92/7.22 thf(fact_4452_le__diff__eq,axiom,
% 6.92/7.22 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C2 @ B ) )
% 6.92/7.22 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_diff_eq
% 6.92/7.22 thf(fact_4453_le__diff__eq,axiom,
% 6.92/7.22 ! [A: int,C2: int,B: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C2 @ B ) )
% 6.92/7.22 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_diff_eq
% 6.92/7.22 thf(fact_4454_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
% 6.92/7.22 ! [A: nat,B: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.22 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 6.92/7.22 = B ) ) ).
% 6.92/7.22
% 6.92/7.22 % ordered_cancel_comm_monoid_diff_class.diff_add
% 6.92/7.22 thf(fact_4455_le__add__diff,axiom,
% 6.92/7.22 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.22 => ( ord_less_eq_nat @ C2 @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_add_diff
% 6.92/7.22 thf(fact_4456_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 6.92/7.22 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.22 => ( ( ord_less_eq_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 6.92/7.22 = ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 6.92/7.22 thf(fact_4457_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 6.92/7.22 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.22 => ( ( plus_plus_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 6.92/7.22 = ( minus_minus_nat @ ( plus_plus_nat @ C2 @ B ) @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 6.92/7.22 thf(fact_4458_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 6.92/7.22 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.22 => ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ B ) @ A )
% 6.92/7.22 = ( plus_plus_nat @ C2 @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 6.92/7.22 thf(fact_4459_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 6.92/7.22 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.22 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C2 )
% 6.92/7.22 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 6.92/7.22 thf(fact_4460_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 6.92/7.22 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.22 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A )
% 6.92/7.22 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 6.92/7.22 thf(fact_4461_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 6.92/7.22 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.22 => ( ( minus_minus_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 6.92/7.22 = ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A ) @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 6.92/7.22 thf(fact_4462_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 6.92/7.22 ! [A: nat,B: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.22 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 6.92/7.22 = B ) ) ).
% 6.92/7.22
% 6.92/7.22 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 6.92/7.22 thf(fact_4463_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 6.92/7.22 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.22 => ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.22 => ( ( ( minus_minus_nat @ B @ A )
% 6.92/7.22 = C2 )
% 6.92/7.22 = ( B
% 6.92/7.22 = ( plus_plus_nat @ C2 @ A ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 6.92/7.22 thf(fact_4464_add__le__imp__le__diff,axiom,
% 6.92/7.22 ! [I2: rat,K2: rat,N2: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ N2 )
% 6.92/7.22 => ( ord_less_eq_rat @ I2 @ ( minus_minus_rat @ N2 @ K2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_le_imp_le_diff
% 6.92/7.22 thf(fact_4465_add__le__imp__le__diff,axiom,
% 6.92/7.22 ! [I2: nat,K2: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ N2 )
% 6.92/7.22 => ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ N2 @ K2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_le_imp_le_diff
% 6.92/7.22 thf(fact_4466_add__le__imp__le__diff,axiom,
% 6.92/7.22 ! [I2: int,K2: int,N2: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ N2 )
% 6.92/7.22 => ( ord_less_eq_int @ I2 @ ( minus_minus_int @ N2 @ K2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_le_imp_le_diff
% 6.92/7.22 thf(fact_4467_add__le__add__imp__diff__le,axiom,
% 6.92/7.22 ! [I2: rat,K2: rat,N2: rat,J2: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ N2 )
% 6.92/7.22 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J2 @ K2 ) )
% 6.92/7.22 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ N2 )
% 6.92/7.22 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J2 @ K2 ) )
% 6.92/7.22 => ( ord_less_eq_rat @ ( minus_minus_rat @ N2 @ K2 ) @ J2 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_le_add_imp_diff_le
% 6.92/7.22 thf(fact_4468_add__le__add__imp__diff__le,axiom,
% 6.92/7.22 ! [I2: nat,K2: nat,N2: nat,J2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ N2 )
% 6.92/7.22 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J2 @ K2 ) )
% 6.92/7.22 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ N2 )
% 6.92/7.22 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J2 @ K2 ) )
% 6.92/7.22 => ( ord_less_eq_nat @ ( minus_minus_nat @ N2 @ K2 ) @ J2 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_le_add_imp_diff_le
% 6.92/7.22 thf(fact_4469_add__le__add__imp__diff__le,axiom,
% 6.92/7.22 ! [I2: int,K2: int,N2: int,J2: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ N2 )
% 6.92/7.22 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J2 @ K2 ) )
% 6.92/7.22 => ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ N2 )
% 6.92/7.22 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J2 @ K2 ) )
% 6.92/7.22 => ( ord_less_eq_int @ ( minus_minus_int @ N2 @ K2 ) @ J2 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_le_add_imp_diff_le
% 6.92/7.22 thf(fact_4470_diff__shunt__var,axiom,
% 6.92/7.22 ! [X: set_o,Y: set_o] :
% 6.92/7.22 ( ( ( minus_minus_set_o @ X @ Y )
% 6.92/7.22 = bot_bot_set_o )
% 6.92/7.22 = ( ord_less_eq_set_o @ X @ Y ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_shunt_var
% 6.92/7.22 thf(fact_4471_diff__shunt__var,axiom,
% 6.92/7.22 ! [X: set_nat,Y: set_nat] :
% 6.92/7.22 ( ( ( minus_minus_set_nat @ X @ Y )
% 6.92/7.22 = bot_bot_set_nat )
% 6.92/7.22 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_shunt_var
% 6.92/7.22 thf(fact_4472_diff__shunt__var,axiom,
% 6.92/7.22 ! [X: assn,Y: assn] :
% 6.92/7.22 ( ( ( minus_minus_assn @ X @ Y )
% 6.92/7.22 = bot_bot_assn )
% 6.92/7.22 = ( ord_less_eq_assn @ X @ Y ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_shunt_var
% 6.92/7.22 thf(fact_4473_diff__shunt__var,axiom,
% 6.92/7.22 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ( minus_1356011639430497352at_nat @ X @ Y )
% 6.92/7.22 = bot_bo2099793752762293965at_nat )
% 6.92/7.22 = ( ord_le3146513528884898305at_nat @ X @ Y ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_shunt_var
% 6.92/7.22 thf(fact_4474_diff__shunt__var,axiom,
% 6.92/7.22 ! [X: set_int,Y: set_int] :
% 6.92/7.22 ( ( ( minus_minus_set_int @ X @ Y )
% 6.92/7.22 = bot_bot_set_int )
% 6.92/7.22 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_shunt_var
% 6.92/7.22 thf(fact_4475_less__diff__eq,axiom,
% 6.92/7.22 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C2 @ B ) )
% 6.92/7.22 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_diff_eq
% 6.92/7.22 thf(fact_4476_less__diff__eq,axiom,
% 6.92/7.22 ! [A: int,C2: int,B: int] :
% 6.92/7.22 ( ( ord_less_int @ A @ ( minus_minus_int @ C2 @ B ) )
% 6.92/7.22 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_diff_eq
% 6.92/7.22 thf(fact_4477_diff__less__eq,axiom,
% 6.92/7.22 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.22 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 6.92/7.22 = ( ord_less_rat @ A @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_less_eq
% 6.92/7.22 thf(fact_4478_diff__less__eq,axiom,
% 6.92/7.22 ! [A: int,B: int,C2: int] :
% 6.92/7.22 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 6.92/7.22 = ( ord_less_int @ A @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_less_eq
% 6.92/7.22 thf(fact_4479_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ~ ( ord_less_rat @ A @ B )
% 6.92/7.22 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 6.92/7.22 = A ) ) ).
% 6.92/7.22
% 6.92/7.22 % linordered_semidom_class.add_diff_inverse
% 6.92/7.22 thf(fact_4480_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 6.92/7.22 ! [A: nat,B: nat] :
% 6.92/7.22 ( ~ ( ord_less_nat @ A @ B )
% 6.92/7.22 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 6.92/7.22 = A ) ) ).
% 6.92/7.22
% 6.92/7.22 % linordered_semidom_class.add_diff_inverse
% 6.92/7.22 thf(fact_4481_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ~ ( ord_less_int @ A @ B )
% 6.92/7.22 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 6.92/7.22 = A ) ) ).
% 6.92/7.22
% 6.92/7.22 % linordered_semidom_class.add_diff_inverse
% 6.92/7.22 thf(fact_4482_eq__add__iff1,axiom,
% 6.92/7.22 ! [A: rat,E: rat,C2: rat,B: rat,D2: rat] :
% 6.92/7.22 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 )
% 6.92/7.22 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 6.92/7.22 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C2 )
% 6.92/7.22 = D2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % eq_add_iff1
% 6.92/7.22 thf(fact_4483_eq__add__iff1,axiom,
% 6.92/7.22 ! [A: int,E: int,C2: int,B: int,D2: int] :
% 6.92/7.22 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 )
% 6.92/7.22 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 6.92/7.22 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C2 )
% 6.92/7.22 = D2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % eq_add_iff1
% 6.92/7.22 thf(fact_4484_eq__add__iff2,axiom,
% 6.92/7.22 ! [A: rat,E: rat,C2: rat,B: rat,D2: rat] :
% 6.92/7.22 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 )
% 6.92/7.22 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 6.92/7.22 = ( C2
% 6.92/7.22 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % eq_add_iff2
% 6.92/7.22 thf(fact_4485_eq__add__iff2,axiom,
% 6.92/7.22 ! [A: int,E: int,C2: int,B: int,D2: int] :
% 6.92/7.22 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 )
% 6.92/7.22 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 6.92/7.22 = ( C2
% 6.92/7.22 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % eq_add_iff2
% 6.92/7.22 thf(fact_4486_square__diff__square__factored,axiom,
% 6.92/7.22 ! [X: rat,Y: rat] :
% 6.92/7.22 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 6.92/7.22 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % square_diff_square_factored
% 6.92/7.22 thf(fact_4487_square__diff__square__factored,axiom,
% 6.92/7.22 ! [X: int,Y: int] :
% 6.92/7.22 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 6.92/7.22 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % square_diff_square_factored
% 6.92/7.22 thf(fact_4488_nat__mono,axiom,
% 6.92/7.22 ! [X: int,Y: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.22 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_mono
% 6.92/7.22 thf(fact_4489_ex__nat,axiom,
% 6.92/7.22 ( ( ^ [P4: nat > $o] :
% 6.92/7.22 ? [X5: nat] : ( P4 @ X5 ) )
% 6.92/7.22 = ( ^ [P5: nat > $o] :
% 6.92/7.22 ? [X4: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 6.92/7.22 & ( P5 @ ( nat2 @ X4 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % ex_nat
% 6.92/7.22 thf(fact_4490_all__nat,axiom,
% 6.92/7.22 ( ( ^ [P4: nat > $o] :
% 6.92/7.22 ! [X5: nat] : ( P4 @ X5 ) )
% 6.92/7.22 = ( ^ [P5: nat > $o] :
% 6.92/7.22 ! [X4: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 6.92/7.22 => ( P5 @ ( nat2 @ X4 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % all_nat
% 6.92/7.22 thf(fact_4491_eq__nat__nat__iff,axiom,
% 6.92/7.22 ! [Z3: int,Z7: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.22 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 6.92/7.22 => ( ( ( nat2 @ Z3 )
% 6.92/7.22 = ( nat2 @ Z7 ) )
% 6.92/7.22 = ( Z3 = Z7 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % eq_nat_nat_iff
% 6.92/7.22 thf(fact_4492_minus__mod__int__eq,axiom,
% 6.92/7.22 ! [L: int,K2: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 6.92/7.22 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K2 ) @ L )
% 6.92/7.22 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K2 @ one_one_int ) @ L ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % minus_mod_int_eq
% 6.92/7.22 thf(fact_4493_zmod__minus1,axiom,
% 6.92/7.22 ! [B: int] :
% 6.92/7.22 ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.22 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 6.92/7.22 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % zmod_minus1
% 6.92/7.22 thf(fact_4494_neg__eq__iff__add__eq__0,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( ( uminus_uminus_int @ A )
% 6.92/7.22 = B )
% 6.92/7.22 = ( ( plus_plus_int @ A @ B )
% 6.92/7.22 = zero_zero_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_eq_iff_add_eq_0
% 6.92/7.22 thf(fact_4495_neg__eq__iff__add__eq__0,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( ( uminus1351360451143612070nteger @ A )
% 6.92/7.22 = B )
% 6.92/7.22 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 6.92/7.22 = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_eq_iff_add_eq_0
% 6.92/7.22 thf(fact_4496_neg__eq__iff__add__eq__0,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( ( uminus_uminus_rat @ A )
% 6.92/7.22 = B )
% 6.92/7.22 = ( ( plus_plus_rat @ A @ B )
% 6.92/7.22 = zero_zero_rat ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_eq_iff_add_eq_0
% 6.92/7.22 thf(fact_4497_eq__neg__iff__add__eq__0,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( A
% 6.92/7.22 = ( uminus_uminus_int @ B ) )
% 6.92/7.22 = ( ( plus_plus_int @ A @ B )
% 6.92/7.22 = zero_zero_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % eq_neg_iff_add_eq_0
% 6.92/7.22 thf(fact_4498_eq__neg__iff__add__eq__0,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( A
% 6.92/7.22 = ( uminus1351360451143612070nteger @ B ) )
% 6.92/7.22 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 6.92/7.22 = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.22
% 6.92/7.22 % eq_neg_iff_add_eq_0
% 6.92/7.22 thf(fact_4499_eq__neg__iff__add__eq__0,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( A
% 6.92/7.22 = ( uminus_uminus_rat @ B ) )
% 6.92/7.22 = ( ( plus_plus_rat @ A @ B )
% 6.92/7.22 = zero_zero_rat ) ) ).
% 6.92/7.22
% 6.92/7.22 % eq_neg_iff_add_eq_0
% 6.92/7.22 thf(fact_4500_add_Oinverse__unique,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( ( plus_plus_int @ A @ B )
% 6.92/7.22 = zero_zero_int )
% 6.92/7.22 => ( ( uminus_uminus_int @ A )
% 6.92/7.22 = B ) ) ).
% 6.92/7.22
% 6.92/7.22 % add.inverse_unique
% 6.92/7.22 thf(fact_4501_add_Oinverse__unique,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 6.92/7.22 = zero_z3403309356797280102nteger )
% 6.92/7.22 => ( ( uminus1351360451143612070nteger @ A )
% 6.92/7.22 = B ) ) ).
% 6.92/7.22
% 6.92/7.22 % add.inverse_unique
% 6.92/7.22 thf(fact_4502_add_Oinverse__unique,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( ( plus_plus_rat @ A @ B )
% 6.92/7.22 = zero_zero_rat )
% 6.92/7.22 => ( ( uminus_uminus_rat @ A )
% 6.92/7.22 = B ) ) ).
% 6.92/7.22
% 6.92/7.22 % add.inverse_unique
% 6.92/7.22 thf(fact_4503_ab__group__add__class_Oab__left__minus,axiom,
% 6.92/7.22 ! [A: int] :
% 6.92/7.22 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 6.92/7.22 = zero_zero_int ) ).
% 6.92/7.22
% 6.92/7.22 % ab_group_add_class.ab_left_minus
% 6.92/7.22 thf(fact_4504_ab__group__add__class_Oab__left__minus,axiom,
% 6.92/7.22 ! [A: code_integer] :
% 6.92/7.22 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 6.92/7.22 = zero_z3403309356797280102nteger ) ).
% 6.92/7.22
% 6.92/7.22 % ab_group_add_class.ab_left_minus
% 6.92/7.22 thf(fact_4505_ab__group__add__class_Oab__left__minus,axiom,
% 6.92/7.22 ! [A: rat] :
% 6.92/7.22 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 6.92/7.22 = zero_zero_rat ) ).
% 6.92/7.22
% 6.92/7.22 % ab_group_add_class.ab_left_minus
% 6.92/7.22 thf(fact_4506_add__eq__0__iff,axiom,
% 6.92/7.22 ! [A: int,B: int] :
% 6.92/7.22 ( ( ( plus_plus_int @ A @ B )
% 6.92/7.22 = zero_zero_int )
% 6.92/7.22 = ( B
% 6.92/7.22 = ( uminus_uminus_int @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_eq_0_iff
% 6.92/7.22 thf(fact_4507_add__eq__0__iff,axiom,
% 6.92/7.22 ! [A: code_integer,B: code_integer] :
% 6.92/7.22 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 6.92/7.22 = zero_z3403309356797280102nteger )
% 6.92/7.22 = ( B
% 6.92/7.22 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_eq_0_iff
% 6.92/7.22 thf(fact_4508_add__eq__0__iff,axiom,
% 6.92/7.22 ! [A: rat,B: rat] :
% 6.92/7.22 ( ( ( plus_plus_rat @ A @ B )
% 6.92/7.22 = zero_zero_rat )
% 6.92/7.22 = ( B
% 6.92/7.22 = ( uminus_uminus_rat @ A ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_eq_0_iff
% 6.92/7.22 thf(fact_4509_le__minus__one__simps_I2_J,axiom,
% 6.92/7.22 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 6.92/7.22
% 6.92/7.22 % le_minus_one_simps(2)
% 6.92/7.22 thf(fact_4510_le__minus__one__simps_I2_J,axiom,
% 6.92/7.22 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 6.92/7.22
% 6.92/7.22 % le_minus_one_simps(2)
% 6.92/7.22 thf(fact_4511_le__minus__one__simps_I2_J,axiom,
% 6.92/7.22 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 6.92/7.22
% 6.92/7.22 % le_minus_one_simps(2)
% 6.92/7.22 thf(fact_4512_le__minus__one__simps_I4_J,axiom,
% 6.92/7.22 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_minus_one_simps(4)
% 6.92/7.22 thf(fact_4513_le__minus__one__simps_I4_J,axiom,
% 6.92/7.22 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_minus_one_simps(4)
% 6.92/7.22 thf(fact_4514_le__minus__one__simps_I4_J,axiom,
% 6.92/7.22 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_minus_one_simps(4)
% 6.92/7.22 thf(fact_4515_nat__one__as__int,axiom,
% 6.92/7.22 ( one_one_nat
% 6.92/7.22 = ( nat2 @ one_one_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_one_as_int
% 6.92/7.22 thf(fact_4516_less__minus__one__simps_I2_J,axiom,
% 6.92/7.22 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 6.92/7.22
% 6.92/7.22 % less_minus_one_simps(2)
% 6.92/7.22 thf(fact_4517_less__minus__one__simps_I2_J,axiom,
% 6.92/7.22 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 6.92/7.22
% 6.92/7.22 % less_minus_one_simps(2)
% 6.92/7.22 thf(fact_4518_less__minus__one__simps_I2_J,axiom,
% 6.92/7.22 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 6.92/7.22
% 6.92/7.22 % less_minus_one_simps(2)
% 6.92/7.22 thf(fact_4519_less__minus__one__simps_I4_J,axiom,
% 6.92/7.22 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_minus_one_simps(4)
% 6.92/7.22 thf(fact_4520_less__minus__one__simps_I4_J,axiom,
% 6.92/7.22 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_minus_one_simps(4)
% 6.92/7.22 thf(fact_4521_less__minus__one__simps_I4_J,axiom,
% 6.92/7.22 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_minus_one_simps(4)
% 6.92/7.22 thf(fact_4522_Suc__to__right,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( ( suc @ N2 )
% 6.92/7.22 = M )
% 6.92/7.22 => ( N2
% 6.92/7.22 = ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Suc_to_right
% 6.92/7.22 thf(fact_4523_diff__less,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.22 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.22 => ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_less
% 6.92/7.22 thf(fact_4524_Suc__diff__Suc,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( ord_less_nat @ N2 @ M )
% 6.92/7.22 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.22 = ( minus_minus_nat @ M @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Suc_diff_Suc
% 6.92/7.22 thf(fact_4525_diff__less__Suc,axiom,
% 6.92/7.22 ! [M: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ ( suc @ M ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_less_Suc
% 6.92/7.22 thf(fact_4526_Suc__diff__le,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 6.92/7.22 = ( suc @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Suc_diff_le
% 6.92/7.22 thf(fact_4527_diff__add__0,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) )
% 6.92/7.22 = zero_zero_nat ) ).
% 6.92/7.22
% 6.92/7.22 % diff_add_0
% 6.92/7.22 thf(fact_4528_less__diff__iff,axiom,
% 6.92/7.22 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ M )
% 6.92/7.22 => ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.22 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K2 ) @ ( minus_minus_nat @ N2 @ K2 ) )
% 6.92/7.22 = ( ord_less_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_diff_iff
% 6.92/7.22 thf(fact_4529_diff__less__mono,axiom,
% 6.92/7.22 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.22 ( ( ord_less_nat @ A @ B )
% 6.92/7.22 => ( ( ord_less_eq_nat @ C2 @ A )
% 6.92/7.22 => ( ord_less_nat @ ( minus_minus_nat @ A @ C2 ) @ ( minus_minus_nat @ B @ C2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_less_mono
% 6.92/7.22 thf(fact_4530_less__diff__conv,axiom,
% 6.92/7.22 ! [I2: nat,J2: nat,K2: nat] :
% 6.92/7.22 ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 6.92/7.22 = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ J2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_diff_conv
% 6.92/7.22 thf(fact_4531_add__diff__inverse__nat,axiom,
% 6.92/7.22 ! [M: nat,N2: nat] :
% 6.92/7.22 ( ~ ( ord_less_nat @ M @ N2 )
% 6.92/7.22 => ( ( plus_plus_nat @ N2 @ ( minus_minus_nat @ M @ N2 ) )
% 6.92/7.22 = M ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_diff_inverse_nat
% 6.92/7.22 thf(fact_4532_Nat_Ole__imp__diff__is__add,axiom,
% 6.92/7.22 ! [I2: nat,J2: nat,K2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.22 => ( ( ( minus_minus_nat @ J2 @ I2 )
% 6.92/7.22 = K2 )
% 6.92/7.22 = ( J2
% 6.92/7.22 = ( plus_plus_nat @ K2 @ I2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Nat.le_imp_diff_is_add
% 6.92/7.22 thf(fact_4533_Nat_Odiff__add__assoc2,axiom,
% 6.92/7.22 ! [K2: nat,J2: nat,I2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ J2 )
% 6.92/7.22 => ( ( minus_minus_nat @ ( plus_plus_nat @ J2 @ I2 ) @ K2 )
% 6.92/7.22 = ( plus_plus_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Nat.diff_add_assoc2
% 6.92/7.22 thf(fact_4534_Nat_Odiff__add__assoc,axiom,
% 6.92/7.22 ! [K2: nat,J2: nat,I2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ J2 )
% 6.92/7.22 => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J2 ) @ K2 )
% 6.92/7.22 = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Nat.diff_add_assoc
% 6.92/7.22 thf(fact_4535_Nat_Ole__diff__conv2,axiom,
% 6.92/7.22 ! [K2: nat,J2: nat,I2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ J2 )
% 6.92/7.22 => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 6.92/7.22 = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ J2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Nat.le_diff_conv2
% 6.92/7.22 thf(fact_4536_le__diff__conv,axiom,
% 6.92/7.22 ! [J2: nat,K2: nat,I2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 )
% 6.92/7.22 = ( ord_less_eq_nat @ J2 @ ( plus_plus_nat @ I2 @ K2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_diff_conv
% 6.92/7.22 thf(fact_4537_int__le__induct,axiom,
% 6.92/7.22 ! [I2: int,K2: int,P2: int > $o] :
% 6.92/7.22 ( ( ord_less_eq_int @ I2 @ K2 )
% 6.92/7.22 => ( ( P2 @ K2 )
% 6.92/7.22 => ( ! [I3: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ I3 @ K2 )
% 6.92/7.22 => ( ( P2 @ I3 )
% 6.92/7.22 => ( P2 @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 6.92/7.22 => ( P2 @ I2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % int_le_induct
% 6.92/7.22 thf(fact_4538_diff__Suc__eq__diff__pred,axiom,
% 6.92/7.22 ! [M: nat,N2: nat] :
% 6.92/7.22 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 6.92/7.22 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_Suc_eq_diff_pred
% 6.92/7.22 thf(fact_4539_int__less__induct,axiom,
% 6.92/7.22 ! [I2: int,K2: int,P2: int > $o] :
% 6.92/7.22 ( ( ord_less_int @ I2 @ K2 )
% 6.92/7.22 => ( ( P2 @ ( minus_minus_int @ K2 @ one_one_int ) )
% 6.92/7.22 => ( ! [I3: int] :
% 6.92/7.22 ( ( ord_less_int @ I3 @ K2 )
% 6.92/7.22 => ( ( P2 @ I3 )
% 6.92/7.22 => ( P2 @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 6.92/7.22 => ( P2 @ I2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % int_less_induct
% 6.92/7.22 thf(fact_4540_mod__geq,axiom,
% 6.92/7.22 ! [M: nat,N2: nat] :
% 6.92/7.22 ( ~ ( ord_less_nat @ M @ N2 )
% 6.92/7.22 => ( ( modulo_modulo_nat @ M @ N2 )
% 6.92/7.22 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % mod_geq
% 6.92/7.22 thf(fact_4541_mod__if,axiom,
% 6.92/7.22 ( modulo_modulo_nat
% 6.92/7.22 = ( ^ [M3: nat,N: nat] : ( if_nat @ ( ord_less_nat @ M3 @ N ) @ M3 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M3 @ N ) @ N ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % mod_if
% 6.92/7.22 thf(fact_4542_le__mod__geq,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( modulo_modulo_nat @ M @ N2 )
% 6.92/7.22 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_mod_geq
% 6.92/7.22 thf(fact_4543_not__int__zless__negative,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % not_int_zless_negative
% 6.92/7.22 thf(fact_4544_le__add__iff1,axiom,
% 6.92/7.22 ! [A: rat,E: rat,C2: rat,B: rat,D2: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 6.92/7.22 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C2 ) @ D2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_add_iff1
% 6.92/7.22 thf(fact_4545_le__add__iff1,axiom,
% 6.92/7.22 ! [A: int,E: int,C2: int,B: int,D2: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 6.92/7.22 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C2 ) @ D2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_add_iff1
% 6.92/7.22 thf(fact_4546_le__add__iff2,axiom,
% 6.92/7.22 ! [A: rat,E: rat,C2: rat,B: rat,D2: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 6.92/7.22 = ( ord_less_eq_rat @ C2 @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_add_iff2
% 6.92/7.22 thf(fact_4547_le__add__iff2,axiom,
% 6.92/7.22 ! [A: int,E: int,C2: int,B: int,D2: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 6.92/7.22 = ( ord_less_eq_int @ C2 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_add_iff2
% 6.92/7.22 thf(fact_4548_less__add__iff2,axiom,
% 6.92/7.22 ! [A: rat,E: rat,C2: rat,B: rat,D2: rat] :
% 6.92/7.22 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 6.92/7.22 = ( ord_less_rat @ C2 @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_add_iff2
% 6.92/7.22 thf(fact_4549_less__add__iff2,axiom,
% 6.92/7.22 ! [A: int,E: int,C2: int,B: int,D2: int] :
% 6.92/7.22 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 6.92/7.22 = ( ord_less_int @ C2 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_add_iff2
% 6.92/7.22 thf(fact_4550_less__add__iff1,axiom,
% 6.92/7.22 ! [A: rat,E: rat,C2: rat,B: rat,D2: rat] :
% 6.92/7.22 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 6.92/7.22 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C2 ) @ D2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_add_iff1
% 6.92/7.22 thf(fact_4551_less__add__iff1,axiom,
% 6.92/7.22 ! [A: int,E: int,C2: int,B: int,D2: int] :
% 6.92/7.22 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 6.92/7.22 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C2 ) @ D2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_add_iff1
% 6.92/7.22 thf(fact_4552_nat__mono__iff,axiom,
% 6.92/7.22 ! [Z3: int,W2: int] :
% 6.92/7.22 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 6.92/7.22 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z3 ) )
% 6.92/7.22 = ( ord_less_int @ W2 @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_mono_iff
% 6.92/7.22 thf(fact_4553_square__diff__one__factored,axiom,
% 6.92/7.22 ! [X: code_integer] :
% 6.92/7.22 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ one_one_Code_integer )
% 6.92/7.22 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % square_diff_one_factored
% 6.92/7.22 thf(fact_4554_square__diff__one__factored,axiom,
% 6.92/7.22 ! [X: rat] :
% 6.92/7.22 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 6.92/7.22 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % square_diff_one_factored
% 6.92/7.22 thf(fact_4555_square__diff__one__factored,axiom,
% 6.92/7.22 ! [X: int] :
% 6.92/7.22 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 6.92/7.22 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % square_diff_one_factored
% 6.92/7.22 thf(fact_4556_le__minus__one__simps_I1_J,axiom,
% 6.92/7.22 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 6.92/7.22
% 6.92/7.22 % le_minus_one_simps(1)
% 6.92/7.22 thf(fact_4557_le__minus__one__simps_I1_J,axiom,
% 6.92/7.22 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 6.92/7.22
% 6.92/7.22 % le_minus_one_simps(1)
% 6.92/7.22 thf(fact_4558_le__minus__one__simps_I1_J,axiom,
% 6.92/7.22 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 6.92/7.22
% 6.92/7.22 % le_minus_one_simps(1)
% 6.92/7.22 thf(fact_4559_le__minus__one__simps_I3_J,axiom,
% 6.92/7.22 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_minus_one_simps(3)
% 6.92/7.22 thf(fact_4560_le__minus__one__simps_I3_J,axiom,
% 6.92/7.22 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_minus_one_simps(3)
% 6.92/7.22 thf(fact_4561_le__minus__one__simps_I3_J,axiom,
% 6.92/7.22 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_minus_one_simps(3)
% 6.92/7.22 thf(fact_4562_zless__nat__eq__int__zless,axiom,
% 6.92/7.22 ! [M: nat,Z3: int] :
% 6.92/7.22 ( ( ord_less_nat @ M @ ( nat2 @ Z3 ) )
% 6.92/7.22 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z3 ) ) ).
% 6.92/7.22
% 6.92/7.22 % zless_nat_eq_int_zless
% 6.92/7.22 thf(fact_4563_less__minus__one__simps_I1_J,axiom,
% 6.92/7.22 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 6.92/7.22
% 6.92/7.22 % less_minus_one_simps(1)
% 6.92/7.22 thf(fact_4564_less__minus__one__simps_I1_J,axiom,
% 6.92/7.22 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 6.92/7.22
% 6.92/7.22 % less_minus_one_simps(1)
% 6.92/7.22 thf(fact_4565_less__minus__one__simps_I1_J,axiom,
% 6.92/7.22 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 6.92/7.22
% 6.92/7.22 % less_minus_one_simps(1)
% 6.92/7.22 thf(fact_4566_less__minus__one__simps_I3_J,axiom,
% 6.92/7.22 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_minus_one_simps(3)
% 6.92/7.22 thf(fact_4567_less__minus__one__simps_I3_J,axiom,
% 6.92/7.22 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_minus_one_simps(3)
% 6.92/7.22 thf(fact_4568_less__minus__one__simps_I3_J,axiom,
% 6.92/7.22 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_minus_one_simps(3)
% 6.92/7.22 thf(fact_4569_nat__le__iff,axiom,
% 6.92/7.22 ! [X: int,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N2 )
% 6.92/7.22 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_le_iff
% 6.92/7.22 thf(fact_4570_int__eq__iff,axiom,
% 6.92/7.22 ! [M: nat,Z3: int] :
% 6.92/7.22 ( ( ( semiri1314217659103216013at_int @ M )
% 6.92/7.22 = Z3 )
% 6.92/7.22 = ( ( M
% 6.92/7.22 = ( nat2 @ Z3 ) )
% 6.92/7.22 & ( ord_less_eq_int @ zero_zero_int @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % int_eq_iff
% 6.92/7.22 thf(fact_4571_nat__0__le,axiom,
% 6.92/7.22 ! [Z3: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.22 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z3 ) )
% 6.92/7.22 = Z3 ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_0_le
% 6.92/7.22 thf(fact_4572_nat__int__add,axiom,
% 6.92/7.22 ! [A: nat,B: nat] :
% 6.92/7.22 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 6.92/7.22 = ( plus_plus_nat @ A @ B ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_int_add
% 6.92/7.22 thf(fact_4573_inf__shunt,axiom,
% 6.92/7.22 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 6.92/7.22 ( ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 6.92/7.22 = bot_bo8147686125503663512_int_o )
% 6.92/7.22 = ( ord_le8369615600986905444_int_o @ X @ ( uminus7117520113953359693_int_o @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % inf_shunt
% 6.92/7.22 thf(fact_4574_inf__shunt,axiom,
% 6.92/7.22 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 6.92/7.22 = bot_bo2099793752762293965at_nat )
% 6.92/7.22 = ( ord_le3146513528884898305at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % inf_shunt
% 6.92/7.22 thf(fact_4575_inf__shunt,axiom,
% 6.92/7.22 ! [X: set_o,Y: set_o] :
% 6.92/7.22 ( ( ( inf_inf_set_o @ X @ Y )
% 6.92/7.22 = bot_bot_set_o )
% 6.92/7.22 = ( ord_less_eq_set_o @ X @ ( uminus_uminus_set_o @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % inf_shunt
% 6.92/7.22 thf(fact_4576_inf__shunt,axiom,
% 6.92/7.22 ! [X: set_nat,Y: set_nat] :
% 6.92/7.22 ( ( ( inf_inf_set_nat @ X @ Y )
% 6.92/7.22 = bot_bot_set_nat )
% 6.92/7.22 = ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % inf_shunt
% 6.92/7.22 thf(fact_4577_inf__shunt,axiom,
% 6.92/7.22 ! [X: assn,Y: assn] :
% 6.92/7.22 ( ( ( inf_inf_assn @ X @ Y )
% 6.92/7.22 = bot_bot_assn )
% 6.92/7.22 = ( ord_less_eq_assn @ X @ ( uminus_uminus_assn @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % inf_shunt
% 6.92/7.22 thf(fact_4578_inf__shunt,axiom,
% 6.92/7.22 ! [X: product_unit,Y: product_unit] :
% 6.92/7.22 ( ( ( inf_inf_Product_unit @ X @ Y )
% 6.92/7.22 = bot_bot_Product_unit )
% 6.92/7.22 = ( ord_le3221252021190050221t_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % inf_shunt
% 6.92/7.22 thf(fact_4579_inf__shunt,axiom,
% 6.92/7.22 ! [X: set_int,Y: set_int] :
% 6.92/7.22 ( ( ( inf_inf_set_int @ X @ Y )
% 6.92/7.22 = bot_bot_set_int )
% 6.92/7.22 = ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % inf_shunt
% 6.92/7.22 thf(fact_4580_shunt1,axiom,
% 6.92/7.22 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z3 )
% 6.92/7.22 = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ Y ) @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt1
% 6.92/7.22 thf(fact_4581_shunt1,axiom,
% 6.92/7.22 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o] :
% 6.92/7.22 ( ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Z3 )
% 6.92/7.22 = ( ord_le8369615600986905444_int_o @ X @ ( sup_su8463660629351352368_int_o @ ( uminus7117520113953359693_int_o @ Y ) @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt1
% 6.92/7.22 thf(fact_4582_shunt1,axiom,
% 6.92/7.22 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( ord_le8081472938463900775at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ Z3 )
% 6.92/7.22 = ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ Y ) @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt1
% 6.92/7.22 thf(fact_4583_shunt1,axiom,
% 6.92/7.22 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ Z3 )
% 6.92/7.22 = ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ Y ) @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt1
% 6.92/7.22 thf(fact_4584_shunt1,axiom,
% 6.92/7.22 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 6.92/7.22 ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z3 )
% 6.92/7.22 = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt1
% 6.92/7.22 thf(fact_4585_shunt1,axiom,
% 6.92/7.22 ! [X: assn,Y: assn,Z3: assn] :
% 6.92/7.22 ( ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ Z3 )
% 6.92/7.22 = ( ord_less_eq_assn @ X @ ( sup_sup_assn @ ( uminus_uminus_assn @ Y ) @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt1
% 6.92/7.22 thf(fact_4586_shunt1,axiom,
% 6.92/7.22 ! [X: product_unit,Y: product_unit,Z3: product_unit] :
% 6.92/7.22 ( ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X @ Y ) @ Z3 )
% 6.92/7.22 = ( ord_le3221252021190050221t_unit @ X @ ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ Y ) @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt1
% 6.92/7.22 thf(fact_4587_shunt1,axiom,
% 6.92/7.22 ! [X: set_int,Y: set_int,Z3: set_int] :
% 6.92/7.22 ( ( ord_less_eq_set_int @ ( inf_inf_set_int @ X @ Y ) @ Z3 )
% 6.92/7.22 = ( ord_less_eq_set_int @ X @ ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ Y ) @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt1
% 6.92/7.22 thf(fact_4588_shunt2,axiom,
% 6.92/7.22 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) @ Z3 )
% 6.92/7.22 = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt2
% 6.92/7.22 thf(fact_4589_shunt2,axiom,
% 6.92/7.22 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z3: product_prod_int_int > $o] :
% 6.92/7.22 ( ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ ( uminus7117520113953359693_int_o @ Y ) ) @ Z3 )
% 6.92/7.22 = ( ord_le8369615600986905444_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt2
% 6.92/7.22 thf(fact_4590_shunt2,axiom,
% 6.92/7.22 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z3: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( ord_le8081472938463900775at_nat @ ( inf_in1697001100524423349at_nat @ X @ ( uminus2330091110623919550at_nat @ Y ) ) @ Z3 )
% 6.92/7.22 = ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt2
% 6.92/7.22 thf(fact_4591_shunt2,axiom,
% 6.92/7.22 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z3: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ X @ ( uminus935396558254630718at_nat @ Y ) ) @ Z3 )
% 6.92/7.22 = ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt2
% 6.92/7.22 thf(fact_4592_shunt2,axiom,
% 6.92/7.22 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 6.92/7.22 ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) @ Z3 )
% 6.92/7.22 = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt2
% 6.92/7.22 thf(fact_4593_shunt2,axiom,
% 6.92/7.22 ! [X: assn,Y: assn,Z3: assn] :
% 6.92/7.22 ( ( ord_less_eq_assn @ ( inf_inf_assn @ X @ ( uminus_uminus_assn @ Y ) ) @ Z3 )
% 6.92/7.22 = ( ord_less_eq_assn @ X @ ( sup_sup_assn @ Y @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt2
% 6.92/7.22 thf(fact_4594_shunt2,axiom,
% 6.92/7.22 ! [X: product_unit,Y: product_unit,Z3: product_unit] :
% 6.92/7.22 ( ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) @ Z3 )
% 6.92/7.22 = ( ord_le3221252021190050221t_unit @ X @ ( sup_sup_Product_unit @ Y @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt2
% 6.92/7.22 thf(fact_4595_shunt2,axiom,
% 6.92/7.22 ! [X: set_int,Y: set_int,Z3: set_int] :
% 6.92/7.22 ( ( ord_less_eq_set_int @ ( inf_inf_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) @ Z3 )
% 6.92/7.22 = ( ord_less_eq_set_int @ X @ ( sup_sup_set_int @ Y @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % shunt2
% 6.92/7.22 thf(fact_4596_sup__neg__inf,axiom,
% 6.92/7.22 ! [P3: set_Pr1261947904930325089at_nat,Q6: set_Pr1261947904930325089at_nat,R2: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ord_le3146513528884898305at_nat @ P3 @ ( sup_su6327502436637775413at_nat @ Q6 @ R2 ) )
% 6.92/7.22 = ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ P3 @ ( uminus6524753893492686040at_nat @ Q6 ) ) @ R2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % sup_neg_inf
% 6.92/7.22 thf(fact_4597_sup__neg__inf,axiom,
% 6.92/7.22 ! [P3: product_prod_int_int > $o,Q6: product_prod_int_int > $o,R2: product_prod_int_int > $o] :
% 6.92/7.22 ( ( ord_le8369615600986905444_int_o @ P3 @ ( sup_su8463660629351352368_int_o @ Q6 @ R2 ) )
% 6.92/7.22 = ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ P3 @ ( uminus7117520113953359693_int_o @ Q6 ) ) @ R2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % sup_neg_inf
% 6.92/7.22 thf(fact_4598_sup__neg__inf,axiom,
% 6.92/7.22 ! [P3: set_Pr8551490117392284871at_nat,Q6: set_Pr8551490117392284871at_nat,R2: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( ord_le8081472938463900775at_nat @ P3 @ ( sup_su3035147773818789531at_nat @ Q6 @ R2 ) )
% 6.92/7.22 = ( ord_le8081472938463900775at_nat @ ( inf_in1697001100524423349at_nat @ P3 @ ( uminus2330091110623919550at_nat @ Q6 ) ) @ R2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % sup_neg_inf
% 6.92/7.22 thf(fact_4599_sup__neg__inf,axiom,
% 6.92/7.22 ! [P3: set_Pr4329608150637261639at_nat,Q6: set_Pr4329608150637261639at_nat,R2: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( ord_le1268244103169919719at_nat @ P3 @ ( sup_su5525570899277871387at_nat @ Q6 @ R2 ) )
% 6.92/7.22 = ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ P3 @ ( uminus935396558254630718at_nat @ Q6 ) ) @ R2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % sup_neg_inf
% 6.92/7.22 thf(fact_4600_sup__neg__inf,axiom,
% 6.92/7.22 ! [P3: set_nat,Q6: set_nat,R2: set_nat] :
% 6.92/7.22 ( ( ord_less_eq_set_nat @ P3 @ ( sup_sup_set_nat @ Q6 @ R2 ) )
% 6.92/7.22 = ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ P3 @ ( uminus5710092332889474511et_nat @ Q6 ) ) @ R2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % sup_neg_inf
% 6.92/7.22 thf(fact_4601_sup__neg__inf,axiom,
% 6.92/7.22 ! [P3: assn,Q6: assn,R2: assn] :
% 6.92/7.22 ( ( ord_less_eq_assn @ P3 @ ( sup_sup_assn @ Q6 @ R2 ) )
% 6.92/7.22 = ( ord_less_eq_assn @ ( inf_inf_assn @ P3 @ ( uminus_uminus_assn @ Q6 ) ) @ R2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % sup_neg_inf
% 6.92/7.22 thf(fact_4602_sup__neg__inf,axiom,
% 6.92/7.22 ! [P3: product_unit,Q6: product_unit,R2: product_unit] :
% 6.92/7.22 ( ( ord_le3221252021190050221t_unit @ P3 @ ( sup_sup_Product_unit @ Q6 @ R2 ) )
% 6.92/7.22 = ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ P3 @ ( uminus2952777764628376836t_unit @ Q6 ) ) @ R2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % sup_neg_inf
% 6.92/7.22 thf(fact_4603_sup__neg__inf,axiom,
% 6.92/7.22 ! [P3: set_int,Q6: set_int,R2: set_int] :
% 6.92/7.22 ( ( ord_less_eq_set_int @ P3 @ ( sup_sup_set_int @ Q6 @ R2 ) )
% 6.92/7.22 = ( ord_less_eq_set_int @ ( inf_inf_set_int @ P3 @ ( uminus1532241313380277803et_int @ Q6 ) ) @ R2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % sup_neg_inf
% 6.92/7.22 thf(fact_4604_nat__power__eq,axiom,
% 6.92/7.22 ! [Z3: int,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.22 => ( ( nat2 @ ( power_power_int @ Z3 @ N2 ) )
% 6.92/7.22 = ( power_power_nat @ ( nat2 @ Z3 ) @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_power_eq
% 6.92/7.22 thf(fact_4605_diff__Suc__less,axiom,
% 6.92/7.22 ! [N2: nat,I2: nat] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.22 => ( ord_less_nat @ ( minus_minus_nat @ N2 @ ( suc @ I2 ) ) @ N2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_Suc_less
% 6.92/7.22 thf(fact_4606_nat__diff__split__asm,axiom,
% 6.92/7.22 ! [P2: nat > $o,A: nat,B: nat] :
% 6.92/7.22 ( ( P2 @ ( minus_minus_nat @ A @ B ) )
% 6.92/7.22 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 6.92/7.22 & ~ ( P2 @ zero_zero_nat ) )
% 6.92/7.22 | ? [D5: nat] :
% 6.92/7.22 ( ( A
% 6.92/7.22 = ( plus_plus_nat @ B @ D5 ) )
% 6.92/7.22 & ~ ( P2 @ D5 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_diff_split_asm
% 6.92/7.22 thf(fact_4607_nat__diff__split,axiom,
% 6.92/7.22 ! [P2: nat > $o,A: nat,B: nat] :
% 6.92/7.22 ( ( P2 @ ( minus_minus_nat @ A @ B ) )
% 6.92/7.22 = ( ( ( ord_less_nat @ A @ B )
% 6.92/7.22 => ( P2 @ zero_zero_nat ) )
% 6.92/7.22 & ! [D5: nat] :
% 6.92/7.22 ( ( A
% 6.92/7.22 = ( plus_plus_nat @ B @ D5 ) )
% 6.92/7.22 => ( P2 @ D5 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_diff_split
% 6.92/7.22 thf(fact_4608_less__diff__conv2,axiom,
% 6.92/7.22 ! [K2: nat,J2: nat,I2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ J2 )
% 6.92/7.22 => ( ( ord_less_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 )
% 6.92/7.22 = ( ord_less_nat @ J2 @ ( plus_plus_nat @ I2 @ K2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_diff_conv2
% 6.92/7.22 thf(fact_4609_minusinfinity,axiom,
% 6.92/7.22 ! [D2: int,P1: int > $o,P2: int > $o] :
% 6.92/7.22 ( ( ord_less_int @ zero_zero_int @ D2 )
% 6.92/7.22 => ( ! [X3: int,K: int] :
% 6.92/7.22 ( ( P1 @ X3 )
% 6.92/7.22 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D2 ) ) ) )
% 6.92/7.22 => ( ? [Z6: int] :
% 6.92/7.22 ! [X3: int] :
% 6.92/7.22 ( ( ord_less_int @ X3 @ Z6 )
% 6.92/7.22 => ( ( P2 @ X3 )
% 6.92/7.22 = ( P1 @ X3 ) ) )
% 6.92/7.22 => ( ? [X_12: int] : ( P1 @ X_12 )
% 6.92/7.22 => ? [X_1: int] : ( P2 @ X_1 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % minusinfinity
% 6.92/7.22 thf(fact_4610_plusinfinity,axiom,
% 6.92/7.22 ! [D2: int,P6: int > $o,P2: int > $o] :
% 6.92/7.22 ( ( ord_less_int @ zero_zero_int @ D2 )
% 6.92/7.22 => ( ! [X3: int,K: int] :
% 6.92/7.22 ( ( P6 @ X3 )
% 6.92/7.22 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D2 ) ) ) )
% 6.92/7.22 => ( ? [Z6: int] :
% 6.92/7.22 ! [X3: int] :
% 6.92/7.22 ( ( ord_less_int @ Z6 @ X3 )
% 6.92/7.22 => ( ( P2 @ X3 )
% 6.92/7.22 = ( P6 @ X3 ) ) )
% 6.92/7.22 => ( ? [X_12: int] : ( P6 @ X_12 )
% 6.92/7.22 => ? [X_1: int] : ( P2 @ X_1 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % plusinfinity
% 6.92/7.22 thf(fact_4611_int__cases4,axiom,
% 6.92/7.22 ! [M: int] :
% 6.92/7.22 ( ! [N5: nat] :
% 6.92/7.22 ( M
% 6.92/7.22 != ( semiri1314217659103216013at_int @ N5 ) )
% 6.92/7.22 => ~ ! [N5: nat] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 6.92/7.22 => ( M
% 6.92/7.22 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N5 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % int_cases4
% 6.92/7.22 thf(fact_4612_nat__eq__add__iff1,axiom,
% 6.92/7.22 ! [J2: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ J2 @ I2 )
% 6.92/7.22 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 6.92/7.22 = ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N2 ) )
% 6.92/7.22 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M )
% 6.92/7.22 = N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_eq_add_iff1
% 6.92/7.22 thf(fact_4613_nat__eq__add__iff2,axiom,
% 6.92/7.22 ! [I2: nat,J2: nat,U: nat,M: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.22 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 6.92/7.22 = ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N2 ) )
% 6.92/7.22 = ( M
% 6.92/7.22 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_eq_add_iff2
% 6.92/7.22 thf(fact_4614_nat__le__add__iff1,axiom,
% 6.92/7.22 ! [J2: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ J2 @ I2 )
% 6.92/7.22 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N2 ) )
% 6.92/7.22 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M ) @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_le_add_iff1
% 6.92/7.22 thf(fact_4615_nat__le__add__iff2,axiom,
% 6.92/7.22 ! [I2: nat,J2: nat,U: nat,M: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.22 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N2 ) )
% 6.92/7.22 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_le_add_iff2
% 6.92/7.22 thf(fact_4616_nat__diff__add__eq1,axiom,
% 6.92/7.22 ! [J2: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ J2 @ I2 )
% 6.92/7.22 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N2 ) )
% 6.92/7.22 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M ) @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_diff_add_eq1
% 6.92/7.22 thf(fact_4617_nat__diff__add__eq2,axiom,
% 6.92/7.22 ! [I2: nat,J2: nat,U: nat,M: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.22 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N2 ) )
% 6.92/7.22 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_diff_add_eq2
% 6.92/7.22 thf(fact_4618_int__induct,axiom,
% 6.92/7.22 ! [P2: int > $o,K2: int,I2: int] :
% 6.92/7.22 ( ( P2 @ K2 )
% 6.92/7.22 => ( ! [I3: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ K2 @ I3 )
% 6.92/7.22 => ( ( P2 @ I3 )
% 6.92/7.22 => ( P2 @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 6.92/7.22 => ( ! [I3: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ I3 @ K2 )
% 6.92/7.22 => ( ( P2 @ I3 )
% 6.92/7.22 => ( P2 @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 6.92/7.22 => ( P2 @ I2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % int_induct
% 6.92/7.22 thf(fact_4619_int__zle__neg,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 6.92/7.22 = ( ( N2 = zero_zero_nat )
% 6.92/7.22 & ( M = zero_zero_nat ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % int_zle_neg
% 6.92/7.22 thf(fact_4620_nonpos__int__cases,axiom,
% 6.92/7.22 ! [K2: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ K2 @ zero_zero_int )
% 6.92/7.22 => ~ ! [N5: nat] :
% 6.92/7.22 ( K2
% 6.92/7.22 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N5 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nonpos_int_cases
% 6.92/7.22 thf(fact_4621_negative__zle__0,axiom,
% 6.92/7.22 ! [N2: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ zero_zero_int ) ).
% 6.92/7.22
% 6.92/7.22 % negative_zle_0
% 6.92/7.22 thf(fact_4622_nat__plus__as__int,axiom,
% 6.92/7.22 ( plus_plus_nat
% 6.92/7.22 = ( ^ [A5: nat,B4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_plus_as_int
% 6.92/7.22 thf(fact_4623_nat__times__as__int,axiom,
% 6.92/7.22 ( times_times_nat
% 6.92/7.22 = ( ^ [A5: nat,B4: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_times_as_int
% 6.92/7.22 thf(fact_4624_nat__div__as__int,axiom,
% 6.92/7.22 ( divide_divide_nat
% 6.92/7.22 = ( ^ [A5: nat,B4: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_div_as_int
% 6.92/7.22 thf(fact_4625_nat__mod__as__int,axiom,
% 6.92/7.22 ( modulo_modulo_nat
% 6.92/7.22 = ( ^ [A5: nat,B4: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_mod_as_int
% 6.92/7.22 thf(fact_4626_frac__le__eq,axiom,
% 6.92/7.22 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 6.92/7.22 ( ( Y != zero_zero_rat )
% 6.92/7.22 => ( ( Z3 != zero_zero_rat )
% 6.92/7.22 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z3 ) )
% 6.92/7.22 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z3 ) ) @ zero_zero_rat ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % frac_le_eq
% 6.92/7.22 thf(fact_4627_frac__less__eq,axiom,
% 6.92/7.22 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 6.92/7.22 ( ( Y != zero_zero_rat )
% 6.92/7.22 => ( ( Z3 != zero_zero_rat )
% 6.92/7.22 => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z3 ) )
% 6.92/7.22 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z3 ) ) @ zero_zero_rat ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % frac_less_eq
% 6.92/7.22 thf(fact_4628_nat__less__eq__zless,axiom,
% 6.92/7.22 ! [W2: int,Z3: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 6.92/7.22 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z3 ) )
% 6.92/7.22 = ( ord_less_int @ W2 @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_less_eq_zless
% 6.92/7.22 thf(fact_4629_nat__le__eq__zle,axiom,
% 6.92/7.22 ! [W2: int,Z3: int] :
% 6.92/7.22 ( ( ( ord_less_int @ zero_zero_int @ W2 )
% 6.92/7.22 | ( ord_less_eq_int @ zero_zero_int @ Z3 ) )
% 6.92/7.22 => ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z3 ) )
% 6.92/7.22 = ( ord_less_eq_int @ W2 @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_le_eq_zle
% 6.92/7.22 thf(fact_4630_nat__eq__iff,axiom,
% 6.92/7.22 ! [W2: int,M: nat] :
% 6.92/7.22 ( ( ( nat2 @ W2 )
% 6.92/7.22 = M )
% 6.92/7.22 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 6.92/7.22 => ( W2
% 6.92/7.22 = ( semiri1314217659103216013at_int @ M ) ) )
% 6.92/7.22 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 6.92/7.22 => ( M = zero_zero_nat ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_eq_iff
% 6.92/7.22 thf(fact_4631_nat__eq__iff2,axiom,
% 6.92/7.22 ! [M: nat,W2: int] :
% 6.92/7.22 ( ( M
% 6.92/7.22 = ( nat2 @ W2 ) )
% 6.92/7.22 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 6.92/7.22 => ( W2
% 6.92/7.22 = ( semiri1314217659103216013at_int @ M ) ) )
% 6.92/7.22 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 6.92/7.22 => ( M = zero_zero_nat ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_eq_iff2
% 6.92/7.22 thf(fact_4632_split__nat,axiom,
% 6.92/7.22 ! [P2: nat > $o,I2: int] :
% 6.92/7.22 ( ( P2 @ ( nat2 @ I2 ) )
% 6.92/7.22 = ( ! [N: nat] :
% 6.92/7.22 ( ( I2
% 6.92/7.22 = ( semiri1314217659103216013at_int @ N ) )
% 6.92/7.22 => ( P2 @ N ) )
% 6.92/7.22 & ( ( ord_less_int @ I2 @ zero_zero_int )
% 6.92/7.22 => ( P2 @ zero_zero_nat ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % split_nat
% 6.92/7.22 thf(fact_4633_le__nat__iff,axiom,
% 6.92/7.22 ! [K2: int,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.22 => ( ( ord_less_eq_nat @ N2 @ ( nat2 @ K2 ) )
% 6.92/7.22 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ K2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_nat_iff
% 6.92/7.22 thf(fact_4634_nat__add__distrib,axiom,
% 6.92/7.22 ! [Z3: int,Z7: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.22 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 6.92/7.22 => ( ( nat2 @ ( plus_plus_int @ Z3 @ Z7 ) )
% 6.92/7.22 = ( plus_plus_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_add_distrib
% 6.92/7.22 thf(fact_4635_nat__mult__distrib,axiom,
% 6.92/7.22 ! [Z3: int,Z7: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.22 => ( ( nat2 @ ( times_times_int @ Z3 @ Z7 ) )
% 6.92/7.22 = ( times_times_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z7 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_mult_distrib
% 6.92/7.22 thf(fact_4636_Suc__as__int,axiom,
% 6.92/7.22 ( suc
% 6.92/7.22 = ( ^ [A5: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A5 ) @ one_one_int ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Suc_as_int
% 6.92/7.22 thf(fact_4637_pos__minus__divide__less__eq,axiom,
% 6.92/7.22 ! [C2: rat,B: rat,A: rat] :
% 6.92/7.22 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.22 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 6.92/7.22 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pos_minus_divide_less_eq
% 6.92/7.22 thf(fact_4638_pos__less__minus__divide__eq,axiom,
% 6.92/7.22 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.22 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 6.92/7.22 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pos_less_minus_divide_eq
% 6.92/7.22 thf(fact_4639_neg__minus__divide__less__eq,axiom,
% 6.92/7.22 ! [C2: rat,B: rat,A: rat] :
% 6.92/7.22 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.22 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 6.92/7.22 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_minus_divide_less_eq
% 6.92/7.22 thf(fact_4640_neg__less__minus__divide__eq,axiom,
% 6.92/7.22 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.22 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 6.92/7.22 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_less_minus_divide_eq
% 6.92/7.22 thf(fact_4641_minus__divide__less__eq,axiom,
% 6.92/7.22 ! [B: rat,C2: rat,A: rat] :
% 6.92/7.22 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 6.92/7.22 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.22 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 6.92/7.22 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.22 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.22 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 6.92/7.22 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.22 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % minus_divide_less_eq
% 6.92/7.22 thf(fact_4642_less__minus__divide__eq,axiom,
% 6.92/7.22 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.22 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 6.92/7.22 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.22 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 6.92/7.22 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.22 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.22 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 6.92/7.22 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.22 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % less_minus_divide_eq
% 6.92/7.22 thf(fact_4643_minus__divide__add__eq__iff,axiom,
% 6.92/7.22 ! [Z3: rat,X: rat,Y: rat] :
% 6.92/7.22 ( ( Z3 != zero_zero_rat )
% 6.92/7.22 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z3 ) ) @ Y )
% 6.92/7.22 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % minus_divide_add_eq_iff
% 6.92/7.22 thf(fact_4644_add__divide__eq__if__simps_I3_J,axiom,
% 6.92/7.22 ! [Z3: rat,A: rat,B: rat] :
% 6.92/7.22 ( ( ( Z3 = zero_zero_rat )
% 6.92/7.22 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z3 ) ) @ B )
% 6.92/7.22 = B ) )
% 6.92/7.22 & ( ( Z3 != zero_zero_rat )
% 6.92/7.22 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z3 ) ) @ B )
% 6.92/7.22 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_divide_eq_if_simps(3)
% 6.92/7.22 thf(fact_4645_nat__div__distrib,axiom,
% 6.92/7.22 ! [X: int,Y: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.22 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 6.92/7.22 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_div_distrib
% 6.92/7.22 thf(fact_4646_nat__div__distrib_H,axiom,
% 6.92/7.22 ! [Y: int,X: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.22 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 6.92/7.22 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_div_distrib'
% 6.92/7.22 thf(fact_4647_nat__mod__distrib,axiom,
% 6.92/7.22 ! [X: int,Y: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.22 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.22 => ( ( nat2 @ ( modulo_modulo_int @ X @ Y ) )
% 6.92/7.22 = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_mod_distrib
% 6.92/7.22 thf(fact_4648_power__diff,axiom,
% 6.92/7.22 ! [A: code_integer,N2: nat,M: nat] :
% 6.92/7.22 ( ( A != zero_z3403309356797280102nteger )
% 6.92/7.22 => ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N2 ) )
% 6.92/7.22 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % power_diff
% 6.92/7.22 thf(fact_4649_power__diff,axiom,
% 6.92/7.22 ! [A: nat,N2: nat,M: nat] :
% 6.92/7.22 ( ( A != zero_zero_nat )
% 6.92/7.22 => ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 6.92/7.22 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % power_diff
% 6.92/7.22 thf(fact_4650_power__diff,axiom,
% 6.92/7.22 ! [A: int,N2: nat,M: nat] :
% 6.92/7.22 ( ( A != zero_zero_int )
% 6.92/7.22 => ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) )
% 6.92/7.22 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % power_diff
% 6.92/7.22 thf(fact_4651_power__diff,axiom,
% 6.92/7.22 ! [A: code_natural,N2: nat,M: nat] :
% 6.92/7.22 ( ( A != zero_z2226904508553997617atural )
% 6.92/7.22 => ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ M @ N2 ) )
% 6.92/7.22 = ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N2 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % power_diff
% 6.92/7.22 thf(fact_4652_power__diff,axiom,
% 6.92/7.22 ! [A: rat,N2: nat,M: nat] :
% 6.92/7.22 ( ( A != zero_zero_rat )
% 6.92/7.22 => ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 6.92/7.22 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % power_diff
% 6.92/7.22 thf(fact_4653_nz__le__conv__less,axiom,
% 6.92/7.22 ! [K2: nat,M: nat] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.22 => ( ( ord_less_eq_nat @ K2 @ M )
% 6.92/7.22 => ( ord_less_nat @ ( minus_minus_nat @ K2 @ ( suc @ zero_zero_nat ) ) @ M ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nz_le_conv_less
% 6.92/7.22 thf(fact_4654_Suc__diff__eq__diff__pred,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.22 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 6.92/7.22 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Suc_diff_eq_diff_pred
% 6.92/7.22 thf(fact_4655_Suc__pred_H,axiom,
% 6.92/7.22 ! [N2: nat] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.22 => ( N2
% 6.92/7.22 = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Suc_pred'
% 6.92/7.22 thf(fact_4656_add__eq__if,axiom,
% 6.92/7.22 ( plus_plus_nat
% 6.92/7.22 = ( ^ [M3: nat,N: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % add_eq_if
% 6.92/7.22 thf(fact_4657_Suc__n__minus__m__eq,axiom,
% 6.92/7.22 ! [M: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.22 => ( ( ord_less_nat @ one_one_nat @ M )
% 6.92/7.22 => ( ( suc @ ( minus_minus_nat @ N2 @ M ) )
% 6.92/7.22 = ( minus_minus_nat @ N2 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Suc_n_minus_m_eq
% 6.92/7.22 thf(fact_4658_nat__less__add__iff1,axiom,
% 6.92/7.22 ! [J2: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ J2 @ I2 )
% 6.92/7.22 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N2 ) )
% 6.92/7.22 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M ) @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_less_add_iff1
% 6.92/7.22 thf(fact_4659_nat__less__add__iff2,axiom,
% 6.92/7.22 ! [I2: nat,J2: nat,U: nat,M: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.22 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N2 ) )
% 6.92/7.22 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_less_add_iff2
% 6.92/7.22 thf(fact_4660_decr__mult__lemma,axiom,
% 6.92/7.22 ! [D2: int,P2: int > $o,K2: int] :
% 6.92/7.22 ( ( ord_less_int @ zero_zero_int @ D2 )
% 6.92/7.22 => ( ! [X3: int] :
% 6.92/7.22 ( ( P2 @ X3 )
% 6.92/7.22 => ( P2 @ ( minus_minus_int @ X3 @ D2 ) ) )
% 6.92/7.22 => ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.22 => ! [X6: int] :
% 6.92/7.22 ( ( P2 @ X6 )
% 6.92/7.22 => ( P2 @ ( minus_minus_int @ X6 @ ( times_times_int @ K2 @ D2 ) ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % decr_mult_lemma
% 6.92/7.22 thf(fact_4661_div__if,axiom,
% 6.92/7.22 ( divide_divide_nat
% 6.92/7.22 = ( ^ [M3: nat,N: nat] :
% 6.92/7.22 ( if_nat
% 6.92/7.22 @ ( ( ord_less_nat @ M3 @ N )
% 6.92/7.22 | ( N = zero_zero_nat ) )
% 6.92/7.22 @ zero_zero_nat
% 6.92/7.22 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M3 @ N ) @ N ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % div_if
% 6.92/7.22 thf(fact_4662_div__geq,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.22 => ( ~ ( ord_less_nat @ M @ N2 )
% 6.92/7.22 => ( ( divide_divide_nat @ M @ N2 )
% 6.92/7.22 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % div_geq
% 6.92/7.22 thf(fact_4663_int__cases3,axiom,
% 6.92/7.22 ! [K2: int] :
% 6.92/7.22 ( ( K2 != zero_zero_int )
% 6.92/7.22 => ( ! [N5: nat] :
% 6.92/7.22 ( ( K2
% 6.92/7.22 = ( semiri1314217659103216013at_int @ N5 ) )
% 6.92/7.22 => ~ ( ord_less_nat @ zero_zero_nat @ N5 ) )
% 6.92/7.22 => ~ ! [N5: nat] :
% 6.92/7.22 ( ( K2
% 6.92/7.22 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N5 ) ) )
% 6.92/7.22 => ~ ( ord_less_nat @ zero_zero_nat @ N5 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % int_cases3
% 6.92/7.22 thf(fact_4664_mult__eq__if,axiom,
% 6.92/7.22 ( times_times_nat
% 6.92/7.22 = ( ^ [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 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % mult_eq_if
% 6.92/7.22 thf(fact_4665_not__zle__0__negative,axiom,
% 6.92/7.22 ! [N2: nat] :
% 6.92/7.22 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % not_zle_0_negative
% 6.92/7.22 thf(fact_4666_negD,axiom,
% 6.92/7.22 ! [X: int] :
% 6.92/7.22 ( ( ord_less_int @ X @ zero_zero_int )
% 6.92/7.22 => ? [N5: nat] :
% 6.92/7.22 ( X
% 6.92/7.22 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N5 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % negD
% 6.92/7.22 thf(fact_4667_negative__zless__0,axiom,
% 6.92/7.22 ! [N2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ zero_zero_int ) ).
% 6.92/7.22
% 6.92/7.22 % negative_zless_0
% 6.92/7.22 thf(fact_4668_mod__pos__geq,axiom,
% 6.92/7.22 ! [L: int,K2: int] :
% 6.92/7.22 ( ( ord_less_int @ zero_zero_int @ L )
% 6.92/7.22 => ( ( ord_less_eq_int @ L @ K2 )
% 6.92/7.22 => ( ( modulo_modulo_int @ K2 @ L )
% 6.92/7.22 = ( modulo_modulo_int @ ( minus_minus_int @ K2 @ L ) @ L ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % mod_pos_geq
% 6.92/7.22 thf(fact_4669_verit__less__mono__div__int2,axiom,
% 6.92/7.22 ! [A4: int,B5: int,N2: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ A4 @ B5 )
% 6.92/7.22 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N2 ) )
% 6.92/7.22 => ( ord_less_eq_int @ ( divide_divide_int @ B5 @ N2 ) @ ( divide_divide_int @ A4 @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % verit_less_mono_div_int2
% 6.92/7.22 thf(fact_4670_div__eq__minus1,axiom,
% 6.92/7.22 ! [B: int] :
% 6.92/7.22 ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.22 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 6.92/7.22 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % div_eq_minus1
% 6.92/7.22 thf(fact_4671_scaling__mono,axiom,
% 6.92/7.22 ! [U: rat,V: rat,R2: rat,S2: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ U @ V )
% 6.92/7.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 6.92/7.22 => ( ( ord_less_eq_rat @ R2 @ S2 )
% 6.92/7.22 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % scaling_mono
% 6.92/7.22 thf(fact_4672_Suc__nat__eq__nat__zadd1,axiom,
% 6.92/7.22 ! [Z3: int] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.22 => ( ( suc @ ( nat2 @ Z3 ) )
% 6.92/7.22 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z3 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Suc_nat_eq_nat_zadd1
% 6.92/7.22 thf(fact_4673_nat__less__iff,axiom,
% 6.92/7.22 ! [W2: int,M: nat] :
% 6.92/7.22 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 6.92/7.22 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ M )
% 6.92/7.22 = ( ord_less_int @ W2 @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % nat_less_iff
% 6.92/7.22 thf(fact_4674_pos__minus__divide__le__eq,axiom,
% 6.92/7.22 ! [C2: rat,B: rat,A: rat] :
% 6.92/7.22 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.22 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 6.92/7.22 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pos_minus_divide_le_eq
% 6.92/7.22 thf(fact_4675_pos__le__minus__divide__eq,axiom,
% 6.92/7.22 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.22 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 6.92/7.22 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pos_le_minus_divide_eq
% 6.92/7.22 thf(fact_4676_neg__minus__divide__le__eq,axiom,
% 6.92/7.22 ! [C2: rat,B: rat,A: rat] :
% 6.92/7.22 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.22 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 6.92/7.22 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_minus_divide_le_eq
% 6.92/7.22 thf(fact_4677_neg__le__minus__divide__eq,axiom,
% 6.92/7.22 ! [C2: rat,A: rat,B: rat] :
% 6.92/7.22 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.22 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 6.92/7.22 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_le_minus_divide_eq
% 6.92/7.22 thf(fact_4678_minus__divide__le__eq,axiom,
% 6.92/7.22 ! [B: rat,C2: rat,A: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 6.92/7.22 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.22 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 6.92/7.22 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.22 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.22 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 6.92/7.22 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.22 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % minus_divide_le_eq
% 6.92/7.22 thf(fact_4679_le__minus__divide__eq,axiom,
% 6.92/7.22 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.22 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 6.92/7.22 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.22 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 6.92/7.22 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.22 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.22 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 6.92/7.22 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.22 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_minus_divide_eq
% 6.92/7.22 thf(fact_4680_power__diff__power__eq,axiom,
% 6.92/7.22 ! [A: code_integer,N2: nat,M: nat] :
% 6.92/7.22 ( ( A != zero_z3403309356797280102nteger )
% 6.92/7.22 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 6.92/7.22 = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 6.92/7.22 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 6.92/7.22 = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % power_diff_power_eq
% 6.92/7.22 thf(fact_4681_power__diff__power__eq,axiom,
% 6.92/7.22 ! [A: nat,N2: nat,M: nat] :
% 6.92/7.22 ( ( A != zero_zero_nat )
% 6.92/7.22 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 6.92/7.22 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 6.92/7.22 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 6.92/7.22 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % power_diff_power_eq
% 6.92/7.22 thf(fact_4682_power__diff__power__eq,axiom,
% 6.92/7.22 ! [A: int,N2: nat,M: nat] :
% 6.92/7.22 ( ( A != zero_zero_int )
% 6.92/7.22 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 6.92/7.22 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 6.92/7.22 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 6.92/7.22 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % power_diff_power_eq
% 6.92/7.22 thf(fact_4683_power__diff__power__eq,axiom,
% 6.92/7.22 ! [A: code_natural,N2: nat,M: nat] :
% 6.92/7.22 ( ( A != zero_z2226904508553997617atural )
% 6.92/7.22 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N2 ) )
% 6.92/7.22 = ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 6.92/7.22 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N2 ) )
% 6.92/7.22 = ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % power_diff_power_eq
% 6.92/7.22 thf(fact_4684_power__minus__mult,axiom,
% 6.92/7.22 ! [N2: nat,A: assn] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.22 => ( ( times_times_assn @ ( power_power_assn @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 6.92/7.22 = ( power_power_assn @ A @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % power_minus_mult
% 6.92/7.22 thf(fact_4685_power__minus__mult,axiom,
% 6.92/7.22 ! [N2: nat,A: rat] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.22 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 6.92/7.22 = ( power_power_rat @ A @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % power_minus_mult
% 6.92/7.22 thf(fact_4686_power__minus__mult,axiom,
% 6.92/7.22 ! [N2: nat,A: nat] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.22 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 6.92/7.22 = ( power_power_nat @ A @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % power_minus_mult
% 6.92/7.22 thf(fact_4687_power__minus__mult,axiom,
% 6.92/7.22 ! [N2: nat,A: int] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.22 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 6.92/7.22 = ( power_power_int @ A @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % power_minus_mult
% 6.92/7.22 thf(fact_4688_le__div__geq,axiom,
% 6.92/7.22 ! [N2: nat,M: nat] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.22 => ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( divide_divide_nat @ M @ N2 )
% 6.92/7.22 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % le_div_geq
% 6.92/7.22 thf(fact_4689_neg__int__cases,axiom,
% 6.92/7.22 ! [K2: int] :
% 6.92/7.22 ( ( ord_less_int @ K2 @ zero_zero_int )
% 6.92/7.22 => ~ ! [N5: nat] :
% 6.92/7.22 ( ( K2
% 6.92/7.22 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N5 ) ) )
% 6.92/7.22 => ~ ( ord_less_nat @ zero_zero_nat @ N5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_int_cases
% 6.92/7.22 thf(fact_4690_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 6.92/7.22 ! [K2: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.22 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N2 @ K2 ) )
% 6.92/7.22 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N2 @ K2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_one_power_add_eq_neg_one_power_diff
% 6.92/7.22 thf(fact_4691_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 6.92/7.22 ! [K2: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.22 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N2 @ K2 ) )
% 6.92/7.22 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N2 @ K2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_one_power_add_eq_neg_one_power_diff
% 6.92/7.22 thf(fact_4692_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 6.92/7.22 ! [K2: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.22 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N2 @ K2 ) )
% 6.92/7.22 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N2 @ K2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % neg_one_power_add_eq_neg_one_power_diff
% 6.92/7.22 thf(fact_4693_pochhammer__code,axiom,
% 6.92/7.22 ( comm_s4028243227959126397er_rat
% 6.92/7.22 = ( ^ [A5: rat,N: nat] :
% 6.92/7.22 ( if_rat @ ( N = zero_zero_nat ) @ one_one_rat
% 6.92/7.22 @ ( set_fo1949268297981939178at_rat
% 6.92/7.22 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ O ) ) )
% 6.92/7.22 @ zero_zero_nat
% 6.92/7.22 @ ( minus_minus_nat @ N @ one_one_nat )
% 6.92/7.22 @ one_one_rat ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_code
% 6.92/7.22 thf(fact_4694_pochhammer__code,axiom,
% 6.92/7.22 ( comm_s4660882817536571857er_int
% 6.92/7.22 = ( ^ [A5: int,N: nat] :
% 6.92/7.22 ( if_int @ ( N = zero_zero_nat ) @ one_one_int
% 6.92/7.22 @ ( set_fo2581907887559384638at_int
% 6.92/7.22 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ O ) ) )
% 6.92/7.22 @ zero_zero_nat
% 6.92/7.22 @ ( minus_minus_nat @ N @ one_one_nat )
% 6.92/7.22 @ one_one_int ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_code
% 6.92/7.22 thf(fact_4695_pochhammer__code,axiom,
% 6.92/7.22 ( comm_s8582702949713902594nteger
% 6.92/7.22 = ( ^ [A5: code_integer,N: nat] :
% 6.92/7.22 ( if_Code_integer @ ( N = zero_zero_nat ) @ one_one_Code_integer
% 6.92/7.22 @ ( set_fo1084959871951514735nteger
% 6.92/7.22 @ ^ [O: nat] : ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A5 @ ( semiri4939895301339042750nteger @ O ) ) )
% 6.92/7.22 @ zero_zero_nat
% 6.92/7.22 @ ( minus_minus_nat @ N @ one_one_nat )
% 6.92/7.22 @ one_one_Code_integer ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_code
% 6.92/7.22 thf(fact_4696_pochhammer__code,axiom,
% 6.92/7.22 ( comm_s4663373288045622133er_nat
% 6.92/7.22 = ( ^ [A5: nat,N: nat] :
% 6.92/7.22 ( if_nat @ ( N = zero_zero_nat ) @ one_one_nat
% 6.92/7.22 @ ( set_fo2584398358068434914at_nat
% 6.92/7.22 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 6.92/7.22 @ zero_zero_nat
% 6.92/7.22 @ ( minus_minus_nat @ N @ one_one_nat )
% 6.92/7.22 @ one_one_nat ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_code
% 6.92/7.22 thf(fact_4697_size__union,axiom,
% 6.92/7.22 ! [M6: multis2468970476368604999at_nat,N7: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( size_s8510653225128441779at_nat @ ( plus_p7104986032573967614at_nat @ M6 @ N7 ) )
% 6.92/7.22 = ( plus_plus_nat @ ( size_s8510653225128441779at_nat @ M6 ) @ ( size_s8510653225128441779at_nat @ N7 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % size_union
% 6.92/7.22 thf(fact_4698_normalize__negative,axiom,
% 6.92/7.22 ! [Q6: int,P3: int] :
% 6.92/7.22 ( ( ord_less_int @ Q6 @ zero_zero_int )
% 6.92/7.22 => ( ( normalize @ ( product_Pair_int_int @ P3 @ Q6 ) )
% 6.92/7.22 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P3 ) @ ( uminus_uminus_int @ Q6 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % normalize_negative
% 6.92/7.22 thf(fact_4699_length__rule,axiom,
% 6.92/7.22 ! [A: array_nat,Xs: list_nat] :
% 6.92/7.22 ( hoare_3067605981109127869le_nat @ ( snga_assn_nat @ A @ Xs ) @ ( array_len_nat @ A )
% 6.92/7.22 @ ^ [R5: nat] :
% 6.92/7.22 ( times_times_assn @ ( snga_assn_nat @ A @ Xs )
% 6.92/7.22 @ ( pure_assn
% 6.92/7.22 @ ( R5
% 6.92/7.22 = ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % length_rule
% 6.92/7.22 thf(fact_4700_length__rule,axiom,
% 6.92/7.22 ! [A: array_o,Xs: list_o] :
% 6.92/7.22 ( hoare_3067605981109127869le_nat @ ( snga_assn_o @ A @ Xs ) @ ( array_len_o @ A )
% 6.92/7.22 @ ^ [R5: nat] :
% 6.92/7.22 ( times_times_assn @ ( snga_assn_o @ A @ Xs )
% 6.92/7.22 @ ( pure_assn
% 6.92/7.22 @ ( R5
% 6.92/7.22 = ( size_size_list_o @ Xs ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % length_rule
% 6.92/7.22 thf(fact_4701_length__rule,axiom,
% 6.92/7.22 ! [A: array_int,Xs: list_int] :
% 6.92/7.22 ( hoare_3067605981109127869le_nat @ ( snga_assn_int @ A @ Xs ) @ ( array_len_int @ A )
% 6.92/7.22 @ ^ [R5: nat] :
% 6.92/7.22 ( times_times_assn @ ( snga_assn_int @ A @ Xs )
% 6.92/7.22 @ ( pure_assn
% 6.92/7.22 @ ( R5
% 6.92/7.22 = ( size_size_list_int @ Xs ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % length_rule
% 6.92/7.22 thf(fact_4702_Diff__cancel,axiom,
% 6.92/7.22 ! [A4: set_o] :
% 6.92/7.22 ( ( minus_minus_set_o @ A4 @ A4 )
% 6.92/7.22 = bot_bot_set_o ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_cancel
% 6.92/7.22 thf(fact_4703_Diff__cancel,axiom,
% 6.92/7.22 ! [A4: set_nat] :
% 6.92/7.22 ( ( minus_minus_set_nat @ A4 @ A4 )
% 6.92/7.22 = bot_bot_set_nat ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_cancel
% 6.92/7.22 thf(fact_4704_Diff__cancel,axiom,
% 6.92/7.22 ! [A4: set_int] :
% 6.92/7.22 ( ( minus_minus_set_int @ A4 @ A4 )
% 6.92/7.22 = bot_bot_set_int ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_cancel
% 6.92/7.22 thf(fact_4705_Diff__cancel,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( minus_1356011639430497352at_nat @ A4 @ A4 )
% 6.92/7.22 = bot_bo2099793752762293965at_nat ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_cancel
% 6.92/7.22 thf(fact_4706_empty__Diff,axiom,
% 6.92/7.22 ! [A4: set_o] :
% 6.92/7.22 ( ( minus_minus_set_o @ bot_bot_set_o @ A4 )
% 6.92/7.22 = bot_bot_set_o ) ).
% 6.92/7.22
% 6.92/7.22 % empty_Diff
% 6.92/7.22 thf(fact_4707_empty__Diff,axiom,
% 6.92/7.22 ! [A4: set_nat] :
% 6.92/7.22 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A4 )
% 6.92/7.22 = bot_bot_set_nat ) ).
% 6.92/7.22
% 6.92/7.22 % empty_Diff
% 6.92/7.22 thf(fact_4708_empty__Diff,axiom,
% 6.92/7.22 ! [A4: set_int] :
% 6.92/7.22 ( ( minus_minus_set_int @ bot_bot_set_int @ A4 )
% 6.92/7.22 = bot_bot_set_int ) ).
% 6.92/7.22
% 6.92/7.22 % empty_Diff
% 6.92/7.22 thf(fact_4709_empty__Diff,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( minus_1356011639430497352at_nat @ bot_bo2099793752762293965at_nat @ A4 )
% 6.92/7.22 = bot_bo2099793752762293965at_nat ) ).
% 6.92/7.22
% 6.92/7.22 % empty_Diff
% 6.92/7.22 thf(fact_4710_Diff__empty,axiom,
% 6.92/7.22 ! [A4: set_o] :
% 6.92/7.22 ( ( minus_minus_set_o @ A4 @ bot_bot_set_o )
% 6.92/7.22 = A4 ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_empty
% 6.92/7.22 thf(fact_4711_Diff__empty,axiom,
% 6.92/7.22 ! [A4: set_nat] :
% 6.92/7.22 ( ( minus_minus_set_nat @ A4 @ bot_bot_set_nat )
% 6.92/7.22 = A4 ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_empty
% 6.92/7.22 thf(fact_4712_Diff__empty,axiom,
% 6.92/7.22 ! [A4: set_int] :
% 6.92/7.22 ( ( minus_minus_set_int @ A4 @ bot_bot_set_int )
% 6.92/7.22 = A4 ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_empty
% 6.92/7.22 thf(fact_4713_Diff__empty,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( minus_1356011639430497352at_nat @ A4 @ bot_bo2099793752762293965at_nat )
% 6.92/7.22 = A4 ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_empty
% 6.92/7.22 thf(fact_4714_Compl__anti__mono,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int] :
% 6.92/7.22 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.22 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B5 ) @ ( uminus1532241313380277803et_int @ A4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_anti_mono
% 6.92/7.22 thf(fact_4715_Compl__subset__Compl__iff,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int] :
% 6.92/7.22 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A4 ) @ ( uminus1532241313380277803et_int @ B5 ) )
% 6.92/7.22 = ( ord_less_eq_set_int @ B5 @ A4 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_subset_Compl_iff
% 6.92/7.22 thf(fact_4716_Diff__Compl,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( minus_minus_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ B5 ) )
% 6.92/7.22 = ( inf_inf_set_nat @ A4 @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Compl
% 6.92/7.22 thf(fact_4717_Diff__Compl,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( minus_1356011639430497352at_nat @ A4 @ ( uminus6524753893492686040at_nat @ B5 ) )
% 6.92/7.22 = ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Compl
% 6.92/7.22 thf(fact_4718_inter__compl__diff__conv,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( inf_inf_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ B5 ) )
% 6.92/7.22 = ( minus_minus_set_nat @ A4 @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % inter_compl_diff_conv
% 6.92/7.22 thf(fact_4719_inter__compl__diff__conv,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( inf_in2572325071724192079at_nat @ A4 @ ( uminus6524753893492686040at_nat @ B5 ) )
% 6.92/7.22 = ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % inter_compl_diff_conv
% 6.92/7.22 thf(fact_4720_Compl__Diff__eq,axiom,
% 6.92/7.22 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( uminus2330091110623919550at_nat @ ( minus_5060654252129873198at_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ A4 ) @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_Diff_eq
% 6.92/7.22 thf(fact_4721_Compl__Diff__eq,axiom,
% 6.92/7.22 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( uminus935396558254630718at_nat @ ( minus_3314409938677909166at_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ A4 ) @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_Diff_eq
% 6.92/7.22 thf(fact_4722_Compl__Diff__eq,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( uminus5710092332889474511et_nat @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A4 ) @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_Diff_eq
% 6.92/7.22 thf(fact_4723_Compl__Diff__eq,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( uminus6524753893492686040at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ A4 ) @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_Diff_eq
% 6.92/7.22 thf(fact_4724_Un__Diff__cancel,axiom,
% 6.92/7.22 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( sup_su3035147773818789531at_nat @ A4 @ ( minus_5060654252129873198at_nat @ B5 @ A4 ) )
% 6.92/7.22 = ( sup_su3035147773818789531at_nat @ A4 @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff_cancel
% 6.92/7.22 thf(fact_4725_Un__Diff__cancel,axiom,
% 6.92/7.22 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( sup_su5525570899277871387at_nat @ A4 @ ( minus_3314409938677909166at_nat @ B5 @ A4 ) )
% 6.92/7.22 = ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff_cancel
% 6.92/7.22 thf(fact_4726_Un__Diff__cancel,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( sup_sup_set_nat @ A4 @ ( minus_minus_set_nat @ B5 @ A4 ) )
% 6.92/7.22 = ( sup_sup_set_nat @ A4 @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff_cancel
% 6.92/7.22 thf(fact_4727_Un__Diff__cancel,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( sup_su6327502436637775413at_nat @ A4 @ ( minus_1356011639430497352at_nat @ B5 @ A4 ) )
% 6.92/7.22 = ( sup_su6327502436637775413at_nat @ A4 @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff_cancel
% 6.92/7.22 thf(fact_4728_Un__Diff__cancel2,axiom,
% 6.92/7.22 ! [B5: set_Pr8551490117392284871at_nat,A4: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ B5 @ A4 ) @ A4 )
% 6.92/7.22 = ( sup_su3035147773818789531at_nat @ B5 @ A4 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff_cancel2
% 6.92/7.22 thf(fact_4729_Un__Diff__cancel2,axiom,
% 6.92/7.22 ! [B5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ B5 @ A4 ) @ A4 )
% 6.92/7.22 = ( sup_su5525570899277871387at_nat @ B5 @ A4 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff_cancel2
% 6.92/7.22 thf(fact_4730_Un__Diff__cancel2,axiom,
% 6.92/7.22 ! [B5: set_nat,A4: set_nat] :
% 6.92/7.22 ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ B5 @ A4 ) @ A4 )
% 6.92/7.22 = ( sup_sup_set_nat @ B5 @ A4 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff_cancel2
% 6.92/7.22 thf(fact_4731_Un__Diff__cancel2,axiom,
% 6.92/7.22 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ B5 @ A4 ) @ A4 )
% 6.92/7.22 = ( sup_su6327502436637775413at_nat @ B5 @ A4 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff_cancel2
% 6.92/7.22 thf(fact_4732_diff__diff__add__mset,axiom,
% 6.92/7.22 ! [M6: multis2468970476368604999at_nat,N7: multis2468970476368604999at_nat,P2: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( minus_4286766774447292334at_nat @ ( minus_4286766774447292334at_nat @ M6 @ N7 ) @ P2 )
% 6.92/7.22 = ( minus_4286766774447292334at_nat @ M6 @ ( plus_p7104986032573967614at_nat @ N7 @ P2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % diff_diff_add_mset
% 6.92/7.22 thf(fact_4733_union__eq__empty,axiom,
% 6.92/7.22 ! [M6: multis2468970476368604999at_nat,N7: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( ( plus_p7104986032573967614at_nat @ M6 @ N7 )
% 6.92/7.22 = zero_z1048942125864253310at_nat )
% 6.92/7.22 = ( ( M6 = zero_z1048942125864253310at_nat )
% 6.92/7.22 & ( N7 = zero_z1048942125864253310at_nat ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % union_eq_empty
% 6.92/7.22 thf(fact_4734_empty__eq__union,axiom,
% 6.92/7.22 ! [M6: multis2468970476368604999at_nat,N7: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( zero_z1048942125864253310at_nat
% 6.92/7.22 = ( plus_p7104986032573967614at_nat @ M6 @ N7 ) )
% 6.92/7.22 = ( ( M6 = zero_z1048942125864253310at_nat )
% 6.92/7.22 & ( N7 = zero_z1048942125864253310at_nat ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % empty_eq_union
% 6.92/7.22 thf(fact_4735_subset__mset_Ozero__eq__add__iff__both__eq__0,axiom,
% 6.92/7.22 ! [X: multis2468970476368604999at_nat,Y: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( zero_z1048942125864253310at_nat
% 6.92/7.22 = ( plus_p7104986032573967614at_nat @ X @ Y ) )
% 6.92/7.22 = ( ( X = zero_z1048942125864253310at_nat )
% 6.92/7.22 & ( Y = zero_z1048942125864253310at_nat ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % subset_mset.zero_eq_add_iff_both_eq_0
% 6.92/7.22 thf(fact_4736_subset__mset_Oadd__eq__0__iff__both__eq__0,axiom,
% 6.92/7.22 ! [X: multis2468970476368604999at_nat,Y: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( ( plus_p7104986032573967614at_nat @ X @ Y )
% 6.92/7.22 = zero_z1048942125864253310at_nat )
% 6.92/7.22 = ( ( X = zero_z1048942125864253310at_nat )
% 6.92/7.22 & ( Y = zero_z1048942125864253310at_nat ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % subset_mset.add_eq_0_iff_both_eq_0
% 6.92/7.22 thf(fact_4737_Diff__eq__empty__iff,axiom,
% 6.92/7.22 ! [A4: set_o,B5: set_o] :
% 6.92/7.22 ( ( ( minus_minus_set_o @ A4 @ B5 )
% 6.92/7.22 = bot_bot_set_o )
% 6.92/7.22 = ( ord_less_eq_set_o @ A4 @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_eq_empty_iff
% 6.92/7.22 thf(fact_4738_Diff__eq__empty__iff,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( ( minus_minus_set_nat @ A4 @ B5 )
% 6.92/7.22 = bot_bot_set_nat )
% 6.92/7.22 = ( ord_less_eq_set_nat @ A4 @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_eq_empty_iff
% 6.92/7.22 thf(fact_4739_Diff__eq__empty__iff,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ( minus_1356011639430497352at_nat @ A4 @ B5 )
% 6.92/7.22 = bot_bo2099793752762293965at_nat )
% 6.92/7.22 = ( ord_le3146513528884898305at_nat @ A4 @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_eq_empty_iff
% 6.92/7.22 thf(fact_4740_Diff__eq__empty__iff,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int] :
% 6.92/7.22 ( ( ( minus_minus_set_int @ A4 @ B5 )
% 6.92/7.22 = bot_bot_set_int )
% 6.92/7.22 = ( ord_less_eq_set_int @ A4 @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_eq_empty_iff
% 6.92/7.22 thf(fact_4741_Diff__disjoint,axiom,
% 6.92/7.22 ! [A4: set_o,B5: set_o] :
% 6.92/7.22 ( ( inf_inf_set_o @ A4 @ ( minus_minus_set_o @ B5 @ A4 ) )
% 6.92/7.22 = bot_bot_set_o ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_disjoint
% 6.92/7.22 thf(fact_4742_Diff__disjoint,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( inf_inf_set_nat @ A4 @ ( minus_minus_set_nat @ B5 @ A4 ) )
% 6.92/7.22 = bot_bot_set_nat ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_disjoint
% 6.92/7.22 thf(fact_4743_Diff__disjoint,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int] :
% 6.92/7.22 ( ( inf_inf_set_int @ A4 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 6.92/7.22 = bot_bot_set_int ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_disjoint
% 6.92/7.22 thf(fact_4744_Diff__disjoint,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( inf_in2572325071724192079at_nat @ A4 @ ( minus_1356011639430497352at_nat @ B5 @ A4 ) )
% 6.92/7.22 = bot_bo2099793752762293965at_nat ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_disjoint
% 6.92/7.22 thf(fact_4745_Compl__disjoint,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( inf_in2572325071724192079at_nat @ A4 @ ( uminus6524753893492686040at_nat @ A4 ) )
% 6.92/7.22 = bot_bo2099793752762293965at_nat ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_disjoint
% 6.92/7.22 thf(fact_4746_Compl__disjoint,axiom,
% 6.92/7.22 ! [A4: set_o] :
% 6.92/7.22 ( ( inf_inf_set_o @ A4 @ ( uminus_uminus_set_o @ A4 ) )
% 6.92/7.22 = bot_bot_set_o ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_disjoint
% 6.92/7.22 thf(fact_4747_Compl__disjoint,axiom,
% 6.92/7.22 ! [A4: set_nat] :
% 6.92/7.22 ( ( inf_inf_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ A4 ) )
% 6.92/7.22 = bot_bot_set_nat ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_disjoint
% 6.92/7.22 thf(fact_4748_Compl__disjoint,axiom,
% 6.92/7.22 ! [A4: set_int] :
% 6.92/7.22 ( ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ A4 ) )
% 6.92/7.22 = bot_bot_set_int ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_disjoint
% 6.92/7.22 thf(fact_4749_Compl__disjoint2,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ A4 ) @ A4 )
% 6.92/7.22 = bot_bo2099793752762293965at_nat ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_disjoint2
% 6.92/7.22 thf(fact_4750_Compl__disjoint2,axiom,
% 6.92/7.22 ! [A4: set_o] :
% 6.92/7.22 ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ A4 ) @ A4 )
% 6.92/7.22 = bot_bot_set_o ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_disjoint2
% 6.92/7.22 thf(fact_4751_Compl__disjoint2,axiom,
% 6.92/7.22 ! [A4: set_nat] :
% 6.92/7.22 ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A4 ) @ A4 )
% 6.92/7.22 = bot_bot_set_nat ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_disjoint2
% 6.92/7.22 thf(fact_4752_Compl__disjoint2,axiom,
% 6.92/7.22 ! [A4: set_int] :
% 6.92/7.22 ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ A4 ) @ A4 )
% 6.92/7.22 = bot_bot_set_int ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_disjoint2
% 6.92/7.22 thf(fact_4753_mod__not__dist,axiom,
% 6.92/7.22 ! [P2: assn,H: produc3658429121746597890et_nat] :
% 6.92/7.22 ( ( rep_assn @ ( uminus_uminus_assn @ P2 ) @ H )
% 6.92/7.22 = ( ( in_range @ H )
% 6.92/7.22 & ~ ( rep_assn @ P2 @ H ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % mod_not_dist
% 6.92/7.22 thf(fact_4754_minus__assn__def,axiom,
% 6.92/7.22 ( minus_minus_assn
% 6.92/7.22 = ( ^ [A5: assn,B4: assn] : ( inf_inf_assn @ A5 @ ( uminus_uminus_assn @ B4 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % minus_assn_def
% 6.92/7.22 thf(fact_4755_Multiset_Odiff__add,axiom,
% 6.92/7.22 ! [M6: multis2468970476368604999at_nat,N7: multis2468970476368604999at_nat,Q2: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( minus_4286766774447292334at_nat @ M6 @ ( plus_p7104986032573967614at_nat @ N7 @ Q2 ) )
% 6.92/7.22 = ( minus_4286766774447292334at_nat @ ( minus_4286766774447292334at_nat @ M6 @ N7 ) @ Q2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Multiset.diff_add
% 6.92/7.22 thf(fact_4756_diff__union__cancelL,axiom,
% 6.92/7.22 ! [N7: multis2468970476368604999at_nat,M6: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ N7 @ M6 ) @ N7 )
% 6.92/7.22 = M6 ) ).
% 6.92/7.22
% 6.92/7.22 % diff_union_cancelL
% 6.92/7.22 thf(fact_4757_diff__union__cancelR,axiom,
% 6.92/7.22 ! [M6: multis2468970476368604999at_nat,N7: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ M6 @ N7 ) @ N7 )
% 6.92/7.22 = M6 ) ).
% 6.92/7.22
% 6.92/7.22 % diff_union_cancelR
% 6.92/7.22 thf(fact_4758_union__diff__assoc,axiom,
% 6.92/7.22 ! [C4: multis2468970476368604999at_nat,B5: multis2468970476368604999at_nat,A4: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( ( minus_4286766774447292334at_nat @ C4 @ B5 )
% 6.92/7.22 = zero_z1048942125864253310at_nat )
% 6.92/7.22 => ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( plus_p7104986032573967614at_nat @ A4 @ ( minus_4286766774447292334at_nat @ B5 @ C4 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % union_diff_assoc
% 6.92/7.22 thf(fact_4759_empty__neutral_I1_J,axiom,
% 6.92/7.22 ! [X: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat @ X )
% 6.92/7.22 = X ) ).
% 6.92/7.22
% 6.92/7.22 % empty_neutral(1)
% 6.92/7.22 thf(fact_4760_empty__neutral_I2_J,axiom,
% 6.92/7.22 ! [X: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( plus_p7104986032573967614at_nat @ X @ zero_z1048942125864253310at_nat )
% 6.92/7.22 = X ) ).
% 6.92/7.22
% 6.92/7.22 % empty_neutral(2)
% 6.92/7.22 thf(fact_4761_mset__distrib,axiom,
% 6.92/7.22 ! [A4: multis2468970476368604999at_nat,B5: multis2468970476368604999at_nat,M6: multis2468970476368604999at_nat,N7: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( ( plus_p7104986032573967614at_nat @ A4 @ B5 )
% 6.92/7.22 = ( plus_p7104986032573967614at_nat @ M6 @ N7 ) )
% 6.92/7.22 => ~ ! [Am: multis2468970476368604999at_nat,An: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( A4
% 6.92/7.22 = ( plus_p7104986032573967614at_nat @ Am @ An ) )
% 6.92/7.22 => ! [Bm: multis2468970476368604999at_nat,Bn: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( B5
% 6.92/7.22 = ( plus_p7104986032573967614at_nat @ Bm @ Bn ) )
% 6.92/7.22 => ( ( M6
% 6.92/7.22 = ( plus_p7104986032573967614at_nat @ Am @ Bm ) )
% 6.92/7.22 => ( N7
% 6.92/7.22 != ( plus_p7104986032573967614at_nat @ An @ Bn ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % mset_distrib
% 6.92/7.22 thf(fact_4762_multi__union__self__other__eq,axiom,
% 6.92/7.22 ! [A4: multis2468970476368604999at_nat,X7: multis2468970476368604999at_nat,Y7: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( ( plus_p7104986032573967614at_nat @ A4 @ X7 )
% 6.92/7.22 = ( plus_p7104986032573967614at_nat @ A4 @ Y7 ) )
% 6.92/7.22 => ( X7 = Y7 ) ) ).
% 6.92/7.22
% 6.92/7.22 % multi_union_self_other_eq
% 6.92/7.22 thf(fact_4763_union__right__cancel,axiom,
% 6.92/7.22 ! [M6: multis2468970476368604999at_nat,K5: multis2468970476368604999at_nat,N7: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( ( plus_p7104986032573967614at_nat @ M6 @ K5 )
% 6.92/7.22 = ( plus_p7104986032573967614at_nat @ N7 @ K5 ) )
% 6.92/7.22 = ( M6 = N7 ) ) ).
% 6.92/7.22
% 6.92/7.22 % union_right_cancel
% 6.92/7.22 thf(fact_4764_union__left__cancel,axiom,
% 6.92/7.22 ! [K5: multis2468970476368604999at_nat,M6: multis2468970476368604999at_nat,N7: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( ( plus_p7104986032573967614at_nat @ K5 @ M6 )
% 6.92/7.22 = ( plus_p7104986032573967614at_nat @ K5 @ N7 ) )
% 6.92/7.22 = ( M6 = N7 ) ) ).
% 6.92/7.22
% 6.92/7.22 % union_left_cancel
% 6.92/7.22 thf(fact_4765_union__commute,axiom,
% 6.92/7.22 ( plus_p7104986032573967614at_nat
% 6.92/7.22 = ( ^ [M9: multis2468970476368604999at_nat,N8: multis2468970476368604999at_nat] : ( plus_p7104986032573967614at_nat @ N8 @ M9 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % union_commute
% 6.92/7.22 thf(fact_4766_union__lcomm,axiom,
% 6.92/7.22 ! [M6: multis2468970476368604999at_nat,N7: multis2468970476368604999at_nat,K5: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( plus_p7104986032573967614at_nat @ M6 @ ( plus_p7104986032573967614at_nat @ N7 @ K5 ) )
% 6.92/7.22 = ( plus_p7104986032573967614at_nat @ N7 @ ( plus_p7104986032573967614at_nat @ M6 @ K5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % union_lcomm
% 6.92/7.22 thf(fact_4767_union__assoc,axiom,
% 6.92/7.22 ! [M6: multis2468970476368604999at_nat,N7: multis2468970476368604999at_nat,K5: multis2468970476368604999at_nat] :
% 6.92/7.22 ( ( plus_p7104986032573967614at_nat @ ( plus_p7104986032573967614at_nat @ M6 @ N7 ) @ K5 )
% 6.92/7.22 = ( plus_p7104986032573967614at_nat @ M6 @ ( plus_p7104986032573967614at_nat @ N7 @ K5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % union_assoc
% 6.92/7.22 thf(fact_4768_Diff__mono,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat,D4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ord_le3146513528884898305at_nat @ A4 @ C4 )
% 6.92/7.22 => ( ( ord_le3146513528884898305at_nat @ D4 @ B5 )
% 6.92/7.22 => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) @ ( minus_1356011639430497352at_nat @ C4 @ D4 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_mono
% 6.92/7.22 thf(fact_4769_Diff__mono,axiom,
% 6.92/7.22 ! [A4: set_int,C4: set_int,D4: set_int,B5: set_int] :
% 6.92/7.22 ( ( ord_less_eq_set_int @ A4 @ C4 )
% 6.92/7.22 => ( ( ord_less_eq_set_int @ D4 @ B5 )
% 6.92/7.22 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ B5 ) @ ( minus_minus_set_int @ C4 @ D4 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_mono
% 6.92/7.22 thf(fact_4770_Diff__subset,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) @ A4 ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_subset
% 6.92/7.22 thf(fact_4771_Diff__subset,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ B5 ) @ A4 ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_subset
% 6.92/7.22 thf(fact_4772_double__diff,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 6.92/7.22 => ( ( ord_le3146513528884898305at_nat @ B5 @ C4 )
% 6.92/7.22 => ( ( minus_1356011639430497352at_nat @ B5 @ ( minus_1356011639430497352at_nat @ C4 @ A4 ) )
% 6.92/7.22 = A4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % double_diff
% 6.92/7.22 thf(fact_4773_double__diff,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int,C4: set_int] :
% 6.92/7.22 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.22 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 6.92/7.22 => ( ( minus_minus_set_int @ B5 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 6.92/7.22 = A4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % double_diff
% 6.92/7.22 thf(fact_4774_Diff__Int__distrib2,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.22 ( ( inf_inf_set_nat @ ( minus_minus_set_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A4 @ C4 ) @ ( inf_inf_set_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Int_distrib2
% 6.92/7.22 thf(fact_4775_Diff__Int__distrib2,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( inf_in2572325071724192079at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ C4 ) @ ( inf_in2572325071724192079at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Int_distrib2
% 6.92/7.22 thf(fact_4776_Diff__Int__distrib,axiom,
% 6.92/7.22 ! [C4: set_nat,A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( inf_inf_set_nat @ C4 @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ C4 @ A4 ) @ ( inf_inf_set_nat @ C4 @ B5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Int_distrib
% 6.92/7.22 thf(fact_4777_Diff__Int__distrib,axiom,
% 6.92/7.22 ! [C4: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( inf_in2572325071724192079at_nat @ C4 @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ C4 @ A4 ) @ ( inf_in2572325071724192079at_nat @ C4 @ B5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Int_distrib
% 6.92/7.22 thf(fact_4778_Diff__Diff__Int,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( minus_minus_set_nat @ A4 @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( inf_inf_set_nat @ A4 @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Diff_Int
% 6.92/7.22 thf(fact_4779_Diff__Diff__Int,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( minus_1356011639430497352at_nat @ A4 @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Diff_Int
% 6.92/7.22 thf(fact_4780_Diff__Int2,axiom,
% 6.92/7.22 ! [A4: set_nat,C4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A4 @ C4 ) @ ( inf_inf_set_nat @ B5 @ C4 ) )
% 6.92/7.22 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A4 @ C4 ) @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Int2
% 6.92/7.22 thf(fact_4781_Diff__Int2,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ C4 ) @ ( inf_in2572325071724192079at_nat @ B5 @ C4 ) )
% 6.92/7.22 = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ C4 ) @ B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Int2
% 6.92/7.22 thf(fact_4782_Int__Diff,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.22 ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( inf_inf_set_nat @ A4 @ ( minus_minus_set_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Int_Diff
% 6.92/7.22 thf(fact_4783_Int__Diff,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( inf_in2572325071724192079at_nat @ A4 @ ( minus_1356011639430497352at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Int_Diff
% 6.92/7.22 thf(fact_4784_Un__Diff,axiom,
% 6.92/7.22 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( minus_5060654252129873198at_nat @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ A4 @ C4 ) @ ( minus_5060654252129873198at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff
% 6.92/7.22 thf(fact_4785_Un__Diff,axiom,
% 6.92/7.22 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( minus_3314409938677909166at_nat @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A4 @ C4 ) @ ( minus_3314409938677909166at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff
% 6.92/7.22 thf(fact_4786_Un__Diff,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.22 ( ( minus_minus_set_nat @ ( sup_sup_set_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A4 @ C4 ) @ ( minus_minus_set_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff
% 6.92/7.22 thf(fact_4787_Un__Diff,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( minus_1356011639430497352at_nat @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ A4 @ C4 ) @ ( minus_1356011639430497352at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff
% 6.92/7.22 thf(fact_4788_set__diff__diff__left,axiom,
% 6.92/7.22 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( minus_5060654252129873198at_nat @ ( minus_5060654252129873198at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( minus_5060654252129873198at_nat @ A4 @ ( sup_su3035147773818789531at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % set_diff_diff_left
% 6.92/7.22 thf(fact_4789_set__diff__diff__left,axiom,
% 6.92/7.22 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( minus_3314409938677909166at_nat @ ( minus_3314409938677909166at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( minus_3314409938677909166at_nat @ A4 @ ( sup_su5525570899277871387at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % set_diff_diff_left
% 6.92/7.22 thf(fact_4790_set__diff__diff__left,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.22 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( minus_minus_set_nat @ A4 @ ( sup_sup_set_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % set_diff_diff_left
% 6.92/7.22 thf(fact_4791_set__diff__diff__left,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( minus_1356011639430497352at_nat @ A4 @ ( sup_su6327502436637775413at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % set_diff_diff_left
% 6.92/7.22 thf(fact_4792_psubset__imp__ex__mem,axiom,
% 6.92/7.22 ! [A4: set_o,B5: set_o] :
% 6.92/7.22 ( ( ord_less_set_o @ A4 @ B5 )
% 6.92/7.22 => ? [B3: $o] : ( member_o @ B3 @ ( minus_minus_set_o @ B5 @ A4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % psubset_imp_ex_mem
% 6.92/7.22 thf(fact_4793_psubset__imp__ex__mem,axiom,
% 6.92/7.22 ! [A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.22 ( ( ord_le1924305788584680229nt_int @ A4 @ B5 )
% 6.92/7.22 => ? [B3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ B3 @ ( minus_2612819937483484256nt_int @ B5 @ A4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % psubset_imp_ex_mem
% 6.92/7.22 thf(fact_4794_psubset__imp__ex__mem,axiom,
% 6.92/7.22 ! [A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.22 ( ( ord_less_set_set_nat @ A4 @ B5 )
% 6.92/7.22 => ? [B3: set_nat] : ( member_set_nat @ B3 @ ( minus_2163939370556025621et_nat @ B5 @ A4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % psubset_imp_ex_mem
% 6.92/7.22 thf(fact_4795_psubset__imp__ex__mem,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( ord_less_set_nat @ A4 @ B5 )
% 6.92/7.22 => ? [B3: nat] : ( member_nat @ B3 @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % psubset_imp_ex_mem
% 6.92/7.22 thf(fact_4796_psubset__imp__ex__mem,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int] :
% 6.92/7.22 ( ( ord_less_set_int @ A4 @ B5 )
% 6.92/7.22 => ? [B3: int] : ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % psubset_imp_ex_mem
% 6.92/7.22 thf(fact_4797_psubset__imp__ex__mem,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ord_le7866589430770878221at_nat @ A4 @ B5 )
% 6.92/7.22 => ? [B3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ B3 @ ( minus_1356011639430497352at_nat @ B5 @ A4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % psubset_imp_ex_mem
% 6.92/7.22 thf(fact_4798_uminus__unit__def,axiom,
% 6.92/7.22 ( uminus2952777764628376836t_unit
% 6.92/7.22 = ( ^ [Uu3: product_unit] : product_Unity ) ) ).
% 6.92/7.22
% 6.92/7.22 % uminus_unit_def
% 6.92/7.22 thf(fact_4799_Collect__imp__eq,axiom,
% 6.92/7.22 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 6.92/7.22 ( ( collect_list_nat
% 6.92/7.22 @ ^ [X4: list_nat] :
% 6.92/7.22 ( ( P2 @ X4 )
% 6.92/7.22 => ( Q2 @ X4 ) ) )
% 6.92/7.22 = ( sup_sup_set_list_nat @ ( uminus3195874150345416415st_nat @ ( collect_list_nat @ P2 ) ) @ ( collect_list_nat @ Q2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Collect_imp_eq
% 6.92/7.22 thf(fact_4800_Collect__imp__eq,axiom,
% 6.92/7.22 ! [P2: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.22 ( ( collec5210948495886036740nt_int
% 6.92/7.22 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.22 ( ( P2 @ X4 )
% 6.92/7.22 => ( Q2 @ X4 ) ) )
% 6.92/7.22 = ( sup_su2047564715030645325nt_int @ ( uminus6423885277529793776nt_int @ ( collec5210948495886036740nt_int @ P2 ) ) @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Collect_imp_eq
% 6.92/7.22 thf(fact_4801_Collect__imp__eq,axiom,
% 6.92/7.22 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 6.92/7.22 ( ( collect_set_nat
% 6.92/7.22 @ ^ [X4: set_nat] :
% 6.92/7.22 ( ( P2 @ X4 )
% 6.92/7.22 => ( Q2 @ X4 ) ) )
% 6.92/7.22 = ( sup_sup_set_set_nat @ ( uminus613421341184616069et_nat @ ( collect_set_nat @ P2 ) ) @ ( collect_set_nat @ Q2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Collect_imp_eq
% 6.92/7.22 thf(fact_4802_Collect__imp__eq,axiom,
% 6.92/7.22 ! [P2: int > $o,Q2: int > $o] :
% 6.92/7.22 ( ( collect_int
% 6.92/7.22 @ ^ [X4: int] :
% 6.92/7.22 ( ( P2 @ X4 )
% 6.92/7.22 => ( Q2 @ X4 ) ) )
% 6.92/7.22 = ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) @ ( collect_int @ Q2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Collect_imp_eq
% 6.92/7.22 thf(fact_4803_Collect__imp__eq,axiom,
% 6.92/7.22 ! [P2: produc4166570645942440679at_nat > $o,Q2: produc4166570645942440679at_nat > $o] :
% 6.92/7.22 ( ( collec5204685387357076818at_nat
% 6.92/7.22 @ ^ [X4: produc4166570645942440679at_nat] :
% 6.92/7.22 ( ( P2 @ X4 )
% 6.92/7.22 => ( Q2 @ X4 ) ) )
% 6.92/7.22 = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ ( collec5204685387357076818at_nat @ P2 ) ) @ ( collec5204685387357076818at_nat @ Q2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Collect_imp_eq
% 6.92/7.22 thf(fact_4804_Collect__imp__eq,axiom,
% 6.92/7.22 ! [P2: produc3843707927480180839at_nat > $o,Q2: produc3843707927480180839at_nat > $o] :
% 6.92/7.22 ( ( collec6321179662152712658at_nat
% 6.92/7.22 @ ^ [X4: produc3843707927480180839at_nat] :
% 6.92/7.22 ( ( P2 @ X4 )
% 6.92/7.22 => ( Q2 @ X4 ) ) )
% 6.92/7.22 = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ ( collec6321179662152712658at_nat @ P2 ) ) @ ( collec6321179662152712658at_nat @ Q2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Collect_imp_eq
% 6.92/7.22 thf(fact_4805_Collect__imp__eq,axiom,
% 6.92/7.22 ! [P2: nat > $o,Q2: nat > $o] :
% 6.92/7.22 ( ( collect_nat
% 6.92/7.22 @ ^ [X4: nat] :
% 6.92/7.22 ( ( P2 @ X4 )
% 6.92/7.22 => ( Q2 @ X4 ) ) )
% 6.92/7.22 = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) @ ( collect_nat @ Q2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Collect_imp_eq
% 6.92/7.22 thf(fact_4806_subset__minus__empty,axiom,
% 6.92/7.22 ! [A4: set_o,B5: set_o] :
% 6.92/7.22 ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.92/7.22 => ( ( minus_minus_set_o @ A4 @ B5 )
% 6.92/7.22 = bot_bot_set_o ) ) ).
% 6.92/7.22
% 6.92/7.22 % subset_minus_empty
% 6.92/7.22 thf(fact_4807_subset__minus__empty,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.92/7.22 => ( ( minus_minus_set_nat @ A4 @ B5 )
% 6.92/7.22 = bot_bot_set_nat ) ) ).
% 6.92/7.22
% 6.92/7.22 % subset_minus_empty
% 6.92/7.22 thf(fact_4808_subset__minus__empty,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 6.92/7.22 => ( ( minus_1356011639430497352at_nat @ A4 @ B5 )
% 6.92/7.22 = bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.22
% 6.92/7.22 % subset_minus_empty
% 6.92/7.22 thf(fact_4809_subset__minus__empty,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int] :
% 6.92/7.22 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.22 => ( ( minus_minus_set_int @ A4 @ B5 )
% 6.92/7.22 = bot_bot_set_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % subset_minus_empty
% 6.92/7.22 thf(fact_4810_subset__Compl__self__eq,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ord_le3146513528884898305at_nat @ A4 @ ( uminus6524753893492686040at_nat @ A4 ) )
% 6.92/7.22 = ( A4 = bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.22
% 6.92/7.22 % subset_Compl_self_eq
% 6.92/7.22 thf(fact_4811_subset__Compl__self__eq,axiom,
% 6.92/7.22 ! [A4: set_o] :
% 6.92/7.22 ( ( ord_less_eq_set_o @ A4 @ ( uminus_uminus_set_o @ A4 ) )
% 6.92/7.22 = ( A4 = bot_bot_set_o ) ) ).
% 6.92/7.22
% 6.92/7.22 % subset_Compl_self_eq
% 6.92/7.22 thf(fact_4812_subset__Compl__self__eq,axiom,
% 6.92/7.22 ! [A4: set_nat] :
% 6.92/7.22 ( ( ord_less_eq_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ A4 ) )
% 6.92/7.22 = ( A4 = bot_bot_set_nat ) ) ).
% 6.92/7.22
% 6.92/7.22 % subset_Compl_self_eq
% 6.92/7.22 thf(fact_4813_subset__Compl__self__eq,axiom,
% 6.92/7.22 ! [A4: set_int] :
% 6.92/7.22 ( ( ord_less_eq_set_int @ A4 @ ( uminus1532241313380277803et_int @ A4 ) )
% 6.92/7.22 = ( A4 = bot_bot_set_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % subset_Compl_self_eq
% 6.92/7.22 thf(fact_4814_disjoint__alt__simp2,axiom,
% 6.92/7.22 ! [A4: set_o,B5: set_o] :
% 6.92/7.22 ( ( ( minus_minus_set_o @ A4 @ B5 )
% 6.92/7.22 != A4 )
% 6.92/7.22 = ( ( inf_inf_set_o @ A4 @ B5 )
% 6.92/7.22 != bot_bot_set_o ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_alt_simp2
% 6.92/7.22 thf(fact_4815_disjoint__alt__simp2,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( ( minus_minus_set_nat @ A4 @ B5 )
% 6.92/7.22 != A4 )
% 6.92/7.22 = ( ( inf_inf_set_nat @ A4 @ B5 )
% 6.92/7.22 != bot_bot_set_nat ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_alt_simp2
% 6.92/7.22 thf(fact_4816_disjoint__alt__simp2,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int] :
% 6.92/7.22 ( ( ( minus_minus_set_int @ A4 @ B5 )
% 6.92/7.22 != A4 )
% 6.92/7.22 = ( ( inf_inf_set_int @ A4 @ B5 )
% 6.92/7.22 != bot_bot_set_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_alt_simp2
% 6.92/7.22 thf(fact_4817_disjoint__alt__simp2,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ( minus_1356011639430497352at_nat @ A4 @ B5 )
% 6.92/7.22 != A4 )
% 6.92/7.22 = ( ( inf_in2572325071724192079at_nat @ A4 @ B5 )
% 6.92/7.22 != bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_alt_simp2
% 6.92/7.22 thf(fact_4818_disjoint__alt__simp1,axiom,
% 6.92/7.22 ! [A4: set_o,B5: set_o] :
% 6.92/7.22 ( ( ( minus_minus_set_o @ A4 @ B5 )
% 6.92/7.22 = A4 )
% 6.92/7.22 = ( ( inf_inf_set_o @ A4 @ B5 )
% 6.92/7.22 = bot_bot_set_o ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_alt_simp1
% 6.92/7.22 thf(fact_4819_disjoint__alt__simp1,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( ( minus_minus_set_nat @ A4 @ B5 )
% 6.92/7.22 = A4 )
% 6.92/7.22 = ( ( inf_inf_set_nat @ A4 @ B5 )
% 6.92/7.22 = bot_bot_set_nat ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_alt_simp1
% 6.92/7.22 thf(fact_4820_disjoint__alt__simp1,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int] :
% 6.92/7.22 ( ( ( minus_minus_set_int @ A4 @ B5 )
% 6.92/7.22 = A4 )
% 6.92/7.22 = ( ( inf_inf_set_int @ A4 @ B5 )
% 6.92/7.22 = bot_bot_set_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_alt_simp1
% 6.92/7.22 thf(fact_4821_disjoint__alt__simp1,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ( minus_1356011639430497352at_nat @ A4 @ B5 )
% 6.92/7.22 = A4 )
% 6.92/7.22 = ( ( inf_in2572325071724192079at_nat @ A4 @ B5 )
% 6.92/7.22 = bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_alt_simp1
% 6.92/7.22 thf(fact_4822_Int__Diff__disjoint,axiom,
% 6.92/7.22 ! [A4: set_o,B5: set_o] :
% 6.92/7.22 ( ( inf_inf_set_o @ ( inf_inf_set_o @ A4 @ B5 ) @ ( minus_minus_set_o @ A4 @ B5 ) )
% 6.92/7.22 = bot_bot_set_o ) ).
% 6.92/7.22
% 6.92/7.22 % Int_Diff_disjoint
% 6.92/7.22 thf(fact_4823_Int__Diff__disjoint,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A4 @ B5 ) @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 6.92/7.22 = bot_bot_set_nat ) ).
% 6.92/7.22
% 6.92/7.22 % Int_Diff_disjoint
% 6.92/7.22 thf(fact_4824_Int__Diff__disjoint,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int] :
% 6.92/7.22 ( ( inf_inf_set_int @ ( inf_inf_set_int @ A4 @ B5 ) @ ( minus_minus_set_int @ A4 @ B5 ) )
% 6.92/7.22 = bot_bot_set_int ) ).
% 6.92/7.22
% 6.92/7.22 % Int_Diff_disjoint
% 6.92/7.22 thf(fact_4825_Int__Diff__disjoint,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) )
% 6.92/7.22 = bot_bo2099793752762293965at_nat ) ).
% 6.92/7.22
% 6.92/7.22 % Int_Diff_disjoint
% 6.92/7.22 thf(fact_4826_Diff__triv,axiom,
% 6.92/7.22 ! [A4: set_o,B5: set_o] :
% 6.92/7.22 ( ( ( inf_inf_set_o @ A4 @ B5 )
% 6.92/7.22 = bot_bot_set_o )
% 6.92/7.22 => ( ( minus_minus_set_o @ A4 @ B5 )
% 6.92/7.22 = A4 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_triv
% 6.92/7.22 thf(fact_4827_Diff__triv,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( ( inf_inf_set_nat @ A4 @ B5 )
% 6.92/7.22 = bot_bot_set_nat )
% 6.92/7.22 => ( ( minus_minus_set_nat @ A4 @ B5 )
% 6.92/7.22 = A4 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_triv
% 6.92/7.22 thf(fact_4828_Diff__triv,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int] :
% 6.92/7.22 ( ( ( inf_inf_set_int @ A4 @ B5 )
% 6.92/7.22 = bot_bot_set_int )
% 6.92/7.22 => ( ( minus_minus_set_int @ A4 @ B5 )
% 6.92/7.22 = A4 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_triv
% 6.92/7.22 thf(fact_4829_Diff__triv,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ( inf_in2572325071724192079at_nat @ A4 @ B5 )
% 6.92/7.22 = bot_bo2099793752762293965at_nat )
% 6.92/7.22 => ( ( minus_1356011639430497352at_nat @ A4 @ B5 )
% 6.92/7.22 = A4 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_triv
% 6.92/7.22 thf(fact_4830_Diff__subset__conv,axiom,
% 6.92/7.22 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( ord_le8081472938463900775at_nat @ ( minus_5060654252129873198at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( ord_le8081472938463900775at_nat @ A4 @ ( sup_su3035147773818789531at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_subset_conv
% 6.92/7.22 thf(fact_4831_Diff__subset__conv,axiom,
% 6.92/7.22 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( ord_le1268244103169919719at_nat @ ( minus_3314409938677909166at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( ord_le1268244103169919719at_nat @ A4 @ ( sup_su5525570899277871387at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_subset_conv
% 6.92/7.22 thf(fact_4832_Diff__subset__conv,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.22 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( ord_less_eq_set_nat @ A4 @ ( sup_sup_set_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_subset_conv
% 6.92/7.22 thf(fact_4833_Diff__subset__conv,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( ord_le3146513528884898305at_nat @ A4 @ ( sup_su6327502436637775413at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_subset_conv
% 6.92/7.22 thf(fact_4834_Diff__subset__conv,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int,C4: set_int] :
% 6.92/7.22 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ B5 ) @ C4 )
% 6.92/7.22 = ( ord_less_eq_set_int @ A4 @ ( sup_sup_set_int @ B5 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_subset_conv
% 6.92/7.22 thf(fact_4835_Diff__partition,axiom,
% 6.92/7.22 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( ord_le8081472938463900775at_nat @ A4 @ B5 )
% 6.92/7.22 => ( ( sup_su3035147773818789531at_nat @ A4 @ ( minus_5060654252129873198at_nat @ B5 @ A4 ) )
% 6.92/7.22 = B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_partition
% 6.92/7.22 thf(fact_4836_Diff__partition,axiom,
% 6.92/7.22 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( ord_le1268244103169919719at_nat @ A4 @ B5 )
% 6.92/7.22 => ( ( sup_su5525570899277871387at_nat @ A4 @ ( minus_3314409938677909166at_nat @ B5 @ A4 ) )
% 6.92/7.22 = B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_partition
% 6.92/7.22 thf(fact_4837_Diff__partition,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.92/7.22 => ( ( sup_sup_set_nat @ A4 @ ( minus_minus_set_nat @ B5 @ A4 ) )
% 6.92/7.22 = B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_partition
% 6.92/7.22 thf(fact_4838_Diff__partition,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 6.92/7.22 => ( ( sup_su6327502436637775413at_nat @ A4 @ ( minus_1356011639430497352at_nat @ B5 @ A4 ) )
% 6.92/7.22 = B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_partition
% 6.92/7.22 thf(fact_4839_Diff__partition,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int] :
% 6.92/7.22 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.22 => ( ( sup_sup_set_int @ A4 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 6.92/7.22 = B5 ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_partition
% 6.92/7.22 thf(fact_4840_pochhammer__pos,axiom,
% 6.92/7.22 ! [X: code_integer,N2: nat] :
% 6.92/7.22 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X )
% 6.92/7.22 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( comm_s8582702949713902594nteger @ X @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_pos
% 6.92/7.22 thf(fact_4841_pochhammer__pos,axiom,
% 6.92/7.22 ! [X: rat,N2: nat] :
% 6.92/7.22 ( ( ord_less_rat @ zero_zero_rat @ X )
% 6.92/7.22 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_pos
% 6.92/7.22 thf(fact_4842_pochhammer__pos,axiom,
% 6.92/7.22 ! [X: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ X )
% 6.92/7.22 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_pos
% 6.92/7.22 thf(fact_4843_pochhammer__pos,axiom,
% 6.92/7.22 ! [X: int,N2: nat] :
% 6.92/7.22 ( ( ord_less_int @ zero_zero_int @ X )
% 6.92/7.22 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_pos
% 6.92/7.22 thf(fact_4844_Un__Diff__Int,axiom,
% 6.92/7.22 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ A4 @ B5 ) @ ( inf_in1697001100524423349at_nat @ A4 @ B5 ) )
% 6.92/7.22 = A4 ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff_Int
% 6.92/7.22 thf(fact_4845_Un__Diff__Int,axiom,
% 6.92/7.22 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A4 @ B5 ) @ ( inf_in7913087082777306421at_nat @ A4 @ B5 ) )
% 6.92/7.22 = A4 ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff_Int
% 6.92/7.22 thf(fact_4846_Un__Diff__Int,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ A4 @ B5 ) @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 6.92/7.22 = A4 ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff_Int
% 6.92/7.22 thf(fact_4847_Un__Diff__Int,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) )
% 6.92/7.22 = A4 ) ).
% 6.92/7.22
% 6.92/7.22 % Un_Diff_Int
% 6.92/7.22 thf(fact_4848_Int__Diff__Un,axiom,
% 6.92/7.22 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A4 @ B5 ) @ ( minus_5060654252129873198at_nat @ A4 @ B5 ) )
% 6.92/7.22 = A4 ) ).
% 6.92/7.22
% 6.92/7.22 % Int_Diff_Un
% 6.92/7.22 thf(fact_4849_Int__Diff__Un,axiom,
% 6.92/7.22 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A4 @ B5 ) @ ( minus_3314409938677909166at_nat @ A4 @ B5 ) )
% 6.92/7.22 = A4 ) ).
% 6.92/7.22
% 6.92/7.22 % Int_Diff_Un
% 6.92/7.22 thf(fact_4850_Int__Diff__Un,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A4 @ B5 ) @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 6.92/7.22 = A4 ) ).
% 6.92/7.22
% 6.92/7.22 % Int_Diff_Un
% 6.92/7.22 thf(fact_4851_Int__Diff__Un,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) )
% 6.92/7.22 = A4 ) ).
% 6.92/7.22
% 6.92/7.22 % Int_Diff_Un
% 6.92/7.22 thf(fact_4852_Diff__Int,axiom,
% 6.92/7.22 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( minus_5060654252129873198at_nat @ A4 @ ( inf_in1697001100524423349at_nat @ B5 @ C4 ) )
% 6.92/7.22 = ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ A4 @ B5 ) @ ( minus_5060654252129873198at_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Int
% 6.92/7.22 thf(fact_4853_Diff__Int,axiom,
% 6.92/7.22 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( minus_3314409938677909166at_nat @ A4 @ ( inf_in7913087082777306421at_nat @ B5 @ C4 ) )
% 6.92/7.22 = ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A4 @ B5 ) @ ( minus_3314409938677909166at_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Int
% 6.92/7.22 thf(fact_4854_Diff__Int,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.22 ( ( minus_minus_set_nat @ A4 @ ( inf_inf_set_nat @ B5 @ C4 ) )
% 6.92/7.22 = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A4 @ B5 ) @ ( minus_minus_set_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Int
% 6.92/7.22 thf(fact_4855_Diff__Int,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( minus_1356011639430497352at_nat @ A4 @ ( inf_in2572325071724192079at_nat @ B5 @ C4 ) )
% 6.92/7.22 = ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) @ ( minus_1356011639430497352at_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Int
% 6.92/7.22 thf(fact_4856_Diff__Un,axiom,
% 6.92/7.22 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( minus_5060654252129873198at_nat @ A4 @ ( sup_su3035147773818789531at_nat @ B5 @ C4 ) )
% 6.92/7.22 = ( inf_in1697001100524423349at_nat @ ( minus_5060654252129873198at_nat @ A4 @ B5 ) @ ( minus_5060654252129873198at_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Un
% 6.92/7.22 thf(fact_4857_Diff__Un,axiom,
% 6.92/7.22 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( minus_3314409938677909166at_nat @ A4 @ ( sup_su5525570899277871387at_nat @ B5 @ C4 ) )
% 6.92/7.22 = ( inf_in7913087082777306421at_nat @ ( minus_3314409938677909166at_nat @ A4 @ B5 ) @ ( minus_3314409938677909166at_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Un
% 6.92/7.22 thf(fact_4858_Diff__Un,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat,C4: set_nat] :
% 6.92/7.22 ( ( minus_minus_set_nat @ A4 @ ( sup_sup_set_nat @ B5 @ C4 ) )
% 6.92/7.22 = ( inf_inf_set_nat @ ( minus_minus_set_nat @ A4 @ B5 ) @ ( minus_minus_set_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Un
% 6.92/7.22 thf(fact_4859_Diff__Un,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( minus_1356011639430497352at_nat @ A4 @ ( sup_su6327502436637775413at_nat @ B5 @ C4 ) )
% 6.92/7.22 = ( inf_in2572325071724192079at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) @ ( minus_1356011639430497352at_nat @ A4 @ C4 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Diff_Un
% 6.92/7.22 thf(fact_4860_Compl__Int,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( uminus6524753893492686040at_nat @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ A4 ) @ ( uminus6524753893492686040at_nat @ B5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_Int
% 6.92/7.22 thf(fact_4861_Compl__Int,axiom,
% 6.92/7.22 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( uminus2330091110623919550at_nat @ ( inf_in1697001100524423349at_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ A4 ) @ ( uminus2330091110623919550at_nat @ B5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_Int
% 6.92/7.22 thf(fact_4862_Compl__Int,axiom,
% 6.92/7.22 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( uminus935396558254630718at_nat @ ( inf_in7913087082777306421at_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ A4 ) @ ( uminus935396558254630718at_nat @ B5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_Int
% 6.92/7.22 thf(fact_4863_Compl__Int,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( uminus5710092332889474511et_nat @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A4 ) @ ( uminus5710092332889474511et_nat @ B5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_Int
% 6.92/7.22 thf(fact_4864_Compl__Un,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( uminus6524753893492686040at_nat @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ A4 ) @ ( uminus6524753893492686040at_nat @ B5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_Un
% 6.92/7.22 thf(fact_4865_Compl__Un,axiom,
% 6.92/7.22 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.22 ( ( uminus2330091110623919550at_nat @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( inf_in1697001100524423349at_nat @ ( uminus2330091110623919550at_nat @ A4 ) @ ( uminus2330091110623919550at_nat @ B5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_Un
% 6.92/7.22 thf(fact_4866_Compl__Un,axiom,
% 6.92/7.22 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.22 ( ( uminus935396558254630718at_nat @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( inf_in7913087082777306421at_nat @ ( uminus935396558254630718at_nat @ A4 ) @ ( uminus935396558254630718at_nat @ B5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_Un
% 6.92/7.22 thf(fact_4867_Compl__Un,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( uminus5710092332889474511et_nat @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.92/7.22 = ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A4 ) @ ( uminus5710092332889474511et_nat @ B5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % Compl_Un
% 6.92/7.22 thf(fact_4868_pochhammer__eq__0__mono,axiom,
% 6.92/7.22 ! [A: rat,N2: nat,M: nat] :
% 6.92/7.22 ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 6.92/7.22 = zero_zero_rat )
% 6.92/7.22 => ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 6.92/7.22 = zero_zero_rat ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_eq_0_mono
% 6.92/7.22 thf(fact_4869_pochhammer__neq__0__mono,axiom,
% 6.92/7.22 ! [A: rat,M: nat,N2: nat] :
% 6.92/7.22 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 6.92/7.22 != zero_zero_rat )
% 6.92/7.22 => ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.22 => ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 6.92/7.22 != zero_zero_rat ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_neq_0_mono
% 6.92/7.22 thf(fact_4870_disjoint__eq__subset__Compl,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ( inf_in2572325071724192079at_nat @ A4 @ B5 )
% 6.92/7.22 = bot_bo2099793752762293965at_nat )
% 6.92/7.22 = ( ord_le3146513528884898305at_nat @ A4 @ ( uminus6524753893492686040at_nat @ B5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_eq_subset_Compl
% 6.92/7.22 thf(fact_4871_disjoint__eq__subset__Compl,axiom,
% 6.92/7.22 ! [A4: set_o,B5: set_o] :
% 6.92/7.22 ( ( ( inf_inf_set_o @ A4 @ B5 )
% 6.92/7.22 = bot_bot_set_o )
% 6.92/7.22 = ( ord_less_eq_set_o @ A4 @ ( uminus_uminus_set_o @ B5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_eq_subset_Compl
% 6.92/7.22 thf(fact_4872_disjoint__eq__subset__Compl,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( ( inf_inf_set_nat @ A4 @ B5 )
% 6.92/7.22 = bot_bot_set_nat )
% 6.92/7.22 = ( ord_less_eq_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ B5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_eq_subset_Compl
% 6.92/7.22 thf(fact_4873_disjoint__eq__subset__Compl,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int] :
% 6.92/7.22 ( ( ( inf_inf_set_int @ A4 @ B5 )
% 6.92/7.22 = bot_bot_set_int )
% 6.92/7.22 = ( ord_less_eq_set_int @ A4 @ ( uminus1532241313380277803et_int @ B5 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_eq_subset_Compl
% 6.92/7.22 thf(fact_4874_pochhammer__nonneg,axiom,
% 6.92/7.22 ! [X: code_integer,N2: nat] :
% 6.92/7.22 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X )
% 6.92/7.22 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( comm_s8582702949713902594nteger @ X @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_nonneg
% 6.92/7.22 thf(fact_4875_pochhammer__nonneg,axiom,
% 6.92/7.22 ! [X: rat,N2: nat] :
% 6.92/7.22 ( ( ord_less_rat @ zero_zero_rat @ X )
% 6.92/7.22 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_nonneg
% 6.92/7.22 thf(fact_4876_pochhammer__nonneg,axiom,
% 6.92/7.22 ! [X: nat,N2: nat] :
% 6.92/7.22 ( ( ord_less_nat @ zero_zero_nat @ X )
% 6.92/7.22 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_nonneg
% 6.92/7.22 thf(fact_4877_pochhammer__nonneg,axiom,
% 6.92/7.22 ! [X: int,N2: nat] :
% 6.92/7.22 ( ( ord_less_int @ zero_zero_int @ X )
% 6.92/7.22 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_nonneg
% 6.92/7.22 thf(fact_4878_disjoint__alt__simp3,axiom,
% 6.92/7.22 ! [A4: set_o,B5: set_o] :
% 6.92/7.22 ( ( ord_less_set_o @ ( minus_minus_set_o @ A4 @ B5 ) @ A4 )
% 6.92/7.22 = ( ( inf_inf_set_o @ A4 @ B5 )
% 6.92/7.22 != bot_bot_set_o ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_alt_simp3
% 6.92/7.22 thf(fact_4879_disjoint__alt__simp3,axiom,
% 6.92/7.22 ! [A4: set_nat,B5: set_nat] :
% 6.92/7.22 ( ( ord_less_set_nat @ ( minus_minus_set_nat @ A4 @ B5 ) @ A4 )
% 6.92/7.22 = ( ( inf_inf_set_nat @ A4 @ B5 )
% 6.92/7.22 != bot_bot_set_nat ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_alt_simp3
% 6.92/7.22 thf(fact_4880_disjoint__alt__simp3,axiom,
% 6.92/7.22 ! [A4: set_int,B5: set_int] :
% 6.92/7.22 ( ( ord_less_set_int @ ( minus_minus_set_int @ A4 @ B5 ) @ A4 )
% 6.92/7.22 = ( ( inf_inf_set_int @ A4 @ B5 )
% 6.92/7.22 != bot_bot_set_int ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_alt_simp3
% 6.92/7.22 thf(fact_4881_disjoint__alt__simp3,axiom,
% 6.92/7.22 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.22 ( ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) @ A4 )
% 6.92/7.22 = ( ( inf_in2572325071724192079at_nat @ A4 @ B5 )
% 6.92/7.22 != bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.22
% 6.92/7.22 % disjoint_alt_simp3
% 6.92/7.22 thf(fact_4882_uminus__assn__def,axiom,
% 6.92/7.22 ( uminus_uminus_assn
% 6.92/7.22 = ( ^ [P5: assn] :
% 6.92/7.22 ( abs_assn
% 6.92/7.22 @ ^ [H6: produc3658429121746597890et_nat] :
% 6.92/7.22 ( ( in_range @ H6 )
% 6.92/7.22 & ~ ( rep_assn @ P5 @ H6 ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % uminus_assn_def
% 6.92/7.22 thf(fact_4883_pochhammer__rec,axiom,
% 6.92/7.22 ! [A: code_integer,N2: nat] :
% 6.92/7.22 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 6.92/7.22 = ( times_3573771949741848930nteger @ A @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_rec
% 6.92/7.22 thf(fact_4884_pochhammer__rec,axiom,
% 6.92/7.22 ! [A: rat,N2: nat] :
% 6.92/7.22 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 6.92/7.22 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_rec
% 6.92/7.22 thf(fact_4885_pochhammer__rec,axiom,
% 6.92/7.22 ! [A: nat,N2: nat] :
% 6.92/7.22 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 6.92/7.22 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_rec
% 6.92/7.22 thf(fact_4886_pochhammer__rec,axiom,
% 6.92/7.22 ! [A: int,N2: nat] :
% 6.92/7.22 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 6.92/7.22 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_rec
% 6.92/7.22 thf(fact_4887_pochhammer__Suc,axiom,
% 6.92/7.22 ! [A: rat,N2: nat] :
% 6.92/7.22 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 6.92/7.22 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N2 ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_Suc
% 6.92/7.22 thf(fact_4888_pochhammer__Suc,axiom,
% 6.92/7.22 ! [A: int,N2: nat] :
% 6.92/7.22 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 6.92/7.22 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N2 ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_Suc
% 6.92/7.22 thf(fact_4889_pochhammer__Suc,axiom,
% 6.92/7.22 ! [A: nat,N2: nat] :
% 6.92/7.22 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 6.92/7.22 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N2 ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_Suc
% 6.92/7.22 thf(fact_4890_pochhammer__Suc,axiom,
% 6.92/7.22 ! [A: code_integer,N2: nat] :
% 6.92/7.22 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 6.92/7.22 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ A @ N2 ) @ ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ N2 ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_Suc
% 6.92/7.22 thf(fact_4891_pochhammer__rec_H,axiom,
% 6.92/7.22 ! [Z3: rat,N2: nat] :
% 6.92/7.22 ( ( comm_s4028243227959126397er_rat @ Z3 @ ( suc @ N2 ) )
% 6.92/7.22 = ( times_times_rat @ ( plus_plus_rat @ Z3 @ ( semiri681578069525770553at_rat @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ Z3 @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_rec'
% 6.92/7.22 thf(fact_4892_pochhammer__rec_H,axiom,
% 6.92/7.22 ! [Z3: int,N2: nat] :
% 6.92/7.22 ( ( comm_s4660882817536571857er_int @ Z3 @ ( suc @ N2 ) )
% 6.92/7.22 = ( times_times_int @ ( plus_plus_int @ Z3 @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( comm_s4660882817536571857er_int @ Z3 @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_rec'
% 6.92/7.22 thf(fact_4893_pochhammer__rec_H,axiom,
% 6.92/7.22 ! [Z3: nat,N2: nat] :
% 6.92/7.22 ( ( comm_s4663373288045622133er_nat @ Z3 @ ( suc @ N2 ) )
% 6.92/7.22 = ( times_times_nat @ ( plus_plus_nat @ Z3 @ ( semiri1316708129612266289at_nat @ N2 ) ) @ ( comm_s4663373288045622133er_nat @ Z3 @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_rec'
% 6.92/7.22 thf(fact_4894_pochhammer__rec_H,axiom,
% 6.92/7.22 ! [Z3: code_integer,N2: nat] :
% 6.92/7.22 ( ( comm_s8582702949713902594nteger @ Z3 @ ( suc @ N2 ) )
% 6.92/7.22 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ Z3 @ ( semiri4939895301339042750nteger @ N2 ) ) @ ( comm_s8582702949713902594nteger @ Z3 @ N2 ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_rec'
% 6.92/7.22 thf(fact_4895_pochhammer__eq__0__iff,axiom,
% 6.92/7.22 ! [A: rat,N2: nat] :
% 6.92/7.22 ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 6.92/7.22 = zero_zero_rat )
% 6.92/7.22 = ( ? [K3: nat] :
% 6.92/7.22 ( ( ord_less_nat @ K3 @ N2 )
% 6.92/7.22 & ( A
% 6.92/7.22 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_eq_0_iff
% 6.92/7.22 thf(fact_4896_pochhammer__of__nat__eq__0__iff,axiom,
% 6.92/7.22 ! [N2: nat,K2: nat] :
% 6.92/7.22 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K2 )
% 6.92/7.22 = zero_zero_rat )
% 6.92/7.22 = ( ord_less_nat @ N2 @ K2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_of_nat_eq_0_iff
% 6.92/7.22 thf(fact_4897_pochhammer__of__nat__eq__0__iff,axiom,
% 6.92/7.22 ! [N2: nat,K2: nat] :
% 6.92/7.22 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K2 )
% 6.92/7.22 = zero_zero_int )
% 6.92/7.22 = ( ord_less_nat @ N2 @ K2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_of_nat_eq_0_iff
% 6.92/7.22 thf(fact_4898_pochhammer__of__nat__eq__0__iff,axiom,
% 6.92/7.22 ! [N2: nat,K2: nat] :
% 6.92/7.22 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K2 )
% 6.92/7.22 = zero_z3403309356797280102nteger )
% 6.92/7.22 = ( ord_less_nat @ N2 @ K2 ) ) ).
% 6.92/7.22
% 6.92/7.22 % pochhammer_of_nat_eq_0_iff
% 6.92/7.22 thf(fact_4899_pochhammer__of__nat__eq__0__lemma,axiom,
% 6.92/7.22 ! [N2: nat,K2: nat] :
% 6.92/7.22 ( ( ord_less_nat @ N2 @ K2 )
% 6.92/7.22 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K2 )
% 6.92/7.23 = zero_zero_rat ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_of_nat_eq_0_lemma
% 6.92/7.23 thf(fact_4900_pochhammer__of__nat__eq__0__lemma,axiom,
% 6.92/7.23 ! [N2: nat,K2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ K2 )
% 6.92/7.23 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K2 )
% 6.92/7.23 = zero_zero_int ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_of_nat_eq_0_lemma
% 6.92/7.23 thf(fact_4901_pochhammer__of__nat__eq__0__lemma,axiom,
% 6.92/7.23 ! [N2: nat,K2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ K2 )
% 6.92/7.23 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K2 )
% 6.92/7.23 = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_of_nat_eq_0_lemma
% 6.92/7.23 thf(fact_4902_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 6.92/7.23 ! [K2: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.23 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K2 )
% 6.92/7.23 != zero_zero_rat ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_of_nat_eq_0_lemma'
% 6.92/7.23 thf(fact_4903_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 6.92/7.23 ! [K2: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.23 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K2 )
% 6.92/7.23 != zero_zero_int ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_of_nat_eq_0_lemma'
% 6.92/7.23 thf(fact_4904_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 6.92/7.23 ! [K2: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.23 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K2 )
% 6.92/7.23 != zero_z3403309356797280102nteger ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_of_nat_eq_0_lemma'
% 6.92/7.23 thf(fact_4905_pochhammer__product_H,axiom,
% 6.92/7.23 ! [Z3: rat,N2: nat,M: nat] :
% 6.92/7.23 ( ( comm_s4028243227959126397er_rat @ Z3 @ ( plus_plus_nat @ N2 @ M ) )
% 6.92/7.23 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z3 @ N2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( semiri681578069525770553at_rat @ N2 ) ) @ M ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_product'
% 6.92/7.23 thf(fact_4906_pochhammer__product_H,axiom,
% 6.92/7.23 ! [Z3: int,N2: nat,M: nat] :
% 6.92/7.23 ( ( comm_s4660882817536571857er_int @ Z3 @ ( plus_plus_nat @ N2 @ M ) )
% 6.92/7.23 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z3 @ N2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z3 @ ( semiri1314217659103216013at_int @ N2 ) ) @ M ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_product'
% 6.92/7.23 thf(fact_4907_pochhammer__product_H,axiom,
% 6.92/7.23 ! [Z3: nat,N2: nat,M: nat] :
% 6.92/7.23 ( ( comm_s4663373288045622133er_nat @ Z3 @ ( plus_plus_nat @ N2 @ M ) )
% 6.92/7.23 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z3 @ N2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z3 @ ( semiri1316708129612266289at_nat @ N2 ) ) @ M ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_product'
% 6.92/7.23 thf(fact_4908_pochhammer__product_H,axiom,
% 6.92/7.23 ! [Z3: code_integer,N2: nat,M: nat] :
% 6.92/7.23 ( ( comm_s8582702949713902594nteger @ Z3 @ ( plus_plus_nat @ N2 @ M ) )
% 6.92/7.23 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z3 @ N2 ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z3 @ ( semiri4939895301339042750nteger @ N2 ) ) @ M ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_product'
% 6.92/7.23 thf(fact_4909_normalize__denom__pos,axiom,
% 6.92/7.23 ! [R2: product_prod_int_int,P3: int,Q6: int] :
% 6.92/7.23 ( ( ( normalize @ R2 )
% 6.92/7.23 = ( product_Pair_int_int @ P3 @ Q6 ) )
% 6.92/7.23 => ( ord_less_int @ zero_zero_int @ Q6 ) ) ).
% 6.92/7.23
% 6.92/7.23 % normalize_denom_pos
% 6.92/7.23 thf(fact_4910_pochhammer__product,axiom,
% 6.92/7.23 ! [M: nat,N2: nat,Z3: rat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.23 => ( ( comm_s4028243227959126397er_rat @ Z3 @ N2 )
% 6.92/7.23 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z3 @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_product
% 6.92/7.23 thf(fact_4911_pochhammer__product,axiom,
% 6.92/7.23 ! [M: nat,N2: nat,Z3: int] :
% 6.92/7.23 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.23 => ( ( comm_s4660882817536571857er_int @ Z3 @ N2 )
% 6.92/7.23 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z3 @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z3 @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_product
% 6.92/7.23 thf(fact_4912_pochhammer__product,axiom,
% 6.92/7.23 ! [M: nat,N2: nat,Z3: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.23 => ( ( comm_s4663373288045622133er_nat @ Z3 @ N2 )
% 6.92/7.23 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z3 @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z3 @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_product
% 6.92/7.23 thf(fact_4913_pochhammer__product,axiom,
% 6.92/7.23 ! [M: nat,N2: nat,Z3: code_integer] :
% 6.92/7.23 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.23 => ( ( comm_s8582702949713902594nteger @ Z3 @ N2 )
% 6.92/7.23 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z3 @ M ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z3 @ ( semiri4939895301339042750nteger @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_product
% 6.92/7.23 thf(fact_4914_pochhammer__absorb__comp,axiom,
% 6.92/7.23 ! [R2: rat,K2: nat] :
% 6.92/7.23 ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K2 ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K2 ) )
% 6.92/7.23 = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_absorb_comp
% 6.92/7.23 thf(fact_4915_pochhammer__absorb__comp,axiom,
% 6.92/7.23 ! [R2: int,K2: nat] :
% 6.92/7.23 ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K2 ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K2 ) )
% 6.92/7.23 = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_absorb_comp
% 6.92/7.23 thf(fact_4916_pochhammer__absorb__comp,axiom,
% 6.92/7.23 ! [R2: code_integer,K2: nat] :
% 6.92/7.23 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K2 ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K2 ) )
% 6.92/7.23 = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_absorb_comp
% 6.92/7.23 thf(fact_4917_nonempty__has__size,axiom,
% 6.92/7.23 ! [S: multis2468970476368604999at_nat] :
% 6.92/7.23 ( ( S != zero_z1048942125864253310at_nat )
% 6.92/7.23 = ( ord_less_nat @ zero_zero_nat @ ( size_s8510653225128441779at_nat @ S ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nonempty_has_size
% 6.92/7.23 thf(fact_4918_pochhammer__minus,axiom,
% 6.92/7.23 ! [B: rat,K2: nat] :
% 6.92/7.23 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K2 )
% 6.92/7.23 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_minus
% 6.92/7.23 thf(fact_4919_pochhammer__minus,axiom,
% 6.92/7.23 ! [B: int,K2: nat] :
% 6.92/7.23 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K2 )
% 6.92/7.23 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K2 ) ) @ one_one_int ) @ K2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_minus
% 6.92/7.23 thf(fact_4920_pochhammer__minus,axiom,
% 6.92/7.23 ! [B: code_integer,K2: nat] :
% 6.92/7.23 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K2 )
% 6.92/7.23 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K2 ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K2 ) ) @ one_one_Code_integer ) @ K2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_minus
% 6.92/7.23 thf(fact_4921_pochhammer__minus_H,axiom,
% 6.92/7.23 ! [B: rat,K2: nat] :
% 6.92/7.23 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 )
% 6.92/7.23 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_minus'
% 6.92/7.23 thf(fact_4922_pochhammer__minus_H,axiom,
% 6.92/7.23 ! [B: int,K2: nat] :
% 6.92/7.23 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K2 ) ) @ one_one_int ) @ K2 )
% 6.92/7.23 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K2 ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_minus'
% 6.92/7.23 thf(fact_4923_pochhammer__minus_H,axiom,
% 6.92/7.23 ! [B: code_integer,K2: nat] :
% 6.92/7.23 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K2 ) ) @ one_one_Code_integer ) @ K2 )
% 6.92/7.23 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K2 ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pochhammer_minus'
% 6.92/7.23 thf(fact_4924_nat0__intermed__int__val,axiom,
% 6.92/7.23 ! [N2: nat,F: nat > int,K2: int] :
% 6.92/7.23 ( ! [I3: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I3 @ N2 )
% 6.92/7.23 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 6.92/7.23 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K2 )
% 6.92/7.23 => ( ( ord_less_eq_int @ K2 @ ( F @ N2 ) )
% 6.92/7.23 => ? [I3: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ I3 @ N2 )
% 6.92/7.23 & ( ( F @ I3 )
% 6.92/7.23 = K2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nat0_intermed_int_val
% 6.92/7.23 thf(fact_4925_slice__len,axiom,
% 6.92/7.23 ! [From: nat,To: nat,Xs: list_nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ From @ To )
% 6.92/7.23 => ( ( ord_less_eq_nat @ To @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( ( size_size_list_nat @ ( slice_nat @ From @ To @ Xs ) )
% 6.92/7.23 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % slice_len
% 6.92/7.23 thf(fact_4926_slice__len,axiom,
% 6.92/7.23 ! [From: nat,To: nat,Xs: list_o] :
% 6.92/7.23 ( ( ord_less_eq_nat @ From @ To )
% 6.92/7.23 => ( ( ord_less_eq_nat @ To @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( ( size_size_list_o @ ( slice_o @ From @ To @ Xs ) )
% 6.92/7.23 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % slice_len
% 6.92/7.23 thf(fact_4927_slice__len,axiom,
% 6.92/7.23 ! [From: nat,To: nat,Xs: list_int] :
% 6.92/7.23 ( ( ord_less_eq_nat @ From @ To )
% 6.92/7.23 => ( ( ord_less_eq_nat @ To @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( ( size_size_list_int @ ( slice_int @ From @ To @ Xs ) )
% 6.92/7.23 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % slice_len
% 6.92/7.23 thf(fact_4928_nat__ivt__aux,axiom,
% 6.92/7.23 ! [N2: nat,F: nat > int,K2: int] :
% 6.92/7.23 ( ! [I3: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I3 @ N2 )
% 6.92/7.23 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 6.92/7.23 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K2 )
% 6.92/7.23 => ( ( ord_less_eq_int @ K2 @ ( F @ N2 ) )
% 6.92/7.23 => ? [I3: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ I3 @ N2 )
% 6.92/7.23 & ( ( F @ I3 )
% 6.92/7.23 = K2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nat_ivt_aux
% 6.92/7.23 thf(fact_4929_triangle__Suc,axiom,
% 6.92/7.23 ! [N2: nat] :
% 6.92/7.23 ( ( nat_triangle @ ( suc @ N2 ) )
% 6.92/7.23 = ( plus_plus_nat @ ( nat_triangle @ N2 ) @ ( suc @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % triangle_Suc
% 6.92/7.23 thf(fact_4930_gbinomial__absorption_H,axiom,
% 6.92/7.23 ! [K2: nat,A: rat] :
% 6.92/7.23 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.23 => ( ( gbinomial_rat @ A @ K2 )
% 6.92/7.23 = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % gbinomial_absorption'
% 6.92/7.23 thf(fact_4931_fact__reduce,axiom,
% 6.92/7.23 ! [N2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.23 => ( ( semiri773545260158071498ct_rat @ N2 )
% 6.92/7.23 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_reduce
% 6.92/7.23 thf(fact_4932_fact__reduce,axiom,
% 6.92/7.23 ! [N2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.23 => ( ( semiri1406184849735516958ct_int @ N2 )
% 6.92/7.23 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_reduce
% 6.92/7.23 thf(fact_4933_fact__reduce,axiom,
% 6.92/7.23 ! [N2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.23 => ( ( semiri3624122377584611663nteger @ N2 )
% 6.92/7.23 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_reduce
% 6.92/7.23 thf(fact_4934_fact__reduce,axiom,
% 6.92/7.23 ! [N2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.23 => ( ( semiri1408675320244567234ct_nat @ N2 )
% 6.92/7.23 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_reduce
% 6.92/7.23 thf(fact_4935_DiffI,axiom,
% 6.92/7.23 ! [C2: $o,A4: set_o,B5: set_o] :
% 6.92/7.23 ( ( member_o @ C2 @ A4 )
% 6.92/7.23 => ( ~ ( member_o @ C2 @ B5 )
% 6.92/7.23 => ( member_o @ C2 @ ( minus_minus_set_o @ A4 @ B5 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffI
% 6.92/7.23 thf(fact_4936_DiffI,axiom,
% 6.92/7.23 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.23 ( ( member2340774599025711042nt_int @ C2 @ A4 )
% 6.92/7.23 => ( ~ ( member2340774599025711042nt_int @ C2 @ B5 )
% 6.92/7.23 => ( member2340774599025711042nt_int @ C2 @ ( minus_2612819937483484256nt_int @ A4 @ B5 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffI
% 6.92/7.23 thf(fact_4937_DiffI,axiom,
% 6.92/7.23 ! [C2: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.23 ( ( member_set_nat @ C2 @ A4 )
% 6.92/7.23 => ( ~ ( member_set_nat @ C2 @ B5 )
% 6.92/7.23 => ( member_set_nat @ C2 @ ( minus_2163939370556025621et_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffI
% 6.92/7.23 thf(fact_4938_DiffI,axiom,
% 6.92/7.23 ! [C2: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.23 ( ( member_nat @ C2 @ A4 )
% 6.92/7.23 => ( ~ ( member_nat @ C2 @ B5 )
% 6.92/7.23 => ( member_nat @ C2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffI
% 6.92/7.23 thf(fact_4939_DiffI,axiom,
% 6.92/7.23 ! [C2: int,A4: set_int,B5: set_int] :
% 6.92/7.23 ( ( member_int @ C2 @ A4 )
% 6.92/7.23 => ( ~ ( member_int @ C2 @ B5 )
% 6.92/7.23 => ( member_int @ C2 @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffI
% 6.92/7.23 thf(fact_4940_DiffI,axiom,
% 6.92/7.23 ! [C2: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ C2 @ A4 )
% 6.92/7.23 => ( ~ ( member8440522571783428010at_nat @ C2 @ B5 )
% 6.92/7.23 => ( member8440522571783428010at_nat @ C2 @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffI
% 6.92/7.23 thf(fact_4941_Diff__iff,axiom,
% 6.92/7.23 ! [C2: $o,A4: set_o,B5: set_o] :
% 6.92/7.23 ( ( member_o @ C2 @ ( minus_minus_set_o @ A4 @ B5 ) )
% 6.92/7.23 = ( ( member_o @ C2 @ A4 )
% 6.92/7.23 & ~ ( member_o @ C2 @ B5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Diff_iff
% 6.92/7.23 thf(fact_4942_Diff__iff,axiom,
% 6.92/7.23 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.23 ( ( member2340774599025711042nt_int @ C2 @ ( minus_2612819937483484256nt_int @ A4 @ B5 ) )
% 6.92/7.23 = ( ( member2340774599025711042nt_int @ C2 @ A4 )
% 6.92/7.23 & ~ ( member2340774599025711042nt_int @ C2 @ B5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Diff_iff
% 6.92/7.23 thf(fact_4943_Diff__iff,axiom,
% 6.92/7.23 ! [C2: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.23 ( ( member_set_nat @ C2 @ ( minus_2163939370556025621et_nat @ A4 @ B5 ) )
% 6.92/7.23 = ( ( member_set_nat @ C2 @ A4 )
% 6.92/7.23 & ~ ( member_set_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Diff_iff
% 6.92/7.23 thf(fact_4944_Diff__iff,axiom,
% 6.92/7.23 ! [C2: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.23 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 6.92/7.23 = ( ( member_nat @ C2 @ A4 )
% 6.92/7.23 & ~ ( member_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Diff_iff
% 6.92/7.23 thf(fact_4945_Diff__iff,axiom,
% 6.92/7.23 ! [C2: int,A4: set_int,B5: set_int] :
% 6.92/7.23 ( ( member_int @ C2 @ ( minus_minus_set_int @ A4 @ B5 ) )
% 6.92/7.23 = ( ( member_int @ C2 @ A4 )
% 6.92/7.23 & ~ ( member_int @ C2 @ B5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Diff_iff
% 6.92/7.23 thf(fact_4946_Diff__iff,axiom,
% 6.92/7.23 ! [C2: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ C2 @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) )
% 6.92/7.23 = ( ( member8440522571783428010at_nat @ C2 @ A4 )
% 6.92/7.23 & ~ ( member8440522571783428010at_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Diff_iff
% 6.92/7.23 thf(fact_4947_Diff__idemp,axiom,
% 6.92/7.23 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.23 ( ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) @ B5 )
% 6.92/7.23 = ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) ).
% 6.92/7.23
% 6.92/7.23 % Diff_idemp
% 6.92/7.23 thf(fact_4948_ComplI,axiom,
% 6.92/7.23 ! [C2: $o,A4: set_o] :
% 6.92/7.23 ( ~ ( member_o @ C2 @ A4 )
% 6.92/7.23 => ( member_o @ C2 @ ( uminus_uminus_set_o @ A4 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % ComplI
% 6.92/7.23 thf(fact_4949_ComplI,axiom,
% 6.92/7.23 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int] :
% 6.92/7.23 ( ~ ( member2340774599025711042nt_int @ C2 @ A4 )
% 6.92/7.23 => ( member2340774599025711042nt_int @ C2 @ ( uminus6423885277529793776nt_int @ A4 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % ComplI
% 6.92/7.23 thf(fact_4950_ComplI,axiom,
% 6.92/7.23 ! [C2: set_nat,A4: set_set_nat] :
% 6.92/7.23 ( ~ ( member_set_nat @ C2 @ A4 )
% 6.92/7.23 => ( member_set_nat @ C2 @ ( uminus613421341184616069et_nat @ A4 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % ComplI
% 6.92/7.23 thf(fact_4951_ComplI,axiom,
% 6.92/7.23 ! [C2: nat,A4: set_nat] :
% 6.92/7.23 ( ~ ( member_nat @ C2 @ A4 )
% 6.92/7.23 => ( member_nat @ C2 @ ( uminus5710092332889474511et_nat @ A4 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % ComplI
% 6.92/7.23 thf(fact_4952_ComplI,axiom,
% 6.92/7.23 ! [C2: int,A4: set_int] :
% 6.92/7.23 ( ~ ( member_int @ C2 @ A4 )
% 6.92/7.23 => ( member_int @ C2 @ ( uminus1532241313380277803et_int @ A4 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % ComplI
% 6.92/7.23 thf(fact_4953_Compl__iff,axiom,
% 6.92/7.23 ! [C2: $o,A4: set_o] :
% 6.92/7.23 ( ( member_o @ C2 @ ( uminus_uminus_set_o @ A4 ) )
% 6.92/7.23 = ( ~ ( member_o @ C2 @ A4 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Compl_iff
% 6.92/7.23 thf(fact_4954_Compl__iff,axiom,
% 6.92/7.23 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int] :
% 6.92/7.23 ( ( member2340774599025711042nt_int @ C2 @ ( uminus6423885277529793776nt_int @ A4 ) )
% 6.92/7.23 = ( ~ ( member2340774599025711042nt_int @ C2 @ A4 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Compl_iff
% 6.92/7.23 thf(fact_4955_Compl__iff,axiom,
% 6.92/7.23 ! [C2: set_nat,A4: set_set_nat] :
% 6.92/7.23 ( ( member_set_nat @ C2 @ ( uminus613421341184616069et_nat @ A4 ) )
% 6.92/7.23 = ( ~ ( member_set_nat @ C2 @ A4 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Compl_iff
% 6.92/7.23 thf(fact_4956_Compl__iff,axiom,
% 6.92/7.23 ! [C2: nat,A4: set_nat] :
% 6.92/7.23 ( ( member_nat @ C2 @ ( uminus5710092332889474511et_nat @ A4 ) )
% 6.92/7.23 = ( ~ ( member_nat @ C2 @ A4 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Compl_iff
% 6.92/7.23 thf(fact_4957_Compl__iff,axiom,
% 6.92/7.23 ! [C2: int,A4: set_int] :
% 6.92/7.23 ( ( member_int @ C2 @ ( uminus1532241313380277803et_int @ A4 ) )
% 6.92/7.23 = ( ~ ( member_int @ C2 @ A4 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Compl_iff
% 6.92/7.23 thf(fact_4958_abs__add__abs,axiom,
% 6.92/7.23 ! [A: code_integer,B: code_integer] :
% 6.92/7.23 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 6.92/7.23 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_add_abs
% 6.92/7.23 thf(fact_4959_abs__add__abs,axiom,
% 6.92/7.23 ! [A: rat,B: rat] :
% 6.92/7.23 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 6.92/7.23 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_add_abs
% 6.92/7.23 thf(fact_4960_abs__add__abs,axiom,
% 6.92/7.23 ! [A: int,B: int] :
% 6.92/7.23 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 6.92/7.23 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_add_abs
% 6.92/7.23 thf(fact_4961_abs__of__nat,axiom,
% 6.92/7.23 ! [N2: nat] :
% 6.92/7.23 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 6.92/7.23 = ( semiri681578069525770553at_rat @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_of_nat
% 6.92/7.23 thf(fact_4962_abs__of__nat,axiom,
% 6.92/7.23 ! [N2: nat] :
% 6.92/7.23 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 6.92/7.23 = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_of_nat
% 6.92/7.23 thf(fact_4963_abs__of__nat,axiom,
% 6.92/7.23 ! [N2: nat] :
% 6.92/7.23 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 6.92/7.23 = ( semiri4939895301339042750nteger @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_of_nat
% 6.92/7.23 thf(fact_4964_abs__le__zero__iff,axiom,
% 6.92/7.23 ! [A: code_integer] :
% 6.92/7.23 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 6.92/7.23 = ( A = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_le_zero_iff
% 6.92/7.23 thf(fact_4965_abs__le__zero__iff,axiom,
% 6.92/7.23 ! [A: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 6.92/7.23 = ( A = zero_zero_rat ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_le_zero_iff
% 6.92/7.23 thf(fact_4966_abs__le__zero__iff,axiom,
% 6.92/7.23 ! [A: int] :
% 6.92/7.23 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 6.92/7.23 = ( A = zero_zero_int ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_le_zero_iff
% 6.92/7.23 thf(fact_4967_abs__le__self__iff,axiom,
% 6.92/7.23 ! [A: code_integer] :
% 6.92/7.23 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 6.92/7.23 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_le_self_iff
% 6.92/7.23 thf(fact_4968_abs__le__self__iff,axiom,
% 6.92/7.23 ! [A: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 6.92/7.23 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_le_self_iff
% 6.92/7.23 thf(fact_4969_abs__le__self__iff,axiom,
% 6.92/7.23 ! [A: int] :
% 6.92/7.23 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 6.92/7.23 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_le_self_iff
% 6.92/7.23 thf(fact_4970_abs__of__nonneg,axiom,
% 6.92/7.23 ! [A: code_integer] :
% 6.92/7.23 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.23 => ( ( abs_abs_Code_integer @ A )
% 6.92/7.23 = A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_of_nonneg
% 6.92/7.23 thf(fact_4971_abs__of__nonneg,axiom,
% 6.92/7.23 ! [A: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.23 => ( ( abs_abs_rat @ A )
% 6.92/7.23 = A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_of_nonneg
% 6.92/7.23 thf(fact_4972_abs__of__nonneg,axiom,
% 6.92/7.23 ! [A: int] :
% 6.92/7.23 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.23 => ( ( abs_abs_int @ A )
% 6.92/7.23 = A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_of_nonneg
% 6.92/7.23 thf(fact_4973_zero__less__abs__iff,axiom,
% 6.92/7.23 ! [A: code_integer] :
% 6.92/7.23 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 6.92/7.23 = ( A != zero_z3403309356797280102nteger ) ) ).
% 6.92/7.23
% 6.92/7.23 % zero_less_abs_iff
% 6.92/7.23 thf(fact_4974_zero__less__abs__iff,axiom,
% 6.92/7.23 ! [A: rat] :
% 6.92/7.23 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 6.92/7.23 = ( A != zero_zero_rat ) ) ).
% 6.92/7.23
% 6.92/7.23 % zero_less_abs_iff
% 6.92/7.23 thf(fact_4975_zero__less__abs__iff,axiom,
% 6.92/7.23 ! [A: int] :
% 6.92/7.23 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 6.92/7.23 = ( A != zero_zero_int ) ) ).
% 6.92/7.23
% 6.92/7.23 % zero_less_abs_iff
% 6.92/7.23 thf(fact_4976_slice__complete,axiom,
% 6.92/7.23 ! [Xs: list_nat] :
% 6.92/7.23 ( ( slice_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) @ Xs )
% 6.92/7.23 = Xs ) ).
% 6.92/7.23
% 6.92/7.23 % slice_complete
% 6.92/7.23 thf(fact_4977_slice__complete,axiom,
% 6.92/7.23 ! [Xs: list_o] :
% 6.92/7.23 ( ( slice_o @ zero_zero_nat @ ( size_size_list_o @ Xs ) @ Xs )
% 6.92/7.23 = Xs ) ).
% 6.92/7.23
% 6.92/7.23 % slice_complete
% 6.92/7.23 thf(fact_4978_slice__complete,axiom,
% 6.92/7.23 ! [Xs: list_int] :
% 6.92/7.23 ( ( slice_int @ zero_zero_nat @ ( size_size_list_int @ Xs ) @ Xs )
% 6.92/7.23 = Xs ) ).
% 6.92/7.23
% 6.92/7.23 % slice_complete
% 6.92/7.23 thf(fact_4979_abs__of__nonpos,axiom,
% 6.92/7.23 ! [A: code_integer] :
% 6.92/7.23 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.23 => ( ( abs_abs_Code_integer @ A )
% 6.92/7.23 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_of_nonpos
% 6.92/7.23 thf(fact_4980_abs__of__nonpos,axiom,
% 6.92/7.23 ! [A: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 6.92/7.23 => ( ( abs_abs_rat @ A )
% 6.92/7.23 = ( uminus_uminus_rat @ A ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_of_nonpos
% 6.92/7.23 thf(fact_4981_abs__of__nonpos,axiom,
% 6.92/7.23 ! [A: int] :
% 6.92/7.23 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 6.92/7.23 => ( ( abs_abs_int @ A )
% 6.92/7.23 = ( uminus_uminus_int @ A ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_of_nonpos
% 6.92/7.23 thf(fact_4982_zero__le__divide__abs__iff,axiom,
% 6.92/7.23 ! [A: rat,B: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 6.92/7.23 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.23 | ( B = zero_zero_rat ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zero_le_divide_abs_iff
% 6.92/7.23 thf(fact_4983_divide__le__0__abs__iff,axiom,
% 6.92/7.23 ! [A: rat,B: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 6.92/7.23 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 6.92/7.23 | ( B = zero_zero_rat ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % divide_le_0_abs_iff
% 6.92/7.23 thf(fact_4984_zabs__less__one__iff,axiom,
% 6.92/7.23 ! [Z3: int] :
% 6.92/7.23 ( ( ord_less_int @ ( abs_abs_int @ Z3 ) @ one_one_int )
% 6.92/7.23 = ( Z3 = zero_zero_int ) ) ).
% 6.92/7.23
% 6.92/7.23 % zabs_less_one_iff
% 6.92/7.23 thf(fact_4985_zero__less__power__abs__iff,axiom,
% 6.92/7.23 ! [A: code_integer,N2: nat] :
% 6.92/7.23 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) )
% 6.92/7.23 = ( ( A != zero_z3403309356797280102nteger )
% 6.92/7.23 | ( N2 = zero_zero_nat ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zero_less_power_abs_iff
% 6.92/7.23 thf(fact_4986_zero__less__power__abs__iff,axiom,
% 6.92/7.23 ! [A: rat,N2: nat] :
% 6.92/7.23 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) )
% 6.92/7.23 = ( ( A != zero_zero_rat )
% 6.92/7.23 | ( N2 = zero_zero_nat ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zero_less_power_abs_iff
% 6.92/7.23 thf(fact_4987_zero__less__power__abs__iff,axiom,
% 6.92/7.23 ! [A: int,N2: nat] :
% 6.92/7.23 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) )
% 6.92/7.23 = ( ( A != zero_zero_int )
% 6.92/7.23 | ( N2 = zero_zero_nat ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zero_less_power_abs_iff
% 6.92/7.23 thf(fact_4988_DiffE,axiom,
% 6.92/7.23 ! [C2: $o,A4: set_o,B5: set_o] :
% 6.92/7.23 ( ( member_o @ C2 @ ( minus_minus_set_o @ A4 @ B5 ) )
% 6.92/7.23 => ~ ( ( member_o @ C2 @ A4 )
% 6.92/7.23 => ( member_o @ C2 @ B5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffE
% 6.92/7.23 thf(fact_4989_DiffE,axiom,
% 6.92/7.23 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.23 ( ( member2340774599025711042nt_int @ C2 @ ( minus_2612819937483484256nt_int @ A4 @ B5 ) )
% 6.92/7.23 => ~ ( ( member2340774599025711042nt_int @ C2 @ A4 )
% 6.92/7.23 => ( member2340774599025711042nt_int @ C2 @ B5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffE
% 6.92/7.23 thf(fact_4990_DiffE,axiom,
% 6.92/7.23 ! [C2: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.23 ( ( member_set_nat @ C2 @ ( minus_2163939370556025621et_nat @ A4 @ B5 ) )
% 6.92/7.23 => ~ ( ( member_set_nat @ C2 @ A4 )
% 6.92/7.23 => ( member_set_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffE
% 6.92/7.23 thf(fact_4991_DiffE,axiom,
% 6.92/7.23 ! [C2: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.23 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 6.92/7.23 => ~ ( ( member_nat @ C2 @ A4 )
% 6.92/7.23 => ( member_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffE
% 6.92/7.23 thf(fact_4992_DiffE,axiom,
% 6.92/7.23 ! [C2: int,A4: set_int,B5: set_int] :
% 6.92/7.23 ( ( member_int @ C2 @ ( minus_minus_set_int @ A4 @ B5 ) )
% 6.92/7.23 => ~ ( ( member_int @ C2 @ A4 )
% 6.92/7.23 => ( member_int @ C2 @ B5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffE
% 6.92/7.23 thf(fact_4993_DiffE,axiom,
% 6.92/7.23 ! [C2: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ C2 @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) )
% 6.92/7.23 => ~ ( ( member8440522571783428010at_nat @ C2 @ A4 )
% 6.92/7.23 => ( member8440522571783428010at_nat @ C2 @ B5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffE
% 6.92/7.23 thf(fact_4994_ComplD,axiom,
% 6.92/7.23 ! [C2: $o,A4: set_o] :
% 6.92/7.23 ( ( member_o @ C2 @ ( uminus_uminus_set_o @ A4 ) )
% 6.92/7.23 => ~ ( member_o @ C2 @ A4 ) ) ).
% 6.92/7.23
% 6.92/7.23 % ComplD
% 6.92/7.23 thf(fact_4995_ComplD,axiom,
% 6.92/7.23 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int] :
% 6.92/7.23 ( ( member2340774599025711042nt_int @ C2 @ ( uminus6423885277529793776nt_int @ A4 ) )
% 6.92/7.23 => ~ ( member2340774599025711042nt_int @ C2 @ A4 ) ) ).
% 6.92/7.23
% 6.92/7.23 % ComplD
% 6.92/7.23 thf(fact_4996_ComplD,axiom,
% 6.92/7.23 ! [C2: set_nat,A4: set_set_nat] :
% 6.92/7.23 ( ( member_set_nat @ C2 @ ( uminus613421341184616069et_nat @ A4 ) )
% 6.92/7.23 => ~ ( member_set_nat @ C2 @ A4 ) ) ).
% 6.92/7.23
% 6.92/7.23 % ComplD
% 6.92/7.23 thf(fact_4997_ComplD,axiom,
% 6.92/7.23 ! [C2: nat,A4: set_nat] :
% 6.92/7.23 ( ( member_nat @ C2 @ ( uminus5710092332889474511et_nat @ A4 ) )
% 6.92/7.23 => ~ ( member_nat @ C2 @ A4 ) ) ).
% 6.92/7.23
% 6.92/7.23 % ComplD
% 6.92/7.23 thf(fact_4998_ComplD,axiom,
% 6.92/7.23 ! [C2: int,A4: set_int] :
% 6.92/7.23 ( ( member_int @ C2 @ ( uminus1532241313380277803et_int @ A4 ) )
% 6.92/7.23 => ~ ( member_int @ C2 @ A4 ) ) ).
% 6.92/7.23
% 6.92/7.23 % ComplD
% 6.92/7.23 thf(fact_4999_DiffD1,axiom,
% 6.92/7.23 ! [C2: $o,A4: set_o,B5: set_o] :
% 6.92/7.23 ( ( member_o @ C2 @ ( minus_minus_set_o @ A4 @ B5 ) )
% 6.92/7.23 => ( member_o @ C2 @ A4 ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffD1
% 6.92/7.23 thf(fact_5000_DiffD1,axiom,
% 6.92/7.23 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.23 ( ( member2340774599025711042nt_int @ C2 @ ( minus_2612819937483484256nt_int @ A4 @ B5 ) )
% 6.92/7.23 => ( member2340774599025711042nt_int @ C2 @ A4 ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffD1
% 6.92/7.23 thf(fact_5001_DiffD1,axiom,
% 6.92/7.23 ! [C2: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.23 ( ( member_set_nat @ C2 @ ( minus_2163939370556025621et_nat @ A4 @ B5 ) )
% 6.92/7.23 => ( member_set_nat @ C2 @ A4 ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffD1
% 6.92/7.23 thf(fact_5002_DiffD1,axiom,
% 6.92/7.23 ! [C2: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.23 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 6.92/7.23 => ( member_nat @ C2 @ A4 ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffD1
% 6.92/7.23 thf(fact_5003_DiffD1,axiom,
% 6.92/7.23 ! [C2: int,A4: set_int,B5: set_int] :
% 6.92/7.23 ( ( member_int @ C2 @ ( minus_minus_set_int @ A4 @ B5 ) )
% 6.92/7.23 => ( member_int @ C2 @ A4 ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffD1
% 6.92/7.23 thf(fact_5004_DiffD1,axiom,
% 6.92/7.23 ! [C2: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ C2 @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) )
% 6.92/7.23 => ( member8440522571783428010at_nat @ C2 @ A4 ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffD1
% 6.92/7.23 thf(fact_5005_DiffD2,axiom,
% 6.92/7.23 ! [C2: $o,A4: set_o,B5: set_o] :
% 6.92/7.23 ( ( member_o @ C2 @ ( minus_minus_set_o @ A4 @ B5 ) )
% 6.92/7.23 => ~ ( member_o @ C2 @ B5 ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffD2
% 6.92/7.23 thf(fact_5006_DiffD2,axiom,
% 6.92/7.23 ! [C2: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.23 ( ( member2340774599025711042nt_int @ C2 @ ( minus_2612819937483484256nt_int @ A4 @ B5 ) )
% 6.92/7.23 => ~ ( member2340774599025711042nt_int @ C2 @ B5 ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffD2
% 6.92/7.23 thf(fact_5007_DiffD2,axiom,
% 6.92/7.23 ! [C2: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.23 ( ( member_set_nat @ C2 @ ( minus_2163939370556025621et_nat @ A4 @ B5 ) )
% 6.92/7.23 => ~ ( member_set_nat @ C2 @ B5 ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffD2
% 6.92/7.23 thf(fact_5008_DiffD2,axiom,
% 6.92/7.23 ! [C2: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.23 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 6.92/7.23 => ~ ( member_nat @ C2 @ B5 ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffD2
% 6.92/7.23 thf(fact_5009_DiffD2,axiom,
% 6.92/7.23 ! [C2: int,A4: set_int,B5: set_int] :
% 6.92/7.23 ( ( member_int @ C2 @ ( minus_minus_set_int @ A4 @ B5 ) )
% 6.92/7.23 => ~ ( member_int @ C2 @ B5 ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffD2
% 6.92/7.23 thf(fact_5010_DiffD2,axiom,
% 6.92/7.23 ! [C2: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ C2 @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) )
% 6.92/7.23 => ~ ( member8440522571783428010at_nat @ C2 @ B5 ) ) ).
% 6.92/7.23
% 6.92/7.23 % DiffD2
% 6.92/7.23 thf(fact_5011_uminus__set__def,axiom,
% 6.92/7.23 ( uminus_uminus_set_o
% 6.92/7.23 = ( ^ [A6: set_o] :
% 6.92/7.23 ( collect_o
% 6.92/7.23 @ ( uminus_uminus_o_o
% 6.92/7.23 @ ^ [X4: $o] : ( member_o @ X4 @ A6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % uminus_set_def
% 6.92/7.23 thf(fact_5012_uminus__set__def,axiom,
% 6.92/7.23 ( uminus3195874150345416415st_nat
% 6.92/7.23 = ( ^ [A6: set_list_nat] :
% 6.92/7.23 ( collect_list_nat
% 6.92/7.23 @ ( uminus5770388063884162150_nat_o
% 6.92/7.23 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % uminus_set_def
% 6.92/7.23 thf(fact_5013_uminus__set__def,axiom,
% 6.92/7.23 ( uminus6423885277529793776nt_int
% 6.92/7.23 = ( ^ [A6: set_se6260736226359567993nt_int] :
% 6.92/7.23 ( collec5210948495886036740nt_int
% 6.92/7.23 @ ( uminus8147837162492574189_int_o
% 6.92/7.23 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ A6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % uminus_set_def
% 6.92/7.23 thf(fact_5014_uminus__set__def,axiom,
% 6.92/7.23 ( uminus613421341184616069et_nat
% 6.92/7.23 = ( ^ [A6: set_set_nat] :
% 6.92/7.23 ( collect_set_nat
% 6.92/7.23 @ ( uminus6401447641752708672_nat_o
% 6.92/7.23 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % uminus_set_def
% 6.92/7.23 thf(fact_5015_uminus__set__def,axiom,
% 6.92/7.23 ( uminus5710092332889474511et_nat
% 6.92/7.23 = ( ^ [A6: set_nat] :
% 6.92/7.23 ( collect_nat
% 6.92/7.23 @ ( uminus_uminus_nat_o
% 6.92/7.23 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % uminus_set_def
% 6.92/7.23 thf(fact_5016_uminus__set__def,axiom,
% 6.92/7.23 ( uminus1532241313380277803et_int
% 6.92/7.23 = ( ^ [A6: set_int] :
% 6.92/7.23 ( collect_int
% 6.92/7.23 @ ( uminus_uminus_int_o
% 6.92/7.23 @ ^ [X4: int] : ( member_int @ X4 @ A6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % uminus_set_def
% 6.92/7.23 thf(fact_5017_minus__set__def,axiom,
% 6.92/7.23 ( minus_minus_set_o
% 6.92/7.23 = ( ^ [A6: set_o,B6: set_o] :
% 6.92/7.23 ( collect_o
% 6.92/7.23 @ ( minus_minus_o_o
% 6.92/7.23 @ ^ [X4: $o] : ( member_o @ X4 @ A6 )
% 6.92/7.23 @ ^ [X4: $o] : ( member_o @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % minus_set_def
% 6.92/7.23 thf(fact_5018_minus__set__def,axiom,
% 6.92/7.23 ( minus_7954133019191499631st_nat
% 6.92/7.23 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 6.92/7.23 ( collect_list_nat
% 6.92/7.23 @ ( minus_1139252259498527702_nat_o
% 6.92/7.23 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A6 )
% 6.92/7.23 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % minus_set_def
% 6.92/7.23 thf(fact_5019_minus__set__def,axiom,
% 6.92/7.23 ( minus_2612819937483484256nt_int
% 6.92/7.23 = ( ^ [A6: set_se6260736226359567993nt_int,B6: set_se6260736226359567993nt_int] :
% 6.92/7.23 ( collec5210948495886036740nt_int
% 6.92/7.23 @ ( minus_357216186751819389_int_o
% 6.92/7.23 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ A6 )
% 6.92/7.23 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % minus_set_def
% 6.92/7.23 thf(fact_5020_minus__set__def,axiom,
% 6.92/7.23 ( minus_2163939370556025621et_nat
% 6.92/7.23 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 6.92/7.23 ( collect_set_nat
% 6.92/7.23 @ ( minus_6910147592129066416_nat_o
% 6.92/7.23 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 6.92/7.23 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % minus_set_def
% 6.92/7.23 thf(fact_5021_minus__set__def,axiom,
% 6.92/7.23 ( minus_minus_set_nat
% 6.92/7.23 = ( ^ [A6: set_nat,B6: set_nat] :
% 6.92/7.23 ( collect_nat
% 6.92/7.23 @ ( minus_minus_nat_o
% 6.92/7.23 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 6.92/7.23 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % minus_set_def
% 6.92/7.23 thf(fact_5022_minus__set__def,axiom,
% 6.92/7.23 ( minus_minus_set_int
% 6.92/7.23 = ( ^ [A6: set_int,B6: set_int] :
% 6.92/7.23 ( collect_int
% 6.92/7.23 @ ( minus_minus_int_o
% 6.92/7.23 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 6.92/7.23 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % minus_set_def
% 6.92/7.23 thf(fact_5023_minus__set__def,axiom,
% 6.92/7.23 ( minus_1356011639430497352at_nat
% 6.92/7.23 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 6.92/7.23 ( collec3392354462482085612at_nat
% 6.92/7.23 @ ( minus_2270307095948843157_nat_o
% 6.92/7.23 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ A6 )
% 6.92/7.23 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % minus_set_def
% 6.92/7.23 thf(fact_5024_Collect__neg__eq,axiom,
% 6.92/7.23 ! [P2: list_nat > $o] :
% 6.92/7.23 ( ( collect_list_nat
% 6.92/7.23 @ ^ [X4: list_nat] :
% 6.92/7.23 ~ ( P2 @ X4 ) )
% 6.92/7.23 = ( uminus3195874150345416415st_nat @ ( collect_list_nat @ P2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Collect_neg_eq
% 6.92/7.23 thf(fact_5025_Collect__neg__eq,axiom,
% 6.92/7.23 ! [P2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.23 ( ( collec5210948495886036740nt_int
% 6.92/7.23 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.23 ~ ( P2 @ X4 ) )
% 6.92/7.23 = ( uminus6423885277529793776nt_int @ ( collec5210948495886036740nt_int @ P2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Collect_neg_eq
% 6.92/7.23 thf(fact_5026_Collect__neg__eq,axiom,
% 6.92/7.23 ! [P2: set_nat > $o] :
% 6.92/7.23 ( ( collect_set_nat
% 6.92/7.23 @ ^ [X4: set_nat] :
% 6.92/7.23 ~ ( P2 @ X4 ) )
% 6.92/7.23 = ( uminus613421341184616069et_nat @ ( collect_set_nat @ P2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Collect_neg_eq
% 6.92/7.23 thf(fact_5027_Collect__neg__eq,axiom,
% 6.92/7.23 ! [P2: nat > $o] :
% 6.92/7.23 ( ( collect_nat
% 6.92/7.23 @ ^ [X4: nat] :
% 6.92/7.23 ~ ( P2 @ X4 ) )
% 6.92/7.23 = ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Collect_neg_eq
% 6.92/7.23 thf(fact_5028_Collect__neg__eq,axiom,
% 6.92/7.23 ! [P2: int > $o] :
% 6.92/7.23 ( ( collect_int
% 6.92/7.23 @ ^ [X4: int] :
% 6.92/7.23 ~ ( P2 @ X4 ) )
% 6.92/7.23 = ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Collect_neg_eq
% 6.92/7.23 thf(fact_5029_Compl__eq,axiom,
% 6.92/7.23 ( uminus_uminus_set_o
% 6.92/7.23 = ( ^ [A6: set_o] :
% 6.92/7.23 ( collect_o
% 6.92/7.23 @ ^ [X4: $o] :
% 6.92/7.23 ~ ( member_o @ X4 @ A6 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Compl_eq
% 6.92/7.23 thf(fact_5030_Compl__eq,axiom,
% 6.92/7.23 ( uminus3195874150345416415st_nat
% 6.92/7.23 = ( ^ [A6: set_list_nat] :
% 6.92/7.23 ( collect_list_nat
% 6.92/7.23 @ ^ [X4: list_nat] :
% 6.92/7.23 ~ ( member_list_nat @ X4 @ A6 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Compl_eq
% 6.92/7.23 thf(fact_5031_Compl__eq,axiom,
% 6.92/7.23 ( uminus6423885277529793776nt_int
% 6.92/7.23 = ( ^ [A6: set_se6260736226359567993nt_int] :
% 6.92/7.23 ( collec5210948495886036740nt_int
% 6.92/7.23 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.23 ~ ( member2340774599025711042nt_int @ X4 @ A6 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Compl_eq
% 6.92/7.23 thf(fact_5032_Compl__eq,axiom,
% 6.92/7.23 ( uminus613421341184616069et_nat
% 6.92/7.23 = ( ^ [A6: set_set_nat] :
% 6.92/7.23 ( collect_set_nat
% 6.92/7.23 @ ^ [X4: set_nat] :
% 6.92/7.23 ~ ( member_set_nat @ X4 @ A6 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Compl_eq
% 6.92/7.23 thf(fact_5033_Compl__eq,axiom,
% 6.92/7.23 ( uminus5710092332889474511et_nat
% 6.92/7.23 = ( ^ [A6: set_nat] :
% 6.92/7.23 ( collect_nat
% 6.92/7.23 @ ^ [X4: nat] :
% 6.92/7.23 ~ ( member_nat @ X4 @ A6 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Compl_eq
% 6.92/7.23 thf(fact_5034_Compl__eq,axiom,
% 6.92/7.23 ( uminus1532241313380277803et_int
% 6.92/7.23 = ( ^ [A6: set_int] :
% 6.92/7.23 ( collect_int
% 6.92/7.23 @ ^ [X4: int] :
% 6.92/7.23 ~ ( member_int @ X4 @ A6 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Compl_eq
% 6.92/7.23 thf(fact_5035_set__diff__eq,axiom,
% 6.92/7.23 ( minus_minus_set_o
% 6.92/7.23 = ( ^ [A6: set_o,B6: set_o] :
% 6.92/7.23 ( collect_o
% 6.92/7.23 @ ^ [X4: $o] :
% 6.92/7.23 ( ( member_o @ X4 @ A6 )
% 6.92/7.23 & ~ ( member_o @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % set_diff_eq
% 6.92/7.23 thf(fact_5036_set__diff__eq,axiom,
% 6.92/7.23 ( minus_7954133019191499631st_nat
% 6.92/7.23 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 6.92/7.23 ( collect_list_nat
% 6.92/7.23 @ ^ [X4: list_nat] :
% 6.92/7.23 ( ( member_list_nat @ X4 @ A6 )
% 6.92/7.23 & ~ ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % set_diff_eq
% 6.92/7.23 thf(fact_5037_set__diff__eq,axiom,
% 6.92/7.23 ( minus_2612819937483484256nt_int
% 6.92/7.23 = ( ^ [A6: set_se6260736226359567993nt_int,B6: set_se6260736226359567993nt_int] :
% 6.92/7.23 ( collec5210948495886036740nt_int
% 6.92/7.23 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.23 ( ( member2340774599025711042nt_int @ X4 @ A6 )
% 6.92/7.23 & ~ ( member2340774599025711042nt_int @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % set_diff_eq
% 6.92/7.23 thf(fact_5038_set__diff__eq,axiom,
% 6.92/7.23 ( minus_2163939370556025621et_nat
% 6.92/7.23 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 6.92/7.23 ( collect_set_nat
% 6.92/7.23 @ ^ [X4: set_nat] :
% 6.92/7.23 ( ( member_set_nat @ X4 @ A6 )
% 6.92/7.23 & ~ ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % set_diff_eq
% 6.92/7.23 thf(fact_5039_set__diff__eq,axiom,
% 6.92/7.23 ( minus_minus_set_nat
% 6.92/7.23 = ( ^ [A6: set_nat,B6: set_nat] :
% 6.92/7.23 ( collect_nat
% 6.92/7.23 @ ^ [X4: nat] :
% 6.92/7.23 ( ( member_nat @ X4 @ A6 )
% 6.92/7.23 & ~ ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % set_diff_eq
% 6.92/7.23 thf(fact_5040_set__diff__eq,axiom,
% 6.92/7.23 ( minus_minus_set_int
% 6.92/7.23 = ( ^ [A6: set_int,B6: set_int] :
% 6.92/7.23 ( collect_int
% 6.92/7.23 @ ^ [X4: int] :
% 6.92/7.23 ( ( member_int @ X4 @ A6 )
% 6.92/7.23 & ~ ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % set_diff_eq
% 6.92/7.23 thf(fact_5041_set__diff__eq,axiom,
% 6.92/7.23 ( minus_1356011639430497352at_nat
% 6.92/7.23 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 6.92/7.23 ( collec3392354462482085612at_nat
% 6.92/7.23 @ ^ [X4: product_prod_nat_nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ X4 @ A6 )
% 6.92/7.23 & ~ ( member8440522571783428010at_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % set_diff_eq
% 6.92/7.23 thf(fact_5042_abs__ge__self,axiom,
% 6.92/7.23 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_ge_self
% 6.92/7.23 thf(fact_5043_abs__ge__self,axiom,
% 6.92/7.23 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_ge_self
% 6.92/7.23 thf(fact_5044_abs__ge__self,axiom,
% 6.92/7.23 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_ge_self
% 6.92/7.23 thf(fact_5045_abs__le__D1,axiom,
% 6.92/7.23 ! [A: code_integer,B: code_integer] :
% 6.92/7.23 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 6.92/7.23 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_le_D1
% 6.92/7.23 thf(fact_5046_abs__le__D1,axiom,
% 6.92/7.23 ! [A: rat,B: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 6.92/7.23 => ( ord_less_eq_rat @ A @ B ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_le_D1
% 6.92/7.23 thf(fact_5047_abs__le__D1,axiom,
% 6.92/7.23 ! [A: int,B: int] :
% 6.92/7.23 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 6.92/7.23 => ( ord_less_eq_int @ A @ B ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_le_D1
% 6.92/7.23 thf(fact_5048_fact__mono__nat,axiom,
% 6.92/7.23 ! [M: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.23 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_mono_nat
% 6.92/7.23 thf(fact_5049_fact__ge__self,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_ge_self
% 6.92/7.23 thf(fact_5050_abs__ge__zero,axiom,
% 6.92/7.23 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_ge_zero
% 6.92/7.23 thf(fact_5051_abs__ge__zero,axiom,
% 6.92/7.23 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_ge_zero
% 6.92/7.23 thf(fact_5052_abs__ge__zero,axiom,
% 6.92/7.23 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_ge_zero
% 6.92/7.23 thf(fact_5053_abs__not__less__zero,axiom,
% 6.92/7.23 ! [A: code_integer] :
% 6.92/7.23 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 6.92/7.23
% 6.92/7.23 % abs_not_less_zero
% 6.92/7.23 thf(fact_5054_abs__not__less__zero,axiom,
% 6.92/7.23 ! [A: rat] :
% 6.92/7.23 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 6.92/7.23
% 6.92/7.23 % abs_not_less_zero
% 6.92/7.23 thf(fact_5055_abs__not__less__zero,axiom,
% 6.92/7.23 ! [A: int] :
% 6.92/7.23 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 6.92/7.23
% 6.92/7.23 % abs_not_less_zero
% 6.92/7.23 thf(fact_5056_abs__of__pos,axiom,
% 6.92/7.23 ! [A: code_integer] :
% 6.92/7.23 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.23 => ( ( abs_abs_Code_integer @ A )
% 6.92/7.23 = A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_of_pos
% 6.92/7.23 thf(fact_5057_abs__of__pos,axiom,
% 6.92/7.23 ! [A: rat] :
% 6.92/7.23 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.23 => ( ( abs_abs_rat @ A )
% 6.92/7.23 = A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_of_pos
% 6.92/7.23 thf(fact_5058_abs__of__pos,axiom,
% 6.92/7.23 ! [A: int] :
% 6.92/7.23 ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.23 => ( ( abs_abs_int @ A )
% 6.92/7.23 = A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_of_pos
% 6.92/7.23 thf(fact_5059_abs__triangle__ineq,axiom,
% 6.92/7.23 ! [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 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_triangle_ineq
% 6.92/7.23 thf(fact_5060_abs__triangle__ineq,axiom,
% 6.92/7.23 ! [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 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_triangle_ineq
% 6.92/7.23 thf(fact_5061_abs__triangle__ineq,axiom,
% 6.92/7.23 ! [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 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_triangle_ineq
% 6.92/7.23 thf(fact_5062_abs__triangle__ineq2__sym,axiom,
% 6.92/7.23 ! [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 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_triangle_ineq2_sym
% 6.92/7.23 thf(fact_5063_abs__triangle__ineq2__sym,axiom,
% 6.92/7.23 ! [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 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_triangle_ineq2_sym
% 6.92/7.23 thf(fact_5064_abs__triangle__ineq2__sym,axiom,
% 6.92/7.23 ! [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 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_triangle_ineq2_sym
% 6.92/7.23 thf(fact_5065_abs__triangle__ineq3,axiom,
% 6.92/7.23 ! [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 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_triangle_ineq3
% 6.92/7.23 thf(fact_5066_abs__triangle__ineq3,axiom,
% 6.92/7.23 ! [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 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_triangle_ineq3
% 6.92/7.23 thf(fact_5067_abs__triangle__ineq3,axiom,
% 6.92/7.23 ! [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 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_triangle_ineq3
% 6.92/7.23 thf(fact_5068_abs__triangle__ineq2,axiom,
% 6.92/7.23 ! [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 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_triangle_ineq2
% 6.92/7.23 thf(fact_5069_abs__triangle__ineq2,axiom,
% 6.92/7.23 ! [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 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_triangle_ineq2
% 6.92/7.23 thf(fact_5070_abs__triangle__ineq2,axiom,
% 6.92/7.23 ! [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 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_triangle_ineq2
% 6.92/7.23 thf(fact_5071_abs__mult__less,axiom,
% 6.92/7.23 ! [A: code_integer,C2: code_integer,B: code_integer,D2: code_integer] :
% 6.92/7.23 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C2 )
% 6.92/7.23 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D2 )
% 6.92/7.23 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C2 @ D2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_mult_less
% 6.92/7.23 thf(fact_5072_abs__mult__less,axiom,
% 6.92/7.23 ! [A: rat,C2: rat,B: rat,D2: rat] :
% 6.92/7.23 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C2 )
% 6.92/7.23 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D2 )
% 6.92/7.23 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C2 @ D2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_mult_less
% 6.92/7.23 thf(fact_5073_abs__mult__less,axiom,
% 6.92/7.23 ! [A: int,C2: int,B: int,D2: int] :
% 6.92/7.23 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C2 )
% 6.92/7.23 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D2 )
% 6.92/7.23 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C2 @ D2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_mult_less
% 6.92/7.23 thf(fact_5074_abs__leI,axiom,
% 6.92/7.23 ! [A: code_integer,B: code_integer] :
% 6.92/7.23 ( ( ord_le3102999989581377725nteger @ A @ B )
% 6.92/7.23 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 6.92/7.23 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_leI
% 6.92/7.23 thf(fact_5075_abs__leI,axiom,
% 6.92/7.23 ! [A: rat,B: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.23 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 6.92/7.23 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_leI
% 6.92/7.23 thf(fact_5076_abs__leI,axiom,
% 6.92/7.23 ! [A: int,B: int] :
% 6.92/7.23 ( ( ord_less_eq_int @ A @ B )
% 6.92/7.23 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 6.92/7.23 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_leI
% 6.92/7.23 thf(fact_5077_abs__le__D2,axiom,
% 6.92/7.23 ! [A: code_integer,B: code_integer] :
% 6.92/7.23 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 6.92/7.23 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_le_D2
% 6.92/7.23 thf(fact_5078_abs__le__D2,axiom,
% 6.92/7.23 ! [A: rat,B: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 6.92/7.23 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_le_D2
% 6.92/7.23 thf(fact_5079_abs__le__D2,axiom,
% 6.92/7.23 ! [A: int,B: int] :
% 6.92/7.23 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 6.92/7.23 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_le_D2
% 6.92/7.23 thf(fact_5080_abs__le__iff,axiom,
% 6.92/7.23 ! [A: code_integer,B: code_integer] :
% 6.92/7.23 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 6.92/7.23 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 6.92/7.23 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_le_iff
% 6.92/7.23 thf(fact_5081_abs__le__iff,axiom,
% 6.92/7.23 ! [A: rat,B: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 6.92/7.23 = ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.23 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_le_iff
% 6.92/7.23 thf(fact_5082_abs__le__iff,axiom,
% 6.92/7.23 ! [A: int,B: int] :
% 6.92/7.23 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 6.92/7.23 = ( ( ord_less_eq_int @ A @ B )
% 6.92/7.23 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_le_iff
% 6.92/7.23 thf(fact_5083_abs__ge__minus__self,axiom,
% 6.92/7.23 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_ge_minus_self
% 6.92/7.23 thf(fact_5084_abs__ge__minus__self,axiom,
% 6.92/7.23 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_ge_minus_self
% 6.92/7.23 thf(fact_5085_abs__ge__minus__self,axiom,
% 6.92/7.23 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_ge_minus_self
% 6.92/7.23 thf(fact_5086_abs__less__iff,axiom,
% 6.92/7.23 ! [A: int,B: int] :
% 6.92/7.23 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 6.92/7.23 = ( ( ord_less_int @ A @ B )
% 6.92/7.23 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_less_iff
% 6.92/7.23 thf(fact_5087_abs__less__iff,axiom,
% 6.92/7.23 ! [A: code_integer,B: code_integer] :
% 6.92/7.23 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 6.92/7.23 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 6.92/7.23 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_less_iff
% 6.92/7.23 thf(fact_5088_abs__less__iff,axiom,
% 6.92/7.23 ! [A: rat,B: rat] :
% 6.92/7.23 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 6.92/7.23 = ( ( ord_less_rat @ A @ B )
% 6.92/7.23 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_less_iff
% 6.92/7.23 thf(fact_5089_fact__less__mono__nat,axiom,
% 6.92/7.23 ! [M: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.23 => ( ( ord_less_nat @ M @ N2 )
% 6.92/7.23 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_less_mono_nat
% 6.92/7.23 thf(fact_5090_gbinomial__Suc__Suc,axiom,
% 6.92/7.23 ! [A: rat,K2: nat] :
% 6.92/7.23 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) )
% 6.92/7.23 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K2 ) @ ( gbinomial_rat @ A @ ( suc @ K2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % gbinomial_Suc_Suc
% 6.92/7.23 thf(fact_5091_fact__ge__zero,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( semiri3624122377584611663nteger @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_ge_zero
% 6.92/7.23 thf(fact_5092_fact__ge__zero,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_ge_zero
% 6.92/7.23 thf(fact_5093_fact__ge__zero,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_ge_zero
% 6.92/7.23 thf(fact_5094_fact__ge__zero,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_ge_zero
% 6.92/7.23 thf(fact_5095_fact__not__neg,axiom,
% 6.92/7.23 ! [N2: nat] :
% 6.92/7.23 ~ ( ord_le6747313008572928689nteger @ ( semiri3624122377584611663nteger @ N2 ) @ zero_z3403309356797280102nteger ) ).
% 6.92/7.23
% 6.92/7.23 % fact_not_neg
% 6.92/7.23 thf(fact_5096_fact__not__neg,axiom,
% 6.92/7.23 ! [N2: nat] :
% 6.92/7.23 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ zero_zero_rat ) ).
% 6.92/7.23
% 6.92/7.23 % fact_not_neg
% 6.92/7.23 thf(fact_5097_fact__not__neg,axiom,
% 6.92/7.23 ! [N2: nat] :
% 6.92/7.23 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N2 ) @ zero_zero_int ) ).
% 6.92/7.23
% 6.92/7.23 % fact_not_neg
% 6.92/7.23 thf(fact_5098_fact__not__neg,axiom,
% 6.92/7.23 ! [N2: nat] :
% 6.92/7.23 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ zero_zero_nat ) ).
% 6.92/7.23
% 6.92/7.23 % fact_not_neg
% 6.92/7.23 thf(fact_5099_fact__gt__zero,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( semiri3624122377584611663nteger @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_gt_zero
% 6.92/7.23 thf(fact_5100_fact__gt__zero,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_gt_zero
% 6.92/7.23 thf(fact_5101_fact__gt__zero,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_gt_zero
% 6.92/7.23 thf(fact_5102_fact__gt__zero,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_gt_zero
% 6.92/7.23 thf(fact_5103_fact__ge__1,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( semiri3624122377584611663nteger @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_ge_1
% 6.92/7.23 thf(fact_5104_fact__ge__1,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_ge_1
% 6.92/7.23 thf(fact_5105_fact__ge__1,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_ge_1
% 6.92/7.23 thf(fact_5106_fact__ge__1,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_ge_1
% 6.92/7.23 thf(fact_5107_fact__mono,axiom,
% 6.92/7.23 ! [M: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.23 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_mono
% 6.92/7.23 thf(fact_5108_fact__mono,axiom,
% 6.92/7.23 ! [M: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.23 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_mono
% 6.92/7.23 thf(fact_5109_fact__mono,axiom,
% 6.92/7.23 ! [M: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.23 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_mono
% 6.92/7.23 thf(fact_5110_gbinomial__pochhammer_H,axiom,
% 6.92/7.23 ( gbinomial_rat
% 6.92/7.23 = ( ^ [A5: rat,K3: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ K3 ) ) @ one_one_rat ) @ K3 ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % gbinomial_pochhammer'
% 6.92/7.23 thf(fact_5111_gbinomial__addition__formula,axiom,
% 6.92/7.23 ! [A: rat,K2: nat] :
% 6.92/7.23 ( ( gbinomial_rat @ A @ ( suc @ K2 ) )
% 6.92/7.23 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % gbinomial_addition_formula
% 6.92/7.23 thf(fact_5112_gbinomial__mult__1,axiom,
% 6.92/7.23 ! [A: rat,K2: nat] :
% 6.92/7.23 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K2 ) )
% 6.92/7.23 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K2 ) @ ( gbinomial_rat @ A @ K2 ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) @ ( gbinomial_rat @ A @ ( suc @ K2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % gbinomial_mult_1
% 6.92/7.23 thf(fact_5113_gbinomial__mult__1_H,axiom,
% 6.92/7.23 ! [A: rat,K2: nat] :
% 6.92/7.23 ( ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ A )
% 6.92/7.23 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K2 ) @ ( gbinomial_rat @ A @ K2 ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) @ ( gbinomial_rat @ A @ ( suc @ K2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % gbinomial_mult_1'
% 6.92/7.23 thf(fact_5114_dense__eq0__I,axiom,
% 6.92/7.23 ! [X: rat] :
% 6.92/7.23 ( ! [E2: rat] :
% 6.92/7.23 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 6.92/7.23 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 6.92/7.23 => ( X = zero_zero_rat ) ) ).
% 6.92/7.23
% 6.92/7.23 % dense_eq0_I
% 6.92/7.23 thf(fact_5115_abs__mult__pos,axiom,
% 6.92/7.23 ! [X: code_integer,Y: code_integer] :
% 6.92/7.23 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 6.92/7.23 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X )
% 6.92/7.23 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_mult_pos
% 6.92/7.23 thf(fact_5116_abs__mult__pos,axiom,
% 6.92/7.23 ! [X: rat,Y: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 6.92/7.23 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 6.92/7.23 = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_mult_pos
% 6.92/7.23 thf(fact_5117_abs__mult__pos,axiom,
% 6.92/7.23 ! [X: int,Y: int] :
% 6.92/7.23 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.23 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 6.92/7.23 = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_mult_pos
% 6.92/7.23 thf(fact_5118_abs__eq__mult,axiom,
% 6.92/7.23 ! [A: code_integer,B: code_integer] :
% 6.92/7.23 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.23 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 6.92/7.23 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.23 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 6.92/7.23 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 6.92/7.23 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_eq_mult
% 6.92/7.23 thf(fact_5119_abs__eq__mult,axiom,
% 6.92/7.23 ! [A: rat,B: rat] :
% 6.92/7.23 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.23 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 6.92/7.23 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.23 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 6.92/7.23 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 6.92/7.23 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_eq_mult
% 6.92/7.23 thf(fact_5120_abs__eq__mult,axiom,
% 6.92/7.23 ! [A: int,B: int] :
% 6.92/7.23 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.23 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 6.92/7.23 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 6.92/7.23 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 6.92/7.23 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 6.92/7.23 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_eq_mult
% 6.92/7.23 thf(fact_5121_gbinomial__ge__n__over__k__pow__k,axiom,
% 6.92/7.23 ! [K2: nat,A: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K2 ) @ A )
% 6.92/7.23 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ K2 ) @ ( gbinomial_rat @ A @ K2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % gbinomial_ge_n_over_k_pow_k
% 6.92/7.23 thf(fact_5122_abs__eq__iff_H,axiom,
% 6.92/7.23 ! [A: code_integer,B: code_integer] :
% 6.92/7.23 ( ( ( abs_abs_Code_integer @ A )
% 6.92/7.23 = B )
% 6.92/7.23 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.23 & ( ( A = B )
% 6.92/7.23 | ( A
% 6.92/7.23 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_eq_iff'
% 6.92/7.23 thf(fact_5123_abs__eq__iff_H,axiom,
% 6.92/7.23 ! [A: rat,B: rat] :
% 6.92/7.23 ( ( ( abs_abs_rat @ A )
% 6.92/7.23 = B )
% 6.92/7.23 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.23 & ( ( A = B )
% 6.92/7.23 | ( A
% 6.92/7.23 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_eq_iff'
% 6.92/7.23 thf(fact_5124_abs__eq__iff_H,axiom,
% 6.92/7.23 ! [A: int,B: int] :
% 6.92/7.23 ( ( ( abs_abs_int @ A )
% 6.92/7.23 = B )
% 6.92/7.23 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 6.92/7.23 & ( ( A = B )
% 6.92/7.23 | ( A
% 6.92/7.23 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_eq_iff'
% 6.92/7.23 thf(fact_5125_eq__abs__iff_H,axiom,
% 6.92/7.23 ! [A: code_integer,B: code_integer] :
% 6.92/7.23 ( ( A
% 6.92/7.23 = ( abs_abs_Code_integer @ B ) )
% 6.92/7.23 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.23 & ( ( B = A )
% 6.92/7.23 | ( B
% 6.92/7.23 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % eq_abs_iff'
% 6.92/7.23 thf(fact_5126_eq__abs__iff_H,axiom,
% 6.92/7.23 ! [A: rat,B: rat] :
% 6.92/7.23 ( ( A
% 6.92/7.23 = ( abs_abs_rat @ B ) )
% 6.92/7.23 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.23 & ( ( B = A )
% 6.92/7.23 | ( B
% 6.92/7.23 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % eq_abs_iff'
% 6.92/7.23 thf(fact_5127_eq__abs__iff_H,axiom,
% 6.92/7.23 ! [A: int,B: int] :
% 6.92/7.23 ( ( A
% 6.92/7.23 = ( abs_abs_int @ B ) )
% 6.92/7.23 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.23 & ( ( B = A )
% 6.92/7.23 | ( B
% 6.92/7.23 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % eq_abs_iff'
% 6.92/7.23 thf(fact_5128_abs__minus__le__zero,axiom,
% 6.92/7.23 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 6.92/7.23
% 6.92/7.23 % abs_minus_le_zero
% 6.92/7.23 thf(fact_5129_abs__minus__le__zero,axiom,
% 6.92/7.23 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 6.92/7.23
% 6.92/7.23 % abs_minus_le_zero
% 6.92/7.23 thf(fact_5130_abs__minus__le__zero,axiom,
% 6.92/7.23 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 6.92/7.23
% 6.92/7.23 % abs_minus_le_zero
% 6.92/7.23 thf(fact_5131_abs__triangle__ineq4,axiom,
% 6.92/7.23 ! [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 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_triangle_ineq4
% 6.92/7.23 thf(fact_5132_abs__triangle__ineq4,axiom,
% 6.92/7.23 ! [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 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_triangle_ineq4
% 6.92/7.23 thf(fact_5133_abs__triangle__ineq4,axiom,
% 6.92/7.23 ! [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 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_triangle_ineq4
% 6.92/7.23 thf(fact_5134_abs__diff__triangle__ineq,axiom,
% 6.92/7.23 ! [A: code_integer,B: code_integer,C2: code_integer,D2: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C2 @ D2 ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C2 ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_diff_triangle_ineq
% 6.92/7.23 thf(fact_5135_abs__diff__triangle__ineq,axiom,
% 6.92/7.23 ! [A: rat,B: rat,C2: rat,D2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C2 @ D2 ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C2 ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_diff_triangle_ineq
% 6.92/7.23 thf(fact_5136_abs__diff__triangle__ineq,axiom,
% 6.92/7.23 ! [A: int,B: int,C2: int,D2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C2 @ D2 ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C2 ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_diff_triangle_ineq
% 6.92/7.23 thf(fact_5137_abs__diff__le__iff,axiom,
% 6.92/7.23 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 6.92/7.23 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 6.92/7.23 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 6.92/7.23 & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_diff_le_iff
% 6.92/7.23 thf(fact_5138_abs__diff__le__iff,axiom,
% 6.92/7.23 ! [X: rat,A: rat,R2: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 6.92/7.23 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 6.92/7.23 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_diff_le_iff
% 6.92/7.23 thf(fact_5139_abs__diff__le__iff,axiom,
% 6.92/7.23 ! [X: int,A: int,R2: int] :
% 6.92/7.23 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 6.92/7.23 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 6.92/7.23 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_diff_le_iff
% 6.92/7.23 thf(fact_5140_abs__if,axiom,
% 6.92/7.23 ( abs_abs_int
% 6.92/7.23 = ( ^ [A5: int] : ( if_int @ ( ord_less_int @ A5 @ zero_zero_int ) @ ( uminus_uminus_int @ A5 ) @ A5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_if
% 6.92/7.23 thf(fact_5141_abs__if,axiom,
% 6.92/7.23 ( abs_abs_Code_integer
% 6.92/7.23 = ( ^ [A5: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A5 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A5 ) @ A5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_if
% 6.92/7.23 thf(fact_5142_abs__if,axiom,
% 6.92/7.23 ( abs_abs_rat
% 6.92/7.23 = ( ^ [A5: rat] : ( if_rat @ ( ord_less_rat @ A5 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A5 ) @ A5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_if
% 6.92/7.23 thf(fact_5143_abs__if__raw,axiom,
% 6.92/7.23 ( abs_abs_int
% 6.92/7.23 = ( ^ [A5: int] : ( if_int @ ( ord_less_int @ A5 @ zero_zero_int ) @ ( uminus_uminus_int @ A5 ) @ A5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_if_raw
% 6.92/7.23 thf(fact_5144_abs__if__raw,axiom,
% 6.92/7.23 ( abs_abs_Code_integer
% 6.92/7.23 = ( ^ [A5: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A5 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A5 ) @ A5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_if_raw
% 6.92/7.23 thf(fact_5145_abs__if__raw,axiom,
% 6.92/7.23 ( abs_abs_rat
% 6.92/7.23 = ( ^ [A5: rat] : ( if_rat @ ( ord_less_rat @ A5 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A5 ) @ A5 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_if_raw
% 6.92/7.23 thf(fact_5146_abs__of__neg,axiom,
% 6.92/7.23 ! [A: int] :
% 6.92/7.23 ( ( ord_less_int @ A @ zero_zero_int )
% 6.92/7.23 => ( ( abs_abs_int @ A )
% 6.92/7.23 = ( uminus_uminus_int @ A ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_of_neg
% 6.92/7.23 thf(fact_5147_abs__of__neg,axiom,
% 6.92/7.23 ! [A: code_integer] :
% 6.92/7.23 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.23 => ( ( abs_abs_Code_integer @ A )
% 6.92/7.23 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_of_neg
% 6.92/7.23 thf(fact_5148_abs__of__neg,axiom,
% 6.92/7.23 ! [A: rat] :
% 6.92/7.23 ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.23 => ( ( abs_abs_rat @ A )
% 6.92/7.23 = ( uminus_uminus_rat @ A ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_of_neg
% 6.92/7.23 thf(fact_5149_abs__diff__less__iff,axiom,
% 6.92/7.23 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 6.92/7.23 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 6.92/7.23 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 6.92/7.23 & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_diff_less_iff
% 6.92/7.23 thf(fact_5150_abs__diff__less__iff,axiom,
% 6.92/7.23 ! [X: rat,A: rat,R2: rat] :
% 6.92/7.23 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 6.92/7.23 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 6.92/7.23 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_diff_less_iff
% 6.92/7.23 thf(fact_5151_abs__diff__less__iff,axiom,
% 6.92/7.23 ! [X: int,A: int,R2: int] :
% 6.92/7.23 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 6.92/7.23 = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 6.92/7.23 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_diff_less_iff
% 6.92/7.23 thf(fact_5152_abs__div__pos,axiom,
% 6.92/7.23 ! [Y: rat,X: rat] :
% 6.92/7.23 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 6.92/7.23 => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y )
% 6.92/7.23 = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_div_pos
% 6.92/7.23 thf(fact_5153_zero__le__power__abs,axiom,
% 6.92/7.23 ! [A: code_integer,N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % zero_le_power_abs
% 6.92/7.23 thf(fact_5154_zero__le__power__abs,axiom,
% 6.92/7.23 ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % zero_le_power_abs
% 6.92/7.23 thf(fact_5155_zero__le__power__abs,axiom,
% 6.92/7.23 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % zero_le_power_abs
% 6.92/7.23 thf(fact_5156_fact__ge__Suc__0__nat,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_ge_Suc_0_nat
% 6.92/7.23 thf(fact_5157_zabs__def,axiom,
% 6.92/7.23 ( abs_abs_int
% 6.92/7.23 = ( ^ [I: int] : ( if_int @ ( ord_less_int @ I @ zero_zero_int ) @ ( uminus_uminus_int @ I ) @ I ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zabs_def
% 6.92/7.23 thf(fact_5158_fact__less__mono,axiom,
% 6.92/7.23 ! [M: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.23 => ( ( ord_less_nat @ M @ N2 )
% 6.92/7.23 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_less_mono
% 6.92/7.23 thf(fact_5159_fact__less__mono,axiom,
% 6.92/7.23 ! [M: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.23 => ( ( ord_less_nat @ M @ N2 )
% 6.92/7.23 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_less_mono
% 6.92/7.23 thf(fact_5160_fact__less__mono,axiom,
% 6.92/7.23 ! [M: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.23 => ( ( ord_less_nat @ M @ N2 )
% 6.92/7.23 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_less_mono
% 6.92/7.23 thf(fact_5161_abs__mod__less,axiom,
% 6.92/7.23 ! [L: int,K2: int] :
% 6.92/7.23 ( ( L != zero_zero_int )
% 6.92/7.23 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K2 @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_mod_less
% 6.92/7.23 thf(fact_5162_fact__mod,axiom,
% 6.92/7.23 ! [M: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.23 => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri3624122377584611663nteger @ M ) )
% 6.92/7.23 = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_mod
% 6.92/7.23 thf(fact_5163_fact__mod,axiom,
% 6.92/7.23 ! [M: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.23 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) )
% 6.92/7.23 = zero_zero_int ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_mod
% 6.92/7.23 thf(fact_5164_fact__mod,axiom,
% 6.92/7.23 ! [M: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.23 => ( ( modulo8411746178871703098atural @ ( semiri2447717529341329178atural @ N2 ) @ ( semiri2447717529341329178atural @ M ) )
% 6.92/7.23 = zero_z2226904508553997617atural ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_mod
% 6.92/7.23 thf(fact_5165_fact__mod,axiom,
% 6.92/7.23 ! [M: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.23 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 6.92/7.23 = zero_zero_nat ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_mod
% 6.92/7.23 thf(fact_5166_fact__le__power,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_le3102999989581377725nteger @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri4939895301339042750nteger @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_le_power
% 6.92/7.23 thf(fact_5167_fact__le__power,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_le_power
% 6.92/7.23 thf(fact_5168_fact__le__power,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_le_power
% 6.92/7.23 thf(fact_5169_fact__le__power,axiom,
% 6.92/7.23 ! [N2: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_le_power
% 6.92/7.23 thf(fact_5170_Suc__times__gbinomial,axiom,
% 6.92/7.23 ! [K2: nat,A: rat] :
% 6.92/7.23 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) ) )
% 6.92/7.23 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Suc_times_gbinomial
% 6.92/7.23 thf(fact_5171_gbinomial__trinomial__revision,axiom,
% 6.92/7.23 ! [K2: nat,M: nat,A: rat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ K2 @ M )
% 6.92/7.23 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K2 ) )
% 6.92/7.23 = ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ ( minus_minus_nat @ M @ K2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % gbinomial_trinomial_revision
% 6.92/7.23 thf(fact_5172_abs__add__one__gt__zero,axiom,
% 6.92/7.23 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_add_one_gt_zero
% 6.92/7.23 thf(fact_5173_abs__add__one__gt__zero,axiom,
% 6.92/7.23 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_add_one_gt_zero
% 6.92/7.23 thf(fact_5174_abs__add__one__gt__zero,axiom,
% 6.92/7.23 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % abs_add_one_gt_zero
% 6.92/7.23 thf(fact_5175_gbinomial__code,axiom,
% 6.92/7.23 ( gbinomial_rat
% 6.92/7.23 = ( ^ [A5: rat,K3: nat] :
% 6.92/7.23 ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 6.92/7.23 @ ( divide_divide_rat
% 6.92/7.23 @ ( set_fo1949268297981939178at_rat
% 6.92/7.23 @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 6.92/7.23 @ zero_zero_nat
% 6.92/7.23 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 6.92/7.23 @ one_one_rat )
% 6.92/7.23 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % gbinomial_code
% 6.92/7.23 thf(fact_5176_nat__abs__triangle__ineq,axiom,
% 6.92/7.23 ! [K2: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K2 @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nat_abs_triangle_ineq
% 6.92/7.23 thf(fact_5177_fact__div__fact__le__pow,axiom,
% 6.92/7.23 ! [R2: nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ R2 @ N2 )
% 6.92/7.23 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ R2 ) ) ) @ ( power_power_nat @ N2 @ R2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % fact_div_fact_le_pow
% 6.92/7.23 thf(fact_5178_gbinomial__factors,axiom,
% 6.92/7.23 ! [A: rat,K2: nat] :
% 6.92/7.23 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) )
% 6.92/7.23 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) ) @ ( gbinomial_rat @ A @ K2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % gbinomial_factors
% 6.92/7.23 thf(fact_5179_gbinomial__rec,axiom,
% 6.92/7.23 ! [A: rat,K2: nat] :
% 6.92/7.23 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) )
% 6.92/7.23 = ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % gbinomial_rec
% 6.92/7.23 thf(fact_5180_gbinomial__minus,axiom,
% 6.92/7.23 ! [A: rat,K2: nat] :
% 6.92/7.23 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K2 )
% 6.92/7.23 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % gbinomial_minus
% 6.92/7.23 thf(fact_5181_gbinomial__reduce__nat,axiom,
% 6.92/7.23 ! [K2: nat,A: rat] :
% 6.92/7.23 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.23 => ( ( gbinomial_rat @ A @ K2 )
% 6.92/7.23 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % gbinomial_reduce_nat
% 6.92/7.23 thf(fact_5182_nat__abs__int__diff,axiom,
% 6.92/7.23 ! [A: nat,B: nat] :
% 6.92/7.23 ( ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.23 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 6.92/7.23 = ( minus_minus_nat @ B @ A ) ) )
% 6.92/7.23 & ( ~ ( ord_less_eq_nat @ A @ B )
% 6.92/7.23 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 6.92/7.23 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nat_abs_int_diff
% 6.92/7.23 thf(fact_5183_nat__intermed__int__val,axiom,
% 6.92/7.23 ! [M: nat,N2: nat,F: nat > int,K2: int] :
% 6.92/7.23 ( ! [I3: nat] :
% 6.92/7.23 ( ( ( ord_less_eq_nat @ M @ I3 )
% 6.92/7.23 & ( ord_less_nat @ I3 @ N2 ) )
% 6.92/7.23 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 6.92/7.23 => ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.23 => ( ( ord_less_eq_int @ ( F @ M ) @ K2 )
% 6.92/7.23 => ( ( ord_less_eq_int @ K2 @ ( F @ N2 ) )
% 6.92/7.23 => ? [I3: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ M @ I3 )
% 6.92/7.23 & ( ord_less_eq_nat @ I3 @ N2 )
% 6.92/7.23 & ( ( F @ I3 )
% 6.92/7.23 = K2 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nat_intermed_int_val
% 6.92/7.23 thf(fact_5184_decr__lemma,axiom,
% 6.92/7.23 ! [D2: int,X: int,Z3: int] :
% 6.92/7.23 ( ( ord_less_int @ zero_zero_int @ D2 )
% 6.92/7.23 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z3 ) ) @ one_one_int ) @ D2 ) ) @ Z3 ) ) ).
% 6.92/7.23
% 6.92/7.23 % decr_lemma
% 6.92/7.23 thf(fact_5185_incr__lemma,axiom,
% 6.92/7.23 ! [D2: int,Z3: int,X: int] :
% 6.92/7.23 ( ( ord_less_int @ zero_zero_int @ D2 )
% 6.92/7.23 => ( ord_less_int @ Z3 @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z3 ) ) @ one_one_int ) @ D2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % incr_lemma
% 6.92/7.23 thf(fact_5186_eucl__rel__int_Osimps,axiom,
% 6.92/7.23 ( eucl_rel_int
% 6.92/7.23 = ( ^ [A12: int,A22: int,A32: product_prod_int_int] :
% 6.92/7.23 ( ? [K3: int] :
% 6.92/7.23 ( ( A12 = K3 )
% 6.92/7.23 & ( A22 = zero_zero_int )
% 6.92/7.23 & ( A32
% 6.92/7.23 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 6.92/7.23 | ? [L2: int,K3: int,Q8: int] :
% 6.92/7.23 ( ( A12 = K3 )
% 6.92/7.23 & ( A22 = L2 )
% 6.92/7.23 & ( A32
% 6.92/7.23 = ( product_Pair_int_int @ Q8 @ zero_zero_int ) )
% 6.92/7.23 & ( L2 != zero_zero_int )
% 6.92/7.23 & ( K3
% 6.92/7.23 = ( times_times_int @ Q8 @ L2 ) ) )
% 6.92/7.23 | ? [R5: int,L2: int,K3: int,Q8: int] :
% 6.92/7.23 ( ( A12 = K3 )
% 6.92/7.23 & ( A22 = L2 )
% 6.92/7.23 & ( A32
% 6.92/7.23 = ( product_Pair_int_int @ Q8 @ R5 ) )
% 6.92/7.23 & ( ( sgn_sgn_int @ R5 )
% 6.92/7.23 = ( sgn_sgn_int @ L2 ) )
% 6.92/7.23 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L2 ) )
% 6.92/7.23 & ( K3
% 6.92/7.23 = ( plus_plus_int @ ( times_times_int @ Q8 @ L2 ) @ R5 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % eucl_rel_int.simps
% 6.92/7.23 thf(fact_5187_eucl__rel__int_Ocases,axiom,
% 6.92/7.23 ! [A1: int,A23: int,A33: product_prod_int_int] :
% 6.92/7.23 ( ( eucl_rel_int @ A1 @ A23 @ A33 )
% 6.92/7.23 => ( ( ( A23 = zero_zero_int )
% 6.92/7.23 => ( A33
% 6.92/7.23 != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 6.92/7.23 => ( ! [Q5: int] :
% 6.92/7.23 ( ( A33
% 6.92/7.23 = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 6.92/7.23 => ( ( A23 != zero_zero_int )
% 6.92/7.23 => ( A1
% 6.92/7.23 != ( times_times_int @ Q5 @ A23 ) ) ) )
% 6.92/7.23 => ~ ! [R4: int,Q5: int] :
% 6.92/7.23 ( ( A33
% 6.92/7.23 = ( product_Pair_int_int @ Q5 @ R4 ) )
% 6.92/7.23 => ( ( ( sgn_sgn_int @ R4 )
% 6.92/7.23 = ( sgn_sgn_int @ A23 ) )
% 6.92/7.23 => ( ( ord_less_int @ ( abs_abs_int @ R4 ) @ ( abs_abs_int @ A23 ) )
% 6.92/7.23 => ( A1
% 6.92/7.23 != ( plus_plus_int @ ( times_times_int @ Q5 @ A23 ) @ R4 ) ) ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % eucl_rel_int.cases
% 6.92/7.23 thf(fact_5188_rotate1__length01,axiom,
% 6.92/7.23 ! [Xs: list_nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 6.92/7.23 => ( ( rotate1_nat @ Xs )
% 6.92/7.23 = Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % rotate1_length01
% 6.92/7.23 thf(fact_5189_rotate1__length01,axiom,
% 6.92/7.23 ! [Xs: list_o] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 6.92/7.23 => ( ( rotate1_o @ Xs )
% 6.92/7.23 = Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % rotate1_length01
% 6.92/7.23 thf(fact_5190_rotate1__length01,axiom,
% 6.92/7.23 ! [Xs: list_int] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 6.92/7.23 => ( ( rotate1_int @ Xs )
% 6.92/7.23 = Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % rotate1_length01
% 6.92/7.23 thf(fact_5191_slice__nth,axiom,
% 6.92/7.23 ! [From: nat,To: nat,Xs: list_nat,I2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ From @ To )
% 6.92/7.23 => ( ( ord_less_eq_nat @ To @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ To @ From ) )
% 6.92/7.23 => ( ( nth_nat @ ( slice_nat @ From @ To @ Xs ) @ I2 )
% 6.92/7.23 = ( nth_nat @ Xs @ ( plus_plus_nat @ From @ I2 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % slice_nth
% 6.92/7.23 thf(fact_5192_slice__nth,axiom,
% 6.92/7.23 ! [From: nat,To: nat,Xs: list_o,I2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ From @ To )
% 6.92/7.23 => ( ( ord_less_eq_nat @ To @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ To @ From ) )
% 6.92/7.23 => ( ( nth_o @ ( slice_o @ From @ To @ Xs ) @ I2 )
% 6.92/7.23 = ( nth_o @ Xs @ ( plus_plus_nat @ From @ I2 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % slice_nth
% 6.92/7.23 thf(fact_5193_slice__nth,axiom,
% 6.92/7.23 ! [From: nat,To: nat,Xs: list_int,I2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ From @ To )
% 6.92/7.23 => ( ( ord_less_eq_nat @ To @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ To @ From ) )
% 6.92/7.23 => ( ( nth_int @ ( slice_int @ From @ To @ Xs ) @ I2 )
% 6.92/7.23 = ( nth_int @ Xs @ ( plus_plus_nat @ From @ I2 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % slice_nth
% 6.92/7.23 thf(fact_5194_eucl__rel__int__remainderI,axiom,
% 6.92/7.23 ! [R2: int,L: int,K2: int,Q6: int] :
% 6.92/7.23 ( ( ( sgn_sgn_int @ R2 )
% 6.92/7.23 = ( sgn_sgn_int @ L ) )
% 6.92/7.23 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 6.92/7.23 => ( ( K2
% 6.92/7.23 = ( plus_plus_int @ ( times_times_int @ Q6 @ L ) @ R2 ) )
% 6.92/7.23 => ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q6 @ R2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % eucl_rel_int_remainderI
% 6.92/7.23 thf(fact_5195_dbl__dec__def,axiom,
% 6.92/7.23 ( neg_nu7757733837767384882nteger
% 6.92/7.23 = ( ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ X4 @ X4 ) @ one_one_Code_integer ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % dbl_dec_def
% 6.92/7.23 thf(fact_5196_dbl__dec__def,axiom,
% 6.92/7.23 ( neg_nu3179335615603231917ec_rat
% 6.92/7.23 = ( ^ [X4: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X4 @ X4 ) @ one_one_rat ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % dbl_dec_def
% 6.92/7.23 thf(fact_5197_dbl__dec__def,axiom,
% 6.92/7.23 ( neg_nu3811975205180677377ec_int
% 6.92/7.23 = ( ^ [X4: int] : ( minus_minus_int @ ( plus_plus_int @ X4 @ X4 ) @ one_one_int ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % dbl_dec_def
% 6.92/7.23 thf(fact_5198_sgn__less,axiom,
% 6.92/7.23 ! [A: code_integer] :
% 6.92/7.23 ( ( ord_le6747313008572928689nteger @ ( sgn_sgn_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 6.92/7.23 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_less
% 6.92/7.23 thf(fact_5199_sgn__less,axiom,
% 6.92/7.23 ! [A: rat] :
% 6.92/7.23 ( ( ord_less_rat @ ( sgn_sgn_rat @ A ) @ zero_zero_rat )
% 6.92/7.23 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_less
% 6.92/7.23 thf(fact_5200_sgn__less,axiom,
% 6.92/7.23 ! [A: int] :
% 6.92/7.23 ( ( ord_less_int @ ( sgn_sgn_int @ A ) @ zero_zero_int )
% 6.92/7.23 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_less
% 6.92/7.23 thf(fact_5201_sgn__greater,axiom,
% 6.92/7.23 ! [A: code_integer] :
% 6.92/7.23 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( sgn_sgn_Code_integer @ A ) )
% 6.92/7.23 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_greater
% 6.92/7.23 thf(fact_5202_sgn__greater,axiom,
% 6.92/7.23 ! [A: rat] :
% 6.92/7.23 ( ( ord_less_rat @ zero_zero_rat @ ( sgn_sgn_rat @ A ) )
% 6.92/7.23 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_greater
% 6.92/7.23 thf(fact_5203_sgn__greater,axiom,
% 6.92/7.23 ! [A: int] :
% 6.92/7.23 ( ( ord_less_int @ zero_zero_int @ ( sgn_sgn_int @ A ) )
% 6.92/7.23 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_greater
% 6.92/7.23 thf(fact_5204_sgn__pos,axiom,
% 6.92/7.23 ! [A: code_integer] :
% 6.92/7.23 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.23 => ( ( sgn_sgn_Code_integer @ A )
% 6.92/7.23 = one_one_Code_integer ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_pos
% 6.92/7.23 thf(fact_5205_sgn__pos,axiom,
% 6.92/7.23 ! [A: rat] :
% 6.92/7.23 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.23 => ( ( sgn_sgn_rat @ A )
% 6.92/7.23 = one_one_rat ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_pos
% 6.92/7.23 thf(fact_5206_sgn__pos,axiom,
% 6.92/7.23 ! [A: int] :
% 6.92/7.23 ( ( ord_less_int @ zero_zero_int @ A )
% 6.92/7.23 => ( ( sgn_sgn_int @ A )
% 6.92/7.23 = one_one_int ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_pos
% 6.92/7.23 thf(fact_5207_sgn__neg,axiom,
% 6.92/7.23 ! [A: int] :
% 6.92/7.23 ( ( ord_less_int @ A @ zero_zero_int )
% 6.92/7.23 => ( ( sgn_sgn_int @ A )
% 6.92/7.23 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_neg
% 6.92/7.23 thf(fact_5208_sgn__neg,axiom,
% 6.92/7.23 ! [A: code_integer] :
% 6.92/7.23 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.23 => ( ( sgn_sgn_Code_integer @ A )
% 6.92/7.23 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_neg
% 6.92/7.23 thf(fact_5209_sgn__neg,axiom,
% 6.92/7.23 ! [A: rat] :
% 6.92/7.23 ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.23 => ( ( sgn_sgn_rat @ A )
% 6.92/7.23 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_neg
% 6.92/7.23 thf(fact_5210_same__sgn__sgn__add,axiom,
% 6.92/7.23 ! [B: code_integer,A: code_integer] :
% 6.92/7.23 ( ( ( sgn_sgn_Code_integer @ B )
% 6.92/7.23 = ( sgn_sgn_Code_integer @ A ) )
% 6.92/7.23 => ( ( sgn_sgn_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 6.92/7.23 = ( sgn_sgn_Code_integer @ A ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % same_sgn_sgn_add
% 6.92/7.23 thf(fact_5211_same__sgn__sgn__add,axiom,
% 6.92/7.23 ! [B: rat,A: rat] :
% 6.92/7.23 ( ( ( sgn_sgn_rat @ B )
% 6.92/7.23 = ( sgn_sgn_rat @ A ) )
% 6.92/7.23 => ( ( sgn_sgn_rat @ ( plus_plus_rat @ A @ B ) )
% 6.92/7.23 = ( sgn_sgn_rat @ A ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % same_sgn_sgn_add
% 6.92/7.23 thf(fact_5212_same__sgn__sgn__add,axiom,
% 6.92/7.23 ! [B: int,A: int] :
% 6.92/7.23 ( ( ( sgn_sgn_int @ B )
% 6.92/7.23 = ( sgn_sgn_int @ A ) )
% 6.92/7.23 => ( ( sgn_sgn_int @ ( plus_plus_int @ A @ B ) )
% 6.92/7.23 = ( sgn_sgn_int @ A ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % same_sgn_sgn_add
% 6.92/7.23 thf(fact_5213_list__eq__iff__nth__eq,axiom,
% 6.92/7.23 ( ( ^ [Y6: list_nat,Z4: list_nat] : ( Y6 = Z4 ) )
% 6.92/7.23 = ( ^ [Xs3: list_nat,Ys2: list_nat] :
% 6.92/7.23 ( ( ( size_size_list_nat @ Xs3 )
% 6.92/7.23 = ( size_size_list_nat @ Ys2 ) )
% 6.92/7.23 & ! [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs3 ) )
% 6.92/7.23 => ( ( nth_nat @ Xs3 @ I )
% 6.92/7.23 = ( nth_nat @ Ys2 @ I ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % list_eq_iff_nth_eq
% 6.92/7.23 thf(fact_5214_list__eq__iff__nth__eq,axiom,
% 6.92/7.23 ( ( ^ [Y6: list_o,Z4: list_o] : ( Y6 = Z4 ) )
% 6.92/7.23 = ( ^ [Xs3: list_o,Ys2: list_o] :
% 6.92/7.23 ( ( ( size_size_list_o @ Xs3 )
% 6.92/7.23 = ( size_size_list_o @ Ys2 ) )
% 6.92/7.23 & ! [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs3 ) )
% 6.92/7.23 => ( ( nth_o @ Xs3 @ I )
% 6.92/7.23 = ( nth_o @ Ys2 @ I ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % list_eq_iff_nth_eq
% 6.92/7.23 thf(fact_5215_list__eq__iff__nth__eq,axiom,
% 6.92/7.23 ( ( ^ [Y6: list_int,Z4: list_int] : ( Y6 = Z4 ) )
% 6.92/7.23 = ( ^ [Xs3: list_int,Ys2: list_int] :
% 6.92/7.23 ( ( ( size_size_list_int @ Xs3 )
% 6.92/7.23 = ( size_size_list_int @ Ys2 ) )
% 6.92/7.23 & ! [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs3 ) )
% 6.92/7.23 => ( ( nth_int @ Xs3 @ I )
% 6.92/7.23 = ( nth_int @ Ys2 @ I ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % list_eq_iff_nth_eq
% 6.92/7.23 thf(fact_5216_Skolem__list__nth,axiom,
% 6.92/7.23 ! [K2: nat,P2: nat > nat > $o] :
% 6.92/7.23 ( ( ! [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ K2 )
% 6.92/7.23 => ? [X11: nat] : ( P2 @ I @ X11 ) ) )
% 6.92/7.23 = ( ? [Xs3: list_nat] :
% 6.92/7.23 ( ( ( size_size_list_nat @ Xs3 )
% 6.92/7.23 = K2 )
% 6.92/7.23 & ! [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ K2 )
% 6.92/7.23 => ( P2 @ I @ ( nth_nat @ Xs3 @ I ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Skolem_list_nth
% 6.92/7.23 thf(fact_5217_Skolem__list__nth,axiom,
% 6.92/7.23 ! [K2: nat,P2: nat > $o > $o] :
% 6.92/7.23 ( ( ! [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ K2 )
% 6.92/7.23 => ? [X11: $o] : ( P2 @ I @ X11 ) ) )
% 6.92/7.23 = ( ? [Xs3: list_o] :
% 6.92/7.23 ( ( ( size_size_list_o @ Xs3 )
% 6.92/7.23 = K2 )
% 6.92/7.23 & ! [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ K2 )
% 6.92/7.23 => ( P2 @ I @ ( nth_o @ Xs3 @ I ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Skolem_list_nth
% 6.92/7.23 thf(fact_5218_Skolem__list__nth,axiom,
% 6.92/7.23 ! [K2: nat,P2: nat > int > $o] :
% 6.92/7.23 ( ( ! [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ K2 )
% 6.92/7.23 => ? [X11: int] : ( P2 @ I @ X11 ) ) )
% 6.92/7.23 = ( ? [Xs3: list_int] :
% 6.92/7.23 ( ( ( size_size_list_int @ Xs3 )
% 6.92/7.23 = K2 )
% 6.92/7.23 & ! [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ K2 )
% 6.92/7.23 => ( P2 @ I @ ( nth_int @ Xs3 @ I ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Skolem_list_nth
% 6.92/7.23 thf(fact_5219_nth__equalityI,axiom,
% 6.92/7.23 ! [Xs: list_nat,Ys3: list_nat] :
% 6.92/7.23 ( ( ( size_size_list_nat @ Xs )
% 6.92/7.23 = ( size_size_list_nat @ Ys3 ) )
% 6.92/7.23 => ( ! [I3: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( ( nth_nat @ Xs @ I3 )
% 6.92/7.23 = ( nth_nat @ Ys3 @ I3 ) ) )
% 6.92/7.23 => ( Xs = Ys3 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_equalityI
% 6.92/7.23 thf(fact_5220_nth__equalityI,axiom,
% 6.92/7.23 ! [Xs: list_o,Ys3: list_o] :
% 6.92/7.23 ( ( ( size_size_list_o @ Xs )
% 6.92/7.23 = ( size_size_list_o @ Ys3 ) )
% 6.92/7.23 => ( ! [I3: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( ( nth_o @ Xs @ I3 )
% 6.92/7.23 = ( nth_o @ Ys3 @ I3 ) ) )
% 6.92/7.23 => ( Xs = Ys3 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_equalityI
% 6.92/7.23 thf(fact_5221_nth__equalityI,axiom,
% 6.92/7.23 ! [Xs: list_int,Ys3: list_int] :
% 6.92/7.23 ( ( ( size_size_list_int @ Xs )
% 6.92/7.23 = ( size_size_list_int @ Ys3 ) )
% 6.92/7.23 => ( ! [I3: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( ( nth_int @ Xs @ I3 )
% 6.92/7.23 = ( nth_int @ Ys3 @ I3 ) ) )
% 6.92/7.23 => ( Xs = Ys3 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_equalityI
% 6.92/7.23 thf(fact_5222_obtain__list__from__elements,axiom,
% 6.92/7.23 ! [N2: nat,P2: nat > nat > $o] :
% 6.92/7.23 ( ! [I3: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I3 @ N2 )
% 6.92/7.23 => ? [Li: nat] : ( P2 @ Li @ I3 ) )
% 6.92/7.23 => ~ ! [L3: list_nat] :
% 6.92/7.23 ( ( ( size_size_list_nat @ L3 )
% 6.92/7.23 = N2 )
% 6.92/7.23 => ~ ! [I4: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I4 @ N2 )
% 6.92/7.23 => ( P2 @ ( nth_nat @ L3 @ I4 ) @ I4 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % obtain_list_from_elements
% 6.92/7.23 thf(fact_5223_obtain__list__from__elements,axiom,
% 6.92/7.23 ! [N2: nat,P2: $o > nat > $o] :
% 6.92/7.23 ( ! [I3: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I3 @ N2 )
% 6.92/7.23 => ? [Li: $o] : ( P2 @ Li @ I3 ) )
% 6.92/7.23 => ~ ! [L3: list_o] :
% 6.92/7.23 ( ( ( size_size_list_o @ L3 )
% 6.92/7.23 = N2 )
% 6.92/7.23 => ~ ! [I4: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I4 @ N2 )
% 6.92/7.23 => ( P2 @ ( nth_o @ L3 @ I4 ) @ I4 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % obtain_list_from_elements
% 6.92/7.23 thf(fact_5224_obtain__list__from__elements,axiom,
% 6.92/7.23 ! [N2: nat,P2: int > nat > $o] :
% 6.92/7.23 ( ! [I3: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I3 @ N2 )
% 6.92/7.23 => ? [Li: int] : ( P2 @ Li @ I3 ) )
% 6.92/7.23 => ~ ! [L3: list_int] :
% 6.92/7.23 ( ( ( size_size_list_int @ L3 )
% 6.92/7.23 = N2 )
% 6.92/7.23 => ~ ! [I4: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I4 @ N2 )
% 6.92/7.23 => ( P2 @ ( nth_int @ L3 @ I4 ) @ I4 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % obtain_list_from_elements
% 6.92/7.23 thf(fact_5225_same__sgn__abs__add,axiom,
% 6.92/7.23 ! [B: code_integer,A: code_integer] :
% 6.92/7.23 ( ( ( sgn_sgn_Code_integer @ B )
% 6.92/7.23 = ( sgn_sgn_Code_integer @ A ) )
% 6.92/7.23 => ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 6.92/7.23 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % same_sgn_abs_add
% 6.92/7.23 thf(fact_5226_same__sgn__abs__add,axiom,
% 6.92/7.23 ! [B: rat,A: rat] :
% 6.92/7.23 ( ( ( sgn_sgn_rat @ B )
% 6.92/7.23 = ( sgn_sgn_rat @ A ) )
% 6.92/7.23 => ( ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) )
% 6.92/7.23 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % same_sgn_abs_add
% 6.92/7.23 thf(fact_5227_same__sgn__abs__add,axiom,
% 6.92/7.23 ! [B: int,A: int] :
% 6.92/7.23 ( ( ( sgn_sgn_int @ B )
% 6.92/7.23 = ( sgn_sgn_int @ A ) )
% 6.92/7.23 => ( ( abs_abs_int @ ( plus_plus_int @ A @ B ) )
% 6.92/7.23 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % same_sgn_abs_add
% 6.92/7.23 thf(fact_5228_nth__rotate1,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_nat] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( ( nth_nat @ ( rotate1_nat @ Xs ) @ N2 )
% 6.92/7.23 = ( nth_nat @ Xs @ ( modulo_modulo_nat @ ( suc @ N2 ) @ ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_rotate1
% 6.92/7.23 thf(fact_5229_nth__rotate1,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_o] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( ( nth_o @ ( rotate1_o @ Xs ) @ N2 )
% 6.92/7.23 = ( nth_o @ Xs @ ( modulo_modulo_nat @ ( suc @ N2 ) @ ( size_size_list_o @ Xs ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_rotate1
% 6.92/7.23 thf(fact_5230_nth__rotate1,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_int] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( ( nth_int @ ( rotate1_int @ Xs ) @ N2 )
% 6.92/7.23 = ( nth_int @ Xs @ ( modulo_modulo_nat @ ( suc @ N2 ) @ ( size_size_list_int @ Xs ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_rotate1
% 6.92/7.23 thf(fact_5231_sgn__1__pos,axiom,
% 6.92/7.23 ! [A: code_integer] :
% 6.92/7.23 ( ( ( sgn_sgn_Code_integer @ A )
% 6.92/7.23 = one_one_Code_integer )
% 6.92/7.23 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_1_pos
% 6.92/7.23 thf(fact_5232_sgn__1__pos,axiom,
% 6.92/7.23 ! [A: rat] :
% 6.92/7.23 ( ( ( sgn_sgn_rat @ A )
% 6.92/7.23 = one_one_rat )
% 6.92/7.23 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_1_pos
% 6.92/7.23 thf(fact_5233_sgn__1__pos,axiom,
% 6.92/7.23 ! [A: int] :
% 6.92/7.23 ( ( ( sgn_sgn_int @ A )
% 6.92/7.23 = one_one_int )
% 6.92/7.23 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_1_pos
% 6.92/7.23 thf(fact_5234_zsgn__def,axiom,
% 6.92/7.23 ( sgn_sgn_int
% 6.92/7.23 = ( ^ [I: int] : ( if_int @ ( I = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zsgn_def
% 6.92/7.23 thf(fact_5235_sgn__1__neg,axiom,
% 6.92/7.23 ! [A: int] :
% 6.92/7.23 ( ( ( sgn_sgn_int @ A )
% 6.92/7.23 = ( uminus_uminus_int @ one_one_int ) )
% 6.92/7.23 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_1_neg
% 6.92/7.23 thf(fact_5236_sgn__1__neg,axiom,
% 6.92/7.23 ! [A: code_integer] :
% 6.92/7.23 ( ( ( sgn_sgn_Code_integer @ A )
% 6.92/7.23 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 6.92/7.23 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_1_neg
% 6.92/7.23 thf(fact_5237_sgn__1__neg,axiom,
% 6.92/7.23 ! [A: rat] :
% 6.92/7.23 ( ( ( sgn_sgn_rat @ A )
% 6.92/7.23 = ( uminus_uminus_rat @ one_one_rat ) )
% 6.92/7.23 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_1_neg
% 6.92/7.23 thf(fact_5238_sgn__if,axiom,
% 6.92/7.23 ( sgn_sgn_int
% 6.92/7.23 = ( ^ [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 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_if
% 6.92/7.23 thf(fact_5239_sgn__if,axiom,
% 6.92/7.23 ( sgn_sgn_Code_integer
% 6.92/7.23 = ( ^ [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 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_if
% 6.92/7.23 thf(fact_5240_sgn__if,axiom,
% 6.92/7.23 ( sgn_sgn_rat
% 6.92/7.23 = ( ^ [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 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sgn_if
% 6.92/7.23 thf(fact_5241_nth__rule,axiom,
% 6.92/7.23 ! [I2: nat,Xs: list_nat,A: array_nat] :
% 6.92/7.23 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( hoare_3067605981109127869le_nat @ ( snga_assn_nat @ A @ Xs ) @ ( array_nth_nat @ A @ I2 )
% 6.92/7.23 @ ^ [R5: nat] :
% 6.92/7.23 ( times_times_assn @ ( snga_assn_nat @ A @ Xs )
% 6.92/7.23 @ ( pure_assn
% 6.92/7.23 @ ( R5
% 6.92/7.23 = ( nth_nat @ Xs @ I2 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_rule
% 6.92/7.23 thf(fact_5242_nth__rule,axiom,
% 6.92/7.23 ! [I2: nat,Xs: list_o,A: array_o] :
% 6.92/7.23 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( hoare_hoare_triple_o @ ( snga_assn_o @ A @ Xs ) @ ( array_nth_o @ A @ I2 )
% 6.92/7.23 @ ^ [R5: $o] :
% 6.92/7.23 ( times_times_assn @ ( snga_assn_o @ A @ Xs )
% 6.92/7.23 @ ( pure_assn
% 6.92/7.23 @ ( R5
% 6.92/7.23 = ( nth_o @ Xs @ I2 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_rule
% 6.92/7.23 thf(fact_5243_nth__rule,axiom,
% 6.92/7.23 ! [I2: nat,Xs: list_int,A: array_int] :
% 6.92/7.23 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( hoare_3065115510600077593le_int @ ( snga_assn_int @ A @ Xs ) @ ( array_nth_int @ A @ I2 )
% 6.92/7.23 @ ^ [R5: int] :
% 6.92/7.23 ( times_times_assn @ ( snga_assn_int @ A @ Xs )
% 6.92/7.23 @ ( pure_assn
% 6.92/7.23 @ ( R5
% 6.92/7.23 = ( nth_int @ Xs @ I2 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_rule
% 6.92/7.23 thf(fact_5244_nth__rule,axiom,
% 6.92/7.23 ! [I2: nat,Xs: list_Product_unit,A: array_Product_unit] :
% 6.92/7.23 ( ( ord_less_nat @ I2 @ ( size_s245203480648594047t_unit @ Xs ) )
% 6.92/7.23 => ( hoare_8945653483474564448t_unit @ ( snga_a4522542871529764173t_unit @ A @ Xs ) @ ( array_7872002506669749220t_unit @ A @ I2 )
% 6.92/7.23 @ ^ [R5: product_unit] :
% 6.92/7.23 ( times_times_assn @ ( snga_a4522542871529764173t_unit @ A @ Xs )
% 6.92/7.23 @ ( pure_assn
% 6.92/7.23 @ ( R5
% 6.92/7.23 = ( nth_Product_unit @ Xs @ I2 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_rule
% 6.92/7.23 thf(fact_5245_product__nth,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_nat,Ys3: list_nat] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_nat @ Ys3 ) ) )
% 6.92/7.23 => ( ( nth_Pr7617993195940197384at_nat @ ( product_nat_nat @ Xs @ Ys3 ) @ N2 )
% 6.92/7.23 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % product_nth
% 6.92/7.23 thf(fact_5246_product__nth,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_nat,Ys3: list_o] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys3 ) ) )
% 6.92/7.23 => ( ( nth_Pr112076138515278198_nat_o @ ( product_nat_o @ Xs @ Ys3 ) @ N2 )
% 6.92/7.23 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % product_nth
% 6.92/7.23 thf(fact_5247_product__nth,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_nat,Ys3: list_int] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_int @ Ys3 ) ) )
% 6.92/7.23 => ( ( nth_Pr3440142176431000676at_int @ ( product_nat_int @ Xs @ Ys3 ) @ N2 )
% 6.92/7.23 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % product_nth
% 6.92/7.23 thf(fact_5248_product__nth,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_o,Ys3: list_nat] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys3 ) ) )
% 6.92/7.23 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs @ Ys3 ) @ N2 )
% 6.92/7.23 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % product_nth
% 6.92/7.23 thf(fact_5249_product__nth,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_o,Ys3: list_o] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys3 ) ) )
% 6.92/7.23 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs @ Ys3 ) @ N2 )
% 6.92/7.23 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % product_nth
% 6.92/7.23 thf(fact_5250_product__nth,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_o,Ys3: list_int] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys3 ) ) )
% 6.92/7.23 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs @ Ys3 ) @ N2 )
% 6.92/7.23 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % product_nth
% 6.92/7.23 thf(fact_5251_product__nth,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_int,Ys3: list_nat] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_nat @ Ys3 ) ) )
% 6.92/7.23 => ( ( nth_Pr8617346907841251940nt_nat @ ( product_int_nat @ Xs @ Ys3 ) @ N2 )
% 6.92/7.23 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % product_nth
% 6.92/7.23 thf(fact_5252_product__nth,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_int,Ys3: list_o] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_o @ Ys3 ) ) )
% 6.92/7.23 => ( ( nth_Pr7514405829937366042_int_o @ ( product_int_o @ Xs @ Ys3 ) @ N2 )
% 6.92/7.23 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % product_nth
% 6.92/7.23 thf(fact_5253_product__nth,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_int,Ys3: list_int] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys3 ) ) )
% 6.92/7.23 => ( ( nth_Pr4439495888332055232nt_int @ ( product_int_int @ Xs @ Ys3 ) @ N2 )
% 6.92/7.23 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % product_nth
% 6.92/7.23 thf(fact_5254_product__nth,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_b,Ys3: list_P131111800688179804it_nat] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_b @ Xs ) @ ( size_s341701280123345136it_nat @ Ys3 ) ) )
% 6.92/7.23 => ( ( nth_Pr3591576263217728691it_nat @ ( produc1870533552098665926it_nat @ Xs @ Ys3 ) @ N2 )
% 6.92/7.23 = ( produc4082563078715348724it_nat @ ( nth_b @ Xs @ ( divide_divide_nat @ N2 @ ( size_s341701280123345136it_nat @ Ys3 ) ) ) @ ( nth_Pr4561283279332054789it_nat @ Ys3 @ ( modulo_modulo_nat @ N2 @ ( size_s341701280123345136it_nat @ Ys3 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % product_nth
% 6.92/7.23 thf(fact_5255_sorted__in__between,axiom,
% 6.92/7.23 ! [I2: nat,J2: nat,L: list_o,X: $o] :
% 6.92/7.23 ( ( ord_less_eq_nat @ zero_zero_nat @ I2 )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.23 => ( ( ord_less_nat @ J2 @ ( size_size_list_o @ L ) )
% 6.92/7.23 => ( ( sorted_wrt_o @ ord_less_eq_o @ L )
% 6.92/7.23 => ( ( ord_less_eq_o @ ( nth_o @ L @ I2 ) @ X )
% 6.92/7.23 => ( ( ord_less_o @ X @ ( nth_o @ L @ J2 ) )
% 6.92/7.23 => ~ ! [K: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ I2 @ K )
% 6.92/7.23 => ( ( ord_less_nat @ K @ J2 )
% 6.92/7.23 => ( ( ord_less_eq_o @ ( nth_o @ L @ K ) @ X )
% 6.92/7.23 => ~ ( ord_less_o @ X @ ( nth_o @ L @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_in_between
% 6.92/7.23 thf(fact_5256_sorted__in__between,axiom,
% 6.92/7.23 ! [I2: nat,J2: nat,L: list_rat,X: rat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ zero_zero_nat @ I2 )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.23 => ( ( ord_less_nat @ J2 @ ( size_size_list_rat @ L ) )
% 6.92/7.23 => ( ( sorted_wrt_rat @ ord_less_eq_rat @ L )
% 6.92/7.23 => ( ( ord_less_eq_rat @ ( nth_rat @ L @ I2 ) @ X )
% 6.92/7.23 => ( ( ord_less_rat @ X @ ( nth_rat @ L @ J2 ) )
% 6.92/7.23 => ~ ! [K: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ I2 @ K )
% 6.92/7.23 => ( ( ord_less_nat @ K @ J2 )
% 6.92/7.23 => ( ( ord_less_eq_rat @ ( nth_rat @ L @ K ) @ X )
% 6.92/7.23 => ~ ( ord_less_rat @ X @ ( nth_rat @ L @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_in_between
% 6.92/7.23 thf(fact_5257_sorted__in__between,axiom,
% 6.92/7.23 ! [I2: nat,J2: nat,L: list_num,X: num] :
% 6.92/7.23 ( ( ord_less_eq_nat @ zero_zero_nat @ I2 )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.23 => ( ( ord_less_nat @ J2 @ ( size_size_list_num @ L ) )
% 6.92/7.23 => ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 6.92/7.23 => ( ( ord_less_eq_num @ ( nth_num @ L @ I2 ) @ X )
% 6.92/7.23 => ( ( ord_less_num @ X @ ( nth_num @ L @ J2 ) )
% 6.92/7.23 => ~ ! [K: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ I2 @ K )
% 6.92/7.23 => ( ( ord_less_nat @ K @ J2 )
% 6.92/7.23 => ( ( ord_less_eq_num @ ( nth_num @ L @ K ) @ X )
% 6.92/7.23 => ~ ( ord_less_num @ X @ ( nth_num @ L @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_in_between
% 6.92/7.23 thf(fact_5258_sorted__in__between,axiom,
% 6.92/7.23 ! [I2: nat,J2: nat,L: list_nat,X: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ zero_zero_nat @ I2 )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.23 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ L ) )
% 6.92/7.23 => ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 6.92/7.23 => ( ( ord_less_eq_nat @ ( nth_nat @ L @ I2 ) @ X )
% 6.92/7.23 => ( ( ord_less_nat @ X @ ( nth_nat @ L @ J2 ) )
% 6.92/7.23 => ~ ! [K: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ I2 @ K )
% 6.92/7.23 => ( ( ord_less_nat @ K @ J2 )
% 6.92/7.23 => ( ( ord_less_eq_nat @ ( nth_nat @ L @ K ) @ X )
% 6.92/7.23 => ~ ( ord_less_nat @ X @ ( nth_nat @ L @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_in_between
% 6.92/7.23 thf(fact_5259_sorted__in__between,axiom,
% 6.92/7.23 ! [I2: nat,J2: nat,L: list_int,X: int] :
% 6.92/7.23 ( ( ord_less_eq_nat @ zero_zero_nat @ I2 )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.23 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ L ) )
% 6.92/7.23 => ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 6.92/7.23 => ( ( ord_less_eq_int @ ( nth_int @ L @ I2 ) @ X )
% 6.92/7.23 => ( ( ord_less_int @ X @ ( nth_int @ L @ J2 ) )
% 6.92/7.23 => ~ ! [K: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ I2 @ K )
% 6.92/7.23 => ( ( ord_less_nat @ K @ J2 )
% 6.92/7.23 => ( ( ord_less_eq_int @ ( nth_int @ L @ K ) @ X )
% 6.92/7.23 => ~ ( ord_less_int @ X @ ( nth_int @ L @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_in_between
% 6.92/7.23 thf(fact_5260_nth__enumerate__eq,axiom,
% 6.92/7.23 ! [M: nat,Xs: list_nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ M @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( ( nth_Pr7617993195940197384at_nat @ ( enumerate_nat @ N2 @ Xs ) @ M )
% 6.92/7.23 = ( product_Pair_nat_nat @ ( plus_plus_nat @ N2 @ M ) @ ( nth_nat @ Xs @ M ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_enumerate_eq
% 6.92/7.23 thf(fact_5261_nth__enumerate__eq,axiom,
% 6.92/7.23 ! [M: nat,Xs: list_o,N2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ M @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( ( nth_Pr112076138515278198_nat_o @ ( enumerate_o @ N2 @ Xs ) @ M )
% 6.92/7.23 = ( product_Pair_nat_o @ ( plus_plus_nat @ N2 @ M ) @ ( nth_o @ Xs @ M ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_enumerate_eq
% 6.92/7.23 thf(fact_5262_nth__enumerate__eq,axiom,
% 6.92/7.23 ! [M: nat,Xs: list_int,N2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ M @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( ( nth_Pr3440142176431000676at_int @ ( enumerate_int @ N2 @ Xs ) @ M )
% 6.92/7.23 = ( product_Pair_nat_int @ ( plus_plus_nat @ N2 @ M ) @ ( nth_int @ Xs @ M ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_enumerate_eq
% 6.92/7.23 thf(fact_5263_array__of__list__make,axiom,
% 6.92/7.23 ( array_of_list_nat
% 6.92/7.23 = ( ^ [Xs3: list_nat] : ( array_make_nat @ ( size_size_list_nat @ Xs3 ) @ ( nth_nat @ Xs3 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % array_of_list_make
% 6.92/7.23 thf(fact_5264_array__of__list__make,axiom,
% 6.92/7.23 ( array_of_list_o
% 6.92/7.23 = ( ^ [Xs3: list_o] : ( array_make_o @ ( size_size_list_o @ Xs3 ) @ ( nth_o @ Xs3 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % array_of_list_make
% 6.92/7.23 thf(fact_5265_array__of__list__make,axiom,
% 6.92/7.23 ( array_of_list_int
% 6.92/7.23 = ( ^ [Xs3: list_int] : ( array_make_int @ ( size_size_list_int @ Xs3 ) @ ( nth_int @ Xs3 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % array_of_list_make
% 6.92/7.23 thf(fact_5266_nth__step__trancl,axiom,
% 6.92/7.23 ! [Xs: list_o,R3: set_Product_prod_o_o,N2: nat,M: nat] :
% 6.92/7.23 ( ! [N5: nat] :
% 6.92/7.23 ( ( ord_less_nat @ N5 @ ( minus_minus_nat @ ( size_size_list_o @ Xs ) @ one_one_nat ) )
% 6.92/7.23 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( nth_o @ Xs @ ( suc @ N5 ) ) @ ( nth_o @ Xs @ N5 ) ) @ R3 ) )
% 6.92/7.23 => ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ M @ N2 )
% 6.92/7.23 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( nth_o @ Xs @ N2 ) @ ( nth_o @ Xs @ M ) ) @ ( transitive_trancl_o @ R3 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_step_trancl
% 6.92/7.23 thf(fact_5267_nth__step__trancl,axiom,
% 6.92/7.23 ! [Xs: list_int,R3: set_Pr958786334691620121nt_int,N2: nat,M: nat] :
% 6.92/7.23 ( ! [N5: nat] :
% 6.92/7.23 ( ( ord_less_nat @ N5 @ ( minus_minus_nat @ ( size_size_list_int @ Xs ) @ one_one_nat ) )
% 6.92/7.23 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( nth_int @ Xs @ ( suc @ N5 ) ) @ ( nth_int @ Xs @ N5 ) ) @ R3 ) )
% 6.92/7.23 => ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ M @ N2 )
% 6.92/7.23 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( nth_int @ Xs @ N2 ) @ ( nth_int @ Xs @ M ) ) @ ( transi6261509568448316235cl_int @ R3 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_step_trancl
% 6.92/7.23 thf(fact_5268_nth__step__trancl,axiom,
% 6.92/7.23 ! [Xs: list_nat,R3: set_Pr1261947904930325089at_nat,N2: nat,M: nat] :
% 6.92/7.23 ( ! [N5: nat] :
% 6.92/7.23 ( ( ord_less_nat @ N5 @ ( minus_minus_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat ) )
% 6.92/7.23 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( nth_nat @ Xs @ ( suc @ N5 ) ) @ ( nth_nat @ Xs @ N5 ) ) @ R3 ) )
% 6.92/7.23 => ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ M @ N2 )
% 6.92/7.23 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( nth_nat @ Xs @ N2 ) @ ( nth_nat @ Xs @ M ) ) @ ( transi6264000038957366511cl_nat @ R3 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_step_trancl
% 6.92/7.23 thf(fact_5269_nth__rotate,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_nat,M: nat] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( ( nth_nat @ ( rotate_nat @ M @ Xs ) @ N2 )
% 6.92/7.23 = ( nth_nat @ Xs @ ( modulo_modulo_nat @ ( plus_plus_nat @ M @ N2 ) @ ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_rotate
% 6.92/7.23 thf(fact_5270_nth__rotate,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_o,M: nat] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( ( nth_o @ ( rotate_o @ M @ Xs ) @ N2 )
% 6.92/7.23 = ( nth_o @ Xs @ ( modulo_modulo_nat @ ( plus_plus_nat @ M @ N2 ) @ ( size_size_list_o @ Xs ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_rotate
% 6.92/7.23 thf(fact_5271_nth__rotate,axiom,
% 6.92/7.23 ! [N2: nat,Xs: list_int,M: nat] :
% 6.92/7.23 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( ( nth_int @ ( rotate_int @ M @ Xs ) @ N2 )
% 6.92/7.23 = ( nth_int @ Xs @ ( modulo_modulo_nat @ ( plus_plus_nat @ M @ N2 ) @ ( size_size_list_int @ Xs ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_rotate
% 6.92/7.23 thf(fact_5272_rotate__length01,axiom,
% 6.92/7.23 ! [Xs: list_nat,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 6.92/7.23 => ( ( rotate_nat @ N2 @ Xs )
% 6.92/7.23 = Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % rotate_length01
% 6.92/7.23 thf(fact_5273_rotate__length01,axiom,
% 6.92/7.23 ! [Xs: list_o,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 6.92/7.23 => ( ( rotate_o @ N2 @ Xs )
% 6.92/7.23 = Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % rotate_length01
% 6.92/7.23 thf(fact_5274_rotate__length01,axiom,
% 6.92/7.23 ! [Xs: list_int,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 6.92/7.23 => ( ( rotate_int @ N2 @ Xs )
% 6.92/7.23 = Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % rotate_length01
% 6.92/7.23 thf(fact_5275_sorted__wrt__true,axiom,
% 6.92/7.23 ! [Xs: list_nat] :
% 6.92/7.23 ( sorted_wrt_nat
% 6.92/7.23 @ ^ [Uu2: nat,Uv2: nat] : $true
% 6.92/7.23 @ Xs ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_wrt_true
% 6.92/7.23 thf(fact_5276_sorted__wrt__true,axiom,
% 6.92/7.23 ! [Xs: list_int] :
% 6.92/7.23 ( sorted_wrt_int
% 6.92/7.23 @ ^ [Uu2: int,Uv2: int] : $true
% 6.92/7.23 @ Xs ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_wrt_true
% 6.92/7.23 thf(fact_5277_trancl_Ocases,axiom,
% 6.92/7.23 ! [A1: int,A23: int,R2: set_Pr958786334691620121nt_int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ A23 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ A23 ) @ R2 )
% 6.92/7.23 => ~ ! [B3: int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ B3 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B3 @ A23 ) @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl.cases
% 6.92/7.23 thf(fact_5278_trancl_Ocases,axiom,
% 6.92/7.23 ! [A1: nat,A23: nat,R2: set_Pr1261947904930325089at_nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ A23 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ A23 ) @ R2 )
% 6.92/7.23 => ~ ! [B3: nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ B3 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B3 @ A23 ) @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl.cases
% 6.92/7.23 thf(fact_5279_trancl_Osimps,axiom,
% 6.92/7.23 ! [A1: int,A23: int,R2: set_Pr958786334691620121nt_int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ A23 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 = ( ? [A5: int,B4: int] :
% 6.92/7.23 ( ( A1 = A5 )
% 6.92/7.23 & ( A23 = B4 )
% 6.92/7.23 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A5 @ B4 ) @ R2 ) )
% 6.92/7.23 | ? [A5: int,B4: int,C3: int] :
% 6.92/7.23 ( ( A1 = A5 )
% 6.92/7.23 & ( A23 = C3 )
% 6.92/7.23 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A5 @ B4 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B4 @ C3 ) @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl.simps
% 6.92/7.23 thf(fact_5280_trancl_Osimps,axiom,
% 6.92/7.23 ! [A1: nat,A23: nat,R2: set_Pr1261947904930325089at_nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ A23 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 = ( ? [A5: nat,B4: nat] :
% 6.92/7.23 ( ( A1 = A5 )
% 6.92/7.23 & ( A23 = B4 )
% 6.92/7.23 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A5 @ B4 ) @ R2 ) )
% 6.92/7.23 | ? [A5: nat,B4: nat,C3: nat] :
% 6.92/7.23 ( ( A1 = A5 )
% 6.92/7.23 & ( A23 = C3 )
% 6.92/7.23 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A5 @ B4 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B4 @ C3 ) @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl.simps
% 6.92/7.23 thf(fact_5281_trancl_Or__into__trancl,axiom,
% 6.92/7.23 ! [A: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R2 )
% 6.92/7.23 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl.r_into_trancl
% 6.92/7.23 thf(fact_5282_trancl_Or__into__trancl,axiom,
% 6.92/7.23 ! [A: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R2 )
% 6.92/7.23 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl.r_into_trancl
% 6.92/7.23 thf(fact_5283_tranclE,axiom,
% 6.92/7.23 ! [A: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R2 )
% 6.92/7.23 => ~ ! [C: int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ C ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ C @ B ) @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % tranclE
% 6.92/7.23 thf(fact_5284_tranclE,axiom,
% 6.92/7.23 ! [A: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R2 )
% 6.92/7.23 => ~ ! [C: nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ C ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ C @ B ) @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % tranclE
% 6.92/7.23 thf(fact_5285_trancl__trans,axiom,
% 6.92/7.23 ! [X: int,Y: int,R2: set_Pr958786334691620121nt_int,Z3: int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ Z3 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z3 ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_trans
% 6.92/7.23 thf(fact_5286_trancl__trans,axiom,
% 6.92/7.23 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat,Z3: nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Z3 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z3 ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_trans
% 6.92/7.23 thf(fact_5287_trancl__induct,axiom,
% 6.92/7.23 ! [A: int,B: int,R2: set_Pr958786334691620121nt_int,P2: int > $o] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ( ! [Y3: int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ Y3 ) @ R2 )
% 6.92/7.23 => ( P2 @ Y3 ) )
% 6.92/7.23 => ( ! [Y3: int,Z2: int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ Y3 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ Z2 ) @ R2 )
% 6.92/7.23 => ( ( P2 @ Y3 )
% 6.92/7.23 => ( P2 @ Z2 ) ) ) )
% 6.92/7.23 => ( P2 @ B ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_induct
% 6.92/7.23 thf(fact_5288_trancl__induct,axiom,
% 6.92/7.23 ! [A: nat,B: nat,R2: set_Pr1261947904930325089at_nat,P2: nat > $o] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( ! [Y3: nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ Y3 ) @ R2 )
% 6.92/7.23 => ( P2 @ Y3 ) )
% 6.92/7.23 => ( ! [Y3: nat,Z2: nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ Y3 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z2 ) @ R2 )
% 6.92/7.23 => ( ( P2 @ Y3 )
% 6.92/7.23 => ( P2 @ Z2 ) ) ) )
% 6.92/7.23 => ( P2 @ B ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_induct
% 6.92/7.23 thf(fact_5289_r__r__into__trancl,axiom,
% 6.92/7.23 ! [A: int,B: int,R3: set_Pr958786334691620121nt_int,C2: int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R3 )
% 6.92/7.23 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C2 ) @ R3 )
% 6.92/7.23 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ C2 ) @ ( transi6261509568448316235cl_int @ R3 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % r_r_into_trancl
% 6.92/7.23 thf(fact_5290_r__r__into__trancl,axiom,
% 6.92/7.23 ! [A: nat,B: nat,R3: set_Pr1261947904930325089at_nat,C2: nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R3 )
% 6.92/7.23 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C2 ) @ R3 )
% 6.92/7.23 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ C2 ) @ ( transi6264000038957366511cl_nat @ R3 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % r_r_into_trancl
% 6.92/7.23 thf(fact_5291_converse__tranclE,axiom,
% 6.92/7.23 ! [X: int,Z3: int,R2: set_Pr958786334691620121nt_int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z3 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z3 ) @ R2 )
% 6.92/7.23 => ~ ! [Y3: int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y3 ) @ R2 )
% 6.92/7.23 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ Z3 ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % converse_tranclE
% 6.92/7.23 thf(fact_5292_converse__tranclE,axiom,
% 6.92/7.23 ! [X: nat,Z3: nat,R2: set_Pr1261947904930325089at_nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z3 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z3 ) @ R2 )
% 6.92/7.23 => ~ ! [Y3: nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y3 ) @ R2 )
% 6.92/7.23 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z3 ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % converse_tranclE
% 6.92/7.23 thf(fact_5293_irrefl__trancl__rD,axiom,
% 6.92/7.23 ! [R2: set_Pr958786334691620121nt_int,X: int,Y: int] :
% 6.92/7.23 ( ! [X3: int] :
% 6.92/7.23 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ X3 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 )
% 6.92/7.23 => ( X != Y ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % irrefl_trancl_rD
% 6.92/7.23 thf(fact_5294_irrefl__trancl__rD,axiom,
% 6.92/7.23 ! [R2: set_Pr1261947904930325089at_nat,X: nat,Y: nat] :
% 6.92/7.23 ( ! [X3: nat] :
% 6.92/7.23 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 )
% 6.92/7.23 => ( X != Y ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % irrefl_trancl_rD
% 6.92/7.23 thf(fact_5295_Transitive__Closure_Otrancl__into__trancl,axiom,
% 6.92/7.23 ! [A: int,B: int,R2: set_Pr958786334691620121nt_int,C2: int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C2 ) @ R2 )
% 6.92/7.23 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ C2 ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Transitive_Closure.trancl_into_trancl
% 6.92/7.23 thf(fact_5296_Transitive__Closure_Otrancl__into__trancl,axiom,
% 6.92/7.23 ! [A: nat,B: nat,R2: set_Pr1261947904930325089at_nat,C2: nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C2 ) @ R2 )
% 6.92/7.23 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ C2 ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % Transitive_Closure.trancl_into_trancl
% 6.92/7.23 thf(fact_5297_trancl__into__trancl2,axiom,
% 6.92/7.23 ! [A: int,B: int,R2: set_Pr958786334691620121nt_int,C2: int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R2 )
% 6.92/7.23 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C2 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ C2 ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_into_trancl2
% 6.92/7.23 thf(fact_5298_trancl__into__trancl2,axiom,
% 6.92/7.23 ! [A: nat,B: nat,R2: set_Pr1261947904930325089at_nat,C2: nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R2 )
% 6.92/7.23 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C2 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ C2 ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_into_trancl2
% 6.92/7.23 thf(fact_5299_trancl__trans__induct,axiom,
% 6.92/7.23 ! [X: int,Y: int,R2: set_Pr958786334691620121nt_int,P2: int > int > $o] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ( ! [X3: int,Y3: int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ R2 )
% 6.92/7.23 => ( P2 @ X3 @ Y3 ) )
% 6.92/7.23 => ( ! [X3: int,Y3: int,Z2: int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ( ( P2 @ X3 @ Y3 )
% 6.92/7.23 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ Z2 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ( ( P2 @ Y3 @ Z2 )
% 6.92/7.23 => ( P2 @ X3 @ Z2 ) ) ) ) )
% 6.92/7.23 => ( P2 @ X @ Y ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_trans_induct
% 6.92/7.23 thf(fact_5300_trancl__trans__induct,axiom,
% 6.92/7.23 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat,P2: nat > nat > $o] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R2 )
% 6.92/7.23 => ( P2 @ X3 @ Y3 ) )
% 6.92/7.23 => ( ! [X3: nat,Y3: nat,Z2: nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( ( P2 @ X3 @ Y3 )
% 6.92/7.23 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z2 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( ( P2 @ Y3 @ Z2 )
% 6.92/7.23 => ( P2 @ X3 @ Z2 ) ) ) ) )
% 6.92/7.23 => ( P2 @ X @ Y ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_trans_induct
% 6.92/7.23 thf(fact_5301_converse__trancl__induct,axiom,
% 6.92/7.23 ! [A: int,B: int,R2: set_Pr958786334691620121nt_int,P2: int > $o] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ( ! [Y3: int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ B ) @ R2 )
% 6.92/7.23 => ( P2 @ Y3 ) )
% 6.92/7.23 => ( ! [Y3: int,Z2: int] :
% 6.92/7.23 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ Z2 ) @ R2 )
% 6.92/7.23 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Z2 @ B ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.23 => ( ( P2 @ Z2 )
% 6.92/7.23 => ( P2 @ Y3 ) ) ) )
% 6.92/7.23 => ( P2 @ A ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % converse_trancl_induct
% 6.92/7.23 thf(fact_5302_converse__trancl__induct,axiom,
% 6.92/7.23 ! [A: nat,B: nat,R2: set_Pr1261947904930325089at_nat,P2: nat > $o] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( ! [Y3: nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ B ) @ R2 )
% 6.92/7.23 => ( P2 @ Y3 ) )
% 6.92/7.23 => ( ! [Y3: nat,Z2: nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z2 ) @ R2 )
% 6.92/7.23 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Z2 @ B ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( ( P2 @ Z2 )
% 6.92/7.23 => ( P2 @ Y3 ) ) ) )
% 6.92/7.23 => ( P2 @ A ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % converse_trancl_induct
% 6.92/7.23 thf(fact_5303_trancl__induct2,axiom,
% 6.92/7.23 ! [Ax: int,Ay: int,Bx: int,By: int,R2: set_Pr2560585780119916871nt_int,P2: int > int > $o] :
% 6.92/7.23 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Ax @ Ay ) @ ( product_Pair_int_int @ Bx @ By ) ) @ ( transi6288783178788033498nt_int @ R2 ) )
% 6.92/7.23 => ( ! [A3: int,B3: int] :
% 6.92/7.23 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Ax @ Ay ) @ ( product_Pair_int_int @ A3 @ B3 ) ) @ R2 )
% 6.92/7.23 => ( P2 @ A3 @ B3 ) )
% 6.92/7.23 => ( ! [A3: int,B3: int,Aa2: int,Ba: int] :
% 6.92/7.23 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Ax @ Ay ) @ ( product_Pair_int_int @ A3 @ B3 ) ) @ ( transi6288783178788033498nt_int @ R2 ) )
% 6.92/7.23 => ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ A3 @ B3 ) @ ( product_Pair_int_int @ Aa2 @ Ba ) ) @ R2 )
% 6.92/7.23 => ( ( P2 @ A3 @ B3 )
% 6.92/7.23 => ( P2 @ Aa2 @ Ba ) ) ) )
% 6.92/7.23 => ( P2 @ Bx @ By ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_induct2
% 6.92/7.23 thf(fact_5304_trancl__induct2,axiom,
% 6.92/7.23 ! [Ax: produc3658429121746597890et_nat > $o,Ay: produc3658429121746597890et_nat,Bx: produc3658429121746597890et_nat > $o,By: produc3658429121746597890et_nat,R2: set_Pr7928877670098842301et_nat,P2: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 6.92/7.23 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ Bx @ By ) ) @ ( transi3145040225084697757et_nat @ R2 ) )
% 6.92/7.23 => ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 6.92/7.23 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ A3 @ B3 ) ) @ R2 )
% 6.92/7.23 => ( P2 @ A3 @ B3 ) )
% 6.92/7.23 => ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat,Aa2: produc3658429121746597890et_nat > $o,Ba: produc3658429121746597890et_nat] :
% 6.92/7.23 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ A3 @ B3 ) ) @ ( transi3145040225084697757et_nat @ R2 ) )
% 6.92/7.23 => ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ A3 @ B3 ) @ ( produc5001842942810119800et_nat @ Aa2 @ Ba ) ) @ R2 )
% 6.92/7.23 => ( ( P2 @ A3 @ B3 )
% 6.92/7.23 => ( P2 @ Aa2 @ Ba ) ) ) )
% 6.92/7.23 => ( P2 @ Bx @ By ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_induct2
% 6.92/7.23 thf(fact_5305_trancl__induct2,axiom,
% 6.92/7.23 ! [Ax: produc3658429121746597890et_nat > $o,Ay: produc3925858234332021118et_nat,Bx: produc3658429121746597890et_nat > $o,By: produc3925858234332021118et_nat,R2: set_Pr3444600963470892981et_nat,P2: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 6.92/7.23 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ Bx @ By ) ) @ ( transi5221092739591632921et_nat @ R2 ) )
% 6.92/7.23 => ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 6.92/7.23 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ A3 @ B3 ) ) @ R2 )
% 6.92/7.23 => ( P2 @ A3 @ B3 ) )
% 6.92/7.23 => ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat,Aa2: produc3658429121746597890et_nat > $o,Ba: produc3925858234332021118et_nat] :
% 6.92/7.23 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ A3 @ B3 ) ) @ ( transi5221092739591632921et_nat @ R2 ) )
% 6.92/7.23 => ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ A3 @ B3 ) @ ( produc2245416461498447860et_nat @ Aa2 @ Ba ) ) @ R2 )
% 6.92/7.23 => ( ( P2 @ A3 @ B3 )
% 6.92/7.23 => ( P2 @ Aa2 @ Ba ) ) ) )
% 6.92/7.23 => ( P2 @ Bx @ By ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_induct2
% 6.92/7.23 thf(fact_5306_trancl__induct2,axiom,
% 6.92/7.23 ! [Ax: b,Ay: produc6653097349344004940it_nat,Bx: b,By: produc6653097349344004940it_nat,R2: set_Pr5508209795250834101it_nat,P2: b > produc6653097349344004940it_nat > $o] :
% 6.92/7.23 ( ( member6820296301096096254it_nat @ ( produc6853161671299316109it_nat @ ( produc4082563078715348724it_nat @ Ax @ Ay ) @ ( produc4082563078715348724it_nat @ Bx @ By ) ) @ ( transi2518514244971309593it_nat @ R2 ) )
% 6.92/7.23 => ( ! [A3: b,B3: produc6653097349344004940it_nat] :
% 6.92/7.23 ( ( member6820296301096096254it_nat @ ( produc6853161671299316109it_nat @ ( produc4082563078715348724it_nat @ Ax @ Ay ) @ ( produc4082563078715348724it_nat @ A3 @ B3 ) ) @ R2 )
% 6.92/7.23 => ( P2 @ A3 @ B3 ) )
% 6.92/7.23 => ( ! [A3: b,B3: produc6653097349344004940it_nat,Aa2: b,Ba: produc6653097349344004940it_nat] :
% 6.92/7.23 ( ( member6820296301096096254it_nat @ ( produc6853161671299316109it_nat @ ( produc4082563078715348724it_nat @ Ax @ Ay ) @ ( produc4082563078715348724it_nat @ A3 @ B3 ) ) @ ( transi2518514244971309593it_nat @ R2 ) )
% 6.92/7.23 => ( ( member6820296301096096254it_nat @ ( produc6853161671299316109it_nat @ ( produc4082563078715348724it_nat @ A3 @ B3 ) @ ( produc4082563078715348724it_nat @ Aa2 @ Ba ) ) @ R2 )
% 6.92/7.23 => ( ( P2 @ A3 @ B3 )
% 6.92/7.23 => ( P2 @ Aa2 @ Ba ) ) ) )
% 6.92/7.23 => ( P2 @ Bx @ By ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_induct2
% 6.92/7.23 thf(fact_5307_trancl__induct2,axiom,
% 6.92/7.23 ! [Ax: a,Ay: produc6653097349344004940it_nat,Bx: a,By: produc6653097349344004940it_nat,R2: set_Pr2819221443900773171it_nat,P2: a > produc6653097349344004940it_nat > $o] :
% 6.92/7.23 ( ( member5335690527091456380it_nat @ ( produc1743342482959036555it_nat @ ( produc9178034014595674355it_nat @ Ax @ Ay ) @ ( produc9178034014595674355it_nat @ Bx @ By ) ) @ ( transi7613985180851635224it_nat @ R2 ) )
% 6.92/7.23 => ( ! [A3: a,B3: produc6653097349344004940it_nat] :
% 6.92/7.23 ( ( member5335690527091456380it_nat @ ( produc1743342482959036555it_nat @ ( produc9178034014595674355it_nat @ Ax @ Ay ) @ ( produc9178034014595674355it_nat @ A3 @ B3 ) ) @ R2 )
% 6.92/7.23 => ( P2 @ A3 @ B3 ) )
% 6.92/7.23 => ( ! [A3: a,B3: produc6653097349344004940it_nat,Aa2: a,Ba: produc6653097349344004940it_nat] :
% 6.92/7.23 ( ( member5335690527091456380it_nat @ ( produc1743342482959036555it_nat @ ( produc9178034014595674355it_nat @ Ax @ Ay ) @ ( produc9178034014595674355it_nat @ A3 @ B3 ) ) @ ( transi7613985180851635224it_nat @ R2 ) )
% 6.92/7.23 => ( ( member5335690527091456380it_nat @ ( produc1743342482959036555it_nat @ ( produc9178034014595674355it_nat @ A3 @ B3 ) @ ( produc9178034014595674355it_nat @ Aa2 @ Ba ) ) @ R2 )
% 6.92/7.23 => ( ( P2 @ A3 @ B3 )
% 6.92/7.23 => ( P2 @ Aa2 @ Ba ) ) ) )
% 6.92/7.23 => ( P2 @ Bx @ By ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_induct2
% 6.92/7.23 thf(fact_5308_trancl__mono,axiom,
% 6.92/7.23 ! [P3: product_prod_nat_nat,R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 6.92/7.23 ( ( member8440522571783428010at_nat @ P3 @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.23 => ( ( ord_le3146513528884898305at_nat @ R2 @ S2 )
% 6.92/7.23 => ( member8440522571783428010at_nat @ P3 @ ( transi6264000038957366511cl_nat @ S2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_mono
% 6.92/7.23 thf(fact_5309_trancl__mono__mp,axiom,
% 6.92/7.23 ! [U2: set_Pr1261947904930325089at_nat,V3: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 6.92/7.23 ( ( ord_le3146513528884898305at_nat @ U2 @ V3 )
% 6.92/7.23 => ( ( member8440522571783428010at_nat @ X @ ( transi6264000038957366511cl_nat @ U2 ) )
% 6.92/7.23 => ( member8440522571783428010at_nat @ X @ ( transi6264000038957366511cl_nat @ V3 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_mono_mp
% 6.92/7.23 thf(fact_5310_trancl__sub,axiom,
% 6.92/7.23 ! [R3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ R3 @ ( transi6264000038957366511cl_nat @ R3 ) ) ).
% 6.92/7.23
% 6.92/7.23 % trancl_sub
% 6.92/7.23 thf(fact_5311_strict__sorted__imp__sorted,axiom,
% 6.92/7.23 ! [Xs: list_rat] :
% 6.92/7.23 ( ( sorted_wrt_rat @ ord_less_rat @ Xs )
% 6.92/7.23 => ( sorted_wrt_rat @ ord_less_eq_rat @ Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % strict_sorted_imp_sorted
% 6.92/7.23 thf(fact_5312_strict__sorted__imp__sorted,axiom,
% 6.92/7.23 ! [Xs: list_num] :
% 6.92/7.23 ( ( sorted_wrt_num @ ord_less_num @ Xs )
% 6.92/7.23 => ( sorted_wrt_num @ ord_less_eq_num @ Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % strict_sorted_imp_sorted
% 6.92/7.23 thf(fact_5313_strict__sorted__imp__sorted,axiom,
% 6.92/7.23 ! [Xs: list_nat] :
% 6.92/7.23 ( ( sorted_wrt_nat @ ord_less_nat @ Xs )
% 6.92/7.23 => ( sorted_wrt_nat @ ord_less_eq_nat @ Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % strict_sorted_imp_sorted
% 6.92/7.23 thf(fact_5314_strict__sorted__imp__sorted,axiom,
% 6.92/7.23 ! [Xs: list_int] :
% 6.92/7.23 ( ( sorted_wrt_int @ ord_less_int @ Xs )
% 6.92/7.23 => ( sorted_wrt_int @ ord_less_eq_int @ Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % strict_sorted_imp_sorted
% 6.92/7.23 thf(fact_5315_sorted__wrt__less__idx,axiom,
% 6.92/7.23 ! [Ns: list_nat,I2: nat] :
% 6.92/7.23 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 6.92/7.23 => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_wrt_less_idx
% 6.92/7.23 thf(fact_5316_sorted__wrt__iff__nth__less,axiom,
% 6.92/7.23 ( sorted_wrt_nat
% 6.92/7.23 = ( ^ [P5: nat > nat > $o,Xs3: list_nat] :
% 6.92/7.23 ! [I: nat,J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ J )
% 6.92/7.23 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs3 ) )
% 6.92/7.23 => ( P5 @ ( nth_nat @ Xs3 @ I ) @ ( nth_nat @ Xs3 @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_wrt_iff_nth_less
% 6.92/7.23 thf(fact_5317_sorted__wrt__iff__nth__less,axiom,
% 6.92/7.23 ( sorted_wrt_o
% 6.92/7.23 = ( ^ [P5: $o > $o > $o,Xs3: list_o] :
% 6.92/7.23 ! [I: nat,J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ J )
% 6.92/7.23 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs3 ) )
% 6.92/7.23 => ( P5 @ ( nth_o @ Xs3 @ I ) @ ( nth_o @ Xs3 @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_wrt_iff_nth_less
% 6.92/7.23 thf(fact_5318_sorted__wrt__iff__nth__less,axiom,
% 6.92/7.23 ( sorted_wrt_int
% 6.92/7.23 = ( ^ [P5: int > int > $o,Xs3: list_int] :
% 6.92/7.23 ! [I: nat,J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ J )
% 6.92/7.23 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs3 ) )
% 6.92/7.23 => ( P5 @ ( nth_int @ Xs3 @ I ) @ ( nth_int @ Xs3 @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_wrt_iff_nth_less
% 6.92/7.23 thf(fact_5319_sorted__wrt__nth__less,axiom,
% 6.92/7.23 ! [P2: nat > nat > $o,Xs: list_nat,I2: nat,J2: nat] :
% 6.92/7.23 ( ( sorted_wrt_nat @ P2 @ Xs )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.23 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( P2 @ ( nth_nat @ Xs @ I2 ) @ ( nth_nat @ Xs @ J2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_wrt_nth_less
% 6.92/7.23 thf(fact_5320_sorted__wrt__nth__less,axiom,
% 6.92/7.23 ! [P2: $o > $o > $o,Xs: list_o,I2: nat,J2: nat] :
% 6.92/7.23 ( ( sorted_wrt_o @ P2 @ Xs )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.23 => ( ( ord_less_nat @ J2 @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( P2 @ ( nth_o @ Xs @ I2 ) @ ( nth_o @ Xs @ J2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_wrt_nth_less
% 6.92/7.23 thf(fact_5321_sorted__wrt__nth__less,axiom,
% 6.92/7.23 ! [P2: int > int > $o,Xs: list_int,I2: nat,J2: nat] :
% 6.92/7.23 ( ( sorted_wrt_int @ P2 @ Xs )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ J2 )
% 6.92/7.23 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( P2 @ ( nth_int @ Xs @ I2 ) @ ( nth_int @ Xs @ J2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_wrt_nth_less
% 6.92/7.23 thf(fact_5322_sorted__wrt01,axiom,
% 6.92/7.23 ! [Xs: list_nat,P2: nat > nat > $o] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 6.92/7.23 => ( sorted_wrt_nat @ P2 @ Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_wrt01
% 6.92/7.23 thf(fact_5323_sorted__wrt01,axiom,
% 6.92/7.23 ! [Xs: list_o,P2: $o > $o > $o] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 6.92/7.23 => ( sorted_wrt_o @ P2 @ Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_wrt01
% 6.92/7.23 thf(fact_5324_sorted__wrt01,axiom,
% 6.92/7.23 ! [Xs: list_int,P2: int > int > $o] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 6.92/7.23 => ( sorted_wrt_int @ P2 @ Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_wrt01
% 6.92/7.23 thf(fact_5325_sorted__iff__nth__mono__less,axiom,
% 6.92/7.23 ! [Xs: list_o] :
% 6.92/7.23 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 6.92/7.23 = ( ! [I: nat,J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ J )
% 6.92/7.23 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_o @ ( nth_o @ Xs @ I ) @ ( nth_o @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_iff_nth_mono_less
% 6.92/7.23 thf(fact_5326_sorted__iff__nth__mono__less,axiom,
% 6.92/7.23 ! [Xs: list_rat] :
% 6.92/7.23 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 6.92/7.23 = ( ! [I: nat,J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ J )
% 6.92/7.23 => ( ( ord_less_nat @ J @ ( size_size_list_rat @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I ) @ ( nth_rat @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_iff_nth_mono_less
% 6.92/7.23 thf(fact_5327_sorted__iff__nth__mono__less,axiom,
% 6.92/7.23 ! [Xs: list_num] :
% 6.92/7.23 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 6.92/7.23 = ( ! [I: nat,J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ J )
% 6.92/7.23 => ( ( ord_less_nat @ J @ ( size_size_list_num @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_num @ ( nth_num @ Xs @ I ) @ ( nth_num @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_iff_nth_mono_less
% 6.92/7.23 thf(fact_5328_sorted__iff__nth__mono__less,axiom,
% 6.92/7.23 ! [Xs: list_nat] :
% 6.92/7.23 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 6.92/7.23 = ( ! [I: nat,J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ J )
% 6.92/7.23 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I ) @ ( nth_nat @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_iff_nth_mono_less
% 6.92/7.23 thf(fact_5329_sorted__iff__nth__mono__less,axiom,
% 6.92/7.23 ! [Xs: list_int] :
% 6.92/7.23 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 6.92/7.23 = ( ! [I: nat,J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ J )
% 6.92/7.23 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_int @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_iff_nth_mono_less
% 6.92/7.23 thf(fact_5330_sorted01,axiom,
% 6.92/7.23 ! [Xs: list_o] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 6.92/7.23 => ( sorted_wrt_o @ ord_less_eq_o @ Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted01
% 6.92/7.23 thf(fact_5331_sorted01,axiom,
% 6.92/7.23 ! [Xs: list_rat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( size_size_list_rat @ Xs ) @ one_one_nat )
% 6.92/7.23 => ( sorted_wrt_rat @ ord_less_eq_rat @ Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted01
% 6.92/7.23 thf(fact_5332_sorted01,axiom,
% 6.92/7.23 ! [Xs: list_num] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( size_size_list_num @ Xs ) @ one_one_nat )
% 6.92/7.23 => ( sorted_wrt_num @ ord_less_eq_num @ Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted01
% 6.92/7.23 thf(fact_5333_sorted01,axiom,
% 6.92/7.23 ! [Xs: list_nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 6.92/7.23 => ( sorted_wrt_nat @ ord_less_eq_nat @ Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted01
% 6.92/7.23 thf(fact_5334_sorted01,axiom,
% 6.92/7.23 ! [Xs: list_int] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 6.92/7.23 => ( sorted_wrt_int @ ord_less_eq_int @ Xs ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted01
% 6.92/7.23 thf(fact_5335_sorted__iff__nth__Suc,axiom,
% 6.92/7.23 ! [Xs: list_o] :
% 6.92/7.23 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 6.92/7.23 = ( ! [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ ( suc @ I ) @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_o @ ( nth_o @ Xs @ I ) @ ( nth_o @ Xs @ ( suc @ I ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_iff_nth_Suc
% 6.92/7.23 thf(fact_5336_sorted__iff__nth__Suc,axiom,
% 6.92/7.23 ! [Xs: list_rat] :
% 6.92/7.23 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 6.92/7.23 = ( ! [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ ( suc @ I ) @ ( size_size_list_rat @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I ) @ ( nth_rat @ Xs @ ( suc @ I ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_iff_nth_Suc
% 6.92/7.23 thf(fact_5337_sorted__iff__nth__Suc,axiom,
% 6.92/7.23 ! [Xs: list_num] :
% 6.92/7.23 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 6.92/7.23 = ( ! [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ ( suc @ I ) @ ( size_size_list_num @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_num @ ( nth_num @ Xs @ I ) @ ( nth_num @ Xs @ ( suc @ I ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_iff_nth_Suc
% 6.92/7.23 thf(fact_5338_sorted__iff__nth__Suc,axiom,
% 6.92/7.23 ! [Xs: list_nat] :
% 6.92/7.23 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 6.92/7.23 = ( ! [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ ( suc @ I ) @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I ) @ ( nth_nat @ Xs @ ( suc @ I ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_iff_nth_Suc
% 6.92/7.23 thf(fact_5339_sorted__iff__nth__Suc,axiom,
% 6.92/7.23 ! [Xs: list_int] :
% 6.92/7.23 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 6.92/7.23 = ( ! [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ ( suc @ I ) @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_int @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xs @ ( suc @ I ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_iff_nth_Suc
% 6.92/7.23 thf(fact_5340_sorted__iff__nth__mono,axiom,
% 6.92/7.23 ! [Xs: list_o] :
% 6.92/7.23 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 6.92/7.23 = ( ! [I: nat,J: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ I @ J )
% 6.92/7.23 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_o @ ( nth_o @ Xs @ I ) @ ( nth_o @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_iff_nth_mono
% 6.92/7.23 thf(fact_5341_sorted__iff__nth__mono,axiom,
% 6.92/7.23 ! [Xs: list_rat] :
% 6.92/7.23 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 6.92/7.23 = ( ! [I: nat,J: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ I @ J )
% 6.92/7.23 => ( ( ord_less_nat @ J @ ( size_size_list_rat @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I ) @ ( nth_rat @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_iff_nth_mono
% 6.92/7.23 thf(fact_5342_sorted__iff__nth__mono,axiom,
% 6.92/7.23 ! [Xs: list_num] :
% 6.92/7.23 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 6.92/7.23 = ( ! [I: nat,J: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ I @ J )
% 6.92/7.23 => ( ( ord_less_nat @ J @ ( size_size_list_num @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_num @ ( nth_num @ Xs @ I ) @ ( nth_num @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_iff_nth_mono
% 6.92/7.23 thf(fact_5343_sorted__iff__nth__mono,axiom,
% 6.92/7.23 ! [Xs: list_nat] :
% 6.92/7.23 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 6.92/7.23 = ( ! [I: nat,J: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ I @ J )
% 6.92/7.23 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I ) @ ( nth_nat @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_iff_nth_mono
% 6.92/7.23 thf(fact_5344_sorted__iff__nth__mono,axiom,
% 6.92/7.23 ! [Xs: list_int] :
% 6.92/7.23 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 6.92/7.23 = ( ! [I: nat,J: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ I @ J )
% 6.92/7.23 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_int @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_iff_nth_mono
% 6.92/7.23 thf(fact_5345_sorted__nth__mono,axiom,
% 6.92/7.23 ! [Xs: list_o,I2: nat,J2: nat] :
% 6.92/7.23 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 6.92/7.23 => ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.23 => ( ( ord_less_nat @ J2 @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_o @ ( nth_o @ Xs @ I2 ) @ ( nth_o @ Xs @ J2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_nth_mono
% 6.92/7.23 thf(fact_5346_sorted__nth__mono,axiom,
% 6.92/7.23 ! [Xs: list_rat,I2: nat,J2: nat] :
% 6.92/7.23 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 6.92/7.23 => ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.23 => ( ( ord_less_nat @ J2 @ ( size_size_list_rat @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I2 ) @ ( nth_rat @ Xs @ J2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_nth_mono
% 6.92/7.23 thf(fact_5347_sorted__nth__mono,axiom,
% 6.92/7.23 ! [Xs: list_num,I2: nat,J2: nat] :
% 6.92/7.23 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 6.92/7.23 => ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.23 => ( ( ord_less_nat @ J2 @ ( size_size_list_num @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_num @ ( nth_num @ Xs @ I2 ) @ ( nth_num @ Xs @ J2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_nth_mono
% 6.92/7.23 thf(fact_5348_sorted__nth__mono,axiom,
% 6.92/7.23 ! [Xs: list_nat,I2: nat,J2: nat] :
% 6.92/7.23 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 6.92/7.23 => ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.23 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I2 ) @ ( nth_nat @ Xs @ J2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_nth_mono
% 6.92/7.23 thf(fact_5349_sorted__nth__mono,axiom,
% 6.92/7.23 ! [Xs: list_int,I2: nat,J2: nat] :
% 6.92/7.23 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 6.92/7.23 => ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.23 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( ord_less_eq_int @ ( nth_int @ Xs @ I2 ) @ ( nth_int @ Xs @ J2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % sorted_nth_mono
% 6.92/7.23 thf(fact_5350_nth__zip,axiom,
% 6.92/7.23 ! [I2: nat,Xs: list_nat,Ys3: list_nat] :
% 6.92/7.23 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ys3 ) )
% 6.92/7.23 => ( ( nth_Pr7617993195940197384at_nat @ ( zip_nat_nat @ Xs @ Ys3 ) @ I2 )
% 6.92/7.23 = ( product_Pair_nat_nat @ ( nth_nat @ Xs @ I2 ) @ ( nth_nat @ Ys3 @ I2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_zip
% 6.92/7.23 thf(fact_5351_nth__zip,axiom,
% 6.92/7.23 ! [I2: nat,Xs: list_nat,Ys3: list_o] :
% 6.92/7.23 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Ys3 ) )
% 6.92/7.23 => ( ( nth_Pr112076138515278198_nat_o @ ( zip_nat_o @ Xs @ Ys3 ) @ I2 )
% 6.92/7.23 = ( product_Pair_nat_o @ ( nth_nat @ Xs @ I2 ) @ ( nth_o @ Ys3 @ I2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_zip
% 6.92/7.23 thf(fact_5352_nth__zip,axiom,
% 6.92/7.23 ! [I2: nat,Xs: list_nat,Ys3: list_int] :
% 6.92/7.23 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Ys3 ) )
% 6.92/7.23 => ( ( nth_Pr3440142176431000676at_int @ ( zip_nat_int @ Xs @ Ys3 ) @ I2 )
% 6.92/7.23 = ( product_Pair_nat_int @ ( nth_nat @ Xs @ I2 ) @ ( nth_int @ Ys3 @ I2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_zip
% 6.92/7.23 thf(fact_5353_nth__zip,axiom,
% 6.92/7.23 ! [I2: nat,Xs: list_o,Ys3: list_nat] :
% 6.92/7.23 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ys3 ) )
% 6.92/7.23 => ( ( nth_Pr5826913651314560976_o_nat @ ( zip_o_nat @ Xs @ Ys3 ) @ I2 )
% 6.92/7.23 = ( product_Pair_o_nat @ ( nth_o @ Xs @ I2 ) @ ( nth_nat @ Ys3 @ I2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_zip
% 6.92/7.23 thf(fact_5354_nth__zip,axiom,
% 6.92/7.23 ! [I2: nat,Xs: list_o,Ys3: list_o] :
% 6.92/7.23 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Ys3 ) )
% 6.92/7.23 => ( ( nth_Product_prod_o_o @ ( zip_o_o @ Xs @ Ys3 ) @ I2 )
% 6.92/7.23 = ( product_Pair_o_o @ ( nth_o @ Xs @ I2 ) @ ( nth_o @ Ys3 @ I2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_zip
% 6.92/7.23 thf(fact_5355_nth__zip,axiom,
% 6.92/7.23 ! [I2: nat,Xs: list_o,Ys3: list_int] :
% 6.92/7.23 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Ys3 ) )
% 6.92/7.23 => ( ( nth_Pr1649062631805364268_o_int @ ( zip_o_int @ Xs @ Ys3 ) @ I2 )
% 6.92/7.23 = ( product_Pair_o_int @ ( nth_o @ Xs @ I2 ) @ ( nth_int @ Ys3 @ I2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_zip
% 6.92/7.23 thf(fact_5356_nth__zip,axiom,
% 6.92/7.23 ! [I2: nat,Xs: list_int,Ys3: list_nat] :
% 6.92/7.23 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ys3 ) )
% 6.92/7.23 => ( ( nth_Pr8617346907841251940nt_nat @ ( zip_int_nat @ Xs @ Ys3 ) @ I2 )
% 6.92/7.23 = ( product_Pair_int_nat @ ( nth_int @ Xs @ I2 ) @ ( nth_nat @ Ys3 @ I2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_zip
% 6.92/7.23 thf(fact_5357_nth__zip,axiom,
% 6.92/7.23 ! [I2: nat,Xs: list_int,Ys3: list_o] :
% 6.92/7.23 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Ys3 ) )
% 6.92/7.23 => ( ( nth_Pr7514405829937366042_int_o @ ( zip_int_o @ Xs @ Ys3 ) @ I2 )
% 6.92/7.23 = ( product_Pair_int_o @ ( nth_int @ Xs @ I2 ) @ ( nth_o @ Ys3 @ I2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_zip
% 6.92/7.23 thf(fact_5358_nth__zip,axiom,
% 6.92/7.23 ! [I2: nat,Xs: list_int,Ys3: list_int] :
% 6.92/7.23 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Ys3 ) )
% 6.92/7.23 => ( ( nth_Pr4439495888332055232nt_int @ ( zip_int_int @ Xs @ Ys3 ) @ I2 )
% 6.92/7.23 = ( product_Pair_int_int @ ( nth_int @ Xs @ I2 ) @ ( nth_int @ Ys3 @ I2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_zip
% 6.92/7.23 thf(fact_5359_nth__zip,axiom,
% 6.92/7.23 ! [I2: nat,Xs: list_b,Ys3: list_P131111800688179804it_nat] :
% 6.92/7.23 ( ( ord_less_nat @ I2 @ ( size_size_list_b @ Xs ) )
% 6.92/7.23 => ( ( ord_less_nat @ I2 @ ( size_s341701280123345136it_nat @ Ys3 ) )
% 6.92/7.23 => ( ( nth_Pr3591576263217728691it_nat @ ( zip_b_5987488365222434772it_nat @ Xs @ Ys3 ) @ I2 )
% 6.92/7.23 = ( produc4082563078715348724it_nat @ ( nth_b @ Xs @ I2 ) @ ( nth_Pr4561283279332054789it_nat @ Ys3 @ I2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_zip
% 6.92/7.23 thf(fact_5360_nth__Cons__pos,axiom,
% 6.92/7.23 ! [N2: nat,X: int,Xs: list_int] :
% 6.92/7.23 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.23 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N2 )
% 6.92/7.23 = ( nth_int @ Xs @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_Cons_pos
% 6.92/7.23 thf(fact_5361_nth__Cons__pos,axiom,
% 6.92/7.23 ! [N2: nat,X: nat,Xs: list_nat] :
% 6.92/7.23 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.23 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N2 )
% 6.92/7.23 = ( nth_nat @ Xs @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nth_Cons_pos
% 6.92/7.23 thf(fact_5362_find__Some__iff,axiom,
% 6.92/7.23 ! [P2: produc7388388658123137530it_nat > $o,Xs: list_P7438302566501821706it_nat,X: produc7388388658123137530it_nat] :
% 6.92/7.23 ( ( ( find_P8943372834735446238it_nat @ P2 @ Xs )
% 6.92/7.23 = ( some_P2818173045054083285it_nat @ X ) )
% 6.92/7.23 = ( ? [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_s4572066133376685982it_nat @ Xs ) )
% 6.92/7.23 & ( P2 @ ( nth_Pr3591576263217728691it_nat @ Xs @ I ) )
% 6.92/7.23 & ( X
% 6.92/7.23 = ( nth_Pr3591576263217728691it_nat @ Xs @ I ) )
% 6.92/7.23 & ! [J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ J @ I )
% 6.92/7.23 => ~ ( P2 @ ( nth_Pr3591576263217728691it_nat @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find_Some_iff
% 6.92/7.23 thf(fact_5363_find__Some__iff,axiom,
% 6.92/7.23 ! [P2: produc3260487557148687353it_nat > $o,Xs: list_P6935614879863011209it_nat,X: produc3260487557148687353it_nat] :
% 6.92/7.23 ( ( ( find_P4815471733760996061it_nat @ P2 @ Xs )
% 6.92/7.23 = ( some_P7913643980934408916it_nat @ X ) )
% 6.92/7.23 = ( ? [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_s4069378446737875485it_nat @ Xs ) )
% 6.92/7.23 & ( P2 @ ( nth_Pr8687047199098054322it_nat @ Xs @ I ) )
% 6.92/7.23 & ( X
% 6.92/7.23 = ( nth_Pr8687047199098054322it_nat @ Xs @ I ) )
% 6.92/7.23 & ! [J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ J @ I )
% 6.92/7.23 => ~ ( P2 @ ( nth_Pr8687047199098054322it_nat @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find_Some_iff
% 6.92/7.23 thf(fact_5364_find__Some__iff,axiom,
% 6.92/7.23 ! [P2: produc8664842809031399944it_nat > $o,Xs: list_P626663023886443800it_nat,X: produc8664842809031399944it_nat] :
% 6.92/7.23 ( ( ( find_P5317947125398478060it_nat @ P2 @ Xs )
% 6.92/7.23 = ( some_P1914260805536162275it_nat @ X ) )
% 6.92/7.23 = ( ? [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_s4881146867534228396it_nat @ Xs ) )
% 6.92/7.23 & ( P2 @ ( nth_Pr2956344619228612545it_nat @ Xs @ I ) )
% 6.92/7.23 & ( X
% 6.92/7.23 = ( nth_Pr2956344619228612545it_nat @ Xs @ I ) )
% 6.92/7.23 & ! [J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ J @ I )
% 6.92/7.23 => ~ ( P2 @ ( nth_Pr2956344619228612545it_nat @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find_Some_iff
% 6.92/7.23 thf(fact_5365_find__Some__iff,axiom,
% 6.92/7.23 ! [P2: num > $o,Xs: list_num,X: num] :
% 6.92/7.23 ( ( ( find_num @ P2 @ Xs )
% 6.92/7.23 = ( some_num @ X ) )
% 6.92/7.23 = ( ? [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_size_list_num @ Xs ) )
% 6.92/7.23 & ( P2 @ ( nth_num @ Xs @ I ) )
% 6.92/7.23 & ( X
% 6.92/7.23 = ( nth_num @ Xs @ I ) )
% 6.92/7.23 & ! [J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ J @ I )
% 6.92/7.23 => ~ ( P2 @ ( nth_num @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find_Some_iff
% 6.92/7.23 thf(fact_5366_find__Some__iff,axiom,
% 6.92/7.23 ! [P2: nat > $o,Xs: list_nat,X: nat] :
% 6.92/7.23 ( ( ( find_nat @ P2 @ Xs )
% 6.92/7.23 = ( some_nat @ X ) )
% 6.92/7.23 = ( ? [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 & ( P2 @ ( nth_nat @ Xs @ I ) )
% 6.92/7.23 & ( X
% 6.92/7.23 = ( nth_nat @ Xs @ I ) )
% 6.92/7.23 & ! [J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ J @ I )
% 6.92/7.23 => ~ ( P2 @ ( nth_nat @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find_Some_iff
% 6.92/7.23 thf(fact_5367_find__Some__iff,axiom,
% 6.92/7.23 ! [P2: $o > $o,Xs: list_o,X: $o] :
% 6.92/7.23 ( ( ( find_o @ P2 @ Xs )
% 6.92/7.23 = ( some_o @ X ) )
% 6.92/7.23 = ( ? [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 & ( P2 @ ( nth_o @ Xs @ I ) )
% 6.92/7.23 & ( X
% 6.92/7.23 = ( nth_o @ Xs @ I ) )
% 6.92/7.23 & ! [J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ J @ I )
% 6.92/7.23 => ~ ( P2 @ ( nth_o @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find_Some_iff
% 6.92/7.23 thf(fact_5368_find__Some__iff,axiom,
% 6.92/7.23 ! [P2: int > $o,Xs: list_int,X: int] :
% 6.92/7.23 ( ( ( find_int @ P2 @ Xs )
% 6.92/7.23 = ( some_int @ X ) )
% 6.92/7.23 = ( ? [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 & ( P2 @ ( nth_int @ Xs @ I ) )
% 6.92/7.23 & ( X
% 6.92/7.23 = ( nth_int @ Xs @ I ) )
% 6.92/7.23 & ! [J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ J @ I )
% 6.92/7.23 => ~ ( P2 @ ( nth_int @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find_Some_iff
% 6.92/7.23 thf(fact_5369_find__Some__iff2,axiom,
% 6.92/7.23 ! [X: produc7388388658123137530it_nat,P2: produc7388388658123137530it_nat > $o,Xs: list_P7438302566501821706it_nat] :
% 6.92/7.23 ( ( ( some_P2818173045054083285it_nat @ X )
% 6.92/7.23 = ( find_P8943372834735446238it_nat @ P2 @ Xs ) )
% 6.92/7.23 = ( ? [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_s4572066133376685982it_nat @ Xs ) )
% 6.92/7.23 & ( P2 @ ( nth_Pr3591576263217728691it_nat @ Xs @ I ) )
% 6.92/7.23 & ( X
% 6.92/7.23 = ( nth_Pr3591576263217728691it_nat @ Xs @ I ) )
% 6.92/7.23 & ! [J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ J @ I )
% 6.92/7.23 => ~ ( P2 @ ( nth_Pr3591576263217728691it_nat @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find_Some_iff2
% 6.92/7.23 thf(fact_5370_find__Some__iff2,axiom,
% 6.92/7.23 ! [X: produc3260487557148687353it_nat,P2: produc3260487557148687353it_nat > $o,Xs: list_P6935614879863011209it_nat] :
% 6.92/7.23 ( ( ( some_P7913643980934408916it_nat @ X )
% 6.92/7.23 = ( find_P4815471733760996061it_nat @ P2 @ Xs ) )
% 6.92/7.23 = ( ? [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_s4069378446737875485it_nat @ Xs ) )
% 6.92/7.23 & ( P2 @ ( nth_Pr8687047199098054322it_nat @ Xs @ I ) )
% 6.92/7.23 & ( X
% 6.92/7.23 = ( nth_Pr8687047199098054322it_nat @ Xs @ I ) )
% 6.92/7.23 & ! [J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ J @ I )
% 6.92/7.23 => ~ ( P2 @ ( nth_Pr8687047199098054322it_nat @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find_Some_iff2
% 6.92/7.23 thf(fact_5371_find__Some__iff2,axiom,
% 6.92/7.23 ! [X: produc8664842809031399944it_nat,P2: produc8664842809031399944it_nat > $o,Xs: list_P626663023886443800it_nat] :
% 6.92/7.23 ( ( ( some_P1914260805536162275it_nat @ X )
% 6.92/7.23 = ( find_P5317947125398478060it_nat @ P2 @ Xs ) )
% 6.92/7.23 = ( ? [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_s4881146867534228396it_nat @ Xs ) )
% 6.92/7.23 & ( P2 @ ( nth_Pr2956344619228612545it_nat @ Xs @ I ) )
% 6.92/7.23 & ( X
% 6.92/7.23 = ( nth_Pr2956344619228612545it_nat @ Xs @ I ) )
% 6.92/7.23 & ! [J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ J @ I )
% 6.92/7.23 => ~ ( P2 @ ( nth_Pr2956344619228612545it_nat @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find_Some_iff2
% 6.92/7.23 thf(fact_5372_find__Some__iff2,axiom,
% 6.92/7.23 ! [X: num,P2: num > $o,Xs: list_num] :
% 6.92/7.23 ( ( ( some_num @ X )
% 6.92/7.23 = ( find_num @ P2 @ Xs ) )
% 6.92/7.23 = ( ? [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_size_list_num @ Xs ) )
% 6.92/7.23 & ( P2 @ ( nth_num @ Xs @ I ) )
% 6.92/7.23 & ( X
% 6.92/7.23 = ( nth_num @ Xs @ I ) )
% 6.92/7.23 & ! [J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ J @ I )
% 6.92/7.23 => ~ ( P2 @ ( nth_num @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find_Some_iff2
% 6.92/7.23 thf(fact_5373_find__Some__iff2,axiom,
% 6.92/7.23 ! [X: nat,P2: nat > $o,Xs: list_nat] :
% 6.92/7.23 ( ( ( some_nat @ X )
% 6.92/7.23 = ( find_nat @ P2 @ Xs ) )
% 6.92/7.23 = ( ? [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 6.92/7.23 & ( P2 @ ( nth_nat @ Xs @ I ) )
% 6.92/7.23 & ( X
% 6.92/7.23 = ( nth_nat @ Xs @ I ) )
% 6.92/7.23 & ! [J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ J @ I )
% 6.92/7.23 => ~ ( P2 @ ( nth_nat @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find_Some_iff2
% 6.92/7.23 thf(fact_5374_find__Some__iff2,axiom,
% 6.92/7.23 ! [X: $o,P2: $o > $o,Xs: list_o] :
% 6.92/7.23 ( ( ( some_o @ X )
% 6.92/7.23 = ( find_o @ P2 @ Xs ) )
% 6.92/7.23 = ( ? [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 6.92/7.23 & ( P2 @ ( nth_o @ Xs @ I ) )
% 6.92/7.23 & ( X
% 6.92/7.23 = ( nth_o @ Xs @ I ) )
% 6.92/7.23 & ! [J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ J @ I )
% 6.92/7.23 => ~ ( P2 @ ( nth_o @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find_Some_iff2
% 6.92/7.23 thf(fact_5375_find__Some__iff2,axiom,
% 6.92/7.23 ! [X: int,P2: int > $o,Xs: list_int] :
% 6.92/7.23 ( ( ( some_int @ X )
% 6.92/7.23 = ( find_int @ P2 @ Xs ) )
% 6.92/7.23 = ( ? [I: nat] :
% 6.92/7.23 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 6.92/7.23 & ( P2 @ ( nth_int @ Xs @ I ) )
% 6.92/7.23 & ( X
% 6.92/7.23 = ( nth_int @ Xs @ I ) )
% 6.92/7.23 & ! [J: nat] :
% 6.92/7.23 ( ( ord_less_nat @ J @ I )
% 6.92/7.23 => ~ ( P2 @ ( nth_int @ Xs @ J ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find_Some_iff2
% 6.92/7.23 thf(fact_5376_divide__le__eq__numeral_I2_J,axiom,
% 6.92/7.23 ! [B: rat,C2: rat,W2: num] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 6.92/7.23 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.23 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 6.92/7.23 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.23 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.23 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 6.92/7.23 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.23 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % divide_le_eq_numeral(2)
% 6.92/7.23 thf(fact_5377_le__divide__eq__numeral_I2_J,axiom,
% 6.92/7.23 ! [W2: num,B: rat,C2: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C2 ) )
% 6.92/7.23 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.23 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 6.92/7.23 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.23 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.23 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 6.92/7.23 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.23 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % le_divide_eq_numeral(2)
% 6.92/7.23 thf(fact_5378_numeral__le__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N2 ) )
% 6.92/7.23 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_le_iff
% 6.92/7.23 thf(fact_5379_numeral__le__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 6.92/7.23 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_le_iff
% 6.92/7.23 thf(fact_5380_numeral__le__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 6.92/7.23 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_le_iff
% 6.92/7.23 thf(fact_5381_numeral__le__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 6.92/7.23 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_le_iff
% 6.92/7.23 thf(fact_5382_numeral__le__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 6.92/7.23 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_le_iff
% 6.92/7.23 thf(fact_5383_numeral__less__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 6.92/7.23 = ( ord_less_num @ M @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_less_iff
% 6.92/7.23 thf(fact_5384_numeral__less__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 6.92/7.23 = ( ord_less_num @ M @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_less_iff
% 6.92/7.23 thf(fact_5385_numeral__less__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 6.92/7.23 = ( ord_less_num @ M @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_less_iff
% 6.92/7.23 thf(fact_5386_numeral__less__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N2 ) )
% 6.92/7.23 = ( ord_less_num @ M @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_less_iff
% 6.92/7.23 thf(fact_5387_numeral__less__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 6.92/7.23 = ( ord_less_num @ M @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_less_iff
% 6.92/7.23 thf(fact_5388_numeral__plus__numeral,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 6.92/7.23 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_plus_numeral
% 6.92/7.23 thf(fact_5389_numeral__plus__numeral,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 6.92/7.23 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_plus_numeral
% 6.92/7.23 thf(fact_5390_numeral__plus__numeral,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 6.92/7.23 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_plus_numeral
% 6.92/7.23 thf(fact_5391_numeral__plus__numeral,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N2 ) )
% 6.92/7.23 = ( numera5444537566228673987atural @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_plus_numeral
% 6.92/7.23 thf(fact_5392_numeral__plus__numeral,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 6.92/7.23 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_plus_numeral
% 6.92/7.23 thf(fact_5393_add__numeral__left,axiom,
% 6.92/7.23 ! [V: num,W2: num,Z3: rat] :
% 6.92/7.23 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W2 ) @ Z3 ) )
% 6.92/7.23 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W2 ) ) @ Z3 ) ) ).
% 6.92/7.23
% 6.92/7.23 % add_numeral_left
% 6.92/7.23 thf(fact_5394_add__numeral__left,axiom,
% 6.92/7.23 ! [V: num,W2: num,Z3: nat] :
% 6.92/7.23 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W2 ) @ Z3 ) )
% 6.92/7.23 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W2 ) ) @ Z3 ) ) ).
% 6.92/7.23
% 6.92/7.23 % add_numeral_left
% 6.92/7.23 thf(fact_5395_add__numeral__left,axiom,
% 6.92/7.23 ! [V: num,W2: num,Z3: int] :
% 6.92/7.23 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W2 ) @ Z3 ) )
% 6.92/7.23 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W2 ) ) @ Z3 ) ) ).
% 6.92/7.23
% 6.92/7.23 % add_numeral_left
% 6.92/7.23 thf(fact_5396_add__numeral__left,axiom,
% 6.92/7.23 ! [V: num,W2: num,Z3: code_natural] :
% 6.92/7.23 ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ V ) @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ W2 ) @ Z3 ) )
% 6.92/7.23 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ ( plus_plus_num @ V @ W2 ) ) @ Z3 ) ) ).
% 6.92/7.23
% 6.92/7.23 % add_numeral_left
% 6.92/7.23 thf(fact_5397_add__numeral__left,axiom,
% 6.92/7.23 ! [V: num,W2: num,Z3: code_integer] :
% 6.92/7.23 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ W2 ) @ Z3 ) )
% 6.92/7.23 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W2 ) ) @ Z3 ) ) ).
% 6.92/7.23
% 6.92/7.23 % add_numeral_left
% 6.92/7.23 thf(fact_5398_power__add__numeral2,axiom,
% 6.92/7.23 ! [A: assn,M: num,N2: num,B: assn] :
% 6.92/7.23 ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 6.92/7.23 = ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 6.92/7.23
% 6.92/7.23 % power_add_numeral2
% 6.92/7.23 thf(fact_5399_power__add__numeral2,axiom,
% 6.92/7.23 ! [A: rat,M: num,N2: num,B: rat] :
% 6.92/7.23 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 6.92/7.23 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 6.92/7.23
% 6.92/7.23 % power_add_numeral2
% 6.92/7.23 thf(fact_5400_power__add__numeral2,axiom,
% 6.92/7.23 ! [A: nat,M: num,N2: num,B: nat] :
% 6.92/7.23 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 6.92/7.23 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 6.92/7.23
% 6.92/7.23 % power_add_numeral2
% 6.92/7.23 thf(fact_5401_power__add__numeral2,axiom,
% 6.92/7.23 ! [A: int,M: num,N2: num,B: int] :
% 6.92/7.23 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 6.92/7.23 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 6.92/7.23
% 6.92/7.23 % power_add_numeral2
% 6.92/7.23 thf(fact_5402_power__add__numeral,axiom,
% 6.92/7.23 ! [A: assn,M: num,N2: num] :
% 6.92/7.23 ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 6.92/7.23 = ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % power_add_numeral
% 6.92/7.23 thf(fact_5403_power__add__numeral,axiom,
% 6.92/7.23 ! [A: rat,M: num,N2: num] :
% 6.92/7.23 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 6.92/7.23 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % power_add_numeral
% 6.92/7.23 thf(fact_5404_power__add__numeral,axiom,
% 6.92/7.23 ! [A: nat,M: num,N2: num] :
% 6.92/7.23 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 6.92/7.23 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % power_add_numeral
% 6.92/7.23 thf(fact_5405_power__add__numeral,axiom,
% 6.92/7.23 ! [A: int,M: num,N2: num] :
% 6.92/7.23 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 6.92/7.23 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % power_add_numeral
% 6.92/7.23 thf(fact_5406_zip__eq__zip__same__len,axiom,
% 6.92/7.23 ! [A: list_nat,B: list_nat,A2: list_nat,B2: list_nat] :
% 6.92/7.23 ( ( ( size_size_list_nat @ A )
% 6.92/7.23 = ( size_size_list_nat @ B ) )
% 6.92/7.23 => ( ( ( size_size_list_nat @ A2 )
% 6.92/7.23 = ( size_size_list_nat @ B2 ) )
% 6.92/7.23 => ( ( ( zip_nat_nat @ A @ B )
% 6.92/7.23 = ( zip_nat_nat @ A2 @ B2 ) )
% 6.92/7.23 = ( ( A = A2 )
% 6.92/7.23 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_zip_same_len
% 6.92/7.23 thf(fact_5407_zip__eq__zip__same__len,axiom,
% 6.92/7.23 ! [A: list_nat,B: list_o,A2: list_nat,B2: list_o] :
% 6.92/7.23 ( ( ( size_size_list_nat @ A )
% 6.92/7.23 = ( size_size_list_o @ B ) )
% 6.92/7.23 => ( ( ( size_size_list_nat @ A2 )
% 6.92/7.23 = ( size_size_list_o @ B2 ) )
% 6.92/7.23 => ( ( ( zip_nat_o @ A @ B )
% 6.92/7.23 = ( zip_nat_o @ A2 @ B2 ) )
% 6.92/7.23 = ( ( A = A2 )
% 6.92/7.23 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_zip_same_len
% 6.92/7.23 thf(fact_5408_zip__eq__zip__same__len,axiom,
% 6.92/7.23 ! [A: list_nat,B: list_int,A2: list_nat,B2: list_int] :
% 6.92/7.23 ( ( ( size_size_list_nat @ A )
% 6.92/7.23 = ( size_size_list_int @ B ) )
% 6.92/7.23 => ( ( ( size_size_list_nat @ A2 )
% 6.92/7.23 = ( size_size_list_int @ B2 ) )
% 6.92/7.23 => ( ( ( zip_nat_int @ A @ B )
% 6.92/7.23 = ( zip_nat_int @ A2 @ B2 ) )
% 6.92/7.23 = ( ( A = A2 )
% 6.92/7.23 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_zip_same_len
% 6.92/7.23 thf(fact_5409_zip__eq__zip__same__len,axiom,
% 6.92/7.23 ! [A: list_o,B: list_nat,A2: list_o,B2: list_nat] :
% 6.92/7.23 ( ( ( size_size_list_o @ A )
% 6.92/7.23 = ( size_size_list_nat @ B ) )
% 6.92/7.23 => ( ( ( size_size_list_o @ A2 )
% 6.92/7.23 = ( size_size_list_nat @ B2 ) )
% 6.92/7.23 => ( ( ( zip_o_nat @ A @ B )
% 6.92/7.23 = ( zip_o_nat @ A2 @ B2 ) )
% 6.92/7.23 = ( ( A = A2 )
% 6.92/7.23 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_zip_same_len
% 6.92/7.23 thf(fact_5410_zip__eq__zip__same__len,axiom,
% 6.92/7.23 ! [A: list_o,B: list_o,A2: list_o,B2: list_o] :
% 6.92/7.23 ( ( ( size_size_list_o @ A )
% 6.92/7.23 = ( size_size_list_o @ B ) )
% 6.92/7.23 => ( ( ( size_size_list_o @ A2 )
% 6.92/7.23 = ( size_size_list_o @ B2 ) )
% 6.92/7.23 => ( ( ( zip_o_o @ A @ B )
% 6.92/7.23 = ( zip_o_o @ A2 @ B2 ) )
% 6.92/7.23 = ( ( A = A2 )
% 6.92/7.23 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_zip_same_len
% 6.92/7.23 thf(fact_5411_zip__eq__zip__same__len,axiom,
% 6.92/7.23 ! [A: list_o,B: list_int,A2: list_o,B2: list_int] :
% 6.92/7.23 ( ( ( size_size_list_o @ A )
% 6.92/7.23 = ( size_size_list_int @ B ) )
% 6.92/7.23 => ( ( ( size_size_list_o @ A2 )
% 6.92/7.23 = ( size_size_list_int @ B2 ) )
% 6.92/7.23 => ( ( ( zip_o_int @ A @ B )
% 6.92/7.23 = ( zip_o_int @ A2 @ B2 ) )
% 6.92/7.23 = ( ( A = A2 )
% 6.92/7.23 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_zip_same_len
% 6.92/7.23 thf(fact_5412_zip__eq__zip__same__len,axiom,
% 6.92/7.23 ! [A: list_int,B: list_nat,A2: list_int,B2: list_nat] :
% 6.92/7.23 ( ( ( size_size_list_int @ A )
% 6.92/7.23 = ( size_size_list_nat @ B ) )
% 6.92/7.23 => ( ( ( size_size_list_int @ A2 )
% 6.92/7.23 = ( size_size_list_nat @ B2 ) )
% 6.92/7.23 => ( ( ( zip_int_nat @ A @ B )
% 6.92/7.23 = ( zip_int_nat @ A2 @ B2 ) )
% 6.92/7.23 = ( ( A = A2 )
% 6.92/7.23 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_zip_same_len
% 6.92/7.23 thf(fact_5413_zip__eq__zip__same__len,axiom,
% 6.92/7.23 ! [A: list_int,B: list_o,A2: list_int,B2: list_o] :
% 6.92/7.23 ( ( ( size_size_list_int @ A )
% 6.92/7.23 = ( size_size_list_o @ B ) )
% 6.92/7.23 => ( ( ( size_size_list_int @ A2 )
% 6.92/7.23 = ( size_size_list_o @ B2 ) )
% 6.92/7.23 => ( ( ( zip_int_o @ A @ B )
% 6.92/7.23 = ( zip_int_o @ A2 @ B2 ) )
% 6.92/7.23 = ( ( A = A2 )
% 6.92/7.23 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_zip_same_len
% 6.92/7.23 thf(fact_5414_zip__eq__zip__same__len,axiom,
% 6.92/7.23 ! [A: list_int,B: list_int,A2: list_int,B2: list_int] :
% 6.92/7.23 ( ( ( size_size_list_int @ A )
% 6.92/7.23 = ( size_size_list_int @ B ) )
% 6.92/7.23 => ( ( ( size_size_list_int @ A2 )
% 6.92/7.23 = ( size_size_list_int @ B2 ) )
% 6.92/7.23 => ( ( ( zip_int_int @ A @ B )
% 6.92/7.23 = ( zip_int_int @ A2 @ B2 ) )
% 6.92/7.23 = ( ( A = A2 )
% 6.92/7.23 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_zip_same_len
% 6.92/7.23 thf(fact_5415_neg__numeral__le__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 6.92/7.23 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 6.92/7.23
% 6.92/7.23 % neg_numeral_le_iff
% 6.92/7.23 thf(fact_5416_neg__numeral__le__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 6.92/7.23 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 6.92/7.23
% 6.92/7.23 % neg_numeral_le_iff
% 6.92/7.23 thf(fact_5417_neg__numeral__le__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.92/7.23 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 6.92/7.23
% 6.92/7.23 % neg_numeral_le_iff
% 6.92/7.23 thf(fact_5418_distrib__left__numeral,axiom,
% 6.92/7.23 ! [V: num,B: rat,C2: rat] :
% 6.92/7.23 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C2 ) )
% 6.92/7.23 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % distrib_left_numeral
% 6.92/7.23 thf(fact_5419_distrib__left__numeral,axiom,
% 6.92/7.23 ! [V: num,B: nat,C2: nat] :
% 6.92/7.23 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C2 ) )
% 6.92/7.23 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % distrib_left_numeral
% 6.92/7.23 thf(fact_5420_distrib__left__numeral,axiom,
% 6.92/7.23 ! [V: num,B: int,C2: int] :
% 6.92/7.23 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C2 ) )
% 6.92/7.23 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % distrib_left_numeral
% 6.92/7.23 thf(fact_5421_distrib__left__numeral,axiom,
% 6.92/7.23 ! [V: num,B: code_natural,C2: code_natural] :
% 6.92/7.23 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ ( plus_p4538020629002901425atural @ B @ C2 ) )
% 6.92/7.23 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ B ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ C2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % distrib_left_numeral
% 6.92/7.23 thf(fact_5422_distrib__left__numeral,axiom,
% 6.92/7.23 ! [V: num,B: code_integer,C2: code_integer] :
% 6.92/7.23 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ B @ C2 ) )
% 6.92/7.23 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % distrib_left_numeral
% 6.92/7.23 thf(fact_5423_distrib__right__numeral,axiom,
% 6.92/7.23 ! [A: rat,B: rat,V: num] :
% 6.92/7.23 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 6.92/7.23 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % distrib_right_numeral
% 6.92/7.23 thf(fact_5424_distrib__right__numeral,axiom,
% 6.92/7.23 ! [A: nat,B: nat,V: num] :
% 6.92/7.23 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 6.92/7.23 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % distrib_right_numeral
% 6.92/7.23 thf(fact_5425_distrib__right__numeral,axiom,
% 6.92/7.23 ! [A: int,B: int,V: num] :
% 6.92/7.23 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 6.92/7.23 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % distrib_right_numeral
% 6.92/7.23 thf(fact_5426_distrib__right__numeral,axiom,
% 6.92/7.23 ! [A: code_natural,B: code_natural,V: num] :
% 6.92/7.23 ( ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A @ B ) @ ( numera5444537566228673987atural @ V ) )
% 6.92/7.23 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ V ) ) @ ( times_2397367101498566445atural @ B @ ( numera5444537566228673987atural @ V ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % distrib_right_numeral
% 6.92/7.23 thf(fact_5427_distrib__right__numeral,axiom,
% 6.92/7.23 ! [A: code_integer,B: code_integer,V: num] :
% 6.92/7.23 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 6.92/7.23 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % distrib_right_numeral
% 6.92/7.23 thf(fact_5428_neg__numeral__less__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.92/7.23 = ( ord_less_num @ N2 @ M ) ) ).
% 6.92/7.23
% 6.92/7.23 % neg_numeral_less_iff
% 6.92/7.23 thf(fact_5429_neg__numeral__less__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 6.92/7.23 = ( ord_less_num @ N2 @ M ) ) ).
% 6.92/7.23
% 6.92/7.23 % neg_numeral_less_iff
% 6.92/7.23 thf(fact_5430_neg__numeral__less__iff,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 6.92/7.23 = ( ord_less_num @ N2 @ M ) ) ).
% 6.92/7.23
% 6.92/7.23 % neg_numeral_less_iff
% 6.92/7.23 thf(fact_5431_add__neg__numeral__simps_I3_J,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.92/7.23 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % add_neg_numeral_simps(3)
% 6.92/7.23 thf(fact_5432_add__neg__numeral__simps_I3_J,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 6.92/7.23 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % add_neg_numeral_simps(3)
% 6.92/7.23 thf(fact_5433_add__neg__numeral__simps_I3_J,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 6.92/7.23 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % add_neg_numeral_simps(3)
% 6.92/7.23 thf(fact_5434_semiring__norm_I168_J,axiom,
% 6.92/7.23 ! [V: num,W2: num,Y: int] :
% 6.92/7.23 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y ) )
% 6.92/7.23 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 6.92/7.23
% 6.92/7.23 % semiring_norm(168)
% 6.92/7.23 thf(fact_5435_semiring__norm_I168_J,axiom,
% 6.92/7.23 ! [V: num,W2: num,Y: code_integer] :
% 6.92/7.23 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y ) )
% 6.92/7.23 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 6.92/7.23
% 6.92/7.23 % semiring_norm(168)
% 6.92/7.23 thf(fact_5436_semiring__norm_I168_J,axiom,
% 6.92/7.23 ! [V: num,W2: num,Y: rat] :
% 6.92/7.23 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y ) )
% 6.92/7.23 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W2 ) ) ) @ Y ) ) ).
% 6.92/7.23
% 6.92/7.23 % semiring_norm(168)
% 6.92/7.23 thf(fact_5437_diff__numeral__simps_I3_J,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 6.92/7.23 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % diff_numeral_simps(3)
% 6.92/7.23 thf(fact_5438_diff__numeral__simps_I3_J,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 6.92/7.23 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % diff_numeral_simps(3)
% 6.92/7.23 thf(fact_5439_diff__numeral__simps_I3_J,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 6.92/7.23 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % diff_numeral_simps(3)
% 6.92/7.23 thf(fact_5440_diff__numeral__simps_I2_J,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.92/7.23 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % diff_numeral_simps(2)
% 6.92/7.23 thf(fact_5441_diff__numeral__simps_I2_J,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 6.92/7.23 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % diff_numeral_simps(2)
% 6.92/7.23 thf(fact_5442_diff__numeral__simps_I2_J,axiom,
% 6.92/7.23 ! [M: num,N2: num] :
% 6.92/7.23 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 6.92/7.23 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % diff_numeral_simps(2)
% 6.92/7.23 thf(fact_5443_zip__Cons__Cons,axiom,
% 6.92/7.23 ! [X: int,Xs: list_int,Y: nat,Ys3: list_nat] :
% 6.92/7.23 ( ( zip_int_nat @ ( cons_int @ X @ Xs ) @ ( cons_nat @ Y @ Ys3 ) )
% 6.92/7.23 = ( cons_P7512249878480867347nt_nat @ ( product_Pair_int_nat @ X @ Y ) @ ( zip_int_nat @ Xs @ Ys3 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_Cons_Cons
% 6.92/7.23 thf(fact_5444_zip__Cons__Cons,axiom,
% 6.92/7.23 ! [X: nat,Xs: list_nat,Y: int,Ys3: list_int] :
% 6.92/7.23 ( ( zip_nat_int @ ( cons_nat @ X @ Xs ) @ ( cons_int @ Y @ Ys3 ) )
% 6.92/7.23 = ( cons_P2335045147070616083at_int @ ( product_Pair_nat_int @ X @ Y ) @ ( zip_nat_int @ Xs @ Ys3 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_Cons_Cons
% 6.92/7.23 thf(fact_5445_zip__Cons__Cons,axiom,
% 6.92/7.23 ! [X: nat,Xs: list_nat,Y: nat,Ys3: list_nat] :
% 6.92/7.23 ( ( zip_nat_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Ys3 ) )
% 6.92/7.23 = ( cons_P6512896166579812791at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( zip_nat_nat @ Xs @ Ys3 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_Cons_Cons
% 6.92/7.23 thf(fact_5446_zip__Cons__Cons,axiom,
% 6.92/7.23 ! [X: int,Xs: list_int,Y: int,Ys3: list_int] :
% 6.92/7.23 ( ( zip_int_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ Y @ Ys3 ) )
% 6.92/7.23 = ( cons_P3334398858971670639nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( zip_int_int @ Xs @ Ys3 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_Cons_Cons
% 6.92/7.23 thf(fact_5447_zip__Cons__Cons,axiom,
% 6.92/7.23 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o,Y: produc3658429121746597890et_nat,Ys3: list_P9062070895058802706et_nat] :
% 6.92/7.23 ( ( zip_Pr7134870689397686104et_nat @ ( cons_P6219271836124797827_nat_o @ X @ Xs ) @ ( cons_P2869003950965171916et_nat @ Y @ Ys3 ) )
% 6.92/7.23 = ( cons_P3419706843779801160et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ ( zip_Pr7134870689397686104et_nat @ Xs @ Ys3 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_Cons_Cons
% 6.92/7.23 thf(fact_5448_zip__Cons__Cons,axiom,
% 6.92/7.23 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o,Y: produc3925858234332021118et_nat,Ys3: list_P2321686559999237006et_nat] :
% 6.92/7.23 ( ( zip_Pr8136144321567152340et_nat @ ( cons_P6219271836124797827_nat_o @ X @ Xs ) @ ( cons_P3419706843779801160et_nat @ Y @ Ys3 ) )
% 6.92/7.23 = ( cons_P6329468272379687876et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ ( zip_Pr8136144321567152340et_nat @ Xs @ Ys3 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_Cons_Cons
% 6.92/7.23 thf(fact_5449_zip__Cons__Cons,axiom,
% 6.92/7.23 ! [X: b,Xs: list_b,Y: produc6653097349344004940it_nat,Ys3: list_P131111800688179804it_nat] :
% 6.92/7.23 ( ( zip_b_5987488365222434772it_nat @ ( cons_b @ X @ Xs ) @ ( cons_P7873165156130251286it_nat @ Y @ Ys3 ) )
% 6.92/7.23 = ( cons_P6467324686191779524it_nat @ ( produc4082563078715348724it_nat @ X @ Y ) @ ( zip_b_5987488365222434772it_nat @ Xs @ Ys3 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_Cons_Cons
% 6.92/7.23 thf(fact_5450_zip__Cons__Cons,axiom,
% 6.92/7.23 ! [X: a,Xs: list_a,Y: produc6653097349344004940it_nat,Ys3: list_P131111800688179804it_nat] :
% 6.92/7.23 ( ( zip_a_1859587264247984595it_nat @ ( cons_a @ X @ Xs ) @ ( cons_P7873165156130251286it_nat @ Y @ Ys3 ) )
% 6.92/7.23 = ( cons_P2339423585217329347it_nat @ ( produc9178034014595674355it_nat @ X @ Y ) @ ( zip_a_1859587264247984595it_nat @ Xs @ Ys3 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_Cons_Cons
% 6.92/7.23 thf(fact_5451_le__divide__eq__numeral1_I1_J,axiom,
% 6.92/7.23 ! [A: rat,B: rat,W2: num] :
% 6.92/7.23 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 6.92/7.23 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 6.92/7.23
% 6.92/7.23 % le_divide_eq_numeral1(1)
% 6.92/7.23 thf(fact_5452_divide__le__eq__numeral1_I1_J,axiom,
% 6.92/7.23 ! [B: rat,W2: num,A: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 6.92/7.23 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % divide_le_eq_numeral1(1)
% 6.92/7.23 thf(fact_5453_less__divide__eq__numeral1_I1_J,axiom,
% 6.92/7.23 ! [A: rat,B: rat,W2: num] :
% 6.92/7.23 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 6.92/7.23 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 6.92/7.23
% 6.92/7.23 % less_divide_eq_numeral1(1)
% 6.92/7.23 thf(fact_5454_divide__less__eq__numeral1_I1_J,axiom,
% 6.92/7.23 ! [B: rat,W2: num,A: rat] :
% 6.92/7.23 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 6.92/7.23 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % divide_less_eq_numeral1(1)
% 6.92/7.23 thf(fact_5455_le__divide__eq__numeral1_I2_J,axiom,
% 6.92/7.23 ! [A: rat,B: rat,W2: num] :
% 6.92/7.23 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 6.92/7.23 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % le_divide_eq_numeral1(2)
% 6.92/7.23 thf(fact_5456_divide__le__eq__numeral1_I2_J,axiom,
% 6.92/7.23 ! [B: rat,W2: num,A: rat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 6.92/7.23 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 6.92/7.23
% 6.92/7.23 % divide_le_eq_numeral1(2)
% 6.92/7.23 thf(fact_5457_less__divide__eq__numeral1_I2_J,axiom,
% 6.92/7.23 ! [A: rat,B: rat,W2: num] :
% 6.92/7.23 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 6.92/7.23 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % less_divide_eq_numeral1(2)
% 6.92/7.23 thf(fact_5458_divide__less__eq__numeral1_I2_J,axiom,
% 6.92/7.23 ! [B: rat,W2: num,A: rat] :
% 6.92/7.23 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 6.92/7.23 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 6.92/7.23
% 6.92/7.23 % divide_less_eq_numeral1(2)
% 6.92/7.23 thf(fact_5459_nat__less__numeral__power__cancel__iff,axiom,
% 6.92/7.23 ! [A: int,X: num,N2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 6.92/7.23 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nat_less_numeral_power_cancel_iff
% 6.92/7.23 thf(fact_5460_numeral__power__less__nat__cancel__iff,axiom,
% 6.92/7.23 ! [X: num,N2: nat,A: int] :
% 6.92/7.23 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) @ ( nat2 @ A ) )
% 6.92/7.23 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_power_less_nat_cancel_iff
% 6.92/7.23 thf(fact_5461_nat__le__numeral__power__cancel__iff,axiom,
% 6.92/7.23 ! [A: int,X: num,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 6.92/7.23 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nat_le_numeral_power_cancel_iff
% 6.92/7.23 thf(fact_5462_numeral__power__le__nat__cancel__iff,axiom,
% 6.92/7.23 ! [X: num,N2: nat,A: int] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) @ ( nat2 @ A ) )
% 6.92/7.23 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_power_le_nat_cancel_iff
% 6.92/7.23 thf(fact_5463_of__nat__less__numeral__power__cancel__iff,axiom,
% 6.92/7.23 ! [X: nat,I2: num,N2: nat] :
% 6.92/7.23 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) )
% 6.92/7.23 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % of_nat_less_numeral_power_cancel_iff
% 6.92/7.23 thf(fact_5464_of__nat__less__numeral__power__cancel__iff,axiom,
% 6.92/7.23 ! [X: nat,I2: num,N2: nat] :
% 6.92/7.23 ( ( ord_le5570908160329646204atural @ ( semiri3763490453095760265atural @ X ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I2 ) @ N2 ) )
% 6.92/7.23 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % of_nat_less_numeral_power_cancel_iff
% 6.92/7.23 thf(fact_5465_of__nat__less__numeral__power__cancel__iff,axiom,
% 6.92/7.23 ! [X: nat,I2: num,N2: nat] :
% 6.92/7.23 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) )
% 6.92/7.23 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % of_nat_less_numeral_power_cancel_iff
% 6.92/7.23 thf(fact_5466_of__nat__less__numeral__power__cancel__iff,axiom,
% 6.92/7.23 ! [X: nat,I2: num,N2: nat] :
% 6.92/7.23 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) )
% 6.92/7.23 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % of_nat_less_numeral_power_cancel_iff
% 6.92/7.23 thf(fact_5467_of__nat__less__numeral__power__cancel__iff,axiom,
% 6.92/7.23 ! [X: nat,I2: num,N2: nat] :
% 6.92/7.23 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) )
% 6.92/7.23 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % of_nat_less_numeral_power_cancel_iff
% 6.92/7.23 thf(fact_5468_numeral__power__less__of__nat__cancel__iff,axiom,
% 6.92/7.23 ! [I2: num,N2: nat,X: nat] :
% 6.92/7.23 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 6.92/7.23 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_power_less_of_nat_cancel_iff
% 6.92/7.23 thf(fact_5469_numeral__power__less__of__nat__cancel__iff,axiom,
% 6.92/7.23 ! [I2: num,N2: nat,X: nat] :
% 6.92/7.23 ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I2 ) @ N2 ) @ ( semiri3763490453095760265atural @ X ) )
% 6.92/7.23 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_power_less_of_nat_cancel_iff
% 6.92/7.23 thf(fact_5470_numeral__power__less__of__nat__cancel__iff,axiom,
% 6.92/7.23 ! [I2: num,N2: nat,X: nat] :
% 6.92/7.23 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 6.92/7.23 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_power_less_of_nat_cancel_iff
% 6.92/7.23 thf(fact_5471_numeral__power__less__of__nat__cancel__iff,axiom,
% 6.92/7.23 ! [I2: num,N2: nat,X: nat] :
% 6.92/7.23 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 6.92/7.23 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_power_less_of_nat_cancel_iff
% 6.92/7.23 thf(fact_5472_numeral__power__less__of__nat__cancel__iff,axiom,
% 6.92/7.23 ! [I2: num,N2: nat,X: nat] :
% 6.92/7.23 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 6.92/7.23 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_power_less_of_nat_cancel_iff
% 6.92/7.23 thf(fact_5473_of__nat__le__numeral__power__cancel__iff,axiom,
% 6.92/7.23 ! [X: nat,I2: num,N2: nat] :
% 6.92/7.23 ( ( ord_le1926595141338095240atural @ ( semiri3763490453095760265atural @ X ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I2 ) @ N2 ) )
% 6.92/7.23 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % of_nat_le_numeral_power_cancel_iff
% 6.92/7.23 thf(fact_5474_of__nat__le__numeral__power__cancel__iff,axiom,
% 6.92/7.23 ! [X: nat,I2: num,N2: nat] :
% 6.92/7.23 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) )
% 6.92/7.23 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % of_nat_le_numeral_power_cancel_iff
% 6.92/7.23 thf(fact_5475_of__nat__le__numeral__power__cancel__iff,axiom,
% 6.92/7.23 ! [X: nat,I2: num,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) )
% 6.92/7.23 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % of_nat_le_numeral_power_cancel_iff
% 6.92/7.23 thf(fact_5476_of__nat__le__numeral__power__cancel__iff,axiom,
% 6.92/7.23 ! [X: nat,I2: num,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) )
% 6.92/7.23 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % of_nat_le_numeral_power_cancel_iff
% 6.92/7.23 thf(fact_5477_of__nat__le__numeral__power__cancel__iff,axiom,
% 6.92/7.23 ! [X: nat,I2: num,N2: nat] :
% 6.92/7.23 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) )
% 6.92/7.23 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % of_nat_le_numeral_power_cancel_iff
% 6.92/7.23 thf(fact_5478_numeral__power__le__of__nat__cancel__iff,axiom,
% 6.92/7.23 ! [I2: num,N2: nat,X: nat] :
% 6.92/7.23 ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I2 ) @ N2 ) @ ( semiri3763490453095760265atural @ X ) )
% 6.92/7.23 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_power_le_of_nat_cancel_iff
% 6.92/7.23 thf(fact_5479_numeral__power__le__of__nat__cancel__iff,axiom,
% 6.92/7.23 ! [I2: num,N2: nat,X: nat] :
% 6.92/7.23 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 6.92/7.23 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_power_le_of_nat_cancel_iff
% 6.92/7.23 thf(fact_5480_numeral__power__le__of__nat__cancel__iff,axiom,
% 6.92/7.23 ! [I2: num,N2: nat,X: nat] :
% 6.92/7.23 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 6.92/7.23 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_power_le_of_nat_cancel_iff
% 6.92/7.23 thf(fact_5481_numeral__power__le__of__nat__cancel__iff,axiom,
% 6.92/7.23 ! [I2: num,N2: nat,X: nat] :
% 6.92/7.23 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 6.92/7.23 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_power_le_of_nat_cancel_iff
% 6.92/7.23 thf(fact_5482_numeral__power__le__of__nat__cancel__iff,axiom,
% 6.92/7.23 ! [I2: num,N2: nat,X: nat] :
% 6.92/7.23 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 6.92/7.23 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 6.92/7.23
% 6.92/7.23 % numeral_power_le_of_nat_cancel_iff
% 6.92/7.23 thf(fact_5483_nat__numeral__as__int,axiom,
% 6.92/7.23 ( numeral_numeral_nat
% 6.92/7.23 = ( ^ [I: num] : ( nat2 @ ( numeral_numeral_int @ I ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % nat_numeral_as_int
% 6.92/7.23 thf(fact_5484_int__ops_I3_J,axiom,
% 6.92/7.23 ! [N2: num] :
% 6.92/7.23 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 6.92/7.23 = ( numeral_numeral_int @ N2 ) ) ).
% 6.92/7.23
% 6.92/7.23 % int_ops(3)
% 6.92/7.23 thf(fact_5485_list__tail__coinc,axiom,
% 6.92/7.23 ! [N1: int,R12: list_int,N22: int,R23: list_int] :
% 6.92/7.23 ( ( ( cons_int @ N1 @ R12 )
% 6.92/7.23 = ( cons_int @ N22 @ R23 ) )
% 6.92/7.23 => ( ( N1 = N22 )
% 6.92/7.23 & ( R12 = R23 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % list_tail_coinc
% 6.92/7.23 thf(fact_5486_list__tail__coinc,axiom,
% 6.92/7.23 ! [N1: nat,R12: list_nat,N22: nat,R23: list_nat] :
% 6.92/7.23 ( ( ( cons_nat @ N1 @ R12 )
% 6.92/7.23 = ( cons_nat @ N22 @ R23 ) )
% 6.92/7.23 => ( ( N1 = N22 )
% 6.92/7.23 & ( R12 = R23 ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % list_tail_coinc
% 6.92/7.23 thf(fact_5487_zip__eq__ConsE,axiom,
% 6.92/7.23 ! [Xs: list_int,Ys3: list_nat,Xy: product_prod_int_nat,Xys: list_P8198026277950538467nt_nat] :
% 6.92/7.23 ( ( ( zip_int_nat @ Xs @ Ys3 )
% 6.92/7.23 = ( cons_P7512249878480867347nt_nat @ Xy @ Xys ) )
% 6.92/7.23 => ~ ! [X3: int,Xs4: list_int] :
% 6.92/7.23 ( ( Xs
% 6.92/7.23 = ( cons_int @ X3 @ Xs4 ) )
% 6.92/7.23 => ! [Y3: nat,Ys4: list_nat] :
% 6.92/7.23 ( ( Ys3
% 6.92/7.23 = ( cons_nat @ Y3 @ Ys4 ) )
% 6.92/7.23 => ( ( Xy
% 6.92/7.23 = ( product_Pair_int_nat @ X3 @ Y3 ) )
% 6.92/7.23 => ( Xys
% 6.92/7.23 != ( zip_int_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_ConsE
% 6.92/7.23 thf(fact_5488_zip__eq__ConsE,axiom,
% 6.92/7.23 ! [Xs: list_nat,Ys3: list_int,Xy: product_prod_nat_int,Xys: list_P3521021558325789923at_int] :
% 6.92/7.23 ( ( ( zip_nat_int @ Xs @ Ys3 )
% 6.92/7.23 = ( cons_P2335045147070616083at_int @ Xy @ Xys ) )
% 6.92/7.23 => ~ ! [X3: nat,Xs4: list_nat] :
% 6.92/7.23 ( ( Xs
% 6.92/7.23 = ( cons_nat @ X3 @ Xs4 ) )
% 6.92/7.23 => ! [Y3: int,Ys4: list_int] :
% 6.92/7.23 ( ( Ys3
% 6.92/7.23 = ( cons_int @ Y3 @ Ys4 ) )
% 6.92/7.23 => ( ( Xy
% 6.92/7.23 = ( product_Pair_nat_int @ X3 @ Y3 ) )
% 6.92/7.23 => ( Xys
% 6.92/7.23 != ( zip_nat_int @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_ConsE
% 6.92/7.23 thf(fact_5489_zip__eq__ConsE,axiom,
% 6.92/7.23 ! [Xs: list_nat,Ys3: list_nat,Xy: product_prod_nat_nat,Xys: list_P6011104703257516679at_nat] :
% 6.92/7.23 ( ( ( zip_nat_nat @ Xs @ Ys3 )
% 6.92/7.23 = ( cons_P6512896166579812791at_nat @ Xy @ Xys ) )
% 6.92/7.23 => ~ ! [X3: nat,Xs4: list_nat] :
% 6.92/7.23 ( ( Xs
% 6.92/7.23 = ( cons_nat @ X3 @ Xs4 ) )
% 6.92/7.23 => ! [Y3: nat,Ys4: list_nat] :
% 6.92/7.23 ( ( Ys3
% 6.92/7.23 = ( cons_nat @ Y3 @ Ys4 ) )
% 6.92/7.23 => ( ( Xy
% 6.92/7.23 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 6.92/7.23 => ( Xys
% 6.92/7.23 != ( zip_nat_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_ConsE
% 6.92/7.23 thf(fact_5490_zip__eq__ConsE,axiom,
% 6.92/7.23 ! [Xs: list_int,Ys3: list_int,Xy: product_prod_int_int,Xys: list_P5707943133018811711nt_int] :
% 6.92/7.23 ( ( ( zip_int_int @ Xs @ Ys3 )
% 6.92/7.23 = ( cons_P3334398858971670639nt_int @ Xy @ Xys ) )
% 6.92/7.23 => ~ ! [X3: int,Xs4: list_int] :
% 6.92/7.23 ( ( Xs
% 6.92/7.23 = ( cons_int @ X3 @ Xs4 ) )
% 6.92/7.23 => ! [Y3: int,Ys4: list_int] :
% 6.92/7.23 ( ( Ys3
% 6.92/7.23 = ( cons_int @ Y3 @ Ys4 ) )
% 6.92/7.23 => ( ( Xy
% 6.92/7.23 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 6.92/7.23 => ( Xys
% 6.92/7.23 != ( zip_int_int @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_ConsE
% 6.92/7.23 thf(fact_5491_zip__eq__ConsE,axiom,
% 6.92/7.23 ! [Xs: list_P7985473006766602707_nat_o,Ys3: list_P9062070895058802706et_nat,Xy: produc3925858234332021118et_nat,Xys: list_P2321686559999237006et_nat] :
% 6.92/7.23 ( ( ( zip_Pr7134870689397686104et_nat @ Xs @ Ys3 )
% 6.92/7.23 = ( cons_P3419706843779801160et_nat @ Xy @ Xys ) )
% 6.92/7.23 => ~ ! [X3: produc3658429121746597890et_nat > $o,Xs4: list_P7985473006766602707_nat_o] :
% 6.92/7.23 ( ( Xs
% 6.92/7.23 = ( cons_P6219271836124797827_nat_o @ X3 @ Xs4 ) )
% 6.92/7.23 => ! [Y3: produc3658429121746597890et_nat,Ys4: list_P9062070895058802706et_nat] :
% 6.92/7.23 ( ( Ys3
% 6.92/7.23 = ( cons_P2869003950965171916et_nat @ Y3 @ Ys4 ) )
% 6.92/7.23 => ( ( Xy
% 6.92/7.23 = ( produc5001842942810119800et_nat @ X3 @ Y3 ) )
% 6.92/7.23 => ( Xys
% 6.92/7.23 != ( zip_Pr7134870689397686104et_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_ConsE
% 6.92/7.23 thf(fact_5492_zip__eq__ConsE,axiom,
% 6.92/7.23 ! [Xs: list_P7985473006766602707_nat_o,Ys3: list_P2321686559999237006et_nat,Xy: produc2732055786443039994et_nat,Xys: list_P362550909693114634et_nat] :
% 6.92/7.23 ( ( ( zip_Pr8136144321567152340et_nat @ Xs @ Ys3 )
% 6.92/7.23 = ( cons_P6329468272379687876et_nat @ Xy @ Xys ) )
% 6.92/7.23 => ~ ! [X3: produc3658429121746597890et_nat > $o,Xs4: list_P7985473006766602707_nat_o] :
% 6.92/7.23 ( ( Xs
% 6.92/7.23 = ( cons_P6219271836124797827_nat_o @ X3 @ Xs4 ) )
% 6.92/7.23 => ! [Y3: produc3925858234332021118et_nat,Ys4: list_P2321686559999237006et_nat] :
% 6.92/7.23 ( ( Ys3
% 6.92/7.23 = ( cons_P3419706843779801160et_nat @ Y3 @ Ys4 ) )
% 6.92/7.23 => ( ( Xy
% 6.92/7.23 = ( produc2245416461498447860et_nat @ X3 @ Y3 ) )
% 6.92/7.23 => ( Xys
% 6.92/7.23 != ( zip_Pr8136144321567152340et_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_ConsE
% 6.92/7.23 thf(fact_5493_zip__eq__ConsE,axiom,
% 6.92/7.23 ! [Xs: list_b,Ys3: list_P131111800688179804it_nat,Xy: produc7388388658123137530it_nat,Xys: list_P7438302566501821706it_nat] :
% 6.92/7.23 ( ( ( zip_b_5987488365222434772it_nat @ Xs @ Ys3 )
% 6.92/7.23 = ( cons_P6467324686191779524it_nat @ Xy @ Xys ) )
% 6.92/7.23 => ~ ! [X3: b,Xs4: list_b] :
% 6.92/7.23 ( ( Xs
% 6.92/7.23 = ( cons_b @ X3 @ Xs4 ) )
% 6.92/7.23 => ! [Y3: produc6653097349344004940it_nat,Ys4: list_P131111800688179804it_nat] :
% 6.92/7.23 ( ( Ys3
% 6.92/7.23 = ( cons_P7873165156130251286it_nat @ Y3 @ Ys4 ) )
% 6.92/7.23 => ( ( Xy
% 6.92/7.23 = ( produc4082563078715348724it_nat @ X3 @ Y3 ) )
% 6.92/7.23 => ( Xys
% 6.92/7.23 != ( zip_b_5987488365222434772it_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_ConsE
% 6.92/7.23 thf(fact_5494_zip__eq__ConsE,axiom,
% 6.92/7.23 ! [Xs: list_a,Ys3: list_P131111800688179804it_nat,Xy: produc3260487557148687353it_nat,Xys: list_P6935614879863011209it_nat] :
% 6.92/7.23 ( ( ( zip_a_1859587264247984595it_nat @ Xs @ Ys3 )
% 6.92/7.23 = ( cons_P2339423585217329347it_nat @ Xy @ Xys ) )
% 6.92/7.23 => ~ ! [X3: a,Xs4: list_a] :
% 6.92/7.23 ( ( Xs
% 6.92/7.23 = ( cons_a @ X3 @ Xs4 ) )
% 6.92/7.23 => ! [Y3: produc6653097349344004940it_nat,Ys4: list_P131111800688179804it_nat] :
% 6.92/7.23 ( ( Ys3
% 6.92/7.23 = ( cons_P7873165156130251286it_nat @ Y3 @ Ys4 ) )
% 6.92/7.23 => ( ( Xy
% 6.92/7.23 = ( produc9178034014595674355it_nat @ X3 @ Y3 ) )
% 6.92/7.23 => ( Xys
% 6.92/7.23 != ( zip_a_1859587264247984595it_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_eq_ConsE
% 6.92/7.23 thf(fact_5495_find_Osimps_I2_J,axiom,
% 6.92/7.23 ! [P2: int > $o,X: int,Xs: list_int] :
% 6.92/7.23 ( ( ( P2 @ X )
% 6.92/7.23 => ( ( find_int @ P2 @ ( cons_int @ X @ Xs ) )
% 6.92/7.23 = ( some_int @ X ) ) )
% 6.92/7.23 & ( ~ ( P2 @ X )
% 6.92/7.23 => ( ( find_int @ P2 @ ( cons_int @ X @ Xs ) )
% 6.92/7.23 = ( find_int @ P2 @ Xs ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find.simps(2)
% 6.92/7.23 thf(fact_5496_find_Osimps_I2_J,axiom,
% 6.92/7.23 ! [P2: nat > $o,X: nat,Xs: list_nat] :
% 6.92/7.23 ( ( ( P2 @ X )
% 6.92/7.23 => ( ( find_nat @ P2 @ ( cons_nat @ X @ Xs ) )
% 6.92/7.23 = ( some_nat @ X ) ) )
% 6.92/7.23 & ( ~ ( P2 @ X )
% 6.92/7.23 => ( ( find_nat @ P2 @ ( cons_nat @ X @ Xs ) )
% 6.92/7.23 = ( find_nat @ P2 @ Xs ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find.simps(2)
% 6.92/7.23 thf(fact_5497_find_Osimps_I2_J,axiom,
% 6.92/7.23 ! [P2: produc7388388658123137530it_nat > $o,X: produc7388388658123137530it_nat,Xs: list_P7438302566501821706it_nat] :
% 6.92/7.23 ( ( ( P2 @ X )
% 6.92/7.23 => ( ( find_P8943372834735446238it_nat @ P2 @ ( cons_P6467324686191779524it_nat @ X @ Xs ) )
% 6.92/7.23 = ( some_P2818173045054083285it_nat @ X ) ) )
% 6.92/7.23 & ( ~ ( P2 @ X )
% 6.92/7.23 => ( ( find_P8943372834735446238it_nat @ P2 @ ( cons_P6467324686191779524it_nat @ X @ Xs ) )
% 6.92/7.23 = ( find_P8943372834735446238it_nat @ P2 @ Xs ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find.simps(2)
% 6.92/7.23 thf(fact_5498_find_Osimps_I2_J,axiom,
% 6.92/7.23 ! [P2: produc3260487557148687353it_nat > $o,X: produc3260487557148687353it_nat,Xs: list_P6935614879863011209it_nat] :
% 6.92/7.23 ( ( ( P2 @ X )
% 6.92/7.23 => ( ( find_P4815471733760996061it_nat @ P2 @ ( cons_P2339423585217329347it_nat @ X @ Xs ) )
% 6.92/7.23 = ( some_P7913643980934408916it_nat @ X ) ) )
% 6.92/7.23 & ( ~ ( P2 @ X )
% 6.92/7.23 => ( ( find_P4815471733760996061it_nat @ P2 @ ( cons_P2339423585217329347it_nat @ X @ Xs ) )
% 6.92/7.23 = ( find_P4815471733760996061it_nat @ P2 @ Xs ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find.simps(2)
% 6.92/7.23 thf(fact_5499_find_Osimps_I2_J,axiom,
% 6.92/7.23 ! [P2: produc8664842809031399944it_nat > $o,X: produc8664842809031399944it_nat,Xs: list_P626663023886443800it_nat] :
% 6.92/7.23 ( ( ( P2 @ X )
% 6.92/7.23 => ( ( find_P5317947125398478060it_nat @ P2 @ ( cons_P4136552807766418642it_nat @ X @ Xs ) )
% 6.92/7.23 = ( some_P1914260805536162275it_nat @ X ) ) )
% 6.92/7.23 & ( ~ ( P2 @ X )
% 6.92/7.23 => ( ( find_P5317947125398478060it_nat @ P2 @ ( cons_P4136552807766418642it_nat @ X @ Xs ) )
% 6.92/7.23 = ( find_P5317947125398478060it_nat @ P2 @ Xs ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find.simps(2)
% 6.92/7.23 thf(fact_5500_find_Osimps_I2_J,axiom,
% 6.92/7.23 ! [P2: num > $o,X: num,Xs: list_num] :
% 6.92/7.23 ( ( ( P2 @ X )
% 6.92/7.23 => ( ( find_num @ P2 @ ( cons_num @ X @ Xs ) )
% 6.92/7.23 = ( some_num @ X ) ) )
% 6.92/7.23 & ( ~ ( P2 @ X )
% 6.92/7.23 => ( ( find_num @ P2 @ ( cons_num @ X @ Xs ) )
% 6.92/7.23 = ( find_num @ P2 @ Xs ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % find.simps(2)
% 6.92/7.23 thf(fact_5501_pair__list__split,axiom,
% 6.92/7.23 ! [L: list_P6011104703257516679at_nat] :
% 6.92/7.23 ~ ! [L1: list_nat,L22: list_nat] :
% 6.92/7.23 ( ( L
% 6.92/7.23 = ( zip_nat_nat @ L1 @ L22 ) )
% 6.92/7.23 => ( ( ( size_size_list_nat @ L1 )
% 6.92/7.23 = ( size_size_list_nat @ L22 ) )
% 6.92/7.23 => ( ( size_s5460976970255530739at_nat @ L )
% 6.92/7.23 != ( size_size_list_nat @ L22 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pair_list_split
% 6.92/7.23 thf(fact_5502_pair__list__split,axiom,
% 6.92/7.23 ! [L: list_P7333126701944960589_nat_o] :
% 6.92/7.23 ~ ! [L1: list_nat,L22: list_o] :
% 6.92/7.23 ( ( L
% 6.92/7.23 = ( zip_nat_o @ L1 @ L22 ) )
% 6.92/7.23 => ( ( ( size_size_list_nat @ L1 )
% 6.92/7.23 = ( size_size_list_o @ L22 ) )
% 6.92/7.23 => ( ( size_s6491369823275344609_nat_o @ L )
% 6.92/7.23 != ( size_size_list_o @ L22 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pair_list_split
% 6.92/7.23 thf(fact_5503_pair__list__split,axiom,
% 6.92/7.23 ! [L: list_P3521021558325789923at_int] :
% 6.92/7.23 ~ ! [L1: list_nat,L22: list_int] :
% 6.92/7.23 ( ( L
% 6.92/7.23 = ( zip_nat_int @ L1 @ L22 ) )
% 6.92/7.23 => ( ( ( size_size_list_nat @ L1 )
% 6.92/7.23 = ( size_size_list_int @ L22 ) )
% 6.92/7.23 => ( ( size_s2970893825323803983at_int @ L )
% 6.92/7.23 != ( size_size_list_int @ L22 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pair_list_split
% 6.92/7.23 thf(fact_5504_pair__list__split,axiom,
% 6.92/7.23 ! [L: list_P6285523579766656935_o_nat] :
% 6.92/7.23 ~ ! [L1: list_o,L22: list_nat] :
% 6.92/7.23 ( ( L
% 6.92/7.23 = ( zip_o_nat @ L1 @ L22 ) )
% 6.92/7.23 => ( ( ( size_size_list_o @ L1 )
% 6.92/7.23 = ( size_size_list_nat @ L22 ) )
% 6.92/7.23 => ( ( size_s5443766701097040955_o_nat @ L )
% 6.92/7.23 != ( size_size_list_nat @ L22 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pair_list_split
% 6.92/7.23 thf(fact_5505_pair__list__split,axiom,
% 6.92/7.23 ! [L: list_P4002435161011370285od_o_o] :
% 6.92/7.23 ~ ! [L1: list_o,L22: list_o] :
% 6.92/7.23 ( ( L
% 6.92/7.23 = ( zip_o_o @ L1 @ L22 ) )
% 6.92/7.23 => ( ( ( size_size_list_o @ L1 )
% 6.92/7.23 = ( size_size_list_o @ L22 ) )
% 6.92/7.23 => ( ( size_s1515746228057227161od_o_o @ L )
% 6.92/7.23 != ( size_size_list_o @ L22 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pair_list_split
% 6.92/7.23 thf(fact_5506_pair__list__split,axiom,
% 6.92/7.23 ! [L: list_P3795440434834930179_o_int] :
% 6.92/7.23 ~ ! [L1: list_o,L22: list_int] :
% 6.92/7.23 ( ( L
% 6.92/7.23 = ( zip_o_int @ L1 @ L22 ) )
% 6.92/7.23 => ( ( ( size_size_list_o @ L1 )
% 6.92/7.23 = ( size_size_list_int @ L22 ) )
% 6.92/7.23 => ( ( size_s2953683556165314199_o_int @ L )
% 6.92/7.23 != ( size_size_list_int @ L22 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pair_list_split
% 6.92/7.23 thf(fact_5507_pair__list__split,axiom,
% 6.92/7.23 ! [L: list_P8198026277950538467nt_nat] :
% 6.92/7.23 ~ ! [L1: list_int,L22: list_nat] :
% 6.92/7.23 ( ( L
% 6.92/7.23 = ( zip_int_nat @ L1 @ L22 ) )
% 6.92/7.23 => ( ( ( size_size_list_int @ L1 )
% 6.92/7.23 = ( size_size_list_nat @ L22 ) )
% 6.92/7.23 => ( ( size_s7647898544948552527nt_nat @ L )
% 6.92/7.23 != ( size_size_list_nat @ L22 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pair_list_split
% 6.92/7.23 thf(fact_5508_pair__list__split,axiom,
% 6.92/7.23 ! [L: list_P5087981734274514673_int_o] :
% 6.92/7.23 ~ ! [L1: list_int,L22: list_o] :
% 6.92/7.23 ( ( L
% 6.92/7.23 = ( zip_int_o @ L1 @ L22 ) )
% 6.92/7.23 => ( ( ( size_size_list_int @ L1 )
% 6.92/7.23 = ( size_size_list_o @ L22 ) )
% 6.92/7.23 => ( ( size_s4246224855604898693_int_o @ L )
% 6.92/7.23 != ( size_size_list_o @ L22 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pair_list_split
% 6.92/7.23 thf(fact_5509_pair__list__split,axiom,
% 6.92/7.23 ! [L: list_P5707943133018811711nt_int] :
% 6.92/7.23 ~ ! [L1: list_int,L22: list_int] :
% 6.92/7.23 ( ( L
% 6.92/7.23 = ( zip_int_int @ L1 @ L22 ) )
% 6.92/7.23 => ( ( ( size_size_list_int @ L1 )
% 6.92/7.23 = ( size_size_list_int @ L22 ) )
% 6.92/7.23 => ( ( size_s5157815400016825771nt_int @ L )
% 6.92/7.23 != ( size_size_list_int @ L22 ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % pair_list_split
% 6.92/7.23 thf(fact_5510_zip__inj,axiom,
% 6.92/7.23 ! [A: list_nat,B: list_nat,A2: list_nat,B2: list_nat] :
% 6.92/7.23 ( ( ( size_size_list_nat @ A )
% 6.92/7.23 = ( size_size_list_nat @ B ) )
% 6.92/7.23 => ( ( ( size_size_list_nat @ A2 )
% 6.92/7.23 = ( size_size_list_nat @ B2 ) )
% 6.92/7.23 => ( ( ( zip_nat_nat @ A @ B )
% 6.92/7.23 = ( zip_nat_nat @ A2 @ B2 ) )
% 6.92/7.23 => ( ( A = A2 )
% 6.92/7.23 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_inj
% 6.92/7.23 thf(fact_5511_zip__inj,axiom,
% 6.92/7.23 ! [A: list_nat,B: list_o,A2: list_nat,B2: list_o] :
% 6.92/7.23 ( ( ( size_size_list_nat @ A )
% 6.92/7.23 = ( size_size_list_o @ B ) )
% 6.92/7.23 => ( ( ( size_size_list_nat @ A2 )
% 6.92/7.23 = ( size_size_list_o @ B2 ) )
% 6.92/7.23 => ( ( ( zip_nat_o @ A @ B )
% 6.92/7.23 = ( zip_nat_o @ A2 @ B2 ) )
% 6.92/7.23 => ( ( A = A2 )
% 6.92/7.23 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_inj
% 6.92/7.23 thf(fact_5512_zip__inj,axiom,
% 6.92/7.23 ! [A: list_nat,B: list_int,A2: list_nat,B2: list_int] :
% 6.92/7.23 ( ( ( size_size_list_nat @ A )
% 6.92/7.23 = ( size_size_list_int @ B ) )
% 6.92/7.23 => ( ( ( size_size_list_nat @ A2 )
% 6.92/7.23 = ( size_size_list_int @ B2 ) )
% 6.92/7.23 => ( ( ( zip_nat_int @ A @ B )
% 6.92/7.23 = ( zip_nat_int @ A2 @ B2 ) )
% 6.92/7.23 => ( ( A = A2 )
% 6.92/7.23 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.23
% 6.92/7.23 % zip_inj
% 6.92/7.23 thf(fact_5513_zip__inj,axiom,
% 6.92/7.23 ! [A: list_o,B: list_nat,A2: list_o,B2: list_nat] :
% 6.92/7.23 ( ( ( size_size_list_o @ A )
% 6.92/7.24 = ( size_size_list_nat @ B ) )
% 6.92/7.24 => ( ( ( size_size_list_o @ A2 )
% 6.92/7.24 = ( size_size_list_nat @ B2 ) )
% 6.92/7.24 => ( ( ( zip_o_nat @ A @ B )
% 6.92/7.24 = ( zip_o_nat @ A2 @ B2 ) )
% 6.92/7.24 => ( ( A = A2 )
% 6.92/7.24 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % zip_inj
% 6.92/7.24 thf(fact_5514_zip__inj,axiom,
% 6.92/7.24 ! [A: list_o,B: list_o,A2: list_o,B2: list_o] :
% 6.92/7.24 ( ( ( size_size_list_o @ A )
% 6.92/7.24 = ( size_size_list_o @ B ) )
% 6.92/7.24 => ( ( ( size_size_list_o @ A2 )
% 6.92/7.24 = ( size_size_list_o @ B2 ) )
% 6.92/7.24 => ( ( ( zip_o_o @ A @ B )
% 6.92/7.24 = ( zip_o_o @ A2 @ B2 ) )
% 6.92/7.24 => ( ( A = A2 )
% 6.92/7.24 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % zip_inj
% 6.92/7.24 thf(fact_5515_zip__inj,axiom,
% 6.92/7.24 ! [A: list_o,B: list_int,A2: list_o,B2: list_int] :
% 6.92/7.24 ( ( ( size_size_list_o @ A )
% 6.92/7.24 = ( size_size_list_int @ B ) )
% 6.92/7.24 => ( ( ( size_size_list_o @ A2 )
% 6.92/7.24 = ( size_size_list_int @ B2 ) )
% 6.92/7.24 => ( ( ( zip_o_int @ A @ B )
% 6.92/7.24 = ( zip_o_int @ A2 @ B2 ) )
% 6.92/7.24 => ( ( A = A2 )
% 6.92/7.24 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % zip_inj
% 6.92/7.24 thf(fact_5516_zip__inj,axiom,
% 6.92/7.24 ! [A: list_int,B: list_nat,A2: list_int,B2: list_nat] :
% 6.92/7.24 ( ( ( size_size_list_int @ A )
% 6.92/7.24 = ( size_size_list_nat @ B ) )
% 6.92/7.24 => ( ( ( size_size_list_int @ A2 )
% 6.92/7.24 = ( size_size_list_nat @ B2 ) )
% 6.92/7.24 => ( ( ( zip_int_nat @ A @ B )
% 6.92/7.24 = ( zip_int_nat @ A2 @ B2 ) )
% 6.92/7.24 => ( ( A = A2 )
% 6.92/7.24 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % zip_inj
% 6.92/7.24 thf(fact_5517_zip__inj,axiom,
% 6.92/7.24 ! [A: list_int,B: list_o,A2: list_int,B2: list_o] :
% 6.92/7.24 ( ( ( size_size_list_int @ A )
% 6.92/7.24 = ( size_size_list_o @ B ) )
% 6.92/7.24 => ( ( ( size_size_list_int @ A2 )
% 6.92/7.24 = ( size_size_list_o @ B2 ) )
% 6.92/7.24 => ( ( ( zip_int_o @ A @ B )
% 6.92/7.24 = ( zip_int_o @ A2 @ B2 ) )
% 6.92/7.24 => ( ( A = A2 )
% 6.92/7.24 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % zip_inj
% 6.92/7.24 thf(fact_5518_zip__inj,axiom,
% 6.92/7.24 ! [A: list_int,B: list_int,A2: list_int,B2: list_int] :
% 6.92/7.24 ( ( ( size_size_list_int @ A )
% 6.92/7.24 = ( size_size_list_int @ B ) )
% 6.92/7.24 => ( ( ( size_size_list_int @ A2 )
% 6.92/7.24 = ( size_size_list_int @ B2 ) )
% 6.92/7.24 => ( ( ( zip_int_int @ A @ B )
% 6.92/7.24 = ( zip_int_int @ A2 @ B2 ) )
% 6.92/7.24 => ( ( A = A2 )
% 6.92/7.24 & ( B = B2 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % zip_inj
% 6.92/7.24 thf(fact_5519_find__SomeD_I1_J,axiom,
% 6.92/7.24 ! [P2: produc7388388658123137530it_nat > $o,Xs: list_P7438302566501821706it_nat,X: produc7388388658123137530it_nat] :
% 6.92/7.24 ( ( ( find_P8943372834735446238it_nat @ P2 @ Xs )
% 6.92/7.24 = ( some_P2818173045054083285it_nat @ X ) )
% 6.92/7.24 => ( P2 @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % find_SomeD(1)
% 6.92/7.24 thf(fact_5520_find__SomeD_I1_J,axiom,
% 6.92/7.24 ! [P2: produc3260487557148687353it_nat > $o,Xs: list_P6935614879863011209it_nat,X: produc3260487557148687353it_nat] :
% 6.92/7.24 ( ( ( find_P4815471733760996061it_nat @ P2 @ Xs )
% 6.92/7.24 = ( some_P7913643980934408916it_nat @ X ) )
% 6.92/7.24 => ( P2 @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % find_SomeD(1)
% 6.92/7.24 thf(fact_5521_find__SomeD_I1_J,axiom,
% 6.92/7.24 ! [P2: produc8664842809031399944it_nat > $o,Xs: list_P626663023886443800it_nat,X: produc8664842809031399944it_nat] :
% 6.92/7.24 ( ( ( find_P5317947125398478060it_nat @ P2 @ Xs )
% 6.92/7.24 = ( some_P1914260805536162275it_nat @ X ) )
% 6.92/7.24 => ( P2 @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % find_SomeD(1)
% 6.92/7.24 thf(fact_5522_find__SomeD_I1_J,axiom,
% 6.92/7.24 ! [P2: num > $o,Xs: list_num,X: num] :
% 6.92/7.24 ( ( ( find_num @ P2 @ Xs )
% 6.92/7.24 = ( some_num @ X ) )
% 6.92/7.24 => ( P2 @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % find_SomeD(1)
% 6.92/7.24 thf(fact_5523_not__numeral__le__zero,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ N2 ) @ zero_z2226904508553997617atural ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_le_zero
% 6.92/7.24 thf(fact_5524_not__numeral__le__zero,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N2 ) @ zero_z3403309356797280102nteger ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_le_zero
% 6.92/7.24 thf(fact_5525_not__numeral__le__zero,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_le_zero
% 6.92/7.24 thf(fact_5526_not__numeral__le__zero,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_le_zero
% 6.92/7.24 thf(fact_5527_not__numeral__le__zero,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_le_zero
% 6.92/7.24 thf(fact_5528_zero__le__numeral,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( numera5444537566228673987atural @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_le_numeral
% 6.92/7.24 thf(fact_5529_zero__le__numeral,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_le_numeral
% 6.92/7.24 thf(fact_5530_zero__le__numeral,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_le_numeral
% 6.92/7.24 thf(fact_5531_zero__le__numeral,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_le_numeral
% 6.92/7.24 thf(fact_5532_zero__le__numeral,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_le_numeral
% 6.92/7.24 thf(fact_5533_not__numeral__less__zero,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_zero
% 6.92/7.24 thf(fact_5534_not__numeral__less__zero,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_zero
% 6.92/7.24 thf(fact_5535_not__numeral__less__zero,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_zero
% 6.92/7.24 thf(fact_5536_not__numeral__less__zero,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ N2 ) @ zero_z2226904508553997617atural ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_zero
% 6.92/7.24 thf(fact_5537_not__numeral__less__zero,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N2 ) @ zero_z3403309356797280102nteger ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_zero
% 6.92/7.24 thf(fact_5538_zero__less__numeral,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_less_numeral
% 6.92/7.24 thf(fact_5539_zero__less__numeral,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_less_numeral
% 6.92/7.24 thf(fact_5540_zero__less__numeral,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_less_numeral
% 6.92/7.24 thf(fact_5541_zero__less__numeral,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( numera5444537566228673987atural @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_less_numeral
% 6.92/7.24 thf(fact_5542_zero__less__numeral,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_less_numeral
% 6.92/7.24 thf(fact_5543_one__le__numeral,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_le_numeral
% 6.92/7.24 thf(fact_5544_one__le__numeral,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_le_numeral
% 6.92/7.24 thf(fact_5545_one__le__numeral,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_le_numeral
% 6.92/7.24 thf(fact_5546_one__le__numeral,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_le_numeral
% 6.92/7.24 thf(fact_5547_one__le__numeral,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_le_numeral
% 6.92/7.24 thf(fact_5548_not__numeral__less__one,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_one
% 6.92/7.24 thf(fact_5549_not__numeral__less__one,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_one
% 6.92/7.24 thf(fact_5550_not__numeral__less__one,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_one
% 6.92/7.24 thf(fact_5551_not__numeral__less__one,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ N2 ) @ one_one_Code_natural ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_one
% 6.92/7.24 thf(fact_5552_not__numeral__less__one,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_one
% 6.92/7.24 thf(fact_5553_not__numeral__le__neg__numeral,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_le_neg_numeral
% 6.92/7.24 thf(fact_5554_not__numeral__le__neg__numeral,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_le_neg_numeral
% 6.92/7.24 thf(fact_5555_not__numeral__le__neg__numeral,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_le_neg_numeral
% 6.92/7.24 thf(fact_5556_neg__numeral__le__numeral,axiom,
% 6.92/7.24 ! [M: num,N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_le_numeral
% 6.92/7.24 thf(fact_5557_neg__numeral__le__numeral,axiom,
% 6.92/7.24 ! [M: num,N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_le_numeral
% 6.92/7.24 thf(fact_5558_neg__numeral__le__numeral,axiom,
% 6.92/7.24 ! [M: num,N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_le_numeral
% 6.92/7.24 thf(fact_5559_one__plus__numeral__commute,axiom,
% 6.92/7.24 ! [X: num] :
% 6.92/7.24 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 6.92/7.24 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_plus_numeral_commute
% 6.92/7.24 thf(fact_5560_one__plus__numeral__commute,axiom,
% 6.92/7.24 ! [X: num] :
% 6.92/7.24 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 6.92/7.24 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_plus_numeral_commute
% 6.92/7.24 thf(fact_5561_one__plus__numeral__commute,axiom,
% 6.92/7.24 ! [X: num] :
% 6.92/7.24 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 6.92/7.24 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_plus_numeral_commute
% 6.92/7.24 thf(fact_5562_one__plus__numeral__commute,axiom,
% 6.92/7.24 ! [X: num] :
% 6.92/7.24 ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ X ) )
% 6.92/7.24 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_plus_numeral_commute
% 6.92/7.24 thf(fact_5563_one__plus__numeral__commute,axiom,
% 6.92/7.24 ! [X: num] :
% 6.92/7.24 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 6.92/7.24 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_plus_numeral_commute
% 6.92/7.24 thf(fact_5564_not__numeral__less__neg__numeral,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_neg_numeral
% 6.92/7.24 thf(fact_5565_not__numeral__less__neg__numeral,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_neg_numeral
% 6.92/7.24 thf(fact_5566_not__numeral__less__neg__numeral,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_neg_numeral
% 6.92/7.24 thf(fact_5567_neg__numeral__less__numeral,axiom,
% 6.92/7.24 ! [M: num,N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_less_numeral
% 6.92/7.24 thf(fact_5568_neg__numeral__less__numeral,axiom,
% 6.92/7.24 ! [M: num,N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_less_numeral
% 6.92/7.24 thf(fact_5569_neg__numeral__less__numeral,axiom,
% 6.92/7.24 ! [M: num,N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_less_numeral
% 6.92/7.24 thf(fact_5570_length__Cons,axiom,
% 6.92/7.24 ! [X: nat,Xs: list_nat] :
% 6.92/7.24 ( ( size_size_list_nat @ ( cons_nat @ X @ Xs ) )
% 6.92/7.24 = ( suc @ ( size_size_list_nat @ Xs ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % length_Cons
% 6.92/7.24 thf(fact_5571_length__Cons,axiom,
% 6.92/7.24 ! [X: $o,Xs: list_o] :
% 6.92/7.24 ( ( size_size_list_o @ ( cons_o @ X @ Xs ) )
% 6.92/7.24 = ( suc @ ( size_size_list_o @ Xs ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % length_Cons
% 6.92/7.24 thf(fact_5572_length__Cons,axiom,
% 6.92/7.24 ! [X: int,Xs: list_int] :
% 6.92/7.24 ( ( size_size_list_int @ ( cons_int @ X @ Xs ) )
% 6.92/7.24 = ( suc @ ( size_size_list_int @ Xs ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % length_Cons
% 6.92/7.24 thf(fact_5573_impossible__Cons,axiom,
% 6.92/7.24 ! [Xs: list_nat,Ys3: list_nat,X: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_nat @ Ys3 ) )
% 6.92/7.24 => ( Xs
% 6.92/7.24 != ( cons_nat @ X @ Ys3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % impossible_Cons
% 6.92/7.24 thf(fact_5574_impossible__Cons,axiom,
% 6.92/7.24 ! [Xs: list_o,Ys3: list_o,X: $o] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys3 ) )
% 6.92/7.24 => ( Xs
% 6.92/7.24 != ( cons_o @ X @ Ys3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % impossible_Cons
% 6.92/7.24 thf(fact_5575_impossible__Cons,axiom,
% 6.92/7.24 ! [Xs: list_int,Ys3: list_int,X: int] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys3 ) )
% 6.92/7.24 => ( Xs
% 6.92/7.24 != ( cons_int @ X @ Ys3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % impossible_Cons
% 6.92/7.24 thf(fact_5576_sorted2,axiom,
% 6.92/7.24 ! [X: rat,Y: rat,Zs: list_rat] :
% 6.92/7.24 ( ( sorted_wrt_rat @ ord_less_eq_rat @ ( cons_rat @ X @ ( cons_rat @ Y @ Zs ) ) )
% 6.92/7.24 = ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.24 & ( sorted_wrt_rat @ ord_less_eq_rat @ ( cons_rat @ Y @ Zs ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sorted2
% 6.92/7.24 thf(fact_5577_sorted2,axiom,
% 6.92/7.24 ! [X: num,Y: num,Zs: list_num] :
% 6.92/7.24 ( ( sorted_wrt_num @ ord_less_eq_num @ ( cons_num @ X @ ( cons_num @ Y @ Zs ) ) )
% 6.92/7.24 = ( ( ord_less_eq_num @ X @ Y )
% 6.92/7.24 & ( sorted_wrt_num @ ord_less_eq_num @ ( cons_num @ Y @ Zs ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sorted2
% 6.92/7.24 thf(fact_5578_sorted2,axiom,
% 6.92/7.24 ! [X: nat,Y: nat,Zs: list_nat] :
% 6.92/7.24 ( ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ X @ ( cons_nat @ Y @ Zs ) ) )
% 6.92/7.24 = ( ( ord_less_eq_nat @ X @ Y )
% 6.92/7.24 & ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ Y @ Zs ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sorted2
% 6.92/7.24 thf(fact_5579_sorted2,axiom,
% 6.92/7.24 ! [X: int,Y: int,Zs: list_int] :
% 6.92/7.24 ( ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ X @ ( cons_int @ Y @ Zs ) ) )
% 6.92/7.24 = ( ( ord_less_eq_int @ X @ Y )
% 6.92/7.24 & ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ Y @ Zs ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sorted2
% 6.92/7.24 thf(fact_5580_not__zero__le__neg__numeral,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_zero_le_neg_numeral
% 6.92/7.24 thf(fact_5581_not__zero__le__neg__numeral,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_zero_le_neg_numeral
% 6.92/7.24 thf(fact_5582_not__zero__le__neg__numeral,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_zero_le_neg_numeral
% 6.92/7.24 thf(fact_5583_neg__numeral__le__zero,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_le_zero
% 6.92/7.24 thf(fact_5584_neg__numeral__le__zero,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_le_zero
% 6.92/7.24 thf(fact_5585_neg__numeral__le__zero,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_le_zero
% 6.92/7.24 thf(fact_5586_not__zero__less__neg__numeral,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_zero_less_neg_numeral
% 6.92/7.24 thf(fact_5587_not__zero__less__neg__numeral,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_zero_less_neg_numeral
% 6.92/7.24 thf(fact_5588_not__zero__less__neg__numeral,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_zero_less_neg_numeral
% 6.92/7.24 thf(fact_5589_neg__numeral__less__zero,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_less_zero
% 6.92/7.24 thf(fact_5590_neg__numeral__less__zero,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_less_zero
% 6.92/7.24 thf(fact_5591_neg__numeral__less__zero,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_less_zero
% 6.92/7.24 thf(fact_5592_neg__numeral__le__one,axiom,
% 6.92/7.24 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_le_one
% 6.92/7.24 thf(fact_5593_neg__numeral__le__one,axiom,
% 6.92/7.24 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_le_one
% 6.92/7.24 thf(fact_5594_neg__numeral__le__one,axiom,
% 6.92/7.24 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_le_one
% 6.92/7.24 thf(fact_5595_neg__one__le__numeral,axiom,
% 6.92/7.24 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_one_le_numeral
% 6.92/7.24 thf(fact_5596_neg__one__le__numeral,axiom,
% 6.92/7.24 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_one_le_numeral
% 6.92/7.24 thf(fact_5597_neg__one__le__numeral,axiom,
% 6.92/7.24 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_one_le_numeral
% 6.92/7.24 thf(fact_5598_neg__numeral__le__neg__one,axiom,
% 6.92/7.24 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_le_neg_one
% 6.92/7.24 thf(fact_5599_neg__numeral__le__neg__one,axiom,
% 6.92/7.24 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_le_neg_one
% 6.92/7.24 thf(fact_5600_neg__numeral__le__neg__one,axiom,
% 6.92/7.24 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_le_neg_one
% 6.92/7.24 thf(fact_5601_not__numeral__le__neg__one,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_le_neg_one
% 6.92/7.24 thf(fact_5602_not__numeral__le__neg__one,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_le_neg_one
% 6.92/7.24 thf(fact_5603_not__numeral__le__neg__one,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_le_neg_one
% 6.92/7.24 thf(fact_5604_not__one__le__neg__numeral,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_one_le_neg_numeral
% 6.92/7.24 thf(fact_5605_not__one__le__neg__numeral,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_one_le_neg_numeral
% 6.92/7.24 thf(fact_5606_not__one__le__neg__numeral,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_one_le_neg_numeral
% 6.92/7.24 thf(fact_5607_neg__numeral__less__one,axiom,
% 6.92/7.24 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_less_one
% 6.92/7.24 thf(fact_5608_neg__numeral__less__one,axiom,
% 6.92/7.24 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_less_one
% 6.92/7.24 thf(fact_5609_neg__numeral__less__one,axiom,
% 6.92/7.24 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_less_one
% 6.92/7.24 thf(fact_5610_neg__one__less__numeral,axiom,
% 6.92/7.24 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_one_less_numeral
% 6.92/7.24 thf(fact_5611_neg__one__less__numeral,axiom,
% 6.92/7.24 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_one_less_numeral
% 6.92/7.24 thf(fact_5612_neg__one__less__numeral,axiom,
% 6.92/7.24 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_one_less_numeral
% 6.92/7.24 thf(fact_5613_not__numeral__less__neg__one,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_neg_one
% 6.92/7.24 thf(fact_5614_not__numeral__less__neg__one,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_neg_one
% 6.92/7.24 thf(fact_5615_not__numeral__less__neg__one,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_numeral_less_neg_one
% 6.92/7.24 thf(fact_5616_not__one__less__neg__numeral,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_one_less_neg_numeral
% 6.92/7.24 thf(fact_5617_not__one__less__neg__numeral,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_one_less_neg_numeral
% 6.92/7.24 thf(fact_5618_not__one__less__neg__numeral,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_one_less_neg_numeral
% 6.92/7.24 thf(fact_5619_not__neg__one__less__neg__numeral,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_neg_one_less_neg_numeral
% 6.92/7.24 thf(fact_5620_not__neg__one__less__neg__numeral,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_neg_one_less_neg_numeral
% 6.92/7.24 thf(fact_5621_not__neg__one__less__neg__numeral,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_neg_one_less_neg_numeral
% 6.92/7.24 thf(fact_5622_Suc__le__length__iff,axiom,
% 6.92/7.24 ! [N2: nat,Xs: list_nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( size_size_list_nat @ Xs ) )
% 6.92/7.24 = ( ? [X4: nat,Ys2: list_nat] :
% 6.92/7.24 ( ( Xs
% 6.92/7.24 = ( cons_nat @ X4 @ Ys2 ) )
% 6.92/7.24 & ( ord_less_eq_nat @ N2 @ ( size_size_list_nat @ Ys2 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Suc_le_length_iff
% 6.92/7.24 thf(fact_5623_Suc__le__length__iff,axiom,
% 6.92/7.24 ! [N2: nat,Xs: list_o] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( size_size_list_o @ Xs ) )
% 6.92/7.24 = ( ? [X4: $o,Ys2: list_o] :
% 6.92/7.24 ( ( Xs
% 6.92/7.24 = ( cons_o @ X4 @ Ys2 ) )
% 6.92/7.24 & ( ord_less_eq_nat @ N2 @ ( size_size_list_o @ Ys2 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Suc_le_length_iff
% 6.92/7.24 thf(fact_5624_Suc__le__length__iff,axiom,
% 6.92/7.24 ! [N2: nat,Xs: list_int] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( size_size_list_int @ Xs ) )
% 6.92/7.24 = ( ? [X4: int,Ys2: list_int] :
% 6.92/7.24 ( ( Xs
% 6.92/7.24 = ( cons_int @ X4 @ Ys2 ) )
% 6.92/7.24 & ( ord_less_eq_nat @ N2 @ ( size_size_list_int @ Ys2 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Suc_le_length_iff
% 6.92/7.24 thf(fact_5625_less__divide__eq__numeral_I1_J,axiom,
% 6.92/7.24 ! [W2: num,B: rat,C2: rat] :
% 6.92/7.24 ( ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 6.92/7.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.24 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 6.92/7.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.24 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.24 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 6.92/7.24 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.24 => ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % less_divide_eq_numeral(1)
% 6.92/7.24 thf(fact_5626_divide__less__eq__numeral_I1_J,axiom,
% 6.92/7.24 ! [B: rat,C2: rat,W2: num] :
% 6.92/7.24 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ ( numeral_numeral_rat @ W2 ) )
% 6.92/7.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.24 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 6.92/7.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.24 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.24 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 6.92/7.24 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.24 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divide_less_eq_numeral(1)
% 6.92/7.24 thf(fact_5627_list_Osize_I4_J,axiom,
% 6.92/7.24 ! [X21: nat,X222: list_nat] :
% 6.92/7.24 ( ( size_size_list_nat @ ( cons_nat @ X21 @ X222 ) )
% 6.92/7.24 = ( plus_plus_nat @ ( size_size_list_nat @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % list.size(4)
% 6.92/7.24 thf(fact_5628_list_Osize_I4_J,axiom,
% 6.92/7.24 ! [X21: $o,X222: list_o] :
% 6.92/7.24 ( ( size_size_list_o @ ( cons_o @ X21 @ X222 ) )
% 6.92/7.24 = ( plus_plus_nat @ ( size_size_list_o @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % list.size(4)
% 6.92/7.24 thf(fact_5629_list_Osize_I4_J,axiom,
% 6.92/7.24 ! [X21: int,X222: list_int] :
% 6.92/7.24 ( ( size_size_list_int @ ( cons_int @ X21 @ X222 ) )
% 6.92/7.24 = ( plus_plus_nat @ ( size_size_list_int @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % list.size(4)
% 6.92/7.24 thf(fact_5630_le__divide__eq__numeral_I1_J,axiom,
% 6.92/7.24 ! [W2: num,B: rat,C2: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 6.92/7.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.24 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 6.92/7.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.24 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.24 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 6.92/7.24 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.24 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % le_divide_eq_numeral(1)
% 6.92/7.24 thf(fact_5631_divide__le__eq__numeral_I1_J,axiom,
% 6.92/7.24 ! [B: rat,C2: rat,W2: num] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ ( numeral_numeral_rat @ W2 ) )
% 6.92/7.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.24 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 6.92/7.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.24 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.24 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 6.92/7.24 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.24 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divide_le_eq_numeral(1)
% 6.92/7.24 thf(fact_5632_less__divide__eq__numeral_I2_J,axiom,
% 6.92/7.24 ! [W2: num,B: rat,C2: rat] :
% 6.92/7.24 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C2 ) )
% 6.92/7.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.24 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 6.92/7.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.24 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.24 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 6.92/7.24 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.24 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % less_divide_eq_numeral(2)
% 6.92/7.24 thf(fact_5633_divide__less__eq__numeral_I2_J,axiom,
% 6.92/7.24 ! [B: rat,C2: rat,W2: num] :
% 6.92/7.24 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 6.92/7.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.24 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 6.92/7.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 6.92/7.24 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.24 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 6.92/7.24 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 6.92/7.24 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divide_less_eq_numeral(2)
% 6.92/7.24 thf(fact_5634_nth__non__equal__first__eq,axiom,
% 6.92/7.24 ! [X: int,Y: int,Xs: list_int,N2: nat] :
% 6.92/7.24 ( ( X != Y )
% 6.92/7.24 => ( ( ( nth_int @ ( cons_int @ X @ Xs ) @ N2 )
% 6.92/7.24 = Y )
% 6.92/7.24 = ( ( ( nth_int @ Xs @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 6.92/7.24 = Y )
% 6.92/7.24 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % nth_non_equal_first_eq
% 6.92/7.24 thf(fact_5635_nth__non__equal__first__eq,axiom,
% 6.92/7.24 ! [X: nat,Y: nat,Xs: list_nat,N2: nat] :
% 6.92/7.24 ( ( X != Y )
% 6.92/7.24 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N2 )
% 6.92/7.24 = Y )
% 6.92/7.24 = ( ( ( nth_nat @ Xs @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 6.92/7.24 = Y )
% 6.92/7.24 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % nth_non_equal_first_eq
% 6.92/7.24 thf(fact_5636_slice__Cons,axiom,
% 6.92/7.24 ! [Begin: nat,End: nat,X: int,Xs: list_int] :
% 6.92/7.24 ( ( ( ( Begin = zero_zero_nat )
% 6.92/7.24 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 6.92/7.24 => ( ( slice_int @ Begin @ End @ ( cons_int @ X @ Xs ) )
% 6.92/7.24 = ( cons_int @ X @ ( slice_int @ Begin @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) )
% 6.92/7.24 & ( ~ ( ( Begin = zero_zero_nat )
% 6.92/7.24 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 6.92/7.24 => ( ( slice_int @ Begin @ End @ ( cons_int @ X @ Xs ) )
% 6.92/7.24 = ( slice_int @ ( minus_minus_nat @ Begin @ one_one_nat ) @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % slice_Cons
% 6.92/7.24 thf(fact_5637_slice__Cons,axiom,
% 6.92/7.24 ! [Begin: nat,End: nat,X: nat,Xs: list_nat] :
% 6.92/7.24 ( ( ( ( Begin = zero_zero_nat )
% 6.92/7.24 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 6.92/7.24 => ( ( slice_nat @ Begin @ End @ ( cons_nat @ X @ Xs ) )
% 6.92/7.24 = ( cons_nat @ X @ ( slice_nat @ Begin @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) )
% 6.92/7.24 & ( ~ ( ( Begin = zero_zero_nat )
% 6.92/7.24 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 6.92/7.24 => ( ( slice_nat @ Begin @ End @ ( cons_nat @ X @ Xs ) )
% 6.92/7.24 = ( slice_nat @ ( minus_minus_nat @ Begin @ one_one_nat ) @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % slice_Cons
% 6.92/7.24 thf(fact_5638_same__fstI,axiom,
% 6.92/7.24 ! [P2: ( produc3658429121746597890et_nat > $o ) > $o,X: produc3658429121746597890et_nat > $o,Y8: produc3658429121746597890et_nat,Y: produc3658429121746597890et_nat,R3: ( produc3658429121746597890et_nat > $o ) > set_Pr719794911490849221et_nat] :
% 6.92/7.24 ( ( P2 @ X )
% 6.92/7.24 => ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ Y8 @ Y ) @ ( R3 @ X ) )
% 6.92/7.24 => ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ X @ Y8 ) @ ( produc5001842942810119800et_nat @ X @ Y ) ) @ ( same_f7251492184213700963et_nat @ P2 @ R3 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % same_fstI
% 6.92/7.24 thf(fact_5639_same__fstI,axiom,
% 6.92/7.24 ! [P2: ( produc3658429121746597890et_nat > $o ) > $o,X: produc3658429121746597890et_nat > $o,Y8: produc3925858234332021118et_nat,Y: produc3925858234332021118et_nat,R3: ( produc3658429121746597890et_nat > $o ) > set_Pr7928877670098842301et_nat] :
% 6.92/7.24 ( ( P2 @ X )
% 6.92/7.24 => ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ Y8 @ Y ) @ ( R3 @ X ) )
% 6.92/7.24 => ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ X @ Y8 ) @ ( produc2245416461498447860et_nat @ X @ Y ) ) @ ( same_f1912051055550046943et_nat @ P2 @ R3 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % same_fstI
% 6.92/7.24 thf(fact_5640_same__fstI,axiom,
% 6.92/7.24 ! [P2: b > $o,X: b,Y8: produc6653097349344004940it_nat,Y: produc6653097349344004940it_nat,R3: b > set_Pr4389693562480114009it_nat] :
% 6.92/7.24 ( ( P2 @ X )
% 6.92/7.24 => ( ( member5617269971687963298it_nat @ ( produc3130510018828335921it_nat @ Y8 @ Y ) @ ( R3 @ X ) )
% 6.92/7.24 => ( member6820296301096096254it_nat @ ( produc6853161671299316109it_nat @ ( produc4082563078715348724it_nat @ X @ Y8 ) @ ( produc4082563078715348724it_nat @ X @ Y ) ) @ ( same_f3722904161141537503it_nat @ P2 @ R3 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % same_fstI
% 6.92/7.24 thf(fact_5641_same__fstI,axiom,
% 6.92/7.24 ! [P2: a > $o,X: a,Y8: produc6653097349344004940it_nat,Y: produc6653097349344004940it_nat,R3: a > set_Pr4389693562480114009it_nat] :
% 6.92/7.24 ( ( P2 @ X )
% 6.92/7.24 => ( ( member5617269971687963298it_nat @ ( produc3130510018828335921it_nat @ Y8 @ Y ) @ ( R3 @ X ) )
% 6.92/7.24 => ( member5335690527091456380it_nat @ ( produc1743342482959036555it_nat @ ( produc9178034014595674355it_nat @ X @ Y8 ) @ ( produc9178034014595674355it_nat @ X @ Y ) ) @ ( same_f8818375097021863134it_nat @ P2 @ R3 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % same_fstI
% 6.92/7.24 thf(fact_5642_same__fstI,axiom,
% 6.92/7.24 ! [P2: int > $o,X: int,Y8: int,Y: int,R3: int > set_Pr958786334691620121nt_int] :
% 6.92/7.24 ( ( P2 @ X )
% 6.92/7.24 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y8 @ Y ) @ ( R3 @ X ) )
% 6.92/7.24 => ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ X @ Y8 ) @ ( product_Pair_int_int @ X @ Y ) ) @ ( same_fst_int_int @ P2 @ R3 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % same_fstI
% 6.92/7.24 thf(fact_5643_upto__aux__rec,axiom,
% 6.92/7.24 ( upto_aux
% 6.92/7.24 = ( ^ [I: int,J: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J @ I ) @ Js @ ( upto_aux @ I @ ( minus_minus_int @ J @ one_one_int ) @ ( cons_int @ J @ Js ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % upto_aux_rec
% 6.92/7.24 thf(fact_5644_neg__numeral__le__ceiling,axiom,
% 6.92/7.24 ! [V: num,X: rat] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 6.92/7.24 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_le_ceiling
% 6.92/7.24 thf(fact_5645_ceiling__less__neg__numeral,axiom,
% 6.92/7.24 ! [X: rat,V: num] :
% 6.92/7.24 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 6.92/7.24 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_less_neg_numeral
% 6.92/7.24 thf(fact_5646_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 6.92/7.24 ! [A: int,X: num,N2: nat] :
% 6.92/7.24 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) )
% 6.92/7.24 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_neg_numeral_power_cancel_iff
% 6.92/7.24 thf(fact_5647_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 6.92/7.24 ! [A: int,X: num,N2: nat] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) )
% 6.92/7.24 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_neg_numeral_power_cancel_iff
% 6.92/7.24 thf(fact_5648_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 6.92/7.24 ! [A: int,X: num,N2: nat] :
% 6.92/7.24 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N2 ) )
% 6.92/7.24 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_neg_numeral_power_cancel_iff
% 6.92/7.24 thf(fact_5649_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: num,N2: nat,A: int] :
% 6.92/7.24 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 6.92/7.24 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_power_less_of_int_cancel_iff
% 6.92/7.24 thf(fact_5650_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: num,N2: nat,A: int] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 6.92/7.24 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_power_less_of_int_cancel_iff
% 6.92/7.24 thf(fact_5651_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: num,N2: nat,A: int] :
% 6.92/7.24 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 6.92/7.24 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_power_less_of_int_cancel_iff
% 6.92/7.24 thf(fact_5652_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 6.92/7.24 ! [A: int,X: num,N2: nat] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) )
% 6.92/7.24 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_neg_numeral_power_cancel_iff
% 6.92/7.24 thf(fact_5653_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 6.92/7.24 ! [A: int,X: num,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N2 ) )
% 6.92/7.24 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_neg_numeral_power_cancel_iff
% 6.92/7.24 thf(fact_5654_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 6.92/7.24 ! [A: int,X: num,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) )
% 6.92/7.24 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_neg_numeral_power_cancel_iff
% 6.92/7.24 thf(fact_5655_of__int__le__iff,axiom,
% 6.92/7.24 ! [W2: int,Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z3 ) )
% 6.92/7.24 = ( ord_less_eq_int @ W2 @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_iff
% 6.92/7.24 thf(fact_5656_of__int__le__iff,axiom,
% 6.92/7.24 ! [W2: int,Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z3 ) )
% 6.92/7.24 = ( ord_less_eq_int @ W2 @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_iff
% 6.92/7.24 thf(fact_5657_of__int__less__iff,axiom,
% 6.92/7.24 ! [W2: int,Z3: int] :
% 6.92/7.24 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z3 ) )
% 6.92/7.24 = ( ord_less_int @ W2 @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_iff
% 6.92/7.24 thf(fact_5658_of__int__less__iff,axiom,
% 6.92/7.24 ! [W2: int,Z3: int] :
% 6.92/7.24 ( ( ord_less_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z3 ) )
% 6.92/7.24 = ( ord_less_int @ W2 @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_iff
% 6.92/7.24 thf(fact_5659_of__int__add,axiom,
% 6.92/7.24 ! [W2: int,Z3: int] :
% 6.92/7.24 ( ( ring_1_of_int_int @ ( plus_plus_int @ W2 @ Z3 ) )
% 6.92/7.24 = ( plus_plus_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_add
% 6.92/7.24 thf(fact_5660_of__int__add,axiom,
% 6.92/7.24 ! [W2: int,Z3: int] :
% 6.92/7.24 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W2 @ Z3 ) )
% 6.92/7.24 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_add
% 6.92/7.24 thf(fact_5661_ceiling__add__of__int,axiom,
% 6.92/7.24 ! [X: rat,Z3: int] :
% 6.92/7.24 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z3 ) ) )
% 6.92/7.24 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_add_of_int
% 6.92/7.24 thf(fact_5662_of__int__le__0__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.24 = ( ord_less_eq_int @ Z3 @ zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_0_iff
% 6.92/7.24 thf(fact_5663_of__int__le__0__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ zero_zero_rat )
% 6.92/7.24 = ( ord_less_eq_int @ Z3 @ zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_0_iff
% 6.92/7.24 thf(fact_5664_of__int__le__0__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z3 ) @ zero_zero_int )
% 6.92/7.24 = ( ord_less_eq_int @ Z3 @ zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_0_iff
% 6.92/7.24 thf(fact_5665_of__int__0__le__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z3 ) )
% 6.92/7.24 = ( ord_less_eq_int @ zero_zero_int @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_0_le_iff
% 6.92/7.24 thf(fact_5666_of__int__0__le__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z3 ) )
% 6.92/7.24 = ( ord_less_eq_int @ zero_zero_int @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_0_le_iff
% 6.92/7.24 thf(fact_5667_of__int__0__le__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z3 ) )
% 6.92/7.24 = ( ord_less_eq_int @ zero_zero_int @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_0_le_iff
% 6.92/7.24 thf(fact_5668_of__int__less__0__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.24 = ( ord_less_int @ Z3 @ zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_0_iff
% 6.92/7.24 thf(fact_5669_of__int__less__0__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ zero_zero_rat )
% 6.92/7.24 = ( ord_less_int @ Z3 @ zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_0_iff
% 6.92/7.24 thf(fact_5670_of__int__less__0__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_int @ ( ring_1_of_int_int @ Z3 ) @ zero_zero_int )
% 6.92/7.24 = ( ord_less_int @ Z3 @ zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_0_iff
% 6.92/7.24 thf(fact_5671_of__int__0__less__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z3 ) )
% 6.92/7.24 = ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_0_less_iff
% 6.92/7.24 thf(fact_5672_of__int__0__less__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z3 ) )
% 6.92/7.24 = ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_0_less_iff
% 6.92/7.24 thf(fact_5673_of__int__0__less__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z3 ) )
% 6.92/7.24 = ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_0_less_iff
% 6.92/7.24 thf(fact_5674_of__int__numeral__le__iff,axiom,
% 6.92/7.24 ! [N2: num,Z3: int] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( ring_18347121197199848620nteger @ Z3 ) )
% 6.92/7.24 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_numeral_le_iff
% 6.92/7.24 thf(fact_5675_of__int__numeral__le__iff,axiom,
% 6.92/7.24 ! [N2: num,Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z3 ) )
% 6.92/7.24 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_numeral_le_iff
% 6.92/7.24 thf(fact_5676_of__int__numeral__le__iff,axiom,
% 6.92/7.24 ! [N2: num,Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z3 ) )
% 6.92/7.24 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_numeral_le_iff
% 6.92/7.24 thf(fact_5677_of__int__le__numeral__iff,axiom,
% 6.92/7.24 ! [Z3: int,N2: num] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z3 ) @ ( numera6620942414471956472nteger @ N2 ) )
% 6.92/7.24 = ( ord_less_eq_int @ Z3 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_numeral_iff
% 6.92/7.24 thf(fact_5678_of__int__le__numeral__iff,axiom,
% 6.92/7.24 ! [Z3: int,N2: num] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ ( numeral_numeral_rat @ N2 ) )
% 6.92/7.24 = ( ord_less_eq_int @ Z3 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_numeral_iff
% 6.92/7.24 thf(fact_5679_of__int__le__numeral__iff,axiom,
% 6.92/7.24 ! [Z3: int,N2: num] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z3 ) @ ( numeral_numeral_int @ N2 ) )
% 6.92/7.24 = ( ord_less_eq_int @ Z3 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_numeral_iff
% 6.92/7.24 thf(fact_5680_of__int__numeral__less__iff,axiom,
% 6.92/7.24 ! [N2: num,Z3: int] :
% 6.92/7.24 ( ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z3 ) )
% 6.92/7.24 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_numeral_less_iff
% 6.92/7.24 thf(fact_5681_of__int__numeral__less__iff,axiom,
% 6.92/7.24 ! [N2: num,Z3: int] :
% 6.92/7.24 ( ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z3 ) )
% 6.92/7.24 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_numeral_less_iff
% 6.92/7.24 thf(fact_5682_of__int__numeral__less__iff,axiom,
% 6.92/7.24 ! [N2: num,Z3: int] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( ring_18347121197199848620nteger @ Z3 ) )
% 6.92/7.24 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_numeral_less_iff
% 6.92/7.24 thf(fact_5683_of__int__less__numeral__iff,axiom,
% 6.92/7.24 ! [Z3: int,N2: num] :
% 6.92/7.24 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ ( numeral_numeral_rat @ N2 ) )
% 6.92/7.24 = ( ord_less_int @ Z3 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_numeral_iff
% 6.92/7.24 thf(fact_5684_of__int__less__numeral__iff,axiom,
% 6.92/7.24 ! [Z3: int,N2: num] :
% 6.92/7.24 ( ( ord_less_int @ ( ring_1_of_int_int @ Z3 ) @ ( numeral_numeral_int @ N2 ) )
% 6.92/7.24 = ( ord_less_int @ Z3 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_numeral_iff
% 6.92/7.24 thf(fact_5685_of__int__less__numeral__iff,axiom,
% 6.92/7.24 ! [Z3: int,N2: num] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z3 ) @ ( numera6620942414471956472nteger @ N2 ) )
% 6.92/7.24 = ( ord_less_int @ Z3 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_numeral_iff
% 6.92/7.24 thf(fact_5686_of__int__le__1__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z3 ) @ one_one_Code_integer )
% 6.92/7.24 = ( ord_less_eq_int @ Z3 @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_1_iff
% 6.92/7.24 thf(fact_5687_of__int__le__1__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ one_one_rat )
% 6.92/7.24 = ( ord_less_eq_int @ Z3 @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_1_iff
% 6.92/7.24 thf(fact_5688_of__int__le__1__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z3 ) @ one_one_int )
% 6.92/7.24 = ( ord_less_eq_int @ Z3 @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_1_iff
% 6.92/7.24 thf(fact_5689_of__int__1__le__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z3 ) )
% 6.92/7.24 = ( ord_less_eq_int @ one_one_int @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_1_le_iff
% 6.92/7.24 thf(fact_5690_of__int__1__le__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z3 ) )
% 6.92/7.24 = ( ord_less_eq_int @ one_one_int @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_1_le_iff
% 6.92/7.24 thf(fact_5691_of__int__1__le__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z3 ) )
% 6.92/7.24 = ( ord_less_eq_int @ one_one_int @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_1_le_iff
% 6.92/7.24 thf(fact_5692_of__int__less__1__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z3 ) @ one_one_Code_integer )
% 6.92/7.24 = ( ord_less_int @ Z3 @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_1_iff
% 6.92/7.24 thf(fact_5693_of__int__less__1__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ one_one_rat )
% 6.92/7.24 = ( ord_less_int @ Z3 @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_1_iff
% 6.92/7.24 thf(fact_5694_of__int__less__1__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_int @ ( ring_1_of_int_int @ Z3 ) @ one_one_int )
% 6.92/7.24 = ( ord_less_int @ Z3 @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_1_iff
% 6.92/7.24 thf(fact_5695_of__int__1__less__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z3 ) )
% 6.92/7.24 = ( ord_less_int @ one_one_int @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_1_less_iff
% 6.92/7.24 thf(fact_5696_of__int__1__less__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z3 ) )
% 6.92/7.24 = ( ord_less_int @ one_one_int @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_1_less_iff
% 6.92/7.24 thf(fact_5697_of__int__1__less__iff,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z3 ) )
% 6.92/7.24 = ( ord_less_int @ one_one_int @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_1_less_iff
% 6.92/7.24 thf(fact_5698_ceiling__le__zero,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 6.92/7.24 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_le_zero
% 6.92/7.24 thf(fact_5699_zero__less__ceiling,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 6.92/7.24 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_less_ceiling
% 6.92/7.24 thf(fact_5700_ceiling__le__numeral,axiom,
% 6.92/7.24 ! [X: rat,V: num] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 6.92/7.24 = ( ord_less_eq_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_le_numeral
% 6.92/7.24 thf(fact_5701_ceiling__less__one,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 6.92/7.24 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_less_one
% 6.92/7.24 thf(fact_5702_one__le__ceiling,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 6.92/7.24 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_le_ceiling
% 6.92/7.24 thf(fact_5703_numeral__less__ceiling,axiom,
% 6.92/7.24 ! [V: num,X: rat] :
% 6.92/7.24 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 6.92/7.24 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_less_ceiling
% 6.92/7.24 thf(fact_5704_ceiling__le__one,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 6.92/7.24 = ( ord_less_eq_rat @ X @ one_one_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_le_one
% 6.92/7.24 thf(fact_5705_one__less__ceiling,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 6.92/7.24 = ( ord_less_rat @ one_one_rat @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_less_ceiling
% 6.92/7.24 thf(fact_5706_ceiling__add__numeral,axiom,
% 6.92/7.24 ! [X: rat,V: num] :
% 6.92/7.24 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 6.92/7.24 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_add_numeral
% 6.92/7.24 thf(fact_5707_ceiling__add__one,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 6.92/7.24 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_add_one
% 6.92/7.24 thf(fact_5708_of__nat__nat,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.24 => ( ( semiri681578069525770553at_rat @ ( nat2 @ Z3 ) )
% 6.92/7.24 = ( ring_1_of_int_rat @ Z3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_nat_nat
% 6.92/7.24 thf(fact_5709_of__nat__nat,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.24 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z3 ) )
% 6.92/7.24 = ( ring_1_of_int_int @ Z3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_nat_nat
% 6.92/7.24 thf(fact_5710_of__nat__nat,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.24 => ( ( semiri4939895301339042750nteger @ ( nat2 @ Z3 ) )
% 6.92/7.24 = ( ring_18347121197199848620nteger @ Z3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_nat_nat
% 6.92/7.24 thf(fact_5711_of__int__le__of__int__power__cancel__iff,axiom,
% 6.92/7.24 ! [B: int,W2: nat,X: int] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X ) )
% 6.92/7.24 = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_of_int_power_cancel_iff
% 6.92/7.24 thf(fact_5712_of__int__le__of__int__power__cancel__iff,axiom,
% 6.92/7.24 ! [B: int,W2: nat,X: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X ) )
% 6.92/7.24 = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_of_int_power_cancel_iff
% 6.92/7.24 thf(fact_5713_of__int__power__le__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: int,B: int,W2: nat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 6.92/7.24 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_power_le_of_int_cancel_iff
% 6.92/7.24 thf(fact_5714_of__int__power__le__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: int,B: int,W2: nat] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 6.92/7.24 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_power_le_of_int_cancel_iff
% 6.92/7.24 thf(fact_5715_of__int__less__of__int__power__cancel__iff,axiom,
% 6.92/7.24 ! [B: int,W2: nat,X: int] :
% 6.92/7.24 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X ) )
% 6.92/7.24 = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_of_int_power_cancel_iff
% 6.92/7.24 thf(fact_5716_of__int__less__of__int__power__cancel__iff,axiom,
% 6.92/7.24 ! [B: int,W2: nat,X: int] :
% 6.92/7.24 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X ) )
% 6.92/7.24 = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_of_int_power_cancel_iff
% 6.92/7.24 thf(fact_5717_of__int__power__less__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: int,B: int,W2: nat] :
% 6.92/7.24 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 6.92/7.24 = ( ord_less_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_power_less_of_int_cancel_iff
% 6.92/7.24 thf(fact_5718_of__int__power__less__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: int,B: int,W2: nat] :
% 6.92/7.24 ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 6.92/7.24 = ( ord_less_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_power_less_of_int_cancel_iff
% 6.92/7.24 thf(fact_5719_ceiling__less__zero,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 6.92/7.24 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_less_zero
% 6.92/7.24 thf(fact_5720_zero__le__ceiling,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 6.92/7.24 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_le_ceiling
% 6.92/7.24 thf(fact_5721_ceiling__less__numeral,axiom,
% 6.92/7.24 ! [X: rat,V: num] :
% 6.92/7.24 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 6.92/7.24 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_less_numeral
% 6.92/7.24 thf(fact_5722_numeral__le__ceiling,axiom,
% 6.92/7.24 ! [V: num,X: rat] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 6.92/7.24 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_le_ceiling
% 6.92/7.24 thf(fact_5723_ceiling__le__neg__numeral,axiom,
% 6.92/7.24 ! [X: rat,V: num] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 6.92/7.24 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_le_neg_numeral
% 6.92/7.24 thf(fact_5724_neg__numeral__less__ceiling,axiom,
% 6.92/7.24 ! [V: num,X: rat] :
% 6.92/7.24 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 6.92/7.24 = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_less_ceiling
% 6.92/7.24 thf(fact_5725_numeral__power__le__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: num,N2: nat,A: int] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 6.92/7.24 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_power_le_of_int_cancel_iff
% 6.92/7.24 thf(fact_5726_numeral__power__le__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: num,N2: nat,A: int] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 6.92/7.24 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_power_le_of_int_cancel_iff
% 6.92/7.24 thf(fact_5727_numeral__power__le__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: num,N2: nat,A: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 6.92/7.24 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_power_le_of_int_cancel_iff
% 6.92/7.24 thf(fact_5728_of__int__le__numeral__power__cancel__iff,axiom,
% 6.92/7.24 ! [A: int,X: num,N2: nat] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N2 ) )
% 6.92/7.24 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_numeral_power_cancel_iff
% 6.92/7.24 thf(fact_5729_of__int__le__numeral__power__cancel__iff,axiom,
% 6.92/7.24 ! [A: int,X: num,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) )
% 6.92/7.24 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_numeral_power_cancel_iff
% 6.92/7.24 thf(fact_5730_of__int__le__numeral__power__cancel__iff,axiom,
% 6.92/7.24 ! [A: int,X: num,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 6.92/7.24 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_le_numeral_power_cancel_iff
% 6.92/7.24 thf(fact_5731_numeral__power__less__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: num,N2: nat,A: int] :
% 6.92/7.24 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 6.92/7.24 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_power_less_of_int_cancel_iff
% 6.92/7.24 thf(fact_5732_numeral__power__less__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: num,N2: nat,A: int] :
% 6.92/7.24 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 6.92/7.24 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_power_less_of_int_cancel_iff
% 6.92/7.24 thf(fact_5733_numeral__power__less__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: num,N2: nat,A: int] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 6.92/7.24 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_power_less_of_int_cancel_iff
% 6.92/7.24 thf(fact_5734_of__int__less__numeral__power__cancel__iff,axiom,
% 6.92/7.24 ! [A: int,X: num,N2: nat] :
% 6.92/7.24 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) )
% 6.92/7.24 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_numeral_power_cancel_iff
% 6.92/7.24 thf(fact_5735_of__int__less__numeral__power__cancel__iff,axiom,
% 6.92/7.24 ! [A: int,X: num,N2: nat] :
% 6.92/7.24 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 6.92/7.24 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_numeral_power_cancel_iff
% 6.92/7.24 thf(fact_5736_of__int__less__numeral__power__cancel__iff,axiom,
% 6.92/7.24 ! [A: int,X: num,N2: nat] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N2 ) )
% 6.92/7.24 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_less_numeral_power_cancel_iff
% 6.92/7.24 thf(fact_5737_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: num,N2: nat,A: int] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 6.92/7.24 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_power_le_of_int_cancel_iff
% 6.92/7.24 thf(fact_5738_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: num,N2: nat,A: int] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 6.92/7.24 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_power_le_of_int_cancel_iff
% 6.92/7.24 thf(fact_5739_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 6.92/7.24 ! [X: num,N2: nat,A: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 6.92/7.24 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_power_le_of_int_cancel_iff
% 6.92/7.24 thf(fact_5740_le__of__int__ceiling,axiom,
% 6.92/7.24 ! [X: rat] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % le_of_int_ceiling
% 6.92/7.24 thf(fact_5741_ceiling__le__iff,axiom,
% 6.92/7.24 ! [X: rat,Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ Z3 )
% 6.92/7.24 = ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_le_iff
% 6.92/7.24 thf(fact_5742_less__ceiling__iff,axiom,
% 6.92/7.24 ! [Z3: int,X: rat] :
% 6.92/7.24 ( ( ord_less_int @ Z3 @ ( archim2889992004027027881ng_rat @ X ) )
% 6.92/7.24 = ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % less_ceiling_iff
% 6.92/7.24 thf(fact_5743_ex__le__of__int,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ? [Z2: int] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % ex_le_of_int
% 6.92/7.24 thf(fact_5744_ex__of__int__less,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ? [Z2: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ X ) ).
% 6.92/7.24
% 6.92/7.24 % ex_of_int_less
% 6.92/7.24 thf(fact_5745_ex__less__of__int,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ? [Z2: int] : ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % ex_less_of_int
% 6.92/7.24 thf(fact_5746_ceiling__correct,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) @ one_one_rat ) @ X )
% 6.92/7.24 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_correct
% 6.92/7.24 thf(fact_5747_ceiling__unique,axiom,
% 6.92/7.24 ! [Z3: int,X: rat] :
% 6.92/7.24 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z3 ) @ one_one_rat ) @ X )
% 6.92/7.24 => ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z3 ) )
% 6.92/7.24 => ( ( archim2889992004027027881ng_rat @ X )
% 6.92/7.24 = Z3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_unique
% 6.92/7.24 thf(fact_5748_ceiling__eq__iff,axiom,
% 6.92/7.24 ! [X: rat,A: int] :
% 6.92/7.24 ( ( ( archim2889992004027027881ng_rat @ X )
% 6.92/7.24 = A )
% 6.92/7.24 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X )
% 6.92/7.24 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_eq_iff
% 6.92/7.24 thf(fact_5749_ceiling__split,axiom,
% 6.92/7.24 ! [P2: int > $o,T6: rat] :
% 6.92/7.24 ( ( P2 @ ( archim2889992004027027881ng_rat @ T6 ) )
% 6.92/7.24 = ( ! [I: int] :
% 6.92/7.24 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I ) @ one_one_rat ) @ T6 )
% 6.92/7.24 & ( ord_less_eq_rat @ T6 @ ( ring_1_of_int_rat @ I ) ) )
% 6.92/7.24 => ( P2 @ I ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_split
% 6.92/7.24 thf(fact_5750_ceiling__less__iff,axiom,
% 6.92/7.24 ! [X: rat,Z3: int] :
% 6.92/7.24 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ Z3 )
% 6.92/7.24 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z3 ) @ one_one_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_less_iff
% 6.92/7.24 thf(fact_5751_le__ceiling__iff,axiom,
% 6.92/7.24 ! [Z3: int,X: rat] :
% 6.92/7.24 ( ( ord_less_eq_int @ Z3 @ ( archim2889992004027027881ng_rat @ X ) )
% 6.92/7.24 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z3 ) @ one_one_rat ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % le_ceiling_iff
% 6.92/7.24 thf(fact_5752_ceiling__mono,axiom,
% 6.92/7.24 ! [Y: rat,X: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ Y @ X )
% 6.92/7.24 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y ) @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_mono
% 6.92/7.24 thf(fact_5753_ceiling__less__cancel,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y ) )
% 6.92/7.24 => ( ord_less_rat @ X @ Y ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_less_cancel
% 6.92/7.24 thf(fact_5754_ceiling__divide__upper,axiom,
% 6.92/7.24 ! [Q6: rat,P3: rat] :
% 6.92/7.24 ( ( ord_less_rat @ zero_zero_rat @ Q6 )
% 6.92/7.24 => ( ord_less_eq_rat @ P3 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P3 @ Q6 ) ) ) @ Q6 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_divide_upper
% 6.92/7.24 thf(fact_5755_ceiling__divide__lower,axiom,
% 6.92/7.24 ! [Q6: rat,P3: rat] :
% 6.92/7.24 ( ( ord_less_rat @ zero_zero_rat @ Q6 )
% 6.92/7.24 => ( 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 ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_divide_lower
% 6.92/7.24 thf(fact_5756_of__nat__ceiling,axiom,
% 6.92/7.24 ! [R2: rat] : ( ord_less_eq_rat @ R2 @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim2889992004027027881ng_rat @ R2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_nat_ceiling
% 6.92/7.24 thf(fact_5757_ceiling__add__le,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ Y ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_add_le
% 6.92/7.24 thf(fact_5758_of__int__nonneg,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.24 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_nonneg
% 6.92/7.24 thf(fact_5759_of__int__nonneg,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.24 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_nonneg
% 6.92/7.24 thf(fact_5760_of__int__nonneg,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.24 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_nonneg
% 6.92/7.24 thf(fact_5761_of__int__pos,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 6.92/7.24 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_pos
% 6.92/7.24 thf(fact_5762_of__int__pos,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 6.92/7.24 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_pos
% 6.92/7.24 thf(fact_5763_of__int__pos,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 6.92/7.24 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_pos
% 6.92/7.24 thf(fact_5764_of__int__leD,axiom,
% 6.92/7.24 ! [N2: int,X: code_integer] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X )
% 6.92/7.24 => ( ( N2 = zero_zero_int )
% 6.92/7.24 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_leD
% 6.92/7.24 thf(fact_5765_of__int__leD,axiom,
% 6.92/7.24 ! [N2: int,X: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X )
% 6.92/7.24 => ( ( N2 = zero_zero_int )
% 6.92/7.24 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_leD
% 6.92/7.24 thf(fact_5766_of__int__leD,axiom,
% 6.92/7.24 ! [N2: int,X: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X )
% 6.92/7.24 => ( ( N2 = zero_zero_int )
% 6.92/7.24 | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_leD
% 6.92/7.24 thf(fact_5767_of__int__lessD,axiom,
% 6.92/7.24 ! [N2: int,X: code_integer] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X )
% 6.92/7.24 => ( ( N2 = zero_zero_int )
% 6.92/7.24 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_lessD
% 6.92/7.24 thf(fact_5768_of__int__lessD,axiom,
% 6.92/7.24 ! [N2: int,X: rat] :
% 6.92/7.24 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X )
% 6.92/7.24 => ( ( N2 = zero_zero_int )
% 6.92/7.24 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_lessD
% 6.92/7.24 thf(fact_5769_of__int__lessD,axiom,
% 6.92/7.24 ! [N2: int,X: int] :
% 6.92/7.24 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X )
% 6.92/7.24 => ( ( N2 = zero_zero_int )
% 6.92/7.24 | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_lessD
% 6.92/7.24 thf(fact_5770_floor__exists,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ? [Z2: int] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X )
% 6.92/7.24 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_exists
% 6.92/7.24 thf(fact_5771_floor__exists1,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ? [X3: int] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ X )
% 6.92/7.24 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 6.92/7.24 & ! [Y5: int] :
% 6.92/7.24 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y5 ) @ X )
% 6.92/7.24 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 6.92/7.24 => ( Y5 = X3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_exists1
% 6.92/7.24 thf(fact_5772_of__nat__less__of__int__iff,axiom,
% 6.92/7.24 ! [N2: nat,X: int] :
% 6.92/7.24 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( ring_1_of_int_rat @ X ) )
% 6.92/7.24 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_nat_less_of_int_iff
% 6.92/7.24 thf(fact_5773_of__nat__less__of__int__iff,axiom,
% 6.92/7.24 ! [N2: nat,X: int] :
% 6.92/7.24 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( ring_1_of_int_int @ X ) )
% 6.92/7.24 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_nat_less_of_int_iff
% 6.92/7.24 thf(fact_5774_of__nat__less__of__int__iff,axiom,
% 6.92/7.24 ! [N2: nat,X: int] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( ring_18347121197199848620nteger @ X ) )
% 6.92/7.24 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_nat_less_of_int_iff
% 6.92/7.24 thf(fact_5775_mult__ceiling__le,axiom,
% 6.92/7.24 ! [A: rat,B: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.24 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_ceiling_le
% 6.92/7.24 thf(fact_5776_of__int__of__nat,axiom,
% 6.92/7.24 ( ring_1_of_int_rat
% 6.92/7.24 = ( ^ [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 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_of_nat
% 6.92/7.24 thf(fact_5777_of__int__of__nat,axiom,
% 6.92/7.24 ( ring_1_of_int_int
% 6.92/7.24 = ( ^ [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 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_of_nat
% 6.92/7.24 thf(fact_5778_of__int__of__nat,axiom,
% 6.92/7.24 ( ring_18347121197199848620nteger
% 6.92/7.24 = ( ^ [K3: int] : ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri4939895301339042750nteger @ ( nat2 @ K3 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_of_nat
% 6.92/7.24 thf(fact_5779_floor__le__neg__numeral,axiom,
% 6.92/7.24 ! [X: rat,V: num] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 6.92/7.24 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_le_neg_numeral
% 6.92/7.24 thf(fact_5780_neg__numeral__less__floor,axiom,
% 6.92/7.24 ! [V: num,X: rat] :
% 6.92/7.24 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 6.92/7.24 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_less_floor
% 6.92/7.24 thf(fact_5781_in__lex__prod,axiom,
% 6.92/7.24 ! [A: int,B: int,A2: int,B2: int,R2: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 6.92/7.24 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ A @ B ) @ ( product_Pair_int_int @ A2 @ B2 ) ) @ ( lex_prod_int_int @ R2 @ S2 ) )
% 6.92/7.24 = ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ A2 ) @ R2 )
% 6.92/7.24 | ( ( A = A2 )
% 6.92/7.24 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ B2 ) @ S2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % in_lex_prod
% 6.92/7.24 thf(fact_5782_in__lex__prod,axiom,
% 6.92/7.24 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat,R2: set_Pr2161125870931222855_nat_o,S2: set_Pr719794911490849221et_nat] :
% 6.92/7.24 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ ( produc5001842942810119800et_nat @ A2 @ B2 ) ) @ ( lex_pr5340572901959109728et_nat @ R2 @ S2 ) )
% 6.92/7.24 = ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A @ A2 ) @ R2 )
% 6.92/7.24 | ( ( A = A2 )
% 6.92/7.24 & ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ B @ B2 ) @ S2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % in_lex_prod
% 6.92/7.24 thf(fact_5783_in__lex__prod,axiom,
% 6.92/7.24 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat,R2: set_Pr2161125870931222855_nat_o,S2: set_Pr7928877670098842301et_nat] :
% 6.92/7.24 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ ( produc2245416461498447860et_nat @ A2 @ B2 ) ) @ ( lex_pr4722427456421979612et_nat @ R2 @ S2 ) )
% 6.92/7.24 = ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A @ A2 ) @ R2 )
% 6.92/7.24 | ( ( A = A2 )
% 6.92/7.24 & ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ B @ B2 ) @ S2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % in_lex_prod
% 6.92/7.24 thf(fact_5784_in__lex__prod,axiom,
% 6.92/7.24 ! [A: b,B: produc6653097349344004940it_nat,A2: b,B2: produc6653097349344004940it_nat,R2: set_Product_prod_b_b,S2: set_Pr4389693562480114009it_nat] :
% 6.92/7.24 ( ( member6820296301096096254it_nat @ ( produc6853161671299316109it_nat @ ( produc4082563078715348724it_nat @ A @ B ) @ ( produc4082563078715348724it_nat @ A2 @ B2 ) ) @ ( lex_pr2603589247317408988it_nat @ R2 @ S2 ) )
% 6.92/7.24 = ( ( member7862447936710763792od_b_b @ ( product_Pair_b_b @ A @ A2 ) @ R2 )
% 6.92/7.24 | ( ( A = A2 )
% 6.92/7.24 & ( member5617269971687963298it_nat @ ( produc3130510018828335921it_nat @ B @ B2 ) @ S2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % in_lex_prod
% 6.92/7.24 thf(fact_5785_in__lex__prod,axiom,
% 6.92/7.24 ! [A: a,B: produc6653097349344004940it_nat,A2: a,B2: produc6653097349344004940it_nat,R2: set_Product_prod_a_a,S2: set_Pr4389693562480114009it_nat] :
% 6.92/7.24 ( ( member5335690527091456380it_nat @ ( produc1743342482959036555it_nat @ ( produc9178034014595674355it_nat @ A @ B ) @ ( produc9178034014595674355it_nat @ A2 @ B2 ) ) @ ( lex_pr7699060183197734619it_nat @ R2 @ S2 ) )
% 6.92/7.24 = ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ A @ A2 ) @ R2 )
% 6.92/7.24 | ( ( A = A2 )
% 6.92/7.24 & ( member5617269971687963298it_nat @ ( produc3130510018828335921it_nat @ B @ B2 ) @ S2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % in_lex_prod
% 6.92/7.24 thf(fact_5786_in__lex__prod,axiom,
% 6.92/7.24 ! [A: nat,B: nat,A2: nat,B2: nat,R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 6.92/7.24 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( product_Pair_nat_nat @ A2 @ B2 ) ) @ ( lex_prod_nat_nat @ R2 @ S2 ) )
% 6.92/7.24 = ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A2 ) @ R2 )
% 6.92/7.24 | ( ( A = A2 )
% 6.92/7.24 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ B2 ) @ S2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % in_lex_prod
% 6.92/7.24 thf(fact_5787_mult__ceiling__le__Ints,axiom,
% 6.92/7.24 ! [A: rat,B: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.24 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 6.92/7.24 => ( 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 ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_ceiling_le_Ints
% 6.92/7.24 thf(fact_5788_mult__ceiling__le__Ints,axiom,
% 6.92/7.24 ! [A: rat,B: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.24 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 6.92/7.24 => ( 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 ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_ceiling_le_Ints
% 6.92/7.24 thf(fact_5789_floor__less__neg__numeral,axiom,
% 6.92/7.24 ! [X: rat,V: num] :
% 6.92/7.24 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 6.92/7.24 = ( ord_less_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_less_neg_numeral
% 6.92/7.24 thf(fact_5790_neg__numeral__le__floor,axiom,
% 6.92/7.24 ! [V: num,X: rat] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 6.92/7.24 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_le_floor
% 6.92/7.24 thf(fact_5791_floor__add2,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( ( member_rat @ X @ ring_1_Ints_rat )
% 6.92/7.24 | ( member_rat @ Y @ ring_1_Ints_rat ) )
% 6.92/7.24 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 6.92/7.24 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_add2
% 6.92/7.24 thf(fact_5792_zero__le__floor,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 6.92/7.24 = ( ord_less_eq_rat @ zero_zero_rat @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_le_floor
% 6.92/7.24 thf(fact_5793_floor__less__zero,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 6.92/7.24 = ( ord_less_rat @ X @ zero_zero_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_less_zero
% 6.92/7.24 thf(fact_5794_numeral__le__floor,axiom,
% 6.92/7.24 ! [V: num,X: rat] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 6.92/7.24 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_le_floor
% 6.92/7.24 thf(fact_5795_zero__less__floor,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 6.92/7.24 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_less_floor
% 6.92/7.24 thf(fact_5796_floor__le__zero,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 6.92/7.24 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_le_zero
% 6.92/7.24 thf(fact_5797_floor__less__numeral,axiom,
% 6.92/7.24 ! [X: rat,V: num] :
% 6.92/7.24 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 6.92/7.24 = ( ord_less_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_less_numeral
% 6.92/7.24 thf(fact_5798_one__le__floor,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 6.92/7.24 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_le_floor
% 6.92/7.24 thf(fact_5799_floor__less__one,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 6.92/7.24 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_less_one
% 6.92/7.24 thf(fact_5800_numeral__less__floor,axiom,
% 6.92/7.24 ! [V: num,X: rat] :
% 6.92/7.24 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 6.92/7.24 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_less_floor
% 6.92/7.24 thf(fact_5801_floor__le__numeral,axiom,
% 6.92/7.24 ! [X: rat,V: num] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 6.92/7.24 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_le_numeral
% 6.92/7.24 thf(fact_5802_Ints__add,axiom,
% 6.92/7.24 ! [A: rat,B: rat] :
% 6.92/7.24 ( ( member_rat @ A @ ring_1_Ints_rat )
% 6.92/7.24 => ( ( member_rat @ B @ ring_1_Ints_rat )
% 6.92/7.24 => ( member_rat @ ( plus_plus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_add
% 6.92/7.24 thf(fact_5803_Ints__add,axiom,
% 6.92/7.24 ! [A: int,B: int] :
% 6.92/7.24 ( ( member_int @ A @ ring_1_Ints_int )
% 6.92/7.24 => ( ( member_int @ B @ ring_1_Ints_int )
% 6.92/7.24 => ( member_int @ ( plus_plus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_add
% 6.92/7.24 thf(fact_5804_floor__mono,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.24 => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_mono
% 6.92/7.24 thf(fact_5805_floor__less__cancel,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) )
% 6.92/7.24 => ( ord_less_rat @ X @ Y ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_less_cancel
% 6.92/7.24 thf(fact_5806_of__int__floor__le,axiom,
% 6.92/7.24 ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_floor_le
% 6.92/7.24 thf(fact_5807_floor__le__ceiling,axiom,
% 6.92/7.24 ! [X: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim2889992004027027881ng_rat @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_le_ceiling
% 6.92/7.24 thf(fact_5808_Ints__double__eq__0__iff,axiom,
% 6.92/7.24 ! [A: code_integer] :
% 6.92/7.24 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 6.92/7.24 => ( ( ( plus_p5714425477246183910nteger @ A @ A )
% 6.92/7.24 = zero_z3403309356797280102nteger )
% 6.92/7.24 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_double_eq_0_iff
% 6.92/7.24 thf(fact_5809_Ints__double__eq__0__iff,axiom,
% 6.92/7.24 ! [A: rat] :
% 6.92/7.24 ( ( member_rat @ A @ ring_1_Ints_rat )
% 6.92/7.24 => ( ( ( plus_plus_rat @ A @ A )
% 6.92/7.24 = zero_zero_rat )
% 6.92/7.24 = ( A = zero_zero_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_double_eq_0_iff
% 6.92/7.24 thf(fact_5810_Ints__double__eq__0__iff,axiom,
% 6.92/7.24 ! [A: int] :
% 6.92/7.24 ( ( member_int @ A @ ring_1_Ints_int )
% 6.92/7.24 => ( ( ( plus_plus_int @ A @ A )
% 6.92/7.24 = zero_zero_int )
% 6.92/7.24 = ( A = zero_zero_int ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_double_eq_0_iff
% 6.92/7.24 thf(fact_5811_le__mult__floor__Ints,axiom,
% 6.92/7.24 ! [A: rat,B: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.24 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 6.92/7.24 => ( 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 ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % le_mult_floor_Ints
% 6.92/7.24 thf(fact_5812_le__mult__floor__Ints,axiom,
% 6.92/7.24 ! [A: rat,B: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.24 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 6.92/7.24 => ( 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 ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % le_mult_floor_Ints
% 6.92/7.24 thf(fact_5813_le__floor__iff,axiom,
% 6.92/7.24 ! [Z3: int,X: rat] :
% 6.92/7.24 ( ( ord_less_eq_int @ Z3 @ ( archim3151403230148437115or_rat @ X ) )
% 6.92/7.24 = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % le_floor_iff
% 6.92/7.24 thf(fact_5814_le__floor__add,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % le_floor_add
% 6.92/7.24 thf(fact_5815_floor__less__iff,axiom,
% 6.92/7.24 ! [X: rat,Z3: int] :
% 6.92/7.24 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ Z3 )
% 6.92/7.24 = ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_less_iff
% 6.92/7.24 thf(fact_5816_floor__add__int,axiom,
% 6.92/7.24 ! [X: rat,Z3: int] :
% 6.92/7.24 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ Z3 )
% 6.92/7.24 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z3 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_add_int
% 6.92/7.24 thf(fact_5817_int__add__floor,axiom,
% 6.92/7.24 ! [Z3: int,X: rat] :
% 6.92/7.24 ( ( plus_plus_int @ Z3 @ ( archim3151403230148437115or_rat @ X ) )
% 6.92/7.24 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z3 ) @ X ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % int_add_floor
% 6.92/7.24 thf(fact_5818_Ints__odd__nonzero,axiom,
% 6.92/7.24 ! [A: code_integer] :
% 6.92/7.24 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 6.92/7.24 => ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ A )
% 6.92/7.24 != zero_z3403309356797280102nteger ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_odd_nonzero
% 6.92/7.24 thf(fact_5819_Ints__odd__nonzero,axiom,
% 6.92/7.24 ! [A: rat] :
% 6.92/7.24 ( ( member_rat @ A @ ring_1_Ints_rat )
% 6.92/7.24 => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A )
% 6.92/7.24 != zero_zero_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_odd_nonzero
% 6.92/7.24 thf(fact_5820_Ints__odd__nonzero,axiom,
% 6.92/7.24 ! [A: int] :
% 6.92/7.24 ( ( member_int @ A @ ring_1_Ints_int )
% 6.92/7.24 => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
% 6.92/7.24 != zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_odd_nonzero
% 6.92/7.24 thf(fact_5821_of__nat__floor,axiom,
% 6.92/7.24 ! [R2: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 6.92/7.24 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R2 ) ) ) @ R2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_nat_floor
% 6.92/7.24 thf(fact_5822_one__add__floor,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 6.92/7.24 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ one_one_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_add_floor
% 6.92/7.24 thf(fact_5823_ceiling__diff__floor__le__1,axiom,
% 6.92/7.24 ! [X: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) @ one_one_int ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_diff_floor_le_1
% 6.92/7.24 thf(fact_5824_ceiling__altdef,axiom,
% 6.92/7.24 ( archim2889992004027027881ng_rat
% 6.92/7.24 = ( ^ [X4: rat] :
% 6.92/7.24 ( if_int
% 6.92/7.24 @ ( X4
% 6.92/7.24 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) ) )
% 6.92/7.24 @ ( archim3151403230148437115or_rat @ X4 )
% 6.92/7.24 @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ceiling_altdef
% 6.92/7.24 thf(fact_5825_Ints__odd__less__0,axiom,
% 6.92/7.24 ! [A: code_integer] :
% 6.92/7.24 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 6.92/7.24 => ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ A ) @ zero_z3403309356797280102nteger )
% 6.92/7.24 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_odd_less_0
% 6.92/7.24 thf(fact_5826_Ints__odd__less__0,axiom,
% 6.92/7.24 ! [A: rat] :
% 6.92/7.24 ( ( member_rat @ A @ ring_1_Ints_rat )
% 6.92/7.24 => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 6.92/7.24 = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_odd_less_0
% 6.92/7.24 thf(fact_5827_Ints__odd__less__0,axiom,
% 6.92/7.24 ! [A: int] :
% 6.92/7.24 ( ( member_int @ A @ ring_1_Ints_int )
% 6.92/7.24 => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 6.92/7.24 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_odd_less_0
% 6.92/7.24 thf(fact_5828_Ints__nonzero__abs__ge1,axiom,
% 6.92/7.24 ! [X: code_integer] :
% 6.92/7.24 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 6.92/7.24 => ( ( X != zero_z3403309356797280102nteger )
% 6.92/7.24 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_nonzero_abs_ge1
% 6.92/7.24 thf(fact_5829_Ints__nonzero__abs__ge1,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( member_rat @ X @ ring_1_Ints_rat )
% 6.92/7.24 => ( ( X != zero_zero_rat )
% 6.92/7.24 => ( ord_less_eq_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_nonzero_abs_ge1
% 6.92/7.24 thf(fact_5830_Ints__nonzero__abs__ge1,axiom,
% 6.92/7.24 ! [X: int] :
% 6.92/7.24 ( ( member_int @ X @ ring_1_Ints_int )
% 6.92/7.24 => ( ( X != zero_zero_int )
% 6.92/7.24 => ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_nonzero_abs_ge1
% 6.92/7.24 thf(fact_5831_Ints__nonzero__abs__less1,axiom,
% 6.92/7.24 ! [X: code_integer] :
% 6.92/7.24 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 6.92/7.24 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer )
% 6.92/7.24 => ( X = zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_nonzero_abs_less1
% 6.92/7.24 thf(fact_5832_Ints__nonzero__abs__less1,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( member_rat @ X @ ring_1_Ints_rat )
% 6.92/7.24 => ( ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat )
% 6.92/7.24 => ( X = zero_zero_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_nonzero_abs_less1
% 6.92/7.24 thf(fact_5833_Ints__nonzero__abs__less1,axiom,
% 6.92/7.24 ! [X: int] :
% 6.92/7.24 ( ( member_int @ X @ ring_1_Ints_int )
% 6.92/7.24 => ( ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int )
% 6.92/7.24 => ( X = zero_zero_int ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_nonzero_abs_less1
% 6.92/7.24 thf(fact_5834_Ints__eq__abs__less1,axiom,
% 6.92/7.24 ! [X: code_integer,Y: code_integer] :
% 6.92/7.24 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 6.92/7.24 => ( ( member_Code_integer @ Y @ ring_11222124179247155820nteger )
% 6.92/7.24 => ( ( X = Y )
% 6.92/7.24 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ Y ) ) @ one_one_Code_integer ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_eq_abs_less1
% 6.92/7.24 thf(fact_5835_Ints__eq__abs__less1,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( member_rat @ X @ ring_1_Ints_rat )
% 6.92/7.24 => ( ( member_rat @ Y @ ring_1_Ints_rat )
% 6.92/7.24 => ( ( X = Y )
% 6.92/7.24 = ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ Y ) ) @ one_one_rat ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_eq_abs_less1
% 6.92/7.24 thf(fact_5836_Ints__eq__abs__less1,axiom,
% 6.92/7.24 ! [X: int,Y: int] :
% 6.92/7.24 ( ( member_int @ X @ ring_1_Ints_int )
% 6.92/7.24 => ( ( member_int @ Y @ ring_1_Ints_int )
% 6.92/7.24 => ( ( X = Y )
% 6.92/7.24 = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Y ) ) @ one_one_int ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Ints_eq_abs_less1
% 6.92/7.24 thf(fact_5837_floor__unique,axiom,
% 6.92/7.24 ! [Z3: int,X: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X )
% 6.92/7.24 => ( ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z3 ) @ one_one_rat ) )
% 6.92/7.24 => ( ( archim3151403230148437115or_rat @ X )
% 6.92/7.24 = Z3 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_unique
% 6.92/7.24 thf(fact_5838_floor__eq__iff,axiom,
% 6.92/7.24 ! [X: rat,A: int] :
% 6.92/7.24 ( ( ( archim3151403230148437115or_rat @ X )
% 6.92/7.24 = A )
% 6.92/7.24 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X )
% 6.92/7.24 & ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_eq_iff
% 6.92/7.24 thf(fact_5839_floor__split,axiom,
% 6.92/7.24 ! [P2: int > $o,T6: rat] :
% 6.92/7.24 ( ( P2 @ ( archim3151403230148437115or_rat @ T6 ) )
% 6.92/7.24 = ( ! [I: int] :
% 6.92/7.24 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I ) @ T6 )
% 6.92/7.24 & ( ord_less_rat @ T6 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I ) @ one_one_rat ) ) )
% 6.92/7.24 => ( P2 @ I ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_split
% 6.92/7.24 thf(fact_5840_le__mult__floor,axiom,
% 6.92/7.24 ! [A: rat,B: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 6.92/7.24 => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % le_mult_floor
% 6.92/7.24 thf(fact_5841_less__floor__iff,axiom,
% 6.92/7.24 ! [Z3: int,X: rat] :
% 6.92/7.24 ( ( ord_less_int @ Z3 @ ( archim3151403230148437115or_rat @ X ) )
% 6.92/7.24 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z3 ) @ one_one_rat ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % less_floor_iff
% 6.92/7.24 thf(fact_5842_floor__le__iff,axiom,
% 6.92/7.24 ! [X: rat,Z3: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ Z3 )
% 6.92/7.24 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z3 ) @ one_one_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_le_iff
% 6.92/7.24 thf(fact_5843_floor__correct,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X )
% 6.92/7.24 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_correct
% 6.92/7.24 thf(fact_5844_floor__divide__lower,axiom,
% 6.92/7.24 ! [Q6: rat,P3: rat] :
% 6.92/7.24 ( ( ord_less_rat @ zero_zero_rat @ Q6 )
% 6.92/7.24 => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P3 @ Q6 ) ) ) @ Q6 ) @ P3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_divide_lower
% 6.92/7.24 thf(fact_5845_floor__divide__upper,axiom,
% 6.92/7.24 ! [Q6: rat,P3: rat] :
% 6.92/7.24 ( ( ord_less_rat @ zero_zero_rat @ Q6 )
% 6.92/7.24 => ( 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 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_divide_upper
% 6.92/7.24 thf(fact_5846_floor__add,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 6.92/7.24 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 6.92/7.24 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) )
% 6.92/7.24 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 6.92/7.24 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 6.92/7.24 = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ one_one_int ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_add
% 6.92/7.24 thf(fact_5847_frac__unique__iff,axiom,
% 6.92/7.24 ! [X: rat,A: rat] :
% 6.92/7.24 ( ( ( archimedean_frac_rat @ X )
% 6.92/7.24 = A )
% 6.92/7.24 = ( ( member_rat @ ( minus_minus_rat @ X @ A ) @ ring_1_Ints_rat )
% 6.92/7.24 & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 6.92/7.24 & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % frac_unique_iff
% 6.92/7.24 thf(fact_5848_diff__numeral__special_I4_J,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 6.92/7.24 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % diff_numeral_special(4)
% 6.92/7.24 thf(fact_5849_diff__numeral__special_I4_J,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 6.92/7.24 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % diff_numeral_special(4)
% 6.92/7.24 thf(fact_5850_diff__numeral__special_I4_J,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 6.92/7.24 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % diff_numeral_special(4)
% 6.92/7.24 thf(fact_5851_diff__numeral__special_I3_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.92/7.24 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % diff_numeral_special(3)
% 6.92/7.24 thf(fact_5852_diff__numeral__special_I3_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 6.92/7.24 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % diff_numeral_special(3)
% 6.92/7.24 thf(fact_5853_diff__numeral__special_I3_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 6.92/7.24 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % diff_numeral_special(3)
% 6.92/7.24 thf(fact_5854_add__neg__numeral__special_I5_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.92/7.24 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % add_neg_numeral_special(5)
% 6.92/7.24 thf(fact_5855_add__neg__numeral__special_I5_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 6.92/7.24 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % add_neg_numeral_special(5)
% 6.92/7.24 thf(fact_5856_add__neg__numeral__special_I5_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 6.92/7.24 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % add_neg_numeral_special(5)
% 6.92/7.24 thf(fact_5857_add__neg__numeral__special_I6_J,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 6.92/7.24 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % add_neg_numeral_special(6)
% 6.92/7.24 thf(fact_5858_add__neg__numeral__special_I6_J,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 6.92/7.24 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % add_neg_numeral_special(6)
% 6.92/7.24 thf(fact_5859_add__neg__numeral__special_I6_J,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 6.92/7.24 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % add_neg_numeral_special(6)
% 6.92/7.24 thf(fact_5860_semiring__norm_I68_J,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_eq_num @ one @ N2 ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(68)
% 6.92/7.24 thf(fact_5861_semiring__norm_I75_J,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_less_num @ M @ one ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(75)
% 6.92/7.24 thf(fact_5862_Suc__numeral,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( suc @ ( numeral_numeral_nat @ N2 ) )
% 6.92/7.24 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Suc_numeral
% 6.92/7.24 thf(fact_5863_frac__gt__0__iff,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) )
% 6.92/7.24 = ( ~ ( member_rat @ X @ ring_1_Ints_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % frac_gt_0_iff
% 6.92/7.24 thf(fact_5864_not__neg__one__le__neg__numeral__iff,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 6.92/7.24 = ( M != one ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_neg_one_le_neg_numeral_iff
% 6.92/7.24 thf(fact_5865_not__neg__one__le__neg__numeral__iff,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 6.92/7.24 = ( M != one ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_neg_one_le_neg_numeral_iff
% 6.92/7.24 thf(fact_5866_not__neg__one__le__neg__numeral__iff,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 6.92/7.24 = ( M != one ) ) ).
% 6.92/7.24
% 6.92/7.24 % not_neg_one_le_neg_numeral_iff
% 6.92/7.24 thf(fact_5867_neg__numeral__less__neg__one__iff,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 6.92/7.24 = ( M != one ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_less_neg_one_iff
% 6.92/7.24 thf(fact_5868_neg__numeral__less__neg__one__iff,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 6.92/7.24 = ( M != one ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_less_neg_one_iff
% 6.92/7.24 thf(fact_5869_neg__numeral__less__neg__one__iff,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 6.92/7.24 = ( M != one ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_numeral_less_neg_one_iff
% 6.92/7.24 thf(fact_5870_one__plus__numeral,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 6.92/7.24 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_plus_numeral
% 6.92/7.24 thf(fact_5871_one__plus__numeral,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 6.92/7.24 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_plus_numeral
% 6.92/7.24 thf(fact_5872_one__plus__numeral,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 6.92/7.24 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_plus_numeral
% 6.92/7.24 thf(fact_5873_one__plus__numeral,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N2 ) )
% 6.92/7.24 = ( numera5444537566228673987atural @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_plus_numeral
% 6.92/7.24 thf(fact_5874_one__plus__numeral,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 6.92/7.24 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_plus_numeral
% 6.92/7.24 thf(fact_5875_numeral__plus__one,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 6.92/7.24 = ( numeral_numeral_rat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_plus_one
% 6.92/7.24 thf(fact_5876_numeral__plus__one,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 6.92/7.24 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_plus_one
% 6.92/7.24 thf(fact_5877_numeral__plus__one,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 6.92/7.24 = ( numeral_numeral_int @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_plus_one
% 6.92/7.24 thf(fact_5878_numeral__plus__one,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ one_one_Code_natural )
% 6.92/7.24 = ( numera5444537566228673987atural @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_plus_one
% 6.92/7.24 thf(fact_5879_numeral__plus__one,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer )
% 6.92/7.24 = ( numera6620942414471956472nteger @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_plus_one
% 6.92/7.24 thf(fact_5880_numeral__le__one__iff,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ N2 ) @ one_one_Code_natural )
% 6.92/7.24 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_le_one_iff
% 6.92/7.24 thf(fact_5881_numeral__le__one__iff,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer )
% 6.92/7.24 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_le_one_iff
% 6.92/7.24 thf(fact_5882_numeral__le__one__iff,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 6.92/7.24 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_le_one_iff
% 6.92/7.24 thf(fact_5883_numeral__le__one__iff,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 6.92/7.24 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_le_one_iff
% 6.92/7.24 thf(fact_5884_numeral__le__one__iff,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 6.92/7.24 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_le_one_iff
% 6.92/7.24 thf(fact_5885_one__less__numeral__iff,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 6.92/7.24 = ( ord_less_num @ one @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_less_numeral_iff
% 6.92/7.24 thf(fact_5886_one__less__numeral__iff,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 6.92/7.24 = ( ord_less_num @ one @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_less_numeral_iff
% 6.92/7.24 thf(fact_5887_one__less__numeral__iff,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 6.92/7.24 = ( ord_less_num @ one @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_less_numeral_iff
% 6.92/7.24 thf(fact_5888_one__less__numeral__iff,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N2 ) )
% 6.92/7.24 = ( ord_less_num @ one @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_less_numeral_iff
% 6.92/7.24 thf(fact_5889_one__less__numeral__iff,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 6.92/7.24 = ( ord_less_num @ one @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_less_numeral_iff
% 6.92/7.24 thf(fact_5890_add__One,axiom,
% 6.92/7.24 ! [X: num] :
% 6.92/7.24 ( ( plus_plus_num @ X @ one )
% 6.92/7.24 = ( inc @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % add_One
% 6.92/7.24 thf(fact_5891_add__One__commute,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_plus_num @ one @ N2 )
% 6.92/7.24 = ( plus_plus_num @ N2 @ one ) ) ).
% 6.92/7.24
% 6.92/7.24 % add_One_commute
% 6.92/7.24 thf(fact_5892_le__num__One__iff,axiom,
% 6.92/7.24 ! [X: num] :
% 6.92/7.24 ( ( ord_less_eq_num @ X @ one )
% 6.92/7.24 = ( X = one ) ) ).
% 6.92/7.24
% 6.92/7.24 % le_num_One_iff
% 6.92/7.24 thf(fact_5893_add__inc,axiom,
% 6.92/7.24 ! [X: num,Y: num] :
% 6.92/7.24 ( ( plus_plus_num @ X @ ( inc @ Y ) )
% 6.92/7.24 = ( inc @ ( plus_plus_num @ X @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % add_inc
% 6.92/7.24 thf(fact_5894_mult__inc,axiom,
% 6.92/7.24 ! [X: num,Y: num] :
% 6.92/7.24 ( ( times_times_num @ X @ ( inc @ Y ) )
% 6.92/7.24 = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_inc
% 6.92/7.24 thf(fact_5895_frac__ge__0,axiom,
% 6.92/7.24 ! [X: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % frac_ge_0
% 6.92/7.24 thf(fact_5896_frac__lt__1,axiom,
% 6.92/7.24 ! [X: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X ) @ one_one_rat ) ).
% 6.92/7.24
% 6.92/7.24 % frac_lt_1
% 6.92/7.24 thf(fact_5897_frac__1__eq,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 6.92/7.24 = ( archimedean_frac_rat @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % frac_1_eq
% 6.92/7.24 thf(fact_5898_numeral__inc,axiom,
% 6.92/7.24 ! [X: num] :
% 6.92/7.24 ( ( numeral_numeral_rat @ ( inc @ X ) )
% 6.92/7.24 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_inc
% 6.92/7.24 thf(fact_5899_numeral__inc,axiom,
% 6.92/7.24 ! [X: num] :
% 6.92/7.24 ( ( numeral_numeral_nat @ ( inc @ X ) )
% 6.92/7.24 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_inc
% 6.92/7.24 thf(fact_5900_numeral__inc,axiom,
% 6.92/7.24 ! [X: num] :
% 6.92/7.24 ( ( numeral_numeral_int @ ( inc @ X ) )
% 6.92/7.24 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_inc
% 6.92/7.24 thf(fact_5901_numeral__inc,axiom,
% 6.92/7.24 ! [X: num] :
% 6.92/7.24 ( ( numera5444537566228673987atural @ ( inc @ X ) )
% 6.92/7.24 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_inc
% 6.92/7.24 thf(fact_5902_numeral__inc,axiom,
% 6.92/7.24 ! [X: num] :
% 6.92/7.24 ( ( numera6620942414471956472nteger @ ( inc @ X ) )
% 6.92/7.24 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_inc
% 6.92/7.24 thf(fact_5903_Suc__nat__number__of__add,axiom,
% 6.92/7.24 ! [V: num,N2: nat] :
% 6.92/7.24 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 6.92/7.24 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % Suc_nat_number_of_add
% 6.92/7.24 thf(fact_5904_frac__eq,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ( archimedean_frac_rat @ X )
% 6.92/7.24 = X )
% 6.92/7.24 = ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 6.92/7.24 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % frac_eq
% 6.92/7.24 thf(fact_5905_frac__add,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 6.92/7.24 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 6.92/7.24 = ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 6.92/7.24 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 6.92/7.24 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 6.92/7.24 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % frac_add
% 6.92/7.24 thf(fact_5906_pochhammer__double,axiom,
% 6.92/7.24 ! [Z3: rat,N2: nat] :
% 6.92/7.24 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.24 = ( 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 @ Z3 @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % pochhammer_double
% 6.92/7.24 thf(fact_5907_neg__eucl__rel__int__mult__2,axiom,
% 6.92/7.24 ! [B: int,A: int,Q6: int,R2: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 6.92/7.24 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 6.92/7.24 => ( 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 ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_eucl_rel_int_mult_2
% 6.92/7.24 thf(fact_5908_execute__change,axiom,
% 6.92/7.24 ! [F: product_unit > product_unit,R2: ref_Product_unit,H: heap_e7401611519738050253t_unit] :
% 6.92/7.24 ( ( heap_T875086893843062177t_unit @ ( ref_ch7259622376331601608t_unit @ F @ R2 ) @ H )
% 6.92/7.24 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ ( F @ ( ref_get_Product_unit @ H @ R2 ) ) @ ( produc584006145561248582it_nat @ ( ref_set_Product_unit @ R2 @ ( F @ ( ref_get_Product_unit @ H @ R2 ) ) @ H ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % execute_change
% 6.92/7.24 thf(fact_5909_divmod__digit__1_I1_J,axiom,
% 6.92/7.24 ! [A: code_integer,B: code_integer] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.24 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.24 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 6.92/7.24 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 6.92/7.24 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_digit_1(1)
% 6.92/7.24 thf(fact_5910_divmod__digit__1_I1_J,axiom,
% 6.92/7.24 ! [A: nat,B: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.24 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 6.92/7.24 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 6.92/7.24 => ( ( 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 )
% 6.92/7.24 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_digit_1(1)
% 6.92/7.24 thf(fact_5911_divmod__digit__1_I1_J,axiom,
% 6.92/7.24 ! [A: int,B: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.24 => ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.24 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 6.92/7.24 => ( ( 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 )
% 6.92/7.24 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_digit_1(1)
% 6.92/7.24 thf(fact_5912_pos__eucl__rel__int__mult__2,axiom,
% 6.92/7.24 ! [B: int,A: int,Q6: int,R2: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 6.92/7.24 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 6.92/7.24 => ( 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 ) ) @ R2 ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % pos_eucl_rel_int_mult_2
% 6.92/7.24 thf(fact_5913_neg__zmod__mult__2,axiom,
% 6.92/7.24 ! [A: int,B: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 6.92/7.24 => ( ( 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 ) )
% 6.92/7.24 = ( 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 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_zmod_mult_2
% 6.92/7.24 thf(fact_5914_verit__eq__simplify_I8_J,axiom,
% 6.92/7.24 ! [X2: num,Y2: num] :
% 6.92/7.24 ( ( ( bit0 @ X2 )
% 6.92/7.24 = ( bit0 @ Y2 ) )
% 6.92/7.24 = ( X2 = Y2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % verit_eq_simplify(8)
% 6.92/7.24 thf(fact_5915_verit__eq__simplify_I9_J,axiom,
% 6.92/7.24 ! [X32: num,Y32: num] :
% 6.92/7.24 ( ( ( bit1 @ X32 )
% 6.92/7.24 = ( bit1 @ Y32 ) )
% 6.92/7.24 = ( X32 = Y32 ) ) ).
% 6.92/7.24
% 6.92/7.24 % verit_eq_simplify(9)
% 6.92/7.24 thf(fact_5916_semiring__norm_I6_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( bit0 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(6)
% 6.92/7.24 thf(fact_5917_semiring__norm_I78_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( ord_less_num @ M @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(78)
% 6.92/7.24 thf(fact_5918_semiring__norm_I71_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(71)
% 6.92/7.24 thf(fact_5919_semiring__norm_I80_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( ord_less_num @ M @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(80)
% 6.92/7.24 thf(fact_5920_semiring__norm_I73_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(73)
% 6.92/7.24 thf(fact_5921_semiring__norm_I2_J,axiom,
% 6.92/7.24 ( ( plus_plus_num @ one @ one )
% 6.92/7.24 = ( bit0 @ one ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(2)
% 6.92/7.24 thf(fact_5922_semiring__norm_I9_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(9)
% 6.92/7.24 thf(fact_5923_semiring__norm_I7_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(7)
% 6.92/7.24 thf(fact_5924_semiring__norm_I69_J,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(69)
% 6.92/7.24 thf(fact_5925_semiring__norm_I76_J,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_num @ one @ ( bit0 @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(76)
% 6.92/7.24 thf(fact_5926_semiring__norm_I72_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(72)
% 6.92/7.24 thf(fact_5927_semiring__norm_I81_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( ord_less_num @ M @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(81)
% 6.92/7.24 thf(fact_5928_semiring__norm_I70_J,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(70)
% 6.92/7.24 thf(fact_5929_semiring__norm_I77_J,axiom,
% 6.92/7.24 ! [N2: num] : ( ord_less_num @ one @ ( bit1 @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(77)
% 6.92/7.24 thf(fact_5930_semiring__norm_I10_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(10)
% 6.92/7.24 thf(fact_5931_semiring__norm_I8_J,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 6.92/7.24 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(8)
% 6.92/7.24 thf(fact_5932_semiring__norm_I5_J,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 6.92/7.24 = ( bit1 @ M ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(5)
% 6.92/7.24 thf(fact_5933_semiring__norm_I4_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_plus_num @ one @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( bit0 @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(4)
% 6.92/7.24 thf(fact_5934_semiring__norm_I3_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( plus_plus_num @ one @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( bit1 @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(3)
% 6.92/7.24 thf(fact_5935_semiring__norm_I16_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(16)
% 6.92/7.24 thf(fact_5936_semiring__norm_I79_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(79)
% 6.92/7.24 thf(fact_5937_semiring__norm_I74_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( ord_less_num @ M @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % semiring_norm(74)
% 6.92/7.24 thf(fact_5938_one__add__one,axiom,
% 6.92/7.24 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 6.92/7.24 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_add_one
% 6.92/7.24 thf(fact_5939_one__add__one,axiom,
% 6.92/7.24 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 6.92/7.24 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_add_one
% 6.92/7.24 thf(fact_5940_one__add__one,axiom,
% 6.92/7.24 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 6.92/7.24 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_add_one
% 6.92/7.24 thf(fact_5941_one__add__one,axiom,
% 6.92/7.24 ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ one_one_Code_natural )
% 6.92/7.24 = ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_add_one
% 6.92/7.24 thf(fact_5942_one__add__one,axiom,
% 6.92/7.24 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer )
% 6.92/7.24 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_add_one
% 6.92/7.24 thf(fact_5943_add__2__eq__Suc_H,axiom,
% 6.92/7.24 ! [N2: nat] :
% 6.92/7.24 ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( suc @ ( suc @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % add_2_eq_Suc'
% 6.92/7.24 thf(fact_5944_add__2__eq__Suc,axiom,
% 6.92/7.24 ! [N2: nat] :
% 6.92/7.24 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.24 = ( suc @ ( suc @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % add_2_eq_Suc
% 6.92/7.24 thf(fact_5945_add__self__div__2,axiom,
% 6.92/7.24 ! [M: nat] :
% 6.92/7.24 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = M ) ).
% 6.92/7.24
% 6.92/7.24 % add_self_div_2
% 6.92/7.24 thf(fact_5946_add__neg__numeral__special_I9_J,axiom,
% 6.92/7.24 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 6.92/7.24 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % add_neg_numeral_special(9)
% 6.92/7.24 thf(fact_5947_add__neg__numeral__special_I9_J,axiom,
% 6.92/7.24 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 6.92/7.24 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % add_neg_numeral_special(9)
% 6.92/7.24 thf(fact_5948_add__neg__numeral__special_I9_J,axiom,
% 6.92/7.24 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 6.92/7.24 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % add_neg_numeral_special(9)
% 6.92/7.24 thf(fact_5949_power2__less__eq__zero__iff,axiom,
% 6.92/7.24 ! [A: code_integer] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_z3403309356797280102nteger )
% 6.92/7.24 = ( A = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_less_eq_zero_iff
% 6.92/7.24 thf(fact_5950_power2__less__eq__zero__iff,axiom,
% 6.92/7.24 ! [A: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 6.92/7.24 = ( A = zero_zero_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_less_eq_zero_iff
% 6.92/7.24 thf(fact_5951_power2__less__eq__zero__iff,axiom,
% 6.92/7.24 ! [A: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 6.92/7.24 = ( A = zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_less_eq_zero_iff
% 6.92/7.24 thf(fact_5952_power2__eq__iff__nonneg,axiom,
% 6.92/7.24 ! [X: code_integer,Y: code_integer] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 6.92/7.24 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 6.92/7.24 => ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = ( X = Y ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_eq_iff_nonneg
% 6.92/7.24 thf(fact_5953_power2__eq__iff__nonneg,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 6.92/7.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 6.92/7.24 => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = ( X = Y ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_eq_iff_nonneg
% 6.92/7.24 thf(fact_5954_power2__eq__iff__nonneg,axiom,
% 6.92/7.24 ! [X: nat,Y: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 6.92/7.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 6.92/7.24 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = ( X = Y ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_eq_iff_nonneg
% 6.92/7.24 thf(fact_5955_power2__eq__iff__nonneg,axiom,
% 6.92/7.24 ! [X: int,Y: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.24 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.24 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = ( X = Y ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_eq_iff_nonneg
% 6.92/7.24 thf(fact_5956_zero__less__power2,axiom,
% 6.92/7.24 ! [A: code_integer] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = ( A != zero_z3403309356797280102nteger ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_less_power2
% 6.92/7.24 thf(fact_5957_zero__less__power2,axiom,
% 6.92/7.24 ! [A: rat] :
% 6.92/7.24 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = ( A != zero_zero_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_less_power2
% 6.92/7.24 thf(fact_5958_zero__less__power2,axiom,
% 6.92/7.24 ! [A: int] :
% 6.92/7.24 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = ( A != zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_less_power2
% 6.92/7.24 thf(fact_5959_add__self__mod__2,axiom,
% 6.92/7.24 ! [M: nat] :
% 6.92/7.24 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = zero_zero_nat ) ).
% 6.92/7.24
% 6.92/7.24 % add_self_mod_2
% 6.92/7.24 thf(fact_5960_mod__Suc__eq__mod__add3,axiom,
% 6.92/7.24 ! [M: nat,N2: nat] :
% 6.92/7.24 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 6.92/7.24 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % mod_Suc_eq_mod_add3
% 6.92/7.24 thf(fact_5961_Suc__mod__eq__add3__mod__numeral,axiom,
% 6.92/7.24 ! [M: nat,V: num] :
% 6.92/7.24 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 6.92/7.24 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Suc_mod_eq_add3_mod_numeral
% 6.92/7.24 thf(fact_5962_div__Suc__eq__div__add3,axiom,
% 6.92/7.24 ! [M: nat,N2: nat] :
% 6.92/7.24 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 6.92/7.24 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % div_Suc_eq_div_add3
% 6.92/7.24 thf(fact_5963_Suc__div__eq__add3__div__numeral,axiom,
% 6.92/7.24 ! [M: nat,V: num] :
% 6.92/7.24 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 6.92/7.24 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Suc_div_eq_add3_div_numeral
% 6.92/7.24 thf(fact_5964_one__less__floor,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 6.92/7.24 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % one_less_floor
% 6.92/7.24 thf(fact_5965_floor__le__one,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 6.92/7.24 = ( ord_less_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_le_one
% 6.92/7.24 thf(fact_5966_mod2__gr__0,axiom,
% 6.92/7.24 ! [M: nat] :
% 6.92/7.24 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = one_one_nat ) ) ).
% 6.92/7.24
% 6.92/7.24 % mod2_gr_0
% 6.92/7.24 thf(fact_5967_zmod__numeral__Bit1,axiom,
% 6.92/7.24 ! [V: num,W2: num] :
% 6.92/7.24 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 6.92/7.24 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W2 ) ) ) @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % zmod_numeral_Bit1
% 6.92/7.24 thf(fact_5968_verit__eq__simplify_I14_J,axiom,
% 6.92/7.24 ! [X2: num,X32: num] :
% 6.92/7.24 ( ( bit0 @ X2 )
% 6.92/7.24 != ( bit1 @ X32 ) ) ).
% 6.92/7.24
% 6.92/7.24 % verit_eq_simplify(14)
% 6.92/7.24 thf(fact_5969_verit__eq__simplify_I12_J,axiom,
% 6.92/7.24 ! [X32: num] :
% 6.92/7.24 ( one
% 6.92/7.24 != ( bit1 @ X32 ) ) ).
% 6.92/7.24
% 6.92/7.24 % verit_eq_simplify(12)
% 6.92/7.24 thf(fact_5970_verit__eq__simplify_I10_J,axiom,
% 6.92/7.24 ! [X2: num] :
% 6.92/7.24 ( one
% 6.92/7.24 != ( bit0 @ X2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % verit_eq_simplify(10)
% 6.92/7.24 thf(fact_5971_numeral__Bit0,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_Bit0
% 6.92/7.24 thf(fact_5972_numeral__Bit0,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_Bit0
% 6.92/7.24 thf(fact_5973_numeral__Bit0,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_Bit0
% 6.92/7.24 thf(fact_5974_numeral__Bit0,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numera5444537566228673987atural @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ ( numera5444537566228673987atural @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_Bit0
% 6.92/7.24 thf(fact_5975_numeral__Bit0,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numera6620942414471956472nteger @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_Bit0
% 6.92/7.24 thf(fact_5976_numeral__code_I2_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_code(2)
% 6.92/7.24 thf(fact_5977_numeral__code_I2_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_code(2)
% 6.92/7.24 thf(fact_5978_numeral__code_I2_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_code(2)
% 6.92/7.24 thf(fact_5979_numeral__code_I2_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numera5444537566228673987atural @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ ( numera5444537566228673987atural @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_code(2)
% 6.92/7.24 thf(fact_5980_numeral__code_I2_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numera6620942414471956472nteger @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_code(2)
% 6.92/7.24 thf(fact_5981_numeral__Bit1,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_Bit1
% 6.92/7.24 thf(fact_5982_numeral__Bit1,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_Bit1
% 6.92/7.24 thf(fact_5983_numeral__Bit1,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_Bit1
% 6.92/7.24 thf(fact_5984_numeral__Bit1,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numera5444537566228673987atural @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ ( numera5444537566228673987atural @ N2 ) ) @ one_one_Code_natural ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_Bit1
% 6.92/7.24 thf(fact_5985_numeral__Bit1,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numera6620942414471956472nteger @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ one_one_Code_integer ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_Bit1
% 6.92/7.24 thf(fact_5986_num_Osize_I6_J,axiom,
% 6.92/7.24 ! [X32: num] :
% 6.92/7.24 ( ( size_size_num @ ( bit1 @ X32 ) )
% 6.92/7.24 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % num.size(6)
% 6.92/7.24 thf(fact_5987_num_Osize_I5_J,axiom,
% 6.92/7.24 ! [X2: num] :
% 6.92/7.24 ( ( size_size_num @ ( bit0 @ X2 ) )
% 6.92/7.24 = ( plus_plus_nat @ ( size_size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % num.size(5)
% 6.92/7.24 thf(fact_5988_numeral__code_I3_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_code(3)
% 6.92/7.24 thf(fact_5989_numeral__code_I3_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_code(3)
% 6.92/7.24 thf(fact_5990_numeral__code_I3_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_code(3)
% 6.92/7.24 thf(fact_5991_numeral__code_I3_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numera5444537566228673987atural @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ ( numera5444537566228673987atural @ N2 ) ) @ one_one_Code_natural ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_code(3)
% 6.92/7.24 thf(fact_5992_numeral__code_I3_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( numera6620942414471956472nteger @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ one_one_Code_integer ) ) ).
% 6.92/7.24
% 6.92/7.24 % numeral_code(3)
% 6.92/7.24 thf(fact_5993_power__numeral__odd,axiom,
% 6.92/7.24 ! [Z3: assn,W2: num] :
% 6.92/7.24 ( ( power_power_assn @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 6.92/7.24 = ( times_times_assn @ ( times_times_assn @ Z3 @ ( power_power_assn @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_assn @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power_numeral_odd
% 6.92/7.24 thf(fact_5994_power__numeral__odd,axiom,
% 6.92/7.24 ! [Z3: rat,W2: num] :
% 6.92/7.24 ( ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 6.92/7.24 = ( times_times_rat @ ( times_times_rat @ Z3 @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power_numeral_odd
% 6.92/7.24 thf(fact_5995_power__numeral__odd,axiom,
% 6.92/7.24 ! [Z3: nat,W2: num] :
% 6.92/7.24 ( ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 6.92/7.24 = ( times_times_nat @ ( times_times_nat @ Z3 @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power_numeral_odd
% 6.92/7.24 thf(fact_5996_power__numeral__odd,axiom,
% 6.92/7.24 ! [Z3: int,W2: num] :
% 6.92/7.24 ( ( power_power_int @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 6.92/7.24 = ( times_times_int @ ( times_times_int @ Z3 @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power_numeral_odd
% 6.92/7.24 thf(fact_5997_power__numeral__even,axiom,
% 6.92/7.24 ! [Z3: assn,W2: num] :
% 6.92/7.24 ( ( power_power_assn @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 6.92/7.24 = ( times_times_assn @ ( power_power_assn @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_assn @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power_numeral_even
% 6.92/7.24 thf(fact_5998_power__numeral__even,axiom,
% 6.92/7.24 ! [Z3: rat,W2: num] :
% 6.92/7.24 ( ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 6.92/7.24 = ( times_times_rat @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power_numeral_even
% 6.92/7.24 thf(fact_5999_power__numeral__even,axiom,
% 6.92/7.24 ! [Z3: nat,W2: num] :
% 6.92/7.24 ( ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 6.92/7.24 = ( times_times_nat @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power_numeral_even
% 6.92/7.24 thf(fact_6000_power__numeral__even,axiom,
% 6.92/7.24 ! [Z3: int,W2: num] :
% 6.92/7.24 ( ( power_power_int @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 6.92/7.24 = ( times_times_int @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power_numeral_even
% 6.92/7.24 thf(fact_6001_Suc3__eq__add__3,axiom,
% 6.92/7.24 ! [N2: nat] :
% 6.92/7.24 ( ( suc @ ( suc @ ( suc @ N2 ) ) )
% 6.92/7.24 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % Suc3_eq_add_3
% 6.92/7.24 thf(fact_6002_mult__2,axiom,
% 6.92/7.24 ! [Z3: rat] :
% 6.92/7.24 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z3 )
% 6.92/7.24 = ( plus_plus_rat @ Z3 @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_2
% 6.92/7.24 thf(fact_6003_mult__2,axiom,
% 6.92/7.24 ! [Z3: nat] :
% 6.92/7.24 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z3 )
% 6.92/7.24 = ( plus_plus_nat @ Z3 @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_2
% 6.92/7.24 thf(fact_6004_mult__2,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z3 )
% 6.92/7.24 = ( plus_plus_int @ Z3 @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_2
% 6.92/7.24 thf(fact_6005_mult__2,axiom,
% 6.92/7.24 ! [Z3: code_natural] :
% 6.92/7.24 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ Z3 )
% 6.92/7.24 = ( plus_p4538020629002901425atural @ Z3 @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_2
% 6.92/7.24 thf(fact_6006_mult__2,axiom,
% 6.92/7.24 ! [Z3: code_integer] :
% 6.92/7.24 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Z3 )
% 6.92/7.24 = ( plus_p5714425477246183910nteger @ Z3 @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_2
% 6.92/7.24 thf(fact_6007_mult__2__right,axiom,
% 6.92/7.24 ! [Z3: rat] :
% 6.92/7.24 ( ( times_times_rat @ Z3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( plus_plus_rat @ Z3 @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_2_right
% 6.92/7.24 thf(fact_6008_mult__2__right,axiom,
% 6.92/7.24 ! [Z3: nat] :
% 6.92/7.24 ( ( times_times_nat @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( plus_plus_nat @ Z3 @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_2_right
% 6.92/7.24 thf(fact_6009_mult__2__right,axiom,
% 6.92/7.24 ! [Z3: int] :
% 6.92/7.24 ( ( times_times_int @ Z3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( plus_plus_int @ Z3 @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_2_right
% 6.92/7.24 thf(fact_6010_mult__2__right,axiom,
% 6.92/7.24 ! [Z3: code_natural] :
% 6.92/7.24 ( ( times_2397367101498566445atural @ Z3 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( plus_p4538020629002901425atural @ Z3 @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_2_right
% 6.92/7.24 thf(fact_6011_mult__2__right,axiom,
% 6.92/7.24 ! [Z3: code_integer] :
% 6.92/7.24 ( ( times_3573771949741848930nteger @ Z3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( plus_p5714425477246183910nteger @ Z3 @ Z3 ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_2_right
% 6.92/7.24 thf(fact_6012_left__add__twice,axiom,
% 6.92/7.24 ! [A: rat,B: rat] :
% 6.92/7.24 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 6.92/7.24 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 6.92/7.24
% 6.92/7.24 % left_add_twice
% 6.92/7.24 thf(fact_6013_left__add__twice,axiom,
% 6.92/7.24 ! [A: nat,B: nat] :
% 6.92/7.24 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 6.92/7.24 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 6.92/7.24
% 6.92/7.24 % left_add_twice
% 6.92/7.24 thf(fact_6014_left__add__twice,axiom,
% 6.92/7.24 ! [A: int,B: int] :
% 6.92/7.24 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 6.92/7.24 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 6.92/7.24
% 6.92/7.24 % left_add_twice
% 6.92/7.24 thf(fact_6015_left__add__twice,axiom,
% 6.92/7.24 ! [A: code_natural,B: code_natural] :
% 6.92/7.24 ( ( plus_p4538020629002901425atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 6.92/7.24 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 6.92/7.24
% 6.92/7.24 % left_add_twice
% 6.92/7.24 thf(fact_6016_left__add__twice,axiom,
% 6.92/7.24 ! [A: code_integer,B: code_integer] :
% 6.92/7.24 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 6.92/7.24 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 6.92/7.24
% 6.92/7.24 % left_add_twice
% 6.92/7.24 thf(fact_6017_nat__1__add__1,axiom,
% 6.92/7.24 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 6.92/7.24 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % nat_1_add_1
% 6.92/7.24 thf(fact_6018_less__exp,axiom,
% 6.92/7.24 ! [N2: nat] : ( ord_less_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % less_exp
% 6.92/7.24 thf(fact_6019_power2__nat__le__imp__le,axiom,
% 6.92/7.24 ! [M: nat,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 6.92/7.24 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_nat_le_imp_le
% 6.92/7.24 thf(fact_6020_power2__nat__le__eq__le,axiom,
% 6.92/7.24 ! [M: nat,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_nat_le_eq_le
% 6.92/7.24 thf(fact_6021_self__le__ge2__pow,axiom,
% 6.92/7.24 ! [K2: nat,M: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 6.92/7.24 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K2 @ M ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % self_le_ge2_pow
% 6.92/7.24 thf(fact_6022_half__gt__zero__iff,axiom,
% 6.92/7.24 ! [A: rat] :
% 6.92/7.24 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % half_gt_zero_iff
% 6.92/7.24 thf(fact_6023_half__gt__zero,axiom,
% 6.92/7.24 ! [A: rat] :
% 6.92/7.24 ( ( ord_less_rat @ zero_zero_rat @ A )
% 6.92/7.24 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % half_gt_zero
% 6.92/7.24 thf(fact_6024_zero__le__power2,axiom,
% 6.92/7.24 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_le_power2
% 6.92/7.24 thf(fact_6025_zero__le__power2,axiom,
% 6.92/7.24 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_le_power2
% 6.92/7.24 thf(fact_6026_zero__le__power2,axiom,
% 6.92/7.24 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_le_power2
% 6.92/7.24 thf(fact_6027_power2__eq__imp__eq,axiom,
% 6.92/7.24 ! [X: code_integer,Y: code_integer] :
% 6.92/7.24 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 6.92/7.24 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 6.92/7.24 => ( X = Y ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_eq_imp_eq
% 6.92/7.24 thf(fact_6028_power2__eq__imp__eq,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 6.92/7.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 6.92/7.24 => ( X = Y ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_eq_imp_eq
% 6.92/7.24 thf(fact_6029_power2__eq__imp__eq,axiom,
% 6.92/7.24 ! [X: nat,Y: nat] :
% 6.92/7.24 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 6.92/7.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 6.92/7.24 => ( X = Y ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_eq_imp_eq
% 6.92/7.24 thf(fact_6030_power2__eq__imp__eq,axiom,
% 6.92/7.24 ! [X: int,Y: int] :
% 6.92/7.24 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.24 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.24 => ( X = Y ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_eq_imp_eq
% 6.92/7.24 thf(fact_6031_power2__le__imp__le,axiom,
% 6.92/7.24 ! [X: code_integer,Y: code_integer] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 6.92/7.24 => ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_le_imp_le
% 6.92/7.24 thf(fact_6032_power2__le__imp__le,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 6.92/7.24 => ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_le_imp_le
% 6.92/7.24 thf(fact_6033_power2__le__imp__le,axiom,
% 6.92/7.24 ! [X: nat,Y: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 6.92/7.24 => ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_le_imp_le
% 6.92/7.24 thf(fact_6034_power2__le__imp__le,axiom,
% 6.92/7.24 ! [X: int,Y: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.24 => ( ord_less_eq_int @ X @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_le_imp_le
% 6.92/7.24 thf(fact_6035_power2__less__0,axiom,
% 6.92/7.24 ! [A: code_integer] :
% 6.92/7.24 ~ ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_z3403309356797280102nteger ) ).
% 6.92/7.24
% 6.92/7.24 % power2_less_0
% 6.92/7.24 thf(fact_6036_power2__less__0,axiom,
% 6.92/7.24 ! [A: rat] :
% 6.92/7.24 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 6.92/7.24
% 6.92/7.24 % power2_less_0
% 6.92/7.24 thf(fact_6037_power2__less__0,axiom,
% 6.92/7.24 ! [A: int] :
% 6.92/7.24 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 6.92/7.24
% 6.92/7.24 % power2_less_0
% 6.92/7.24 thf(fact_6038_Suc__mod__eq__add3__mod,axiom,
% 6.92/7.24 ! [M: nat,N2: nat] :
% 6.92/7.24 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 6.92/7.24 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % Suc_mod_eq_add3_mod
% 6.92/7.24 thf(fact_6039_Suc__div__eq__add3__div,axiom,
% 6.92/7.24 ! [M: nat,N2: nat] :
% 6.92/7.24 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 6.92/7.24 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % Suc_div_eq_add3_div
% 6.92/7.24 thf(fact_6040_sum__power2__eq__zero__iff,axiom,
% 6.92/7.24 ! [X: code_integer,Y: code_integer] :
% 6.92/7.24 ( ( ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = zero_z3403309356797280102nteger )
% 6.92/7.24 = ( ( X = zero_z3403309356797280102nteger )
% 6.92/7.24 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sum_power2_eq_zero_iff
% 6.92/7.24 thf(fact_6041_sum__power2__eq__zero__iff,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = zero_zero_rat )
% 6.92/7.24 = ( ( X = zero_zero_rat )
% 6.92/7.24 & ( Y = zero_zero_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sum_power2_eq_zero_iff
% 6.92/7.24 thf(fact_6042_sum__power2__eq__zero__iff,axiom,
% 6.92/7.24 ! [X: int,Y: int] :
% 6.92/7.24 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = zero_zero_int )
% 6.92/7.24 = ( ( X = zero_zero_int )
% 6.92/7.24 & ( Y = zero_zero_int ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sum_power2_eq_zero_iff
% 6.92/7.24 thf(fact_6043_less__2__cases,axiom,
% 6.92/7.24 ! [N2: nat] :
% 6.92/7.24 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 => ( ( N2 = zero_zero_nat )
% 6.92/7.24 | ( N2
% 6.92/7.24 = ( suc @ zero_zero_nat ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % less_2_cases
% 6.92/7.24 thf(fact_6044_less__2__cases__iff,axiom,
% 6.92/7.24 ! [N2: nat] :
% 6.92/7.24 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( ( N2 = zero_zero_nat )
% 6.92/7.24 | ( N2
% 6.92/7.24 = ( suc @ zero_zero_nat ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % less_2_cases_iff
% 6.92/7.24 thf(fact_6045_abs__le__square__iff,axiom,
% 6.92/7.24 ! [X: code_integer,Y: code_integer] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y ) )
% 6.92/7.24 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % abs_le_square_iff
% 6.92/7.24 thf(fact_6046_abs__le__square__iff,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ ( abs_abs_rat @ Y ) )
% 6.92/7.24 = ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % abs_le_square_iff
% 6.92/7.24 thf(fact_6047_abs__le__square__iff,axiom,
% 6.92/7.24 ! [X: int,Y: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) )
% 6.92/7.24 = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % abs_le_square_iff
% 6.92/7.24 thf(fact_6048_nat__induct2,axiom,
% 6.92/7.24 ! [P2: nat > $o,N2: nat] :
% 6.92/7.24 ( ( P2 @ zero_zero_nat )
% 6.92/7.24 => ( ( P2 @ one_one_nat )
% 6.92/7.24 => ( ! [N5: nat] :
% 6.92/7.24 ( ( P2 @ N5 )
% 6.92/7.24 => ( P2 @ ( plus_plus_nat @ N5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 6.92/7.24 => ( P2 @ N2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % nat_induct2
% 6.92/7.24 thf(fact_6049_diff__le__diff__pow,axiom,
% 6.92/7.24 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 6.92/7.24 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ ( minus_minus_nat @ ( power_power_nat @ K2 @ M ) @ ( power_power_nat @ K2 @ N2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % diff_le_diff_pow
% 6.92/7.24 thf(fact_6050_divmod__digit__0_I2_J,axiom,
% 6.92/7.24 ! [B: code_integer,A: code_integer] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.24 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 6.92/7.24 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 6.92/7.24 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_digit_0(2)
% 6.92/7.24 thf(fact_6051_divmod__digit__0_I2_J,axiom,
% 6.92/7.24 ! [B: nat,A: nat] :
% 6.92/7.24 ( ( ord_less_nat @ zero_zero_nat @ B )
% 6.92/7.24 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 6.92/7.24 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 6.92/7.24 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_digit_0(2)
% 6.92/7.24 thf(fact_6052_divmod__digit__0_I2_J,axiom,
% 6.92/7.24 ! [B: int,A: int] :
% 6.92/7.24 ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.24 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 6.92/7.24 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 6.92/7.24 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_digit_0(2)
% 6.92/7.24 thf(fact_6053_power2__less__imp__less,axiom,
% 6.92/7.24 ! [X: code_integer,Y: code_integer] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 6.92/7.24 => ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_less_imp_less
% 6.92/7.24 thf(fact_6054_power2__less__imp__less,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 6.92/7.24 => ( ord_less_rat @ X @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_less_imp_less
% 6.92/7.24 thf(fact_6055_power2__less__imp__less,axiom,
% 6.92/7.24 ! [X: nat,Y: nat] :
% 6.92/7.24 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 6.92/7.24 => ( ord_less_nat @ X @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_less_imp_less
% 6.92/7.24 thf(fact_6056_power2__less__imp__less,axiom,
% 6.92/7.24 ! [X: int,Y: int] :
% 6.92/7.24 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.24 => ( ord_less_int @ X @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_less_imp_less
% 6.92/7.24 thf(fact_6057_sum__power2__le__zero__iff,axiom,
% 6.92/7.24 ! [X: code_integer,Y: code_integer] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_z3403309356797280102nteger )
% 6.92/7.24 = ( ( X = zero_z3403309356797280102nteger )
% 6.92/7.24 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sum_power2_le_zero_iff
% 6.92/7.24 thf(fact_6058_sum__power2__le__zero__iff,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( 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 )
% 6.92/7.24 = ( ( X = zero_zero_rat )
% 6.92/7.24 & ( Y = zero_zero_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sum_power2_le_zero_iff
% 6.92/7.24 thf(fact_6059_sum__power2__le__zero__iff,axiom,
% 6.92/7.24 ! [X: int,Y: int] :
% 6.92/7.24 ( ( 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 )
% 6.92/7.24 = ( ( X = zero_zero_int )
% 6.92/7.24 & ( Y = zero_zero_int ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sum_power2_le_zero_iff
% 6.92/7.24 thf(fact_6060_sum__power2__ge__zero,axiom,
% 6.92/7.24 ! [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 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sum_power2_ge_zero
% 6.92/7.24 thf(fact_6061_sum__power2__ge__zero,axiom,
% 6.92/7.24 ! [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 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sum_power2_ge_zero
% 6.92/7.24 thf(fact_6062_sum__power2__ge__zero,axiom,
% 6.92/7.24 ! [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 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sum_power2_ge_zero
% 6.92/7.24 thf(fact_6063_sum__power2__gt__zero__iff,axiom,
% 6.92/7.24 ! [X: code_integer,Y: code_integer] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 6.92/7.24 = ( ( X != zero_z3403309356797280102nteger )
% 6.92/7.24 | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sum_power2_gt_zero_iff
% 6.92/7.24 thf(fact_6064_sum__power2__gt__zero__iff,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( 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 ) ) ) ) )
% 6.92/7.24 = ( ( X != zero_zero_rat )
% 6.92/7.24 | ( Y != zero_zero_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sum_power2_gt_zero_iff
% 6.92/7.24 thf(fact_6065_sum__power2__gt__zero__iff,axiom,
% 6.92/7.24 ! [X: int,Y: int] :
% 6.92/7.24 ( ( 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 ) ) ) ) )
% 6.92/7.24 = ( ( X != zero_zero_int )
% 6.92/7.24 | ( Y != zero_zero_int ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % sum_power2_gt_zero_iff
% 6.92/7.24 thf(fact_6066_not__sum__power2__lt__zero,axiom,
% 6.92/7.24 ! [X: code_integer,Y: code_integer] :
% 6.92/7.24 ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_z3403309356797280102nteger ) ).
% 6.92/7.24
% 6.92/7.24 % not_sum_power2_lt_zero
% 6.92/7.24 thf(fact_6067_not__sum__power2__lt__zero,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ~ ( 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 ) ).
% 6.92/7.24
% 6.92/7.24 % not_sum_power2_lt_zero
% 6.92/7.24 thf(fact_6068_not__sum__power2__lt__zero,axiom,
% 6.92/7.24 ! [X: int,Y: int] :
% 6.92/7.24 ~ ( 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 ) ).
% 6.92/7.24
% 6.92/7.24 % not_sum_power2_lt_zero
% 6.92/7.24 thf(fact_6069_power2__sum,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( 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 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_sum
% 6.92/7.24 thf(fact_6070_power2__sum,axiom,
% 6.92/7.24 ! [X: nat,Y: nat] :
% 6.92/7.24 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( 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 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_sum
% 6.92/7.24 thf(fact_6071_power2__sum,axiom,
% 6.92/7.24 ! [X: int,Y: int] :
% 6.92/7.24 ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( 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 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_sum
% 6.92/7.24 thf(fact_6072_power2__sum,axiom,
% 6.92/7.24 ! [X: code_natural,Y: code_natural] :
% 6.92/7.24 ( ( power_7079662738309270450atural @ ( plus_p4538020629002901425atural @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( 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 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_sum
% 6.92/7.24 thf(fact_6073_power2__sum,axiom,
% 6.92/7.24 ! [X: code_integer,Y: code_integer] :
% 6.92/7.24 ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( 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 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_sum
% 6.92/7.24 thf(fact_6074_square__le__1,axiom,
% 6.92/7.24 ! [X: code_integer] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 6.92/7.24 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 6.92/7.24 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % square_le_1
% 6.92/7.24 thf(fact_6075_square__le__1,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 6.92/7.24 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 6.92/7.24 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % square_le_1
% 6.92/7.24 thf(fact_6076_square__le__1,axiom,
% 6.92/7.24 ! [X: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 6.92/7.24 => ( ( ord_less_eq_int @ X @ one_one_int )
% 6.92/7.24 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % square_le_1
% 6.92/7.24 thf(fact_6077_zero__le__even__power_H,axiom,
% 6.92/7.24 ! [A: code_integer,N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_le_even_power'
% 6.92/7.24 thf(fact_6078_zero__le__even__power_H,axiom,
% 6.92/7.24 ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_le_even_power'
% 6.92/7.24 thf(fact_6079_zero__le__even__power_H,axiom,
% 6.92/7.24 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_le_even_power'
% 6.92/7.24 thf(fact_6080_power2__le__iff__abs__le,axiom,
% 6.92/7.24 ! [Y: code_integer,X: code_integer] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 6.92/7.24 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_le_iff_abs_le
% 6.92/7.24 thf(fact_6081_power2__le__iff__abs__le,axiom,
% 6.92/7.24 ! [Y: rat,X: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 6.92/7.24 => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_le_iff_abs_le
% 6.92/7.24 thf(fact_6082_power2__le__iff__abs__le,axiom,
% 6.92/7.24 ! [Y: int,X: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.24 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_le_iff_abs_le
% 6.92/7.24 thf(fact_6083_abs__square__le__1,axiom,
% 6.92/7.24 ! [X: code_integer] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 6.92/7.24 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 6.92/7.24
% 6.92/7.24 % abs_square_le_1
% 6.92/7.24 thf(fact_6084_abs__square__le__1,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 6.92/7.24 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % abs_square_le_1
% 6.92/7.24 thf(fact_6085_abs__square__le__1,axiom,
% 6.92/7.24 ! [X: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 6.92/7.24 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % abs_square_le_1
% 6.92/7.24 thf(fact_6086_abs__square__less__1,axiom,
% 6.92/7.24 ! [X: code_integer] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 6.92/7.24 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 6.92/7.24
% 6.92/7.24 % abs_square_less_1
% 6.92/7.24 thf(fact_6087_abs__square__less__1,axiom,
% 6.92/7.24 ! [X: rat] :
% 6.92/7.24 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 6.92/7.24 = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % abs_square_less_1
% 6.92/7.24 thf(fact_6088_abs__square__less__1,axiom,
% 6.92/7.24 ! [X: int] :
% 6.92/7.24 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 6.92/7.24 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % abs_square_less_1
% 6.92/7.24 thf(fact_6089_Suc__n__div__2__gt__zero,axiom,
% 6.92/7.24 ! [N2: nat] :
% 6.92/7.24 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.24 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Suc_n_div_2_gt_zero
% 6.92/7.24 thf(fact_6090_div__2__gt__zero,axiom,
% 6.92/7.24 ! [N2: nat] :
% 6.92/7.24 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 6.92/7.24 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % div_2_gt_zero
% 6.92/7.24 thf(fact_6091_divmod__digit__0_I1_J,axiom,
% 6.92/7.24 ! [B: code_integer,A: code_integer] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.24 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 6.92/7.24 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 6.92/7.24 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_digit_0(1)
% 6.92/7.24 thf(fact_6092_divmod__digit__0_I1_J,axiom,
% 6.92/7.24 ! [B: nat,A: nat] :
% 6.92/7.24 ( ( ord_less_nat @ zero_zero_nat @ B )
% 6.92/7.24 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 6.92/7.24 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 6.92/7.24 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_digit_0(1)
% 6.92/7.24 thf(fact_6093_divmod__digit__0_I1_J,axiom,
% 6.92/7.24 ! [B: int,A: int] :
% 6.92/7.24 ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.24 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 6.92/7.24 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 6.92/7.24 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_digit_0(1)
% 6.92/7.24 thf(fact_6094_power2__diff,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( 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 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_diff
% 6.92/7.24 thf(fact_6095_power2__diff,axiom,
% 6.92/7.24 ! [X: int,Y: int] :
% 6.92/7.24 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( 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 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_diff
% 6.92/7.24 thf(fact_6096_power2__diff,axiom,
% 6.92/7.24 ! [X: code_integer,Y: code_integer] :
% 6.92/7.24 ( ( power_8256067586552552935nteger @ ( minus_8373710615458151222nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = ( 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 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % power2_diff
% 6.92/7.24 thf(fact_6097_odd__0__le__power__imp__0__le,axiom,
% 6.92/7.24 ! [A: code_integer,N2: nat] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 6.92/7.24 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % odd_0_le_power_imp_0_le
% 6.92/7.24 thf(fact_6098_odd__0__le__power__imp__0__le,axiom,
% 6.92/7.24 ! [A: rat,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 6.92/7.24 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % odd_0_le_power_imp_0_le
% 6.92/7.24 thf(fact_6099_odd__0__le__power__imp__0__le,axiom,
% 6.92/7.24 ! [A: int,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 6.92/7.24 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 6.92/7.24
% 6.92/7.24 % odd_0_le_power_imp_0_le
% 6.92/7.24 thf(fact_6100_odd__power__less__zero,axiom,
% 6.92/7.24 ! [A: code_integer,N2: nat] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 6.92/7.24 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.24
% 6.92/7.24 % odd_power_less_zero
% 6.92/7.24 thf(fact_6101_odd__power__less__zero,axiom,
% 6.92/7.24 ! [A: rat,N2: nat] :
% 6.92/7.24 ( ( ord_less_rat @ A @ zero_zero_rat )
% 6.92/7.24 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_rat ) ) ).
% 6.92/7.24
% 6.92/7.24 % odd_power_less_zero
% 6.92/7.24 thf(fact_6102_odd__power__less__zero,axiom,
% 6.92/7.24 ! [A: int,N2: nat] :
% 6.92/7.24 ( ( ord_less_int @ A @ zero_zero_int )
% 6.92/7.24 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % odd_power_less_zero
% 6.92/7.24 thf(fact_6103_ex__power__ivl1,axiom,
% 6.92/7.24 ! [B: nat,K2: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 6.92/7.24 => ( ( ord_less_eq_nat @ one_one_nat @ K2 )
% 6.92/7.24 => ? [N5: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N5 ) @ K2 )
% 6.92/7.24 & ( ord_less_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N5 @ one_one_nat ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ex_power_ivl1
% 6.92/7.24 thf(fact_6104_ex__power__ivl2,axiom,
% 6.92/7.24 ! [B: nat,K2: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 6.92/7.24 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 6.92/7.24 => ? [N5: nat] :
% 6.92/7.24 ( ( ord_less_nat @ ( power_power_nat @ B @ N5 ) @ K2 )
% 6.92/7.24 & ( ord_less_eq_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N5 @ one_one_nat ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % ex_power_ivl2
% 6.92/7.24 thf(fact_6105_mod__double__modulus,axiom,
% 6.92/7.24 ! [M: code_integer,X: code_integer] :
% 6.92/7.24 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 6.92/7.24 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 6.92/7.24 => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 6.92/7.24 = ( modulo364778990260209775nteger @ X @ M ) )
% 6.92/7.24 | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 6.92/7.24 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M ) @ M ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % mod_double_modulus
% 6.92/7.24 thf(fact_6106_mod__double__modulus,axiom,
% 6.92/7.24 ! [M: nat,X: nat] :
% 6.92/7.24 ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 6.92/7.24 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 6.92/7.24 = ( modulo_modulo_nat @ X @ M ) )
% 6.92/7.24 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 6.92/7.24 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % mod_double_modulus
% 6.92/7.24 thf(fact_6107_mod__double__modulus,axiom,
% 6.92/7.24 ! [M: int,X: int] :
% 6.92/7.24 ( ( ord_less_int @ zero_zero_int @ M )
% 6.92/7.24 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.24 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 6.92/7.24 = ( modulo_modulo_int @ X @ M ) )
% 6.92/7.24 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 6.92/7.24 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % mod_double_modulus
% 6.92/7.24 thf(fact_6108_divmod__digit__1_I2_J,axiom,
% 6.92/7.24 ! [A: code_integer,B: code_integer] :
% 6.92/7.24 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 6.92/7.24 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 6.92/7.24 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 6.92/7.24 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 6.92/7.24 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_digit_1(2)
% 6.92/7.24 thf(fact_6109_divmod__digit__1_I2_J,axiom,
% 6.92/7.24 ! [A: nat,B: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 6.92/7.24 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 6.92/7.24 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 6.92/7.24 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 6.92/7.24 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_digit_1(2)
% 6.92/7.24 thf(fact_6110_divmod__digit__1_I2_J,axiom,
% 6.92/7.24 ! [A: int,B: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.24 => ( ( ord_less_int @ zero_zero_int @ B )
% 6.92/7.24 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 6.92/7.24 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 6.92/7.24 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_digit_1(2)
% 6.92/7.24 thf(fact_6111_pos__zdiv__mult__2,axiom,
% 6.92/7.24 ! [A: int,B: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.24 => ( ( 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 ) )
% 6.92/7.24 = ( divide_divide_int @ B @ A ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % pos_zdiv_mult_2
% 6.92/7.24 thf(fact_6112_neg__zdiv__mult__2,axiom,
% 6.92/7.24 ! [A: int,B: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 6.92/7.24 => ( ( 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 ) )
% 6.92/7.24 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % neg_zdiv_mult_2
% 6.92/7.24 thf(fact_6113_pos__zmod__mult__2,axiom,
% 6.92/7.24 ! [A: int,B: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 6.92/7.24 => ( ( 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 ) )
% 6.92/7.24 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % pos_zmod_mult_2
% 6.92/7.24 thf(fact_6114_half__negative__int__iff,axiom,
% 6.92/7.24 ! [K2: int] :
% 6.92/7.24 ( ( ord_less_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 6.92/7.24 = ( ord_less_int @ K2 @ zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % half_negative_int_iff
% 6.92/7.24 thf(fact_6115_half__nonnegative__int__iff,axiom,
% 6.92/7.24 ! [K2: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = ( ord_less_eq_int @ zero_zero_int @ K2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % half_nonnegative_int_iff
% 6.92/7.24 thf(fact_6116_divmod__step__eq,axiom,
% 6.92/7.24 ! [L: num,R2: nat,Q6: nat] :
% 6.92/7.24 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 6.92/7.24 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q6 @ R2 ) )
% 6.92/7.24 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q6 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 6.92/7.24 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 6.92/7.24 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q6 @ R2 ) )
% 6.92/7.24 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q6 ) @ R2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_step_eq
% 6.92/7.24 thf(fact_6117_divmod__step__eq,axiom,
% 6.92/7.24 ! [L: num,R2: int,Q6: int] :
% 6.92/7.24 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 6.92/7.24 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 6.92/7.24 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q6 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L ) ) ) ) )
% 6.92/7.24 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 6.92/7.24 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 6.92/7.24 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q6 ) @ R2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_step_eq
% 6.92/7.24 thf(fact_6118_divmod__step__eq,axiom,
% 6.92/7.24 ! [L: num,R2: code_integer,Q6: code_integer] :
% 6.92/7.24 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 6.92/7.24 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q6 @ R2 ) )
% 6.92/7.24 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 6.92/7.24 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 6.92/7.24 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q6 @ R2 ) )
% 6.92/7.24 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ R2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_step_eq
% 6.92/7.24 thf(fact_6119_int__bit__induct,axiom,
% 6.92/7.24 ! [P2: int > $o,K2: int] :
% 6.92/7.24 ( ( P2 @ zero_zero_int )
% 6.92/7.24 => ( ( P2 @ ( uminus_uminus_int @ one_one_int ) )
% 6.92/7.24 => ( ! [K: int] :
% 6.92/7.24 ( ( P2 @ K )
% 6.92/7.24 => ( ( K != zero_zero_int )
% 6.92/7.24 => ( P2 @ ( times_times_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 6.92/7.24 => ( ! [K: int] :
% 6.92/7.24 ( ( P2 @ K )
% 6.92/7.24 => ( ( K
% 6.92/7.24 != ( uminus_uminus_int @ one_one_int ) )
% 6.92/7.24 => ( P2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 6.92/7.24 => ( P2 @ K2 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % int_bit_induct
% 6.92/7.24 thf(fact_6120_mult__exp__mod__exp__eq,axiom,
% 6.92/7.24 ! [M: nat,N2: nat,A: code_integer] :
% 6.92/7.24 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.24 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.24 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_exp_mod_exp_eq
% 6.92/7.24 thf(fact_6121_mult__exp__mod__exp__eq,axiom,
% 6.92/7.24 ! [M: nat,N2: nat,A: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.24 => ( ( 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 ) )
% 6.92/7.24 = ( 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 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_exp_mod_exp_eq
% 6.92/7.24 thf(fact_6122_mult__exp__mod__exp__eq,axiom,
% 6.92/7.24 ! [M: nat,N2: nat,A: int] :
% 6.92/7.24 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.24 => ( ( 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 ) )
% 6.92/7.24 = ( 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 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_exp_mod_exp_eq
% 6.92/7.24 thf(fact_6123_mult__exp__mod__exp__eq,axiom,
% 6.92/7.24 ! [M: nat,N2: nat,A: code_natural] :
% 6.92/7.24 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.24 => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.24 = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % mult_exp_mod_exp_eq
% 6.92/7.24 thf(fact_6124_nat__bit__induct,axiom,
% 6.92/7.24 ! [P2: nat > $o,N2: nat] :
% 6.92/7.24 ( ( P2 @ zero_zero_nat )
% 6.92/7.24 => ( ! [N5: nat] :
% 6.92/7.24 ( ( P2 @ N5 )
% 6.92/7.24 => ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 6.92/7.24 => ( P2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N5 ) ) ) )
% 6.92/7.24 => ( ! [N5: nat] :
% 6.92/7.24 ( ( P2 @ N5 )
% 6.92/7.24 => ( P2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N5 ) ) ) )
% 6.92/7.24 => ( P2 @ N2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % nat_bit_induct
% 6.92/7.24 thf(fact_6125_exp__add__not__zero__imp__right,axiom,
% 6.92/7.24 ! [M: nat,N2: nat] :
% 6.92/7.24 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.24 != zero_zero_nat )
% 6.92/7.24 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.24 != zero_zero_nat ) ) ).
% 6.92/7.24
% 6.92/7.24 % exp_add_not_zero_imp_right
% 6.92/7.24 thf(fact_6126_exp__add__not__zero__imp__right,axiom,
% 6.92/7.24 ! [M: nat,N2: nat] :
% 6.92/7.24 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.24 != zero_zero_int )
% 6.92/7.24 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.24 != zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % exp_add_not_zero_imp_right
% 6.92/7.24 thf(fact_6127_exp__add__not__zero__imp__right,axiom,
% 6.92/7.24 ! [M: nat,N2: nat] :
% 6.92/7.24 ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.24 != zero_z2226904508553997617atural )
% 6.92/7.24 => ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.24 != zero_z2226904508553997617atural ) ) ).
% 6.92/7.24
% 6.92/7.24 % exp_add_not_zero_imp_right
% 6.92/7.24 thf(fact_6128_exp__add__not__zero__imp__right,axiom,
% 6.92/7.24 ! [M: nat,N2: nat] :
% 6.92/7.24 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.24 != zero_z3403309356797280102nteger )
% 6.92/7.24 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.24 != zero_z3403309356797280102nteger ) ) ).
% 6.92/7.24
% 6.92/7.24 % exp_add_not_zero_imp_right
% 6.92/7.24 thf(fact_6129_exp__add__not__zero__imp__left,axiom,
% 6.92/7.24 ! [M: nat,N2: nat] :
% 6.92/7.24 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.24 != zero_zero_nat )
% 6.92/7.24 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 6.92/7.24 != zero_zero_nat ) ) ).
% 6.92/7.24
% 6.92/7.24 % exp_add_not_zero_imp_left
% 6.92/7.24 thf(fact_6130_exp__add__not__zero__imp__left,axiom,
% 6.92/7.24 ! [M: nat,N2: nat] :
% 6.92/7.24 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.24 != zero_zero_int )
% 6.92/7.24 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 6.92/7.24 != zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % exp_add_not_zero_imp_left
% 6.92/7.24 thf(fact_6131_exp__add__not__zero__imp__left,axiom,
% 6.92/7.24 ! [M: nat,N2: nat] :
% 6.92/7.24 ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.24 != zero_z2226904508553997617atural )
% 6.92/7.24 => ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M )
% 6.92/7.24 != zero_z2226904508553997617atural ) ) ).
% 6.92/7.24
% 6.92/7.24 % exp_add_not_zero_imp_left
% 6.92/7.24 thf(fact_6132_exp__add__not__zero__imp__left,axiom,
% 6.92/7.24 ! [M: nat,N2: nat] :
% 6.92/7.24 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 6.92/7.24 != zero_z3403309356797280102nteger )
% 6.92/7.24 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 6.92/7.24 != zero_z3403309356797280102nteger ) ) ).
% 6.92/7.24
% 6.92/7.24 % exp_add_not_zero_imp_left
% 6.92/7.24 thf(fact_6133_div__exp__eq,axiom,
% 6.92/7.24 ! [A: code_integer,M: nat,N2: nat] :
% 6.92/7.24 ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.24 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % div_exp_eq
% 6.92/7.24 thf(fact_6134_div__exp__eq,axiom,
% 6.92/7.24 ! [A: nat,M: nat,N2: nat] :
% 6.92/7.24 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.24 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % div_exp_eq
% 6.92/7.24 thf(fact_6135_div__exp__eq,axiom,
% 6.92/7.24 ! [A: int,M: nat,N2: nat] :
% 6.92/7.24 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.24 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % div_exp_eq
% 6.92/7.24 thf(fact_6136_div__exp__eq,axiom,
% 6.92/7.24 ! [A: code_natural,M: nat,N2: nat] :
% 6.92/7.24 ( ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.24 = ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % div_exp_eq
% 6.92/7.24 thf(fact_6137_not__exp__less__eq__0__int,axiom,
% 6.92/7.24 ! [N2: nat] :
% 6.92/7.24 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_int ) ).
% 6.92/7.24
% 6.92/7.24 % not_exp_less_eq_0_int
% 6.92/7.24 thf(fact_6138_bits__stable__imp__add__self,axiom,
% 6.92/7.24 ! [A: code_integer] :
% 6.92/7.24 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 6.92/7.24 = A )
% 6.92/7.24 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.24
% 6.92/7.24 % bits_stable_imp_add_self
% 6.92/7.24 thf(fact_6139_bits__stable__imp__add__self,axiom,
% 6.92/7.24 ! [A: nat] :
% 6.92/7.24 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.24 = A )
% 6.92/7.24 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = zero_zero_nat ) ) ).
% 6.92/7.24
% 6.92/7.24 % bits_stable_imp_add_self
% 6.92/7.24 thf(fact_6140_bits__stable__imp__add__self,axiom,
% 6.92/7.24 ! [A: int] :
% 6.92/7.24 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 6.92/7.24 = A )
% 6.92/7.24 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % bits_stable_imp_add_self
% 6.92/7.24 thf(fact_6141_bits__stable__imp__add__self,axiom,
% 6.92/7.24 ! [A: code_natural] :
% 6.92/7.24 ( ( ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 6.92/7.24 = A )
% 6.92/7.24 => ( ( plus_p4538020629002901425atural @ A @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) )
% 6.92/7.24 = zero_z2226904508553997617atural ) ) ).
% 6.92/7.24
% 6.92/7.24 % bits_stable_imp_add_self
% 6.92/7.24 thf(fact_6142_div__exp__mod__exp__eq,axiom,
% 6.92/7.24 ! [A: code_integer,N2: nat,M: nat] :
% 6.92/7.24 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 6.92/7.24 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % div_exp_mod_exp_eq
% 6.92/7.24 thf(fact_6143_div__exp__mod__exp__eq,axiom,
% 6.92/7.24 ! [A: nat,N2: nat,M: nat] :
% 6.92/7.24 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 6.92/7.24 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % div_exp_mod_exp_eq
% 6.92/7.24 thf(fact_6144_div__exp__mod__exp__eq,axiom,
% 6.92/7.24 ! [A: int,N2: nat,M: nat] :
% 6.92/7.24 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 6.92/7.24 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % div_exp_mod_exp_eq
% 6.92/7.24 thf(fact_6145_div__exp__mod__exp__eq,axiom,
% 6.92/7.24 ! [A: code_natural,N2: nat,M: nat] :
% 6.92/7.24 ( ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) )
% 6.92/7.24 = ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % div_exp_mod_exp_eq
% 6.92/7.24 thf(fact_6146_set__bit__0,axiom,
% 6.92/7.24 ! [A: code_integer] :
% 6.92/7.24 ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 6.92/7.24 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % set_bit_0
% 6.92/7.24 thf(fact_6147_set__bit__0,axiom,
% 6.92/7.24 ! [A: nat] :
% 6.92/7.24 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 6.92/7.24 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % set_bit_0
% 6.92/7.24 thf(fact_6148_set__bit__0,axiom,
% 6.92/7.24 ! [A: code_natural] :
% 6.92/7.24 ( ( bit_se1617098188084679374atural @ zero_zero_nat @ A )
% 6.92/7.24 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % set_bit_0
% 6.92/7.24 thf(fact_6149_set__bit__0,axiom,
% 6.92/7.24 ! [A: int] :
% 6.92/7.24 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 6.92/7.24 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % set_bit_0
% 6.92/7.24 thf(fact_6150_unset__bit__Suc,axiom,
% 6.92/7.24 ! [N2: nat,A: code_integer] :
% 6.92/7.24 ( ( bit_se8260200283734997820nteger @ ( suc @ N2 ) @ A )
% 6.92/7.24 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % unset_bit_Suc
% 6.92/7.24 thf(fact_6151_unset__bit__Suc,axiom,
% 6.92/7.24 ! [N2: nat,A: nat] :
% 6.92/7.24 ( ( bit_se4205575877204974255it_nat @ ( suc @ N2 ) @ A )
% 6.92/7.24 = ( 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 ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % unset_bit_Suc
% 6.92/7.24 thf(fact_6152_unset__bit__Suc,axiom,
% 6.92/7.24 ! [N2: nat,A: code_natural] :
% 6.92/7.24 ( ( bit_se7083795435491715335atural @ ( suc @ N2 ) @ A )
% 6.92/7.24 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se7083795435491715335atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % unset_bit_Suc
% 6.92/7.24 thf(fact_6153_unset__bit__Suc,axiom,
% 6.92/7.24 ! [N2: nat,A: int] :
% 6.92/7.24 ( ( bit_se4203085406695923979it_int @ ( suc @ N2 ) @ A )
% 6.92/7.24 = ( 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 ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % unset_bit_Suc
% 6.92/7.24 thf(fact_6154_flip__bit__Suc,axiom,
% 6.92/7.24 ! [N2: nat,A: code_integer] :
% 6.92/7.24 ( ( bit_se1345352211410354436nteger @ ( suc @ N2 ) @ A )
% 6.92/7.24 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % flip_bit_Suc
% 6.92/7.24 thf(fact_6155_flip__bit__Suc,axiom,
% 6.92/7.24 ! [N2: nat,A: nat] :
% 6.92/7.24 ( ( bit_se2161824704523386999it_nat @ ( suc @ N2 ) @ A )
% 6.92/7.24 = ( 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 ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % flip_bit_Suc
% 6.92/7.24 thf(fact_6156_flip__bit__Suc,axiom,
% 6.92/7.24 ! [N2: nat,A: code_natural] :
% 6.92/7.24 ( ( bit_se168947363167071951atural @ ( suc @ N2 ) @ A )
% 6.92/7.24 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se168947363167071951atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % flip_bit_Suc
% 6.92/7.24 thf(fact_6157_flip__bit__Suc,axiom,
% 6.92/7.24 ! [N2: nat,A: int] :
% 6.92/7.24 ( ( bit_se2159334234014336723it_int @ ( suc @ N2 ) @ A )
% 6.92/7.24 = ( 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 ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % flip_bit_Suc
% 6.92/7.24 thf(fact_6158_set__bit__Suc,axiom,
% 6.92/7.24 ! [N2: nat,A: code_integer] :
% 6.92/7.24 ( ( bit_se2793503036327961859nteger @ ( suc @ N2 ) @ A )
% 6.92/7.24 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % set_bit_Suc
% 6.92/7.24 thf(fact_6159_set__bit__Suc,axiom,
% 6.92/7.24 ! [N2: nat,A: nat] :
% 6.92/7.24 ( ( bit_se7882103937844011126it_nat @ ( suc @ N2 ) @ A )
% 6.92/7.24 = ( 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 ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % set_bit_Suc
% 6.92/7.24 thf(fact_6160_set__bit__Suc,axiom,
% 6.92/7.24 ! [N2: nat,A: code_natural] :
% 6.92/7.24 ( ( bit_se1617098188084679374atural @ ( suc @ N2 ) @ A )
% 6.92/7.24 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se1617098188084679374atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % set_bit_Suc
% 6.92/7.24 thf(fact_6161_set__bit__Suc,axiom,
% 6.92/7.24 ! [N2: nat,A: int] :
% 6.92/7.24 ( ( bit_se7879613467334960850it_int @ ( suc @ N2 ) @ A )
% 6.92/7.24 = ( 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 ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % set_bit_Suc
% 6.92/7.24 thf(fact_6162_signed__take__bit__rec,axiom,
% 6.92/7.24 ( bit_ri6519982836138164636nteger
% 6.92/7.24 = ( ^ [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 ) ) ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_rec
% 6.92/7.24 thf(fact_6163_signed__take__bit__rec,axiom,
% 6.92/7.24 ( bit_ri631733984087533419it_int
% 6.92/7.24 = ( ^ [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 ) ) ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_rec
% 6.92/7.24 thf(fact_6164_round__unique,axiom,
% 6.92/7.24 ! [X: rat,Y: int] :
% 6.92/7.24 ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 6.92/7.24 => ( ( 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 ) ) ) ) )
% 6.92/7.24 => ( ( archim7778729529865785530nd_rat @ X )
% 6.92/7.24 = Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % round_unique
% 6.92/7.24 thf(fact_6165_unset__bit__nonnegative__int__iff,axiom,
% 6.92/7.24 ! [N2: nat,K2: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N2 @ K2 ) )
% 6.92/7.24 = ( ord_less_eq_int @ zero_zero_int @ K2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % unset_bit_nonnegative_int_iff
% 6.92/7.24 thf(fact_6166_set__bit__nonnegative__int__iff,axiom,
% 6.92/7.24 ! [N2: nat,K2: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N2 @ K2 ) )
% 6.92/7.24 = ( ord_less_eq_int @ zero_zero_int @ K2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % set_bit_nonnegative_int_iff
% 6.92/7.24 thf(fact_6167_flip__bit__nonnegative__int__iff,axiom,
% 6.92/7.24 ! [N2: nat,K2: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N2 @ K2 ) )
% 6.92/7.24 = ( ord_less_eq_int @ zero_zero_int @ K2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % flip_bit_nonnegative_int_iff
% 6.92/7.24 thf(fact_6168_unset__bit__negative__int__iff,axiom,
% 6.92/7.24 ! [N2: nat,K2: int] :
% 6.92/7.24 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N2 @ K2 ) @ zero_zero_int )
% 6.92/7.24 = ( ord_less_int @ K2 @ zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % unset_bit_negative_int_iff
% 6.92/7.24 thf(fact_6169_set__bit__negative__int__iff,axiom,
% 6.92/7.24 ! [N2: nat,K2: int] :
% 6.92/7.24 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N2 @ K2 ) @ zero_zero_int )
% 6.92/7.24 = ( ord_less_int @ K2 @ zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % set_bit_negative_int_iff
% 6.92/7.24 thf(fact_6170_flip__bit__negative__int__iff,axiom,
% 6.92/7.24 ! [N2: nat,K2: int] :
% 6.92/7.24 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N2 @ K2 ) @ zero_zero_int )
% 6.92/7.24 = ( ord_less_int @ K2 @ zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % flip_bit_negative_int_iff
% 6.92/7.24 thf(fact_6171_signed__take__bit__Suc__bit1,axiom,
% 6.92/7.24 ! [N2: nat,K2: num] :
% 6.92/7.24 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) )
% 6.92/7.24 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_Suc_bit1
% 6.92/7.24 thf(fact_6172_signed__take__bit__Suc__minus__bit1,axiom,
% 6.92/7.24 ! [N2: nat,K2: num] :
% 6.92/7.24 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 6.92/7.24 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_Suc_minus_bit1
% 6.92/7.24 thf(fact_6173_signed__take__bit__add,axiom,
% 6.92/7.24 ! [N2: nat,K2: int,L: int] :
% 6.92/7.24 ( ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N2 @ K2 ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 6.92/7.24 = ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ K2 @ L ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_add
% 6.92/7.24 thf(fact_6174_unset__bit__less__eq,axiom,
% 6.92/7.24 ! [N2: nat,K2: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N2 @ K2 ) @ K2 ) ).
% 6.92/7.24
% 6.92/7.24 % unset_bit_less_eq
% 6.92/7.24 thf(fact_6175_set__bit__greater__eq,axiom,
% 6.92/7.24 ! [K2: int,N2: nat] : ( ord_less_eq_int @ K2 @ ( bit_se7879613467334960850it_int @ N2 @ K2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % set_bit_greater_eq
% 6.92/7.24 thf(fact_6176_round__mono,axiom,
% 6.92/7.24 ! [X: rat,Y: rat] :
% 6.92/7.24 ( ( ord_less_eq_rat @ X @ Y )
% 6.92/7.24 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % round_mono
% 6.92/7.24 thf(fact_6177_floor__le__round,axiom,
% 6.92/7.24 ! [X: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim7778729529865785530nd_rat @ X ) ) ).
% 6.92/7.24
% 6.92/7.24 % floor_le_round
% 6.92/7.24 thf(fact_6178_signed__take__bit__int__less__exp,axiom,
% 6.92/7.24 ! [N2: nat,K2: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_int_less_exp
% 6.92/7.24 thf(fact_6179_round__diff__minimal,axiom,
% 6.92/7.24 ! [Z3: rat,M: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z3 @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z3 ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z3 @ ( ring_1_of_int_rat @ M ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % round_diff_minimal
% 6.92/7.24 thf(fact_6180_signed__take__bit__int__greater__eq__self__iff,axiom,
% 6.92/7.24 ! [K2: int,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_int @ K2 @ ( bit_ri631733984087533419it_int @ N2 @ K2 ) )
% 6.92/7.24 = ( ord_less_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_int_greater_eq_self_iff
% 6.92/7.24 thf(fact_6181_signed__take__bit__int__less__self__iff,axiom,
% 6.92/7.24 ! [N2: nat,K2: int] :
% 6.92/7.24 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K2 ) @ K2 )
% 6.92/7.24 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_int_less_self_iff
% 6.92/7.24 thf(fact_6182_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 6.92/7.24 ! [N2: nat,K2: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_int_greater_eq_minus_exp
% 6.92/7.24 thf(fact_6183_signed__take__bit__int__less__eq__self__iff,axiom,
% 6.92/7.24 ! [N2: nat,K2: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K2 ) @ K2 )
% 6.92/7.24 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_int_less_eq_self_iff
% 6.92/7.24 thf(fact_6184_signed__take__bit__int__greater__self__iff,axiom,
% 6.92/7.24 ! [K2: int,N2: nat] :
% 6.92/7.24 ( ( ord_less_int @ K2 @ ( bit_ri631733984087533419it_int @ N2 @ K2 ) )
% 6.92/7.24 = ( ord_less_int @ K2 @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_int_greater_self_iff
% 6.92/7.24 thf(fact_6185_signed__take__bit__int__less__eq,axiom,
% 6.92/7.24 ! [N2: nat,K2: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K2 )
% 6.92/7.24 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K2 ) @ ( minus_minus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_int_less_eq
% 6.92/7.24 thf(fact_6186_signed__take__bit__int__eq__self__iff,axiom,
% 6.92/7.24 ! [N2: nat,K2: int] :
% 6.92/7.24 ( ( ( bit_ri631733984087533419it_int @ N2 @ K2 )
% 6.92/7.24 = K2 )
% 6.92/7.24 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K2 )
% 6.92/7.24 & ( ord_less_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_int_eq_self_iff
% 6.92/7.24 thf(fact_6187_signed__take__bit__int__eq__self,axiom,
% 6.92/7.24 ! [N2: nat,K2: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K2 )
% 6.92/7.24 => ( ( ord_less_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.24 => ( ( bit_ri631733984087533419it_int @ N2 @ K2 )
% 6.92/7.24 = K2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_int_eq_self
% 6.92/7.24 thf(fact_6188_signed__take__bit__int__greater__eq,axiom,
% 6.92/7.24 ! [K2: int,N2: nat] :
% 6.92/7.24 ( ( ord_less_int @ K2 @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 6.92/7.24 => ( ord_less_eq_int @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_int_greater_eq
% 6.92/7.24 thf(fact_6189_round__def,axiom,
% 6.92/7.24 ( archim7778729529865785530nd_rat
% 6.92/7.24 = ( ^ [X4: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % round_def
% 6.92/7.24 thf(fact_6190_signed__take__bit__Suc,axiom,
% 6.92/7.24 ! [N2: nat,A: code_integer] :
% 6.92/7.24 ( ( bit_ri6519982836138164636nteger @ ( suc @ N2 ) @ A )
% 6.92/7.24 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_Suc
% 6.92/7.24 thf(fact_6191_signed__take__bit__Suc,axiom,
% 6.92/7.24 ! [N2: nat,A: int] :
% 6.92/7.24 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ A )
% 6.92/7.24 = ( 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 ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_Suc
% 6.92/7.24 thf(fact_6192_of__int__round__le,axiom,
% 6.92/7.24 ! [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 ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_round_le
% 6.92/7.24 thf(fact_6193_of__int__round__ge,axiom,
% 6.92/7.24 ! [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 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_round_ge
% 6.92/7.24 thf(fact_6194_of__int__round__gt,axiom,
% 6.92/7.24 ! [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 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_round_gt
% 6.92/7.24 thf(fact_6195_of__int__round__abs__le,axiom,
% 6.92/7.24 ! [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 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % of_int_round_abs_le
% 6.92/7.24 thf(fact_6196_round__unique_H,axiom,
% 6.92/7.24 ! [X: rat,N2: int] :
% 6.92/7.24 ( ( 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 ) ) ) )
% 6.92/7.24 => ( ( archim7778729529865785530nd_rat @ X )
% 6.92/7.24 = N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % round_unique'
% 6.92/7.24 thf(fact_6197_round__altdef,axiom,
% 6.92/7.24 ( archim7778729529865785530nd_rat
% 6.92/7.24 = ( ^ [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 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % round_altdef
% 6.92/7.24 thf(fact_6198_divmod__algorithm__code_I8_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( ( ord_less_num @ M @ N2 )
% 6.92/7.24 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 6.92/7.24 & ( ~ ( ord_less_num @ M @ N2 )
% 6.92/7.24 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_algorithm_code(8)
% 6.92/7.24 thf(fact_6199_divmod__algorithm__code_I8_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( ( ord_less_num @ M @ N2 )
% 6.92/7.24 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 6.92/7.24 & ( ~ ( ord_less_num @ M @ N2 )
% 6.92/7.24 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_algorithm_code(8)
% 6.92/7.24 thf(fact_6200_divmod__algorithm__code_I8_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( ( ord_less_num @ M @ N2 )
% 6.92/7.24 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 6.92/7.24 & ( ~ ( ord_less_num @ M @ N2 )
% 6.92/7.24 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_algorithm_code(8)
% 6.92/7.24 thf(fact_6201_divmod__algorithm__code_I7_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( ( ord_less_eq_num @ M @ N2 )
% 6.92/7.24 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 6.92/7.24 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 6.92/7.24 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_algorithm_code(7)
% 6.92/7.24 thf(fact_6202_divmod__algorithm__code_I7_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( ( ord_less_eq_num @ M @ N2 )
% 6.92/7.24 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 6.92/7.24 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 6.92/7.24 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_algorithm_code(7)
% 6.92/7.24 thf(fact_6203_divmod__algorithm__code_I7_J,axiom,
% 6.92/7.24 ! [M: num,N2: num] :
% 6.92/7.24 ( ( ( ord_less_eq_num @ M @ N2 )
% 6.92/7.24 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 6.92/7.24 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 6.92/7.24 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_algorithm_code(7)
% 6.92/7.24 thf(fact_6204_signed__take__bit__numeral__minus__bit1,axiom,
% 6.92/7.24 ! [L: num,K2: num] :
% 6.92/7.24 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 6.92/7.24 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_numeral_minus_bit1
% 6.92/7.24 thf(fact_6205_concat__bit__Suc,axiom,
% 6.92/7.24 ! [N2: nat,K2: int,L: int] :
% 6.92/7.24 ( ( bit_concat_bit @ ( suc @ N2 ) @ K2 @ L )
% 6.92/7.24 = ( plus_plus_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N2 @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % concat_bit_Suc
% 6.92/7.24 thf(fact_6206_binomial__code,axiom,
% 6.92/7.24 ( binomial
% 6.92/7.24 = ( ^ [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 ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % binomial_code
% 6.92/7.24 thf(fact_6207_signed__take__bit__numeral__bit1,axiom,
% 6.92/7.24 ! [L: num,K2: num] :
% 6.92/7.24 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) )
% 6.92/7.24 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % signed_take_bit_numeral_bit1
% 6.92/7.24 thf(fact_6208_binomial__eq__0__iff,axiom,
% 6.92/7.24 ! [N2: nat,K2: nat] :
% 6.92/7.24 ( ( ( binomial @ N2 @ K2 )
% 6.92/7.24 = zero_zero_nat )
% 6.92/7.24 = ( ord_less_nat @ N2 @ K2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % binomial_eq_0_iff
% 6.92/7.24 thf(fact_6209_binomial__Suc__Suc,axiom,
% 6.92/7.24 ! [N2: nat,K2: nat] :
% 6.92/7.24 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K2 ) )
% 6.92/7.24 = ( plus_plus_nat @ ( binomial @ N2 @ K2 ) @ ( binomial @ N2 @ ( suc @ K2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % binomial_Suc_Suc
% 6.92/7.24 thf(fact_6210_concat__bit__nonnegative__iff,axiom,
% 6.92/7.24 ! [N2: nat,K2: int,L: int] :
% 6.92/7.24 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N2 @ K2 @ L ) )
% 6.92/7.24 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 6.92/7.24
% 6.92/7.24 % concat_bit_nonnegative_iff
% 6.92/7.24 thf(fact_6211_concat__bit__negative__iff,axiom,
% 6.92/7.24 ! [N2: nat,K2: int,L: int] :
% 6.92/7.24 ( ( ord_less_int @ ( bit_concat_bit @ N2 @ K2 @ L ) @ zero_zero_int )
% 6.92/7.24 = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % concat_bit_negative_iff
% 6.92/7.24 thf(fact_6212_zero__less__binomial__iff,axiom,
% 6.92/7.24 ! [N2: nat,K2: nat] :
% 6.92/7.24 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K2 ) )
% 6.92/7.24 = ( ord_less_eq_nat @ K2 @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_less_binomial_iff
% 6.92/7.24 thf(fact_6213_less__numeral__Suc,axiom,
% 6.92/7.24 ! [K2: num,N2: nat] :
% 6.92/7.24 ( ( ord_less_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N2 ) )
% 6.92/7.24 = ( ord_less_nat @ ( pred_numeral @ K2 ) @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % less_numeral_Suc
% 6.92/7.24 thf(fact_6214_less__Suc__numeral,axiom,
% 6.92/7.24 ! [N2: nat,K2: num] :
% 6.92/7.24 ( ( ord_less_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K2 ) )
% 6.92/7.24 = ( ord_less_nat @ N2 @ ( pred_numeral @ K2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % less_Suc_numeral
% 6.92/7.24 thf(fact_6215_le__numeral__Suc,axiom,
% 6.92/7.24 ! [K2: num,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N2 ) )
% 6.92/7.24 = ( ord_less_eq_nat @ ( pred_numeral @ K2 ) @ N2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % le_numeral_Suc
% 6.92/7.24 thf(fact_6216_le__Suc__numeral,axiom,
% 6.92/7.24 ! [N2: nat,K2: num] :
% 6.92/7.24 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K2 ) )
% 6.92/7.24 = ( ord_less_eq_nat @ N2 @ ( pred_numeral @ K2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % le_Suc_numeral
% 6.92/7.24 thf(fact_6217_divmod__algorithm__code_I2_J,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( unique5055182867167087721od_nat @ M @ one )
% 6.92/7.24 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_algorithm_code(2)
% 6.92/7.24 thf(fact_6218_divmod__algorithm__code_I2_J,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( unique5052692396658037445od_int @ M @ one )
% 6.92/7.24 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_algorithm_code(2)
% 6.92/7.24 thf(fact_6219_divmod__algorithm__code_I2_J,axiom,
% 6.92/7.24 ! [M: num] :
% 6.92/7.24 ( ( unique3479559517661332726nteger @ M @ one )
% 6.92/7.24 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_algorithm_code(2)
% 6.92/7.24 thf(fact_6220_divmod__algorithm__code_I3_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_algorithm_code(3)
% 6.92/7.24 thf(fact_6221_divmod__algorithm__code_I3_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_algorithm_code(3)
% 6.92/7.24 thf(fact_6222_divmod__algorithm__code_I3_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N2 ) )
% 6.92/7.24 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_algorithm_code(3)
% 6.92/7.24 thf(fact_6223_divmod__algorithm__code_I4_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_algorithm_code(4)
% 6.92/7.24 thf(fact_6224_divmod__algorithm__code_I4_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_algorithm_code(4)
% 6.92/7.24 thf(fact_6225_divmod__algorithm__code_I4_J,axiom,
% 6.92/7.24 ! [N2: num] :
% 6.92/7.24 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N2 ) )
% 6.92/7.24 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % divmod_algorithm_code(4)
% 6.92/7.24 thf(fact_6226_concat__bit__assoc,axiom,
% 6.92/7.24 ! [N2: nat,K2: int,M: nat,L: int,R2: int] :
% 6.92/7.24 ( ( bit_concat_bit @ N2 @ K2 @ ( bit_concat_bit @ M @ L @ R2 ) )
% 6.92/7.24 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N2 ) @ ( bit_concat_bit @ N2 @ K2 @ L ) @ R2 ) ) ).
% 6.92/7.24
% 6.92/7.24 % concat_bit_assoc
% 6.92/7.24 thf(fact_6227_binomial__eq__0,axiom,
% 6.92/7.24 ! [N2: nat,K2: nat] :
% 6.92/7.24 ( ( ord_less_nat @ N2 @ K2 )
% 6.92/7.24 => ( ( binomial @ N2 @ K2 )
% 6.92/7.24 = zero_zero_nat ) ) ).
% 6.92/7.24
% 6.92/7.24 % binomial_eq_0
% 6.92/7.24 thf(fact_6228_binomial__symmetric,axiom,
% 6.92/7.24 ! [K2: nat,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.24 => ( ( binomial @ N2 @ K2 )
% 6.92/7.24 = ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K2 ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % binomial_symmetric
% 6.92/7.24 thf(fact_6229_choose__mult__lemma,axiom,
% 6.92/7.24 ! [M: nat,R2: nat,K2: nat] :
% 6.92/7.24 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K2 ) @ ( plus_plus_nat @ M @ K2 ) ) @ ( binomial @ ( plus_plus_nat @ M @ K2 ) @ K2 ) )
% 6.92/7.24 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K2 ) @ K2 ) @ ( binomial @ ( plus_plus_nat @ M @ R2 ) @ M ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % choose_mult_lemma
% 6.92/7.24 thf(fact_6230_binomial__le__pow,axiom,
% 6.92/7.24 ! [R2: nat,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ R2 @ N2 )
% 6.92/7.24 => ( ord_less_eq_nat @ ( binomial @ N2 @ R2 ) @ ( power_power_nat @ N2 @ R2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % binomial_le_pow
% 6.92/7.24 thf(fact_6231_zero__less__binomial,axiom,
% 6.92/7.24 ! [K2: nat,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.24 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % zero_less_binomial
% 6.92/7.24 thf(fact_6232_Suc__times__binomial__add,axiom,
% 6.92/7.24 ! [A: nat,B: nat] :
% 6.92/7.24 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 6.92/7.24 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % Suc_times_binomial_add
% 6.92/7.24 thf(fact_6233_choose__mult,axiom,
% 6.92/7.24 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ K2 @ M )
% 6.92/7.24 => ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.24 => ( ( times_times_nat @ ( binomial @ N2 @ M ) @ ( binomial @ M @ K2 ) )
% 6.92/7.24 = ( times_times_nat @ ( binomial @ N2 @ K2 ) @ ( binomial @ ( minus_minus_nat @ N2 @ K2 ) @ ( minus_minus_nat @ M @ K2 ) ) ) ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % choose_mult
% 6.92/7.24 thf(fact_6234_binomial__fact__lemma,axiom,
% 6.92/7.24 ! [K2: nat,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.24 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K2 ) ) ) @ ( binomial @ N2 @ K2 ) )
% 6.92/7.24 = ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 6.92/7.24
% 6.92/7.24 % binomial_fact_lemma
% 6.92/7.24 thf(fact_6235_binomial__ge__n__over__k__pow__k,axiom,
% 6.92/7.24 ! [K2: nat,N2: nat] :
% 6.92/7.24 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.25 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri681578069525770553at_rat @ K2 ) ) @ K2 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % binomial_ge_n_over_k_pow_k
% 6.92/7.25 thf(fact_6236_choose__reduce__nat,axiom,
% 6.92/7.25 ! [N2: nat,K2: nat] :
% 6.92/7.25 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.25 => ( ( binomial @ N2 @ K2 )
% 6.92/7.25 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % choose_reduce_nat
% 6.92/7.25 thf(fact_6237_times__binomial__minus1__eq,axiom,
% 6.92/7.25 ! [K2: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.25 => ( ( times_times_nat @ K2 @ ( binomial @ N2 @ K2 ) )
% 6.92/7.25 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % times_binomial_minus1_eq
% 6.92/7.25 thf(fact_6238_binomial__le__pow2,axiom,
% 6.92/7.25 ! [N2: nat,K2: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % binomial_le_pow2
% 6.92/7.25 thf(fact_6239_binomial__altdef__nat,axiom,
% 6.92/7.25 ! [K2: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.25 => ( ( binomial @ N2 @ K2 )
% 6.92/7.25 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K2 ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % binomial_altdef_nat
% 6.92/7.25 thf(fact_6240_divmod__def,axiom,
% 6.92/7.25 ( unique3479559517661332726nteger
% 6.92/7.25 = ( ^ [M3: num,N: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_def
% 6.92/7.25 thf(fact_6241_divmod__def,axiom,
% 6.92/7.25 ( unique5055182867167087721od_nat
% 6.92/7.25 = ( ^ [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 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_def
% 6.92/7.25 thf(fact_6242_divmod__def,axiom,
% 6.92/7.25 ( unique5052692396658037445od_int
% 6.92/7.25 = ( ^ [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 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_def
% 6.92/7.25 thf(fact_6243_binomial__addition__formula,axiom,
% 6.92/7.25 ! [N2: nat,K2: nat] :
% 6.92/7.25 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 => ( ( binomial @ N2 @ ( suc @ K2 ) )
% 6.92/7.25 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( suc @ K2 ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % binomial_addition_formula
% 6.92/7.25 thf(fact_6244_fact__binomial,axiom,
% 6.92/7.25 ! [K2: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.25 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K2 ) ) )
% 6.92/7.25 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ K2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % fact_binomial
% 6.92/7.25 thf(fact_6245_binomial__fact,axiom,
% 6.92/7.25 ! [K2: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.25 => ( ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K2 ) )
% 6.92/7.25 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ K2 ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % binomial_fact
% 6.92/7.25 thf(fact_6246_divmod__divmod__step,axiom,
% 6.92/7.25 ( unique5055182867167087721od_nat
% 6.92/7.25 = ( ^ [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 ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_divmod_step
% 6.92/7.25 thf(fact_6247_divmod__divmod__step,axiom,
% 6.92/7.25 ( unique5052692396658037445od_int
% 6.92/7.25 = ( ^ [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 ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_divmod_step
% 6.92/7.25 thf(fact_6248_divmod__divmod__step,axiom,
% 6.92/7.25 ( unique3479559517661332726nteger
% 6.92/7.25 = ( ^ [M3: num,N: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M3 @ N ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M3 ) ) @ ( unique4921790084139445826nteger @ N @ ( unique3479559517661332726nteger @ M3 @ ( bit0 @ N ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_divmod_step
% 6.92/7.25 thf(fact_6249_take__bit__numeral__minus__bit1,axiom,
% 6.92/7.25 ! [L: num,K2: num] :
% 6.92/7.25 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 6.92/7.25 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K2 ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_numeral_minus_bit1
% 6.92/7.25 thf(fact_6250_even__succ__mod__exp,axiom,
% 6.92/7.25 ! [A: code_integer,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_mod_exp
% 6.92/7.25 thf(fact_6251_even__succ__mod__exp,axiom,
% 6.92/7.25 ! [A: nat,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_mod_exp
% 6.92/7.25 thf(fact_6252_even__succ__mod__exp,axiom,
% 6.92/7.25 ! [A: int,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_mod_exp
% 6.92/7.25 thf(fact_6253_even__succ__mod__exp,axiom,
% 6.92/7.25 ! [A: code_natural,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_mod_exp
% 6.92/7.25 thf(fact_6254_even__succ__div__exp,axiom,
% 6.92/7.25 ! [A: code_integer,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_div_exp
% 6.92/7.25 thf(fact_6255_even__succ__div__exp,axiom,
% 6.92/7.25 ! [A: nat,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_div_exp
% 6.92/7.25 thf(fact_6256_even__succ__div__exp,axiom,
% 6.92/7.25 ! [A: int,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_div_exp
% 6.92/7.25 thf(fact_6257_even__succ__div__exp,axiom,
% 6.92/7.25 ! [A: code_natural,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_div_exp
% 6.92/7.25 thf(fact_6258_divmod__algorithm__code_I6_J,axiom,
% 6.92/7.25 ! [M: num,N2: num] :
% 6.92/7.25 ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 6.92/7.25 = ( produc2626176000494625587at_nat
% 6.92/7.25 @ ^ [Q8: nat,R5: nat] : ( product_Pair_nat_nat @ Q8 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 6.92/7.25 @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_algorithm_code(6)
% 6.92/7.25 thf(fact_6259_divmod__algorithm__code_I6_J,axiom,
% 6.92/7.25 ! [M: num,N2: num] :
% 6.92/7.25 ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 6.92/7.25 = ( produc6916734918728496179nteger
% 6.92/7.25 @ ^ [Q8: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q8 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 6.92/7.25 @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_algorithm_code(6)
% 6.92/7.25 thf(fact_6260_divmod__algorithm__code_I6_J,axiom,
% 6.92/7.25 ! [M: num,N2: num] :
% 6.92/7.25 ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 6.92/7.25 = ( produc4245557441103728435nt_int
% 6.92/7.25 @ ^ [Q8: int,R5: int] : ( product_Pair_int_int @ Q8 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 6.92/7.25 @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_algorithm_code(6)
% 6.92/7.25 thf(fact_6261_mask__numeral,axiom,
% 6.92/7.25 ! [N2: num] :
% 6.92/7.25 ( ( bit_se943457434206027407atural @ ( numeral_numeral_nat @ N2 ) )
% 6.92/7.25 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se943457434206027407atural @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mask_numeral
% 6.92/7.25 thf(fact_6262_mask__numeral,axiom,
% 6.92/7.25 ! [N2: num] :
% 6.92/7.25 ( ( bit_se2119862282449309892nteger @ ( numeral_numeral_nat @ N2 ) )
% 6.92/7.25 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mask_numeral
% 6.92/7.25 thf(fact_6263_mask__numeral,axiom,
% 6.92/7.25 ! [N2: num] :
% 6.92/7.25 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N2 ) )
% 6.92/7.25 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mask_numeral
% 6.92/7.25 thf(fact_6264_mask__numeral,axiom,
% 6.92/7.25 ! [N2: num] :
% 6.92/7.25 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N2 ) )
% 6.92/7.25 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mask_numeral
% 6.92/7.25 thf(fact_6265_take__bit__rec,axiom,
% 6.92/7.25 ( bit_se1745604003318907178nteger
% 6.92/7.25 = ( ^ [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 ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_rec
% 6.92/7.25 thf(fact_6266_take__bit__rec,axiom,
% 6.92/7.25 ( bit_se569199155075624693atural
% 6.92/7.25 = ( ^ [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 ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_rec
% 6.92/7.25 thf(fact_6267_take__bit__rec,axiom,
% 6.92/7.25 ( bit_se2923211474154528505it_int
% 6.92/7.25 = ( ^ [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 ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_rec
% 6.92/7.25 thf(fact_6268_take__bit__rec,axiom,
% 6.92/7.25 ( bit_se2925701944663578781it_nat
% 6.92/7.25 = ( ^ [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 ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_rec
% 6.92/7.25 thf(fact_6269_nat__dvd__1__iff__1,axiom,
% 6.92/7.25 ! [M: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 6.92/7.25 = ( M = one_one_nat ) ) ).
% 6.92/7.25
% 6.92/7.25 % nat_dvd_1_iff_1
% 6.92/7.25 thf(fact_6270_dvd__add__triv__left__iff,axiom,
% 6.92/7.25 ! [A: rat,B: rat] :
% 6.92/7.25 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 6.92/7.25 = ( dvd_dvd_rat @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_triv_left_iff
% 6.92/7.25 thf(fact_6271_dvd__add__triv__left__iff,axiom,
% 6.92/7.25 ! [A: nat,B: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 6.92/7.25 = ( dvd_dvd_nat @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_triv_left_iff
% 6.92/7.25 thf(fact_6272_dvd__add__triv__left__iff,axiom,
% 6.92/7.25 ! [A: int,B: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 6.92/7.25 = ( dvd_dvd_int @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_triv_left_iff
% 6.92/7.25 thf(fact_6273_dvd__add__triv__right__iff,axiom,
% 6.92/7.25 ! [A: rat,B: rat] :
% 6.92/7.25 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 6.92/7.25 = ( dvd_dvd_rat @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_triv_right_iff
% 6.92/7.25 thf(fact_6274_dvd__add__triv__right__iff,axiom,
% 6.92/7.25 ! [A: nat,B: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 6.92/7.25 = ( dvd_dvd_nat @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_triv_right_iff
% 6.92/7.25 thf(fact_6275_dvd__add__triv__right__iff,axiom,
% 6.92/7.25 ! [A: int,B: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 6.92/7.25 = ( dvd_dvd_int @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_triv_right_iff
% 6.92/7.25 thf(fact_6276_dvd__1__left,axiom,
% 6.92/7.25 ! [K2: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K2 ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_1_left
% 6.92/7.25 thf(fact_6277_dvd__1__iff__1,axiom,
% 6.92/7.25 ! [M: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 6.92/7.25 = ( M
% 6.92/7.25 = ( suc @ zero_zero_nat ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_1_iff_1
% 6.92/7.25 thf(fact_6278_mask__nat__positive__iff,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 6.92/7.25 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % mask_nat_positive_iff
% 6.92/7.25 thf(fact_6279_case__prod__conv,axiom,
% 6.92/7.25 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 6.92/7.25 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 6.92/7.25 = ( F @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_conv
% 6.92/7.25 thf(fact_6280_case__prod__conv,axiom,
% 6.92/7.25 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 6.92/7.25 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 6.92/7.25 = ( F @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_conv
% 6.92/7.25 thf(fact_6281_case__prod__conv,axiom,
% 6.92/7.25 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 6.92/7.25 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 6.92/7.25 = ( F @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_conv
% 6.92/7.25 thf(fact_6282_case__prod__conv,axiom,
% 6.92/7.25 ! [F: int > int > $o,A: int,B: int] :
% 6.92/7.25 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 6.92/7.25 = ( F @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_conv
% 6.92/7.25 thf(fact_6283_case__prod__conv,axiom,
% 6.92/7.25 ! [F: int > int > int,A: int,B: int] :
% 6.92/7.25 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 6.92/7.25 = ( F @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_conv
% 6.92/7.25 thf(fact_6284_curry__case__prod,axiom,
% 6.92/7.25 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat] :
% 6.92/7.25 ( ( produc3610074571335452306at_nat @ ( produc27273713700761075at_nat @ F ) )
% 6.92/7.25 = F ) ).
% 6.92/7.25
% 6.92/7.25 % curry_case_prod
% 6.92/7.25 thf(fact_6285_curry__case__prod,axiom,
% 6.92/7.25 ! [F: nat > nat > product_prod_nat_nat > $o] :
% 6.92/7.25 ( ( produc3704529784387675049_nat_o @ ( produc8739625826339149834_nat_o @ F ) )
% 6.92/7.25 = F ) ).
% 6.92/7.25
% 6.92/7.25 % curry_case_prod
% 6.92/7.25 thf(fact_6286_curry__case__prod,axiom,
% 6.92/7.25 ! [F: int > int > product_prod_int_int] :
% 6.92/7.25 ( ( produc8249235968001453780nt_int @ ( produc4245557441103728435nt_int @ F ) )
% 6.92/7.25 = F ) ).
% 6.92/7.25
% 6.92/7.25 % curry_case_prod
% 6.92/7.25 thf(fact_6287_curry__case__prod,axiom,
% 6.92/7.25 ! [F: int > int > $o] :
% 6.92/7.25 ( ( produc175634133007206835_int_o @ ( produc4947309494688390418_int_o @ F ) )
% 6.92/7.25 = F ) ).
% 6.92/7.25
% 6.92/7.25 % curry_case_prod
% 6.92/7.25 thf(fact_6288_curry__case__prod,axiom,
% 6.92/7.25 ! [F: int > int > int] :
% 6.92/7.25 ( ( produc1016772743285680337nt_int @ ( produc8211389475949308722nt_int @ F ) )
% 6.92/7.25 = F ) ).
% 6.92/7.25
% 6.92/7.25 % curry_case_prod
% 6.92/7.25 thf(fact_6289_case__prod__curry,axiom,
% 6.92/7.25 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 6.92/7.25 ( ( produc27273713700761075at_nat @ ( produc3610074571335452306at_nat @ F ) )
% 6.92/7.25 = F ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_curry
% 6.92/7.25 thf(fact_6290_case__prod__curry,axiom,
% 6.92/7.25 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 6.92/7.25 ( ( produc8739625826339149834_nat_o @ ( produc3704529784387675049_nat_o @ F ) )
% 6.92/7.25 = F ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_curry
% 6.92/7.25 thf(fact_6291_case__prod__curry,axiom,
% 6.92/7.25 ! [F: product_prod_int_int > product_prod_int_int] :
% 6.92/7.25 ( ( produc4245557441103728435nt_int @ ( produc8249235968001453780nt_int @ F ) )
% 6.92/7.25 = F ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_curry
% 6.92/7.25 thf(fact_6292_case__prod__curry,axiom,
% 6.92/7.25 ! [F: product_prod_int_int > $o] :
% 6.92/7.25 ( ( produc4947309494688390418_int_o @ ( produc175634133007206835_int_o @ F ) )
% 6.92/7.25 = F ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_curry
% 6.92/7.25 thf(fact_6293_case__prod__curry,axiom,
% 6.92/7.25 ! [F: product_prod_int_int > int] :
% 6.92/7.25 ( ( produc8211389475949308722nt_int @ ( produc1016772743285680337nt_int @ F ) )
% 6.92/7.25 = F ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_curry
% 6.92/7.25 thf(fact_6294_dvd__add__times__triv__left__iff,axiom,
% 6.92/7.25 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.25 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C2 @ A ) @ B ) )
% 6.92/7.25 = ( dvd_dvd_rat @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_times_triv_left_iff
% 6.92/7.25 thf(fact_6295_dvd__add__times__triv__left__iff,axiom,
% 6.92/7.25 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C2 @ A ) @ B ) )
% 6.92/7.25 = ( dvd_dvd_nat @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_times_triv_left_iff
% 6.92/7.25 thf(fact_6296_dvd__add__times__triv__left__iff,axiom,
% 6.92/7.25 ! [A: int,C2: int,B: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C2 @ A ) @ B ) )
% 6.92/7.25 = ( dvd_dvd_int @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_times_triv_left_iff
% 6.92/7.25 thf(fact_6297_dvd__add__times__triv__right__iff,axiom,
% 6.92/7.25 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.25 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C2 @ A ) ) )
% 6.92/7.25 = ( dvd_dvd_rat @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_times_triv_right_iff
% 6.92/7.25 thf(fact_6298_dvd__add__times__triv__right__iff,axiom,
% 6.92/7.25 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C2 @ A ) ) )
% 6.92/7.25 = ( dvd_dvd_nat @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_times_triv_right_iff
% 6.92/7.25 thf(fact_6299_dvd__add__times__triv__right__iff,axiom,
% 6.92/7.25 ! [A: int,B: int,C2: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C2 @ A ) ) )
% 6.92/7.25 = ( dvd_dvd_int @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_times_triv_right_iff
% 6.92/7.25 thf(fact_6300_div__add,axiom,
% 6.92/7.25 ! [C2: nat,A: nat,B: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ C2 @ A )
% 6.92/7.25 => ( ( dvd_dvd_nat @ C2 @ B )
% 6.92/7.25 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 6.92/7.25 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C2 ) @ ( divide_divide_nat @ B @ C2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % div_add
% 6.92/7.25 thf(fact_6301_div__add,axiom,
% 6.92/7.25 ! [C2: int,A: int,B: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ C2 @ A )
% 6.92/7.25 => ( ( dvd_dvd_int @ C2 @ B )
% 6.92/7.25 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 6.92/7.25 = ( plus_plus_int @ ( divide_divide_int @ A @ C2 ) @ ( divide_divide_int @ B @ C2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % div_add
% 6.92/7.25 thf(fact_6302_div__add,axiom,
% 6.92/7.25 ! [C2: code_natural,A: code_natural,B: code_natural] :
% 6.92/7.25 ( ( dvd_dvd_Code_natural @ C2 @ A )
% 6.92/7.25 => ( ( dvd_dvd_Code_natural @ C2 @ B )
% 6.92/7.25 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C2 )
% 6.92/7.25 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ C2 ) @ ( divide5121882707175180666atural @ B @ C2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % div_add
% 6.92/7.25 thf(fact_6303_pow__divides__pow__iff,axiom,
% 6.92/7.25 ! [N2: nat,A: nat,B: nat] :
% 6.92/7.25 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 6.92/7.25 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % pow_divides_pow_iff
% 6.92/7.25 thf(fact_6304_pow__divides__pow__iff,axiom,
% 6.92/7.25 ! [N2: nat,A: int,B: int] :
% 6.92/7.25 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 6.92/7.25 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % pow_divides_pow_iff
% 6.92/7.25 thf(fact_6305_odd__add,axiom,
% 6.92/7.25 ! [A: nat,B: nat] :
% 6.92/7.25 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 6.92/7.25 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 6.92/7.25 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_add
% 6.92/7.25 thf(fact_6306_odd__add,axiom,
% 6.92/7.25 ! [A: int,B: int] :
% 6.92/7.25 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 6.92/7.25 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 6.92/7.25 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_add
% 6.92/7.25 thf(fact_6307_odd__add,axiom,
% 6.92/7.25 ! [A: code_natural,B: code_natural] :
% 6.92/7.25 ( ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_p4538020629002901425atural @ A @ B ) ) )
% 6.92/7.25 = ( ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) )
% 6.92/7.25 != ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_add
% 6.92/7.25 thf(fact_6308_odd__add,axiom,
% 6.92/7.25 ! [A: code_integer,B: code_integer] :
% 6.92/7.25 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 6.92/7.25 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 6.92/7.25 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_add
% 6.92/7.25 thf(fact_6309_even__add,axiom,
% 6.92/7.25 ! [A: nat,B: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 6.92/7.25 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_add
% 6.92/7.25 thf(fact_6310_even__add,axiom,
% 6.92/7.25 ! [A: int,B: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 6.92/7.25 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_add
% 6.92/7.25 thf(fact_6311_even__add,axiom,
% 6.92/7.25 ! [A: code_natural,B: code_natural] :
% 6.92/7.25 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_p4538020629002901425atural @ A @ B ) )
% 6.92/7.25 = ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 = ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_add
% 6.92/7.25 thf(fact_6312_even__add,axiom,
% 6.92/7.25 ! [A: code_integer,B: code_integer] :
% 6.92/7.25 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 6.92/7.25 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_add
% 6.92/7.25 thf(fact_6313_even__plus__one__iff,axiom,
% 6.92/7.25 ! [A: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 6.92/7.25 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_plus_one_iff
% 6.92/7.25 thf(fact_6314_even__plus__one__iff,axiom,
% 6.92/7.25 ! [A: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 6.92/7.25 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_plus_one_iff
% 6.92/7.25 thf(fact_6315_even__plus__one__iff,axiom,
% 6.92/7.25 ! [A: code_natural] :
% 6.92/7.25 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) )
% 6.92/7.25 = ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_plus_one_iff
% 6.92/7.25 thf(fact_6316_even__plus__one__iff,axiom,
% 6.92/7.25 ! [A: code_integer] :
% 6.92/7.25 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 6.92/7.25 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_plus_one_iff
% 6.92/7.25 thf(fact_6317_even__diff,axiom,
% 6.92/7.25 ! [A: int,B: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 6.92/7.25 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_diff
% 6.92/7.25 thf(fact_6318_even__diff,axiom,
% 6.92/7.25 ! [A: code_integer,B: code_integer] :
% 6.92/7.25 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 6.92/7.25 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_diff
% 6.92/7.25 thf(fact_6319_zero__le__power__eq__numeral,axiom,
% 6.92/7.25 ! [A: code_integer,W2: num] :
% 6.92/7.25 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 6.92/7.25 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_le_power_eq_numeral
% 6.92/7.25 thf(fact_6320_zero__le__power__eq__numeral,axiom,
% 6.92/7.25 ! [A: rat,W2: num] :
% 6.92/7.25 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 6.92/7.25 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_le_power_eq_numeral
% 6.92/7.25 thf(fact_6321_zero__le__power__eq__numeral,axiom,
% 6.92/7.25 ! [A: int,W2: num] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 6.92/7.25 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_le_power_eq_numeral
% 6.92/7.25 thf(fact_6322_power__less__zero__eq__numeral,axiom,
% 6.92/7.25 ! [A: code_integer,W2: num] :
% 6.92/7.25 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_z3403309356797280102nteger )
% 6.92/7.25 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_less_zero_eq_numeral
% 6.92/7.25 thf(fact_6323_power__less__zero__eq__numeral,axiom,
% 6.92/7.25 ! [A: rat,W2: num] :
% 6.92/7.25 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 6.92/7.25 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_less_zero_eq_numeral
% 6.92/7.25 thf(fact_6324_power__less__zero__eq__numeral,axiom,
% 6.92/7.25 ! [A: int,W2: num] :
% 6.92/7.25 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 6.92/7.25 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_less_zero_eq_numeral
% 6.92/7.25 thf(fact_6325_power__less__zero__eq,axiom,
% 6.92/7.25 ! [A: code_integer,N2: nat] :
% 6.92/7.25 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ zero_z3403309356797280102nteger )
% 6.92/7.25 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_less_zero_eq
% 6.92/7.25 thf(fact_6326_power__less__zero__eq,axiom,
% 6.92/7.25 ! [A: rat,N2: nat] :
% 6.92/7.25 ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 6.92/7.25 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_less_zero_eq
% 6.92/7.25 thf(fact_6327_power__less__zero__eq,axiom,
% 6.92/7.25 ! [A: int,N2: nat] :
% 6.92/7.25 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 6.92/7.25 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_less_zero_eq
% 6.92/7.25 thf(fact_6328_even__diff__nat,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) )
% 6.92/7.25 = ( ( ord_less_nat @ M @ N2 )
% 6.92/7.25 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_diff_nat
% 6.92/7.25 thf(fact_6329_odd__succ__div__two,axiom,
% 6.92/7.25 ! [A: code_integer] :
% 6.92/7.25 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_succ_div_two
% 6.92/7.25 thf(fact_6330_odd__succ__div__two,axiom,
% 6.92/7.25 ! [A: nat] :
% 6.92/7.25 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_succ_div_two
% 6.92/7.25 thf(fact_6331_odd__succ__div__two,axiom,
% 6.92/7.25 ! [A: int] :
% 6.92/7.25 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_succ_div_two
% 6.92/7.25 thf(fact_6332_odd__succ__div__two,axiom,
% 6.92/7.25 ! [A: code_natural] :
% 6.92/7.25 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_succ_div_two
% 6.92/7.25 thf(fact_6333_even__succ__div__two,axiom,
% 6.92/7.25 ! [A: code_integer] :
% 6.92/7.25 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_div_two
% 6.92/7.25 thf(fact_6334_even__succ__div__two,axiom,
% 6.92/7.25 ! [A: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_div_two
% 6.92/7.25 thf(fact_6335_even__succ__div__two,axiom,
% 6.92/7.25 ! [A: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_div_two
% 6.92/7.25 thf(fact_6336_even__succ__div__two,axiom,
% 6.92/7.25 ! [A: code_natural] :
% 6.92/7.25 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_div_two
% 6.92/7.25 thf(fact_6337_even__succ__div__2,axiom,
% 6.92/7.25 ! [A: code_integer] :
% 6.92/7.25 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_div_2
% 6.92/7.25 thf(fact_6338_even__succ__div__2,axiom,
% 6.92/7.25 ! [A: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_div_2
% 6.92/7.25 thf(fact_6339_even__succ__div__2,axiom,
% 6.92/7.25 ! [A: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_div_2
% 6.92/7.25 thf(fact_6340_even__succ__div__2,axiom,
% 6.92/7.25 ! [A: code_natural] :
% 6.92/7.25 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_succ_div_2
% 6.92/7.25 thf(fact_6341_zero__less__power__eq__numeral,axiom,
% 6.92/7.25 ! [A: code_integer,W2: num] :
% 6.92/7.25 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 6.92/7.25 = ( ( ( numeral_numeral_nat @ W2 )
% 6.92/7.25 = zero_zero_nat )
% 6.92/7.25 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( A != zero_z3403309356797280102nteger ) )
% 6.92/7.25 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_less_power_eq_numeral
% 6.92/7.25 thf(fact_6342_zero__less__power__eq__numeral,axiom,
% 6.92/7.25 ! [A: rat,W2: num] :
% 6.92/7.25 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 6.92/7.25 = ( ( ( numeral_numeral_nat @ W2 )
% 6.92/7.25 = zero_zero_nat )
% 6.92/7.25 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( A != zero_zero_rat ) )
% 6.92/7.25 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_less_power_eq_numeral
% 6.92/7.25 thf(fact_6343_zero__less__power__eq__numeral,axiom,
% 6.92/7.25 ! [A: int,W2: num] :
% 6.92/7.25 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 6.92/7.25 = ( ( ( numeral_numeral_nat @ W2 )
% 6.92/7.25 = zero_zero_nat )
% 6.92/7.25 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( A != zero_zero_int ) )
% 6.92/7.25 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_less_power_eq_numeral
% 6.92/7.25 thf(fact_6344_even__power,axiom,
% 6.92/7.25 ! [A: nat,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N2 ) )
% 6.92/7.25 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_power
% 6.92/7.25 thf(fact_6345_even__power,axiom,
% 6.92/7.25 ! [A: int,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N2 ) )
% 6.92/7.25 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_power
% 6.92/7.25 thf(fact_6346_even__power,axiom,
% 6.92/7.25 ! [A: code_natural,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( power_7079662738309270450atural @ A @ N2 ) )
% 6.92/7.25 = ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_power
% 6.92/7.25 thf(fact_6347_even__power,axiom,
% 6.92/7.25 ! [A: code_integer,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 6.92/7.25 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_power
% 6.92/7.25 thf(fact_6348_divmod__algorithm__code_I5_J,axiom,
% 6.92/7.25 ! [M: num,N2: num] :
% 6.92/7.25 ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 6.92/7.25 = ( produc2626176000494625587at_nat
% 6.92/7.25 @ ^ [Q8: nat,R5: nat] : ( product_Pair_nat_nat @ Q8 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 6.92/7.25 @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_algorithm_code(5)
% 6.92/7.25 thf(fact_6349_divmod__algorithm__code_I5_J,axiom,
% 6.92/7.25 ! [M: num,N2: num] :
% 6.92/7.25 ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 6.92/7.25 = ( produc6916734918728496179nteger
% 6.92/7.25 @ ^ [Q8: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q8 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) )
% 6.92/7.25 @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_algorithm_code(5)
% 6.92/7.25 thf(fact_6350_divmod__algorithm__code_I5_J,axiom,
% 6.92/7.25 ! [M: num,N2: num] :
% 6.92/7.25 ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 6.92/7.25 = ( produc4245557441103728435nt_int
% 6.92/7.25 @ ^ [Q8: int,R5: int] : ( product_Pair_int_int @ Q8 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 6.92/7.25 @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_algorithm_code(5)
% 6.92/7.25 thf(fact_6351_odd__two__times__div__two__succ,axiom,
% 6.92/7.25 ! [A: code_integer] :
% 6.92/7.25 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 6.92/7.25 = A ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_two_times_div_two_succ
% 6.92/7.25 thf(fact_6352_odd__two__times__div__two__succ,axiom,
% 6.92/7.25 ! [A: nat] :
% 6.92/7.25 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 6.92/7.25 = A ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_two_times_div_two_succ
% 6.92/7.25 thf(fact_6353_odd__two__times__div__two__succ,axiom,
% 6.92/7.25 ! [A: int] :
% 6.92/7.25 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 6.92/7.25 = A ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_two_times_div_two_succ
% 6.92/7.25 thf(fact_6354_odd__two__times__div__two__succ,axiom,
% 6.92/7.25 ! [A: code_natural] :
% 6.92/7.25 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ one_one_Code_natural )
% 6.92/7.25 = A ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_two_times_div_two_succ
% 6.92/7.25 thf(fact_6355_power__le__zero__eq__numeral,axiom,
% 6.92/7.25 ! [A: code_integer,W2: num] :
% 6.92/7.25 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_z3403309356797280102nteger )
% 6.92/7.25 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 6.92/7.25 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( A = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_le_zero_eq_numeral
% 6.92/7.25 thf(fact_6356_power__le__zero__eq__numeral,axiom,
% 6.92/7.25 ! [A: rat,W2: num] :
% 6.92/7.25 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 6.92/7.25 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 6.92/7.25 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( A = zero_zero_rat ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_le_zero_eq_numeral
% 6.92/7.25 thf(fact_6357_power__le__zero__eq__numeral,axiom,
% 6.92/7.25 ! [A: int,W2: num] :
% 6.92/7.25 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 6.92/7.25 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 6.92/7.25 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 6.92/7.25 & ( A = zero_zero_int ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_le_zero_eq_numeral
% 6.92/7.25 thf(fact_6358_case__prod__app,axiom,
% 6.92/7.25 ( produc27273713700761075at_nat
% 6.92/7.25 = ( ^ [F3: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X4: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 6.92/7.25 ( produc2626176000494625587at_nat
% 6.92/7.25 @ ^ [L2: nat,R5: nat] : ( F3 @ L2 @ R5 @ Y4 )
% 6.92/7.25 @ X4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_app
% 6.92/7.25 thf(fact_6359_case__prod__app,axiom,
% 6.92/7.25 ( produc8739625826339149834_nat_o
% 6.92/7.25 = ( ^ [F3: nat > nat > product_prod_nat_nat > $o,X4: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 6.92/7.25 ( produc6081775807080527818_nat_o
% 6.92/7.25 @ ^ [L2: nat,R5: nat] : ( F3 @ L2 @ R5 @ Y4 )
% 6.92/7.25 @ X4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_app
% 6.92/7.25 thf(fact_6360_nested__case__prod__simp,axiom,
% 6.92/7.25 ( produc27273713700761075at_nat
% 6.92/7.25 = ( ^ [F3: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X4: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 6.92/7.25 ( produc2626176000494625587at_nat
% 6.92/7.25 @ ^ [A5: nat,B4: nat] : ( F3 @ A5 @ B4 @ Y4 )
% 6.92/7.25 @ X4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % nested_case_prod_simp
% 6.92/7.25 thf(fact_6361_nested__case__prod__simp,axiom,
% 6.92/7.25 ( produc8739625826339149834_nat_o
% 6.92/7.25 = ( ^ [F3: nat > nat > product_prod_nat_nat > $o,X4: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 6.92/7.25 ( produc6081775807080527818_nat_o
% 6.92/7.25 @ ^ [A5: nat,B4: nat] : ( F3 @ A5 @ B4 @ Y4 )
% 6.92/7.25 @ X4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % nested_case_prod_simp
% 6.92/7.25 thf(fact_6362_prod_Ocase__distrib,axiom,
% 6.92/7.25 ! [H: $o > $o,F: int > int > $o,Prod: product_prod_int_int] :
% 6.92/7.25 ( ( H @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 6.92/7.25 = ( produc4947309494688390418_int_o
% 6.92/7.25 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 6.92/7.25 @ Prod ) ) ).
% 6.92/7.25
% 6.92/7.25 % prod.case_distrib
% 6.92/7.25 thf(fact_6363_prod_Ocase__distrib,axiom,
% 6.92/7.25 ! [H: $o > int,F: int > int > $o,Prod: product_prod_int_int] :
% 6.92/7.25 ( ( H @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 6.92/7.25 = ( produc8211389475949308722nt_int
% 6.92/7.25 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 6.92/7.25 @ Prod ) ) ).
% 6.92/7.25
% 6.92/7.25 % prod.case_distrib
% 6.92/7.25 thf(fact_6364_prod_Ocase__distrib,axiom,
% 6.92/7.25 ! [H: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 6.92/7.25 ( ( H @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 6.92/7.25 = ( produc4947309494688390418_int_o
% 6.92/7.25 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 6.92/7.25 @ Prod ) ) ).
% 6.92/7.25
% 6.92/7.25 % prod.case_distrib
% 6.92/7.25 thf(fact_6365_prod_Ocase__distrib,axiom,
% 6.92/7.25 ! [H: int > int,F: int > int > int,Prod: product_prod_int_int] :
% 6.92/7.25 ( ( H @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 6.92/7.25 = ( produc8211389475949308722nt_int
% 6.92/7.25 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 6.92/7.25 @ Prod ) ) ).
% 6.92/7.25
% 6.92/7.25 % prod.case_distrib
% 6.92/7.25 thf(fact_6366_prod_Ocase__distrib,axiom,
% 6.92/7.25 ! [H: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 6.92/7.25 ( ( H @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 6.92/7.25 = ( produc4947309494688390418_int_o
% 6.92/7.25 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 6.92/7.25 @ Prod ) ) ).
% 6.92/7.25
% 6.92/7.25 % prod.case_distrib
% 6.92/7.25 thf(fact_6367_prod_Ocase__distrib,axiom,
% 6.92/7.25 ! [H: product_prod_int_int > int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 6.92/7.25 ( ( H @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 6.92/7.25 = ( produc8211389475949308722nt_int
% 6.92/7.25 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 6.92/7.25 @ Prod ) ) ).
% 6.92/7.25
% 6.92/7.25 % prod.case_distrib
% 6.92/7.25 thf(fact_6368_prod_Ocase__distrib,axiom,
% 6.92/7.25 ! [H: $o > product_prod_int_int,F: int > int > $o,Prod: product_prod_int_int] :
% 6.92/7.25 ( ( H @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 6.92/7.25 = ( produc4245557441103728435nt_int
% 6.92/7.25 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 6.92/7.25 @ Prod ) ) ).
% 6.92/7.25
% 6.92/7.25 % prod.case_distrib
% 6.92/7.25 thf(fact_6369_prod_Ocase__distrib,axiom,
% 6.92/7.25 ! [H: int > product_prod_int_int,F: int > int > int,Prod: product_prod_int_int] :
% 6.92/7.25 ( ( H @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 6.92/7.25 = ( produc4245557441103728435nt_int
% 6.92/7.25 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 6.92/7.25 @ Prod ) ) ).
% 6.92/7.25
% 6.92/7.25 % prod.case_distrib
% 6.92/7.25 thf(fact_6370_prod_Ocase__distrib,axiom,
% 6.92/7.25 ! [H: product_prod_int_int > product_prod_int_int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 6.92/7.25 ( ( H @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 6.92/7.25 = ( produc4245557441103728435nt_int
% 6.92/7.25 @ ^ [X12: int,X23: int] : ( H @ ( F @ X12 @ X23 ) )
% 6.92/7.25 @ Prod ) ) ).
% 6.92/7.25
% 6.92/7.25 % prod.case_distrib
% 6.92/7.25 thf(fact_6371_prod_Ocase__distrib,axiom,
% 6.92/7.25 ! [H: ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 6.92/7.25 ( ( H @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 6.92/7.25 = ( produc8739625826339149834_nat_o
% 6.92/7.25 @ ^ [X12: nat,X23: nat] : ( H @ ( F @ X12 @ X23 ) )
% 6.92/7.25 @ Prod ) ) ).
% 6.92/7.25
% 6.92/7.25 % prod.case_distrib
% 6.92/7.25 thf(fact_6372_take__bit__add,axiom,
% 6.92/7.25 ! [N2: nat,A: int,B: int] :
% 6.92/7.25 ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) )
% 6.92/7.25 = ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ A @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_add
% 6.92/7.25 thf(fact_6373_take__bit__add,axiom,
% 6.92/7.25 ! [N2: nat,A: nat,B: nat] :
% 6.92/7.25 ( ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) )
% 6.92/7.25 = ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ A @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_add
% 6.92/7.25 thf(fact_6374_take__bit__tightened,axiom,
% 6.92/7.25 ! [N2: nat,A: int,B: int,M: nat] :
% 6.92/7.25 ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 6.92/7.25 = ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 6.92/7.25 => ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.25 => ( ( bit_se2923211474154528505it_int @ M @ A )
% 6.92/7.25 = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_tightened
% 6.92/7.25 thf(fact_6375_take__bit__tightened,axiom,
% 6.92/7.25 ! [N2: nat,A: nat,B: nat,M: nat] :
% 6.92/7.25 ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 6.92/7.25 = ( bit_se2925701944663578781it_nat @ N2 @ B ) )
% 6.92/7.25 => ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.25 => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 6.92/7.25 = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_tightened
% 6.92/7.25 thf(fact_6376_take__bit__tightened__less__eq__nat,axiom,
% 6.92/7.25 ! [M: nat,N2: nat,Q6: nat] :
% 6.92/7.25 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.25 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q6 ) @ ( bit_se2925701944663578781it_nat @ N2 @ Q6 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_tightened_less_eq_nat
% 6.92/7.25 thf(fact_6377_take__bit__nat__less__eq__self,axiom,
% 6.92/7.25 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_nat_less_eq_self
% 6.92/7.25 thf(fact_6378_dvd__add,axiom,
% 6.92/7.25 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.25 ( ( dvd_dvd_rat @ A @ B )
% 6.92/7.25 => ( ( dvd_dvd_rat @ A @ C2 )
% 6.92/7.25 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add
% 6.92/7.25 thf(fact_6379_dvd__add,axiom,
% 6.92/7.25 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ A @ B )
% 6.92/7.25 => ( ( dvd_dvd_nat @ A @ C2 )
% 6.92/7.25 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add
% 6.92/7.25 thf(fact_6380_dvd__add,axiom,
% 6.92/7.25 ! [A: int,B: int,C2: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ A @ B )
% 6.92/7.25 => ( ( dvd_dvd_int @ A @ C2 )
% 6.92/7.25 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add
% 6.92/7.25 thf(fact_6381_dvd__add__left__iff,axiom,
% 6.92/7.25 ! [A: rat,C2: rat,B: rat] :
% 6.92/7.25 ( ( dvd_dvd_rat @ A @ C2 )
% 6.92/7.25 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 6.92/7.25 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_left_iff
% 6.92/7.25 thf(fact_6382_dvd__add__left__iff,axiom,
% 6.92/7.25 ! [A: nat,C2: nat,B: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ A @ C2 )
% 6.92/7.25 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C2 ) )
% 6.92/7.25 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_left_iff
% 6.92/7.25 thf(fact_6383_dvd__add__left__iff,axiom,
% 6.92/7.25 ! [A: int,C2: int,B: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ A @ C2 )
% 6.92/7.25 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 6.92/7.25 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_left_iff
% 6.92/7.25 thf(fact_6384_dvd__add__right__iff,axiom,
% 6.92/7.25 ! [A: rat,B: rat,C2: rat] :
% 6.92/7.25 ( ( dvd_dvd_rat @ A @ B )
% 6.92/7.25 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 6.92/7.25 = ( dvd_dvd_rat @ A @ C2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_right_iff
% 6.92/7.25 thf(fact_6385_dvd__add__right__iff,axiom,
% 6.92/7.25 ! [A: nat,B: nat,C2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ A @ B )
% 6.92/7.25 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C2 ) )
% 6.92/7.25 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_right_iff
% 6.92/7.25 thf(fact_6386_dvd__add__right__iff,axiom,
% 6.92/7.25 ! [A: int,B: int,C2: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ A @ B )
% 6.92/7.25 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 6.92/7.25 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_add_right_iff
% 6.92/7.25 thf(fact_6387_old_Oprod_Ocase,axiom,
% 6.92/7.25 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X2: nat] :
% 6.92/7.25 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X2 ) )
% 6.92/7.25 = ( F @ X1 @ X2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % old.prod.case
% 6.92/7.25 thf(fact_6388_old_Oprod_Ocase,axiom,
% 6.92/7.25 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X2: nat] :
% 6.92/7.25 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X2 ) )
% 6.92/7.25 = ( F @ X1 @ X2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % old.prod.case
% 6.92/7.25 thf(fact_6389_old_Oprod_Ocase,axiom,
% 6.92/7.25 ! [F: int > int > product_prod_int_int,X1: int,X2: int] :
% 6.92/7.25 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X2 ) )
% 6.92/7.25 = ( F @ X1 @ X2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % old.prod.case
% 6.92/7.25 thf(fact_6390_old_Oprod_Ocase,axiom,
% 6.92/7.25 ! [F: int > int > $o,X1: int,X2: int] :
% 6.92/7.25 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ X1 @ X2 ) )
% 6.92/7.25 = ( F @ X1 @ X2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % old.prod.case
% 6.92/7.25 thf(fact_6391_old_Oprod_Ocase,axiom,
% 6.92/7.25 ! [F: int > int > int,X1: int,X2: int] :
% 6.92/7.25 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X2 ) )
% 6.92/7.25 = ( F @ X1 @ X2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % old.prod.case
% 6.92/7.25 thf(fact_6392_split__cong,axiom,
% 6.92/7.25 ! [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] :
% 6.92/7.25 ( ! [X3: nat,Y3: nat] :
% 6.92/7.25 ( ( ( product_Pair_nat_nat @ X3 @ Y3 )
% 6.92/7.25 = Q6 )
% 6.92/7.25 => ( ( F @ X3 @ Y3 )
% 6.92/7.25 = ( G @ X3 @ Y3 ) ) )
% 6.92/7.25 => ( ( P3 = Q6 )
% 6.92/7.25 => ( ( produc27273713700761075at_nat @ F @ P3 )
% 6.92/7.25 = ( produc27273713700761075at_nat @ G @ Q6 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % split_cong
% 6.92/7.25 thf(fact_6393_split__cong,axiom,
% 6.92/7.25 ! [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] :
% 6.92/7.25 ( ! [X3: nat,Y3: nat] :
% 6.92/7.25 ( ( ( product_Pair_nat_nat @ X3 @ Y3 )
% 6.92/7.25 = Q6 )
% 6.92/7.25 => ( ( F @ X3 @ Y3 )
% 6.92/7.25 = ( G @ X3 @ Y3 ) ) )
% 6.92/7.25 => ( ( P3 = Q6 )
% 6.92/7.25 => ( ( produc8739625826339149834_nat_o @ F @ P3 )
% 6.92/7.25 = ( produc8739625826339149834_nat_o @ G @ Q6 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % split_cong
% 6.92/7.25 thf(fact_6394_split__cong,axiom,
% 6.92/7.25 ! [Q6: product_prod_int_int,F: int > int > product_prod_int_int,G: int > int > product_prod_int_int,P3: product_prod_int_int] :
% 6.92/7.25 ( ! [X3: int,Y3: int] :
% 6.92/7.25 ( ( ( product_Pair_int_int @ X3 @ Y3 )
% 6.92/7.25 = Q6 )
% 6.92/7.25 => ( ( F @ X3 @ Y3 )
% 6.92/7.25 = ( G @ X3 @ Y3 ) ) )
% 6.92/7.25 => ( ( P3 = Q6 )
% 6.92/7.25 => ( ( produc4245557441103728435nt_int @ F @ P3 )
% 6.92/7.25 = ( produc4245557441103728435nt_int @ G @ Q6 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % split_cong
% 6.92/7.25 thf(fact_6395_split__cong,axiom,
% 6.92/7.25 ! [Q6: product_prod_int_int,F: int > int > $o,G: int > int > $o,P3: product_prod_int_int] :
% 6.92/7.25 ( ! [X3: int,Y3: int] :
% 6.92/7.25 ( ( ( product_Pair_int_int @ X3 @ Y3 )
% 6.92/7.25 = Q6 )
% 6.92/7.25 => ( ( F @ X3 @ Y3 )
% 6.92/7.25 = ( G @ X3 @ Y3 ) ) )
% 6.92/7.25 => ( ( P3 = Q6 )
% 6.92/7.25 => ( ( produc4947309494688390418_int_o @ F @ P3 )
% 6.92/7.25 = ( produc4947309494688390418_int_o @ G @ Q6 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % split_cong
% 6.92/7.25 thf(fact_6396_split__cong,axiom,
% 6.92/7.25 ! [Q6: product_prod_int_int,F: int > int > int,G: int > int > int,P3: product_prod_int_int] :
% 6.92/7.25 ( ! [X3: int,Y3: int] :
% 6.92/7.25 ( ( ( product_Pair_int_int @ X3 @ Y3 )
% 6.92/7.25 = Q6 )
% 6.92/7.25 => ( ( F @ X3 @ Y3 )
% 6.92/7.25 = ( G @ X3 @ Y3 ) ) )
% 6.92/7.25 => ( ( P3 = Q6 )
% 6.92/7.25 => ( ( produc8211389475949308722nt_int @ F @ P3 )
% 6.92/7.25 = ( produc8211389475949308722nt_int @ G @ Q6 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % split_cong
% 6.92/7.25 thf(fact_6397_dvd__diff__nat,axiom,
% 6.92/7.25 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ K2 @ M )
% 6.92/7.25 => ( ( dvd_dvd_nat @ K2 @ N2 )
% 6.92/7.25 => ( dvd_dvd_nat @ K2 @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_diff_nat
% 6.92/7.25 thf(fact_6398_uminus__dvd__conv_I1_J,axiom,
% 6.92/7.25 ( dvd_dvd_int
% 6.92/7.25 = ( ^ [D5: int] : ( dvd_dvd_int @ ( uminus_uminus_int @ D5 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % uminus_dvd_conv(1)
% 6.92/7.25 thf(fact_6399_uminus__dvd__conv_I2_J,axiom,
% 6.92/7.25 ( dvd_dvd_int
% 6.92/7.25 = ( ^ [D5: int,T4: int] : ( dvd_dvd_int @ D5 @ ( uminus_uminus_int @ T4 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % uminus_dvd_conv(2)
% 6.92/7.25 thf(fact_6400_less__eq__mask,axiom,
% 6.92/7.25 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % less_eq_mask
% 6.92/7.25 thf(fact_6401_case__prod__Pair__iden,axiom,
% 6.92/7.25 ! [P3: produc3925858234332021118et_nat] :
% 6.92/7.25 ( ( produc4058941399401191971et_nat @ produc5001842942810119800et_nat @ P3 )
% 6.92/7.25 = P3 ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_Pair_iden
% 6.92/7.25 thf(fact_6402_case__prod__Pair__iden,axiom,
% 6.92/7.25 ! [P3: produc2732055786443039994et_nat] :
% 6.92/7.25 ( ( produc2377985495875741467et_nat @ produc2245416461498447860et_nat @ P3 )
% 6.92/7.25 = P3 ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_Pair_iden
% 6.92/7.25 thf(fact_6403_case__prod__Pair__iden,axiom,
% 6.92/7.25 ! [P3: produc7388388658123137530it_nat] :
% 6.92/7.25 ( ( produc7293086598567236123it_nat @ produc4082563078715348724it_nat @ P3 )
% 6.92/7.25 = P3 ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_Pair_iden
% 6.92/7.25 thf(fact_6404_case__prod__Pair__iden,axiom,
% 6.92/7.25 ! [P3: produc3260487557148687353it_nat] :
% 6.92/7.25 ( ( produc2183267410226956569it_nat @ produc9178034014595674355it_nat @ P3 )
% 6.92/7.25 = P3 ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_Pair_iden
% 6.92/7.25 thf(fact_6405_case__prod__Pair__iden,axiom,
% 6.92/7.25 ! [P3: product_prod_int_int] :
% 6.92/7.25 ( ( produc4245557441103728435nt_int @ product_Pair_int_int @ P3 )
% 6.92/7.25 = P3 ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_Pair_iden
% 6.92/7.25 thf(fact_6406_nat__take__bit__eq,axiom,
% 6.92/7.25 ! [K2: int,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.25 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) )
% 6.92/7.25 = ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % nat_take_bit_eq
% 6.92/7.25 thf(fact_6407_take__bit__nat__eq,axiom,
% 6.92/7.25 ! [K2: int,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.25 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K2 ) )
% 6.92/7.25 = ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_nat_eq
% 6.92/7.25 thf(fact_6408_case__prodE2,axiom,
% 6.92/7.25 ! [Q2: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z3: product_prod_nat_nat] :
% 6.92/7.25 ( ( Q2 @ ( produc27273713700761075at_nat @ P2 @ Z3 ) )
% 6.92/7.25 => ~ ! [X3: nat,Y3: nat] :
% 6.92/7.25 ( ( Z3
% 6.92/7.25 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( Q2 @ ( P2 @ X3 @ Y3 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodE2
% 6.92/7.25 thf(fact_6409_case__prodE2,axiom,
% 6.92/7.25 ! [Q2: ( product_prod_nat_nat > $o ) > $o,P2: nat > nat > product_prod_nat_nat > $o,Z3: product_prod_nat_nat] :
% 6.92/7.25 ( ( Q2 @ ( produc8739625826339149834_nat_o @ P2 @ Z3 ) )
% 6.92/7.25 => ~ ! [X3: nat,Y3: nat] :
% 6.92/7.25 ( ( Z3
% 6.92/7.25 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( Q2 @ ( P2 @ X3 @ Y3 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodE2
% 6.92/7.25 thf(fact_6410_case__prodE2,axiom,
% 6.92/7.25 ! [Q2: product_prod_int_int > $o,P2: int > int > product_prod_int_int,Z3: product_prod_int_int] :
% 6.92/7.25 ( ( Q2 @ ( produc4245557441103728435nt_int @ P2 @ Z3 ) )
% 6.92/7.25 => ~ ! [X3: int,Y3: int] :
% 6.92/7.25 ( ( Z3
% 6.92/7.25 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( Q2 @ ( P2 @ X3 @ Y3 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodE2
% 6.92/7.25 thf(fact_6411_case__prodE2,axiom,
% 6.92/7.25 ! [Q2: $o > $o,P2: int > int > $o,Z3: product_prod_int_int] :
% 6.92/7.25 ( ( Q2 @ ( produc4947309494688390418_int_o @ P2 @ Z3 ) )
% 6.92/7.25 => ~ ! [X3: int,Y3: int] :
% 6.92/7.25 ( ( Z3
% 6.92/7.25 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( Q2 @ ( P2 @ X3 @ Y3 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodE2
% 6.92/7.25 thf(fact_6412_case__prodE2,axiom,
% 6.92/7.25 ! [Q2: int > $o,P2: int > int > int,Z3: product_prod_int_int] :
% 6.92/7.25 ( ( Q2 @ ( produc8211389475949308722nt_int @ P2 @ Z3 ) )
% 6.92/7.25 => ~ ! [X3: int,Y3: int] :
% 6.92/7.25 ( ( Z3
% 6.92/7.25 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( Q2 @ ( P2 @ X3 @ Y3 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodE2
% 6.92/7.25 thf(fact_6413_case__prod__eta,axiom,
% 6.92/7.25 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 6.92/7.25 ( ( produc27273713700761075at_nat
% 6.92/7.25 @ ^ [X4: nat,Y4: nat] : ( F @ ( product_Pair_nat_nat @ X4 @ Y4 ) ) )
% 6.92/7.25 = F ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_eta
% 6.92/7.25 thf(fact_6414_case__prod__eta,axiom,
% 6.92/7.25 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 6.92/7.25 ( ( produc8739625826339149834_nat_o
% 6.92/7.25 @ ^ [X4: nat,Y4: nat] : ( F @ ( product_Pair_nat_nat @ X4 @ Y4 ) ) )
% 6.92/7.25 = F ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_eta
% 6.92/7.25 thf(fact_6415_case__prod__eta,axiom,
% 6.92/7.25 ! [F: product_prod_int_int > product_prod_int_int] :
% 6.92/7.25 ( ( produc4245557441103728435nt_int
% 6.92/7.25 @ ^ [X4: int,Y4: int] : ( F @ ( product_Pair_int_int @ X4 @ Y4 ) ) )
% 6.92/7.25 = F ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_eta
% 6.92/7.25 thf(fact_6416_case__prod__eta,axiom,
% 6.92/7.25 ! [F: product_prod_int_int > $o] :
% 6.92/7.25 ( ( produc4947309494688390418_int_o
% 6.92/7.25 @ ^ [X4: int,Y4: int] : ( F @ ( product_Pair_int_int @ X4 @ Y4 ) ) )
% 6.92/7.25 = F ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_eta
% 6.92/7.25 thf(fact_6417_case__prod__eta,axiom,
% 6.92/7.25 ! [F: product_prod_int_int > int] :
% 6.92/7.25 ( ( produc8211389475949308722nt_int
% 6.92/7.25 @ ^ [X4: int,Y4: int] : ( F @ ( product_Pair_int_int @ X4 @ Y4 ) ) )
% 6.92/7.25 = F ) ).
% 6.92/7.25
% 6.92/7.25 % case_prod_eta
% 6.92/7.25 thf(fact_6418_cond__case__prod__eta,axiom,
% 6.92/7.25 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 6.92/7.25 ( ! [X3: nat,Y3: nat] :
% 6.92/7.25 ( ( F @ X3 @ Y3 )
% 6.92/7.25 = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 6.92/7.25 => ( ( produc27273713700761075at_nat @ F )
% 6.92/7.25 = G ) ) ).
% 6.92/7.25
% 6.92/7.25 % cond_case_prod_eta
% 6.92/7.25 thf(fact_6419_cond__case__prod__eta,axiom,
% 6.92/7.25 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 6.92/7.25 ( ! [X3: nat,Y3: nat] :
% 6.92/7.25 ( ( F @ X3 @ Y3 )
% 6.92/7.25 = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 6.92/7.25 => ( ( produc8739625826339149834_nat_o @ F )
% 6.92/7.25 = G ) ) ).
% 6.92/7.25
% 6.92/7.25 % cond_case_prod_eta
% 6.92/7.25 thf(fact_6420_cond__case__prod__eta,axiom,
% 6.92/7.25 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 6.92/7.25 ( ! [X3: int,Y3: int] :
% 6.92/7.25 ( ( F @ X3 @ Y3 )
% 6.92/7.25 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 6.92/7.25 => ( ( produc4245557441103728435nt_int @ F )
% 6.92/7.25 = G ) ) ).
% 6.92/7.25
% 6.92/7.25 % cond_case_prod_eta
% 6.92/7.25 thf(fact_6421_cond__case__prod__eta,axiom,
% 6.92/7.25 ! [F: int > int > $o,G: product_prod_int_int > $o] :
% 6.92/7.25 ( ! [X3: int,Y3: int] :
% 6.92/7.25 ( ( F @ X3 @ Y3 )
% 6.92/7.25 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 6.92/7.25 => ( ( produc4947309494688390418_int_o @ F )
% 6.92/7.25 = G ) ) ).
% 6.92/7.25
% 6.92/7.25 % cond_case_prod_eta
% 6.92/7.25 thf(fact_6422_cond__case__prod__eta,axiom,
% 6.92/7.25 ! [F: int > int > int,G: product_prod_int_int > int] :
% 6.92/7.25 ( ! [X3: int,Y3: int] :
% 6.92/7.25 ( ( F @ X3 @ Y3 )
% 6.92/7.25 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 6.92/7.25 => ( ( produc8211389475949308722nt_int @ F )
% 6.92/7.25 = G ) ) ).
% 6.92/7.25
% 6.92/7.25 % cond_case_prod_eta
% 6.92/7.25 thf(fact_6423_subset__divisors__dvd,axiom,
% 6.92/7.25 ! [A: nat,B: nat] :
% 6.92/7.25 ( ( ord_less_eq_set_nat
% 6.92/7.25 @ ( collect_nat
% 6.92/7.25 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 6.92/7.25 @ ( collect_nat
% 6.92/7.25 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 6.92/7.25 = ( dvd_dvd_nat @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % subset_divisors_dvd
% 6.92/7.25 thf(fact_6424_subset__divisors__dvd,axiom,
% 6.92/7.25 ! [A: int,B: int] :
% 6.92/7.25 ( ( ord_less_eq_set_int
% 6.92/7.25 @ ( collect_int
% 6.92/7.25 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 6.92/7.25 @ ( collect_int
% 6.92/7.25 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 6.92/7.25 = ( dvd_dvd_int @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % subset_divisors_dvd
% 6.92/7.25 thf(fact_6425_take__bit__eq__mask__iff,axiom,
% 6.92/7.25 ! [N2: nat,K2: int] :
% 6.92/7.25 ( ( ( bit_se2923211474154528505it_int @ N2 @ K2 )
% 6.92/7.25 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 6.92/7.25 = ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K2 @ one_one_int ) )
% 6.92/7.25 = zero_zero_int ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_eq_mask_iff
% 6.92/7.25 thf(fact_6426_strict__subset__divisors__dvd,axiom,
% 6.92/7.25 ! [A: nat,B: nat] :
% 6.92/7.25 ( ( ord_less_set_nat
% 6.92/7.25 @ ( collect_nat
% 6.92/7.25 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 6.92/7.25 @ ( collect_nat
% 6.92/7.25 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 6.92/7.25 = ( ( dvd_dvd_nat @ A @ B )
% 6.92/7.25 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % strict_subset_divisors_dvd
% 6.92/7.25 thf(fact_6427_strict__subset__divisors__dvd,axiom,
% 6.92/7.25 ! [A: int,B: int] :
% 6.92/7.25 ( ( ord_less_set_int
% 6.92/7.25 @ ( collect_int
% 6.92/7.25 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 6.92/7.25 @ ( collect_int
% 6.92/7.25 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 6.92/7.25 = ( ( dvd_dvd_int @ A @ B )
% 6.92/7.25 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % strict_subset_divisors_dvd
% 6.92/7.25 thf(fact_6428_take__bit__eq__mask__iff__exp__dvd,axiom,
% 6.92/7.25 ! [N2: nat,K2: int] :
% 6.92/7.25 ( ( ( bit_se2923211474154528505it_int @ N2 @ K2 )
% 6.92/7.25 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 6.92/7.25 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( plus_plus_int @ K2 @ one_one_int ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_eq_mask_iff_exp_dvd
% 6.92/7.25 thf(fact_6429_take__bit__tightened__less__eq__int,axiom,
% 6.92/7.25 ! [M: nat,N2: nat,K2: int] :
% 6.92/7.25 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.25 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K2 ) @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_tightened_less_eq_int
% 6.92/7.25 thf(fact_6430_take__bit__int__less__eq__self__iff,axiom,
% 6.92/7.25 ! [N2: nat,K2: int] :
% 6.92/7.25 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) @ K2 )
% 6.92/7.25 = ( ord_less_eq_int @ zero_zero_int @ K2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_int_less_eq_self_iff
% 6.92/7.25 thf(fact_6431_take__bit__nonnegative,axiom,
% 6.92/7.25 ! [N2: nat,K2: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_nonnegative
% 6.92/7.25 thf(fact_6432_take__bit__int__greater__self__iff,axiom,
% 6.92/7.25 ! [K2: int,N2: nat] :
% 6.92/7.25 ( ( ord_less_int @ K2 @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) )
% 6.92/7.25 = ( ord_less_int @ K2 @ zero_zero_int ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_int_greater_self_iff
% 6.92/7.25 thf(fact_6433_not__take__bit__negative,axiom,
% 6.92/7.25 ! [N2: nat,K2: int] :
% 6.92/7.25 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) @ zero_zero_int ) ).
% 6.92/7.25
% 6.92/7.25 % not_take_bit_negative
% 6.92/7.25 thf(fact_6434_pinf_I9_J,axiom,
% 6.92/7.25 ! [D2: rat,S2: rat] :
% 6.92/7.25 ? [Z2: rat] :
% 6.92/7.25 ! [X6: rat] :
% 6.92/7.25 ( ( ord_less_rat @ Z2 @ X6 )
% 6.92/7.25 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S2 ) )
% 6.92/7.25 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % pinf(9)
% 6.92/7.25 thf(fact_6435_pinf_I9_J,axiom,
% 6.92/7.25 ! [D2: nat,S2: nat] :
% 6.92/7.25 ? [Z2: nat] :
% 6.92/7.25 ! [X6: nat] :
% 6.92/7.25 ( ( ord_less_nat @ Z2 @ X6 )
% 6.92/7.25 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S2 ) )
% 6.92/7.25 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % pinf(9)
% 6.92/7.25 thf(fact_6436_pinf_I9_J,axiom,
% 6.92/7.25 ! [D2: int,S2: int] :
% 6.92/7.25 ? [Z2: int] :
% 6.92/7.25 ! [X6: int] :
% 6.92/7.25 ( ( ord_less_int @ Z2 @ X6 )
% 6.92/7.25 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S2 ) )
% 6.92/7.25 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % pinf(9)
% 6.92/7.25 thf(fact_6437_pinf_I10_J,axiom,
% 6.92/7.25 ! [D2: rat,S2: rat] :
% 6.92/7.25 ? [Z2: rat] :
% 6.92/7.25 ! [X6: rat] :
% 6.92/7.25 ( ( ord_less_rat @ Z2 @ X6 )
% 6.92/7.25 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S2 ) ) )
% 6.92/7.25 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % pinf(10)
% 6.92/7.25 thf(fact_6438_pinf_I10_J,axiom,
% 6.92/7.25 ! [D2: nat,S2: nat] :
% 6.92/7.25 ? [Z2: nat] :
% 6.92/7.25 ! [X6: nat] :
% 6.92/7.25 ( ( ord_less_nat @ Z2 @ X6 )
% 6.92/7.25 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S2 ) ) )
% 6.92/7.25 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % pinf(10)
% 6.92/7.25 thf(fact_6439_pinf_I10_J,axiom,
% 6.92/7.25 ! [D2: int,S2: int] :
% 6.92/7.25 ? [Z2: int] :
% 6.92/7.25 ! [X6: int] :
% 6.92/7.25 ( ( ord_less_int @ Z2 @ X6 )
% 6.92/7.25 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S2 ) ) )
% 6.92/7.25 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % pinf(10)
% 6.92/7.25 thf(fact_6440_minf_I9_J,axiom,
% 6.92/7.25 ! [D2: rat,S2: rat] :
% 6.92/7.25 ? [Z2: rat] :
% 6.92/7.25 ! [X6: rat] :
% 6.92/7.25 ( ( ord_less_rat @ X6 @ Z2 )
% 6.92/7.25 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S2 ) )
% 6.92/7.25 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % minf(9)
% 6.92/7.25 thf(fact_6441_minf_I9_J,axiom,
% 6.92/7.25 ! [D2: nat,S2: nat] :
% 6.92/7.25 ? [Z2: nat] :
% 6.92/7.25 ! [X6: nat] :
% 6.92/7.25 ( ( ord_less_nat @ X6 @ Z2 )
% 6.92/7.25 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S2 ) )
% 6.92/7.25 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % minf(9)
% 6.92/7.25 thf(fact_6442_minf_I9_J,axiom,
% 6.92/7.25 ! [D2: int,S2: int] :
% 6.92/7.25 ? [Z2: int] :
% 6.92/7.25 ! [X6: int] :
% 6.92/7.25 ( ( ord_less_int @ X6 @ Z2 )
% 6.92/7.25 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S2 ) )
% 6.92/7.25 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % minf(9)
% 6.92/7.25 thf(fact_6443_minf_I10_J,axiom,
% 6.92/7.25 ! [D2: rat,S2: rat] :
% 6.92/7.25 ? [Z2: rat] :
% 6.92/7.25 ! [X6: rat] :
% 6.92/7.25 ( ( ord_less_rat @ X6 @ Z2 )
% 6.92/7.25 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S2 ) ) )
% 6.92/7.25 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ S2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % minf(10)
% 6.92/7.25 thf(fact_6444_minf_I10_J,axiom,
% 6.92/7.25 ! [D2: nat,S2: nat] :
% 6.92/7.25 ? [Z2: nat] :
% 6.92/7.25 ! [X6: nat] :
% 6.92/7.25 ( ( ord_less_nat @ X6 @ Z2 )
% 6.92/7.25 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S2 ) ) )
% 6.92/7.25 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X6 @ S2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % minf(10)
% 6.92/7.25 thf(fact_6445_minf_I10_J,axiom,
% 6.92/7.25 ! [D2: int,S2: int] :
% 6.92/7.25 ? [Z2: int] :
% 6.92/7.25 ! [X6: int] :
% 6.92/7.25 ( ( ord_less_int @ X6 @ Z2 )
% 6.92/7.25 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S2 ) ) )
% 6.92/7.25 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ S2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % minf(10)
% 6.92/7.25 thf(fact_6446_signed__take__bit__take__bit,axiom,
% 6.92/7.25 ! [M: nat,N2: nat,A: int] :
% 6.92/7.25 ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 6.92/7.25 = ( if_int_int @ ( ord_less_eq_nat @ N2 @ M ) @ ( bit_se2923211474154528505it_int @ N2 ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 6.92/7.25
% 6.92/7.25 % signed_take_bit_take_bit
% 6.92/7.25 thf(fact_6447_div__plus__div__distrib__dvd__left,axiom,
% 6.92/7.25 ! [C2: nat,A: nat,B: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ C2 @ A )
% 6.92/7.25 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 6.92/7.25 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C2 ) @ ( divide_divide_nat @ B @ C2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % div_plus_div_distrib_dvd_left
% 6.92/7.25 thf(fact_6448_div__plus__div__distrib__dvd__left,axiom,
% 6.92/7.25 ! [C2: int,A: int,B: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ C2 @ A )
% 6.92/7.25 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 6.92/7.25 = ( plus_plus_int @ ( divide_divide_int @ A @ C2 ) @ ( divide_divide_int @ B @ C2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % div_plus_div_distrib_dvd_left
% 6.92/7.25 thf(fact_6449_div__plus__div__distrib__dvd__left,axiom,
% 6.92/7.25 ! [C2: code_natural,A: code_natural,B: code_natural] :
% 6.92/7.25 ( ( dvd_dvd_Code_natural @ C2 @ A )
% 6.92/7.25 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C2 )
% 6.92/7.25 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ C2 ) @ ( divide5121882707175180666atural @ B @ C2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % div_plus_div_distrib_dvd_left
% 6.92/7.25 thf(fact_6450_div__plus__div__distrib__dvd__right,axiom,
% 6.92/7.25 ! [C2: nat,B: nat,A: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ C2 @ B )
% 6.92/7.25 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 6.92/7.25 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C2 ) @ ( divide_divide_nat @ B @ C2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % div_plus_div_distrib_dvd_right
% 6.92/7.25 thf(fact_6451_div__plus__div__distrib__dvd__right,axiom,
% 6.92/7.25 ! [C2: int,B: int,A: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ C2 @ B )
% 6.92/7.25 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 6.92/7.25 = ( plus_plus_int @ ( divide_divide_int @ A @ C2 ) @ ( divide_divide_int @ B @ C2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % div_plus_div_distrib_dvd_right
% 6.92/7.25 thf(fact_6452_div__plus__div__distrib__dvd__right,axiom,
% 6.92/7.25 ! [C2: code_natural,B: code_natural,A: code_natural] :
% 6.92/7.25 ( ( dvd_dvd_Code_natural @ C2 @ B )
% 6.92/7.25 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C2 )
% 6.92/7.25 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ C2 ) @ ( divide5121882707175180666atural @ B @ C2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % div_plus_div_distrib_dvd_right
% 6.92/7.25 thf(fact_6453_take__bit__unset__bit__eq,axiom,
% 6.92/7.25 ! [N2: nat,M: nat,A: nat] :
% 6.92/7.25 ( ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 6.92/7.25 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 6.92/7.25 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 6.92/7.25 = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_unset_bit_eq
% 6.92/7.25 thf(fact_6454_take__bit__unset__bit__eq,axiom,
% 6.92/7.25 ! [N2: nat,M: nat,A: int] :
% 6.92/7.25 ( ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 6.92/7.25 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 6.92/7.25 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 6.92/7.25 = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_unset_bit_eq
% 6.92/7.25 thf(fact_6455_take__bit__set__bit__eq,axiom,
% 6.92/7.25 ! [N2: nat,M: nat,A: int] :
% 6.92/7.25 ( ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 6.92/7.25 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 6.92/7.25 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 6.92/7.25 = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_set_bit_eq
% 6.92/7.25 thf(fact_6456_take__bit__set__bit__eq,axiom,
% 6.92/7.25 ! [N2: nat,M: nat,A: nat] :
% 6.92/7.25 ( ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 6.92/7.25 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 6.92/7.25 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 6.92/7.25 = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_set_bit_eq
% 6.92/7.25 thf(fact_6457_take__bit__flip__bit__eq,axiom,
% 6.92/7.25 ! [N2: nat,M: nat,A: int] :
% 6.92/7.25 ( ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 6.92/7.25 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 6.92/7.25 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 6.92/7.25 = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_flip_bit_eq
% 6.92/7.25 thf(fact_6458_take__bit__flip__bit__eq,axiom,
% 6.92/7.25 ! [N2: nat,M: nat,A: nat] :
% 6.92/7.25 ( ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 6.92/7.25 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 6.92/7.25 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 6.92/7.25 = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_flip_bit_eq
% 6.92/7.25 thf(fact_6459_nat__dvd__not__less,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.25 => ( ( ord_less_nat @ M @ N2 )
% 6.92/7.25 => ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % nat_dvd_not_less
% 6.92/7.25 thf(fact_6460_dvd__pos__nat,axiom,
% 6.92/7.25 ! [N2: nat,M: nat] :
% 6.92/7.25 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 => ( ( dvd_dvd_nat @ M @ N2 )
% 6.92/7.25 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_pos_nat
% 6.92/7.25 thf(fact_6461_le__imp__power__dvd,axiom,
% 6.92/7.25 ! [M: nat,N2: nat,A: nat] :
% 6.92/7.25 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.25 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % le_imp_power_dvd
% 6.92/7.25 thf(fact_6462_le__imp__power__dvd,axiom,
% 6.92/7.25 ! [M: nat,N2: nat,A: int] :
% 6.92/7.25 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.25 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % le_imp_power_dvd
% 6.92/7.25 thf(fact_6463_power__le__dvd,axiom,
% 6.92/7.25 ! [A: nat,N2: nat,B: nat,M: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ B )
% 6.92/7.25 => ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.25 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_le_dvd
% 6.92/7.25 thf(fact_6464_power__le__dvd,axiom,
% 6.92/7.25 ! [A: int,N2: nat,B: int,M: nat] :
% 6.92/7.25 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ B )
% 6.92/7.25 => ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.25 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_le_dvd
% 6.92/7.25 thf(fact_6465_dvd__power__le,axiom,
% 6.92/7.25 ! [X: nat,Y: nat,N2: nat,M: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ X @ Y )
% 6.92/7.25 => ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_power_le
% 6.92/7.25 thf(fact_6466_dvd__power__le,axiom,
% 6.92/7.25 ! [X: int,Y: int,N2: nat,M: nat] :
% 6.92/7.25 ( ( dvd_dvd_int @ X @ Y )
% 6.92/7.25 => ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( dvd_dvd_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_power_le
% 6.92/7.25 thf(fact_6467_dvd__minus__self,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) )
% 6.92/7.25 = ( ( ord_less_nat @ N2 @ M )
% 6.92/7.25 | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_minus_self
% 6.92/7.25 thf(fact_6468_zdvd__antisym__nonneg,axiom,
% 6.92/7.25 ! [M: int,N2: int] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 6.92/7.25 => ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 6.92/7.25 => ( ( dvd_dvd_int @ M @ N2 )
% 6.92/7.25 => ( ( dvd_dvd_int @ N2 @ M )
% 6.92/7.25 => ( M = N2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zdvd_antisym_nonneg
% 6.92/7.25 thf(fact_6469_zdvd__not__zless,axiom,
% 6.92/7.25 ! [M: int,N2: int] :
% 6.92/7.25 ( ( ord_less_int @ zero_zero_int @ M )
% 6.92/7.25 => ( ( ord_less_int @ M @ N2 )
% 6.92/7.25 => ~ ( dvd_dvd_int @ N2 @ M ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zdvd_not_zless
% 6.92/7.25 thf(fact_6470_less__eq__dvd__minus,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.25 => ( ( dvd_dvd_nat @ M @ N2 )
% 6.92/7.25 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % less_eq_dvd_minus
% 6.92/7.25 thf(fact_6471_dvd__diffD1,axiom,
% 6.92/7.25 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ K2 @ ( minus_minus_nat @ M @ N2 ) )
% 6.92/7.25 => ( ( dvd_dvd_nat @ K2 @ M )
% 6.92/7.25 => ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( dvd_dvd_nat @ K2 @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_diffD1
% 6.92/7.25 thf(fact_6472_dvd__diffD,axiom,
% 6.92/7.25 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ K2 @ ( minus_minus_nat @ M @ N2 ) )
% 6.92/7.25 => ( ( dvd_dvd_nat @ K2 @ N2 )
% 6.92/7.25 => ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( dvd_dvd_nat @ K2 @ M ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_diffD
% 6.92/7.25 thf(fact_6473_zdvd__mono,axiom,
% 6.92/7.25 ! [K2: int,M: int,T6: int] :
% 6.92/7.25 ( ( K2 != zero_zero_int )
% 6.92/7.25 => ( ( dvd_dvd_int @ M @ T6 )
% 6.92/7.25 = ( dvd_dvd_int @ ( times_times_int @ K2 @ M ) @ ( times_times_int @ K2 @ T6 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zdvd_mono
% 6.92/7.25 thf(fact_6474_bezout__lemma__nat,axiom,
% 6.92/7.25 ! [D2: nat,A: nat,B: nat,X: nat,Y: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ D2 @ A )
% 6.92/7.25 => ( ( dvd_dvd_nat @ D2 @ B )
% 6.92/7.25 => ( ( ( ( times_times_nat @ A @ X )
% 6.92/7.25 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D2 ) )
% 6.92/7.25 | ( ( times_times_nat @ B @ X )
% 6.92/7.25 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D2 ) ) )
% 6.92/7.25 => ? [X3: nat,Y3: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ D2 @ A )
% 6.92/7.25 & ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ A @ B ) )
% 6.92/7.25 & ( ( ( times_times_nat @ A @ X3 )
% 6.92/7.25 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D2 ) )
% 6.92/7.25 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X3 )
% 6.92/7.25 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D2 ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % bezout_lemma_nat
% 6.92/7.25 thf(fact_6475_bezout__add__nat,axiom,
% 6.92/7.25 ! [A: nat,B: nat] :
% 6.92/7.25 ? [D: nat,X3: nat,Y3: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ D @ A )
% 6.92/7.25 & ( dvd_dvd_nat @ D @ B )
% 6.92/7.25 & ( ( ( times_times_nat @ A @ X3 )
% 6.92/7.25 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D ) )
% 6.92/7.25 | ( ( times_times_nat @ B @ X3 )
% 6.92/7.25 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % bezout_add_nat
% 6.92/7.25 thf(fact_6476_zdvd__reduce,axiom,
% 6.92/7.25 ! [K2: int,N2: int,M: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ K2 @ ( plus_plus_int @ N2 @ ( times_times_int @ K2 @ M ) ) )
% 6.92/7.25 = ( dvd_dvd_int @ K2 @ N2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % zdvd_reduce
% 6.92/7.25 thf(fact_6477_zdvd__period,axiom,
% 6.92/7.25 ! [A: int,D2: int,X: int,T6: int,C2: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ A @ D2 )
% 6.92/7.25 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T6 ) )
% 6.92/7.25 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C2 @ D2 ) ) @ T6 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zdvd_period
% 6.92/7.25 thf(fact_6478_fact__dvd,axiom,
% 6.92/7.25 ! [N2: nat,M: nat] :
% 6.92/7.25 ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % fact_dvd
% 6.92/7.25 thf(fact_6479_fact__dvd,axiom,
% 6.92/7.25 ! [N2: nat,M: nat] :
% 6.92/7.25 ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % fact_dvd
% 6.92/7.25 thf(fact_6480_uncurry__def,axiom,
% 6.92/7.25 uncurr8011562610307062878at_nat = produc27273713700761075at_nat ).
% 6.92/7.25
% 6.92/7.25 % uncurry_def
% 6.92/7.25 thf(fact_6481_uncurry__def,axiom,
% 6.92/7.25 uncurr7511940902602773877_nat_o = produc8739625826339149834_nat_o ).
% 6.92/7.25
% 6.92/7.25 % uncurry_def
% 6.92/7.25 thf(fact_6482_uncurry__def,axiom,
% 6.92/7.25 uncurr7650761721940715016nt_int = produc4245557441103728435nt_int ).
% 6.92/7.25
% 6.92/7.25 % uncurry_def
% 6.92/7.25 thf(fact_6483_uncurry__def,axiom,
% 6.92/7.25 uncurry_int_int_o = produc4947309494688390418_int_o ).
% 6.92/7.25
% 6.92/7.25 % uncurry_def
% 6.92/7.25 thf(fact_6484_uncurry__def,axiom,
% 6.92/7.25 uncurry_int_int_int = produc8211389475949308722nt_int ).
% 6.92/7.25
% 6.92/7.25 % uncurry_def
% 6.92/7.25 thf(fact_6485_internal__case__prod__def,axiom,
% 6.92/7.25 produc1854806715440696265at_nat = produc27273713700761075at_nat ).
% 6.92/7.25
% 6.92/7.25 % internal_case_prod_def
% 6.92/7.25 thf(fact_6486_internal__case__prod__def,axiom,
% 6.92/7.25 produc4780622933104268256_nat_o = produc8739625826339149834_nat_o ).
% 6.92/7.25
% 6.92/7.25 % internal_case_prod_def
% 6.92/7.25 thf(fact_6487_internal__case__prod__def,axiom,
% 6.92/7.25 produc297006045350968285nt_int = produc4245557441103728435nt_int ).
% 6.92/7.25
% 6.92/7.25 % internal_case_prod_def
% 6.92/7.25 thf(fact_6488_internal__case__prod__def,axiom,
% 6.92/7.25 produc8005341501107743676_int_o = produc4947309494688390418_int_o ).
% 6.92/7.25
% 6.92/7.25 % internal_case_prod_def
% 6.92/7.25 thf(fact_6489_internal__case__prod__def,axiom,
% 6.92/7.25 produc7926200574084438792nt_int = produc8211389475949308722nt_int ).
% 6.92/7.25
% 6.92/7.25 % internal_case_prod_def
% 6.92/7.25 thf(fact_6490_mask__nonnegative__int,axiom,
% 6.92/7.25 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % mask_nonnegative_int
% 6.92/7.25 thf(fact_6491_not__mask__negative__int,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ zero_zero_int ) ).
% 6.92/7.25
% 6.92/7.25 % not_mask_negative_int
% 6.92/7.25 thf(fact_6492_nat__dvd__iff,axiom,
% 6.92/7.25 ! [Z3: int,M: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( nat2 @ Z3 ) @ M )
% 6.92/7.25 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.25 => ( dvd_dvd_int @ Z3 @ ( semiri1314217659103216013at_int @ M ) ) )
% 6.92/7.25 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 6.92/7.25 => ( M = zero_zero_nat ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % nat_dvd_iff
% 6.92/7.25 thf(fact_6493_take__bit__signed__take__bit,axiom,
% 6.92/7.25 ! [M: nat,N2: nat,A: int] :
% 6.92/7.25 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 6.92/7.25 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N2 @ A ) )
% 6.92/7.25 = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_signed_take_bit
% 6.92/7.25 thf(fact_6494_unity__coeff__ex,axiom,
% 6.92/7.25 ! [P2: code_integer > $o,L: code_integer] :
% 6.92/7.25 ( ( ? [X4: code_integer] : ( P2 @ ( times_3573771949741848930nteger @ L @ X4 ) ) )
% 6.92/7.25 = ( ? [X4: code_integer] :
% 6.92/7.25 ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X4 @ zero_z3403309356797280102nteger ) )
% 6.92/7.25 & ( P2 @ X4 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % unity_coeff_ex
% 6.92/7.25 thf(fact_6495_unity__coeff__ex,axiom,
% 6.92/7.25 ! [P2: rat > $o,L: rat] :
% 6.92/7.25 ( ( ? [X4: rat] : ( P2 @ ( times_times_rat @ L @ X4 ) ) )
% 6.92/7.25 = ( ? [X4: rat] :
% 6.92/7.25 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X4 @ zero_zero_rat ) )
% 6.92/7.25 & ( P2 @ X4 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % unity_coeff_ex
% 6.92/7.25 thf(fact_6496_unity__coeff__ex,axiom,
% 6.92/7.25 ! [P2: nat > $o,L: nat] :
% 6.92/7.25 ( ( ? [X4: nat] : ( P2 @ ( times_times_nat @ L @ X4 ) ) )
% 6.92/7.25 = ( ? [X4: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X4 @ zero_zero_nat ) )
% 6.92/7.25 & ( P2 @ X4 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % unity_coeff_ex
% 6.92/7.25 thf(fact_6497_unity__coeff__ex,axiom,
% 6.92/7.25 ! [P2: int > $o,L: int] :
% 6.92/7.25 ( ( ? [X4: int] : ( P2 @ ( times_times_int @ L @ X4 ) ) )
% 6.92/7.25 = ( ? [X4: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X4 @ zero_zero_int ) )
% 6.92/7.25 & ( P2 @ X4 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % unity_coeff_ex
% 6.92/7.25 thf(fact_6498_inf__period_I3_J,axiom,
% 6.92/7.25 ! [D2: rat,D4: rat,T6: rat] :
% 6.92/7.25 ( ( dvd_dvd_rat @ D2 @ D4 )
% 6.92/7.25 => ! [X6: rat,K4: rat] :
% 6.92/7.25 ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ T6 ) )
% 6.92/7.25 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D4 ) ) @ T6 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % inf_period(3)
% 6.92/7.25 thf(fact_6499_inf__period_I3_J,axiom,
% 6.92/7.25 ! [D2: int,D4: int,T6: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ D2 @ D4 )
% 6.92/7.25 => ! [X6: int,K4: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ T6 ) )
% 6.92/7.25 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D4 ) ) @ T6 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % inf_period(3)
% 6.92/7.25 thf(fact_6500_inf__period_I4_J,axiom,
% 6.92/7.25 ! [D2: rat,D4: rat,T6: rat] :
% 6.92/7.25 ( ( dvd_dvd_rat @ D2 @ D4 )
% 6.92/7.25 => ! [X6: rat,K4: rat] :
% 6.92/7.25 ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ T6 ) ) )
% 6.92/7.25 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K4 @ D4 ) ) @ T6 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % inf_period(4)
% 6.92/7.25 thf(fact_6501_inf__period_I4_J,axiom,
% 6.92/7.25 ! [D2: int,D4: int,T6: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ D2 @ D4 )
% 6.92/7.25 => ! [X6: int,K4: int] :
% 6.92/7.25 ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ T6 ) ) )
% 6.92/7.25 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ ( times_times_int @ K4 @ D4 ) ) @ T6 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % inf_period(4)
% 6.92/7.25 thf(fact_6502_dvd__imp__le,axiom,
% 6.92/7.25 ! [K2: nat,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ K2 @ N2 )
% 6.92/7.25 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 => ( ord_less_eq_nat @ K2 @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_imp_le
% 6.92/7.25 thf(fact_6503_dvd__mult__cancel,axiom,
% 6.92/7.25 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( times_times_nat @ K2 @ M ) @ ( times_times_nat @ K2 @ N2 ) )
% 6.92/7.25 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.25 => ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_mult_cancel
% 6.92/7.25 thf(fact_6504_nat__mult__dvd__cancel1,axiom,
% 6.92/7.25 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 6.92/7.25 => ( ( dvd_dvd_nat @ ( times_times_nat @ K2 @ M ) @ ( times_times_nat @ K2 @ N2 ) )
% 6.92/7.25 = ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % nat_mult_dvd_cancel1
% 6.92/7.25 thf(fact_6505_bezout__add__strong__nat,axiom,
% 6.92/7.25 ! [A: nat,B: nat] :
% 6.92/7.25 ( ( A != zero_zero_nat )
% 6.92/7.25 => ? [D: nat,X3: nat,Y3: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ D @ A )
% 6.92/7.25 & ( dvd_dvd_nat @ D @ B )
% 6.92/7.25 & ( ( times_times_nat @ A @ X3 )
% 6.92/7.25 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % bezout_add_strong_nat
% 6.92/7.25 thf(fact_6506_zdvd__imp__le,axiom,
% 6.92/7.25 ! [Z3: int,N2: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ Z3 @ N2 )
% 6.92/7.25 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 6.92/7.25 => ( ord_less_eq_int @ Z3 @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zdvd_imp_le
% 6.92/7.25 thf(fact_6507_fact__fact__dvd__fact,axiom,
% 6.92/7.25 ! [K2: nat,N2: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri773545260158071498ct_rat @ N2 ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K2 @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % fact_fact_dvd_fact
% 6.92/7.25 thf(fact_6508_fact__fact__dvd__fact,axiom,
% 6.92/7.25 ! [K2: nat,N2: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K2 ) @ ( semiri1406184849735516958ct_int @ N2 ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K2 @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % fact_fact_dvd_fact
% 6.92/7.25 thf(fact_6509_fact__fact__dvd__fact,axiom,
% 6.92/7.25 ! [K2: nat,N2: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K2 @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % fact_fact_dvd_fact
% 6.92/7.25 thf(fact_6510_mod__greater__zero__iff__not__dvd,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 6.92/7.25 = ( ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mod_greater_zero_iff_not_dvd
% 6.92/7.25 thf(fact_6511_dvd__imp__le__int,axiom,
% 6.92/7.25 ! [I2: int,D2: int] :
% 6.92/7.25 ( ( I2 != zero_zero_int )
% 6.92/7.25 => ( ( dvd_dvd_int @ D2 @ I2 )
% 6.92/7.25 => ( ord_less_eq_int @ ( abs_abs_int @ D2 ) @ ( abs_abs_int @ I2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_imp_le_int
% 6.92/7.25 thf(fact_6512_mod__eq__dvd__iff__nat,axiom,
% 6.92/7.25 ! [N2: nat,M: nat,Q6: nat] :
% 6.92/7.25 ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.25 => ( ( ( modulo_modulo_nat @ M @ Q6 )
% 6.92/7.25 = ( modulo_modulo_nat @ N2 @ Q6 ) )
% 6.92/7.25 = ( dvd_dvd_nat @ Q6 @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mod_eq_dvd_iff_nat
% 6.92/7.25 thf(fact_6513_dvd__fact,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 6.92/7.25 => ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.25 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_fact
% 6.92/7.25 thf(fact_6514_less__mask,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 6.92/7.25 => ( ord_less_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % less_mask
% 6.92/7.25 thf(fact_6515_even__nat__iff,axiom,
% 6.92/7.25 ! [K2: int] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.25 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K2 ) )
% 6.92/7.25 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_nat_iff
% 6.92/7.25 thf(fact_6516_gcd__nat_Oordering__top__axioms,axiom,
% 6.92/7.25 ( ordering_top_nat @ dvd_dvd_nat
% 6.92/7.25 @ ^ [M3: nat,N: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ M3 @ N )
% 6.92/7.25 & ( M3 != N ) )
% 6.92/7.25 @ zero_zero_nat ) ).
% 6.92/7.25
% 6.92/7.25 % gcd_nat.ordering_top_axioms
% 6.92/7.25 thf(fact_6517_odd__even__add,axiom,
% 6.92/7.25 ! [A: nat,B: nat] :
% 6.92/7.25 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 6.92/7.25 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_even_add
% 6.92/7.25 thf(fact_6518_odd__even__add,axiom,
% 6.92/7.25 ! [A: int,B: int] :
% 6.92/7.25 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 6.92/7.25 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_even_add
% 6.92/7.25 thf(fact_6519_odd__even__add,axiom,
% 6.92/7.25 ! [A: code_natural,B: code_natural] :
% 6.92/7.25 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B )
% 6.92/7.25 => ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_even_add
% 6.92/7.25 thf(fact_6520_odd__even__add,axiom,
% 6.92/7.25 ! [A: code_integer,B: code_integer] :
% 6.92/7.25 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 6.92/7.25 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_even_add
% 6.92/7.25 thf(fact_6521_dvd__power__iff,axiom,
% 6.92/7.25 ! [X: code_integer,M: nat,N2: nat] :
% 6.92/7.25 ( ( X != zero_z3403309356797280102nteger )
% 6.92/7.25 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 6.92/7.25 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 6.92/7.25 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_power_iff
% 6.92/7.25 thf(fact_6522_dvd__power__iff,axiom,
% 6.92/7.25 ! [X: nat,M: nat,N2: nat] :
% 6.92/7.25 ( ( X != zero_zero_nat )
% 6.92/7.25 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N2 ) )
% 6.92/7.25 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 6.92/7.25 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_power_iff
% 6.92/7.25 thf(fact_6523_dvd__power__iff,axiom,
% 6.92/7.25 ! [X: int,M: nat,N2: nat] :
% 6.92/7.25 ( ( X != zero_zero_int )
% 6.92/7.25 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N2 ) )
% 6.92/7.25 = ( ( dvd_dvd_int @ X @ one_one_int )
% 6.92/7.25 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_power_iff
% 6.92/7.25 thf(fact_6524_dvd__power,axiom,
% 6.92/7.25 ! [N2: nat,X: code_integer] :
% 6.92/7.25 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 | ( X = one_one_Code_integer ) )
% 6.92/7.25 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_power
% 6.92/7.25 thf(fact_6525_dvd__power,axiom,
% 6.92/7.25 ! [N2: nat,X: rat] :
% 6.92/7.25 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 | ( X = one_one_rat ) )
% 6.92/7.25 => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_power
% 6.92/7.25 thf(fact_6526_dvd__power,axiom,
% 6.92/7.25 ! [N2: nat,X: nat] :
% 6.92/7.25 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 | ( X = one_one_nat ) )
% 6.92/7.25 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_power
% 6.92/7.25 thf(fact_6527_dvd__power,axiom,
% 6.92/7.25 ! [N2: nat,X: int] :
% 6.92/7.25 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 | ( X = one_one_int ) )
% 6.92/7.25 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_power
% 6.92/7.25 thf(fact_6528_dvd__mult__cancel1,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.25 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N2 ) @ M )
% 6.92/7.25 = ( N2 = one_one_nat ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_mult_cancel1
% 6.92/7.25 thf(fact_6529_dvd__mult__cancel2,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.25 => ( ( dvd_dvd_nat @ ( times_times_nat @ N2 @ M ) @ M )
% 6.92/7.25 = ( N2 = one_one_nat ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_mult_cancel2
% 6.92/7.25 thf(fact_6530_choose__dvd,axiom,
% 6.92/7.25 ! [K2: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.25 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ K2 ) ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % choose_dvd
% 6.92/7.25 thf(fact_6531_choose__dvd,axiom,
% 6.92/7.25 ! [K2: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.25 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ K2 ) ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % choose_dvd
% 6.92/7.25 thf(fact_6532_choose__dvd,axiom,
% 6.92/7.25 ! [K2: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.25 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K2 ) ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % choose_dvd
% 6.92/7.25 thf(fact_6533_even__even__mod__4__iff,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_even_mod_4_iff
% 6.92/7.25 thf(fact_6534_dvd__minus__add,axiom,
% 6.92/7.25 ! [Q6: nat,N2: nat,R2: nat,M: nat] :
% 6.92/7.25 ( ( ord_less_eq_nat @ Q6 @ N2 )
% 6.92/7.25 => ( ( ord_less_eq_nat @ Q6 @ ( times_times_nat @ R2 @ M ) )
% 6.92/7.25 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ Q6 ) )
% 6.92/7.25 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N2 @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q6 ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_minus_add
% 6.92/7.25 thf(fact_6535_mod__nat__eqI,axiom,
% 6.92/7.25 ! [R2: nat,N2: nat,M: nat] :
% 6.92/7.25 ( ( ord_less_nat @ R2 @ N2 )
% 6.92/7.25 => ( ( ord_less_eq_nat @ R2 @ M )
% 6.92/7.25 => ( ( dvd_dvd_nat @ N2 @ ( minus_minus_nat @ M @ R2 ) )
% 6.92/7.25 => ( ( modulo_modulo_nat @ M @ N2 )
% 6.92/7.25 = R2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mod_nat_eqI
% 6.92/7.25 thf(fact_6536_mod__int__pos__iff,axiom,
% 6.92/7.25 ! [K2: int,L: int] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K2 @ L ) )
% 6.92/7.25 = ( ( dvd_dvd_int @ L @ K2 )
% 6.92/7.25 | ( ( L = zero_zero_int )
% 6.92/7.25 & ( ord_less_eq_int @ zero_zero_int @ K2 ) )
% 6.92/7.25 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mod_int_pos_iff
% 6.92/7.25 thf(fact_6537_power__dvd__imp__le,axiom,
% 6.92/7.25 ! [I2: nat,M: nat,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N2 ) )
% 6.92/7.25 => ( ( ord_less_nat @ one_one_nat @ I2 )
% 6.92/7.25 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_dvd_imp_le
% 6.92/7.25 thf(fact_6538_take__bit__nat__eq__self,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 => ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 6.92/7.25 = M ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_nat_eq_self
% 6.92/7.25 thf(fact_6539_take__bit__nat__less__exp,axiom,
% 6.92/7.25 ! [N2: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_nat_less_exp
% 6.92/7.25 thf(fact_6540_take__bit__nat__eq__self__iff,axiom,
% 6.92/7.25 ! [N2: nat,M: nat] :
% 6.92/7.25 ( ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 6.92/7.25 = M )
% 6.92/7.25 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_nat_eq_self_iff
% 6.92/7.25 thf(fact_6541_take__bit__int__less__exp,axiom,
% 6.92/7.25 ! [N2: nat,K2: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_int_less_exp
% 6.92/7.25 thf(fact_6542_power__mono__odd,axiom,
% 6.92/7.25 ! [N2: nat,A: rat,B: rat] :
% 6.92/7.25 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 => ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.25 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_mono_odd
% 6.92/7.25 thf(fact_6543_power__mono__odd,axiom,
% 6.92/7.25 ! [N2: nat,A: int,B: int] :
% 6.92/7.25 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 => ( ( ord_less_eq_int @ A @ B )
% 6.92/7.25 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_mono_odd
% 6.92/7.25 thf(fact_6544_odd__pos,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_pos
% 6.92/7.25 thf(fact_6545_even__diff__iff,axiom,
% 6.92/7.25 ! [K2: int,L: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K2 @ L ) )
% 6.92/7.25 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K2 @ L ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_diff_iff
% 6.92/7.25 thf(fact_6546_even__add__abs__iff,axiom,
% 6.92/7.25 ! [K2: int,L: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K2 @ ( abs_abs_int @ L ) ) )
% 6.92/7.25 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K2 @ L ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_add_abs_iff
% 6.92/7.25 thf(fact_6547_even__abs__add__iff,axiom,
% 6.92/7.25 ! [K2: int,L: int] :
% 6.92/7.25 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K2 ) @ L ) )
% 6.92/7.25 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K2 @ L ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_abs_add_iff
% 6.92/7.25 thf(fact_6548_dvd__power__iff__le,axiom,
% 6.92/7.25 ! [K2: nat,M: nat,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 6.92/7.25 => ( ( dvd_dvd_nat @ ( power_power_nat @ K2 @ M ) @ ( power_power_nat @ K2 @ N2 ) )
% 6.92/7.25 = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_power_iff_le
% 6.92/7.25 thf(fact_6549_take__bit__nat__less__self__iff,axiom,
% 6.92/7.25 ! [N2: nat,M: nat] :
% 6.92/7.25 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M )
% 6.92/7.25 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_nat_less_self_iff
% 6.92/7.25 thf(fact_6550_mask__nat__less__exp,axiom,
% 6.92/7.25 ! [N2: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % mask_nat_less_exp
% 6.92/7.25 thf(fact_6551_take__bit__int__greater__eq__self__iff,axiom,
% 6.92/7.25 ! [K2: int,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_int @ K2 @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) )
% 6.92/7.25 = ( ord_less_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_int_greater_eq_self_iff
% 6.92/7.25 thf(fact_6552_take__bit__int__less__self__iff,axiom,
% 6.92/7.25 ! [N2: nat,K2: int] :
% 6.92/7.25 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) @ K2 )
% 6.92/7.25 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_int_less_self_iff
% 6.92/7.25 thf(fact_6553_oddE,axiom,
% 6.92/7.25 ! [A: nat] :
% 6.92/7.25 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ~ ! [B3: nat] :
% 6.92/7.25 ( A
% 6.92/7.25 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) @ one_one_nat ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % oddE
% 6.92/7.25 thf(fact_6554_oddE,axiom,
% 6.92/7.25 ! [A: int] :
% 6.92/7.25 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ~ ! [B3: int] :
% 6.92/7.25 ( A
% 6.92/7.25 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) @ one_one_int ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % oddE
% 6.92/7.25 thf(fact_6555_oddE,axiom,
% 6.92/7.25 ! [A: code_natural] :
% 6.92/7.25 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ~ ! [B3: code_natural] :
% 6.92/7.25 ( A
% 6.92/7.25 != ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B3 ) @ one_one_Code_natural ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % oddE
% 6.92/7.25 thf(fact_6556_oddE,axiom,
% 6.92/7.25 ! [A: code_integer] :
% 6.92/7.25 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 6.92/7.25 => ~ ! [B3: code_integer] :
% 6.92/7.25 ( A
% 6.92/7.25 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) @ one_one_Code_integer ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % oddE
% 6.92/7.25 thf(fact_6557_zero__le__power__eq,axiom,
% 6.92/7.25 ! [A: code_integer,N2: nat] :
% 6.92/7.25 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 6.92/7.25 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_le_power_eq
% 6.92/7.25 thf(fact_6558_zero__le__power__eq,axiom,
% 6.92/7.25 ! [A: rat,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 6.92/7.25 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_le_power_eq
% 6.92/7.25 thf(fact_6559_zero__le__power__eq,axiom,
% 6.92/7.25 ! [A: int,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 6.92/7.25 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_le_power_eq
% 6.92/7.25 thf(fact_6560_zero__le__odd__power,axiom,
% 6.92/7.25 ! [N2: nat,A: code_integer] :
% 6.92/7.25 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 6.92/7.25 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_le_odd_power
% 6.92/7.25 thf(fact_6561_zero__le__odd__power,axiom,
% 6.92/7.25 ! [N2: nat,A: rat] :
% 6.92/7.25 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 6.92/7.25 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_le_odd_power
% 6.92/7.25 thf(fact_6562_zero__le__odd__power,axiom,
% 6.92/7.25 ! [N2: nat,A: int] :
% 6.92/7.25 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 6.92/7.25 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_le_odd_power
% 6.92/7.25 thf(fact_6563_zero__le__even__power,axiom,
% 6.92/7.25 ! [N2: nat,A: code_integer] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_le_even_power
% 6.92/7.25 thf(fact_6564_zero__le__even__power,axiom,
% 6.92/7.25 ! [N2: nat,A: rat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_le_even_power
% 6.92/7.25 thf(fact_6565_zero__le__even__power,axiom,
% 6.92/7.25 ! [N2: nat,A: int] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_le_even_power
% 6.92/7.25 thf(fact_6566_power__mono__even,axiom,
% 6.92/7.25 ! [N2: nat,A: code_integer,B: code_integer] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 6.92/7.25 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_mono_even
% 6.92/7.25 thf(fact_6567_power__mono__even,axiom,
% 6.92/7.25 ! [N2: nat,A: rat,B: rat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 6.92/7.25 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_mono_even
% 6.92/7.25 thf(fact_6568_power__mono__even,axiom,
% 6.92/7.25 ! [N2: nat,A: int,B: int] :
% 6.92/7.25 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 6.92/7.25 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_mono_even
% 6.92/7.25 thf(fact_6569_take__bit__int__eq__self,axiom,
% 6.92/7.25 ! [K2: int,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.25 => ( ( ord_less_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 => ( ( bit_se2923211474154528505it_int @ N2 @ K2 )
% 6.92/7.25 = K2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_int_eq_self
% 6.92/7.25 thf(fact_6570_take__bit__int__eq__self__iff,axiom,
% 6.92/7.25 ! [N2: nat,K2: int] :
% 6.92/7.25 ( ( ( bit_se2923211474154528505it_int @ N2 @ K2 )
% 6.92/7.25 = K2 )
% 6.92/7.25 = ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.25 & ( ord_less_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_int_eq_self_iff
% 6.92/7.25 thf(fact_6571_take__bit__incr__eq,axiom,
% 6.92/7.25 ! [N2: nat,K2: int] :
% 6.92/7.25 ( ( ( bit_se2923211474154528505it_int @ N2 @ K2 )
% 6.92/7.25 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 6.92/7.25 => ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K2 @ one_one_int ) )
% 6.92/7.25 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_incr_eq
% 6.92/7.25 thf(fact_6572_zero__less__power__eq,axiom,
% 6.92/7.25 ! [A: code_integer,N2: nat] :
% 6.92/7.25 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 6.92/7.25 = ( ( N2 = zero_zero_nat )
% 6.92/7.25 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( A != zero_z3403309356797280102nteger ) )
% 6.92/7.25 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_less_power_eq
% 6.92/7.25 thf(fact_6573_zero__less__power__eq,axiom,
% 6.92/7.25 ! [A: rat,N2: nat] :
% 6.92/7.25 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 6.92/7.25 = ( ( N2 = zero_zero_nat )
% 6.92/7.25 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( A != zero_zero_rat ) )
% 6.92/7.25 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_less_power_eq
% 6.92/7.25 thf(fact_6574_zero__less__power__eq,axiom,
% 6.92/7.25 ! [A: int,N2: nat] :
% 6.92/7.25 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 6.92/7.25 = ( ( N2 = zero_zero_nat )
% 6.92/7.25 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( A != zero_zero_int ) )
% 6.92/7.25 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_less_power_eq
% 6.92/7.25 thf(fact_6575_take__bit__Suc__bit1,axiom,
% 6.92/7.25 ! [N2: nat,K2: num] :
% 6.92/7.25 ( ( bit_se569199155075624693atural @ ( suc @ N2 ) @ ( numera5444537566228673987atural @ ( bit1 @ K2 ) ) )
% 6.92/7.25 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N2 @ ( numera5444537566228673987atural @ K2 ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_Suc_bit1
% 6.92/7.25 thf(fact_6576_take__bit__Suc__bit1,axiom,
% 6.92/7.25 ! [N2: nat,K2: num] :
% 6.92/7.25 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ ( numera6620942414471956472nteger @ ( bit1 @ K2 ) ) )
% 6.92/7.25 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ K2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_Suc_bit1
% 6.92/7.25 thf(fact_6577_take__bit__Suc__bit1,axiom,
% 6.92/7.25 ! [N2: nat,K2: num] :
% 6.92/7.25 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) )
% 6.92/7.25 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_Suc_bit1
% 6.92/7.25 thf(fact_6578_take__bit__Suc__bit1,axiom,
% 6.92/7.25 ! [N2: nat,K2: num] :
% 6.92/7.25 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit1 @ K2 ) ) )
% 6.92/7.25 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_Suc_bit1
% 6.92/7.25 thf(fact_6579_take__bit__Suc,axiom,
% 6.92/7.25 ! [N2: nat,A: code_integer] :
% 6.92/7.25 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ A )
% 6.92/7.25 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_Suc
% 6.92/7.25 thf(fact_6580_take__bit__Suc,axiom,
% 6.92/7.25 ! [N2: nat,A: code_natural] :
% 6.92/7.25 ( ( bit_se569199155075624693atural @ ( suc @ N2 ) @ A )
% 6.92/7.25 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_Suc
% 6.92/7.25 thf(fact_6581_take__bit__Suc,axiom,
% 6.92/7.25 ! [N2: nat,A: int] :
% 6.92/7.25 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 6.92/7.25 = ( 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 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_Suc
% 6.92/7.25 thf(fact_6582_take__bit__Suc,axiom,
% 6.92/7.25 ! [N2: nat,A: nat] :
% 6.92/7.25 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ A )
% 6.92/7.25 = ( 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 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_Suc
% 6.92/7.25 thf(fact_6583_divmod__step__nat__def,axiom,
% 6.92/7.25 ( unique5026877609467782581ep_nat
% 6.92/7.25 = ( ^ [L2: num] :
% 6.92/7.25 ( produc2626176000494625587at_nat
% 6.92/7.25 @ ^ [Q8: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q8 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q8 ) @ R5 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_step_nat_def
% 6.92/7.25 thf(fact_6584_take__bit__int__less__eq,axiom,
% 6.92/7.25 ! [N2: nat,K2: int] :
% 6.92/7.25 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K2 )
% 6.92/7.25 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) @ ( minus_minus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_int_less_eq
% 6.92/7.25 thf(fact_6585_take__bit__int__greater__eq,axiom,
% 6.92/7.25 ! [K2: int,N2: nat] :
% 6.92/7.25 ( ( ord_less_int @ K2 @ zero_zero_int )
% 6.92/7.25 => ( ord_less_eq_int @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_int_greater_eq
% 6.92/7.25 thf(fact_6586_even__mask__div__iff_H,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( 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 ) ) )
% 6.92/7.25 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_mask_div_iff'
% 6.92/7.25 thf(fact_6587_even__mask__div__iff_H,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( 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 ) ) )
% 6.92/7.25 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_mask_div_iff'
% 6.92/7.25 thf(fact_6588_even__mask__div__iff_H,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( 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 ) ) )
% 6.92/7.25 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_mask_div_iff'
% 6.92/7.25 thf(fact_6589_even__mask__div__iff_H,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( 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 ) ) )
% 6.92/7.25 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_mask_div_iff'
% 6.92/7.25 thf(fact_6590_signed__take__bit__eq__take__bit__shift,axiom,
% 6.92/7.25 ( bit_ri631733984087533419it_int
% 6.92/7.25 = ( ^ [N: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % signed_take_bit_eq_take_bit_shift
% 6.92/7.25 thf(fact_6591_power__le__zero__eq,axiom,
% 6.92/7.25 ! [A: code_integer,N2: nat] :
% 6.92/7.25 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ zero_z3403309356797280102nteger )
% 6.92/7.25 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 6.92/7.25 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( A = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_le_zero_eq
% 6.92/7.25 thf(fact_6592_power__le__zero__eq,axiom,
% 6.92/7.25 ! [A: rat,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 6.92/7.25 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 6.92/7.25 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( A = zero_zero_rat ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_le_zero_eq
% 6.92/7.25 thf(fact_6593_power__le__zero__eq,axiom,
% 6.92/7.25 ! [A: int,N2: nat] :
% 6.92/7.25 ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 6.92/7.25 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.25 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 6.92/7.25 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 & ( A = zero_zero_int ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % power_le_zero_eq
% 6.92/7.25 thf(fact_6594_even__mod__4__div__2,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 6.92/7.25 = ( suc @ zero_zero_nat ) )
% 6.92/7.25 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_mod_4_div_2
% 6.92/7.25 thf(fact_6595_take__bit__numeral__bit1,axiom,
% 6.92/7.25 ! [L: num,K2: num] :
% 6.92/7.25 ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ L ) @ ( numera5444537566228673987atural @ ( bit1 @ K2 ) ) )
% 6.92/7.25 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( pred_numeral @ L ) @ ( numera5444537566228673987atural @ K2 ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_numeral_bit1
% 6.92/7.25 thf(fact_6596_take__bit__numeral__bit1,axiom,
% 6.92/7.25 ! [L: num,K2: num] :
% 6.92/7.25 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ ( numera6620942414471956472nteger @ ( bit1 @ K2 ) ) )
% 6.92/7.25 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( pred_numeral @ L ) @ ( numera6620942414471956472nteger @ K2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_numeral_bit1
% 6.92/7.25 thf(fact_6597_take__bit__numeral__bit1,axiom,
% 6.92/7.25 ! [L: num,K2: num] :
% 6.92/7.25 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) )
% 6.92/7.25 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_numeral_bit1
% 6.92/7.25 thf(fact_6598_take__bit__numeral__bit1,axiom,
% 6.92/7.25 ! [L: num,K2: num] :
% 6.92/7.25 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K2 ) ) )
% 6.92/7.25 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_numeral_bit1
% 6.92/7.25 thf(fact_6599_divmod__step__int__def,axiom,
% 6.92/7.25 ( unique5024387138958732305ep_int
% 6.92/7.25 = ( ^ [L2: num] :
% 6.92/7.25 ( produc4245557441103728435nt_int
% 6.92/7.25 @ ^ [Q8: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q8 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q8 ) @ R5 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_step_int_def
% 6.92/7.25 thf(fact_6600_take__bit__minus__small__eq,axiom,
% 6.92/7.25 ! [K2: int,N2: nat] :
% 6.92/7.25 ( ( ord_less_int @ zero_zero_int @ K2 )
% 6.92/7.25 => ( ( ord_less_eq_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 => ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K2 ) )
% 6.92/7.25 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_minus_small_eq
% 6.92/7.25 thf(fact_6601_even__mask__div__iff,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( 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 ) ) )
% 6.92/7.25 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 = zero_z3403309356797280102nteger )
% 6.92/7.25 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_mask_div_iff
% 6.92/7.25 thf(fact_6602_even__mask__div__iff,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( 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 ) ) )
% 6.92/7.25 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 = zero_zero_nat )
% 6.92/7.25 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_mask_div_iff
% 6.92/7.25 thf(fact_6603_even__mask__div__iff,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( 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 ) ) )
% 6.92/7.25 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 = zero_zero_int )
% 6.92/7.25 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_mask_div_iff
% 6.92/7.25 thf(fact_6604_even__mask__div__iff,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( 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 ) ) )
% 6.92/7.25 = ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 = zero_z2226904508553997617atural )
% 6.92/7.25 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_mask_div_iff
% 6.92/7.25 thf(fact_6605_odd__mod__4__div__2,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 6.92/7.25 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 6.92/7.25 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % odd_mod_4_div_2
% 6.92/7.25 thf(fact_6606_take__bit__Suc__minus__bit1,axiom,
% 6.92/7.25 ! [N2: nat,K2: num] :
% 6.92/7.25 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 6.92/7.25 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K2 ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_Suc_minus_bit1
% 6.92/7.25 thf(fact_6607_even__mult__exp__div__exp__iff,axiom,
% 6.92/7.25 ! [A: code_integer,M: nat,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 6.92/7.25 = ( ( ord_less_nat @ N2 @ M )
% 6.92/7.25 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 = zero_z3403309356797280102nteger )
% 6.92/7.25 | ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.25 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_mult_exp_div_exp_iff
% 6.92/7.25 thf(fact_6608_even__mult__exp__div__exp__iff,axiom,
% 6.92/7.25 ! [A: nat,M: nat,N2: nat] :
% 6.92/7.25 ( ( 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 ) ) )
% 6.92/7.25 = ( ( ord_less_nat @ N2 @ M )
% 6.92/7.25 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 = zero_zero_nat )
% 6.92/7.25 | ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.25 & ( 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 ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_mult_exp_div_exp_iff
% 6.92/7.25 thf(fact_6609_even__mult__exp__div__exp__iff,axiom,
% 6.92/7.25 ! [A: int,M: nat,N2: nat] :
% 6.92/7.25 ( ( 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 ) ) )
% 6.92/7.25 = ( ( ord_less_nat @ N2 @ M )
% 6.92/7.25 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 = zero_zero_int )
% 6.92/7.25 | ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.25 & ( 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 ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_mult_exp_div_exp_iff
% 6.92/7.25 thf(fact_6610_even__mult__exp__div__exp__iff,axiom,
% 6.92/7.25 ! [A: code_natural,M: nat,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) )
% 6.92/7.25 = ( ( ord_less_nat @ N2 @ M )
% 6.92/7.25 | ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 )
% 6.92/7.25 = zero_z2226904508553997617atural )
% 6.92/7.25 | ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.25 & ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % even_mult_exp_div_exp_iff
% 6.92/7.25 thf(fact_6611_divmod__step__def,axiom,
% 6.92/7.25 ( unique5026877609467782581ep_nat
% 6.92/7.25 = ( ^ [L2: num] :
% 6.92/7.25 ( produc2626176000494625587at_nat
% 6.92/7.25 @ ^ [Q8: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q8 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q8 ) @ R5 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_step_def
% 6.92/7.25 thf(fact_6612_divmod__step__def,axiom,
% 6.92/7.25 ( unique5024387138958732305ep_int
% 6.92/7.25 = ( ^ [L2: num] :
% 6.92/7.25 ( produc4245557441103728435nt_int
% 6.92/7.25 @ ^ [Q8: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q8 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q8 ) @ R5 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_step_def
% 6.92/7.25 thf(fact_6613_divmod__step__def,axiom,
% 6.92/7.25 ( unique4921790084139445826nteger
% 6.92/7.25 = ( ^ [L2: num] :
% 6.92/7.25 ( produc6916734918728496179nteger
% 6.92/7.25 @ ^ [Q8: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q8 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q8 ) @ R5 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_step_def
% 6.92/7.25 thf(fact_6614_take__bit__numeral__minus__numeral__int,axiom,
% 6.92/7.25 ! [M: num,N2: num] :
% 6.92/7.25 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.92/7.25 = ( case_option_int_num @ zero_zero_int
% 6.92/7.25 @ ^ [Q8: 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 @ Q8 ) ) )
% 6.92/7.25 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_numeral_minus_numeral_int
% 6.92/7.25 thf(fact_6615_divmod__nat__if,axiom,
% 6.92/7.25 ( divmod_nat
% 6.92/7.25 = ( ^ [M3: nat,N: nat] :
% 6.92/7.25 ( if_Pro6206227464963214023at_nat
% 6.92/7.25 @ ( ( N = zero_zero_nat )
% 6.92/7.25 | ( ord_less_nat @ M3 @ N ) )
% 6.92/7.25 @ ( product_Pair_nat_nat @ zero_zero_nat @ M3 )
% 6.92/7.25 @ ( produc2626176000494625587at_nat
% 6.92/7.25 @ ^ [Q8: nat] : ( product_Pair_nat_nat @ ( suc @ Q8 ) )
% 6.92/7.25 @ ( divmod_nat @ ( minus_minus_nat @ M3 @ N ) @ N ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divmod_nat_if
% 6.92/7.25 thf(fact_6616_flip__bit__0,axiom,
% 6.92/7.25 ! [A: code_natural] :
% 6.92/7.25 ( ( bit_se168947363167071951atural @ zero_zero_nat @ A )
% 6.92/7.25 = ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % flip_bit_0
% 6.92/7.25 thf(fact_6617_flip__bit__0,axiom,
% 6.92/7.25 ! [A: nat] :
% 6.92/7.25 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 6.92/7.25 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % flip_bit_0
% 6.92/7.25 thf(fact_6618_flip__bit__0,axiom,
% 6.92/7.25 ! [A: code_integer] :
% 6.92/7.25 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 6.92/7.25 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % flip_bit_0
% 6.92/7.25 thf(fact_6619_flip__bit__0,axiom,
% 6.92/7.25 ! [A: int] :
% 6.92/7.25 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 6.92/7.25 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % flip_bit_0
% 6.92/7.25 thf(fact_6620_num_Osize__gen_I3_J,axiom,
% 6.92/7.25 ! [X32: num] :
% 6.92/7.25 ( ( size_num @ ( bit1 @ X32 ) )
% 6.92/7.25 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % num.size_gen(3)
% 6.92/7.25 thf(fact_6621_num_Osize__gen_I2_J,axiom,
% 6.92/7.25 ! [X2: num] :
% 6.92/7.25 ( ( size_num @ ( bit0 @ X2 ) )
% 6.92/7.25 = ( plus_plus_nat @ ( size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % num.size_gen(2)
% 6.92/7.25 thf(fact_6622_and__int__unfold,axiom,
% 6.92/7.25 ( bit_se725231765392027082nd_int
% 6.92/7.25 = ( ^ [K3: int,L2: int] :
% 6.92/7.25 ( if_int
% 6.92/7.25 @ ( ( K3 = zero_zero_int )
% 6.92/7.25 | ( L2 = zero_zero_int ) )
% 6.92/7.25 @ zero_zero_int
% 6.92/7.25 @ ( if_int
% 6.92/7.25 @ ( K3
% 6.92/7.25 = ( uminus_uminus_int @ one_one_int ) )
% 6.92/7.25 @ L2
% 6.92/7.25 @ ( if_int
% 6.92/7.25 @ ( L2
% 6.92/7.25 = ( uminus_uminus_int @ one_one_int ) )
% 6.92/7.25 @ K3
% 6.92/7.25 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % and_int_unfold
% 6.92/7.25 thf(fact_6623_case__prodI2,axiom,
% 6.92/7.25 ! [P3: produc3925858234332021118et_nat,C2: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 6.92/7.25 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc5001842942810119800et_nat @ A3 @ B3 ) )
% 6.92/7.25 => ( C2 @ A3 @ B3 ) )
% 6.92/7.25 => ( produc1437786849005270451_nat_o @ C2 @ P3 ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodI2
% 6.92/7.25 thf(fact_6624_case__prodI2,axiom,
% 6.92/7.25 ! [P3: produc2732055786443039994et_nat,C2: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 6.92/7.25 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc2245416461498447860et_nat @ A3 @ B3 ) )
% 6.92/7.25 => ( C2 @ A3 @ B3 ) )
% 6.92/7.25 => ( produc838355143741117751_nat_o @ C2 @ P3 ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodI2
% 6.92/7.25 thf(fact_6625_case__prodI2,axiom,
% 6.92/7.25 ! [P3: produc7388388658123137530it_nat,C2: b > produc6653097349344004940it_nat > $o] :
% 6.92/7.25 ( ! [A3: b,B3: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc4082563078715348724it_nat @ A3 @ B3 ) )
% 6.92/7.25 => ( C2 @ A3 @ B3 ) )
% 6.92/7.25 => ( produc3971132677695353399_nat_o @ C2 @ P3 ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodI2
% 6.92/7.25 thf(fact_6626_case__prodI2,axiom,
% 6.92/7.25 ! [P3: produc3260487557148687353it_nat,C2: a > produc6653097349344004940it_nat > $o] :
% 6.92/7.25 ( ! [A3: a,B3: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc9178034014595674355it_nat @ A3 @ B3 ) )
% 6.92/7.25 => ( C2 @ A3 @ B3 ) )
% 6.92/7.25 => ( produc8860486935419594360_nat_o @ C2 @ P3 ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodI2
% 6.92/7.25 thf(fact_6627_case__prodI2,axiom,
% 6.92/7.25 ! [P3: product_prod_int_int,C2: int > int > $o] :
% 6.92/7.25 ( ! [A3: int,B3: int] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( product_Pair_int_int @ A3 @ B3 ) )
% 6.92/7.25 => ( C2 @ A3 @ B3 ) )
% 6.92/7.25 => ( produc4947309494688390418_int_o @ C2 @ P3 ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodI2
% 6.92/7.25 thf(fact_6628_case__prodI,axiom,
% 6.92/7.25 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 6.92/7.25 ( ( F @ A @ B )
% 6.92/7.25 => ( produc1437786849005270451_nat_o @ F @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodI
% 6.92/7.25 thf(fact_6629_case__prodI,axiom,
% 6.92/7.25 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 6.92/7.25 ( ( F @ A @ B )
% 6.92/7.25 => ( produc838355143741117751_nat_o @ F @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodI
% 6.92/7.25 thf(fact_6630_case__prodI,axiom,
% 6.92/7.25 ! [F: b > produc6653097349344004940it_nat > $o,A: b,B: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( F @ A @ B )
% 6.92/7.25 => ( produc3971132677695353399_nat_o @ F @ ( produc4082563078715348724it_nat @ A @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodI
% 6.92/7.25 thf(fact_6631_case__prodI,axiom,
% 6.92/7.25 ! [F: a > produc6653097349344004940it_nat > $o,A: a,B: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( F @ A @ B )
% 6.92/7.25 => ( produc8860486935419594360_nat_o @ F @ ( produc9178034014595674355it_nat @ A @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodI
% 6.92/7.25 thf(fact_6632_case__prodI,axiom,
% 6.92/7.25 ! [F: int > int > $o,A: int,B: int] :
% 6.92/7.25 ( ( F @ A @ B )
% 6.92/7.25 => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodI
% 6.92/7.25 thf(fact_6633_mem__case__prodI2,axiom,
% 6.92/7.25 ! [P3: product_prod_int_int,Z3: $o,C2: int > int > set_o] :
% 6.92/7.25 ( ! [A3: int,B3: int] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( product_Pair_int_int @ A3 @ B3 ) )
% 6.92/7.25 => ( member_o @ Z3 @ ( C2 @ A3 @ B3 ) ) )
% 6.92/7.25 => ( member_o @ Z3 @ ( produc4257766111578684402_set_o @ C2 @ P3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI2
% 6.92/7.25 thf(fact_6634_mem__case__prodI2,axiom,
% 6.92/7.25 ! [P3: product_prod_int_int,Z3: nat,C2: int > int > set_nat] :
% 6.92/7.25 ( ! [A3: int,B3: int] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( product_Pair_int_int @ A3 @ B3 ) )
% 6.92/7.25 => ( member_nat @ Z3 @ ( C2 @ A3 @ B3 ) ) )
% 6.92/7.25 => ( member_nat @ Z3 @ ( produc4251311855443802252et_nat @ C2 @ P3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI2
% 6.92/7.25 thf(fact_6635_mem__case__prodI2,axiom,
% 6.92/7.25 ! [P3: product_prod_int_int,Z3: int,C2: int > int > set_int] :
% 6.92/7.25 ( ! [A3: int,B3: int] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( product_Pair_int_int @ A3 @ B3 ) )
% 6.92/7.25 => ( member_int @ Z3 @ ( C2 @ A3 @ B3 ) ) )
% 6.92/7.25 => ( member_int @ Z3 @ ( produc73460835934605544et_int @ C2 @ P3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI2
% 6.92/7.25 thf(fact_6636_mem__case__prodI2,axiom,
% 6.92/7.25 ! [P3: product_prod_int_int,Z3: set_nat,C2: int > int > set_set_nat] :
% 6.92/7.25 ( ! [A3: int,B3: int] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( product_Pair_int_int @ A3 @ B3 ) )
% 6.92/7.25 => ( member_set_nat @ Z3 @ ( C2 @ A3 @ B3 ) ) )
% 6.92/7.25 => ( member_set_nat @ Z3 @ ( produc5233655623923918146et_nat @ C2 @ P3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI2
% 6.92/7.25 thf(fact_6637_mem__case__prodI2,axiom,
% 6.92/7.25 ! [P3: product_prod_int_int,Z3: set_Pr958786334691620121nt_int,C2: int > int > set_se6260736226359567993nt_int] :
% 6.92/7.25 ( ! [A3: int,B3: int] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( product_Pair_int_int @ A3 @ B3 ) )
% 6.92/7.25 => ( member2340774599025711042nt_int @ Z3 @ ( C2 @ A3 @ B3 ) ) )
% 6.92/7.25 => ( member2340774599025711042nt_int @ Z3 @ ( produc7771776839612048883nt_int @ C2 @ P3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI2
% 6.92/7.25 thf(fact_6638_mem__case__prodI2,axiom,
% 6.92/7.25 ! [P3: produc7388388658123137530it_nat,Z3: $o,C2: b > produc6653097349344004940it_nat > set_o] :
% 6.92/7.25 ( ! [A3: b,B3: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc4082563078715348724it_nat @ A3 @ B3 ) )
% 6.92/7.25 => ( member_o @ Z3 @ ( C2 @ A3 @ B3 ) ) )
% 6.92/7.25 => ( member_o @ Z3 @ ( produc8188766211626073367_set_o @ C2 @ P3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI2
% 6.92/7.25 thf(fact_6639_mem__case__prodI2,axiom,
% 6.92/7.25 ! [P3: produc7388388658123137530it_nat,Z3: nat,C2: b > produc6653097349344004940it_nat > set_nat] :
% 6.92/7.25 ( ! [A3: b,B3: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc4082563078715348724it_nat @ A3 @ B3 ) )
% 6.92/7.25 => ( member_nat @ Z3 @ ( C2 @ A3 @ B3 ) ) )
% 6.92/7.25 => ( member_nat @ Z3 @ ( produc8058763169506871975et_nat @ C2 @ P3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI2
% 6.92/7.25 thf(fact_6640_mem__case__prodI2,axiom,
% 6.92/7.25 ! [P3: produc7388388658123137530it_nat,Z3: int,C2: b > produc6653097349344004940it_nat > set_int] :
% 6.92/7.25 ( ! [A3: b,B3: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc4082563078715348724it_nat @ A3 @ B3 ) )
% 6.92/7.25 => ( member_int @ Z3 @ ( C2 @ A3 @ B3 ) ) )
% 6.92/7.25 => ( member_int @ Z3 @ ( produc3880912149997675267et_int @ C2 @ P3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI2
% 6.92/7.25 thf(fact_6641_mem__case__prodI2,axiom,
% 6.92/7.25 ! [P3: produc3260487557148687353it_nat,Z3: $o,C2: a > produc6653097349344004940it_nat > set_o] :
% 6.92/7.25 ( ! [A3: a,B3: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc9178034014595674355it_nat @ A3 @ B3 ) )
% 6.92/7.25 => ( member_o @ Z3 @ ( C2 @ A3 @ B3 ) ) )
% 6.92/7.25 => ( member_o @ Z3 @ ( produc5350075035600711000_set_o @ C2 @ P3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI2
% 6.92/7.25 thf(fact_6642_mem__case__prodI2,axiom,
% 6.92/7.25 ! [P3: produc3260487557148687353it_nat,Z3: nat,C2: a > produc6653097349344004940it_nat > set_nat] :
% 6.92/7.25 ( ! [A3: a,B3: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc9178034014595674355it_nat @ A3 @ B3 ) )
% 6.92/7.25 => ( member_nat @ Z3 @ ( C2 @ A3 @ B3 ) ) )
% 6.92/7.25 => ( member_nat @ Z3 @ ( produc7315013382793309350et_nat @ C2 @ P3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI2
% 6.92/7.25 thf(fact_6643_mem__case__prodI,axiom,
% 6.92/7.25 ! [Z3: $o,C2: int > int > set_o,A: int,B: int] :
% 6.92/7.25 ( ( member_o @ Z3 @ ( C2 @ A @ B ) )
% 6.92/7.25 => ( member_o @ Z3 @ ( produc4257766111578684402_set_o @ C2 @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI
% 6.92/7.25 thf(fact_6644_mem__case__prodI,axiom,
% 6.92/7.25 ! [Z3: nat,C2: int > int > set_nat,A: int,B: int] :
% 6.92/7.25 ( ( member_nat @ Z3 @ ( C2 @ A @ B ) )
% 6.92/7.25 => ( member_nat @ Z3 @ ( produc4251311855443802252et_nat @ C2 @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI
% 6.92/7.25 thf(fact_6645_mem__case__prodI,axiom,
% 6.92/7.25 ! [Z3: int,C2: int > int > set_int,A: int,B: int] :
% 6.92/7.25 ( ( member_int @ Z3 @ ( C2 @ A @ B ) )
% 6.92/7.25 => ( member_int @ Z3 @ ( produc73460835934605544et_int @ C2 @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI
% 6.92/7.25 thf(fact_6646_mem__case__prodI,axiom,
% 6.92/7.25 ! [Z3: set_nat,C2: int > int > set_set_nat,A: int,B: int] :
% 6.92/7.25 ( ( member_set_nat @ Z3 @ ( C2 @ A @ B ) )
% 6.92/7.25 => ( member_set_nat @ Z3 @ ( produc5233655623923918146et_nat @ C2 @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI
% 6.92/7.25 thf(fact_6647_mem__case__prodI,axiom,
% 6.92/7.25 ! [Z3: set_Pr958786334691620121nt_int,C2: int > int > set_se6260736226359567993nt_int,A: int,B: int] :
% 6.92/7.25 ( ( member2340774599025711042nt_int @ Z3 @ ( C2 @ A @ B ) )
% 6.92/7.25 => ( member2340774599025711042nt_int @ Z3 @ ( produc7771776839612048883nt_int @ C2 @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI
% 6.92/7.25 thf(fact_6648_mem__case__prodI,axiom,
% 6.92/7.25 ! [Z3: $o,C2: b > produc6653097349344004940it_nat > set_o,A: b,B: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( member_o @ Z3 @ ( C2 @ A @ B ) )
% 6.92/7.25 => ( member_o @ Z3 @ ( produc8188766211626073367_set_o @ C2 @ ( produc4082563078715348724it_nat @ A @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI
% 6.92/7.25 thf(fact_6649_mem__case__prodI,axiom,
% 6.92/7.25 ! [Z3: nat,C2: b > produc6653097349344004940it_nat > set_nat,A: b,B: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( member_nat @ Z3 @ ( C2 @ A @ B ) )
% 6.92/7.25 => ( member_nat @ Z3 @ ( produc8058763169506871975et_nat @ C2 @ ( produc4082563078715348724it_nat @ A @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI
% 6.92/7.25 thf(fact_6650_mem__case__prodI,axiom,
% 6.92/7.25 ! [Z3: int,C2: b > produc6653097349344004940it_nat > set_int,A: b,B: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( member_int @ Z3 @ ( C2 @ A @ B ) )
% 6.92/7.25 => ( member_int @ Z3 @ ( produc3880912149997675267et_int @ C2 @ ( produc4082563078715348724it_nat @ A @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI
% 6.92/7.25 thf(fact_6651_mem__case__prodI,axiom,
% 6.92/7.25 ! [Z3: $o,C2: a > produc6653097349344004940it_nat > set_o,A: a,B: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( member_o @ Z3 @ ( C2 @ A @ B ) )
% 6.92/7.25 => ( member_o @ Z3 @ ( produc5350075035600711000_set_o @ C2 @ ( produc9178034014595674355it_nat @ A @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI
% 6.92/7.25 thf(fact_6652_mem__case__prodI,axiom,
% 6.92/7.25 ! [Z3: nat,C2: a > produc6653097349344004940it_nat > set_nat,A: a,B: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( member_nat @ Z3 @ ( C2 @ A @ B ) )
% 6.92/7.25 => ( member_nat @ Z3 @ ( produc7315013382793309350et_nat @ C2 @ ( produc9178034014595674355it_nat @ A @ B ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodI
% 6.92/7.25 thf(fact_6653_case__prodI2_H,axiom,
% 6.92/7.25 ! [P3: product_prod_nat_nat,C2: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 6.92/7.25 ( ! [A3: nat,B3: nat] :
% 6.92/7.25 ( ( ( product_Pair_nat_nat @ A3 @ B3 )
% 6.92/7.25 = P3 )
% 6.92/7.25 => ( C2 @ A3 @ B3 @ X ) )
% 6.92/7.25 => ( produc8739625826339149834_nat_o @ C2 @ P3 @ X ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodI2'
% 6.92/7.25 thf(fact_6654_of__bool__less__eq__iff,axiom,
% 6.92/7.25 ! [P2: $o,Q2: $o] :
% 6.92/7.25 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ ( zero_n2052037380579107095ol_rat @ Q2 ) )
% 6.92/7.25 = ( P2
% 6.92/7.25 => Q2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_eq_iff
% 6.92/7.25 thf(fact_6655_of__bool__less__eq__iff,axiom,
% 6.92/7.25 ! [P2: $o,Q2: $o] :
% 6.92/7.25 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 6.92/7.25 = ( P2
% 6.92/7.25 => Q2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_eq_iff
% 6.92/7.25 thf(fact_6656_of__bool__less__eq__iff,axiom,
% 6.92/7.25 ! [P2: $o,Q2: $o] :
% 6.92/7.25 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ ( zero_n2684676970156552555ol_int @ Q2 ) )
% 6.92/7.25 = ( P2
% 6.92/7.25 => Q2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_eq_iff
% 6.92/7.25 thf(fact_6657_of__bool__less__eq__iff,axiom,
% 6.92/7.25 ! [P2: $o,Q2: $o] :
% 6.92/7.25 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P2 ) @ ( zero_n356916108424825756nteger @ Q2 ) )
% 6.92/7.25 = ( P2
% 6.92/7.25 => Q2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_eq_iff
% 6.92/7.25 thf(fact_6658_of__bool__less__iff,axiom,
% 6.92/7.25 ! [P2: $o,Q2: $o] :
% 6.92/7.25 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ ( zero_n2052037380579107095ol_rat @ Q2 ) )
% 6.92/7.25 = ( ~ P2
% 6.92/7.25 & Q2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_iff
% 6.92/7.25 thf(fact_6659_of__bool__less__iff,axiom,
% 6.92/7.25 ! [P2: $o,Q2: $o] :
% 6.92/7.25 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 6.92/7.25 = ( ~ P2
% 6.92/7.25 & Q2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_iff
% 6.92/7.25 thf(fact_6660_of__bool__less__iff,axiom,
% 6.92/7.25 ! [P2: $o,Q2: $o] :
% 6.92/7.25 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ ( zero_n2684676970156552555ol_int @ Q2 ) )
% 6.92/7.25 = ( ~ P2
% 6.92/7.25 & Q2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_iff
% 6.92/7.25 thf(fact_6661_of__bool__less__iff,axiom,
% 6.92/7.25 ! [P2: $o,Q2: $o] :
% 6.92/7.25 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P2 ) @ ( zero_n356916108424825756nteger @ Q2 ) )
% 6.92/7.25 = ( ~ P2
% 6.92/7.25 & Q2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_iff
% 6.92/7.25 thf(fact_6662_of__nat__of__bool,axiom,
% 6.92/7.25 ! [P2: $o] :
% 6.92/7.25 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 6.92/7.25 = ( zero_n2687167440665602831ol_nat @ P2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % of_nat_of_bool
% 6.92/7.25 thf(fact_6663_of__nat__of__bool,axiom,
% 6.92/7.25 ! [P2: $o] :
% 6.92/7.25 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 6.92/7.25 = ( zero_n2684676970156552555ol_int @ P2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % of_nat_of_bool
% 6.92/7.25 thf(fact_6664_of__nat__of__bool,axiom,
% 6.92/7.25 ! [P2: $o] :
% 6.92/7.25 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 6.92/7.25 = ( zero_n356916108424825756nteger @ P2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % of_nat_of_bool
% 6.92/7.25 thf(fact_6665_zero__less__of__bool__iff,axiom,
% 6.92/7.25 ! [P2: $o] :
% 6.92/7.25 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 6.92/7.25 = P2 ) ).
% 6.92/7.25
% 6.92/7.25 % zero_less_of_bool_iff
% 6.92/7.25 thf(fact_6666_zero__less__of__bool__iff,axiom,
% 6.92/7.25 ! [P2: $o] :
% 6.92/7.25 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 6.92/7.25 = P2 ) ).
% 6.92/7.25
% 6.92/7.25 % zero_less_of_bool_iff
% 6.92/7.25 thf(fact_6667_zero__less__of__bool__iff,axiom,
% 6.92/7.25 ! [P2: $o] :
% 6.92/7.25 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 6.92/7.25 = P2 ) ).
% 6.92/7.25
% 6.92/7.25 % zero_less_of_bool_iff
% 6.92/7.25 thf(fact_6668_zero__less__of__bool__iff,axiom,
% 6.92/7.25 ! [P2: $o] :
% 6.92/7.25 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P2 ) )
% 6.92/7.25 = P2 ) ).
% 6.92/7.25
% 6.92/7.25 % zero_less_of_bool_iff
% 6.92/7.25 thf(fact_6669_of__bool__less__one__iff,axiom,
% 6.92/7.25 ! [P2: $o] :
% 6.92/7.25 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ one_one_rat )
% 6.92/7.25 = ~ P2 ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_one_iff
% 6.92/7.25 thf(fact_6670_of__bool__less__one__iff,axiom,
% 6.92/7.25 ! [P2: $o] :
% 6.92/7.25 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ one_one_nat )
% 6.92/7.25 = ~ P2 ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_one_iff
% 6.92/7.25 thf(fact_6671_of__bool__less__one__iff,axiom,
% 6.92/7.25 ! [P2: $o] :
% 6.92/7.25 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ one_one_int )
% 6.92/7.25 = ~ P2 ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_one_iff
% 6.92/7.25 thf(fact_6672_of__bool__less__one__iff,axiom,
% 6.92/7.25 ! [P2: $o] :
% 6.92/7.25 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P2 ) @ one_one_Code_integer )
% 6.92/7.25 = ~ P2 ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_one_iff
% 6.92/7.25 thf(fact_6673_and__nonnegative__int__iff,axiom,
% 6.92/7.25 ! [K2: int,L: int] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K2 @ L ) )
% 6.92/7.25 = ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.25 | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % and_nonnegative_int_iff
% 6.92/7.25 thf(fact_6674_and__negative__int__iff,axiom,
% 6.92/7.25 ! [K2: int,L: int] :
% 6.92/7.25 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K2 @ L ) @ zero_zero_int )
% 6.92/7.25 = ( ( ord_less_int @ K2 @ zero_zero_int )
% 6.92/7.25 & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % and_negative_int_iff
% 6.92/7.25 thf(fact_6675_take__bit__num__simps_I3_J,axiom,
% 6.92/7.25 ! [N2: nat,M: num] :
% 6.92/7.25 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit0 @ M ) )
% 6.92/7.25 = ( case_o6005452278849405969um_num @ none_num
% 6.92/7.25 @ ^ [Q8: num] : ( some_num @ ( bit0 @ Q8 ) )
% 6.92/7.25 @ ( bit_take_bit_num @ N2 @ M ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_num_simps(3)
% 6.92/7.25 thf(fact_6676_take__bit__of__Suc__0,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( bit_se2925701944663578781it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 6.92/7.25 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_of_Suc_0
% 6.92/7.25 thf(fact_6677_take__bit__num__simps_I4_J,axiom,
% 6.92/7.25 ! [N2: nat,M: num] :
% 6.92/7.25 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit1 @ M ) )
% 6.92/7.25 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_num_simps(4)
% 6.92/7.25 thf(fact_6678_take__bit__num__simps_I6_J,axiom,
% 6.92/7.25 ! [R2: num,M: num] :
% 6.92/7.25 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M ) )
% 6.92/7.25 = ( case_o6005452278849405969um_num @ none_num
% 6.92/7.25 @ ^ [Q8: num] : ( some_num @ ( bit0 @ Q8 ) )
% 6.92/7.25 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_num_simps(6)
% 6.92/7.25 thf(fact_6679_take__bit__of__1,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( bit_se1745604003318907178nteger @ N2 @ one_one_Code_integer )
% 6.92/7.25 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_of_1
% 6.92/7.25 thf(fact_6680_take__bit__of__1,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 6.92/7.25 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_of_1
% 6.92/7.25 thf(fact_6681_take__bit__of__1,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 6.92/7.25 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_of_1
% 6.92/7.25 thf(fact_6682_sgn__of__nat,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( sgn_sgn_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 6.92/7.25 = ( zero_n2052037380579107095ol_rat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % sgn_of_nat
% 6.92/7.25 thf(fact_6683_sgn__of__nat,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( sgn_sgn_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 6.92/7.25 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % sgn_of_nat
% 6.92/7.25 thf(fact_6684_sgn__of__nat,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( sgn_sgn_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 6.92/7.25 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % sgn_of_nat
% 6.92/7.25 thf(fact_6685_take__bit__num__simps_I7_J,axiom,
% 6.92/7.25 ! [R2: num,M: num] :
% 6.92/7.25 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M ) )
% 6.92/7.25 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_num_simps(7)
% 6.92/7.25 thf(fact_6686_take__bit__numeral__numeral,axiom,
% 6.92/7.25 ! [M: num,N2: num] :
% 6.92/7.25 ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ M ) @ ( numera5444537566228673987atural @ N2 ) )
% 6.92/7.25 = ( case_o5621594795226839503al_num @ zero_z2226904508553997617atural @ numera5444537566228673987atural @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_numeral_numeral
% 6.92/7.25 thf(fact_6687_take__bit__numeral__numeral,axiom,
% 6.92/7.25 ! [M: num,N2: num] :
% 6.92/7.25 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 6.92/7.25 = ( case_o356765784539232260er_num @ zero_z3403309356797280102nteger @ numera6620942414471956472nteger @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_numeral_numeral
% 6.92/7.25 thf(fact_6688_take__bit__numeral__numeral,axiom,
% 6.92/7.25 ! [M: num,N2: num] :
% 6.92/7.25 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_int @ N2 ) )
% 6.92/7.25 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_numeral_numeral
% 6.92/7.25 thf(fact_6689_take__bit__numeral__numeral,axiom,
% 6.92/7.25 ! [M: num,N2: num] :
% 6.92/7.25 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 6.92/7.25 = ( case_option_nat_num @ zero_zero_nat @ numeral_numeral_nat @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_numeral_numeral
% 6.92/7.25 thf(fact_6690_and__numerals_I7_J,axiom,
% 6.92/7.25 ! [X: num,Y: num] :
% 6.92/7.25 ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 6.92/7.25 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % and_numerals(7)
% 6.92/7.25 thf(fact_6691_and__numerals_I7_J,axiom,
% 6.92/7.25 ! [X: num,Y: num] :
% 6.92/7.25 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 6.92/7.25 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % and_numerals(7)
% 6.92/7.25 thf(fact_6692_and__numerals_I7_J,axiom,
% 6.92/7.25 ! [X: num,Y: num] :
% 6.92/7.25 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 6.92/7.25 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % and_numerals(7)
% 6.92/7.25 thf(fact_6693_and__numerals_I7_J,axiom,
% 6.92/7.25 ! [X: num,Y: num] :
% 6.92/7.25 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 6.92/7.25 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % and_numerals(7)
% 6.92/7.25 thf(fact_6694_take__bit__of__exp,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( bit_se569199155075624693atural @ M @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_nat @ N2 @ M ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_of_exp
% 6.92/7.25 thf(fact_6695_take__bit__of__exp,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N2 @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_of_exp
% 6.92/7.25 thf(fact_6696_take__bit__of__exp,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_of_exp
% 6.92/7.25 thf(fact_6697_take__bit__of__exp,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_of_exp
% 6.92/7.25 thf(fact_6698_take__bit__of__2,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( bit_se569199155075624693atural @ N2 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_of_2
% 6.92/7.25 thf(fact_6699_take__bit__of__2,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_of_2
% 6.92/7.25 thf(fact_6700_take__bit__of__2,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_of_2
% 6.92/7.25 thf(fact_6701_take__bit__of__2,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.25 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % take_bit_of_2
% 6.92/7.25 thf(fact_6702_one__mod__2__pow__eq,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( zero_n8403883297036319079atural @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % one_mod_2_pow_eq
% 6.92/7.25 thf(fact_6703_one__mod__2__pow__eq,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % one_mod_2_pow_eq
% 6.92/7.25 thf(fact_6704_one__mod__2__pow__eq,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % one_mod_2_pow_eq
% 6.92/7.25 thf(fact_6705_one__mod__2__pow__eq,axiom,
% 6.92/7.25 ! [N2: nat] :
% 6.92/7.25 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % one_mod_2_pow_eq
% 6.92/7.25 thf(fact_6706_same__fst__def,axiom,
% 6.92/7.25 ( same_fst_int_int
% 6.92/7.25 = ( ^ [P5: int > $o,R: int > set_Pr958786334691620121nt_int] :
% 6.92/7.25 ( collec7447955092554649554nt_int
% 6.92/7.25 @ ( produc1676490119946744748_int_o
% 6.92/7.25 @ ( produc1459180154077124618_int_o
% 6.92/7.25 @ ^ [X8: int,Y9: int] :
% 6.92/7.25 ( produc4947309494688390418_int_o
% 6.92/7.25 @ ^ [X4: int,Y4: int] :
% 6.92/7.25 ( ( X8 = X4 )
% 6.92/7.25 & ( P5 @ X4 )
% 6.92/7.25 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y9 @ Y4 ) @ ( R @ X4 ) ) ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % same_fst_def
% 6.92/7.25 thf(fact_6707_same__fst__def,axiom,
% 6.92/7.25 ( same_fst_nat_nat
% 6.92/7.25 = ( ^ [P5: nat > $o,R: nat > set_Pr1261947904930325089at_nat] :
% 6.92/7.25 ( collec7088162979684241874at_nat
% 6.92/7.25 @ ( produc6590410687421337004_nat_o
% 6.92/7.25 @ ( produc8739625826339149834_nat_o
% 6.92/7.25 @ ^ [X8: nat,Y9: nat] :
% 6.92/7.25 ( produc6081775807080527818_nat_o
% 6.92/7.25 @ ^ [X4: nat,Y4: nat] :
% 6.92/7.25 ( ( X8 = X4 )
% 6.92/7.25 & ( P5 @ X4 )
% 6.92/7.25 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y9 @ Y4 ) @ ( R @ X4 ) ) ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % same_fst_def
% 6.92/7.25 thf(fact_6708_dvd__antisym,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( dvd_dvd_nat @ M @ N2 )
% 6.92/7.25 => ( ( dvd_dvd_nat @ N2 @ M )
% 6.92/7.25 => ( M = N2 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % dvd_antisym
% 6.92/7.25 thf(fact_6709_lex__prod__def,axiom,
% 6.92/7.25 ( lex_prod_int_int
% 6.92/7.25 = ( ^ [Ra: set_Pr958786334691620121nt_int,Rb: set_Pr958786334691620121nt_int] :
% 6.92/7.25 ( collec7447955092554649554nt_int
% 6.92/7.25 @ ( produc1676490119946744748_int_o
% 6.92/7.25 @ ( produc1459180154077124618_int_o
% 6.92/7.25 @ ^ [A5: int,B4: int] :
% 6.92/7.25 ( produc4947309494688390418_int_o
% 6.92/7.25 @ ^ [A8: int,B8: int] :
% 6.92/7.25 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A5 @ A8 ) @ Ra )
% 6.92/7.25 | ( ( A5 = A8 )
% 6.92/7.25 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B4 @ B8 ) @ Rb ) ) ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % lex_prod_def
% 6.92/7.25 thf(fact_6710_lex__prod__def,axiom,
% 6.92/7.25 ( lex_prod_nat_nat
% 6.92/7.25 = ( ^ [Ra: set_Pr1261947904930325089at_nat,Rb: set_Pr1261947904930325089at_nat] :
% 6.92/7.25 ( collec7088162979684241874at_nat
% 6.92/7.25 @ ( produc6590410687421337004_nat_o
% 6.92/7.25 @ ( produc8739625826339149834_nat_o
% 6.92/7.25 @ ^ [A5: nat,B4: nat] :
% 6.92/7.25 ( produc6081775807080527818_nat_o
% 6.92/7.25 @ ^ [A8: nat,B8: nat] :
% 6.92/7.25 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A5 @ A8 ) @ Ra )
% 6.92/7.25 | ( ( A5 = A8 )
% 6.92/7.25 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B4 @ B8 ) @ Rb ) ) ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % lex_prod_def
% 6.92/7.25 thf(fact_6711_mem__case__prodE,axiom,
% 6.92/7.25 ! [Z3: $o,C2: int > int > set_o,P3: product_prod_int_int] :
% 6.92/7.25 ( ( member_o @ Z3 @ ( produc4257766111578684402_set_o @ C2 @ P3 ) )
% 6.92/7.25 => ~ ! [X3: int,Y3: int] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( member_o @ Z3 @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodE
% 6.92/7.25 thf(fact_6712_mem__case__prodE,axiom,
% 6.92/7.25 ! [Z3: nat,C2: int > int > set_nat,P3: product_prod_int_int] :
% 6.92/7.25 ( ( member_nat @ Z3 @ ( produc4251311855443802252et_nat @ C2 @ P3 ) )
% 6.92/7.25 => ~ ! [X3: int,Y3: int] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( member_nat @ Z3 @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodE
% 6.92/7.25 thf(fact_6713_mem__case__prodE,axiom,
% 6.92/7.25 ! [Z3: int,C2: int > int > set_int,P3: product_prod_int_int] :
% 6.92/7.25 ( ( member_int @ Z3 @ ( produc73460835934605544et_int @ C2 @ P3 ) )
% 6.92/7.25 => ~ ! [X3: int,Y3: int] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( member_int @ Z3 @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodE
% 6.92/7.25 thf(fact_6714_mem__case__prodE,axiom,
% 6.92/7.25 ! [Z3: set_nat,C2: int > int > set_set_nat,P3: product_prod_int_int] :
% 6.92/7.25 ( ( member_set_nat @ Z3 @ ( produc5233655623923918146et_nat @ C2 @ P3 ) )
% 6.92/7.25 => ~ ! [X3: int,Y3: int] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( member_set_nat @ Z3 @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodE
% 6.92/7.25 thf(fact_6715_mem__case__prodE,axiom,
% 6.92/7.25 ! [Z3: set_Pr958786334691620121nt_int,C2: int > int > set_se6260736226359567993nt_int,P3: product_prod_int_int] :
% 6.92/7.25 ( ( member2340774599025711042nt_int @ Z3 @ ( produc7771776839612048883nt_int @ C2 @ P3 ) )
% 6.92/7.25 => ~ ! [X3: int,Y3: int] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( member2340774599025711042nt_int @ Z3 @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodE
% 6.92/7.25 thf(fact_6716_mem__case__prodE,axiom,
% 6.92/7.25 ! [Z3: $o,C2: b > produc6653097349344004940it_nat > set_o,P3: produc7388388658123137530it_nat] :
% 6.92/7.25 ( ( member_o @ Z3 @ ( produc8188766211626073367_set_o @ C2 @ P3 ) )
% 6.92/7.25 => ~ ! [X3: b,Y3: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc4082563078715348724it_nat @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( member_o @ Z3 @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodE
% 6.92/7.25 thf(fact_6717_mem__case__prodE,axiom,
% 6.92/7.25 ! [Z3: nat,C2: b > produc6653097349344004940it_nat > set_nat,P3: produc7388388658123137530it_nat] :
% 6.92/7.25 ( ( member_nat @ Z3 @ ( produc8058763169506871975et_nat @ C2 @ P3 ) )
% 6.92/7.25 => ~ ! [X3: b,Y3: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc4082563078715348724it_nat @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( member_nat @ Z3 @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodE
% 6.92/7.25 thf(fact_6718_mem__case__prodE,axiom,
% 6.92/7.25 ! [Z3: int,C2: b > produc6653097349344004940it_nat > set_int,P3: produc7388388658123137530it_nat] :
% 6.92/7.25 ( ( member_int @ Z3 @ ( produc3880912149997675267et_int @ C2 @ P3 ) )
% 6.92/7.25 => ~ ! [X3: b,Y3: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc4082563078715348724it_nat @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( member_int @ Z3 @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodE
% 6.92/7.25 thf(fact_6719_mem__case__prodE,axiom,
% 6.92/7.25 ! [Z3: $o,C2: a > produc6653097349344004940it_nat > set_o,P3: produc3260487557148687353it_nat] :
% 6.92/7.25 ( ( member_o @ Z3 @ ( produc5350075035600711000_set_o @ C2 @ P3 ) )
% 6.92/7.25 => ~ ! [X3: a,Y3: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc9178034014595674355it_nat @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( member_o @ Z3 @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodE
% 6.92/7.25 thf(fact_6720_mem__case__prodE,axiom,
% 6.92/7.25 ! [Z3: nat,C2: a > produc6653097349344004940it_nat > set_nat,P3: produc3260487557148687353it_nat] :
% 6.92/7.25 ( ( member_nat @ Z3 @ ( produc7315013382793309350et_nat @ C2 @ P3 ) )
% 6.92/7.25 => ~ ! [X3: a,Y3: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc9178034014595674355it_nat @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( member_nat @ Z3 @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mem_case_prodE
% 6.92/7.25 thf(fact_6721_case__prodE,axiom,
% 6.92/7.25 ! [C2: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,P3: produc3925858234332021118et_nat] :
% 6.92/7.25 ( ( produc1437786849005270451_nat_o @ C2 @ P3 )
% 6.92/7.25 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc5001842942810119800et_nat @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodE
% 6.92/7.25 thf(fact_6722_case__prodE,axiom,
% 6.92/7.25 ! [C2: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,P3: produc2732055786443039994et_nat] :
% 6.92/7.25 ( ( produc838355143741117751_nat_o @ C2 @ P3 )
% 6.92/7.25 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc2245416461498447860et_nat @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodE
% 6.92/7.25 thf(fact_6723_case__prodE,axiom,
% 6.92/7.25 ! [C2: b > produc6653097349344004940it_nat > $o,P3: produc7388388658123137530it_nat] :
% 6.92/7.25 ( ( produc3971132677695353399_nat_o @ C2 @ P3 )
% 6.92/7.25 => ~ ! [X3: b,Y3: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc4082563078715348724it_nat @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodE
% 6.92/7.25 thf(fact_6724_case__prodE,axiom,
% 6.92/7.25 ! [C2: a > produc6653097349344004940it_nat > $o,P3: produc3260487557148687353it_nat] :
% 6.92/7.25 ( ( produc8860486935419594360_nat_o @ C2 @ P3 )
% 6.92/7.25 => ~ ! [X3: a,Y3: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( produc9178034014595674355it_nat @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodE
% 6.92/7.25 thf(fact_6725_case__prodE,axiom,
% 6.92/7.25 ! [C2: int > int > $o,P3: product_prod_int_int] :
% 6.92/7.25 ( ( produc4947309494688390418_int_o @ C2 @ P3 )
% 6.92/7.25 => ~ ! [X3: int,Y3: int] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodE
% 6.92/7.25 thf(fact_6726_case__prodD,axiom,
% 6.92/7.25 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 6.92/7.25 ( ( produc1437786849005270451_nat_o @ F @ ( produc5001842942810119800et_nat @ A @ B ) )
% 6.92/7.25 => ( F @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodD
% 6.92/7.25 thf(fact_6727_case__prodD,axiom,
% 6.92/7.25 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 6.92/7.25 ( ( produc838355143741117751_nat_o @ F @ ( produc2245416461498447860et_nat @ A @ B ) )
% 6.92/7.25 => ( F @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodD
% 6.92/7.25 thf(fact_6728_case__prodD,axiom,
% 6.92/7.25 ! [F: b > produc6653097349344004940it_nat > $o,A: b,B: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( produc3971132677695353399_nat_o @ F @ ( produc4082563078715348724it_nat @ A @ B ) )
% 6.92/7.25 => ( F @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodD
% 6.92/7.25 thf(fact_6729_case__prodD,axiom,
% 6.92/7.25 ! [F: a > produc6653097349344004940it_nat > $o,A: a,B: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( produc8860486935419594360_nat_o @ F @ ( produc9178034014595674355it_nat @ A @ B ) )
% 6.92/7.25 => ( F @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodD
% 6.92/7.25 thf(fact_6730_case__prodD,axiom,
% 6.92/7.25 ! [F: int > int > $o,A: int,B: int] :
% 6.92/7.25 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 6.92/7.25 => ( F @ A @ B ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodD
% 6.92/7.25 thf(fact_6731_case__prodE_H,axiom,
% 6.92/7.25 ! [C2: nat > nat > product_prod_nat_nat > $o,P3: product_prod_nat_nat,Z3: product_prod_nat_nat] :
% 6.92/7.25 ( ( produc8739625826339149834_nat_o @ C2 @ P3 @ Z3 )
% 6.92/7.25 => ~ ! [X3: nat,Y3: nat] :
% 6.92/7.25 ( ( P3
% 6.92/7.25 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 6.92/7.25 => ~ ( C2 @ X3 @ Y3 @ Z3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodE'
% 6.92/7.25 thf(fact_6732_case__prodD_H,axiom,
% 6.92/7.25 ! [R3: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C2: product_prod_nat_nat] :
% 6.92/7.25 ( ( produc8739625826339149834_nat_o @ R3 @ ( product_Pair_nat_nat @ A @ B ) @ C2 )
% 6.92/7.25 => ( R3 @ A @ B @ C2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % case_prodD'
% 6.92/7.25 thf(fact_6733_zero__less__eq__of__bool,axiom,
% 6.92/7.25 ! [P2: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_less_eq_of_bool
% 6.92/7.25 thf(fact_6734_zero__less__eq__of__bool,axiom,
% 6.92/7.25 ! [P2: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_less_eq_of_bool
% 6.92/7.25 thf(fact_6735_zero__less__eq__of__bool,axiom,
% 6.92/7.25 ! [P2: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_less_eq_of_bool
% 6.92/7.25 thf(fact_6736_zero__less__eq__of__bool,axiom,
% 6.92/7.25 ! [P2: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % zero_less_eq_of_bool
% 6.92/7.25 thf(fact_6737_of__bool__less__eq__one,axiom,
% 6.92/7.25 ! [P2: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ one_one_rat ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_eq_one
% 6.92/7.25 thf(fact_6738_of__bool__less__eq__one,axiom,
% 6.92/7.25 ! [P2: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ one_one_nat ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_eq_one
% 6.92/7.25 thf(fact_6739_of__bool__less__eq__one,axiom,
% 6.92/7.25 ! [P2: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ one_one_int ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_eq_one
% 6.92/7.25 thf(fact_6740_of__bool__less__eq__one,axiom,
% 6.92/7.25 ! [P2: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P2 ) @ one_one_Code_integer ) ).
% 6.92/7.25
% 6.92/7.25 % of_bool_less_eq_one
% 6.92/7.25 thf(fact_6741_AND__lower,axiom,
% 6.92/7.25 ! [X: int,Y: int] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.25 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % AND_lower
% 6.92/7.25 thf(fact_6742_AND__upper1,axiom,
% 6.92/7.25 ! [X: int,Y: int] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.25 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ X ) ) ).
% 6.92/7.25
% 6.92/7.25 % AND_upper1
% 6.92/7.25 thf(fact_6743_AND__upper2,axiom,
% 6.92/7.25 ! [Y: int,X: int] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.25 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Y ) ) ).
% 6.92/7.25
% 6.92/7.25 % AND_upper2
% 6.92/7.25 thf(fact_6744_AND__upper1_H,axiom,
% 6.92/7.25 ! [Y: int,Z3: int,Ya: int] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.25 => ( ( ord_less_eq_int @ Y @ Z3 )
% 6.92/7.25 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % AND_upper1'
% 6.92/7.25 thf(fact_6745_AND__upper2_H,axiom,
% 6.92/7.25 ! [Y: int,Z3: int,X: int] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.25 => ( ( ord_less_eq_int @ Y @ Z3 )
% 6.92/7.25 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % AND_upper2'
% 6.92/7.25 thf(fact_6746_Collect__case__prod__mono,axiom,
% 6.92/7.25 ! [A4: int > int > $o,B5: int > int > $o] :
% 6.92/7.25 ( ( ord_le6741204236512500942_int_o @ A4 @ B5 )
% 6.92/7.25 => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A4 ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ B5 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Collect_case_prod_mono
% 6.92/7.25 thf(fact_6747_execute__bind__case,axiom,
% 6.92/7.25 ! [F: heap_Time_Heap_b,G: b > heap_Time_Heap_b,H: heap_e7401611519738050253t_unit] :
% 6.92/7.25 ( ( heap_Time_execute_b @ ( heap_Time_bind_b_b @ F @ G ) @ H )
% 6.92/7.25 = ( case_o5901184372446974929it_nat @ none_P6779099274072355161it_nat
% 6.92/7.25 @ ( produc3931674313442123243it_nat
% 6.92/7.25 @ ^ [X4: b] :
% 6.92/7.25 ( produc6148253707941125437it_nat
% 6.92/7.25 @ ^ [H7: heap_e7401611519738050253t_unit,N: nat] : ( heap_T7616092557645711336rame_b @ N @ ( heap_Time_execute_b @ ( G @ X4 ) @ H7 ) ) ) )
% 6.92/7.25 @ ( heap_Time_execute_b @ F @ H ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % execute_bind_case
% 6.92/7.25 thf(fact_6748_execute__bind__case,axiom,
% 6.92/7.25 ! [F: heap_Time_Heap_a,G: a > heap_Time_Heap_b,H: heap_e7401611519738050253t_unit] :
% 6.92/7.25 ( ( heap_Time_execute_b @ ( heap_Time_bind_a_b @ F @ G ) @ H )
% 6.92/7.25 = ( case_o1773283271472524752it_nat @ none_P6779099274072355161it_nat
% 6.92/7.25 @ ( produc8352694711413002346it_nat
% 6.92/7.25 @ ^ [X4: a] :
% 6.92/7.25 ( produc6148253707941125437it_nat
% 6.92/7.25 @ ^ [H7: heap_e7401611519738050253t_unit,N: nat] : ( heap_T7616092557645711336rame_b @ N @ ( heap_Time_execute_b @ ( G @ X4 ) @ H7 ) ) ) )
% 6.92/7.25 @ ( heap_Time_execute_a @ F @ H ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % execute_bind_case
% 6.92/7.25 thf(fact_6749_execute__bind__case,axiom,
% 6.92/7.25 ! [F: heap_Time_Heap_b,G: b > heap_Time_Heap_a,H: heap_e7401611519738050253t_unit] :
% 6.92/7.25 ( ( heap_Time_execute_a @ ( heap_Time_bind_b_a @ F @ G ) @ H )
% 6.92/7.25 = ( case_o965627003169710416it_nat @ none_P2651198173097904984it_nat
% 6.92/7.25 @ ( produc3428986626803312746it_nat
% 6.92/7.25 @ ^ [X4: b] :
% 6.92/7.25 ( produc5645566021302314940it_nat
% 6.92/7.25 @ ^ [H7: heap_e7401611519738050253t_unit,N: nat] : ( heap_T7616092557645711335rame_a @ N @ ( heap_Time_execute_a @ ( G @ X4 ) @ H7 ) ) ) )
% 6.92/7.25 @ ( heap_Time_execute_b @ F @ H ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % execute_bind_case
% 6.92/7.25 thf(fact_6750_execute__bind__case,axiom,
% 6.92/7.25 ! [F: heap_Time_Heap_a,G: a > heap_Time_Heap_a,H: heap_e7401611519738050253t_unit] :
% 6.92/7.25 ( ( heap_Time_execute_a @ ( heap_Time_bind_a_a @ F @ G ) @ H )
% 6.92/7.25 = ( case_o6061097939050036047it_nat @ none_P2651198173097904984it_nat
% 6.92/7.25 @ ( produc7850007024774191849it_nat
% 6.92/7.25 @ ^ [X4: a] :
% 6.92/7.25 ( produc5645566021302314940it_nat
% 6.92/7.25 @ ^ [H7: heap_e7401611519738050253t_unit,N: nat] : ( heap_T7616092557645711335rame_a @ N @ ( heap_Time_execute_a @ ( G @ X4 ) @ H7 ) ) ) )
% 6.92/7.25 @ ( heap_Time_execute_a @ F @ H ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % execute_bind_case
% 6.92/7.25 thf(fact_6751_map__to__set__def,axiom,
% 6.92/7.25 ( map_to_set_int_int
% 6.92/7.25 = ( ^ [M3: int > option_int] :
% 6.92/7.25 ( collec213857154873943460nt_int
% 6.92/7.25 @ ( produc4947309494688390418_int_o
% 6.92/7.25 @ ^ [K3: int,V2: int] :
% 6.92/7.25 ( ( M3 @ K3 )
% 6.92/7.25 = ( some_int @ V2 ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % map_to_set_def
% 6.92/7.25 thf(fact_6752_and__int__rec,axiom,
% 6.92/7.25 ( bit_se725231765392027082nd_int
% 6.92/7.25 = ( ^ [K3: int,L2: int] :
% 6.92/7.25 ( plus_plus_int
% 6.92/7.25 @ ( zero_n2684676970156552555ol_int
% 6.92/7.25 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 6.92/7.25 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 6.92/7.25 @ ( 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 ) ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % and_int_rec
% 6.92/7.25 thf(fact_6753_AND__upper2_H_H,axiom,
% 6.92/7.25 ! [Y: int,Z3: int,X: int] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.25 => ( ( ord_less_int @ Y @ Z3 )
% 6.92/7.25 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % AND_upper2''
% 6.92/7.25 thf(fact_6754_AND__upper1_H_H,axiom,
% 6.92/7.25 ! [Y: int,Z3: int,Ya: int] :
% 6.92/7.25 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.25 => ( ( ord_less_int @ Y @ Z3 )
% 6.92/7.25 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z3 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % AND_upper1''
% 6.92/7.25 thf(fact_6755_and__less__eq,axiom,
% 6.92/7.25 ! [L: int,K2: int] :
% 6.92/7.25 ( ( ord_less_int @ L @ zero_zero_int )
% 6.92/7.25 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K2 @ L ) @ K2 ) ) ).
% 6.92/7.25
% 6.92/7.25 % and_less_eq
% 6.92/7.25 thf(fact_6756_Heap__Time__Monad_Obind__def,axiom,
% 6.92/7.25 ( heap_Time_bind_b_b
% 6.92/7.25 = ( ^ [F3: heap_Time_Heap_b,G3: b > heap_Time_Heap_b] :
% 6.92/7.25 ( heap_Time_Heap_b2
% 6.92/7.25 @ ^ [H6: heap_e7401611519738050253t_unit] :
% 6.92/7.25 ( case_o5901184372446974929it_nat @ none_P6779099274072355161it_nat
% 6.92/7.25 @ ( produc3931674313442123243it_nat
% 6.92/7.25 @ ^ [R5: b] :
% 6.92/7.25 ( produc6148253707941125437it_nat
% 6.92/7.25 @ ^ [H7: heap_e7401611519738050253t_unit,N: nat] : ( heap_T7616092557645711336rame_b @ N @ ( heap_Time_execute_b @ ( G3 @ R5 ) @ H7 ) ) ) )
% 6.92/7.25 @ ( heap_Time_execute_b @ F3 @ H6 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Heap_Time_Monad.bind_def
% 6.92/7.25 thf(fact_6757_Heap__Time__Monad_Obind__def,axiom,
% 6.92/7.25 ( heap_Time_bind_a_b
% 6.92/7.25 = ( ^ [F3: heap_Time_Heap_a,G3: a > heap_Time_Heap_b] :
% 6.92/7.25 ( heap_Time_Heap_b2
% 6.92/7.25 @ ^ [H6: heap_e7401611519738050253t_unit] :
% 6.92/7.25 ( case_o1773283271472524752it_nat @ none_P6779099274072355161it_nat
% 6.92/7.25 @ ( produc8352694711413002346it_nat
% 6.92/7.25 @ ^ [R5: a] :
% 6.92/7.25 ( produc6148253707941125437it_nat
% 6.92/7.25 @ ^ [H7: heap_e7401611519738050253t_unit,N: nat] : ( heap_T7616092557645711336rame_b @ N @ ( heap_Time_execute_b @ ( G3 @ R5 ) @ H7 ) ) ) )
% 6.92/7.25 @ ( heap_Time_execute_a @ F3 @ H6 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Heap_Time_Monad.bind_def
% 6.92/7.25 thf(fact_6758_Heap__Time__Monad_Obind__def,axiom,
% 6.92/7.25 ( heap_Time_bind_b_a
% 6.92/7.25 = ( ^ [F3: heap_Time_Heap_b,G3: b > heap_Time_Heap_a] :
% 6.92/7.25 ( heap_Time_Heap_a2
% 6.92/7.25 @ ^ [H6: heap_e7401611519738050253t_unit] :
% 6.92/7.25 ( case_o965627003169710416it_nat @ none_P2651198173097904984it_nat
% 6.92/7.25 @ ( produc3428986626803312746it_nat
% 6.92/7.25 @ ^ [R5: b] :
% 6.92/7.25 ( produc5645566021302314940it_nat
% 6.92/7.25 @ ^ [H7: heap_e7401611519738050253t_unit,N: nat] : ( heap_T7616092557645711335rame_a @ N @ ( heap_Time_execute_a @ ( G3 @ R5 ) @ H7 ) ) ) )
% 6.92/7.25 @ ( heap_Time_execute_b @ F3 @ H6 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Heap_Time_Monad.bind_def
% 6.92/7.25 thf(fact_6759_Heap__Time__Monad_Obind__def,axiom,
% 6.92/7.25 ( heap_Time_bind_a_a
% 6.92/7.25 = ( ^ [F3: heap_Time_Heap_a,G3: a > heap_Time_Heap_a] :
% 6.92/7.25 ( heap_Time_Heap_a2
% 6.92/7.25 @ ^ [H6: heap_e7401611519738050253t_unit] :
% 6.92/7.25 ( case_o6061097939050036047it_nat @ none_P2651198173097904984it_nat
% 6.92/7.25 @ ( produc7850007024774191849it_nat
% 6.92/7.25 @ ^ [R5: a] :
% 6.92/7.25 ( produc5645566021302314940it_nat
% 6.92/7.25 @ ^ [H7: heap_e7401611519738050253t_unit,N: nat] : ( heap_T7616092557645711335rame_a @ N @ ( heap_Time_execute_a @ ( G3 @ R5 ) @ H7 ) ) ) )
% 6.92/7.25 @ ( heap_Time_execute_a @ F3 @ H6 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Heap_Time_Monad.bind_def
% 6.92/7.25 thf(fact_6760_Heap__Time__Monad_Obind__def,axiom,
% 6.92/7.25 ( heap_T3413130826733729493t_unit
% 6.92/7.25 = ( ^ [F3: heap_Time_Heap_b,G3: b > heap_T5738788834812785303t_unit] :
% 6.92/7.25 ( heap_T6183433275982383450t_unit
% 6.92/7.25 @ ^ [H6: heap_e7401611519738050253t_unit] :
% 6.92/7.25 ( case_o2632329678403290591it_nat @ none_P9117596204409417319it_nat
% 6.92/7.25 @ ( produc450363836004716793it_nat
% 6.92/7.25 @ ^ [R5: b] :
% 6.92/7.25 ( produc7488178964372371019it_nat
% 6.92/7.25 @ ^ [H7: heap_e7401611519738050253t_unit,N: nat] : ( heap_T3616969660504097270t_unit @ N @ ( heap_T875086893843062177t_unit @ ( G3 @ R5 ) @ H7 ) ) ) )
% 6.92/7.25 @ ( heap_Time_execute_b @ F3 @ H6 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Heap_Time_Monad.bind_def
% 6.92/7.25 thf(fact_6761_Heap__Time__Monad_Obind__def,axiom,
% 6.92/7.25 ( heap_T8685611227969916822t_unit
% 6.92/7.25 = ( ^ [F3: heap_Time_Heap_a,G3: a > heap_T5738788834812785303t_unit] :
% 6.92/7.25 ( heap_T6183433275982383450t_unit
% 6.92/7.25 @ ^ [H6: heap_e7401611519738050253t_unit] :
% 6.92/7.25 ( case_o7727800614283616222it_nat @ none_P9117596204409417319it_nat
% 6.92/7.25 @ ( produc5648861294512138360it_nat
% 6.92/7.25 @ ^ [R5: a] :
% 6.92/7.25 ( produc7488178964372371019it_nat
% 6.92/7.25 @ ^ [H7: heap_e7401611519738050253t_unit,N: nat] : ( heap_T3616969660504097270t_unit @ N @ ( heap_T875086893843062177t_unit @ ( G3 @ R5 ) @ H7 ) ) ) )
% 6.92/7.25 @ ( heap_Time_execute_a @ F3 @ H6 ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Heap_Time_Monad.bind_def
% 6.92/7.25 thf(fact_6762_rel__of__def,axiom,
% 6.92/7.25 ( rel_of4838799251197538391et_nat
% 6.92/7.25 = ( ^ [M3: ( produc3658429121746597890et_nat > $o ) > option936205604648967762et_nat,P5: produc3925858234332021118et_nat > $o] :
% 6.92/7.25 ( collec1402215087704437587et_nat
% 6.92/7.25 @ ( produc1437786849005270451_nat_o
% 6.92/7.25 @ ^ [K3: produc3658429121746597890et_nat > $o,V2: produc3658429121746597890et_nat] :
% 6.92/7.25 ( ( ( M3 @ K3 )
% 6.92/7.25 = ( some_P624177172695371229et_nat @ V2 ) )
% 6.92/7.25 & ( P5 @ ( produc5001842942810119800et_nat @ K3 @ V2 ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % rel_of_def
% 6.92/7.25 thf(fact_6763_rel__of__def,axiom,
% 6.92/7.25 ( rel_of7774016450764239315et_nat
% 6.92/7.25 = ( ^ [M3: ( produc3658429121746597890et_nat > $o ) > option5190343406534369742et_nat,P5: produc2732055786443039994et_nat > $o] :
% 6.92/7.25 ( collec5543584681430388431et_nat
% 6.92/7.25 @ ( produc838355143741117751_nat_o
% 6.92/7.25 @ ^ [K3: produc3658429121746597890et_nat > $o,V2: produc3925858234332021118et_nat] :
% 6.92/7.25 ( ( ( M3 @ K3 )
% 6.92/7.25 = ( some_P750831030444334937et_nat @ V2 ) )
% 6.92/7.25 & ( P5 @ ( produc2245416461498447860et_nat @ K3 @ V2 ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % rel_of_def
% 6.92/7.25 thf(fact_6764_rel__of__def,axiom,
% 6.92/7.25 ( rel_of6889123638293104083it_nat
% 6.92/7.25 = ( ^ [M3: b > option233860712434008220it_nat,P5: produc7388388658123137530it_nat > $o] :
% 6.92/7.25 ( collec8276579174399660751it_nat
% 6.92/7.25 @ ( produc3971132677695353399_nat_o
% 6.92/7.25 @ ^ [K3: b,V2: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( ( M3 @ K3 )
% 6.92/7.25 = ( some_P1054239925786823975it_nat @ V2 ) )
% 6.92/7.25 & ( P5 @ ( produc4082563078715348724it_nat @ K3 @ V2 ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % rel_of_def
% 6.92/7.25 thf(fact_6765_rel__of__def,axiom,
% 6.92/7.25 ( rel_of2761222537318653906it_nat
% 6.92/7.25 = ( ^ [M3: a > option233860712434008220it_nat,P5: produc3260487557148687353it_nat > $o] :
% 6.92/7.25 ( collec4148678073425210574it_nat
% 6.92/7.25 @ ( produc8860486935419594360_nat_o
% 6.92/7.25 @ ^ [K3: a,V2: produc6653097349344004940it_nat] :
% 6.92/7.25 ( ( ( M3 @ K3 )
% 6.92/7.25 = ( some_P1054239925786823975it_nat @ V2 ) )
% 6.92/7.25 & ( P5 @ ( produc9178034014595674355it_nat @ K3 @ V2 ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % rel_of_def
% 6.92/7.25 thf(fact_6766_rel__of__def,axiom,
% 6.92/7.25 ( rel_of_int_int
% 6.92/7.25 = ( ^ [M3: int > option_int,P5: product_prod_int_int > $o] :
% 6.92/7.25 ( collec213857154873943460nt_int
% 6.92/7.25 @ ( produc4947309494688390418_int_o
% 6.92/7.25 @ ^ [K3: int,V2: int] :
% 6.92/7.25 ( ( ( M3 @ K3 )
% 6.92/7.25 = ( some_int @ V2 ) )
% 6.92/7.25 & ( P5 @ ( product_Pair_int_int @ K3 @ V2 ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % rel_of_def
% 6.92/7.25 thf(fact_6767_bits__induct,axiom,
% 6.92/7.25 ! [P2: code_natural > $o,A: code_natural] :
% 6.92/7.25 ( ! [A3: code_natural] :
% 6.92/7.25 ( ( ( divide5121882707175180666atural @ A3 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 6.92/7.25 = A3 )
% 6.92/7.25 => ( P2 @ A3 ) )
% 6.92/7.25 => ( ! [A3: code_natural,B3: $o] :
% 6.92/7.25 ( ( P2 @ A3 )
% 6.92/7.25 => ( ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ B3 ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A3 ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 6.92/7.25 = A3 )
% 6.92/7.25 => ( P2 @ ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ B3 ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 6.92/7.25 => ( P2 @ A ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % bits_induct
% 6.92/7.25 thf(fact_6768_bits__induct,axiom,
% 6.92/7.25 ! [P2: nat > $o,A: nat] :
% 6.92/7.25 ( ! [A3: nat] :
% 6.92/7.25 ( ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.25 = A3 )
% 6.92/7.25 => ( P2 @ A3 ) )
% 6.92/7.25 => ( ! [A3: nat,B3: $o] :
% 6.92/7.25 ( ( P2 @ A3 )
% 6.92/7.25 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.25 = A3 )
% 6.92/7.25 => ( P2 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 6.92/7.25 => ( P2 @ A ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % bits_induct
% 6.92/7.25 thf(fact_6769_bits__induct,axiom,
% 6.92/7.25 ! [P2: int > $o,A: int] :
% 6.92/7.25 ( ! [A3: int] :
% 6.92/7.25 ( ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 6.92/7.25 = A3 )
% 6.92/7.25 => ( P2 @ A3 ) )
% 6.92/7.25 => ( ! [A3: int,B3: $o] :
% 6.92/7.25 ( ( P2 @ A3 )
% 6.92/7.25 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 6.92/7.25 = A3 )
% 6.92/7.25 => ( P2 @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 6.92/7.25 => ( P2 @ A ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % bits_induct
% 6.92/7.25 thf(fact_6770_bits__induct,axiom,
% 6.92/7.25 ! [P2: code_integer > $o,A: code_integer] :
% 6.92/7.25 ( ! [A3: code_integer] :
% 6.92/7.25 ( ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 6.92/7.25 = A3 )
% 6.92/7.25 => ( P2 @ A3 ) )
% 6.92/7.25 => ( ! [A3: code_integer,B3: $o] :
% 6.92/7.25 ( ( P2 @ A3 )
% 6.92/7.25 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 6.92/7.25 = A3 )
% 6.92/7.25 => ( P2 @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 6.92/7.25 => ( P2 @ A ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % bits_induct
% 6.92/7.25 thf(fact_6771_exp__mod__exp,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( modulo8411746178871703098atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_nat @ M @ N2 ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % exp_mod_exp
% 6.92/7.25 thf(fact_6772_exp__mod__exp,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % exp_mod_exp
% 6.92/7.25 thf(fact_6773_exp__mod__exp,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % exp_mod_exp
% 6.92/7.25 thf(fact_6774_exp__mod__exp,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % exp_mod_exp
% 6.92/7.25 thf(fact_6775_exp__div__exp__eq,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( times_2397367101498566445atural
% 6.92/7.25 @ ( zero_n8403883297036319079atural
% 6.92/7.25 @ ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M )
% 6.92/7.25 != zero_z2226904508553997617atural )
% 6.92/7.25 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 6.92/7.25 @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % exp_div_exp_eq
% 6.92/7.25 thf(fact_6776_exp__div__exp__eq,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( times_times_nat
% 6.92/7.25 @ ( zero_n2687167440665602831ol_nat
% 6.92/7.25 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 6.92/7.25 != zero_zero_nat )
% 6.92/7.25 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 6.92/7.25 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % exp_div_exp_eq
% 6.92/7.25 thf(fact_6777_exp__div__exp__eq,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( times_times_int
% 6.92/7.25 @ ( zero_n2684676970156552555ol_int
% 6.92/7.25 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 6.92/7.25 != zero_zero_int )
% 6.92/7.25 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 6.92/7.25 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % exp_div_exp_eq
% 6.92/7.25 thf(fact_6778_exp__div__exp__eq,axiom,
% 6.92/7.25 ! [M: nat,N2: nat] :
% 6.92/7.25 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.25 = ( times_3573771949741848930nteger
% 6.92/7.25 @ ( zero_n356916108424825756nteger
% 6.92/7.25 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 6.92/7.25 != zero_z3403309356797280102nteger )
% 6.92/7.25 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 6.92/7.25 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % exp_div_exp_eq
% 6.92/7.25 thf(fact_6779_divide__int__unfold,axiom,
% 6.92/7.25 ! [L: int,K2: int,N2: nat,M: nat] :
% 6.92/7.25 ( ( ( ( ( sgn_sgn_int @ L )
% 6.92/7.25 = zero_zero_int )
% 6.92/7.25 | ( ( sgn_sgn_int @ K2 )
% 6.92/7.25 = zero_zero_int )
% 6.92/7.25 | ( N2 = zero_zero_nat ) )
% 6.92/7.25 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 6.92/7.25 = zero_zero_int ) )
% 6.92/7.25 & ( ~ ( ( ( sgn_sgn_int @ L )
% 6.92/7.25 = zero_zero_int )
% 6.92/7.25 | ( ( sgn_sgn_int @ K2 )
% 6.92/7.25 = zero_zero_int )
% 6.92/7.25 | ( N2 = zero_zero_nat ) )
% 6.92/7.25 => ( ( ( ( sgn_sgn_int @ K2 )
% 6.92/7.25 = ( sgn_sgn_int @ L ) )
% 6.92/7.25 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 6.92/7.25 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) )
% 6.92/7.25 & ( ( ( sgn_sgn_int @ K2 )
% 6.92/7.25 != ( sgn_sgn_int @ L ) )
% 6.92/7.25 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 6.92/7.25 = ( uminus_uminus_int
% 6.92/7.25 @ ( semiri1314217659103216013at_int
% 6.92/7.25 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N2 )
% 6.92/7.25 @ ( zero_n2687167440665602831ol_nat
% 6.92/7.25 @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divide_int_unfold
% 6.92/7.25 thf(fact_6780_divide__int__def,axiom,
% 6.92/7.25 ( divide_divide_int
% 6.92/7.25 = ( ^ [K3: int,L2: int] :
% 6.92/7.25 ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 6.92/7.25 @ ( if_int
% 6.92/7.25 @ ( ( sgn_sgn_int @ K3 )
% 6.92/7.25 = ( sgn_sgn_int @ L2 ) )
% 6.92/7.25 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 6.92/7.25 @ ( uminus_uminus_int
% 6.92/7.25 @ ( semiri1314217659103216013at_int
% 6.92/7.25 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 6.92/7.25 @ ( zero_n2687167440665602831ol_nat
% 6.92/7.25 @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % divide_int_def
% 6.92/7.25 thf(fact_6781_mlex__eq,axiom,
% 6.92/7.25 ( mlex_prod_int
% 6.92/7.25 = ( ^ [F3: int > nat,R: set_Pr958786334691620121nt_int] :
% 6.92/7.25 ( collec213857154873943460nt_int
% 6.92/7.25 @ ( produc4947309494688390418_int_o
% 6.92/7.25 @ ^ [X4: int,Y4: int] :
% 6.92/7.25 ( ( ord_less_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) )
% 6.92/7.25 | ( ( ord_less_eq_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) )
% 6.92/7.25 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % mlex_eq
% 6.92/7.25 thf(fact_6782_and__minus__numerals_I4_J,axiom,
% 6.92/7.25 ! [M: num,N2: num] :
% 6.92/7.25 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 6.92/7.25 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % and_minus_numerals(4)
% 6.92/7.25 thf(fact_6783_and__minus__numerals_I8_J,axiom,
% 6.92/7.25 ! [N2: num,M: num] :
% 6.92/7.25 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 6.92/7.25 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % and_minus_numerals(8)
% 6.92/7.25 thf(fact_6784_and__int_Osimps,axiom,
% 6.92/7.25 ( bit_se725231765392027082nd_int
% 6.92/7.25 = ( ^ [K3: int,L2: int] :
% 6.92/7.25 ( if_int
% 6.92/7.25 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 6.92/7.25 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 6.92/7.25 @ ( uminus_uminus_int
% 6.92/7.25 @ ( zero_n2684676970156552555ol_int
% 6.92/7.25 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 6.92/7.25 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 6.92/7.25 @ ( plus_plus_int
% 6.92/7.25 @ ( zero_n2684676970156552555ol_int
% 6.92/7.25 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 6.92/7.25 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 6.92/7.25 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % and_int.simps
% 6.92/7.25 thf(fact_6785_and__int_Oelims,axiom,
% 6.92/7.25 ! [X: int,Xa: int,Y: int] :
% 6.92/7.25 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 6.92/7.25 = Y )
% 6.92/7.25 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 6.92/7.25 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 6.92/7.25 => ( Y
% 6.92/7.25 = ( uminus_uminus_int
% 6.92/7.25 @ ( zero_n2684676970156552555ol_int
% 6.92/7.25 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 6.92/7.25 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 6.92/7.25 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 6.92/7.25 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 6.92/7.25 => ( Y
% 6.92/7.25 = ( plus_plus_int
% 6.92/7.25 @ ( zero_n2684676970156552555ol_int
% 6.92/7.25 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 6.92/7.25 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 6.92/7.25 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % and_int.elims
% 6.92/7.25 thf(fact_6786_Divides_Oadjust__div__eq,axiom,
% 6.92/7.25 ! [Q6: int,R2: int] :
% 6.92/7.25 ( ( adjust_div @ ( product_Pair_int_int @ Q6 @ R2 ) )
% 6.92/7.25 = ( plus_plus_int @ Q6 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Divides.adjust_div_eq
% 6.92/7.25 thf(fact_6787_insert__absorb2,axiom,
% 6.92/7.25 ! [X: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.25 ( ( insert9069300056098147895at_nat @ X @ ( insert9069300056098147895at_nat @ X @ A4 ) )
% 6.92/7.25 = ( insert9069300056098147895at_nat @ X @ A4 ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_absorb2
% 6.92/7.25 thf(fact_6788_insert__absorb2,axiom,
% 6.92/7.25 ! [X: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.25 ( ( insert8211810215607154385at_nat @ X @ ( insert8211810215607154385at_nat @ X @ A4 ) )
% 6.92/7.25 = ( insert8211810215607154385at_nat @ X @ A4 ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_absorb2
% 6.92/7.25 thf(fact_6789_insert__absorb2,axiom,
% 6.92/7.25 ! [X: $o,A4: set_o] :
% 6.92/7.25 ( ( insert_o @ X @ ( insert_o @ X @ A4 ) )
% 6.92/7.25 = ( insert_o @ X @ A4 ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_absorb2
% 6.92/7.25 thf(fact_6790_insert__absorb2,axiom,
% 6.92/7.25 ! [X: nat,A4: set_nat] :
% 6.92/7.25 ( ( insert_nat @ X @ ( insert_nat @ X @ A4 ) )
% 6.92/7.25 = ( insert_nat @ X @ A4 ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_absorb2
% 6.92/7.25 thf(fact_6791_insert__absorb2,axiom,
% 6.92/7.25 ! [X: int,A4: set_int] :
% 6.92/7.25 ( ( insert_int @ X @ ( insert_int @ X @ A4 ) )
% 6.92/7.25 = ( insert_int @ X @ A4 ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_absorb2
% 6.92/7.25 thf(fact_6792_insert__iff,axiom,
% 6.92/7.25 ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.25 ( ( member8757157785044589968at_nat @ A @ ( insert9069300056098147895at_nat @ B @ A4 ) )
% 6.92/7.25 = ( ( A = B )
% 6.92/7.25 | ( member8757157785044589968at_nat @ A @ A4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_iff
% 6.92/7.25 thf(fact_6793_insert__iff,axiom,
% 6.92/7.25 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.25 ( ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ B @ A4 ) )
% 6.92/7.25 = ( ( A = B )
% 6.92/7.25 | ( member8440522571783428010at_nat @ A @ A4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_iff
% 6.92/7.25 thf(fact_6794_insert__iff,axiom,
% 6.92/7.25 ! [A: $o,B: $o,A4: set_o] :
% 6.92/7.25 ( ( member_o @ A @ ( insert_o @ B @ A4 ) )
% 6.92/7.25 = ( ( A = B )
% 6.92/7.25 | ( member_o @ A @ A4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_iff
% 6.92/7.25 thf(fact_6795_insert__iff,axiom,
% 6.92/7.25 ! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int] :
% 6.92/7.25 ( ( member2340774599025711042nt_int @ A @ ( insert8897473484851387113nt_int @ B @ A4 ) )
% 6.92/7.25 = ( ( A = B )
% 6.92/7.25 | ( member2340774599025711042nt_int @ A @ A4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_iff
% 6.92/7.25 thf(fact_6796_insert__iff,axiom,
% 6.92/7.25 ! [A: set_nat,B: set_nat,A4: set_set_nat] :
% 6.92/7.25 ( ( member_set_nat @ A @ ( insert_set_nat @ B @ A4 ) )
% 6.92/7.25 = ( ( A = B )
% 6.92/7.25 | ( member_set_nat @ A @ A4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_iff
% 6.92/7.25 thf(fact_6797_insert__iff,axiom,
% 6.92/7.25 ! [A: nat,B: nat,A4: set_nat] :
% 6.92/7.25 ( ( member_nat @ A @ ( insert_nat @ B @ A4 ) )
% 6.92/7.25 = ( ( A = B )
% 6.92/7.25 | ( member_nat @ A @ A4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_iff
% 6.92/7.25 thf(fact_6798_insert__iff,axiom,
% 6.92/7.25 ! [A: int,B: int,A4: set_int] :
% 6.92/7.25 ( ( member_int @ A @ ( insert_int @ B @ A4 ) )
% 6.92/7.25 = ( ( A = B )
% 6.92/7.25 | ( member_int @ A @ A4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_iff
% 6.92/7.25 thf(fact_6799_insertCI,axiom,
% 6.92/7.25 ! [A: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat] :
% 6.92/7.25 ( ( ~ ( member8757157785044589968at_nat @ A @ B5 )
% 6.92/7.25 => ( A = B ) )
% 6.92/7.25 => ( member8757157785044589968at_nat @ A @ ( insert9069300056098147895at_nat @ B @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insertCI
% 6.92/7.25 thf(fact_6800_insertCI,axiom,
% 6.92/7.25 ! [A: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 6.92/7.25 ( ( ~ ( member8440522571783428010at_nat @ A @ B5 )
% 6.92/7.25 => ( A = B ) )
% 6.92/7.25 => ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ B @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insertCI
% 6.92/7.25 thf(fact_6801_insertCI,axiom,
% 6.92/7.25 ! [A: $o,B5: set_o,B: $o] :
% 6.92/7.25 ( ( ~ ( member_o @ A @ B5 )
% 6.92/7.25 => ( A = B ) )
% 6.92/7.25 => ( member_o @ A @ ( insert_o @ B @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insertCI
% 6.92/7.25 thf(fact_6802_insertCI,axiom,
% 6.92/7.25 ! [A: set_Pr958786334691620121nt_int,B5: set_se6260736226359567993nt_int,B: set_Pr958786334691620121nt_int] :
% 6.92/7.25 ( ( ~ ( member2340774599025711042nt_int @ A @ B5 )
% 6.92/7.25 => ( A = B ) )
% 6.92/7.25 => ( member2340774599025711042nt_int @ A @ ( insert8897473484851387113nt_int @ B @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insertCI
% 6.92/7.25 thf(fact_6803_insertCI,axiom,
% 6.92/7.25 ! [A: set_nat,B5: set_set_nat,B: set_nat] :
% 6.92/7.25 ( ( ~ ( member_set_nat @ A @ B5 )
% 6.92/7.25 => ( A = B ) )
% 6.92/7.25 => ( member_set_nat @ A @ ( insert_set_nat @ B @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insertCI
% 6.92/7.25 thf(fact_6804_insertCI,axiom,
% 6.92/7.25 ! [A: nat,B5: set_nat,B: nat] :
% 6.92/7.25 ( ( ~ ( member_nat @ A @ B5 )
% 6.92/7.25 => ( A = B ) )
% 6.92/7.25 => ( member_nat @ A @ ( insert_nat @ B @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insertCI
% 6.92/7.25 thf(fact_6805_insertCI,axiom,
% 6.92/7.25 ! [A: int,B5: set_int,B: int] :
% 6.92/7.25 ( ( ~ ( member_int @ A @ B5 )
% 6.92/7.25 => ( A = B ) )
% 6.92/7.25 => ( member_int @ A @ ( insert_int @ B @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insertCI
% 6.92/7.25 thf(fact_6806_split__part,axiom,
% 6.92/7.25 ! [P2: $o,Q2: int > int > $o] :
% 6.92/7.25 ( ( produc4947309494688390418_int_o
% 6.92/7.25 @ ^ [A5: int,B4: int] :
% 6.92/7.25 ( P2
% 6.92/7.25 & ( Q2 @ A5 @ B4 ) ) )
% 6.92/7.25 = ( ^ [Ab: product_prod_int_int] :
% 6.92/7.25 ( P2
% 6.92/7.25 & ( produc4947309494688390418_int_o @ Q2 @ Ab ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % split_part
% 6.92/7.25 thf(fact_6807_singletonI,axiom,
% 6.92/7.25 ! [A: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ A @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ).
% 6.92/7.25
% 6.92/7.25 % singletonI
% 6.92/7.25 thf(fact_6808_singletonI,axiom,
% 6.92/7.25 ! [A: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ A @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) ).
% 6.92/7.25
% 6.92/7.25 % singletonI
% 6.92/7.25 thf(fact_6809_singletonI,axiom,
% 6.92/7.25 ! [A: set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 6.92/7.25
% 6.92/7.25 % singletonI
% 6.92/7.25 thf(fact_6810_singletonI,axiom,
% 6.92/7.25 ! [A: product_prod_nat_nat] : ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.25
% 6.92/7.25 % singletonI
% 6.92/7.25 thf(fact_6811_singletonI,axiom,
% 6.92/7.25 ! [A: $o] : ( member_o @ A @ ( insert_o @ A @ bot_bot_set_o ) ) ).
% 6.92/7.25
% 6.92/7.25 % singletonI
% 6.92/7.25 thf(fact_6812_singletonI,axiom,
% 6.92/7.25 ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 6.92/7.25
% 6.92/7.25 % singletonI
% 6.92/7.25 thf(fact_6813_singletonI,axiom,
% 6.92/7.25 ! [A: int] : ( member_int @ A @ ( insert_int @ A @ bot_bot_set_int ) ) ).
% 6.92/7.25
% 6.92/7.25 % singletonI
% 6.92/7.25 thf(fact_6814_insert__subset,axiom,
% 6.92/7.25 ! [X: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.25 ( ( ord_le1268244103169919719at_nat @ ( insert9069300056098147895at_nat @ X @ A4 ) @ B5 )
% 6.92/7.25 = ( ( member8757157785044589968at_nat @ X @ B5 )
% 6.92/7.25 & ( ord_le1268244103169919719at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_subset
% 6.92/7.25 thf(fact_6815_insert__subset,axiom,
% 6.92/7.25 ! [X: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.25 ( ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ X @ A4 ) @ B5 )
% 6.92/7.25 = ( ( member8440522571783428010at_nat @ X @ B5 )
% 6.92/7.25 & ( ord_le3146513528884898305at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_subset
% 6.92/7.25 thf(fact_6816_insert__subset,axiom,
% 6.92/7.25 ! [X: $o,A4: set_o,B5: set_o] :
% 6.92/7.25 ( ( ord_less_eq_set_o @ ( insert_o @ X @ A4 ) @ B5 )
% 6.92/7.25 = ( ( member_o @ X @ B5 )
% 6.92/7.25 & ( ord_less_eq_set_o @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_subset
% 6.92/7.25 thf(fact_6817_insert__subset,axiom,
% 6.92/7.25 ! [X: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.25 ( ( ord_le483042692224249369nt_int @ ( insert8897473484851387113nt_int @ X @ A4 ) @ B5 )
% 6.92/7.25 = ( ( member2340774599025711042nt_int @ X @ B5 )
% 6.92/7.25 & ( ord_le483042692224249369nt_int @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_subset
% 6.92/7.25 thf(fact_6818_insert__subset,axiom,
% 6.92/7.25 ! [X: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.25 ( ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X @ A4 ) @ B5 )
% 6.92/7.25 = ( ( member_set_nat @ X @ B5 )
% 6.92/7.25 & ( ord_le6893508408891458716et_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_subset
% 6.92/7.25 thf(fact_6819_insert__subset,axiom,
% 6.92/7.25 ! [X: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.25 ( ( ord_less_eq_set_nat @ ( insert_nat @ X @ A4 ) @ B5 )
% 6.92/7.25 = ( ( member_nat @ X @ B5 )
% 6.92/7.25 & ( ord_less_eq_set_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_subset
% 6.92/7.25 thf(fact_6820_insert__subset,axiom,
% 6.92/7.25 ! [X: int,A4: set_int,B5: set_int] :
% 6.92/7.25 ( ( ord_less_eq_set_int @ ( insert_int @ X @ A4 ) @ B5 )
% 6.92/7.25 = ( ( member_int @ X @ B5 )
% 6.92/7.25 & ( ord_less_eq_set_int @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_subset
% 6.92/7.25 thf(fact_6821_Int__insert__right__if1,axiom,
% 6.92/7.25 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.25 ( ( member8757157785044589968at_nat @ A @ A4 )
% 6.92/7.25 => ( ( inf_in7913087082777306421at_nat @ A4 @ ( insert9069300056098147895at_nat @ A @ B5 ) )
% 6.92/7.25 = ( insert9069300056098147895at_nat @ A @ ( inf_in7913087082777306421at_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_right_if1
% 6.92/7.25 thf(fact_6822_Int__insert__right__if1,axiom,
% 6.92/7.25 ! [A: $o,A4: set_o,B5: set_o] :
% 6.92/7.25 ( ( member_o @ A @ A4 )
% 6.92/7.25 => ( ( inf_inf_set_o @ A4 @ ( insert_o @ A @ B5 ) )
% 6.92/7.25 = ( insert_o @ A @ ( inf_inf_set_o @ A4 @ B5 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_right_if1
% 6.92/7.25 thf(fact_6823_Int__insert__right__if1,axiom,
% 6.92/7.25 ! [A: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.25 ( ( member2340774599025711042nt_int @ A @ A4 )
% 6.92/7.25 => ( ( inf_in8396524679539076455nt_int @ A4 @ ( insert8897473484851387113nt_int @ A @ B5 ) )
% 6.92/7.25 = ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ A4 @ B5 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_right_if1
% 6.92/7.25 thf(fact_6824_Int__insert__right__if1,axiom,
% 6.92/7.25 ! [A: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.25 ( ( member_set_nat @ A @ A4 )
% 6.92/7.25 => ( ( inf_inf_set_set_nat @ A4 @ ( insert_set_nat @ A @ B5 ) )
% 6.92/7.25 = ( insert_set_nat @ A @ ( inf_inf_set_set_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_right_if1
% 6.92/7.25 thf(fact_6825_Int__insert__right__if1,axiom,
% 6.92/7.25 ! [A: int,A4: set_int,B5: set_int] :
% 6.92/7.25 ( ( member_int @ A @ A4 )
% 6.92/7.25 => ( ( inf_inf_set_int @ A4 @ ( insert_int @ A @ B5 ) )
% 6.92/7.25 = ( insert_int @ A @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_right_if1
% 6.92/7.25 thf(fact_6826_Int__insert__right__if1,axiom,
% 6.92/7.25 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.25 ( ( member8440522571783428010at_nat @ A @ A4 )
% 6.92/7.25 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( insert8211810215607154385at_nat @ A @ B5 ) )
% 6.92/7.25 = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_right_if1
% 6.92/7.25 thf(fact_6827_Int__insert__right__if1,axiom,
% 6.92/7.25 ! [A: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.25 ( ( member_nat @ A @ A4 )
% 6.92/7.25 => ( ( inf_inf_set_nat @ A4 @ ( insert_nat @ A @ B5 ) )
% 6.92/7.25 = ( insert_nat @ A @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_right_if1
% 6.92/7.25 thf(fact_6828_Int__insert__right__if0,axiom,
% 6.92/7.25 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.25 ( ~ ( member8757157785044589968at_nat @ A @ A4 )
% 6.92/7.25 => ( ( inf_in7913087082777306421at_nat @ A4 @ ( insert9069300056098147895at_nat @ A @ B5 ) )
% 6.92/7.25 = ( inf_in7913087082777306421at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_right_if0
% 6.92/7.25 thf(fact_6829_Int__insert__right__if0,axiom,
% 6.92/7.25 ! [A: $o,A4: set_o,B5: set_o] :
% 6.92/7.25 ( ~ ( member_o @ A @ A4 )
% 6.92/7.25 => ( ( inf_inf_set_o @ A4 @ ( insert_o @ A @ B5 ) )
% 6.92/7.25 = ( inf_inf_set_o @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_right_if0
% 6.92/7.25 thf(fact_6830_Int__insert__right__if0,axiom,
% 6.92/7.25 ! [A: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.25 ( ~ ( member2340774599025711042nt_int @ A @ A4 )
% 6.92/7.25 => ( ( inf_in8396524679539076455nt_int @ A4 @ ( insert8897473484851387113nt_int @ A @ B5 ) )
% 6.92/7.25 = ( inf_in8396524679539076455nt_int @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_right_if0
% 6.92/7.25 thf(fact_6831_Int__insert__right__if0,axiom,
% 6.92/7.25 ! [A: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.25 ( ~ ( member_set_nat @ A @ A4 )
% 6.92/7.25 => ( ( inf_inf_set_set_nat @ A4 @ ( insert_set_nat @ A @ B5 ) )
% 6.92/7.25 = ( inf_inf_set_set_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_right_if0
% 6.92/7.25 thf(fact_6832_Int__insert__right__if0,axiom,
% 6.92/7.25 ! [A: int,A4: set_int,B5: set_int] :
% 6.92/7.25 ( ~ ( member_int @ A @ A4 )
% 6.92/7.25 => ( ( inf_inf_set_int @ A4 @ ( insert_int @ A @ B5 ) )
% 6.92/7.25 = ( inf_inf_set_int @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_right_if0
% 6.92/7.25 thf(fact_6833_Int__insert__right__if0,axiom,
% 6.92/7.25 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.25 ( ~ ( member8440522571783428010at_nat @ A @ A4 )
% 6.92/7.25 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( insert8211810215607154385at_nat @ A @ B5 ) )
% 6.92/7.25 = ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_right_if0
% 6.92/7.25 thf(fact_6834_Int__insert__right__if0,axiom,
% 6.92/7.25 ! [A: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.25 ( ~ ( member_nat @ A @ A4 )
% 6.92/7.25 => ( ( inf_inf_set_nat @ A4 @ ( insert_nat @ A @ B5 ) )
% 6.92/7.25 = ( inf_inf_set_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_right_if0
% 6.92/7.25 thf(fact_6835_insert__inter__insert,axiom,
% 6.92/7.25 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.25 ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ A4 ) @ ( insert9069300056098147895at_nat @ A @ B5 ) )
% 6.92/7.25 = ( insert9069300056098147895at_nat @ A @ ( inf_in7913087082777306421at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_inter_insert
% 6.92/7.25 thf(fact_6836_insert__inter__insert,axiom,
% 6.92/7.25 ! [A: $o,A4: set_o,B5: set_o] :
% 6.92/7.25 ( ( inf_inf_set_o @ ( insert_o @ A @ A4 ) @ ( insert_o @ A @ B5 ) )
% 6.92/7.25 = ( insert_o @ A @ ( inf_inf_set_o @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_inter_insert
% 6.92/7.25 thf(fact_6837_insert__inter__insert,axiom,
% 6.92/7.25 ! [A: int,A4: set_int,B5: set_int] :
% 6.92/7.25 ( ( inf_inf_set_int @ ( insert_int @ A @ A4 ) @ ( insert_int @ A @ B5 ) )
% 6.92/7.25 = ( insert_int @ A @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_inter_insert
% 6.92/7.25 thf(fact_6838_insert__inter__insert,axiom,
% 6.92/7.25 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.25 ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ A4 ) @ ( insert8211810215607154385at_nat @ A @ B5 ) )
% 6.92/7.25 = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_inter_insert
% 6.92/7.25 thf(fact_6839_insert__inter__insert,axiom,
% 6.92/7.25 ! [A: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.25 ( ( inf_inf_set_nat @ ( insert_nat @ A @ A4 ) @ ( insert_nat @ A @ B5 ) )
% 6.92/7.25 = ( insert_nat @ A @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % insert_inter_insert
% 6.92/7.25 thf(fact_6840_Int__insert__left__if1,axiom,
% 6.92/7.25 ! [A: produc3843707927480180839at_nat,C4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.25 ( ( member8757157785044589968at_nat @ A @ C4 )
% 6.92/7.25 => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( insert9069300056098147895at_nat @ A @ ( inf_in7913087082777306421at_nat @ B5 @ C4 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_left_if1
% 6.92/7.25 thf(fact_6841_Int__insert__left__if1,axiom,
% 6.92/7.25 ! [A: $o,C4: set_o,B5: set_o] :
% 6.92/7.25 ( ( member_o @ A @ C4 )
% 6.92/7.25 => ( ( inf_inf_set_o @ ( insert_o @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( insert_o @ A @ ( inf_inf_set_o @ B5 @ C4 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_left_if1
% 6.92/7.25 thf(fact_6842_Int__insert__left__if1,axiom,
% 6.92/7.25 ! [A: set_Pr958786334691620121nt_int,C4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.25 ( ( member2340774599025711042nt_int @ A @ C4 )
% 6.92/7.25 => ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ B5 @ C4 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_left_if1
% 6.92/7.25 thf(fact_6843_Int__insert__left__if1,axiom,
% 6.92/7.25 ! [A: set_nat,C4: set_set_nat,B5: set_set_nat] :
% 6.92/7.25 ( ( member_set_nat @ A @ C4 )
% 6.92/7.25 => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( insert_set_nat @ A @ ( inf_inf_set_set_nat @ B5 @ C4 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_left_if1
% 6.92/7.25 thf(fact_6844_Int__insert__left__if1,axiom,
% 6.92/7.25 ! [A: int,C4: set_int,B5: set_int] :
% 6.92/7.25 ( ( member_int @ A @ C4 )
% 6.92/7.25 => ( ( inf_inf_set_int @ ( insert_int @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( insert_int @ A @ ( inf_inf_set_int @ B5 @ C4 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_left_if1
% 6.92/7.25 thf(fact_6845_Int__insert__left__if1,axiom,
% 6.92/7.25 ! [A: product_prod_nat_nat,C4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.25 ( ( member8440522571783428010at_nat @ A @ C4 )
% 6.92/7.25 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ B5 @ C4 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_left_if1
% 6.92/7.25 thf(fact_6846_Int__insert__left__if1,axiom,
% 6.92/7.25 ! [A: nat,C4: set_nat,B5: set_nat] :
% 6.92/7.25 ( ( member_nat @ A @ C4 )
% 6.92/7.25 => ( ( inf_inf_set_nat @ ( insert_nat @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( insert_nat @ A @ ( inf_inf_set_nat @ B5 @ C4 ) ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_left_if1
% 6.92/7.25 thf(fact_6847_Int__insert__left__if0,axiom,
% 6.92/7.25 ! [A: produc3843707927480180839at_nat,C4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.25 ( ~ ( member8757157785044589968at_nat @ A @ C4 )
% 6.92/7.25 => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( inf_in7913087082777306421at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_left_if0
% 6.92/7.25 thf(fact_6848_Int__insert__left__if0,axiom,
% 6.92/7.25 ! [A: $o,C4: set_o,B5: set_o] :
% 6.92/7.25 ( ~ ( member_o @ A @ C4 )
% 6.92/7.25 => ( ( inf_inf_set_o @ ( insert_o @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( inf_inf_set_o @ B5 @ C4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_left_if0
% 6.92/7.25 thf(fact_6849_Int__insert__left__if0,axiom,
% 6.92/7.25 ! [A: set_Pr958786334691620121nt_int,C4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.25 ( ~ ( member2340774599025711042nt_int @ A @ C4 )
% 6.92/7.25 => ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( inf_in8396524679539076455nt_int @ B5 @ C4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_left_if0
% 6.92/7.25 thf(fact_6850_Int__insert__left__if0,axiom,
% 6.92/7.25 ! [A: set_nat,C4: set_set_nat,B5: set_set_nat] :
% 6.92/7.25 ( ~ ( member_set_nat @ A @ C4 )
% 6.92/7.25 => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( inf_inf_set_set_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_left_if0
% 6.92/7.25 thf(fact_6851_Int__insert__left__if0,axiom,
% 6.92/7.25 ! [A: int,C4: set_int,B5: set_int] :
% 6.92/7.25 ( ~ ( member_int @ A @ C4 )
% 6.92/7.25 => ( ( inf_inf_set_int @ ( insert_int @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( inf_inf_set_int @ B5 @ C4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_left_if0
% 6.92/7.25 thf(fact_6852_Int__insert__left__if0,axiom,
% 6.92/7.25 ! [A: product_prod_nat_nat,C4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.25 ( ~ ( member8440522571783428010at_nat @ A @ C4 )
% 6.92/7.25 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( inf_in2572325071724192079at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_left_if0
% 6.92/7.25 thf(fact_6853_Int__insert__left__if0,axiom,
% 6.92/7.25 ! [A: nat,C4: set_nat,B5: set_nat] :
% 6.92/7.25 ( ~ ( member_nat @ A @ C4 )
% 6.92/7.25 => ( ( inf_inf_set_nat @ ( insert_nat @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( inf_inf_set_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Int_insert_left_if0
% 6.92/7.25 thf(fact_6854_Un__insert__left,axiom,
% 6.92/7.25 ! [A: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.25 ( ( sup_su6327502436637775413at_nat @ ( insert8211810215607154385at_nat @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( insert8211810215607154385at_nat @ A @ ( sup_su6327502436637775413at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Un_insert_left
% 6.92/7.25 thf(fact_6855_Un__insert__left,axiom,
% 6.92/7.25 ! [A: $o,B5: set_o,C4: set_o] :
% 6.92/7.25 ( ( sup_sup_set_o @ ( insert_o @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( insert_o @ A @ ( sup_sup_set_o @ B5 @ C4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Un_insert_left
% 6.92/7.25 thf(fact_6856_Un__insert__left,axiom,
% 6.92/7.25 ! [A: int,B5: set_int,C4: set_int] :
% 6.92/7.25 ( ( sup_sup_set_int @ ( insert_int @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( insert_int @ A @ ( sup_sup_set_int @ B5 @ C4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Un_insert_left
% 6.92/7.25 thf(fact_6857_Un__insert__left,axiom,
% 6.92/7.25 ! [A: produc4166570645942440679at_nat,B5: set_Pr8551490117392284871at_nat,C4: set_Pr8551490117392284871at_nat] :
% 6.92/7.25 ( ( sup_su3035147773818789531at_nat @ ( insert6337962749363155127at_nat @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( insert6337962749363155127at_nat @ A @ ( sup_su3035147773818789531at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Un_insert_left
% 6.92/7.25 thf(fact_6858_Un__insert__left,axiom,
% 6.92/7.25 ! [A: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] :
% 6.92/7.25 ( ( sup_su5525570899277871387at_nat @ ( insert9069300056098147895at_nat @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( insert9069300056098147895at_nat @ A @ ( sup_su5525570899277871387at_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Un_insert_left
% 6.92/7.25 thf(fact_6859_Un__insert__left,axiom,
% 6.92/7.25 ! [A: nat,B5: set_nat,C4: set_nat] :
% 6.92/7.25 ( ( sup_sup_set_nat @ ( insert_nat @ A @ B5 ) @ C4 )
% 6.92/7.25 = ( insert_nat @ A @ ( sup_sup_set_nat @ B5 @ C4 ) ) ) ).
% 6.92/7.25
% 6.92/7.25 % Un_insert_left
% 6.92/7.25 thf(fact_6860_Un__insert__right,axiom,
% 6.92/7.25 ! [A4: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.25 ( ( sup_su6327502436637775413at_nat @ A4 @ ( insert8211810215607154385at_nat @ A @ B5 ) )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ A @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Un_insert_right
% 6.92/7.26 thf(fact_6861_Un__insert__right,axiom,
% 6.92/7.26 ! [A4: set_o,A: $o,B5: set_o] :
% 6.92/7.26 ( ( sup_sup_set_o @ A4 @ ( insert_o @ A @ B5 ) )
% 6.92/7.26 = ( insert_o @ A @ ( sup_sup_set_o @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Un_insert_right
% 6.92/7.26 thf(fact_6862_Un__insert__right,axiom,
% 6.92/7.26 ! [A4: set_int,A: int,B5: set_int] :
% 6.92/7.26 ( ( sup_sup_set_int @ A4 @ ( insert_int @ A @ B5 ) )
% 6.92/7.26 = ( insert_int @ A @ ( sup_sup_set_int @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Un_insert_right
% 6.92/7.26 thf(fact_6863_Un__insert__right,axiom,
% 6.92/7.26 ! [A4: set_Pr8551490117392284871at_nat,A: produc4166570645942440679at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.26 ( ( sup_su3035147773818789531at_nat @ A4 @ ( insert6337962749363155127at_nat @ A @ B5 ) )
% 6.92/7.26 = ( insert6337962749363155127at_nat @ A @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Un_insert_right
% 6.92/7.26 thf(fact_6864_Un__insert__right,axiom,
% 6.92/7.26 ! [A4: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( sup_su5525570899277871387at_nat @ A4 @ ( insert9069300056098147895at_nat @ A @ B5 ) )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ A @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Un_insert_right
% 6.92/7.26 thf(fact_6865_Un__insert__right,axiom,
% 6.92/7.26 ! [A4: set_nat,A: nat,B5: set_nat] :
% 6.92/7.26 ( ( sup_sup_set_nat @ A4 @ ( insert_nat @ A @ B5 ) )
% 6.92/7.26 = ( insert_nat @ A @ ( sup_sup_set_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Un_insert_right
% 6.92/7.26 thf(fact_6866_insert__Diff1,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( member8757157785044589968at_nat @ X @ B5 )
% 6.92/7.26 => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( minus_3314409938677909166at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff1
% 6.92/7.26 thf(fact_6867_insert__Diff1,axiom,
% 6.92/7.26 ! [X: $o,B5: set_o,A4: set_o] :
% 6.92/7.26 ( ( member_o @ X @ B5 )
% 6.92/7.26 => ( ( minus_minus_set_o @ ( insert_o @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( minus_minus_set_o @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff1
% 6.92/7.26 thf(fact_6868_insert__Diff1,axiom,
% 6.92/7.26 ! [X: set_Pr958786334691620121nt_int,B5: set_se6260736226359567993nt_int,A4: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( member2340774599025711042nt_int @ X @ B5 )
% 6.92/7.26 => ( ( minus_2612819937483484256nt_int @ ( insert8897473484851387113nt_int @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( minus_2612819937483484256nt_int @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff1
% 6.92/7.26 thf(fact_6869_insert__Diff1,axiom,
% 6.92/7.26 ! [X: set_nat,B5: set_set_nat,A4: set_set_nat] :
% 6.92/7.26 ( ( member_set_nat @ X @ B5 )
% 6.92/7.26 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( minus_2163939370556025621et_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff1
% 6.92/7.26 thf(fact_6870_insert__Diff1,axiom,
% 6.92/7.26 ! [X: nat,B5: set_nat,A4: set_nat] :
% 6.92/7.26 ( ( member_nat @ X @ B5 )
% 6.92/7.26 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( minus_minus_set_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff1
% 6.92/7.26 thf(fact_6871_insert__Diff1,axiom,
% 6.92/7.26 ! [X: int,B5: set_int,A4: set_int] :
% 6.92/7.26 ( ( member_int @ X @ B5 )
% 6.92/7.26 => ( ( minus_minus_set_int @ ( insert_int @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( minus_minus_set_int @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff1
% 6.92/7.26 thf(fact_6872_insert__Diff1,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( member8440522571783428010at_nat @ X @ B5 )
% 6.92/7.26 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff1
% 6.92/7.26 thf(fact_6873_Diff__insert0,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ~ ( member8757157785044589968at_nat @ X @ A4 )
% 6.92/7.26 => ( ( minus_3314409938677909166at_nat @ A4 @ ( insert9069300056098147895at_nat @ X @ B5 ) )
% 6.92/7.26 = ( minus_3314409938677909166at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert0
% 6.92/7.26 thf(fact_6874_Diff__insert0,axiom,
% 6.92/7.26 ! [X: $o,A4: set_o,B5: set_o] :
% 6.92/7.26 ( ~ ( member_o @ X @ A4 )
% 6.92/7.26 => ( ( minus_minus_set_o @ A4 @ ( insert_o @ X @ B5 ) )
% 6.92/7.26 = ( minus_minus_set_o @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert0
% 6.92/7.26 thf(fact_6875_Diff__insert0,axiom,
% 6.92/7.26 ! [X: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ~ ( member2340774599025711042nt_int @ X @ A4 )
% 6.92/7.26 => ( ( minus_2612819937483484256nt_int @ A4 @ ( insert8897473484851387113nt_int @ X @ B5 ) )
% 6.92/7.26 = ( minus_2612819937483484256nt_int @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert0
% 6.92/7.26 thf(fact_6876_Diff__insert0,axiom,
% 6.92/7.26 ! [X: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.26 ( ~ ( member_set_nat @ X @ A4 )
% 6.92/7.26 => ( ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ B5 ) )
% 6.92/7.26 = ( minus_2163939370556025621et_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert0
% 6.92/7.26 thf(fact_6877_Diff__insert0,axiom,
% 6.92/7.26 ! [X: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.26 ( ~ ( member_nat @ X @ A4 )
% 6.92/7.26 => ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ B5 ) )
% 6.92/7.26 = ( minus_minus_set_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert0
% 6.92/7.26 thf(fact_6878_Diff__insert0,axiom,
% 6.92/7.26 ! [X: int,A4: set_int,B5: set_int] :
% 6.92/7.26 ( ~ ( member_int @ X @ A4 )
% 6.92/7.26 => ( ( minus_minus_set_int @ A4 @ ( insert_int @ X @ B5 ) )
% 6.92/7.26 = ( minus_minus_set_int @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert0
% 6.92/7.26 thf(fact_6879_Diff__insert0,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ~ ( member8440522571783428010at_nat @ X @ A4 )
% 6.92/7.26 => ( ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ B5 ) )
% 6.92/7.26 = ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert0
% 6.92/7.26 thf(fact_6880_singleton__conv,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( collec6321179662152712658at_nat
% 6.92/7.26 @ ^ [X4: produc3843707927480180839at_nat] : ( X4 = A ) )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv
% 6.92/7.26 thf(fact_6881_singleton__conv,axiom,
% 6.92/7.26 ! [A: list_nat] :
% 6.92/7.26 ( ( collect_list_nat
% 6.92/7.26 @ ^ [X4: list_nat] : ( X4 = A ) )
% 6.92/7.26 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv
% 6.92/7.26 thf(fact_6882_singleton__conv,axiom,
% 6.92/7.26 ! [A: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( collec5210948495886036740nt_int
% 6.92/7.26 @ ^ [X4: set_Pr958786334691620121nt_int] : ( X4 = A ) )
% 6.92/7.26 = ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv
% 6.92/7.26 thf(fact_6883_singleton__conv,axiom,
% 6.92/7.26 ! [A: set_nat] :
% 6.92/7.26 ( ( collect_set_nat
% 6.92/7.26 @ ^ [X4: set_nat] : ( X4 = A ) )
% 6.92/7.26 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv
% 6.92/7.26 thf(fact_6884_singleton__conv,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat] :
% 6.92/7.26 ( ( collec3392354462482085612at_nat
% 6.92/7.26 @ ^ [X4: product_prod_nat_nat] : ( X4 = A ) )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv
% 6.92/7.26 thf(fact_6885_singleton__conv,axiom,
% 6.92/7.26 ! [A: $o] :
% 6.92/7.26 ( ( collect_o
% 6.92/7.26 @ ^ [X4: $o] : ( X4 = A ) )
% 6.92/7.26 = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv
% 6.92/7.26 thf(fact_6886_singleton__conv,axiom,
% 6.92/7.26 ! [A: nat] :
% 6.92/7.26 ( ( collect_nat
% 6.92/7.26 @ ^ [X4: nat] : ( X4 = A ) )
% 6.92/7.26 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv
% 6.92/7.26 thf(fact_6887_singleton__conv,axiom,
% 6.92/7.26 ! [A: int] :
% 6.92/7.26 ( ( collect_int
% 6.92/7.26 @ ^ [X4: int] : ( X4 = A ) )
% 6.92/7.26 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv
% 6.92/7.26 thf(fact_6888_singleton__conv2,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( collec6321179662152712658at_nat
% 6.92/7.26 @ ( ^ [Y6: produc3843707927480180839at_nat,Z4: produc3843707927480180839at_nat] : ( Y6 = Z4 )
% 6.92/7.26 @ A ) )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv2
% 6.92/7.26 thf(fact_6889_singleton__conv2,axiom,
% 6.92/7.26 ! [A: list_nat] :
% 6.92/7.26 ( ( collect_list_nat
% 6.92/7.26 @ ( ^ [Y6: list_nat,Z4: list_nat] : ( Y6 = Z4 )
% 6.92/7.26 @ A ) )
% 6.92/7.26 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv2
% 6.92/7.26 thf(fact_6890_singleton__conv2,axiom,
% 6.92/7.26 ! [A: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( collec5210948495886036740nt_int
% 6.92/7.26 @ ( ^ [Y6: set_Pr958786334691620121nt_int,Z4: set_Pr958786334691620121nt_int] : ( Y6 = Z4 )
% 6.92/7.26 @ A ) )
% 6.92/7.26 = ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv2
% 6.92/7.26 thf(fact_6891_singleton__conv2,axiom,
% 6.92/7.26 ! [A: set_nat] :
% 6.92/7.26 ( ( collect_set_nat
% 6.92/7.26 @ ( ^ [Y6: set_nat,Z4: set_nat] : ( Y6 = Z4 )
% 6.92/7.26 @ A ) )
% 6.92/7.26 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv2
% 6.92/7.26 thf(fact_6892_singleton__conv2,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat] :
% 6.92/7.26 ( ( collec3392354462482085612at_nat
% 6.92/7.26 @ ( ^ [Y6: product_prod_nat_nat,Z4: product_prod_nat_nat] : ( Y6 = Z4 )
% 6.92/7.26 @ A ) )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv2
% 6.92/7.26 thf(fact_6893_singleton__conv2,axiom,
% 6.92/7.26 ! [A: $o] :
% 6.92/7.26 ( ( collect_o
% 6.92/7.26 @ ( ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 )
% 6.92/7.26 @ A ) )
% 6.92/7.26 = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv2
% 6.92/7.26 thf(fact_6894_singleton__conv2,axiom,
% 6.92/7.26 ! [A: nat] :
% 6.92/7.26 ( ( collect_nat
% 6.92/7.26 @ ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 6.92/7.26 @ A ) )
% 6.92/7.26 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv2
% 6.92/7.26 thf(fact_6895_singleton__conv2,axiom,
% 6.92/7.26 ! [A: int] :
% 6.92/7.26 ( ( collect_int
% 6.92/7.26 @ ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.92/7.26 @ A ) )
% 6.92/7.26 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_conv2
% 6.92/7.26 thf(fact_6896_singleton__insert__inj__eq_H,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( ( insert9069300056098147895at_nat @ A @ A4 )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 = ( ( A = B )
% 6.92/7.26 & ( ord_le1268244103169919719at_nat @ A4 @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_insert_inj_eq'
% 6.92/7.26 thf(fact_6897_singleton__insert__inj__eq_H,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 6.92/7.26 ( ( ( insert8211810215607154385at_nat @ A @ A4 )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 = ( ( A = B )
% 6.92/7.26 & ( ord_le3146513528884898305at_nat @ A4 @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_insert_inj_eq'
% 6.92/7.26 thf(fact_6898_singleton__insert__inj__eq_H,axiom,
% 6.92/7.26 ! [A: $o,A4: set_o,B: $o] :
% 6.92/7.26 ( ( ( insert_o @ A @ A4 )
% 6.92/7.26 = ( insert_o @ B @ bot_bot_set_o ) )
% 6.92/7.26 = ( ( A = B )
% 6.92/7.26 & ( ord_less_eq_set_o @ A4 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_insert_inj_eq'
% 6.92/7.26 thf(fact_6899_singleton__insert__inj__eq_H,axiom,
% 6.92/7.26 ! [A: nat,A4: set_nat,B: nat] :
% 6.92/7.26 ( ( ( insert_nat @ A @ A4 )
% 6.92/7.26 = ( insert_nat @ B @ bot_bot_set_nat ) )
% 6.92/7.26 = ( ( A = B )
% 6.92/7.26 & ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_insert_inj_eq'
% 6.92/7.26 thf(fact_6900_singleton__insert__inj__eq_H,axiom,
% 6.92/7.26 ! [A: int,A4: set_int,B: int] :
% 6.92/7.26 ( ( ( insert_int @ A @ A4 )
% 6.92/7.26 = ( insert_int @ B @ bot_bot_set_int ) )
% 6.92/7.26 = ( ( A = B )
% 6.92/7.26 & ( ord_less_eq_set_int @ A4 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_insert_inj_eq'
% 6.92/7.26 thf(fact_6901_singleton__insert__inj__eq,axiom,
% 6.92/7.26 ! [B: produc3843707927480180839at_nat,A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ A @ A4 ) )
% 6.92/7.26 = ( ( A = B )
% 6.92/7.26 & ( ord_le1268244103169919719at_nat @ A4 @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_insert_inj_eq
% 6.92/7.26 thf(fact_6902_singleton__insert__inj__eq,axiom,
% 6.92/7.26 ! [B: product_prod_nat_nat,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ A @ A4 ) )
% 6.92/7.26 = ( ( A = B )
% 6.92/7.26 & ( ord_le3146513528884898305at_nat @ A4 @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_insert_inj_eq
% 6.92/7.26 thf(fact_6903_singleton__insert__inj__eq,axiom,
% 6.92/7.26 ! [B: $o,A: $o,A4: set_o] :
% 6.92/7.26 ( ( ( insert_o @ B @ bot_bot_set_o )
% 6.92/7.26 = ( insert_o @ A @ A4 ) )
% 6.92/7.26 = ( ( A = B )
% 6.92/7.26 & ( ord_less_eq_set_o @ A4 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_insert_inj_eq
% 6.92/7.26 thf(fact_6904_singleton__insert__inj__eq,axiom,
% 6.92/7.26 ! [B: nat,A: nat,A4: set_nat] :
% 6.92/7.26 ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 6.92/7.26 = ( insert_nat @ A @ A4 ) )
% 6.92/7.26 = ( ( A = B )
% 6.92/7.26 & ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_insert_inj_eq
% 6.92/7.26 thf(fact_6905_singleton__insert__inj__eq,axiom,
% 6.92/7.26 ! [B: int,A: int,A4: set_int] :
% 6.92/7.26 ( ( ( insert_int @ B @ bot_bot_set_int )
% 6.92/7.26 = ( insert_int @ A @ A4 ) )
% 6.92/7.26 = ( ( A = B )
% 6.92/7.26 & ( ord_less_eq_set_int @ A4 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_insert_inj_eq
% 6.92/7.26 thf(fact_6906_disjoint__insert_I2_J,axiom,
% 6.92/7.26 ! [A4: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( bot_bo228742789529271731at_nat
% 6.92/7.26 = ( inf_in7913087082777306421at_nat @ A4 @ ( insert9069300056098147895at_nat @ B @ B5 ) ) )
% 6.92/7.26 = ( ~ ( member8757157785044589968at_nat @ B @ A4 )
% 6.92/7.26 & ( bot_bo228742789529271731at_nat
% 6.92/7.26 = ( inf_in7913087082777306421at_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % disjoint_insert(2)
% 6.92/7.26 thf(fact_6907_disjoint__insert_I2_J,axiom,
% 6.92/7.26 ! [A4: set_se6260736226359567993nt_int,B: set_Pr958786334691620121nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( bot_bo1488462491386950373nt_int
% 6.92/7.26 = ( inf_in8396524679539076455nt_int @ A4 @ ( insert8897473484851387113nt_int @ B @ B5 ) ) )
% 6.92/7.26 = ( ~ ( member2340774599025711042nt_int @ B @ A4 )
% 6.92/7.26 & ( bot_bo1488462491386950373nt_int
% 6.92/7.26 = ( inf_in8396524679539076455nt_int @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % disjoint_insert(2)
% 6.92/7.26 thf(fact_6908_disjoint__insert_I2_J,axiom,
% 6.92/7.26 ! [A4: set_set_nat,B: set_nat,B5: set_set_nat] :
% 6.92/7.26 ( ( bot_bot_set_set_nat
% 6.92/7.26 = ( inf_inf_set_set_nat @ A4 @ ( insert_set_nat @ B @ B5 ) ) )
% 6.92/7.26 = ( ~ ( member_set_nat @ B @ A4 )
% 6.92/7.26 & ( bot_bot_set_set_nat
% 6.92/7.26 = ( inf_inf_set_set_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % disjoint_insert(2)
% 6.92/7.26 thf(fact_6909_disjoint__insert_I2_J,axiom,
% 6.92/7.26 ! [A4: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( bot_bo2099793752762293965at_nat
% 6.92/7.26 = ( inf_in2572325071724192079at_nat @ A4 @ ( insert8211810215607154385at_nat @ B @ B5 ) ) )
% 6.92/7.26 = ( ~ ( member8440522571783428010at_nat @ B @ A4 )
% 6.92/7.26 & ( bot_bo2099793752762293965at_nat
% 6.92/7.26 = ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % disjoint_insert(2)
% 6.92/7.26 thf(fact_6910_disjoint__insert_I2_J,axiom,
% 6.92/7.26 ! [A4: set_o,B: $o,B5: set_o] :
% 6.92/7.26 ( ( bot_bot_set_o
% 6.92/7.26 = ( inf_inf_set_o @ A4 @ ( insert_o @ B @ B5 ) ) )
% 6.92/7.26 = ( ~ ( member_o @ B @ A4 )
% 6.92/7.26 & ( bot_bot_set_o
% 6.92/7.26 = ( inf_inf_set_o @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % disjoint_insert(2)
% 6.92/7.26 thf(fact_6911_disjoint__insert_I2_J,axiom,
% 6.92/7.26 ! [A4: set_nat,B: nat,B5: set_nat] :
% 6.92/7.26 ( ( bot_bot_set_nat
% 6.92/7.26 = ( inf_inf_set_nat @ A4 @ ( insert_nat @ B @ B5 ) ) )
% 6.92/7.26 = ( ~ ( member_nat @ B @ A4 )
% 6.92/7.26 & ( bot_bot_set_nat
% 6.92/7.26 = ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % disjoint_insert(2)
% 6.92/7.26 thf(fact_6912_disjoint__insert_I2_J,axiom,
% 6.92/7.26 ! [A4: set_int,B: int,B5: set_int] :
% 6.92/7.26 ( ( bot_bot_set_int
% 6.92/7.26 = ( inf_inf_set_int @ A4 @ ( insert_int @ B @ B5 ) ) )
% 6.92/7.26 = ( ~ ( member_int @ B @ A4 )
% 6.92/7.26 & ( bot_bot_set_int
% 6.92/7.26 = ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % disjoint_insert(2)
% 6.92/7.26 thf(fact_6913_disjoint__insert_I1_J,axiom,
% 6.92/7.26 ! [B5: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( ( inf_in7913087082777306421at_nat @ B5 @ ( insert9069300056098147895at_nat @ A @ A4 ) )
% 6.92/7.26 = bot_bo228742789529271731at_nat )
% 6.92/7.26 = ( ~ ( member8757157785044589968at_nat @ A @ B5 )
% 6.92/7.26 & ( ( inf_in7913087082777306421at_nat @ B5 @ A4 )
% 6.92/7.26 = bot_bo228742789529271731at_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % disjoint_insert(1)
% 6.92/7.26 thf(fact_6914_disjoint__insert_I1_J,axiom,
% 6.92/7.26 ! [B5: set_se6260736226359567993nt_int,A: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( ( inf_in8396524679539076455nt_int @ B5 @ ( insert8897473484851387113nt_int @ A @ A4 ) )
% 6.92/7.26 = bot_bo1488462491386950373nt_int )
% 6.92/7.26 = ( ~ ( member2340774599025711042nt_int @ A @ B5 )
% 6.92/7.26 & ( ( inf_in8396524679539076455nt_int @ B5 @ A4 )
% 6.92/7.26 = bot_bo1488462491386950373nt_int ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % disjoint_insert(1)
% 6.92/7.26 thf(fact_6915_disjoint__insert_I1_J,axiom,
% 6.92/7.26 ! [B5: set_set_nat,A: set_nat,A4: set_set_nat] :
% 6.92/7.26 ( ( ( inf_inf_set_set_nat @ B5 @ ( insert_set_nat @ A @ A4 ) )
% 6.92/7.26 = bot_bot_set_set_nat )
% 6.92/7.26 = ( ~ ( member_set_nat @ A @ B5 )
% 6.92/7.26 & ( ( inf_inf_set_set_nat @ B5 @ A4 )
% 6.92/7.26 = bot_bot_set_set_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % disjoint_insert(1)
% 6.92/7.26 thf(fact_6916_disjoint__insert_I1_J,axiom,
% 6.92/7.26 ! [B5: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( ( inf_in2572325071724192079at_nat @ B5 @ ( insert8211810215607154385at_nat @ A @ A4 ) )
% 6.92/7.26 = bot_bo2099793752762293965at_nat )
% 6.92/7.26 = ( ~ ( member8440522571783428010at_nat @ A @ B5 )
% 6.92/7.26 & ( ( inf_in2572325071724192079at_nat @ B5 @ A4 )
% 6.92/7.26 = bot_bo2099793752762293965at_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % disjoint_insert(1)
% 6.92/7.26 thf(fact_6917_disjoint__insert_I1_J,axiom,
% 6.92/7.26 ! [B5: set_o,A: $o,A4: set_o] :
% 6.92/7.26 ( ( ( inf_inf_set_o @ B5 @ ( insert_o @ A @ A4 ) )
% 6.92/7.26 = bot_bot_set_o )
% 6.92/7.26 = ( ~ ( member_o @ A @ B5 )
% 6.92/7.26 & ( ( inf_inf_set_o @ B5 @ A4 )
% 6.92/7.26 = bot_bot_set_o ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % disjoint_insert(1)
% 6.92/7.26 thf(fact_6918_disjoint__insert_I1_J,axiom,
% 6.92/7.26 ! [B5: set_nat,A: nat,A4: set_nat] :
% 6.92/7.26 ( ( ( inf_inf_set_nat @ B5 @ ( insert_nat @ A @ A4 ) )
% 6.92/7.26 = bot_bot_set_nat )
% 6.92/7.26 = ( ~ ( member_nat @ A @ B5 )
% 6.92/7.26 & ( ( inf_inf_set_nat @ B5 @ A4 )
% 6.92/7.26 = bot_bot_set_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % disjoint_insert(1)
% 6.92/7.26 thf(fact_6919_disjoint__insert_I1_J,axiom,
% 6.92/7.26 ! [B5: set_int,A: int,A4: set_int] :
% 6.92/7.26 ( ( ( inf_inf_set_int @ B5 @ ( insert_int @ A @ A4 ) )
% 6.92/7.26 = bot_bot_set_int )
% 6.92/7.26 = ( ~ ( member_int @ A @ B5 )
% 6.92/7.26 & ( ( inf_inf_set_int @ B5 @ A4 )
% 6.92/7.26 = bot_bot_set_int ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % disjoint_insert(1)
% 6.92/7.26 thf(fact_6920_insert__disjoint_I2_J,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( bot_bo228742789529271731at_nat
% 6.92/7.26 = ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ A4 ) @ B5 ) )
% 6.92/7.26 = ( ~ ( member8757157785044589968at_nat @ A @ B5 )
% 6.92/7.26 & ( bot_bo228742789529271731at_nat
% 6.92/7.26 = ( inf_in7913087082777306421at_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_disjoint(2)
% 6.92/7.26 thf(fact_6921_insert__disjoint_I2_J,axiom,
% 6.92/7.26 ! [A: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( bot_bo1488462491386950373nt_int
% 6.92/7.26 = ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ A4 ) @ B5 ) )
% 6.92/7.26 = ( ~ ( member2340774599025711042nt_int @ A @ B5 )
% 6.92/7.26 & ( bot_bo1488462491386950373nt_int
% 6.92/7.26 = ( inf_in8396524679539076455nt_int @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_disjoint(2)
% 6.92/7.26 thf(fact_6922_insert__disjoint_I2_J,axiom,
% 6.92/7.26 ! [A: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.26 ( ( bot_bot_set_set_nat
% 6.92/7.26 = ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ A4 ) @ B5 ) )
% 6.92/7.26 = ( ~ ( member_set_nat @ A @ B5 )
% 6.92/7.26 & ( bot_bot_set_set_nat
% 6.92/7.26 = ( inf_inf_set_set_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_disjoint(2)
% 6.92/7.26 thf(fact_6923_insert__disjoint_I2_J,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( bot_bo2099793752762293965at_nat
% 6.92/7.26 = ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ A4 ) @ B5 ) )
% 6.92/7.26 = ( ~ ( member8440522571783428010at_nat @ A @ B5 )
% 6.92/7.26 & ( bot_bo2099793752762293965at_nat
% 6.92/7.26 = ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_disjoint(2)
% 6.92/7.26 thf(fact_6924_insert__disjoint_I2_J,axiom,
% 6.92/7.26 ! [A: $o,A4: set_o,B5: set_o] :
% 6.92/7.26 ( ( bot_bot_set_o
% 6.92/7.26 = ( inf_inf_set_o @ ( insert_o @ A @ A4 ) @ B5 ) )
% 6.92/7.26 = ( ~ ( member_o @ A @ B5 )
% 6.92/7.26 & ( bot_bot_set_o
% 6.92/7.26 = ( inf_inf_set_o @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_disjoint(2)
% 6.92/7.26 thf(fact_6925_insert__disjoint_I2_J,axiom,
% 6.92/7.26 ! [A: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.26 ( ( bot_bot_set_nat
% 6.92/7.26 = ( inf_inf_set_nat @ ( insert_nat @ A @ A4 ) @ B5 ) )
% 6.92/7.26 = ( ~ ( member_nat @ A @ B5 )
% 6.92/7.26 & ( bot_bot_set_nat
% 6.92/7.26 = ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_disjoint(2)
% 6.92/7.26 thf(fact_6926_insert__disjoint_I2_J,axiom,
% 6.92/7.26 ! [A: int,A4: set_int,B5: set_int] :
% 6.92/7.26 ( ( bot_bot_set_int
% 6.92/7.26 = ( inf_inf_set_int @ ( insert_int @ A @ A4 ) @ B5 ) )
% 6.92/7.26 = ( ~ ( member_int @ A @ B5 )
% 6.92/7.26 & ( bot_bot_set_int
% 6.92/7.26 = ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_disjoint(2)
% 6.92/7.26 thf(fact_6927_insert__disjoint_I1_J,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ A4 ) @ B5 )
% 6.92/7.26 = bot_bo228742789529271731at_nat )
% 6.92/7.26 = ( ~ ( member8757157785044589968at_nat @ A @ B5 )
% 6.92/7.26 & ( ( inf_in7913087082777306421at_nat @ A4 @ B5 )
% 6.92/7.26 = bot_bo228742789529271731at_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_disjoint(1)
% 6.92/7.26 thf(fact_6928_insert__disjoint_I1_J,axiom,
% 6.92/7.26 ! [A: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ A4 ) @ B5 )
% 6.92/7.26 = bot_bo1488462491386950373nt_int )
% 6.92/7.26 = ( ~ ( member2340774599025711042nt_int @ A @ B5 )
% 6.92/7.26 & ( ( inf_in8396524679539076455nt_int @ A4 @ B5 )
% 6.92/7.26 = bot_bo1488462491386950373nt_int ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_disjoint(1)
% 6.92/7.26 thf(fact_6929_insert__disjoint_I1_J,axiom,
% 6.92/7.26 ! [A: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.26 ( ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ A4 ) @ B5 )
% 6.92/7.26 = bot_bot_set_set_nat )
% 6.92/7.26 = ( ~ ( member_set_nat @ A @ B5 )
% 6.92/7.26 & ( ( inf_inf_set_set_nat @ A4 @ B5 )
% 6.92/7.26 = bot_bot_set_set_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_disjoint(1)
% 6.92/7.26 thf(fact_6930_insert__disjoint_I1_J,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ A4 ) @ B5 )
% 6.92/7.26 = bot_bo2099793752762293965at_nat )
% 6.92/7.26 = ( ~ ( member8440522571783428010at_nat @ A @ B5 )
% 6.92/7.26 & ( ( inf_in2572325071724192079at_nat @ A4 @ B5 )
% 6.92/7.26 = bot_bo2099793752762293965at_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_disjoint(1)
% 6.92/7.26 thf(fact_6931_insert__disjoint_I1_J,axiom,
% 6.92/7.26 ! [A: $o,A4: set_o,B5: set_o] :
% 6.92/7.26 ( ( ( inf_inf_set_o @ ( insert_o @ A @ A4 ) @ B5 )
% 6.92/7.26 = bot_bot_set_o )
% 6.92/7.26 = ( ~ ( member_o @ A @ B5 )
% 6.92/7.26 & ( ( inf_inf_set_o @ A4 @ B5 )
% 6.92/7.26 = bot_bot_set_o ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_disjoint(1)
% 6.92/7.26 thf(fact_6932_insert__disjoint_I1_J,axiom,
% 6.92/7.26 ! [A: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.26 ( ( ( inf_inf_set_nat @ ( insert_nat @ A @ A4 ) @ B5 )
% 6.92/7.26 = bot_bot_set_nat )
% 6.92/7.26 = ( ~ ( member_nat @ A @ B5 )
% 6.92/7.26 & ( ( inf_inf_set_nat @ A4 @ B5 )
% 6.92/7.26 = bot_bot_set_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_disjoint(1)
% 6.92/7.26 thf(fact_6933_insert__disjoint_I1_J,axiom,
% 6.92/7.26 ! [A: int,A4: set_int,B5: set_int] :
% 6.92/7.26 ( ( ( inf_inf_set_int @ ( insert_int @ A @ A4 ) @ B5 )
% 6.92/7.26 = bot_bot_set_int )
% 6.92/7.26 = ( ~ ( member_int @ A @ B5 )
% 6.92/7.26 & ( ( inf_inf_set_int @ A4 @ B5 )
% 6.92/7.26 = bot_bot_set_int ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_disjoint(1)
% 6.92/7.26 thf(fact_6934_insert__Diff__single,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( insert9069300056098147895at_nat @ A @ ( minus_3314409938677909166at_nat @ A4 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ A @ A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff_single
% 6.92/7.26 thf(fact_6935_insert__Diff__single,axiom,
% 6.92/7.26 ! [A: $o,A4: set_o] :
% 6.92/7.26 ( ( insert_o @ A @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 6.92/7.26 = ( insert_o @ A @ A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff_single
% 6.92/7.26 thf(fact_6936_insert__Diff__single,axiom,
% 6.92/7.26 ! [A: nat,A4: set_nat] :
% 6.92/7.26 ( ( insert_nat @ A @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 6.92/7.26 = ( insert_nat @ A @ A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff_single
% 6.92/7.26 thf(fact_6937_insert__Diff__single,axiom,
% 6.92/7.26 ! [A: int,A4: set_int] :
% 6.92/7.26 ( ( insert_int @ A @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 6.92/7.26 = ( insert_int @ A @ A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff_single
% 6.92/7.26 thf(fact_6938_insert__Diff__single,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ A @ A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff_single
% 6.92/7.26 thf(fact_6939_subset__Compl__singleton,axiom,
% 6.92/7.26 ! [A4: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( ord_le1268244103169919719at_nat @ A4 @ ( uminus935396558254630718at_nat @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) )
% 6.92/7.26 = ( ~ ( member8757157785044589968at_nat @ B @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_Compl_singleton
% 6.92/7.26 thf(fact_6940_subset__Compl__singleton,axiom,
% 6.92/7.26 ! [A4: set_se6260736226359567993nt_int,B: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( ord_le483042692224249369nt_int @ A4 @ ( uminus6423885277529793776nt_int @ ( insert8897473484851387113nt_int @ B @ bot_bo1488462491386950373nt_int ) ) )
% 6.92/7.26 = ( ~ ( member2340774599025711042nt_int @ B @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_Compl_singleton
% 6.92/7.26 thf(fact_6941_subset__Compl__singleton,axiom,
% 6.92/7.26 ! [A4: set_set_nat,B: set_nat] :
% 6.92/7.26 ( ( ord_le6893508408891458716et_nat @ A4 @ ( uminus613421341184616069et_nat @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 6.92/7.26 = ( ~ ( member_set_nat @ B @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_Compl_singleton
% 6.92/7.26 thf(fact_6942_subset__Compl__singleton,axiom,
% 6.92/7.26 ! [A4: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 6.92/7.26 ( ( ord_le3146513528884898305at_nat @ A4 @ ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) )
% 6.92/7.26 = ( ~ ( member8440522571783428010at_nat @ B @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_Compl_singleton
% 6.92/7.26 thf(fact_6943_subset__Compl__singleton,axiom,
% 6.92/7.26 ! [A4: set_o,B: $o] :
% 6.92/7.26 ( ( ord_less_eq_set_o @ A4 @ ( uminus_uminus_set_o @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 6.92/7.26 = ( ~ ( member_o @ B @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_Compl_singleton
% 6.92/7.26 thf(fact_6944_subset__Compl__singleton,axiom,
% 6.92/7.26 ! [A4: set_nat,B: nat] :
% 6.92/7.26 ( ( ord_less_eq_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 6.92/7.26 = ( ~ ( member_nat @ B @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_Compl_singleton
% 6.92/7.26 thf(fact_6945_subset__Compl__singleton,axiom,
% 6.92/7.26 ! [A4: set_int,B: int] :
% 6.92/7.26 ( ( ord_less_eq_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 6.92/7.26 = ( ~ ( member_int @ B @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_Compl_singleton
% 6.92/7.26 thf(fact_6946_prod_Odisc__eq__case,axiom,
% 6.92/7.26 ! [Prod: product_prod_int_int] :
% 6.92/7.26 ( produc4947309494688390418_int_o
% 6.92/7.26 @ ^ [Uu2: int,Uv2: int] : $true
% 6.92/7.26 @ Prod ) ).
% 6.92/7.26
% 6.92/7.26 % prod.disc_eq_case
% 6.92/7.26 thf(fact_6947_mk__disjoint__insert,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( member8757157785044589968at_nat @ A @ A4 )
% 6.92/7.26 => ? [B9: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert9069300056098147895at_nat @ A @ B9 ) )
% 6.92/7.26 & ~ ( member8757157785044589968at_nat @ A @ B9 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % mk_disjoint_insert
% 6.92/7.26 thf(fact_6948_mk__disjoint__insert,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( member8440522571783428010at_nat @ A @ A4 )
% 6.92/7.26 => ? [B9: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert8211810215607154385at_nat @ A @ B9 ) )
% 6.92/7.26 & ~ ( member8440522571783428010at_nat @ A @ B9 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % mk_disjoint_insert
% 6.92/7.26 thf(fact_6949_mk__disjoint__insert,axiom,
% 6.92/7.26 ! [A: $o,A4: set_o] :
% 6.92/7.26 ( ( member_o @ A @ A4 )
% 6.92/7.26 => ? [B9: set_o] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert_o @ A @ B9 ) )
% 6.92/7.26 & ~ ( member_o @ A @ B9 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % mk_disjoint_insert
% 6.92/7.26 thf(fact_6950_mk__disjoint__insert,axiom,
% 6.92/7.26 ! [A: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( member2340774599025711042nt_int @ A @ A4 )
% 6.92/7.26 => ? [B9: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert8897473484851387113nt_int @ A @ B9 ) )
% 6.92/7.26 & ~ ( member2340774599025711042nt_int @ A @ B9 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % mk_disjoint_insert
% 6.92/7.26 thf(fact_6951_mk__disjoint__insert,axiom,
% 6.92/7.26 ! [A: set_nat,A4: set_set_nat] :
% 6.92/7.26 ( ( member_set_nat @ A @ A4 )
% 6.92/7.26 => ? [B9: set_set_nat] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert_set_nat @ A @ B9 ) )
% 6.92/7.26 & ~ ( member_set_nat @ A @ B9 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % mk_disjoint_insert
% 6.92/7.26 thf(fact_6952_mk__disjoint__insert,axiom,
% 6.92/7.26 ! [A: nat,A4: set_nat] :
% 6.92/7.26 ( ( member_nat @ A @ A4 )
% 6.92/7.26 => ? [B9: set_nat] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert_nat @ A @ B9 ) )
% 6.92/7.26 & ~ ( member_nat @ A @ B9 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % mk_disjoint_insert
% 6.92/7.26 thf(fact_6953_mk__disjoint__insert,axiom,
% 6.92/7.26 ! [A: int,A4: set_int] :
% 6.92/7.26 ( ( member_int @ A @ A4 )
% 6.92/7.26 => ? [B9: set_int] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert_int @ A @ B9 ) )
% 6.92/7.26 & ~ ( member_int @ A @ B9 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % mk_disjoint_insert
% 6.92/7.26 thf(fact_6954_insert__commute,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( insert9069300056098147895at_nat @ X @ ( insert9069300056098147895at_nat @ Y @ A4 ) )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ Y @ ( insert9069300056098147895at_nat @ X @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_commute
% 6.92/7.26 thf(fact_6955_insert__commute,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( insert8211810215607154385at_nat @ X @ ( insert8211810215607154385at_nat @ Y @ A4 ) )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ Y @ ( insert8211810215607154385at_nat @ X @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_commute
% 6.92/7.26 thf(fact_6956_insert__commute,axiom,
% 6.92/7.26 ! [X: $o,Y: $o,A4: set_o] :
% 6.92/7.26 ( ( insert_o @ X @ ( insert_o @ Y @ A4 ) )
% 6.92/7.26 = ( insert_o @ Y @ ( insert_o @ X @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_commute
% 6.92/7.26 thf(fact_6957_insert__commute,axiom,
% 6.92/7.26 ! [X: nat,Y: nat,A4: set_nat] :
% 6.92/7.26 ( ( insert_nat @ X @ ( insert_nat @ Y @ A4 ) )
% 6.92/7.26 = ( insert_nat @ Y @ ( insert_nat @ X @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_commute
% 6.92/7.26 thf(fact_6958_insert__commute,axiom,
% 6.92/7.26 ! [X: int,Y: int,A4: set_int] :
% 6.92/7.26 ( ( insert_int @ X @ ( insert_int @ Y @ A4 ) )
% 6.92/7.26 = ( insert_int @ Y @ ( insert_int @ X @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_commute
% 6.92/7.26 thf(fact_6959_insert__eq__iff,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ~ ( member8757157785044589968at_nat @ A @ A4 )
% 6.92/7.26 => ( ~ ( member8757157785044589968at_nat @ B @ B5 )
% 6.92/7.26 => ( ( ( insert9069300056098147895at_nat @ A @ A4 )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ B @ B5 ) )
% 6.92/7.26 = ( ( ( A = B )
% 6.92/7.26 => ( A4 = B5 ) )
% 6.92/7.26 & ( ( A != B )
% 6.92/7.26 => ? [C5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert9069300056098147895at_nat @ B @ C5 ) )
% 6.92/7.26 & ~ ( member8757157785044589968at_nat @ B @ C5 )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert9069300056098147895at_nat @ A @ C5 ) )
% 6.92/7.26 & ~ ( member8757157785044589968at_nat @ A @ C5 ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_eq_iff
% 6.92/7.26 thf(fact_6960_insert__eq__iff,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ~ ( member8440522571783428010at_nat @ A @ A4 )
% 6.92/7.26 => ( ~ ( member8440522571783428010at_nat @ B @ B5 )
% 6.92/7.26 => ( ( ( insert8211810215607154385at_nat @ A @ A4 )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ B @ B5 ) )
% 6.92/7.26 = ( ( ( A = B )
% 6.92/7.26 => ( A4 = B5 ) )
% 6.92/7.26 & ( ( A != B )
% 6.92/7.26 => ? [C5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert8211810215607154385at_nat @ B @ C5 ) )
% 6.92/7.26 & ~ ( member8440522571783428010at_nat @ B @ C5 )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert8211810215607154385at_nat @ A @ C5 ) )
% 6.92/7.26 & ~ ( member8440522571783428010at_nat @ A @ C5 ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_eq_iff
% 6.92/7.26 thf(fact_6961_insert__eq__iff,axiom,
% 6.92/7.26 ! [A: $o,A4: set_o,B: $o,B5: set_o] :
% 6.92/7.26 ( ~ ( member_o @ A @ A4 )
% 6.92/7.26 => ( ~ ( member_o @ B @ B5 )
% 6.92/7.26 => ( ( ( insert_o @ A @ A4 )
% 6.92/7.26 = ( insert_o @ B @ B5 ) )
% 6.92/7.26 = ( ( ( A = B )
% 6.92/7.26 => ( A4 = B5 ) )
% 6.92/7.26 & ( ( A = ~ B )
% 6.92/7.26 => ? [C5: set_o] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert_o @ B @ C5 ) )
% 6.92/7.26 & ~ ( member_o @ B @ C5 )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_o @ A @ C5 ) )
% 6.92/7.26 & ~ ( member_o @ A @ C5 ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_eq_iff
% 6.92/7.26 thf(fact_6962_insert__eq__iff,axiom,
% 6.92/7.26 ! [A: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B: set_Pr958786334691620121nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ~ ( member2340774599025711042nt_int @ A @ A4 )
% 6.92/7.26 => ( ~ ( member2340774599025711042nt_int @ B @ B5 )
% 6.92/7.26 => ( ( ( insert8897473484851387113nt_int @ A @ A4 )
% 6.92/7.26 = ( insert8897473484851387113nt_int @ B @ B5 ) )
% 6.92/7.26 = ( ( ( A = B )
% 6.92/7.26 => ( A4 = B5 ) )
% 6.92/7.26 & ( ( A != B )
% 6.92/7.26 => ? [C5: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert8897473484851387113nt_int @ B @ C5 ) )
% 6.92/7.26 & ~ ( member2340774599025711042nt_int @ B @ C5 )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert8897473484851387113nt_int @ A @ C5 ) )
% 6.92/7.26 & ~ ( member2340774599025711042nt_int @ A @ C5 ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_eq_iff
% 6.92/7.26 thf(fact_6963_insert__eq__iff,axiom,
% 6.92/7.26 ! [A: set_nat,A4: set_set_nat,B: set_nat,B5: set_set_nat] :
% 6.92/7.26 ( ~ ( member_set_nat @ A @ A4 )
% 6.92/7.26 => ( ~ ( member_set_nat @ B @ B5 )
% 6.92/7.26 => ( ( ( insert_set_nat @ A @ A4 )
% 6.92/7.26 = ( insert_set_nat @ B @ B5 ) )
% 6.92/7.26 = ( ( ( A = B )
% 6.92/7.26 => ( A4 = B5 ) )
% 6.92/7.26 & ( ( A != B )
% 6.92/7.26 => ? [C5: set_set_nat] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert_set_nat @ B @ C5 ) )
% 6.92/7.26 & ~ ( member_set_nat @ B @ C5 )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_set_nat @ A @ C5 ) )
% 6.92/7.26 & ~ ( member_set_nat @ A @ C5 ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_eq_iff
% 6.92/7.26 thf(fact_6964_insert__eq__iff,axiom,
% 6.92/7.26 ! [A: nat,A4: set_nat,B: nat,B5: set_nat] :
% 6.92/7.26 ( ~ ( member_nat @ A @ A4 )
% 6.92/7.26 => ( ~ ( member_nat @ B @ B5 )
% 6.92/7.26 => ( ( ( insert_nat @ A @ A4 )
% 6.92/7.26 = ( insert_nat @ B @ B5 ) )
% 6.92/7.26 = ( ( ( A = B )
% 6.92/7.26 => ( A4 = B5 ) )
% 6.92/7.26 & ( ( A != B )
% 6.92/7.26 => ? [C5: set_nat] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert_nat @ B @ C5 ) )
% 6.92/7.26 & ~ ( member_nat @ B @ C5 )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_nat @ A @ C5 ) )
% 6.92/7.26 & ~ ( member_nat @ A @ C5 ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_eq_iff
% 6.92/7.26 thf(fact_6965_insert__eq__iff,axiom,
% 6.92/7.26 ! [A: int,A4: set_int,B: int,B5: set_int] :
% 6.92/7.26 ( ~ ( member_int @ A @ A4 )
% 6.92/7.26 => ( ~ ( member_int @ B @ B5 )
% 6.92/7.26 => ( ( ( insert_int @ A @ A4 )
% 6.92/7.26 = ( insert_int @ B @ B5 ) )
% 6.92/7.26 = ( ( ( A = B )
% 6.92/7.26 => ( A4 = B5 ) )
% 6.92/7.26 & ( ( A != B )
% 6.92/7.26 => ? [C5: set_int] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert_int @ B @ C5 ) )
% 6.92/7.26 & ~ ( member_int @ B @ C5 )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_int @ A @ C5 ) )
% 6.92/7.26 & ~ ( member_int @ A @ C5 ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_eq_iff
% 6.92/7.26 thf(fact_6966_insert__absorb,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( member8757157785044589968at_nat @ A @ A4 )
% 6.92/7.26 => ( ( insert9069300056098147895at_nat @ A @ A4 )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_absorb
% 6.92/7.26 thf(fact_6967_insert__absorb,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( member8440522571783428010at_nat @ A @ A4 )
% 6.92/7.26 => ( ( insert8211810215607154385at_nat @ A @ A4 )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_absorb
% 6.92/7.26 thf(fact_6968_insert__absorb,axiom,
% 6.92/7.26 ! [A: $o,A4: set_o] :
% 6.92/7.26 ( ( member_o @ A @ A4 )
% 6.92/7.26 => ( ( insert_o @ A @ A4 )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_absorb
% 6.92/7.26 thf(fact_6969_insert__absorb,axiom,
% 6.92/7.26 ! [A: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( member2340774599025711042nt_int @ A @ A4 )
% 6.92/7.26 => ( ( insert8897473484851387113nt_int @ A @ A4 )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_absorb
% 6.92/7.26 thf(fact_6970_insert__absorb,axiom,
% 6.92/7.26 ! [A: set_nat,A4: set_set_nat] :
% 6.92/7.26 ( ( member_set_nat @ A @ A4 )
% 6.92/7.26 => ( ( insert_set_nat @ A @ A4 )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_absorb
% 6.92/7.26 thf(fact_6971_insert__absorb,axiom,
% 6.92/7.26 ! [A: nat,A4: set_nat] :
% 6.92/7.26 ( ( member_nat @ A @ A4 )
% 6.92/7.26 => ( ( insert_nat @ A @ A4 )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_absorb
% 6.92/7.26 thf(fact_6972_insert__absorb,axiom,
% 6.92/7.26 ! [A: int,A4: set_int] :
% 6.92/7.26 ( ( member_int @ A @ A4 )
% 6.92/7.26 => ( ( insert_int @ A @ A4 )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_absorb
% 6.92/7.26 thf(fact_6973_insert__ident,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ~ ( member8757157785044589968at_nat @ X @ A4 )
% 6.92/7.26 => ( ~ ( member8757157785044589968at_nat @ X @ B5 )
% 6.92/7.26 => ( ( ( insert9069300056098147895at_nat @ X @ A4 )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ X @ B5 ) )
% 6.92/7.26 = ( A4 = B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_ident
% 6.92/7.26 thf(fact_6974_insert__ident,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ~ ( member8440522571783428010at_nat @ X @ A4 )
% 6.92/7.26 => ( ~ ( member8440522571783428010at_nat @ X @ B5 )
% 6.92/7.26 => ( ( ( insert8211810215607154385at_nat @ X @ A4 )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ X @ B5 ) )
% 6.92/7.26 = ( A4 = B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_ident
% 6.92/7.26 thf(fact_6975_insert__ident,axiom,
% 6.92/7.26 ! [X: $o,A4: set_o,B5: set_o] :
% 6.92/7.26 ( ~ ( member_o @ X @ A4 )
% 6.92/7.26 => ( ~ ( member_o @ X @ B5 )
% 6.92/7.26 => ( ( ( insert_o @ X @ A4 )
% 6.92/7.26 = ( insert_o @ X @ B5 ) )
% 6.92/7.26 = ( A4 = B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_ident
% 6.92/7.26 thf(fact_6976_insert__ident,axiom,
% 6.92/7.26 ! [X: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ~ ( member2340774599025711042nt_int @ X @ A4 )
% 6.92/7.26 => ( ~ ( member2340774599025711042nt_int @ X @ B5 )
% 6.92/7.26 => ( ( ( insert8897473484851387113nt_int @ X @ A4 )
% 6.92/7.26 = ( insert8897473484851387113nt_int @ X @ B5 ) )
% 6.92/7.26 = ( A4 = B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_ident
% 6.92/7.26 thf(fact_6977_insert__ident,axiom,
% 6.92/7.26 ! [X: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.26 ( ~ ( member_set_nat @ X @ A4 )
% 6.92/7.26 => ( ~ ( member_set_nat @ X @ B5 )
% 6.92/7.26 => ( ( ( insert_set_nat @ X @ A4 )
% 6.92/7.26 = ( insert_set_nat @ X @ B5 ) )
% 6.92/7.26 = ( A4 = B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_ident
% 6.92/7.26 thf(fact_6978_insert__ident,axiom,
% 6.92/7.26 ! [X: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.26 ( ~ ( member_nat @ X @ A4 )
% 6.92/7.26 => ( ~ ( member_nat @ X @ B5 )
% 6.92/7.26 => ( ( ( insert_nat @ X @ A4 )
% 6.92/7.26 = ( insert_nat @ X @ B5 ) )
% 6.92/7.26 = ( A4 = B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_ident
% 6.92/7.26 thf(fact_6979_insert__ident,axiom,
% 6.92/7.26 ! [X: int,A4: set_int,B5: set_int] :
% 6.92/7.26 ( ~ ( member_int @ X @ A4 )
% 6.92/7.26 => ( ~ ( member_int @ X @ B5 )
% 6.92/7.26 => ( ( ( insert_int @ X @ A4 )
% 6.92/7.26 = ( insert_int @ X @ B5 ) )
% 6.92/7.26 = ( A4 = B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_ident
% 6.92/7.26 thf(fact_6980_Set_Oset__insert,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( member8757157785044589968at_nat @ X @ A4 )
% 6.92/7.26 => ~ ! [B9: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert9069300056098147895at_nat @ X @ B9 ) )
% 6.92/7.26 => ( member8757157785044589968at_nat @ X @ B9 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Set.set_insert
% 6.92/7.26 thf(fact_6981_Set_Oset__insert,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( member8440522571783428010at_nat @ X @ A4 )
% 6.92/7.26 => ~ ! [B9: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert8211810215607154385at_nat @ X @ B9 ) )
% 6.92/7.26 => ( member8440522571783428010at_nat @ X @ B9 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Set.set_insert
% 6.92/7.26 thf(fact_6982_Set_Oset__insert,axiom,
% 6.92/7.26 ! [X: $o,A4: set_o] :
% 6.92/7.26 ( ( member_o @ X @ A4 )
% 6.92/7.26 => ~ ! [B9: set_o] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert_o @ X @ B9 ) )
% 6.92/7.26 => ( member_o @ X @ B9 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Set.set_insert
% 6.92/7.26 thf(fact_6983_Set_Oset__insert,axiom,
% 6.92/7.26 ! [X: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( member2340774599025711042nt_int @ X @ A4 )
% 6.92/7.26 => ~ ! [B9: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert8897473484851387113nt_int @ X @ B9 ) )
% 6.92/7.26 => ( member2340774599025711042nt_int @ X @ B9 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Set.set_insert
% 6.92/7.26 thf(fact_6984_Set_Oset__insert,axiom,
% 6.92/7.26 ! [X: set_nat,A4: set_set_nat] :
% 6.92/7.26 ( ( member_set_nat @ X @ A4 )
% 6.92/7.26 => ~ ! [B9: set_set_nat] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert_set_nat @ X @ B9 ) )
% 6.92/7.26 => ( member_set_nat @ X @ B9 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Set.set_insert
% 6.92/7.26 thf(fact_6985_Set_Oset__insert,axiom,
% 6.92/7.26 ! [X: nat,A4: set_nat] :
% 6.92/7.26 ( ( member_nat @ X @ A4 )
% 6.92/7.26 => ~ ! [B9: set_nat] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert_nat @ X @ B9 ) )
% 6.92/7.26 => ( member_nat @ X @ B9 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Set.set_insert
% 6.92/7.26 thf(fact_6986_Set_Oset__insert,axiom,
% 6.92/7.26 ! [X: int,A4: set_int] :
% 6.92/7.26 ( ( member_int @ X @ A4 )
% 6.92/7.26 => ~ ! [B9: set_int] :
% 6.92/7.26 ( ( A4
% 6.92/7.26 = ( insert_int @ X @ B9 ) )
% 6.92/7.26 => ( member_int @ X @ B9 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Set.set_insert
% 6.92/7.26 thf(fact_6987_insertI2,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( member8757157785044589968at_nat @ A @ B5 )
% 6.92/7.26 => ( member8757157785044589968at_nat @ A @ ( insert9069300056098147895at_nat @ B @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertI2
% 6.92/7.26 thf(fact_6988_insertI2,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 6.92/7.26 ( ( member8440522571783428010at_nat @ A @ B5 )
% 6.92/7.26 => ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ B @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertI2
% 6.92/7.26 thf(fact_6989_insertI2,axiom,
% 6.92/7.26 ! [A: $o,B5: set_o,B: $o] :
% 6.92/7.26 ( ( member_o @ A @ B5 )
% 6.92/7.26 => ( member_o @ A @ ( insert_o @ B @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertI2
% 6.92/7.26 thf(fact_6990_insertI2,axiom,
% 6.92/7.26 ! [A: set_Pr958786334691620121nt_int,B5: set_se6260736226359567993nt_int,B: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( member2340774599025711042nt_int @ A @ B5 )
% 6.92/7.26 => ( member2340774599025711042nt_int @ A @ ( insert8897473484851387113nt_int @ B @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertI2
% 6.92/7.26 thf(fact_6991_insertI2,axiom,
% 6.92/7.26 ! [A: set_nat,B5: set_set_nat,B: set_nat] :
% 6.92/7.26 ( ( member_set_nat @ A @ B5 )
% 6.92/7.26 => ( member_set_nat @ A @ ( insert_set_nat @ B @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertI2
% 6.92/7.26 thf(fact_6992_insertI2,axiom,
% 6.92/7.26 ! [A: nat,B5: set_nat,B: nat] :
% 6.92/7.26 ( ( member_nat @ A @ B5 )
% 6.92/7.26 => ( member_nat @ A @ ( insert_nat @ B @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertI2
% 6.92/7.26 thf(fact_6993_insertI2,axiom,
% 6.92/7.26 ! [A: int,B5: set_int,B: int] :
% 6.92/7.26 ( ( member_int @ A @ B5 )
% 6.92/7.26 => ( member_int @ A @ ( insert_int @ B @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertI2
% 6.92/7.26 thf(fact_6994_insertI1,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat] : ( member8757157785044589968at_nat @ A @ ( insert9069300056098147895at_nat @ A @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertI1
% 6.92/7.26 thf(fact_6995_insertI1,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] : ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ A @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertI1
% 6.92/7.26 thf(fact_6996_insertI1,axiom,
% 6.92/7.26 ! [A: $o,B5: set_o] : ( member_o @ A @ ( insert_o @ A @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertI1
% 6.92/7.26 thf(fact_6997_insertI1,axiom,
% 6.92/7.26 ! [A: set_Pr958786334691620121nt_int,B5: set_se6260736226359567993nt_int] : ( member2340774599025711042nt_int @ A @ ( insert8897473484851387113nt_int @ A @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertI1
% 6.92/7.26 thf(fact_6998_insertI1,axiom,
% 6.92/7.26 ! [A: set_nat,B5: set_set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertI1
% 6.92/7.26 thf(fact_6999_insertI1,axiom,
% 6.92/7.26 ! [A: nat,B5: set_nat] : ( member_nat @ A @ ( insert_nat @ A @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertI1
% 6.92/7.26 thf(fact_7000_insertI1,axiom,
% 6.92/7.26 ! [A: int,B5: set_int] : ( member_int @ A @ ( insert_int @ A @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertI1
% 6.92/7.26 thf(fact_7001_insertE,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( member8757157785044589968at_nat @ A @ ( insert9069300056098147895at_nat @ B @ A4 ) )
% 6.92/7.26 => ( ( A != B )
% 6.92/7.26 => ( member8757157785044589968at_nat @ A @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertE
% 6.92/7.26 thf(fact_7002_insertE,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ B @ A4 ) )
% 6.92/7.26 => ( ( A != B )
% 6.92/7.26 => ( member8440522571783428010at_nat @ A @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertE
% 6.92/7.26 thf(fact_7003_insertE,axiom,
% 6.92/7.26 ! [A: $o,B: $o,A4: set_o] :
% 6.92/7.26 ( ( member_o @ A @ ( insert_o @ B @ A4 ) )
% 6.92/7.26 => ( ( A = ~ B )
% 6.92/7.26 => ( member_o @ A @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertE
% 6.92/7.26 thf(fact_7004_insertE,axiom,
% 6.92/7.26 ! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( member2340774599025711042nt_int @ A @ ( insert8897473484851387113nt_int @ B @ A4 ) )
% 6.92/7.26 => ( ( A != B )
% 6.92/7.26 => ( member2340774599025711042nt_int @ A @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertE
% 6.92/7.26 thf(fact_7005_insertE,axiom,
% 6.92/7.26 ! [A: set_nat,B: set_nat,A4: set_set_nat] :
% 6.92/7.26 ( ( member_set_nat @ A @ ( insert_set_nat @ B @ A4 ) )
% 6.92/7.26 => ( ( A != B )
% 6.92/7.26 => ( member_set_nat @ A @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertE
% 6.92/7.26 thf(fact_7006_insertE,axiom,
% 6.92/7.26 ! [A: nat,B: nat,A4: set_nat] :
% 6.92/7.26 ( ( member_nat @ A @ ( insert_nat @ B @ A4 ) )
% 6.92/7.26 => ( ( A != B )
% 6.92/7.26 => ( member_nat @ A @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertE
% 6.92/7.26 thf(fact_7007_insertE,axiom,
% 6.92/7.26 ! [A: int,B: int,A4: set_int] :
% 6.92/7.26 ( ( member_int @ A @ ( insert_int @ B @ A4 ) )
% 6.92/7.26 => ( ( A != B )
% 6.92/7.26 => ( member_int @ A @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insertE
% 6.92/7.26 thf(fact_7008_insert__compr,axiom,
% 6.92/7.26 ( insert9069300056098147895at_nat
% 6.92/7.26 = ( ^ [A5: produc3843707927480180839at_nat,B6: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( collec6321179662152712658at_nat
% 6.92/7.26 @ ^ [X4: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( X4 = A5 )
% 6.92/7.26 | ( member8757157785044589968at_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_compr
% 6.92/7.26 thf(fact_7009_insert__compr,axiom,
% 6.92/7.26 ( insert8211810215607154385at_nat
% 6.92/7.26 = ( ^ [A5: product_prod_nat_nat,B6: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( collec3392354462482085612at_nat
% 6.92/7.26 @ ^ [X4: product_prod_nat_nat] :
% 6.92/7.26 ( ( X4 = A5 )
% 6.92/7.26 | ( member8440522571783428010at_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_compr
% 6.92/7.26 thf(fact_7010_insert__compr,axiom,
% 6.92/7.26 ( insert_o
% 6.92/7.26 = ( ^ [A5: $o,B6: set_o] :
% 6.92/7.26 ( collect_o
% 6.92/7.26 @ ^ [X4: $o] :
% 6.92/7.26 ( ( X4 = A5 )
% 6.92/7.26 | ( member_o @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_compr
% 6.92/7.26 thf(fact_7011_insert__compr,axiom,
% 6.92/7.26 ( insert_list_nat
% 6.92/7.26 = ( ^ [A5: list_nat,B6: set_list_nat] :
% 6.92/7.26 ( collect_list_nat
% 6.92/7.26 @ ^ [X4: list_nat] :
% 6.92/7.26 ( ( X4 = A5 )
% 6.92/7.26 | ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_compr
% 6.92/7.26 thf(fact_7012_insert__compr,axiom,
% 6.92/7.26 ( insert8897473484851387113nt_int
% 6.92/7.26 = ( ^ [A5: set_Pr958786334691620121nt_int,B6: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( collec5210948495886036740nt_int
% 6.92/7.26 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( X4 = A5 )
% 6.92/7.26 | ( member2340774599025711042nt_int @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_compr
% 6.92/7.26 thf(fact_7013_insert__compr,axiom,
% 6.92/7.26 ( insert_set_nat
% 6.92/7.26 = ( ^ [A5: set_nat,B6: set_set_nat] :
% 6.92/7.26 ( collect_set_nat
% 6.92/7.26 @ ^ [X4: set_nat] :
% 6.92/7.26 ( ( X4 = A5 )
% 6.92/7.26 | ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_compr
% 6.92/7.26 thf(fact_7014_insert__compr,axiom,
% 6.92/7.26 ( insert_nat
% 6.92/7.26 = ( ^ [A5: nat,B6: set_nat] :
% 6.92/7.26 ( collect_nat
% 6.92/7.26 @ ^ [X4: nat] :
% 6.92/7.26 ( ( X4 = A5 )
% 6.92/7.26 | ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_compr
% 6.92/7.26 thf(fact_7015_insert__compr,axiom,
% 6.92/7.26 ( insert_int
% 6.92/7.26 = ( ^ [A5: int,B6: set_int] :
% 6.92/7.26 ( collect_int
% 6.92/7.26 @ ^ [X4: int] :
% 6.92/7.26 ( ( X4 = A5 )
% 6.92/7.26 | ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_compr
% 6.92/7.26 thf(fact_7016_insert__Collect,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,P2: produc3843707927480180839at_nat > $o] :
% 6.92/7.26 ( ( insert9069300056098147895at_nat @ A @ ( collec6321179662152712658at_nat @ P2 ) )
% 6.92/7.26 = ( collec6321179662152712658at_nat
% 6.92/7.26 @ ^ [U3: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( U3 != A )
% 6.92/7.26 => ( P2 @ U3 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Collect
% 6.92/7.26 thf(fact_7017_insert__Collect,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,P2: product_prod_nat_nat > $o] :
% 6.92/7.26 ( ( insert8211810215607154385at_nat @ A @ ( collec3392354462482085612at_nat @ P2 ) )
% 6.92/7.26 = ( collec3392354462482085612at_nat
% 6.92/7.26 @ ^ [U3: product_prod_nat_nat] :
% 6.92/7.26 ( ( U3 != A )
% 6.92/7.26 => ( P2 @ U3 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Collect
% 6.92/7.26 thf(fact_7018_insert__Collect,axiom,
% 6.92/7.26 ! [A: $o,P2: $o > $o] :
% 6.92/7.26 ( ( insert_o @ A @ ( collect_o @ P2 ) )
% 6.92/7.26 = ( collect_o
% 6.92/7.26 @ ^ [U3: $o] :
% 6.92/7.26 ( ( U3 != A )
% 6.92/7.26 => ( P2 @ U3 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Collect
% 6.92/7.26 thf(fact_7019_insert__Collect,axiom,
% 6.92/7.26 ! [A: list_nat,P2: list_nat > $o] :
% 6.92/7.26 ( ( insert_list_nat @ A @ ( collect_list_nat @ P2 ) )
% 6.92/7.26 = ( collect_list_nat
% 6.92/7.26 @ ^ [U3: list_nat] :
% 6.92/7.26 ( ( U3 != A )
% 6.92/7.26 => ( P2 @ U3 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Collect
% 6.92/7.26 thf(fact_7020_insert__Collect,axiom,
% 6.92/7.26 ! [A: set_Pr958786334691620121nt_int,P2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.26 ( ( insert8897473484851387113nt_int @ A @ ( collec5210948495886036740nt_int @ P2 ) )
% 6.92/7.26 = ( collec5210948495886036740nt_int
% 6.92/7.26 @ ^ [U3: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( U3 != A )
% 6.92/7.26 => ( P2 @ U3 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Collect
% 6.92/7.26 thf(fact_7021_insert__Collect,axiom,
% 6.92/7.26 ! [A: set_nat,P2: set_nat > $o] :
% 6.92/7.26 ( ( insert_set_nat @ A @ ( collect_set_nat @ P2 ) )
% 6.92/7.26 = ( collect_set_nat
% 6.92/7.26 @ ^ [U3: set_nat] :
% 6.92/7.26 ( ( U3 != A )
% 6.92/7.26 => ( P2 @ U3 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Collect
% 6.92/7.26 thf(fact_7022_insert__Collect,axiom,
% 6.92/7.26 ! [A: nat,P2: nat > $o] :
% 6.92/7.26 ( ( insert_nat @ A @ ( collect_nat @ P2 ) )
% 6.92/7.26 = ( collect_nat
% 6.92/7.26 @ ^ [U3: nat] :
% 6.92/7.26 ( ( U3 != A )
% 6.92/7.26 => ( P2 @ U3 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Collect
% 6.92/7.26 thf(fact_7023_insert__Collect,axiom,
% 6.92/7.26 ! [A: int,P2: int > $o] :
% 6.92/7.26 ( ( insert_int @ A @ ( collect_int @ P2 ) )
% 6.92/7.26 = ( collect_int
% 6.92/7.26 @ ^ [U3: int] :
% 6.92/7.26 ( ( U3 != A )
% 6.92/7.26 => ( P2 @ U3 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Collect
% 6.92/7.26 thf(fact_7024_singleton__inject,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 => ( A = B ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_inject
% 6.92/7.26 thf(fact_7025_singleton__inject,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 6.92/7.26 ( ( ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 => ( A = B ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_inject
% 6.92/7.26 thf(fact_7026_singleton__inject,axiom,
% 6.92/7.26 ! [A: $o,B: $o] :
% 6.92/7.26 ( ( ( insert_o @ A @ bot_bot_set_o )
% 6.92/7.26 = ( insert_o @ B @ bot_bot_set_o ) )
% 6.92/7.26 => ( A = B ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_inject
% 6.92/7.26 thf(fact_7027_singleton__inject,axiom,
% 6.92/7.26 ! [A: nat,B: nat] :
% 6.92/7.26 ( ( ( insert_nat @ A @ bot_bot_set_nat )
% 6.92/7.26 = ( insert_nat @ B @ bot_bot_set_nat ) )
% 6.92/7.26 => ( A = B ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_inject
% 6.92/7.26 thf(fact_7028_singleton__inject,axiom,
% 6.92/7.26 ! [A: int,B: int] :
% 6.92/7.26 ( ( ( insert_int @ A @ bot_bot_set_int )
% 6.92/7.26 = ( insert_int @ B @ bot_bot_set_int ) )
% 6.92/7.26 => ( A = B ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_inject
% 6.92/7.26 thf(fact_7029_insert__not__empty,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( insert9069300056098147895at_nat @ A @ A4 )
% 6.92/7.26 != bot_bo228742789529271731at_nat ) ).
% 6.92/7.26
% 6.92/7.26 % insert_not_empty
% 6.92/7.26 thf(fact_7030_insert__not__empty,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( insert8211810215607154385at_nat @ A @ A4 )
% 6.92/7.26 != bot_bo2099793752762293965at_nat ) ).
% 6.92/7.26
% 6.92/7.26 % insert_not_empty
% 6.92/7.26 thf(fact_7031_insert__not__empty,axiom,
% 6.92/7.26 ! [A: $o,A4: set_o] :
% 6.92/7.26 ( ( insert_o @ A @ A4 )
% 6.92/7.26 != bot_bot_set_o ) ).
% 6.92/7.26
% 6.92/7.26 % insert_not_empty
% 6.92/7.26 thf(fact_7032_insert__not__empty,axiom,
% 6.92/7.26 ! [A: nat,A4: set_nat] :
% 6.92/7.26 ( ( insert_nat @ A @ A4 )
% 6.92/7.26 != bot_bot_set_nat ) ).
% 6.92/7.26
% 6.92/7.26 % insert_not_empty
% 6.92/7.26 thf(fact_7033_insert__not__empty,axiom,
% 6.92/7.26 ! [A: int,A4: set_int] :
% 6.92/7.26 ( ( insert_int @ A @ A4 )
% 6.92/7.26 != bot_bot_set_int ) ).
% 6.92/7.26
% 6.92/7.26 % insert_not_empty
% 6.92/7.26 thf(fact_7034_doubleton__eq__iff,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,C2: produc3843707927480180839at_nat,D2: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( ( insert9069300056098147895at_nat @ A @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ C2 @ ( insert9069300056098147895at_nat @ D2 @ bot_bo228742789529271731at_nat ) ) )
% 6.92/7.26 = ( ( ( A = C2 )
% 6.92/7.26 & ( B = D2 ) )
% 6.92/7.26 | ( ( A = D2 )
% 6.92/7.26 & ( B = C2 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % doubleton_eq_iff
% 6.92/7.26 thf(fact_7035_doubleton__eq__iff,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,C2: product_prod_nat_nat,D2: product_prod_nat_nat] :
% 6.92/7.26 ( ( ( insert8211810215607154385at_nat @ A @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ C2 @ ( insert8211810215607154385at_nat @ D2 @ bot_bo2099793752762293965at_nat ) ) )
% 6.92/7.26 = ( ( ( A = C2 )
% 6.92/7.26 & ( B = D2 ) )
% 6.92/7.26 | ( ( A = D2 )
% 6.92/7.26 & ( B = C2 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % doubleton_eq_iff
% 6.92/7.26 thf(fact_7036_doubleton__eq__iff,axiom,
% 6.92/7.26 ! [A: $o,B: $o,C2: $o,D2: $o] :
% 6.92/7.26 ( ( ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) )
% 6.92/7.26 = ( insert_o @ C2 @ ( insert_o @ D2 @ bot_bot_set_o ) ) )
% 6.92/7.26 = ( ( ( A = C2 )
% 6.92/7.26 & ( B = D2 ) )
% 6.92/7.26 | ( ( A = D2 )
% 6.92/7.26 & ( B = C2 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % doubleton_eq_iff
% 6.92/7.26 thf(fact_7037_doubleton__eq__iff,axiom,
% 6.92/7.26 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.26 ( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) )
% 6.92/7.26 = ( insert_nat @ C2 @ ( insert_nat @ D2 @ bot_bot_set_nat ) ) )
% 6.92/7.26 = ( ( ( A = C2 )
% 6.92/7.26 & ( B = D2 ) )
% 6.92/7.26 | ( ( A = D2 )
% 6.92/7.26 & ( B = C2 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % doubleton_eq_iff
% 6.92/7.26 thf(fact_7038_doubleton__eq__iff,axiom,
% 6.92/7.26 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.26 ( ( ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) )
% 6.92/7.26 = ( insert_int @ C2 @ ( insert_int @ D2 @ bot_bot_set_int ) ) )
% 6.92/7.26 = ( ( ( A = C2 )
% 6.92/7.26 & ( B = D2 ) )
% 6.92/7.26 | ( ( A = D2 )
% 6.92/7.26 & ( B = C2 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % doubleton_eq_iff
% 6.92/7.26 thf(fact_7039_singleton__iff,axiom,
% 6.92/7.26 ! [B: produc3843707927480180839at_nat,A: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( member8757157785044589968at_nat @ B @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 = ( B = A ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_iff
% 6.92/7.26 thf(fact_7040_singleton__iff,axiom,
% 6.92/7.26 ! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( member2340774599025711042nt_int @ B @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) )
% 6.92/7.26 = ( B = A ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_iff
% 6.92/7.26 thf(fact_7041_singleton__iff,axiom,
% 6.92/7.26 ! [B: set_nat,A: set_nat] :
% 6.92/7.26 ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 6.92/7.26 = ( B = A ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_iff
% 6.92/7.26 thf(fact_7042_singleton__iff,axiom,
% 6.92/7.26 ! [B: product_prod_nat_nat,A: product_prod_nat_nat] :
% 6.92/7.26 ( ( member8440522571783428010at_nat @ B @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 = ( B = A ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_iff
% 6.92/7.26 thf(fact_7043_singleton__iff,axiom,
% 6.92/7.26 ! [B: $o,A: $o] :
% 6.92/7.26 ( ( member_o @ B @ ( insert_o @ A @ bot_bot_set_o ) )
% 6.92/7.26 = ( B = A ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_iff
% 6.92/7.26 thf(fact_7044_singleton__iff,axiom,
% 6.92/7.26 ! [B: nat,A: nat] :
% 6.92/7.26 ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 6.92/7.26 = ( B = A ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_iff
% 6.92/7.26 thf(fact_7045_singleton__iff,axiom,
% 6.92/7.26 ! [B: int,A: int] :
% 6.92/7.26 ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 6.92/7.26 = ( B = A ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_iff
% 6.92/7.26 thf(fact_7046_singletonD,axiom,
% 6.92/7.26 ! [B: produc3843707927480180839at_nat,A: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( member8757157785044589968at_nat @ B @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 => ( B = A ) ) ).
% 6.92/7.26
% 6.92/7.26 % singletonD
% 6.92/7.26 thf(fact_7047_singletonD,axiom,
% 6.92/7.26 ! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( member2340774599025711042nt_int @ B @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) )
% 6.92/7.26 => ( B = A ) ) ).
% 6.92/7.26
% 6.92/7.26 % singletonD
% 6.92/7.26 thf(fact_7048_singletonD,axiom,
% 6.92/7.26 ! [B: set_nat,A: set_nat] :
% 6.92/7.26 ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 6.92/7.26 => ( B = A ) ) ).
% 6.92/7.26
% 6.92/7.26 % singletonD
% 6.92/7.26 thf(fact_7049_singletonD,axiom,
% 6.92/7.26 ! [B: product_prod_nat_nat,A: product_prod_nat_nat] :
% 6.92/7.26 ( ( member8440522571783428010at_nat @ B @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 => ( B = A ) ) ).
% 6.92/7.26
% 6.92/7.26 % singletonD
% 6.92/7.26 thf(fact_7050_singletonD,axiom,
% 6.92/7.26 ! [B: $o,A: $o] :
% 6.92/7.26 ( ( member_o @ B @ ( insert_o @ A @ bot_bot_set_o ) )
% 6.92/7.26 => ( B = A ) ) ).
% 6.92/7.26
% 6.92/7.26 % singletonD
% 6.92/7.26 thf(fact_7051_singletonD,axiom,
% 6.92/7.26 ! [B: nat,A: nat] :
% 6.92/7.26 ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 6.92/7.26 => ( B = A ) ) ).
% 6.92/7.26
% 6.92/7.26 % singletonD
% 6.92/7.26 thf(fact_7052_singletonD,axiom,
% 6.92/7.26 ! [B: int,A: int] :
% 6.92/7.26 ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 6.92/7.26 => ( B = A ) ) ).
% 6.92/7.26
% 6.92/7.26 % singletonD
% 6.92/7.26 thf(fact_7053_insert__mono,axiom,
% 6.92/7.26 ! [C4: set_Pr4329608150637261639at_nat,D4: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( ord_le1268244103169919719at_nat @ C4 @ D4 )
% 6.92/7.26 => ( ord_le1268244103169919719at_nat @ ( insert9069300056098147895at_nat @ A @ C4 ) @ ( insert9069300056098147895at_nat @ A @ D4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_mono
% 6.92/7.26 thf(fact_7054_insert__mono,axiom,
% 6.92/7.26 ! [C4: set_Pr1261947904930325089at_nat,D4: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 6.92/7.26 ( ( ord_le3146513528884898305at_nat @ C4 @ D4 )
% 6.92/7.26 => ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ A @ C4 ) @ ( insert8211810215607154385at_nat @ A @ D4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_mono
% 6.92/7.26 thf(fact_7055_insert__mono,axiom,
% 6.92/7.26 ! [C4: set_o,D4: set_o,A: $o] :
% 6.92/7.26 ( ( ord_less_eq_set_o @ C4 @ D4 )
% 6.92/7.26 => ( ord_less_eq_set_o @ ( insert_o @ A @ C4 ) @ ( insert_o @ A @ D4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_mono
% 6.92/7.26 thf(fact_7056_insert__mono,axiom,
% 6.92/7.26 ! [C4: set_nat,D4: set_nat,A: nat] :
% 6.92/7.26 ( ( ord_less_eq_set_nat @ C4 @ D4 )
% 6.92/7.26 => ( ord_less_eq_set_nat @ ( insert_nat @ A @ C4 ) @ ( insert_nat @ A @ D4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_mono
% 6.92/7.26 thf(fact_7057_insert__mono,axiom,
% 6.92/7.26 ! [C4: set_int,D4: set_int,A: int] :
% 6.92/7.26 ( ( ord_less_eq_set_int @ C4 @ D4 )
% 6.92/7.26 => ( ord_less_eq_set_int @ ( insert_int @ A @ C4 ) @ ( insert_int @ A @ D4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_mono
% 6.92/7.26 thf(fact_7058_subset__insert,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ~ ( member8757157785044589968at_nat @ X @ A4 )
% 6.92/7.26 => ( ( ord_le1268244103169919719at_nat @ A4 @ ( insert9069300056098147895at_nat @ X @ B5 ) )
% 6.92/7.26 = ( ord_le1268244103169919719at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insert
% 6.92/7.26 thf(fact_7059_subset__insert,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ~ ( member8440522571783428010at_nat @ X @ A4 )
% 6.92/7.26 => ( ( ord_le3146513528884898305at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ B5 ) )
% 6.92/7.26 = ( ord_le3146513528884898305at_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insert
% 6.92/7.26 thf(fact_7060_subset__insert,axiom,
% 6.92/7.26 ! [X: $o,A4: set_o,B5: set_o] :
% 6.92/7.26 ( ~ ( member_o @ X @ A4 )
% 6.92/7.26 => ( ( ord_less_eq_set_o @ A4 @ ( insert_o @ X @ B5 ) )
% 6.92/7.26 = ( ord_less_eq_set_o @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insert
% 6.92/7.26 thf(fact_7061_subset__insert,axiom,
% 6.92/7.26 ! [X: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ~ ( member2340774599025711042nt_int @ X @ A4 )
% 6.92/7.26 => ( ( ord_le483042692224249369nt_int @ A4 @ ( insert8897473484851387113nt_int @ X @ B5 ) )
% 6.92/7.26 = ( ord_le483042692224249369nt_int @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insert
% 6.92/7.26 thf(fact_7062_subset__insert,axiom,
% 6.92/7.26 ! [X: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.26 ( ~ ( member_set_nat @ X @ A4 )
% 6.92/7.26 => ( ( ord_le6893508408891458716et_nat @ A4 @ ( insert_set_nat @ X @ B5 ) )
% 6.92/7.26 = ( ord_le6893508408891458716et_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insert
% 6.92/7.26 thf(fact_7063_subset__insert,axiom,
% 6.92/7.26 ! [X: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.26 ( ~ ( member_nat @ X @ A4 )
% 6.92/7.26 => ( ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ X @ B5 ) )
% 6.92/7.26 = ( ord_less_eq_set_nat @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insert
% 6.92/7.26 thf(fact_7064_subset__insert,axiom,
% 6.92/7.26 ! [X: int,A4: set_int,B5: set_int] :
% 6.92/7.26 ( ~ ( member_int @ X @ A4 )
% 6.92/7.26 => ( ( ord_less_eq_set_int @ A4 @ ( insert_int @ X @ B5 ) )
% 6.92/7.26 = ( ord_less_eq_set_int @ A4 @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insert
% 6.92/7.26 thf(fact_7065_subset__insertI,axiom,
% 6.92/7.26 ! [B5: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat] : ( ord_le1268244103169919719at_nat @ B5 @ ( insert9069300056098147895at_nat @ A @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insertI
% 6.92/7.26 thf(fact_7066_subset__insertI,axiom,
% 6.92/7.26 ! [B5: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ B5 @ ( insert8211810215607154385at_nat @ A @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insertI
% 6.92/7.26 thf(fact_7067_subset__insertI,axiom,
% 6.92/7.26 ! [B5: set_o,A: $o] : ( ord_less_eq_set_o @ B5 @ ( insert_o @ A @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insertI
% 6.92/7.26 thf(fact_7068_subset__insertI,axiom,
% 6.92/7.26 ! [B5: set_nat,A: nat] : ( ord_less_eq_set_nat @ B5 @ ( insert_nat @ A @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insertI
% 6.92/7.26 thf(fact_7069_subset__insertI,axiom,
% 6.92/7.26 ! [B5: set_int,A: int] : ( ord_less_eq_set_int @ B5 @ ( insert_int @ A @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insertI
% 6.92/7.26 thf(fact_7070_subset__insertI2,axiom,
% 6.92/7.26 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( ord_le1268244103169919719at_nat @ A4 @ B5 )
% 6.92/7.26 => ( ord_le1268244103169919719at_nat @ A4 @ ( insert9069300056098147895at_nat @ B @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insertI2
% 6.92/7.26 thf(fact_7071_subset__insertI2,axiom,
% 6.92/7.26 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 6.92/7.26 ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 6.92/7.26 => ( ord_le3146513528884898305at_nat @ A4 @ ( insert8211810215607154385at_nat @ B @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insertI2
% 6.92/7.26 thf(fact_7072_subset__insertI2,axiom,
% 6.92/7.26 ! [A4: set_o,B5: set_o,B: $o] :
% 6.92/7.26 ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.92/7.26 => ( ord_less_eq_set_o @ A4 @ ( insert_o @ B @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insertI2
% 6.92/7.26 thf(fact_7073_subset__insertI2,axiom,
% 6.92/7.26 ! [A4: set_nat,B5: set_nat,B: nat] :
% 6.92/7.26 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.92/7.26 => ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ B @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insertI2
% 6.92/7.26 thf(fact_7074_subset__insertI2,axiom,
% 6.92/7.26 ! [A4: set_int,B5: set_int,B: int] :
% 6.92/7.26 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.26 => ( ord_less_eq_set_int @ A4 @ ( insert_int @ B @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insertI2
% 6.92/7.26 thf(fact_7075_insert__subsetI,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,X7: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( member8757157785044589968at_nat @ X @ A4 )
% 6.92/7.26 => ( ( ord_le1268244103169919719at_nat @ X7 @ A4 )
% 6.92/7.26 => ( ord_le1268244103169919719at_nat @ ( insert9069300056098147895at_nat @ X @ X7 ) @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_subsetI
% 6.92/7.26 thf(fact_7076_insert__subsetI,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,X7: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( member8440522571783428010at_nat @ X @ A4 )
% 6.92/7.26 => ( ( ord_le3146513528884898305at_nat @ X7 @ A4 )
% 6.92/7.26 => ( ord_le3146513528884898305at_nat @ ( insert8211810215607154385at_nat @ X @ X7 ) @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_subsetI
% 6.92/7.26 thf(fact_7077_insert__subsetI,axiom,
% 6.92/7.26 ! [X: $o,A4: set_o,X7: set_o] :
% 6.92/7.26 ( ( member_o @ X @ A4 )
% 6.92/7.26 => ( ( ord_less_eq_set_o @ X7 @ A4 )
% 6.92/7.26 => ( ord_less_eq_set_o @ ( insert_o @ X @ X7 ) @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_subsetI
% 6.92/7.26 thf(fact_7078_insert__subsetI,axiom,
% 6.92/7.26 ! [X: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,X7: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( member2340774599025711042nt_int @ X @ A4 )
% 6.92/7.26 => ( ( ord_le483042692224249369nt_int @ X7 @ A4 )
% 6.92/7.26 => ( ord_le483042692224249369nt_int @ ( insert8897473484851387113nt_int @ X @ X7 ) @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_subsetI
% 6.92/7.26 thf(fact_7079_insert__subsetI,axiom,
% 6.92/7.26 ! [X: set_nat,A4: set_set_nat,X7: set_set_nat] :
% 6.92/7.26 ( ( member_set_nat @ X @ A4 )
% 6.92/7.26 => ( ( ord_le6893508408891458716et_nat @ X7 @ A4 )
% 6.92/7.26 => ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X @ X7 ) @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_subsetI
% 6.92/7.26 thf(fact_7080_insert__subsetI,axiom,
% 6.92/7.26 ! [X: nat,A4: set_nat,X7: set_nat] :
% 6.92/7.26 ( ( member_nat @ X @ A4 )
% 6.92/7.26 => ( ( ord_less_eq_set_nat @ X7 @ A4 )
% 6.92/7.26 => ( ord_less_eq_set_nat @ ( insert_nat @ X @ X7 ) @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_subsetI
% 6.92/7.26 thf(fact_7081_insert__subsetI,axiom,
% 6.92/7.26 ! [X: int,A4: set_int,X7: set_int] :
% 6.92/7.26 ( ( member_int @ X @ A4 )
% 6.92/7.26 => ( ( ord_less_eq_set_int @ X7 @ A4 )
% 6.92/7.26 => ( ord_less_eq_set_int @ ( insert_int @ X @ X7 ) @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_subsetI
% 6.92/7.26 thf(fact_7082_Int__insert__right,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( ( member8757157785044589968at_nat @ A @ A4 )
% 6.92/7.26 => ( ( inf_in7913087082777306421at_nat @ A4 @ ( insert9069300056098147895at_nat @ A @ B5 ) )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ A @ ( inf_in7913087082777306421at_nat @ A4 @ B5 ) ) ) )
% 6.92/7.26 & ( ~ ( member8757157785044589968at_nat @ A @ A4 )
% 6.92/7.26 => ( ( inf_in7913087082777306421at_nat @ A4 @ ( insert9069300056098147895at_nat @ A @ B5 ) )
% 6.92/7.26 = ( inf_in7913087082777306421at_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Int_insert_right
% 6.92/7.26 thf(fact_7083_Int__insert__right,axiom,
% 6.92/7.26 ! [A: $o,A4: set_o,B5: set_o] :
% 6.92/7.26 ( ( ( member_o @ A @ A4 )
% 6.92/7.26 => ( ( inf_inf_set_o @ A4 @ ( insert_o @ A @ B5 ) )
% 6.92/7.26 = ( insert_o @ A @ ( inf_inf_set_o @ A4 @ B5 ) ) ) )
% 6.92/7.26 & ( ~ ( member_o @ A @ A4 )
% 6.92/7.26 => ( ( inf_inf_set_o @ A4 @ ( insert_o @ A @ B5 ) )
% 6.92/7.26 = ( inf_inf_set_o @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Int_insert_right
% 6.92/7.26 thf(fact_7084_Int__insert__right,axiom,
% 6.92/7.26 ! [A: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( ( member2340774599025711042nt_int @ A @ A4 )
% 6.92/7.26 => ( ( inf_in8396524679539076455nt_int @ A4 @ ( insert8897473484851387113nt_int @ A @ B5 ) )
% 6.92/7.26 = ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ A4 @ B5 ) ) ) )
% 6.92/7.26 & ( ~ ( member2340774599025711042nt_int @ A @ A4 )
% 6.92/7.26 => ( ( inf_in8396524679539076455nt_int @ A4 @ ( insert8897473484851387113nt_int @ A @ B5 ) )
% 6.92/7.26 = ( inf_in8396524679539076455nt_int @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Int_insert_right
% 6.92/7.26 thf(fact_7085_Int__insert__right,axiom,
% 6.92/7.26 ! [A: set_nat,A4: set_set_nat,B5: set_set_nat] :
% 6.92/7.26 ( ( ( member_set_nat @ A @ A4 )
% 6.92/7.26 => ( ( inf_inf_set_set_nat @ A4 @ ( insert_set_nat @ A @ B5 ) )
% 6.92/7.26 = ( insert_set_nat @ A @ ( inf_inf_set_set_nat @ A4 @ B5 ) ) ) )
% 6.92/7.26 & ( ~ ( member_set_nat @ A @ A4 )
% 6.92/7.26 => ( ( inf_inf_set_set_nat @ A4 @ ( insert_set_nat @ A @ B5 ) )
% 6.92/7.26 = ( inf_inf_set_set_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Int_insert_right
% 6.92/7.26 thf(fact_7086_Int__insert__right,axiom,
% 6.92/7.26 ! [A: int,A4: set_int,B5: set_int] :
% 6.92/7.26 ( ( ( member_int @ A @ A4 )
% 6.92/7.26 => ( ( inf_inf_set_int @ A4 @ ( insert_int @ A @ B5 ) )
% 6.92/7.26 = ( insert_int @ A @ ( inf_inf_set_int @ A4 @ B5 ) ) ) )
% 6.92/7.26 & ( ~ ( member_int @ A @ A4 )
% 6.92/7.26 => ( ( inf_inf_set_int @ A4 @ ( insert_int @ A @ B5 ) )
% 6.92/7.26 = ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Int_insert_right
% 6.92/7.26 thf(fact_7087_Int__insert__right,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( ( member8440522571783428010at_nat @ A @ A4 )
% 6.92/7.26 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( insert8211810215607154385at_nat @ A @ B5 ) )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) )
% 6.92/7.26 & ( ~ ( member8440522571783428010at_nat @ A @ A4 )
% 6.92/7.26 => ( ( inf_in2572325071724192079at_nat @ A4 @ ( insert8211810215607154385at_nat @ A @ B5 ) )
% 6.92/7.26 = ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Int_insert_right
% 6.92/7.26 thf(fact_7088_Int__insert__right,axiom,
% 6.92/7.26 ! [A: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.26 ( ( ( member_nat @ A @ A4 )
% 6.92/7.26 => ( ( inf_inf_set_nat @ A4 @ ( insert_nat @ A @ B5 ) )
% 6.92/7.26 = ( insert_nat @ A @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) )
% 6.92/7.26 & ( ~ ( member_nat @ A @ A4 )
% 6.92/7.26 => ( ( inf_inf_set_nat @ A4 @ ( insert_nat @ A @ B5 ) )
% 6.92/7.26 = ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Int_insert_right
% 6.92/7.26 thf(fact_7089_Int__insert__left,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,C4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( ( member8757157785044589968at_nat @ A @ C4 )
% 6.92/7.26 => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ B5 ) @ C4 )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ A @ ( inf_in7913087082777306421at_nat @ B5 @ C4 ) ) ) )
% 6.92/7.26 & ( ~ ( member8757157785044589968at_nat @ A @ C4 )
% 6.92/7.26 => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ B5 ) @ C4 )
% 6.92/7.26 = ( inf_in7913087082777306421at_nat @ B5 @ C4 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Int_insert_left
% 6.92/7.26 thf(fact_7090_Int__insert__left,axiom,
% 6.92/7.26 ! [A: $o,C4: set_o,B5: set_o] :
% 6.92/7.26 ( ( ( member_o @ A @ C4 )
% 6.92/7.26 => ( ( inf_inf_set_o @ ( insert_o @ A @ B5 ) @ C4 )
% 6.92/7.26 = ( insert_o @ A @ ( inf_inf_set_o @ B5 @ C4 ) ) ) )
% 6.92/7.26 & ( ~ ( member_o @ A @ C4 )
% 6.92/7.26 => ( ( inf_inf_set_o @ ( insert_o @ A @ B5 ) @ C4 )
% 6.92/7.26 = ( inf_inf_set_o @ B5 @ C4 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Int_insert_left
% 6.92/7.26 thf(fact_7091_Int__insert__left,axiom,
% 6.92/7.26 ! [A: set_Pr958786334691620121nt_int,C4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( ( member2340774599025711042nt_int @ A @ C4 )
% 6.92/7.26 => ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B5 ) @ C4 )
% 6.92/7.26 = ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ B5 @ C4 ) ) ) )
% 6.92/7.26 & ( ~ ( member2340774599025711042nt_int @ A @ C4 )
% 6.92/7.26 => ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B5 ) @ C4 )
% 6.92/7.26 = ( inf_in8396524679539076455nt_int @ B5 @ C4 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Int_insert_left
% 6.92/7.26 thf(fact_7092_Int__insert__left,axiom,
% 6.92/7.26 ! [A: set_nat,C4: set_set_nat,B5: set_set_nat] :
% 6.92/7.26 ( ( ( member_set_nat @ A @ C4 )
% 6.92/7.26 => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ B5 ) @ C4 )
% 6.92/7.26 = ( insert_set_nat @ A @ ( inf_inf_set_set_nat @ B5 @ C4 ) ) ) )
% 6.92/7.26 & ( ~ ( member_set_nat @ A @ C4 )
% 6.92/7.26 => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ B5 ) @ C4 )
% 6.92/7.26 = ( inf_inf_set_set_nat @ B5 @ C4 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Int_insert_left
% 6.92/7.26 thf(fact_7093_Int__insert__left,axiom,
% 6.92/7.26 ! [A: int,C4: set_int,B5: set_int] :
% 6.92/7.26 ( ( ( member_int @ A @ C4 )
% 6.92/7.26 => ( ( inf_inf_set_int @ ( insert_int @ A @ B5 ) @ C4 )
% 6.92/7.26 = ( insert_int @ A @ ( inf_inf_set_int @ B5 @ C4 ) ) ) )
% 6.92/7.26 & ( ~ ( member_int @ A @ C4 )
% 6.92/7.26 => ( ( inf_inf_set_int @ ( insert_int @ A @ B5 ) @ C4 )
% 6.92/7.26 = ( inf_inf_set_int @ B5 @ C4 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Int_insert_left
% 6.92/7.26 thf(fact_7094_Int__insert__left,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,C4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( ( member8440522571783428010at_nat @ A @ C4 )
% 6.92/7.26 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B5 ) @ C4 )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ B5 @ C4 ) ) ) )
% 6.92/7.26 & ( ~ ( member8440522571783428010at_nat @ A @ C4 )
% 6.92/7.26 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B5 ) @ C4 )
% 6.92/7.26 = ( inf_in2572325071724192079at_nat @ B5 @ C4 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Int_insert_left
% 6.92/7.26 thf(fact_7095_Int__insert__left,axiom,
% 6.92/7.26 ! [A: nat,C4: set_nat,B5: set_nat] :
% 6.92/7.26 ( ( ( member_nat @ A @ C4 )
% 6.92/7.26 => ( ( inf_inf_set_nat @ ( insert_nat @ A @ B5 ) @ C4 )
% 6.92/7.26 = ( insert_nat @ A @ ( inf_inf_set_nat @ B5 @ C4 ) ) ) )
% 6.92/7.26 & ( ~ ( member_nat @ A @ C4 )
% 6.92/7.26 => ( ( inf_inf_set_nat @ ( insert_nat @ A @ B5 ) @ C4 )
% 6.92/7.26 = ( inf_inf_set_nat @ B5 @ C4 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Int_insert_left
% 6.92/7.26 thf(fact_7096_insert__Diff__if,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( ( member8757157785044589968at_nat @ X @ B5 )
% 6.92/7.26 => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( minus_3314409938677909166at_nat @ A4 @ B5 ) ) )
% 6.92/7.26 & ( ~ ( member8757157785044589968at_nat @ X @ B5 )
% 6.92/7.26 => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ X @ ( minus_3314409938677909166at_nat @ A4 @ B5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff_if
% 6.92/7.26 thf(fact_7097_insert__Diff__if,axiom,
% 6.92/7.26 ! [X: $o,B5: set_o,A4: set_o] :
% 6.92/7.26 ( ( ( member_o @ X @ B5 )
% 6.92/7.26 => ( ( minus_minus_set_o @ ( insert_o @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( minus_minus_set_o @ A4 @ B5 ) ) )
% 6.92/7.26 & ( ~ ( member_o @ X @ B5 )
% 6.92/7.26 => ( ( minus_minus_set_o @ ( insert_o @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( insert_o @ X @ ( minus_minus_set_o @ A4 @ B5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff_if
% 6.92/7.26 thf(fact_7098_insert__Diff__if,axiom,
% 6.92/7.26 ! [X: set_Pr958786334691620121nt_int,B5: set_se6260736226359567993nt_int,A4: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( ( member2340774599025711042nt_int @ X @ B5 )
% 6.92/7.26 => ( ( minus_2612819937483484256nt_int @ ( insert8897473484851387113nt_int @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( minus_2612819937483484256nt_int @ A4 @ B5 ) ) )
% 6.92/7.26 & ( ~ ( member2340774599025711042nt_int @ X @ B5 )
% 6.92/7.26 => ( ( minus_2612819937483484256nt_int @ ( insert8897473484851387113nt_int @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( insert8897473484851387113nt_int @ X @ ( minus_2612819937483484256nt_int @ A4 @ B5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff_if
% 6.92/7.26 thf(fact_7099_insert__Diff__if,axiom,
% 6.92/7.26 ! [X: set_nat,B5: set_set_nat,A4: set_set_nat] :
% 6.92/7.26 ( ( ( member_set_nat @ X @ B5 )
% 6.92/7.26 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( minus_2163939370556025621et_nat @ A4 @ B5 ) ) )
% 6.92/7.26 & ( ~ ( member_set_nat @ X @ B5 )
% 6.92/7.26 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( insert_set_nat @ X @ ( minus_2163939370556025621et_nat @ A4 @ B5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff_if
% 6.92/7.26 thf(fact_7100_insert__Diff__if,axiom,
% 6.92/7.26 ! [X: nat,B5: set_nat,A4: set_nat] :
% 6.92/7.26 ( ( ( member_nat @ X @ B5 )
% 6.92/7.26 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( minus_minus_set_nat @ A4 @ B5 ) ) )
% 6.92/7.26 & ( ~ ( member_nat @ X @ B5 )
% 6.92/7.26 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( insert_nat @ X @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff_if
% 6.92/7.26 thf(fact_7101_insert__Diff__if,axiom,
% 6.92/7.26 ! [X: int,B5: set_int,A4: set_int] :
% 6.92/7.26 ( ( ( member_int @ X @ B5 )
% 6.92/7.26 => ( ( minus_minus_set_int @ ( insert_int @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( minus_minus_set_int @ A4 @ B5 ) ) )
% 6.92/7.26 & ( ~ ( member_int @ X @ B5 )
% 6.92/7.26 => ( ( minus_minus_set_int @ ( insert_int @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( insert_int @ X @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff_if
% 6.92/7.26 thf(fact_7102_insert__Diff__if,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( ( member8440522571783428010at_nat @ X @ B5 )
% 6.92/7.26 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) )
% 6.92/7.26 & ( ~ ( member8440522571783428010at_nat @ X @ B5 )
% 6.92/7.26 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A4 ) @ B5 )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff_if
% 6.92/7.26 thf(fact_7103_Collect__conv__if,axiom,
% 6.92/7.26 ! [P2: produc3843707927480180839at_nat > $o,A: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collec6321179662152712658at_nat
% 6.92/7.26 @ ^ [X4: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collec6321179662152712658at_nat
% 6.92/7.26 @ ^ [X4: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bo228742789529271731at_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if
% 6.92/7.26 thf(fact_7104_Collect__conv__if,axiom,
% 6.92/7.26 ! [P2: list_nat > $o,A: list_nat] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collect_list_nat
% 6.92/7.26 @ ^ [X4: list_nat] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collect_list_nat
% 6.92/7.26 @ ^ [X4: list_nat] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bot_set_list_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if
% 6.92/7.26 thf(fact_7105_Collect__conv__if,axiom,
% 6.92/7.26 ! [P2: set_Pr958786334691620121nt_int > $o,A: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collec5210948495886036740nt_int
% 6.92/7.26 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collec5210948495886036740nt_int
% 6.92/7.26 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bo1488462491386950373nt_int ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if
% 6.92/7.26 thf(fact_7106_Collect__conv__if,axiom,
% 6.92/7.26 ! [P2: set_nat > $o,A: set_nat] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collect_set_nat
% 6.92/7.26 @ ^ [X4: set_nat] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collect_set_nat
% 6.92/7.26 @ ^ [X4: set_nat] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bot_set_set_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if
% 6.92/7.26 thf(fact_7107_Collect__conv__if,axiom,
% 6.92/7.26 ! [P2: product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collec3392354462482085612at_nat
% 6.92/7.26 @ ^ [X4: product_prod_nat_nat] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collec3392354462482085612at_nat
% 6.92/7.26 @ ^ [X4: product_prod_nat_nat] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bo2099793752762293965at_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if
% 6.92/7.26 thf(fact_7108_Collect__conv__if,axiom,
% 6.92/7.26 ! [P2: $o > $o,A: $o] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collect_o
% 6.92/7.26 @ ^ [X4: $o] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert_o @ A @ bot_bot_set_o ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collect_o
% 6.92/7.26 @ ^ [X4: $o] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bot_set_o ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if
% 6.92/7.26 thf(fact_7109_Collect__conv__if,axiom,
% 6.92/7.26 ! [P2: nat > $o,A: nat] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collect_nat
% 6.92/7.26 @ ^ [X4: nat] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collect_nat
% 6.92/7.26 @ ^ [X4: nat] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bot_set_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if
% 6.92/7.26 thf(fact_7110_Collect__conv__if,axiom,
% 6.92/7.26 ! [P2: int > $o,A: int] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collect_int
% 6.92/7.26 @ ^ [X4: int] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert_int @ A @ bot_bot_set_int ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collect_int
% 6.92/7.26 @ ^ [X4: int] :
% 6.92/7.26 ( ( X4 = A )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bot_set_int ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if
% 6.92/7.26 thf(fact_7111_Collect__conv__if2,axiom,
% 6.92/7.26 ! [P2: produc3843707927480180839at_nat > $o,A: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collec6321179662152712658at_nat
% 6.92/7.26 @ ^ [X4: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collec6321179662152712658at_nat
% 6.92/7.26 @ ^ [X4: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bo228742789529271731at_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if2
% 6.92/7.26 thf(fact_7112_Collect__conv__if2,axiom,
% 6.92/7.26 ! [P2: list_nat > $o,A: list_nat] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collect_list_nat
% 6.92/7.26 @ ^ [X4: list_nat] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collect_list_nat
% 6.92/7.26 @ ^ [X4: list_nat] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bot_set_list_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if2
% 6.92/7.26 thf(fact_7113_Collect__conv__if2,axiom,
% 6.92/7.26 ! [P2: set_Pr958786334691620121nt_int > $o,A: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collec5210948495886036740nt_int
% 6.92/7.26 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collec5210948495886036740nt_int
% 6.92/7.26 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bo1488462491386950373nt_int ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if2
% 6.92/7.26 thf(fact_7114_Collect__conv__if2,axiom,
% 6.92/7.26 ! [P2: set_nat > $o,A: set_nat] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collect_set_nat
% 6.92/7.26 @ ^ [X4: set_nat] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collect_set_nat
% 6.92/7.26 @ ^ [X4: set_nat] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bot_set_set_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if2
% 6.92/7.26 thf(fact_7115_Collect__conv__if2,axiom,
% 6.92/7.26 ! [P2: product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collec3392354462482085612at_nat
% 6.92/7.26 @ ^ [X4: product_prod_nat_nat] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collec3392354462482085612at_nat
% 6.92/7.26 @ ^ [X4: product_prod_nat_nat] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bo2099793752762293965at_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if2
% 6.92/7.26 thf(fact_7116_Collect__conv__if2,axiom,
% 6.92/7.26 ! [P2: $o > $o,A: $o] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collect_o
% 6.92/7.26 @ ^ [X4: $o] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert_o @ A @ bot_bot_set_o ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collect_o
% 6.92/7.26 @ ^ [X4: $o] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bot_set_o ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if2
% 6.92/7.26 thf(fact_7117_Collect__conv__if2,axiom,
% 6.92/7.26 ! [P2: nat > $o,A: nat] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collect_nat
% 6.92/7.26 @ ^ [X4: nat] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collect_nat
% 6.92/7.26 @ ^ [X4: nat] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bot_set_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if2
% 6.92/7.26 thf(fact_7118_Collect__conv__if2,axiom,
% 6.92/7.26 ! [P2: int > $o,A: int] :
% 6.92/7.26 ( ( ( P2 @ A )
% 6.92/7.26 => ( ( collect_int
% 6.92/7.26 @ ^ [X4: int] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = ( insert_int @ A @ bot_bot_set_int ) ) )
% 6.92/7.26 & ( ~ ( P2 @ A )
% 6.92/7.26 => ( ( collect_int
% 6.92/7.26 @ ^ [X4: int] :
% 6.92/7.26 ( ( A = X4 )
% 6.92/7.26 & ( P2 @ X4 ) ) )
% 6.92/7.26 = bot_bot_set_int ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Collect_conv_if2
% 6.92/7.26 thf(fact_7119_insert__def,axiom,
% 6.92/7.26 ( insert8211810215607154385at_nat
% 6.92/7.26 = ( ^ [A5: product_prod_nat_nat] :
% 6.92/7.26 ( sup_su6327502436637775413at_nat
% 6.92/7.26 @ ( collec3392354462482085612at_nat
% 6.92/7.26 @ ^ [X4: product_prod_nat_nat] : ( X4 = A5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_def
% 6.92/7.26 thf(fact_7120_insert__def,axiom,
% 6.92/7.26 ( insert_o
% 6.92/7.26 = ( ^ [A5: $o] :
% 6.92/7.26 ( sup_sup_set_o
% 6.92/7.26 @ ( collect_o
% 6.92/7.26 @ ^ [X4: $o] : ( X4 = A5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_def
% 6.92/7.26 thf(fact_7121_insert__def,axiom,
% 6.92/7.26 ( insert_list_nat
% 6.92/7.26 = ( ^ [A5: list_nat] :
% 6.92/7.26 ( sup_sup_set_list_nat
% 6.92/7.26 @ ( collect_list_nat
% 6.92/7.26 @ ^ [X4: list_nat] : ( X4 = A5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_def
% 6.92/7.26 thf(fact_7122_insert__def,axiom,
% 6.92/7.26 ( insert8897473484851387113nt_int
% 6.92/7.26 = ( ^ [A5: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( sup_su2047564715030645325nt_int
% 6.92/7.26 @ ( collec5210948495886036740nt_int
% 6.92/7.26 @ ^ [X4: set_Pr958786334691620121nt_int] : ( X4 = A5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_def
% 6.92/7.26 thf(fact_7123_insert__def,axiom,
% 6.92/7.26 ( insert_set_nat
% 6.92/7.26 = ( ^ [A5: set_nat] :
% 6.92/7.26 ( sup_sup_set_set_nat
% 6.92/7.26 @ ( collect_set_nat
% 6.92/7.26 @ ^ [X4: set_nat] : ( X4 = A5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_def
% 6.92/7.26 thf(fact_7124_insert__def,axiom,
% 6.92/7.26 ( insert_int
% 6.92/7.26 = ( ^ [A5: int] :
% 6.92/7.26 ( sup_sup_set_int
% 6.92/7.26 @ ( collect_int
% 6.92/7.26 @ ^ [X4: int] : ( X4 = A5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_def
% 6.92/7.26 thf(fact_7125_insert__def,axiom,
% 6.92/7.26 ( insert6337962749363155127at_nat
% 6.92/7.26 = ( ^ [A5: produc4166570645942440679at_nat] :
% 6.92/7.26 ( sup_su3035147773818789531at_nat
% 6.92/7.26 @ ( collec5204685387357076818at_nat
% 6.92/7.26 @ ^ [X4: produc4166570645942440679at_nat] : ( X4 = A5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_def
% 6.92/7.26 thf(fact_7126_insert__def,axiom,
% 6.92/7.26 ( insert9069300056098147895at_nat
% 6.92/7.26 = ( ^ [A5: produc3843707927480180839at_nat] :
% 6.92/7.26 ( sup_su5525570899277871387at_nat
% 6.92/7.26 @ ( collec6321179662152712658at_nat
% 6.92/7.26 @ ^ [X4: produc3843707927480180839at_nat] : ( X4 = A5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_def
% 6.92/7.26 thf(fact_7127_insert__def,axiom,
% 6.92/7.26 ( insert_nat
% 6.92/7.26 = ( ^ [A5: nat] :
% 6.92/7.26 ( sup_sup_set_nat
% 6.92/7.26 @ ( collect_nat
% 6.92/7.26 @ ^ [X4: nat] : ( X4 = A5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_def
% 6.92/7.26 thf(fact_7128_subset__singleton__iff,axiom,
% 6.92/7.26 ! [X7: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( ord_le1268244103169919719at_nat @ X7 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 = ( ( X7 = bot_bo228742789529271731at_nat )
% 6.92/7.26 | ( X7
% 6.92/7.26 = ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_singleton_iff
% 6.92/7.26 thf(fact_7129_subset__singleton__iff,axiom,
% 6.92/7.26 ! [X7: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 6.92/7.26 ( ( ord_le3146513528884898305at_nat @ X7 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 = ( ( X7 = bot_bo2099793752762293965at_nat )
% 6.92/7.26 | ( X7
% 6.92/7.26 = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_singleton_iff
% 6.92/7.26 thf(fact_7130_subset__singleton__iff,axiom,
% 6.92/7.26 ! [X7: set_o,A: $o] :
% 6.92/7.26 ( ( ord_less_eq_set_o @ X7 @ ( insert_o @ A @ bot_bot_set_o ) )
% 6.92/7.26 = ( ( X7 = bot_bot_set_o )
% 6.92/7.26 | ( X7
% 6.92/7.26 = ( insert_o @ A @ bot_bot_set_o ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_singleton_iff
% 6.92/7.26 thf(fact_7131_subset__singleton__iff,axiom,
% 6.92/7.26 ! [X7: set_nat,A: nat] :
% 6.92/7.26 ( ( ord_less_eq_set_nat @ X7 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 6.92/7.26 = ( ( X7 = bot_bot_set_nat )
% 6.92/7.26 | ( X7
% 6.92/7.26 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_singleton_iff
% 6.92/7.26 thf(fact_7132_subset__singleton__iff,axiom,
% 6.92/7.26 ! [X7: set_int,A: int] :
% 6.92/7.26 ( ( ord_less_eq_set_int @ X7 @ ( insert_int @ A @ bot_bot_set_int ) )
% 6.92/7.26 = ( ( X7 = bot_bot_set_int )
% 6.92/7.26 | ( X7
% 6.92/7.26 = ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_singleton_iff
% 6.92/7.26 thf(fact_7133_subset__singletonD,axiom,
% 6.92/7.26 ! [A4: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( ord_le1268244103169919719at_nat @ A4 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 => ( ( A4 = bot_bo228742789529271731at_nat )
% 6.92/7.26 | ( A4
% 6.92/7.26 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_singletonD
% 6.92/7.26 thf(fact_7134_subset__singletonD,axiom,
% 6.92/7.26 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 6.92/7.26 ( ( ord_le3146513528884898305at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 => ( ( A4 = bot_bo2099793752762293965at_nat )
% 6.92/7.26 | ( A4
% 6.92/7.26 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_singletonD
% 6.92/7.26 thf(fact_7135_subset__singletonD,axiom,
% 6.92/7.26 ! [A4: set_o,X: $o] :
% 6.92/7.26 ( ( ord_less_eq_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) )
% 6.92/7.26 => ( ( A4 = bot_bot_set_o )
% 6.92/7.26 | ( A4
% 6.92/7.26 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_singletonD
% 6.92/7.26 thf(fact_7136_subset__singletonD,axiom,
% 6.92/7.26 ! [A4: set_nat,X: nat] :
% 6.92/7.26 ( ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 6.92/7.26 => ( ( A4 = bot_bot_set_nat )
% 6.92/7.26 | ( A4
% 6.92/7.26 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_singletonD
% 6.92/7.26 thf(fact_7137_subset__singletonD,axiom,
% 6.92/7.26 ! [A4: set_int,X: int] :
% 6.92/7.26 ( ( ord_less_eq_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) )
% 6.92/7.26 => ( ( A4 = bot_bot_set_int )
% 6.92/7.26 | ( A4
% 6.92/7.26 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_singletonD
% 6.92/7.26 thf(fact_7138_insert__is__Un,axiom,
% 6.92/7.26 ( insert6337962749363155127at_nat
% 6.92/7.26 = ( ^ [A5: produc4166570645942440679at_nat] : ( sup_su3035147773818789531at_nat @ ( insert6337962749363155127at_nat @ A5 @ bot_bo8422036546324065075at_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_is_Un
% 6.92/7.26 thf(fact_7139_insert__is__Un,axiom,
% 6.92/7.26 ( insert9069300056098147895at_nat
% 6.92/7.26 = ( ^ [A5: produc3843707927480180839at_nat] : ( sup_su5525570899277871387at_nat @ ( insert9069300056098147895at_nat @ A5 @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_is_Un
% 6.92/7.26 thf(fact_7140_insert__is__Un,axiom,
% 6.92/7.26 ( insert8211810215607154385at_nat
% 6.92/7.26 = ( ^ [A5: product_prod_nat_nat] : ( sup_su6327502436637775413at_nat @ ( insert8211810215607154385at_nat @ A5 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_is_Un
% 6.92/7.26 thf(fact_7141_insert__is__Un,axiom,
% 6.92/7.26 ( insert_o
% 6.92/7.26 = ( ^ [A5: $o] : ( sup_sup_set_o @ ( insert_o @ A5 @ bot_bot_set_o ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_is_Un
% 6.92/7.26 thf(fact_7142_insert__is__Un,axiom,
% 6.92/7.26 ( insert_nat
% 6.92/7.26 = ( ^ [A5: nat] : ( sup_sup_set_nat @ ( insert_nat @ A5 @ bot_bot_set_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_is_Un
% 6.92/7.26 thf(fact_7143_insert__is__Un,axiom,
% 6.92/7.26 ( insert_int
% 6.92/7.26 = ( ^ [A5: int] : ( sup_sup_set_int @ ( insert_int @ A5 @ bot_bot_set_int ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_is_Un
% 6.92/7.26 thf(fact_7144_Un__singleton__iff,axiom,
% 6.92/7.26 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,X: produc4166570645942440679at_nat] :
% 6.92/7.26 ( ( ( sup_su3035147773818789531at_nat @ A4 @ B5 )
% 6.92/7.26 = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) )
% 6.92/7.26 = ( ( ( A4 = bot_bo8422036546324065075at_nat )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) )
% 6.92/7.26 & ( B5 = bot_bo8422036546324065075at_nat ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Un_singleton_iff
% 6.92/7.26 thf(fact_7145_Un__singleton__iff,axiom,
% 6.92/7.26 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( ( sup_su5525570899277871387at_nat @ A4 @ B5 )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 = ( ( ( A4 = bot_bo228742789529271731at_nat )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 & ( B5 = bot_bo228742789529271731at_nat ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Un_singleton_iff
% 6.92/7.26 thf(fact_7146_Un__singleton__iff,axiom,
% 6.92/7.26 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 6.92/7.26 ( ( ( sup_su6327502436637775413at_nat @ A4 @ B5 )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 = ( ( ( A4 = bot_bo2099793752762293965at_nat )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 & ( B5 = bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Un_singleton_iff
% 6.92/7.26 thf(fact_7147_Un__singleton__iff,axiom,
% 6.92/7.26 ! [A4: set_o,B5: set_o,X: $o] :
% 6.92/7.26 ( ( ( sup_sup_set_o @ A4 @ B5 )
% 6.92/7.26 = ( insert_o @ X @ bot_bot_set_o ) )
% 6.92/7.26 = ( ( ( A4 = bot_bot_set_o )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_o @ X @ bot_bot_set_o ) ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert_o @ X @ bot_bot_set_o ) )
% 6.92/7.26 & ( B5 = bot_bot_set_o ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert_o @ X @ bot_bot_set_o ) )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Un_singleton_iff
% 6.92/7.26 thf(fact_7148_Un__singleton__iff,axiom,
% 6.92/7.26 ! [A4: set_nat,B5: set_nat,X: nat] :
% 6.92/7.26 ( ( ( sup_sup_set_nat @ A4 @ B5 )
% 6.92/7.26 = ( insert_nat @ X @ bot_bot_set_nat ) )
% 6.92/7.26 = ( ( ( A4 = bot_bot_set_nat )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert_nat @ X @ bot_bot_set_nat ) )
% 6.92/7.26 & ( B5 = bot_bot_set_nat ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert_nat @ X @ bot_bot_set_nat ) )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Un_singleton_iff
% 6.92/7.26 thf(fact_7149_Un__singleton__iff,axiom,
% 6.92/7.26 ! [A4: set_int,B5: set_int,X: int] :
% 6.92/7.26 ( ( ( sup_sup_set_int @ A4 @ B5 )
% 6.92/7.26 = ( insert_int @ X @ bot_bot_set_int ) )
% 6.92/7.26 = ( ( ( A4 = bot_bot_set_int )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_int @ X @ bot_bot_set_int ) ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert_int @ X @ bot_bot_set_int ) )
% 6.92/7.26 & ( B5 = bot_bot_set_int ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert_int @ X @ bot_bot_set_int ) )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Un_singleton_iff
% 6.92/7.26 thf(fact_7150_singleton__Un__iff,axiom,
% 6.92/7.26 ! [X: produc4166570645942440679at_nat,A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 6.92/7.26 ( ( ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat )
% 6.92/7.26 = ( sup_su3035147773818789531at_nat @ A4 @ B5 ) )
% 6.92/7.26 = ( ( ( A4 = bot_bo8422036546324065075at_nat )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) )
% 6.92/7.26 & ( B5 = bot_bo8422036546324065075at_nat ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_Un_iff
% 6.92/7.26 thf(fact_7151_singleton__Un__iff,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat )
% 6.92/7.26 = ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 6.92/7.26 = ( ( ( A4 = bot_bo228742789529271731at_nat )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 & ( B5 = bot_bo228742789529271731at_nat ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_Un_iff
% 6.92/7.26 thf(fact_7152_singleton__Un__iff,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat )
% 6.92/7.26 = ( sup_su6327502436637775413at_nat @ A4 @ B5 ) )
% 6.92/7.26 = ( ( ( A4 = bot_bo2099793752762293965at_nat )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 & ( B5 = bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_Un_iff
% 6.92/7.26 thf(fact_7153_singleton__Un__iff,axiom,
% 6.92/7.26 ! [X: $o,A4: set_o,B5: set_o] :
% 6.92/7.26 ( ( ( insert_o @ X @ bot_bot_set_o )
% 6.92/7.26 = ( sup_sup_set_o @ A4 @ B5 ) )
% 6.92/7.26 = ( ( ( A4 = bot_bot_set_o )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_o @ X @ bot_bot_set_o ) ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert_o @ X @ bot_bot_set_o ) )
% 6.92/7.26 & ( B5 = bot_bot_set_o ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert_o @ X @ bot_bot_set_o ) )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_Un_iff
% 6.92/7.26 thf(fact_7154_singleton__Un__iff,axiom,
% 6.92/7.26 ! [X: nat,A4: set_nat,B5: set_nat] :
% 6.92/7.26 ( ( ( insert_nat @ X @ bot_bot_set_nat )
% 6.92/7.26 = ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.92/7.26 = ( ( ( A4 = bot_bot_set_nat )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert_nat @ X @ bot_bot_set_nat ) )
% 6.92/7.26 & ( B5 = bot_bot_set_nat ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert_nat @ X @ bot_bot_set_nat ) )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_Un_iff
% 6.92/7.26 thf(fact_7155_singleton__Un__iff,axiom,
% 6.92/7.26 ! [X: int,A4: set_int,B5: set_int] :
% 6.92/7.26 ( ( ( insert_int @ X @ bot_bot_set_int )
% 6.92/7.26 = ( sup_sup_set_int @ A4 @ B5 ) )
% 6.92/7.26 = ( ( ( A4 = bot_bot_set_int )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_int @ X @ bot_bot_set_int ) ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert_int @ X @ bot_bot_set_int ) )
% 6.92/7.26 & ( B5 = bot_bot_set_int ) )
% 6.92/7.26 | ( ( A4
% 6.92/7.26 = ( insert_int @ X @ bot_bot_set_int ) )
% 6.92/7.26 & ( B5
% 6.92/7.26 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % singleton_Un_iff
% 6.92/7.26 thf(fact_7156_set__minus__singleton__eq,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat,X7: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ~ ( member8757157785044589968at_nat @ X @ X7 )
% 6.92/7.26 => ( ( minus_3314409938677909166at_nat @ X7 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 = X7 ) ) ).
% 6.92/7.26
% 6.92/7.26 % set_minus_singleton_eq
% 6.92/7.26 thf(fact_7157_set__minus__singleton__eq,axiom,
% 6.92/7.26 ! [X: set_Pr958786334691620121nt_int,X7: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ~ ( member2340774599025711042nt_int @ X @ X7 )
% 6.92/7.26 => ( ( minus_2612819937483484256nt_int @ X7 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
% 6.92/7.26 = X7 ) ) ).
% 6.92/7.26
% 6.92/7.26 % set_minus_singleton_eq
% 6.92/7.26 thf(fact_7158_set__minus__singleton__eq,axiom,
% 6.92/7.26 ! [X: set_nat,X7: set_set_nat] :
% 6.92/7.26 ( ~ ( member_set_nat @ X @ X7 )
% 6.92/7.26 => ( ( minus_2163939370556025621et_nat @ X7 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 6.92/7.26 = X7 ) ) ).
% 6.92/7.26
% 6.92/7.26 % set_minus_singleton_eq
% 6.92/7.26 thf(fact_7159_set__minus__singleton__eq,axiom,
% 6.92/7.26 ! [X: $o,X7: set_o] :
% 6.92/7.26 ( ~ ( member_o @ X @ X7 )
% 6.92/7.26 => ( ( minus_minus_set_o @ X7 @ ( insert_o @ X @ bot_bot_set_o ) )
% 6.92/7.26 = X7 ) ) ).
% 6.92/7.26
% 6.92/7.26 % set_minus_singleton_eq
% 6.92/7.26 thf(fact_7160_set__minus__singleton__eq,axiom,
% 6.92/7.26 ! [X: nat,X7: set_nat] :
% 6.92/7.26 ( ~ ( member_nat @ X @ X7 )
% 6.92/7.26 => ( ( minus_minus_set_nat @ X7 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 6.92/7.26 = X7 ) ) ).
% 6.92/7.26
% 6.92/7.26 % set_minus_singleton_eq
% 6.92/7.26 thf(fact_7161_set__minus__singleton__eq,axiom,
% 6.92/7.26 ! [X: int,X7: set_int] :
% 6.92/7.26 ( ~ ( member_int @ X @ X7 )
% 6.92/7.26 => ( ( minus_minus_set_int @ X7 @ ( insert_int @ X @ bot_bot_set_int ) )
% 6.92/7.26 = X7 ) ) ).
% 6.92/7.26
% 6.92/7.26 % set_minus_singleton_eq
% 6.92/7.26 thf(fact_7162_set__minus__singleton__eq,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat,X7: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ~ ( member8440522571783428010at_nat @ X @ X7 )
% 6.92/7.26 => ( ( minus_1356011639430497352at_nat @ X7 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 = X7 ) ) ).
% 6.92/7.26
% 6.92/7.26 % set_minus_singleton_eq
% 6.92/7.26 thf(fact_7163_insert__minus__eq,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( X != Y )
% 6.92/7.26 => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A4 ) @ ( insert9069300056098147895at_nat @ Y @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ X @ ( minus_3314409938677909166at_nat @ A4 @ ( insert9069300056098147895at_nat @ Y @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_minus_eq
% 6.92/7.26 thf(fact_7164_insert__minus__eq,axiom,
% 6.92/7.26 ! [X: $o,Y: $o,A4: set_o] :
% 6.92/7.26 ( ( X != Y )
% 6.92/7.26 => ( ( minus_minus_set_o @ ( insert_o @ X @ A4 ) @ ( insert_o @ Y @ bot_bot_set_o ) )
% 6.92/7.26 = ( insert_o @ X @ ( minus_minus_set_o @ A4 @ ( insert_o @ Y @ bot_bot_set_o ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_minus_eq
% 6.92/7.26 thf(fact_7165_insert__minus__eq,axiom,
% 6.92/7.26 ! [X: nat,Y: nat,A4: set_nat] :
% 6.92/7.26 ( ( X != Y )
% 6.92/7.26 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A4 ) @ ( insert_nat @ Y @ bot_bot_set_nat ) )
% 6.92/7.26 = ( insert_nat @ X @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ Y @ bot_bot_set_nat ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_minus_eq
% 6.92/7.26 thf(fact_7166_insert__minus__eq,axiom,
% 6.92/7.26 ! [X: int,Y: int,A4: set_int] :
% 6.92/7.26 ( ( X != Y )
% 6.92/7.26 => ( ( minus_minus_set_int @ ( insert_int @ X @ A4 ) @ ( insert_int @ Y @ bot_bot_set_int ) )
% 6.92/7.26 = ( insert_int @ X @ ( minus_minus_set_int @ A4 @ ( insert_int @ Y @ bot_bot_set_int ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_minus_eq
% 6.92/7.26 thf(fact_7167_insert__minus__eq,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( X != Y )
% 6.92/7.26 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A4 ) @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_minus_eq
% 6.92/7.26 thf(fact_7168_Diff__insert__absorb,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ~ ( member8757157785044589968at_nat @ X @ A4 )
% 6.92/7.26 => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A4 ) @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert_absorb
% 6.92/7.26 thf(fact_7169_Diff__insert__absorb,axiom,
% 6.92/7.26 ! [X: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ~ ( member2340774599025711042nt_int @ X @ A4 )
% 6.92/7.26 => ( ( minus_2612819937483484256nt_int @ ( insert8897473484851387113nt_int @ X @ A4 ) @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert_absorb
% 6.92/7.26 thf(fact_7170_Diff__insert__absorb,axiom,
% 6.92/7.26 ! [X: set_nat,A4: set_set_nat] :
% 6.92/7.26 ( ~ ( member_set_nat @ X @ A4 )
% 6.92/7.26 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A4 ) @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert_absorb
% 6.92/7.26 thf(fact_7171_Diff__insert__absorb,axiom,
% 6.92/7.26 ! [X: $o,A4: set_o] :
% 6.92/7.26 ( ~ ( member_o @ X @ A4 )
% 6.92/7.26 => ( ( minus_minus_set_o @ ( insert_o @ X @ A4 ) @ ( insert_o @ X @ bot_bot_set_o ) )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert_absorb
% 6.92/7.26 thf(fact_7172_Diff__insert__absorb,axiom,
% 6.92/7.26 ! [X: nat,A4: set_nat] :
% 6.92/7.26 ( ~ ( member_nat @ X @ A4 )
% 6.92/7.26 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A4 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert_absorb
% 6.92/7.26 thf(fact_7173_Diff__insert__absorb,axiom,
% 6.92/7.26 ! [X: int,A4: set_int] :
% 6.92/7.26 ( ~ ( member_int @ X @ A4 )
% 6.92/7.26 => ( ( minus_minus_set_int @ ( insert_int @ X @ A4 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert_absorb
% 6.92/7.26 thf(fact_7174_Diff__insert__absorb,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ~ ( member8440522571783428010at_nat @ X @ A4 )
% 6.92/7.26 => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A4 ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert_absorb
% 6.92/7.26 thf(fact_7175_Diff__insert2,axiom,
% 6.92/7.26 ! [A4: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( minus_3314409938677909166at_nat @ A4 @ ( insert9069300056098147895at_nat @ A @ B5 ) )
% 6.92/7.26 = ( minus_3314409938677909166at_nat @ ( minus_3314409938677909166at_nat @ A4 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert2
% 6.92/7.26 thf(fact_7176_Diff__insert2,axiom,
% 6.92/7.26 ! [A4: set_o,A: $o,B5: set_o] :
% 6.92/7.26 ( ( minus_minus_set_o @ A4 @ ( insert_o @ A @ B5 ) )
% 6.92/7.26 = ( minus_minus_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert2
% 6.92/7.26 thf(fact_7177_Diff__insert2,axiom,
% 6.92/7.26 ! [A4: set_nat,A: nat,B5: set_nat] :
% 6.92/7.26 ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ B5 ) )
% 6.92/7.26 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert2
% 6.92/7.26 thf(fact_7178_Diff__insert2,axiom,
% 6.92/7.26 ! [A4: set_int,A: int,B5: set_int] :
% 6.92/7.26 ( ( minus_minus_set_int @ A4 @ ( insert_int @ A @ B5 ) )
% 6.92/7.26 = ( minus_minus_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert2
% 6.92/7.26 thf(fact_7179_Diff__insert2,axiom,
% 6.92/7.26 ! [A4: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ A @ B5 ) )
% 6.92/7.26 = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) @ B5 ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert2
% 6.92/7.26 thf(fact_7180_insert__Diff,axiom,
% 6.92/7.26 ! [A: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( member8757157785044589968at_nat @ A @ A4 )
% 6.92/7.26 => ( ( insert9069300056098147895at_nat @ A @ ( minus_3314409938677909166at_nat @ A4 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff
% 6.92/7.26 thf(fact_7181_insert__Diff,axiom,
% 6.92/7.26 ! [A: set_Pr958786334691620121nt_int,A4: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( member2340774599025711042nt_int @ A @ A4 )
% 6.92/7.26 => ( ( insert8897473484851387113nt_int @ A @ ( minus_2612819937483484256nt_int @ A4 @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff
% 6.92/7.26 thf(fact_7182_insert__Diff,axiom,
% 6.92/7.26 ! [A: set_nat,A4: set_set_nat] :
% 6.92/7.26 ( ( member_set_nat @ A @ A4 )
% 6.92/7.26 => ( ( insert_set_nat @ A @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff
% 6.92/7.26 thf(fact_7183_insert__Diff,axiom,
% 6.92/7.26 ! [A: $o,A4: set_o] :
% 6.92/7.26 ( ( member_o @ A @ A4 )
% 6.92/7.26 => ( ( insert_o @ A @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff
% 6.92/7.26 thf(fact_7184_insert__Diff,axiom,
% 6.92/7.26 ! [A: nat,A4: set_nat] :
% 6.92/7.26 ( ( member_nat @ A @ A4 )
% 6.92/7.26 => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff
% 6.92/7.26 thf(fact_7185_insert__Diff,axiom,
% 6.92/7.26 ! [A: int,A4: set_int] :
% 6.92/7.26 ( ( member_int @ A @ A4 )
% 6.92/7.26 => ( ( insert_int @ A @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff
% 6.92/7.26 thf(fact_7186_insert__Diff,axiom,
% 6.92/7.26 ! [A: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( member8440522571783428010at_nat @ A @ A4 )
% 6.92/7.26 => ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 6.92/7.26 = A4 ) ) ).
% 6.92/7.26
% 6.92/7.26 % insert_Diff
% 6.92/7.26 thf(fact_7187_Diff__insert,axiom,
% 6.92/7.26 ! [A4: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( minus_3314409938677909166at_nat @ A4 @ ( insert9069300056098147895at_nat @ A @ B5 ) )
% 6.92/7.26 = ( minus_3314409938677909166at_nat @ ( minus_3314409938677909166at_nat @ A4 @ B5 ) @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert
% 6.92/7.26 thf(fact_7188_Diff__insert,axiom,
% 6.92/7.26 ! [A4: set_o,A: $o,B5: set_o] :
% 6.92/7.26 ( ( minus_minus_set_o @ A4 @ ( insert_o @ A @ B5 ) )
% 6.92/7.26 = ( minus_minus_set_o @ ( minus_minus_set_o @ A4 @ B5 ) @ ( insert_o @ A @ bot_bot_set_o ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert
% 6.92/7.26 thf(fact_7189_Diff__insert,axiom,
% 6.92/7.26 ! [A4: set_nat,A: nat,B5: set_nat] :
% 6.92/7.26 ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ B5 ) )
% 6.92/7.26 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A4 @ B5 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert
% 6.92/7.26 thf(fact_7190_Diff__insert,axiom,
% 6.92/7.26 ! [A4: set_int,A: int,B5: set_int] :
% 6.92/7.26 ( ( minus_minus_set_int @ A4 @ ( insert_int @ A @ B5 ) )
% 6.92/7.26 = ( minus_minus_set_int @ ( minus_minus_set_int @ A4 @ B5 ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert
% 6.92/7.26 thf(fact_7191_Diff__insert,axiom,
% 6.92/7.26 ! [A4: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ A @ B5 ) )
% 6.92/7.26 = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_insert
% 6.92/7.26 thf(fact_7192_subset__Diff__insert,axiom,
% 6.92/7.26 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,C4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( ord_le1268244103169919719at_nat @ A4 @ ( minus_3314409938677909166at_nat @ B5 @ ( insert9069300056098147895at_nat @ X @ C4 ) ) )
% 6.92/7.26 = ( ( ord_le1268244103169919719at_nat @ A4 @ ( minus_3314409938677909166at_nat @ B5 @ C4 ) )
% 6.92/7.26 & ~ ( member8757157785044589968at_nat @ X @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_Diff_insert
% 6.92/7.26 thf(fact_7193_subset__Diff__insert,axiom,
% 6.92/7.26 ! [A4: set_o,B5: set_o,X: $o,C4: set_o] :
% 6.92/7.26 ( ( ord_less_eq_set_o @ A4 @ ( minus_minus_set_o @ B5 @ ( insert_o @ X @ C4 ) ) )
% 6.92/7.26 = ( ( ord_less_eq_set_o @ A4 @ ( minus_minus_set_o @ B5 @ C4 ) )
% 6.92/7.26 & ~ ( member_o @ X @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_Diff_insert
% 6.92/7.26 thf(fact_7194_subset__Diff__insert,axiom,
% 6.92/7.26 ! [A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int,C4: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( ord_le483042692224249369nt_int @ A4 @ ( minus_2612819937483484256nt_int @ B5 @ ( insert8897473484851387113nt_int @ X @ C4 ) ) )
% 6.92/7.26 = ( ( ord_le483042692224249369nt_int @ A4 @ ( minus_2612819937483484256nt_int @ B5 @ C4 ) )
% 6.92/7.26 & ~ ( member2340774599025711042nt_int @ X @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_Diff_insert
% 6.92/7.26 thf(fact_7195_subset__Diff__insert,axiom,
% 6.92/7.26 ! [A4: set_set_nat,B5: set_set_nat,X: set_nat,C4: set_set_nat] :
% 6.92/7.26 ( ( ord_le6893508408891458716et_nat @ A4 @ ( minus_2163939370556025621et_nat @ B5 @ ( insert_set_nat @ X @ C4 ) ) )
% 6.92/7.26 = ( ( ord_le6893508408891458716et_nat @ A4 @ ( minus_2163939370556025621et_nat @ B5 @ C4 ) )
% 6.92/7.26 & ~ ( member_set_nat @ X @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_Diff_insert
% 6.92/7.26 thf(fact_7196_subset__Diff__insert,axiom,
% 6.92/7.26 ! [A4: set_nat,B5: set_nat,X: nat,C4: set_nat] :
% 6.92/7.26 ( ( ord_less_eq_set_nat @ A4 @ ( minus_minus_set_nat @ B5 @ ( insert_nat @ X @ C4 ) ) )
% 6.92/7.26 = ( ( ord_less_eq_set_nat @ A4 @ ( minus_minus_set_nat @ B5 @ C4 ) )
% 6.92/7.26 & ~ ( member_nat @ X @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_Diff_insert
% 6.92/7.26 thf(fact_7197_subset__Diff__insert,axiom,
% 6.92/7.26 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,C4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( ord_le3146513528884898305at_nat @ A4 @ ( minus_1356011639430497352at_nat @ B5 @ ( insert8211810215607154385at_nat @ X @ C4 ) ) )
% 6.92/7.26 = ( ( ord_le3146513528884898305at_nat @ A4 @ ( minus_1356011639430497352at_nat @ B5 @ C4 ) )
% 6.92/7.26 & ~ ( member8440522571783428010at_nat @ X @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_Diff_insert
% 6.92/7.26 thf(fact_7198_subset__Diff__insert,axiom,
% 6.92/7.26 ! [A4: set_int,B5: set_int,X: int,C4: set_int] :
% 6.92/7.26 ( ( ord_less_eq_set_int @ A4 @ ( minus_minus_set_int @ B5 @ ( insert_int @ X @ C4 ) ) )
% 6.92/7.26 = ( ( ord_less_eq_set_int @ A4 @ ( minus_minus_set_int @ B5 @ C4 ) )
% 6.92/7.26 & ~ ( member_int @ X @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_Diff_insert
% 6.92/7.26 thf(fact_7199_subset__insert__iff,axiom,
% 6.92/7.26 ! [A4: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( ord_le1268244103169919719at_nat @ A4 @ ( insert9069300056098147895at_nat @ X @ B5 ) )
% 6.92/7.26 = ( ( ( member8757157785044589968at_nat @ X @ A4 )
% 6.92/7.26 => ( ord_le1268244103169919719at_nat @ ( minus_3314409938677909166at_nat @ A4 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ B5 ) )
% 6.92/7.26 & ( ~ ( member8757157785044589968at_nat @ X @ A4 )
% 6.92/7.26 => ( ord_le1268244103169919719at_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insert_iff
% 6.92/7.26 thf(fact_7200_subset__insert__iff,axiom,
% 6.92/7.26 ! [A4: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( ord_le483042692224249369nt_int @ A4 @ ( insert8897473484851387113nt_int @ X @ B5 ) )
% 6.92/7.26 = ( ( ( member2340774599025711042nt_int @ X @ A4 )
% 6.92/7.26 => ( ord_le483042692224249369nt_int @ ( minus_2612819937483484256nt_int @ A4 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) @ B5 ) )
% 6.92/7.26 & ( ~ ( member2340774599025711042nt_int @ X @ A4 )
% 6.92/7.26 => ( ord_le483042692224249369nt_int @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insert_iff
% 6.92/7.26 thf(fact_7201_subset__insert__iff,axiom,
% 6.92/7.26 ! [A4: set_set_nat,X: set_nat,B5: set_set_nat] :
% 6.92/7.26 ( ( ord_le6893508408891458716et_nat @ A4 @ ( insert_set_nat @ X @ B5 ) )
% 6.92/7.26 = ( ( ( member_set_nat @ X @ A4 )
% 6.92/7.26 => ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B5 ) )
% 6.92/7.26 & ( ~ ( member_set_nat @ X @ A4 )
% 6.92/7.26 => ( ord_le6893508408891458716et_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insert_iff
% 6.92/7.26 thf(fact_7202_subset__insert__iff,axiom,
% 6.92/7.26 ! [A4: set_o,X: $o,B5: set_o] :
% 6.92/7.26 ( ( ord_less_eq_set_o @ A4 @ ( insert_o @ X @ B5 ) )
% 6.92/7.26 = ( ( ( member_o @ X @ A4 )
% 6.92/7.26 => ( ord_less_eq_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B5 ) )
% 6.92/7.26 & ( ~ ( member_o @ X @ A4 )
% 6.92/7.26 => ( ord_less_eq_set_o @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insert_iff
% 6.92/7.26 thf(fact_7203_subset__insert__iff,axiom,
% 6.92/7.26 ! [A4: set_nat,X: nat,B5: set_nat] :
% 6.92/7.26 ( ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ X @ B5 ) )
% 6.92/7.26 = ( ( ( member_nat @ X @ A4 )
% 6.92/7.26 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B5 ) )
% 6.92/7.26 & ( ~ ( member_nat @ X @ A4 )
% 6.92/7.26 => ( ord_less_eq_set_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insert_iff
% 6.92/7.26 thf(fact_7204_subset__insert__iff,axiom,
% 6.92/7.26 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( ord_le3146513528884898305at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ B5 ) )
% 6.92/7.26 = ( ( ( member8440522571783428010at_nat @ X @ A4 )
% 6.92/7.26 => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B5 ) )
% 6.92/7.26 & ( ~ ( member8440522571783428010at_nat @ X @ A4 )
% 6.92/7.26 => ( ord_le3146513528884898305at_nat @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insert_iff
% 6.92/7.26 thf(fact_7205_subset__insert__iff,axiom,
% 6.92/7.26 ! [A4: set_int,X: int,B5: set_int] :
% 6.92/7.26 ( ( ord_less_eq_set_int @ A4 @ ( insert_int @ X @ B5 ) )
% 6.92/7.26 = ( ( ( member_int @ X @ A4 )
% 6.92/7.26 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B5 ) )
% 6.92/7.26 & ( ~ ( member_int @ X @ A4 )
% 6.92/7.26 => ( ord_less_eq_set_int @ A4 @ B5 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_insert_iff
% 6.92/7.26 thf(fact_7206_Diff__single__insert,axiom,
% 6.92/7.26 ! [A4: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( ord_le1268244103169919719at_nat @ ( minus_3314409938677909166at_nat @ A4 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ B5 )
% 6.92/7.26 => ( ord_le1268244103169919719at_nat @ A4 @ ( insert9069300056098147895at_nat @ X @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_single_insert
% 6.92/7.26 thf(fact_7207_Diff__single__insert,axiom,
% 6.92/7.26 ! [A4: set_o,X: $o,B5: set_o] :
% 6.92/7.26 ( ( ord_less_eq_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B5 )
% 6.92/7.26 => ( ord_less_eq_set_o @ A4 @ ( insert_o @ X @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_single_insert
% 6.92/7.26 thf(fact_7208_Diff__single__insert,axiom,
% 6.92/7.26 ! [A4: set_nat,X: nat,B5: set_nat] :
% 6.92/7.26 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B5 )
% 6.92/7.26 => ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ X @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_single_insert
% 6.92/7.26 thf(fact_7209_Diff__single__insert,axiom,
% 6.92/7.26 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B5 )
% 6.92/7.26 => ( ord_le3146513528884898305at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_single_insert
% 6.92/7.26 thf(fact_7210_Diff__single__insert,axiom,
% 6.92/7.26 ! [A4: set_int,X: int,B5: set_int] :
% 6.92/7.26 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B5 )
% 6.92/7.26 => ( ord_less_eq_set_int @ A4 @ ( insert_int @ X @ B5 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Diff_single_insert
% 6.92/7.26 thf(fact_7211_remove__subset,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat,S: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( member8757157785044589968at_nat @ X @ S )
% 6.92/7.26 => ( ord_le2604355607129572851at_nat @ ( minus_3314409938677909166at_nat @ S @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ S ) ) ).
% 6.92/7.26
% 6.92/7.26 % remove_subset
% 6.92/7.26 thf(fact_7212_remove__subset,axiom,
% 6.92/7.26 ! [X: set_Pr958786334691620121nt_int,S: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( member2340774599025711042nt_int @ X @ S )
% 6.92/7.26 => ( ord_le1924305788584680229nt_int @ ( minus_2612819937483484256nt_int @ S @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) @ S ) ) ).
% 6.92/7.26
% 6.92/7.26 % remove_subset
% 6.92/7.26 thf(fact_7213_remove__subset,axiom,
% 6.92/7.26 ! [X: set_nat,S: set_set_nat] :
% 6.92/7.26 ( ( member_set_nat @ X @ S )
% 6.92/7.26 => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ S @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ S ) ) ).
% 6.92/7.26
% 6.92/7.26 % remove_subset
% 6.92/7.26 thf(fact_7214_remove__subset,axiom,
% 6.92/7.26 ! [X: $o,S: set_o] :
% 6.92/7.26 ( ( member_o @ X @ S )
% 6.92/7.26 => ( ord_less_set_o @ ( minus_minus_set_o @ S @ ( insert_o @ X @ bot_bot_set_o ) ) @ S ) ) ).
% 6.92/7.26
% 6.92/7.26 % remove_subset
% 6.92/7.26 thf(fact_7215_remove__subset,axiom,
% 6.92/7.26 ! [X: nat,S: set_nat] :
% 6.92/7.26 ( ( member_nat @ X @ S )
% 6.92/7.26 => ( ord_less_set_nat @ ( minus_minus_set_nat @ S @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ S ) ) ).
% 6.92/7.26
% 6.92/7.26 % remove_subset
% 6.92/7.26 thf(fact_7216_remove__subset,axiom,
% 6.92/7.26 ! [X: int,S: set_int] :
% 6.92/7.26 ( ( member_int @ X @ S )
% 6.92/7.26 => ( ord_less_set_int @ ( minus_minus_set_int @ S @ ( insert_int @ X @ bot_bot_set_int ) ) @ S ) ) ).
% 6.92/7.26
% 6.92/7.26 % remove_subset
% 6.92/7.26 thf(fact_7217_remove__subset,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat,S: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( member8440522571783428010at_nat @ X @ S )
% 6.92/7.26 => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ S @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ S ) ) ).
% 6.92/7.26
% 6.92/7.26 % remove_subset
% 6.92/7.26 thf(fact_7218_Compl__insert,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat,A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( uminus935396558254630718at_nat @ ( insert9069300056098147895at_nat @ X @ A4 ) )
% 6.92/7.26 = ( minus_3314409938677909166at_nat @ ( uminus935396558254630718at_nat @ A4 ) @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Compl_insert
% 6.92/7.26 thf(fact_7219_Compl__insert,axiom,
% 6.92/7.26 ! [X: $o,A4: set_o] :
% 6.92/7.26 ( ( uminus_uminus_set_o @ ( insert_o @ X @ A4 ) )
% 6.92/7.26 = ( minus_minus_set_o @ ( uminus_uminus_set_o @ A4 ) @ ( insert_o @ X @ bot_bot_set_o ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Compl_insert
% 6.92/7.26 thf(fact_7220_Compl__insert,axiom,
% 6.92/7.26 ! [X: nat,A4: set_nat] :
% 6.92/7.26 ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X @ A4 ) )
% 6.92/7.26 = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A4 ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Compl_insert
% 6.92/7.26 thf(fact_7221_Compl__insert,axiom,
% 6.92/7.26 ! [X: int,A4: set_int] :
% 6.92/7.26 ( ( uminus1532241313380277803et_int @ ( insert_int @ X @ A4 ) )
% 6.92/7.26 = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A4 ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Compl_insert
% 6.92/7.26 thf(fact_7222_Compl__insert,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ X @ A4 ) )
% 6.92/7.26 = ( minus_1356011639430497352at_nat @ ( uminus6524753893492686040at_nat @ A4 ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Compl_insert
% 6.92/7.26 thf(fact_7223_psubset__insert__iff,axiom,
% 6.92/7.26 ! [A4: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,B5: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( ord_le2604355607129572851at_nat @ A4 @ ( insert9069300056098147895at_nat @ X @ B5 ) )
% 6.92/7.26 = ( ( ( member8757157785044589968at_nat @ X @ B5 )
% 6.92/7.26 => ( ord_le2604355607129572851at_nat @ A4 @ B5 ) )
% 6.92/7.26 & ( ~ ( member8757157785044589968at_nat @ X @ B5 )
% 6.92/7.26 => ( ( ( member8757157785044589968at_nat @ X @ A4 )
% 6.92/7.26 => ( ord_le2604355607129572851at_nat @ ( minus_3314409938677909166at_nat @ A4 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ B5 ) )
% 6.92/7.26 & ( ~ ( member8757157785044589968at_nat @ X @ A4 )
% 6.92/7.26 => ( ord_le1268244103169919719at_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % psubset_insert_iff
% 6.92/7.26 thf(fact_7224_psubset__insert__iff,axiom,
% 6.92/7.26 ! [A4: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int,B5: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( ord_le1924305788584680229nt_int @ A4 @ ( insert8897473484851387113nt_int @ X @ B5 ) )
% 6.92/7.26 = ( ( ( member2340774599025711042nt_int @ X @ B5 )
% 6.92/7.26 => ( ord_le1924305788584680229nt_int @ A4 @ B5 ) )
% 6.92/7.26 & ( ~ ( member2340774599025711042nt_int @ X @ B5 )
% 6.92/7.26 => ( ( ( member2340774599025711042nt_int @ X @ A4 )
% 6.92/7.26 => ( ord_le1924305788584680229nt_int @ ( minus_2612819937483484256nt_int @ A4 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) @ B5 ) )
% 6.92/7.26 & ( ~ ( member2340774599025711042nt_int @ X @ A4 )
% 6.92/7.26 => ( ord_le483042692224249369nt_int @ A4 @ B5 ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % psubset_insert_iff
% 6.92/7.26 thf(fact_7225_psubset__insert__iff,axiom,
% 6.92/7.26 ! [A4: set_set_nat,X: set_nat,B5: set_set_nat] :
% 6.92/7.26 ( ( ord_less_set_set_nat @ A4 @ ( insert_set_nat @ X @ B5 ) )
% 6.92/7.26 = ( ( ( member_set_nat @ X @ B5 )
% 6.92/7.26 => ( ord_less_set_set_nat @ A4 @ B5 ) )
% 6.92/7.26 & ( ~ ( member_set_nat @ X @ B5 )
% 6.92/7.26 => ( ( ( member_set_nat @ X @ A4 )
% 6.92/7.26 => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B5 ) )
% 6.92/7.26 & ( ~ ( member_set_nat @ X @ A4 )
% 6.92/7.26 => ( ord_le6893508408891458716et_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % psubset_insert_iff
% 6.92/7.26 thf(fact_7226_psubset__insert__iff,axiom,
% 6.92/7.26 ! [A4: set_o,X: $o,B5: set_o] :
% 6.92/7.26 ( ( ord_less_set_o @ A4 @ ( insert_o @ X @ B5 ) )
% 6.92/7.26 = ( ( ( member_o @ X @ B5 )
% 6.92/7.26 => ( ord_less_set_o @ A4 @ B5 ) )
% 6.92/7.26 & ( ~ ( member_o @ X @ B5 )
% 6.92/7.26 => ( ( ( member_o @ X @ A4 )
% 6.92/7.26 => ( ord_less_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B5 ) )
% 6.92/7.26 & ( ~ ( member_o @ X @ A4 )
% 6.92/7.26 => ( ord_less_eq_set_o @ A4 @ B5 ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % psubset_insert_iff
% 6.92/7.26 thf(fact_7227_psubset__insert__iff,axiom,
% 6.92/7.26 ! [A4: set_nat,X: nat,B5: set_nat] :
% 6.92/7.26 ( ( ord_less_set_nat @ A4 @ ( insert_nat @ X @ B5 ) )
% 6.92/7.26 = ( ( ( member_nat @ X @ B5 )
% 6.92/7.26 => ( ord_less_set_nat @ A4 @ B5 ) )
% 6.92/7.26 & ( ~ ( member_nat @ X @ B5 )
% 6.92/7.26 => ( ( ( member_nat @ X @ A4 )
% 6.92/7.26 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B5 ) )
% 6.92/7.26 & ( ~ ( member_nat @ X @ A4 )
% 6.92/7.26 => ( ord_less_eq_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % psubset_insert_iff
% 6.92/7.26 thf(fact_7228_psubset__insert__iff,axiom,
% 6.92/7.26 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( ord_le7866589430770878221at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ B5 ) )
% 6.92/7.26 = ( ( ( member8440522571783428010at_nat @ X @ B5 )
% 6.92/7.26 => ( ord_le7866589430770878221at_nat @ A4 @ B5 ) )
% 6.92/7.26 & ( ~ ( member8440522571783428010at_nat @ X @ B5 )
% 6.92/7.26 => ( ( ( member8440522571783428010at_nat @ X @ A4 )
% 6.92/7.26 => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B5 ) )
% 6.92/7.26 & ( ~ ( member8440522571783428010at_nat @ X @ A4 )
% 6.92/7.26 => ( ord_le3146513528884898305at_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % psubset_insert_iff
% 6.92/7.26 thf(fact_7229_psubset__insert__iff,axiom,
% 6.92/7.26 ! [A4: set_int,X: int,B5: set_int] :
% 6.92/7.26 ( ( ord_less_set_int @ A4 @ ( insert_int @ X @ B5 ) )
% 6.92/7.26 = ( ( ( member_int @ X @ B5 )
% 6.92/7.26 => ( ord_less_set_int @ A4 @ B5 ) )
% 6.92/7.26 & ( ~ ( member_int @ X @ B5 )
% 6.92/7.26 => ( ( ( member_int @ X @ A4 )
% 6.92/7.26 => ( ord_less_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B5 ) )
% 6.92/7.26 & ( ~ ( member_int @ X @ A4 )
% 6.92/7.26 => ( ord_less_eq_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % psubset_insert_iff
% 6.92/7.26 thf(fact_7230_and__not__num_Osimps_I8_J,axiom,
% 6.92/7.26 ! [M: num,N2: num] :
% 6.92/7.26 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 6.92/7.26 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 6.92/7.26 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 6.92/7.26 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % and_not_num.simps(8)
% 6.92/7.26 thf(fact_7231_Divides_Oadjust__div__def,axiom,
% 6.92/7.26 ( adjust_div
% 6.92/7.26 = ( produc8211389475949308722nt_int
% 6.92/7.26 @ ^ [Q8: int,R5: int] : ( plus_plus_int @ Q8 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Divides.adjust_div_def
% 6.92/7.26 thf(fact_7232_and__nat__rec,axiom,
% 6.92/7.26 ( bit_se727722235901077358nd_nat
% 6.92/7.26 = ( ^ [M3: nat,N: nat] :
% 6.92/7.26 ( plus_plus_nat
% 6.92/7.26 @ ( zero_n2687167440665602831ol_nat
% 6.92/7.26 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 6.92/7.26 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 6.92/7.26 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % and_nat_rec
% 6.92/7.26 thf(fact_7233_and__nat__unfold,axiom,
% 6.92/7.26 ( bit_se727722235901077358nd_nat
% 6.92/7.26 = ( ^ [M3: nat,N: nat] :
% 6.92/7.26 ( if_nat
% 6.92/7.26 @ ( ( M3 = zero_zero_nat )
% 6.92/7.26 | ( N = zero_zero_nat ) )
% 6.92/7.26 @ zero_zero_nat
% 6.92/7.26 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % and_nat_unfold
% 6.92/7.26 thf(fact_7234_and__int_Opelims,axiom,
% 6.92/7.26 ! [X: int,Xa: int,Y: int] :
% 6.92/7.26 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 6.92/7.26 = Y )
% 6.92/7.26 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 6.92/7.26 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 6.92/7.26 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( uminus_uminus_int
% 6.92/7.26 @ ( zero_n2684676970156552555ol_int
% 6.92/7.26 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 6.92/7.26 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 6.92/7.26 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 6.92/7.26 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( plus_plus_int
% 6.92/7.26 @ ( zero_n2684676970156552555ol_int
% 6.92/7.26 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 6.92/7.26 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 6.92/7.26 @ ( 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 ) ) ) ) ) ) ) ) )
% 6.92/7.26 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % and_int.pelims
% 6.92/7.26 thf(fact_7235_and__int_Opsimps,axiom,
% 6.92/7.26 ! [K2: int,L: int] :
% 6.92/7.26 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L ) )
% 6.92/7.26 => ( ( ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 6.92/7.26 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 6.92/7.26 => ( ( bit_se725231765392027082nd_int @ K2 @ L )
% 6.92/7.26 = ( uminus_uminus_int
% 6.92/7.26 @ ( zero_n2684676970156552555ol_int
% 6.92/7.26 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 6.92/7.26 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 6.92/7.26 & ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 6.92/7.26 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 6.92/7.26 => ( ( bit_se725231765392027082nd_int @ K2 @ L )
% 6.92/7.26 = ( plus_plus_int
% 6.92/7.26 @ ( zero_n2684676970156552555ol_int
% 6.92/7.26 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 6.92/7.26 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 6.92/7.26 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % and_int.psimps
% 6.92/7.26 thf(fact_7236_and__minus__numerals_I7_J,axiom,
% 6.92/7.26 ! [N2: num,M: num] :
% 6.92/7.26 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 6.92/7.26 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % and_minus_numerals(7)
% 6.92/7.26 thf(fact_7237_and__minus__numerals_I3_J,axiom,
% 6.92/7.26 ! [M: num,N2: num] :
% 6.92/7.26 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 6.92/7.26 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % and_minus_numerals(3)
% 6.92/7.26 thf(fact_7238_int__ge__less__than2__def,axiom,
% 6.92/7.26 ( int_ge_less_than2
% 6.92/7.26 = ( ^ [D5: int] :
% 6.92/7.26 ( collec213857154873943460nt_int
% 6.92/7.26 @ ( produc4947309494688390418_int_o
% 6.92/7.26 @ ^ [Z8: int,Z: int] :
% 6.92/7.26 ( ( ord_less_eq_int @ D5 @ Z )
% 6.92/7.26 & ( ord_less_int @ Z8 @ Z ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % int_ge_less_than2_def
% 6.92/7.26 thf(fact_7239_trancl__single,axiom,
% 6.92/7.26 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( transi2703068831062848130at_nat @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 = ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ bot_bo228742789529271731at_nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % trancl_single
% 6.92/7.26 thf(fact_7240_trancl__single,axiom,
% 6.92/7.26 ! [A: int,B: int] :
% 6.92/7.26 ( ( transi6261509568448316235cl_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A @ B ) @ bot_bo1796632182523588997nt_int ) )
% 6.92/7.26 = ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A @ B ) @ bot_bo1796632182523588997nt_int ) ) ).
% 6.92/7.26
% 6.92/7.26 % trancl_single
% 6.92/7.26 thf(fact_7241_trancl__single,axiom,
% 6.92/7.26 ! [A: nat,B: nat] :
% 6.92/7.26 ( ( transi6264000038957366511cl_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A @ B ) @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 = ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A @ B ) @ bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % trancl_single
% 6.92/7.26 thf(fact_7242_trancl__sub__insert__trancl,axiom,
% 6.92/7.26 ! [R3: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] : ( ord_le1268244103169919719at_nat @ ( transi2703068831062848130at_nat @ R3 ) @ ( transi2703068831062848130at_nat @ ( insert9069300056098147895at_nat @ X @ R3 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % trancl_sub_insert_trancl
% 6.92/7.26 thf(fact_7243_trancl__sub__insert__trancl,axiom,
% 6.92/7.26 ! [R3: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] : ( ord_le3146513528884898305at_nat @ ( transi6264000038957366511cl_nat @ R3 ) @ ( transi6264000038957366511cl_nat @ ( insert8211810215607154385at_nat @ X @ R3 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % trancl_sub_insert_trancl
% 6.92/7.26 thf(fact_7244_one__plus__BitM,axiom,
% 6.92/7.26 ! [N2: num] :
% 6.92/7.26 ( ( plus_plus_num @ one @ ( bitM @ N2 ) )
% 6.92/7.26 = ( bit0 @ N2 ) ) ).
% 6.92/7.26
% 6.92/7.26 % one_plus_BitM
% 6.92/7.26 thf(fact_7245_BitM__plus__one,axiom,
% 6.92/7.26 ! [N2: num] :
% 6.92/7.26 ( ( plus_plus_num @ ( bitM @ N2 ) @ one )
% 6.92/7.26 = ( bit0 @ N2 ) ) ).
% 6.92/7.26
% 6.92/7.26 % BitM_plus_one
% 6.92/7.26 thf(fact_7246_trancl__insert2,axiom,
% 6.92/7.26 ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,R2: set_Pr8551490117392284871at_nat] :
% 6.92/7.26 ( ( transi5749863603491437800at_nat @ ( insert6337962749363155127at_nat @ ( produc4348348721325984599at_nat @ A @ B ) @ R2 ) )
% 6.92/7.26 = ( sup_su3035147773818789531at_nat @ ( transi5749863603491437800at_nat @ R2 )
% 6.92/7.26 @ ( collec5204685387357076818at_nat
% 6.92/7.26 @ ( produc5410597840814988588_nat_o
% 6.92/7.26 @ ^ [X4: multis2468970476368604999at_nat,Y4: multis2468970476368604999at_nat] :
% 6.92/7.26 ( ( ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ X4 @ A ) @ ( transi5749863603491437800at_nat @ R2 ) )
% 6.92/7.26 | ( X4 = A ) )
% 6.92/7.26 & ( ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ B @ Y4 ) @ ( transi5749863603491437800at_nat @ R2 ) )
% 6.92/7.26 | ( Y4 = B ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % trancl_insert2
% 6.92/7.26 thf(fact_7247_trancl__insert2,axiom,
% 6.92/7.26 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( ( transi2703068831062848130at_nat @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ R2 ) )
% 6.92/7.26 = ( sup_su5525570899277871387at_nat @ ( transi2703068831062848130at_nat @ R2 )
% 6.92/7.26 @ ( collec6321179662152712658at_nat
% 6.92/7.26 @ ( produc410239310623530412_nat_o
% 6.92/7.26 @ ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ A ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 6.92/7.26 | ( X4 = A ) )
% 6.92/7.26 & ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ B @ Y4 ) @ ( transi2703068831062848130at_nat @ R2 ) )
% 6.92/7.26 | ( Y4 = B ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % trancl_insert2
% 6.92/7.26 thf(fact_7248_trancl__insert2,axiom,
% 6.92/7.26 ! [A: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( transi6264000038957366511cl_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R2 ) )
% 6.92/7.26 = ( sup_su6327502436637775413at_nat @ ( transi6264000038957366511cl_nat @ R2 )
% 6.92/7.26 @ ( collec3392354462482085612at_nat
% 6.92/7.26 @ ( produc6081775807080527818_nat_o
% 6.92/7.26 @ ^ [X4: nat,Y4: nat] :
% 6.92/7.26 ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ A ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.26 | ( X4 = A ) )
% 6.92/7.26 & ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ Y4 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 6.92/7.26 | ( Y4 = B ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % trancl_insert2
% 6.92/7.26 thf(fact_7249_trancl__insert2,axiom,
% 6.92/7.26 ! [A: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( transi6261509568448316235cl_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A @ B ) @ R2 ) )
% 6.92/7.26 = ( sup_su6024340866399070445nt_int @ ( transi6261509568448316235cl_int @ R2 )
% 6.92/7.26 @ ( collec213857154873943460nt_int
% 6.92/7.26 @ ( produc4947309494688390418_int_o
% 6.92/7.26 @ ^ [X4: int,Y4: int] :
% 6.92/7.26 ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ A ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.26 | ( X4 = A ) )
% 6.92/7.26 & ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ Y4 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 6.92/7.26 | ( Y4 = B ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % trancl_insert2
% 6.92/7.26 thf(fact_7250_int__ge__less__than__def,axiom,
% 6.92/7.26 ( int_ge_less_than
% 6.92/7.26 = ( ^ [D5: int] :
% 6.92/7.26 ( collec213857154873943460nt_int
% 6.92/7.26 @ ( produc4947309494688390418_int_o
% 6.92/7.26 @ ^ [Z8: int,Z: int] :
% 6.92/7.26 ( ( ord_less_eq_int @ D5 @ Z8 )
% 6.92/7.26 & ( ord_less_int @ Z8 @ Z ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % int_ge_less_than_def
% 6.92/7.26 thf(fact_7251_log_Osimps,axiom,
% 6.92/7.26 ( log
% 6.92/7.26 = ( ^ [B4: code_natural,I: code_natural] :
% 6.92/7.26 ( if_Code_natural
% 6.92/7.26 @ ( ( ord_le1926595141338095240atural @ B4 @ one_one_Code_natural )
% 6.92/7.26 | ( ord_le5570908160329646204atural @ I @ B4 ) )
% 6.92/7.26 @ one_one_Code_natural
% 6.92/7.26 @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ B4 @ ( divide5121882707175180666atural @ I @ B4 ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % log.simps
% 6.92/7.26 thf(fact_7252_log_Oelims,axiom,
% 6.92/7.26 ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 6.92/7.26 ( ( ( log @ X @ Xa )
% 6.92/7.26 = Y )
% 6.92/7.26 => ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 6.92/7.26 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 6.92/7.26 => ( Y = one_one_Code_natural ) )
% 6.92/7.26 & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 6.92/7.26 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % log.elims
% 6.92/7.26 thf(fact_7253_log_Opelims,axiom,
% 6.92/7.26 ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 6.92/7.26 ( ( ( log @ X @ Xa )
% 6.92/7.26 = Y )
% 6.92/7.26 => ( ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) )
% 6.92/7.26 => ~ ( ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 6.92/7.26 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 6.92/7.26 => ( Y = one_one_Code_natural ) )
% 6.92/7.26 & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 6.92/7.26 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) )
% 6.92/7.26 => ~ ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % log.pelims
% 6.92/7.26 thf(fact_7254_minus__shift__def,axiom,
% 6.92/7.26 ( minus_shift
% 6.92/7.26 = ( ^ [R5: code_natural,K3: code_natural,L2: code_natural] : ( if_Code_natural @ ( ord_le5570908160329646204atural @ K3 @ L2 ) @ ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ R5 @ K3 ) @ L2 ) @ ( minus_7197305767214868737atural @ K3 @ L2 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % minus_shift_def
% 6.92/7.26 thf(fact_7255_next_Osimps,axiom,
% 6.92/7.26 ! [V: code_natural,W2: code_natural] :
% 6.92/7.26 ( ( next @ ( produc3574140220909816553atural @ V @ W2 ) )
% 6.92/7.26 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % next.simps
% 6.92/7.26 thf(fact_7256_set__decode__def,axiom,
% 6.92/7.26 ( nat_set_decode
% 6.92/7.26 = ( ^ [X4: nat] :
% 6.92/7.26 ( collect_nat
% 6.92/7.26 @ ^ [N: nat] :
% 6.92/7.26 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % set_decode_def
% 6.92/7.26 thf(fact_7257_set__decode__plus__power__2,axiom,
% 6.92/7.26 ! [N2: nat,Z3: nat] :
% 6.92/7.26 ( ~ ( member_nat @ N2 @ ( nat_set_decode @ Z3 ) )
% 6.92/7.26 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ Z3 ) )
% 6.92/7.26 = ( insert_nat @ N2 @ ( nat_set_decode @ Z3 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % set_decode_plus_power_2
% 6.92/7.26 thf(fact_7258_subset__decode__imp__le,axiom,
% 6.92/7.26 ! [M: nat,N2: nat] :
% 6.92/7.26 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N2 ) )
% 6.92/7.26 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.92/7.26
% 6.92/7.26 % subset_decode_imp_le
% 6.92/7.26 thf(fact_7259_take__bit__Suc__from__most,axiom,
% 6.92/7.26 ! [N2: nat,K2: int] :
% 6.92/7.26 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K2 )
% 6.92/7.26 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % take_bit_Suc_from_most
% 6.92/7.26 thf(fact_7260_Random_Orange__def,axiom,
% 6.92/7.26 ( range
% 6.92/7.26 = ( ^ [K3: code_natural] :
% 6.92/7.26 ( produc5538323210962509403atural
% 6.92/7.26 @ ( 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 )
% 6.92/7.26 @ ^ [L2: code_natural] :
% 6.92/7.26 ( produc5538323210962509403atural @ next
% 6.92/7.26 @ ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 6.92/7.26 @ one_one_Code_natural )
% 6.92/7.26 @ ^ [V2: code_natural] : ( produc6639722614265839536atural @ ( modulo8411746178871703098atural @ V2 @ K3 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Random.range_def
% 6.92/7.26 thf(fact_7261_xor__Suc__0__eq,axiom,
% 6.92/7.26 ! [N2: nat] :
% 6.92/7.26 ( ( bit_se6528837805403552850or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 6.92/7.26 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 6.92/7.26 @ ( zero_n2687167440665602831ol_nat
% 6.92/7.26 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_Suc_0_eq
% 6.92/7.26 thf(fact_7262_Suc__0__xor__eq,axiom,
% 6.92/7.26 ! [N2: nat] :
% 6.92/7.26 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 6.92/7.26 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 6.92/7.26 @ ( zero_n2687167440665602831ol_nat
% 6.92/7.26 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % Suc_0_xor_eq
% 6.92/7.26 thf(fact_7263_horner__sum__of__bool__2__less,axiom,
% 6.92/7.26 ! [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 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % horner_sum_of_bool_2_less
% 6.92/7.26 thf(fact_7264_scomp__apply,axiom,
% 6.92/7.26 ( produc5538323210962509403atural
% 6.92/7.26 = ( ^ [F3: produc7822875418678951345atural > produc5835291356934675326atural,G3: code_natural > produc7822875418678951345atural > produc5835291356934675326atural,X4: produc7822875418678951345atural] : ( produc8638916746724166107atural @ G3 @ ( F3 @ X4 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % scomp_apply
% 6.92/7.26 thf(fact_7265_signed__take__bit__nonnegative__iff,axiom,
% 6.92/7.26 ! [N2: nat,K2: int] :
% 6.92/7.26 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N2 @ K2 ) )
% 6.92/7.26 = ( ~ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % signed_take_bit_nonnegative_iff
% 6.92/7.26 thf(fact_7266_signed__take__bit__negative__iff,axiom,
% 6.92/7.26 ! [N2: nat,K2: int] :
% 6.92/7.26 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K2 ) @ zero_zero_int )
% 6.92/7.26 = ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) ).
% 6.92/7.26
% 6.92/7.26 % signed_take_bit_negative_iff
% 6.92/7.26 thf(fact_7267_xor__numerals_I4_J,axiom,
% 6.92/7.26 ! [X: num,Y: num] :
% 6.92/7.26 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 6.92/7.26 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_numerals(4)
% 6.92/7.26 thf(fact_7268_xor__numerals_I4_J,axiom,
% 6.92/7.26 ! [X: num,Y: num] :
% 6.92/7.26 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 6.92/7.26 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_numerals(4)
% 6.92/7.26 thf(fact_7269_xor__numerals_I4_J,axiom,
% 6.92/7.26 ! [X: num,Y: num] :
% 6.92/7.26 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 6.92/7.26 = ( 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 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_numerals(4)
% 6.92/7.26 thf(fact_7270_xor__numerals_I4_J,axiom,
% 6.92/7.26 ! [X: num,Y: num] :
% 6.92/7.26 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 6.92/7.26 = ( 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 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_numerals(4)
% 6.92/7.26 thf(fact_7271_xor__numerals_I6_J,axiom,
% 6.92/7.26 ! [X: num,Y: num] :
% 6.92/7.26 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 6.92/7.26 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_numerals(6)
% 6.92/7.26 thf(fact_7272_xor__numerals_I6_J,axiom,
% 6.92/7.26 ! [X: num,Y: num] :
% 6.92/7.26 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 6.92/7.26 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_numerals(6)
% 6.92/7.26 thf(fact_7273_xor__numerals_I6_J,axiom,
% 6.92/7.26 ! [X: num,Y: num] :
% 6.92/7.26 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 6.92/7.26 = ( 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 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_numerals(6)
% 6.92/7.26 thf(fact_7274_xor__numerals_I6_J,axiom,
% 6.92/7.26 ! [X: num,Y: num] :
% 6.92/7.26 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 6.92/7.26 = ( 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 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_numerals(6)
% 6.92/7.26 thf(fact_7275_scomp__scomp,axiom,
% 6.92/7.26 ! [F: produc7822875418678951345atural > produc5835291356934675326atural,G: code_natural > produc7822875418678951345atural > produc5835291356934675326atural,H: code_natural > produc7822875418678951345atural > produc5835291356934675326atural] :
% 6.92/7.26 ( ( produc5538323210962509403atural @ ( produc5538323210962509403atural @ F @ G ) @ H )
% 6.92/7.26 = ( produc5538323210962509403atural @ F
% 6.92/7.26 @ ^ [X4: code_natural] : ( produc5538323210962509403atural @ ( G @ X4 ) @ H ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % scomp_scomp
% 6.92/7.26 thf(fact_7276_bit__disjunctive__add__iff,axiom,
% 6.92/7.26 ! [A: int,B: int,N2: nat] :
% 6.92/7.26 ( ! [N5: nat] :
% 6.92/7.26 ( ~ ( bit_se1146084159140164899it_int @ A @ N5 )
% 6.92/7.26 | ~ ( bit_se1146084159140164899it_int @ B @ N5 ) )
% 6.92/7.26 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 6.92/7.26 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 6.92/7.26 | ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % bit_disjunctive_add_iff
% 6.92/7.26 thf(fact_7277_bit__disjunctive__add__iff,axiom,
% 6.92/7.26 ! [A: nat,B: nat,N2: nat] :
% 6.92/7.26 ( ! [N5: nat] :
% 6.92/7.26 ( ~ ( bit_se1148574629649215175it_nat @ A @ N5 )
% 6.92/7.26 | ~ ( bit_se1148574629649215175it_nat @ B @ N5 ) )
% 6.92/7.26 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 6.92/7.26 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 6.92/7.26 | ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % bit_disjunctive_add_iff
% 6.92/7.26 thf(fact_7278_scomp__Pair,axiom,
% 6.92/7.26 ! [X: produc7822875418678951345atural > produc5835291356934675326atural] :
% 6.92/7.26 ( ( produc5538323210962509403atural @ X @ produc6639722614265839536atural )
% 6.92/7.26 = X ) ).
% 6.92/7.26
% 6.92/7.26 % scomp_Pair
% 6.92/7.26 thf(fact_7279_Pair__scomp,axiom,
% 6.92/7.26 ! [X: code_natural,F: code_natural > produc7822875418678951345atural > produc5835291356934675326atural] :
% 6.92/7.26 ( ( produc5538323210962509403atural @ ( produc6639722614265839536atural @ X ) @ F )
% 6.92/7.26 = ( F @ X ) ) ).
% 6.92/7.26
% 6.92/7.26 % Pair_scomp
% 6.92/7.26 thf(fact_7280_bit__take__bit__iff,axiom,
% 6.92/7.26 ! [M: nat,A: int,N2: nat] :
% 6.92/7.26 ( ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ M @ A ) @ N2 )
% 6.92/7.26 = ( ( ord_less_nat @ N2 @ M )
% 6.92/7.26 & ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % bit_take_bit_iff
% 6.92/7.26 thf(fact_7281_bit__take__bit__iff,axiom,
% 6.92/7.26 ! [M: nat,A: nat,N2: nat] :
% 6.92/7.26 ( ( bit_se1148574629649215175it_nat @ ( bit_se2925701944663578781it_nat @ M @ A ) @ N2 )
% 6.92/7.26 = ( ( ord_less_nat @ N2 @ M )
% 6.92/7.26 & ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % bit_take_bit_iff
% 6.92/7.26 thf(fact_7282_scomp__def,axiom,
% 6.92/7.26 ( produc5538323210962509403atural
% 6.92/7.26 = ( ^ [F3: produc7822875418678951345atural > produc5835291356934675326atural,G3: code_natural > produc7822875418678951345atural > produc5835291356934675326atural,X4: produc7822875418678951345atural] : ( produc8638916746724166107atural @ G3 @ ( F3 @ X4 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % scomp_def
% 6.92/7.26 thf(fact_7283_bit__horner__sum__bit__iff,axiom,
% 6.92/7.26 ! [Bs: list_o,N2: nat] :
% 6.92/7.26 ( ( bit_se8040316288895769887atural @ ( groups2241214984954800037atural @ zero_n8403883297036319079atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ Bs ) @ N2 )
% 6.92/7.26 = ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Bs ) )
% 6.92/7.26 & ( nth_o @ Bs @ N2 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % bit_horner_sum_bit_iff
% 6.92/7.26 thf(fact_7284_bit__horner__sum__bit__iff,axiom,
% 6.92/7.26 ! [Bs: list_o,N2: nat] :
% 6.92/7.26 ( ( bit_se9216721137139052372nteger @ ( groups3417619833198082522nteger @ zero_n356916108424825756nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Bs ) @ N2 )
% 6.92/7.26 = ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Bs ) )
% 6.92/7.26 & ( nth_o @ Bs @ N2 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % bit_horner_sum_bit_iff
% 6.92/7.26 thf(fact_7285_bit__horner__sum__bit__iff,axiom,
% 6.92/7.26 ! [Bs: list_o,N2: nat] :
% 6.92/7.26 ( ( bit_se1148574629649215175it_nat @ ( groups9119017779487936845_o_nat @ zero_n2687167440665602831ol_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Bs ) @ N2 )
% 6.92/7.26 = ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Bs ) )
% 6.92/7.26 & ( nth_o @ Bs @ N2 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % bit_horner_sum_bit_iff
% 6.92/7.26 thf(fact_7286_bit__horner__sum__bit__iff,axiom,
% 6.92/7.26 ! [Bs: list_o,N2: nat] :
% 6.92/7.26 ( ( bit_se1146084159140164899it_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ N2 )
% 6.92/7.26 = ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Bs ) )
% 6.92/7.26 & ( nth_o @ Bs @ N2 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % bit_horner_sum_bit_iff
% 6.92/7.26 thf(fact_7287_iterate_Osimps,axiom,
% 6.92/7.26 ( iterate_int_int
% 6.92/7.26 = ( ^ [K3: code_natural,F3: int > int > product_prod_int_int,X4: int] : ( if_int2409958687428134794nt_int @ ( K3 = zero_z2226904508553997617atural ) @ ( product_Pair_int_int @ X4 ) @ ( produc6963641260316735276nt_int @ ( F3 @ X4 ) @ ( iterate_int_int @ ( minus_7197305767214868737atural @ K3 @ one_one_Code_natural ) @ F3 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.simps
% 6.92/7.26 thf(fact_7288_iterate_Osimps,axiom,
% 6.92/7.26 ( iterat1233435593421607556et_nat
% 6.92/7.26 = ( ^ [K3: code_natural,F3: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > produc3925858234332021118et_nat,X4: produc3658429121746597890et_nat > $o] : ( if_Pro6440128116348121305et_nat @ ( K3 = zero_z2226904508553997617atural ) @ ( produc5001842942810119800et_nat @ X4 ) @ ( produc2318911012118706502et_nat @ ( F3 @ X4 ) @ ( iterat1233435593421607556et_nat @ ( minus_7197305767214868737atural @ K3 @ one_one_Code_natural ) @ F3 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.simps
% 6.92/7.26 thf(fact_7289_iterate_Osimps,axiom,
% 6.92/7.26 ( iterat2702368289246022656et_nat
% 6.92/7.26 = ( ^ [K3: code_natural,F3: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > produc2732055786443039994et_nat,X4: produc3658429121746597890et_nat > $o] : ( if_Pro5796790085669187537et_nat @ ( K3 = zero_z2226904508553997617atural ) @ ( produc2245416461498447860et_nat @ X4 ) @ ( produc7537777246833756098et_nat @ ( F3 @ X4 ) @ ( iterat2702368289246022656et_nat @ ( minus_7197305767214868737atural @ K3 @ one_one_Code_natural ) @ F3 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.simps
% 6.92/7.26 thf(fact_7290_iterate_Osimps,axiom,
% 6.92/7.26 ( iterat9120928542346325760it_nat
% 6.92/7.26 = ( ^ [K3: code_natural,F3: b > produc6653097349344004940it_nat > produc7388388658123137530it_nat,X4: b] : ( if_Pro4080778131203054751it_nat @ ( K3 = zero_z2226904508553997617atural ) @ ( produc4082563078715348724it_nat @ X4 ) @ ( produc8824551317683396724it_nat @ ( F3 @ X4 ) @ ( iterat9120928542346325760it_nat @ ( minus_7197305767214868737atural @ K3 @ one_one_Code_natural ) @ F3 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.simps
% 6.92/7.26 thf(fact_7291_iterate_Osimps,axiom,
% 6.92/7.26 ( iterat4993027441371875583it_nat
% 6.92/7.26 = ( ^ [K3: code_natural,F3: a > produc6653097349344004940it_nat > produc3260487557148687353it_nat,X4: a] : ( if_Pro3578090444564244254it_nat @ ( K3 = zero_z2226904508553997617atural ) @ ( produc9178034014595674355it_nat @ X4 ) @ ( produc3714732129343117170it_nat @ ( F3 @ X4 ) @ ( iterat4993027441371875583it_nat @ ( minus_7197305767214868737atural @ K3 @ one_one_Code_natural ) @ F3 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.simps
% 6.92/7.26 thf(fact_7292_iterate_Osimps,axiom,
% 6.92/7.26 ( iterat8892046348760725948atural
% 6.92/7.26 = ( ^ [K3: code_natural,F3: code_natural > produc7822875418678951345atural > produc5835291356934675326atural,X4: code_natural] : ( if_Pro2760142802149639654atural @ ( K3 = zero_z2226904508553997617atural ) @ ( produc6639722614265839536atural @ X4 ) @ ( produc5538323210962509403atural @ ( F3 @ X4 ) @ ( iterat8892046348760725948atural @ ( minus_7197305767214868737atural @ K3 @ one_one_Code_natural ) @ F3 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.simps
% 6.92/7.26 thf(fact_7293_iterate_Oelims,axiom,
% 6.92/7.26 ! [X: code_natural,Xa: int > int > product_prod_int_int,Xb: int,Y: int > product_prod_int_int] :
% 6.92/7.26 ( ( ( iterate_int_int @ X @ Xa @ Xb )
% 6.92/7.26 = Y )
% 6.92/7.26 => ( ( ( X = zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( product_Pair_int_int @ Xb ) ) )
% 6.92/7.26 & ( ( X != zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc6963641260316735276nt_int @ ( Xa @ Xb ) @ ( iterate_int_int @ ( minus_7197305767214868737atural @ X @ one_one_Code_natural ) @ Xa ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.elims
% 6.92/7.26 thf(fact_7294_iterate_Oelims,axiom,
% 6.92/7.26 ! [X: code_natural,Xa: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > produc3925858234332021118et_nat,Xb: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > produc3925858234332021118et_nat] :
% 6.92/7.26 ( ( ( iterat1233435593421607556et_nat @ X @ Xa @ Xb )
% 6.92/7.26 = Y )
% 6.92/7.26 => ( ( ( X = zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc5001842942810119800et_nat @ Xb ) ) )
% 6.92/7.26 & ( ( X != zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc2318911012118706502et_nat @ ( Xa @ Xb ) @ ( iterat1233435593421607556et_nat @ ( minus_7197305767214868737atural @ X @ one_one_Code_natural ) @ Xa ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.elims
% 6.92/7.26 thf(fact_7295_iterate_Oelims,axiom,
% 6.92/7.26 ! [X: code_natural,Xa: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > produc2732055786443039994et_nat,Xb: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat > produc2732055786443039994et_nat] :
% 6.92/7.26 ( ( ( iterat2702368289246022656et_nat @ X @ Xa @ Xb )
% 6.92/7.26 = Y )
% 6.92/7.26 => ( ( ( X = zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc2245416461498447860et_nat @ Xb ) ) )
% 6.92/7.26 & ( ( X != zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc7537777246833756098et_nat @ ( Xa @ Xb ) @ ( iterat2702368289246022656et_nat @ ( minus_7197305767214868737atural @ X @ one_one_Code_natural ) @ Xa ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.elims
% 6.92/7.26 thf(fact_7296_iterate_Oelims,axiom,
% 6.92/7.26 ! [X: code_natural,Xa: b > produc6653097349344004940it_nat > produc7388388658123137530it_nat,Xb: b,Y: produc6653097349344004940it_nat > produc7388388658123137530it_nat] :
% 6.92/7.26 ( ( ( iterat9120928542346325760it_nat @ X @ Xa @ Xb )
% 6.92/7.26 = Y )
% 6.92/7.26 => ( ( ( X = zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc4082563078715348724it_nat @ Xb ) ) )
% 6.92/7.26 & ( ( X != zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc8824551317683396724it_nat @ ( Xa @ Xb ) @ ( iterat9120928542346325760it_nat @ ( minus_7197305767214868737atural @ X @ one_one_Code_natural ) @ Xa ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.elims
% 6.92/7.26 thf(fact_7297_iterate_Oelims,axiom,
% 6.92/7.26 ! [X: code_natural,Xa: a > produc6653097349344004940it_nat > produc3260487557148687353it_nat,Xb: a,Y: produc6653097349344004940it_nat > produc3260487557148687353it_nat] :
% 6.92/7.26 ( ( ( iterat4993027441371875583it_nat @ X @ Xa @ Xb )
% 6.92/7.26 = Y )
% 6.92/7.26 => ( ( ( X = zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc9178034014595674355it_nat @ Xb ) ) )
% 6.92/7.26 & ( ( X != zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc3714732129343117170it_nat @ ( Xa @ Xb ) @ ( iterat4993027441371875583it_nat @ ( minus_7197305767214868737atural @ X @ one_one_Code_natural ) @ Xa ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.elims
% 6.92/7.26 thf(fact_7298_iterate_Oelims,axiom,
% 6.92/7.26 ! [X: code_natural,Xa: code_natural > produc7822875418678951345atural > produc5835291356934675326atural,Xb: code_natural,Y: produc7822875418678951345atural > produc5835291356934675326atural] :
% 6.92/7.26 ( ( ( iterat8892046348760725948atural @ X @ Xa @ Xb )
% 6.92/7.26 = Y )
% 6.92/7.26 => ( ( ( X = zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc6639722614265839536atural @ Xb ) ) )
% 6.92/7.26 & ( ( X != zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc5538323210962509403atural @ ( Xa @ Xb ) @ ( iterat8892046348760725948atural @ ( minus_7197305767214868737atural @ X @ one_one_Code_natural ) @ Xa ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.elims
% 6.92/7.26 thf(fact_7299_bit__imp__take__bit__positive,axiom,
% 6.92/7.26 ! [N2: nat,M: nat,K2: int] :
% 6.92/7.26 ( ( ord_less_nat @ N2 @ M )
% 6.92/7.26 => ( ( bit_se1146084159140164899it_int @ K2 @ N2 )
% 6.92/7.26 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K2 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % bit_imp_take_bit_positive
% 6.92/7.26 thf(fact_7300_bit__concat__bit__iff,axiom,
% 6.92/7.26 ! [M: nat,K2: int,L: int,N2: nat] :
% 6.92/7.26 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K2 @ L ) @ N2 )
% 6.92/7.26 = ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.26 & ( bit_se1146084159140164899it_int @ K2 @ N2 ) )
% 6.92/7.26 | ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.26 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % bit_concat_bit_iff
% 6.92/7.26 thf(fact_7301_int__bit__bound,axiom,
% 6.92/7.26 ! [K2: int] :
% 6.92/7.26 ~ ! [N5: nat] :
% 6.92/7.26 ( ! [M4: nat] :
% 6.92/7.26 ( ( ord_less_eq_nat @ N5 @ M4 )
% 6.92/7.26 => ( ( bit_se1146084159140164899it_int @ K2 @ M4 )
% 6.92/7.26 = ( bit_se1146084159140164899it_int @ K2 @ N5 ) ) )
% 6.92/7.26 => ~ ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 6.92/7.26 => ( ( bit_se1146084159140164899it_int @ K2 @ ( minus_minus_nat @ N5 @ one_one_nat ) )
% 6.92/7.26 = ( ~ ( bit_se1146084159140164899it_int @ K2 @ N5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % int_bit_bound
% 6.92/7.26 thf(fact_7302_even__bit__succ__iff,axiom,
% 6.92/7.26 ! [A: code_natural,N2: nat] :
% 6.92/7.26 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 6.92/7.26 => ( ( bit_se8040316288895769887atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ N2 )
% 6.92/7.26 = ( ( bit_se8040316288895769887atural @ A @ N2 )
% 6.92/7.26 | ( N2 = zero_zero_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % even_bit_succ_iff
% 6.92/7.26 thf(fact_7303_even__bit__succ__iff,axiom,
% 6.92/7.26 ! [A: code_integer,N2: nat] :
% 6.92/7.26 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 6.92/7.26 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ N2 )
% 6.92/7.26 = ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 6.92/7.26 | ( N2 = zero_zero_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % even_bit_succ_iff
% 6.92/7.26 thf(fact_7304_even__bit__succ__iff,axiom,
% 6.92/7.26 ! [A: int,N2: nat] :
% 6.92/7.26 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 6.92/7.26 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ one_one_int @ A ) @ N2 )
% 6.92/7.26 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 6.92/7.26 | ( N2 = zero_zero_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % even_bit_succ_iff
% 6.92/7.26 thf(fact_7305_even__bit__succ__iff,axiom,
% 6.92/7.26 ! [A: nat,N2: nat] :
% 6.92/7.26 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 6.92/7.26 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ N2 )
% 6.92/7.26 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 6.92/7.26 | ( N2 = zero_zero_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % even_bit_succ_iff
% 6.92/7.26 thf(fact_7306_bit__sum__mult__2__cases,axiom,
% 6.92/7.26 ! [A: code_natural,B: code_natural,N2: nat] :
% 6.92/7.26 ( ! [J3: nat] :
% 6.92/7.26 ~ ( bit_se8040316288895769887atural @ A @ ( suc @ J3 ) )
% 6.92/7.26 => ( ( bit_se8040316288895769887atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 6.92/7.26 = ( ( ( N2 = zero_zero_nat )
% 6.92/7.26 => ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) )
% 6.92/7.26 & ( ( N2 != zero_zero_nat )
% 6.92/7.26 => ( bit_se8040316288895769887atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % bit_sum_mult_2_cases
% 6.92/7.26 thf(fact_7307_bit__sum__mult__2__cases,axiom,
% 6.92/7.26 ! [A: code_integer,B: code_integer,N2: nat] :
% 6.92/7.26 ( ! [J3: nat] :
% 6.92/7.26 ~ ( bit_se9216721137139052372nteger @ A @ ( suc @ J3 ) )
% 6.92/7.26 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 6.92/7.26 = ( ( ( N2 = zero_zero_nat )
% 6.92/7.26 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 6.92/7.26 & ( ( N2 != zero_zero_nat )
% 6.92/7.26 => ( bit_se9216721137139052372nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % bit_sum_mult_2_cases
% 6.92/7.26 thf(fact_7308_bit__sum__mult__2__cases,axiom,
% 6.92/7.26 ! [A: int,B: int,N2: nat] :
% 6.92/7.26 ( ! [J3: nat] :
% 6.92/7.26 ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J3 ) )
% 6.92/7.26 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 6.92/7.26 = ( ( ( N2 = zero_zero_nat )
% 6.92/7.26 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 6.92/7.26 & ( ( N2 != zero_zero_nat )
% 6.92/7.26 => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % bit_sum_mult_2_cases
% 6.92/7.26 thf(fact_7309_bit__sum__mult__2__cases,axiom,
% 6.92/7.26 ! [A: nat,B: nat,N2: nat] :
% 6.92/7.26 ( ! [J3: nat] :
% 6.92/7.26 ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J3 ) )
% 6.92/7.26 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 6.92/7.26 = ( ( ( N2 = zero_zero_nat )
% 6.92/7.26 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 6.92/7.26 & ( ( N2 != zero_zero_nat )
% 6.92/7.26 => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % bit_sum_mult_2_cases
% 6.92/7.26 thf(fact_7310_xor__nat__unfold,axiom,
% 6.92/7.26 ( bit_se6528837805403552850or_nat
% 6.92/7.26 = ( ^ [M3: nat,N: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N @ ( if_nat @ ( N = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_nat_unfold
% 6.92/7.26 thf(fact_7311_xor__nat__rec,axiom,
% 6.92/7.26 ( bit_se6528837805403552850or_nat
% 6.92/7.26 = ( ^ [M3: nat,N: nat] :
% 6.92/7.26 ( plus_plus_nat
% 6.92/7.26 @ ( zero_n2687167440665602831ol_nat
% 6.92/7.26 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 6.92/7.26 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 6.92/7.26 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_nat_rec
% 6.92/7.26 thf(fact_7312_xor__one__eq,axiom,
% 6.92/7.26 ! [A: code_natural] :
% 6.92/7.26 ( ( bit_se2046307713759805098atural @ A @ one_one_Code_natural )
% 6.92/7.26 = ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) )
% 6.92/7.26 @ ( zero_n8403883297036319079atural
% 6.92/7.26 @ ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_one_eq
% 6.92/7.26 thf(fact_7313_xor__one__eq,axiom,
% 6.92/7.26 ! [A: code_integer] :
% 6.92/7.26 ( ( bit_se3222712562003087583nteger @ A @ one_one_Code_integer )
% 6.92/7.26 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 6.92/7.26 @ ( zero_n356916108424825756nteger
% 6.92/7.26 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_one_eq
% 6.92/7.26 thf(fact_7314_xor__one__eq,axiom,
% 6.92/7.26 ! [A: nat] :
% 6.92/7.26 ( ( bit_se6528837805403552850or_nat @ A @ one_one_nat )
% 6.92/7.26 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 6.92/7.26 @ ( zero_n2687167440665602831ol_nat
% 6.92/7.26 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_one_eq
% 6.92/7.26 thf(fact_7315_xor__one__eq,axiom,
% 6.92/7.26 ! [A: int] :
% 6.92/7.26 ( ( bit_se6526347334894502574or_int @ A @ one_one_int )
% 6.92/7.26 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 6.92/7.26 @ ( zero_n2684676970156552555ol_int
% 6.92/7.26 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_one_eq
% 6.92/7.26 thf(fact_7316_one__xor__eq,axiom,
% 6.92/7.26 ! [A: code_natural] :
% 6.92/7.26 ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ A )
% 6.92/7.26 = ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) )
% 6.92/7.26 @ ( zero_n8403883297036319079atural
% 6.92/7.26 @ ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % one_xor_eq
% 6.92/7.26 thf(fact_7317_one__xor__eq,axiom,
% 6.92/7.26 ! [A: code_integer] :
% 6.92/7.26 ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ A )
% 6.92/7.26 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 6.92/7.26 @ ( zero_n356916108424825756nteger
% 6.92/7.26 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % one_xor_eq
% 6.92/7.26 thf(fact_7318_one__xor__eq,axiom,
% 6.92/7.26 ! [A: nat] :
% 6.92/7.26 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ A )
% 6.92/7.26 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 6.92/7.26 @ ( zero_n2687167440665602831ol_nat
% 6.92/7.26 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % one_xor_eq
% 6.92/7.26 thf(fact_7319_one__xor__eq,axiom,
% 6.92/7.26 ! [A: int] :
% 6.92/7.26 ( ( bit_se6526347334894502574or_int @ one_one_int @ A )
% 6.92/7.26 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 6.92/7.26 @ ( zero_n2684676970156552555ol_int
% 6.92/7.26 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % one_xor_eq
% 6.92/7.26 thf(fact_7320_set__bit__eq,axiom,
% 6.92/7.26 ( bit_se7879613467334960850it_int
% 6.92/7.26 = ( ^ [N: nat,K3: int] :
% 6.92/7.26 ( plus_plus_int @ K3
% 6.92/7.26 @ ( times_times_int
% 6.92/7.26 @ ( zero_n2684676970156552555ol_int
% 6.92/7.26 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N ) )
% 6.92/7.26 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % set_bit_eq
% 6.92/7.26 thf(fact_7321_horner__sum__simps_I2_J,axiom,
% 6.92/7.26 ! [F: int > rat,A: rat,X: int,Xs: list_int] :
% 6.92/7.26 ( ( groups7852591826665563233nt_rat @ F @ A @ ( cons_int @ X @ Xs ) )
% 6.92/7.26 = ( plus_plus_rat @ ( F @ X ) @ ( times_times_rat @ A @ ( groups7852591826665563233nt_rat @ F @ A @ Xs ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % horner_sum_simps(2)
% 6.92/7.26 thf(fact_7322_horner__sum__simps_I2_J,axiom,
% 6.92/7.26 ! [F: nat > rat,A: rat,X: nat,Xs: list_nat] :
% 6.92/7.26 ( ( groups6853238114764508677at_rat @ F @ A @ ( cons_nat @ X @ Xs ) )
% 6.92/7.26 = ( plus_plus_rat @ ( F @ X ) @ ( times_times_rat @ A @ ( groups6853238114764508677at_rat @ F @ A @ Xs ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % horner_sum_simps(2)
% 6.92/7.26 thf(fact_7323_horner__sum__simps_I2_J,axiom,
% 6.92/7.26 ! [F: int > nat,A: nat,X: int,Xs: list_int] :
% 6.92/7.26 ( ( groups8487721886752058969nt_nat @ F @ A @ ( cons_int @ X @ Xs ) )
% 6.92/7.26 = ( plus_plus_nat @ ( F @ X ) @ ( times_times_nat @ A @ ( groups8487721886752058969nt_nat @ F @ A @ Xs ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % horner_sum_simps(2)
% 6.92/7.26 thf(fact_7324_horner__sum__simps_I2_J,axiom,
% 6.92/7.26 ! [F: nat > nat,A: nat,X: nat,Xs: list_nat] :
% 6.92/7.26 ( ( groups7488368174851004413at_nat @ F @ A @ ( cons_nat @ X @ Xs ) )
% 6.92/7.26 = ( plus_plus_nat @ ( F @ X ) @ ( times_times_nat @ A @ ( groups7488368174851004413at_nat @ F @ A @ Xs ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % horner_sum_simps(2)
% 6.92/7.26 thf(fact_7325_horner__sum__simps_I2_J,axiom,
% 6.92/7.26 ! [F: int > int,A: int,X: int,Xs: list_int] :
% 6.92/7.26 ( ( groups8485231416243008693nt_int @ F @ A @ ( cons_int @ X @ Xs ) )
% 6.92/7.26 = ( plus_plus_int @ ( F @ X ) @ ( times_times_int @ A @ ( groups8485231416243008693nt_int @ F @ A @ Xs ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % horner_sum_simps(2)
% 6.92/7.26 thf(fact_7326_horner__sum__simps_I2_J,axiom,
% 6.92/7.26 ! [F: nat > int,A: int,X: nat,Xs: list_nat] :
% 6.92/7.26 ( ( groups7485877704341954137at_int @ F @ A @ ( cons_nat @ X @ Xs ) )
% 6.92/7.26 = ( plus_plus_int @ ( F @ X ) @ ( times_times_int @ A @ ( groups7485877704341954137at_int @ F @ A @ Xs ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % horner_sum_simps(2)
% 6.92/7.26 thf(fact_7327_horner__sum__simps_I2_J,axiom,
% 6.92/7.26 ! [F: $o > int,A: int,X: $o,Xs: list_o] :
% 6.92/7.26 ( ( groups9116527308978886569_o_int @ F @ A @ ( cons_o @ X @ Xs ) )
% 6.92/7.26 = ( plus_plus_int @ ( F @ X ) @ ( times_times_int @ A @ ( groups9116527308978886569_o_int @ F @ A @ Xs ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % horner_sum_simps(2)
% 6.92/7.26 thf(fact_7328_iterate_Opelims,axiom,
% 6.92/7.26 ! [X: code_natural,Xa: int > int > product_prod_int_int,Xb: int,Y: int > product_prod_int_int] :
% 6.92/7.26 ( ( ( iterate_int_int @ X @ Xa @ Xb )
% 6.92/7.26 = Y )
% 6.92/7.26 => ( ( accp_P5309764456724190780nt_int @ iterate_rel_int_int @ ( produc6480503542405096427nt_int @ X @ ( produc8811497915304161060nt_int @ Xa @ Xb ) ) )
% 6.92/7.26 => ~ ( ( ( ( X = zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( product_Pair_int_int @ Xb ) ) )
% 6.92/7.26 & ( ( X != zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc6963641260316735276nt_int @ ( Xa @ Xb ) @ ( iterate_int_int @ ( minus_7197305767214868737atural @ X @ one_one_Code_natural ) @ Xa ) ) ) ) )
% 6.92/7.26 => ~ ( accp_P5309764456724190780nt_int @ iterate_rel_int_int @ ( produc6480503542405096427nt_int @ X @ ( produc8811497915304161060nt_int @ Xa @ Xb ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.pelims
% 6.92/7.26 thf(fact_7329_iterate_Opelims,axiom,
% 6.92/7.26 ! [X: code_natural,Xa: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > produc3925858234332021118et_nat,Xb: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > produc3925858234332021118et_nat] :
% 6.92/7.26 ( ( ( iterat1233435593421607556et_nat @ X @ Xa @ Xb )
% 6.92/7.26 = Y )
% 6.92/7.26 => ( ( accp_P2863604582003348699_nat_o @ iterat2000369294365210145et_nat @ ( produc1685672994636548566_nat_o @ X @ ( produc417064122970982599_nat_o @ Xa @ Xb ) ) )
% 6.92/7.26 => ~ ( ( ( ( X = zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc5001842942810119800et_nat @ Xb ) ) )
% 6.92/7.26 & ( ( X != zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc2318911012118706502et_nat @ ( Xa @ Xb ) @ ( iterat1233435593421607556et_nat @ ( minus_7197305767214868737atural @ X @ one_one_Code_natural ) @ Xa ) ) ) ) )
% 6.92/7.26 => ~ ( accp_P2863604582003348699_nat_o @ iterat2000369294365210145et_nat @ ( produc1685672994636548566_nat_o @ X @ ( produc417064122970982599_nat_o @ Xa @ Xb ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.pelims
% 6.92/7.26 thf(fact_7330_iterate_Opelims,axiom,
% 6.92/7.26 ! [X: code_natural,Xa: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > produc2732055786443039994et_nat,Xb: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat > produc2732055786443039994et_nat] :
% 6.92/7.26 ( ( ( iterat2702368289246022656et_nat @ X @ Xa @ Xb )
% 6.92/7.26 = Y )
% 6.92/7.26 => ( ( accp_P5472185023545635811_nat_o @ iterat7486693702726674333et_nat @ ( produc722914403947760862_nat_o @ X @ ( produc5247183594425207759_nat_o @ Xa @ Xb ) ) )
% 6.92/7.26 => ~ ( ( ( ( X = zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc2245416461498447860et_nat @ Xb ) ) )
% 6.92/7.26 & ( ( X != zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc7537777246833756098et_nat @ ( Xa @ Xb ) @ ( iterat2702368289246022656et_nat @ ( minus_7197305767214868737atural @ X @ one_one_Code_natural ) @ Xa ) ) ) ) )
% 6.92/7.26 => ~ ( accp_P5472185023545635811_nat_o @ iterat7486693702726674333et_nat @ ( produc722914403947760862_nat_o @ X @ ( produc5247183594425207759_nat_o @ Xa @ Xb ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.pelims
% 6.92/7.26 thf(fact_7331_iterate_Opelims,axiom,
% 6.92/7.26 ! [X: code_natural,Xa: b > produc6653097349344004940it_nat > produc7388388658123137530it_nat,Xb: b,Y: produc6653097349344004940it_nat > produc7388388658123137530it_nat] :
% 6.92/7.26 ( ( ( iterat9120928542346325760it_nat @ X @ Xa @ Xb )
% 6.92/7.26 = Y )
% 6.92/7.26 => ( ( accp_P8256022550677833493_nat_b @ iterat7179843830775474589it_nat @ ( produc7509976829882447632_nat_b @ X @ ( produc5258162843807585025_nat_b @ Xa @ Xb ) ) )
% 6.92/7.26 => ~ ( ( ( ( X = zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc4082563078715348724it_nat @ Xb ) ) )
% 6.92/7.26 & ( ( X != zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc8824551317683396724it_nat @ ( Xa @ Xb ) @ ( iterat9120928542346325760it_nat @ ( minus_7197305767214868737atural @ X @ one_one_Code_natural ) @ Xa ) ) ) ) )
% 6.92/7.26 => ~ ( accp_P8256022550677833493_nat_b @ iterat7179843830775474589it_nat @ ( produc7509976829882447632_nat_b @ X @ ( produc5258162843807585025_nat_b @ Xa @ Xb ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.pelims
% 6.92/7.26 thf(fact_7332_iterate_Opelims,axiom,
% 6.92/7.26 ! [X: code_natural,Xa: a > produc6653097349344004940it_nat > produc3260487557148687353it_nat,Xb: a,Y: produc6653097349344004940it_nat > produc3260487557148687353it_nat] :
% 6.92/7.26 ( ( ( iterat4993027441371875583it_nat @ X @ Xa @ Xb )
% 6.92/7.26 = Y )
% 6.92/7.26 => ( ( accp_P7857408453303007510_nat_a @ iterat3051942729801024412it_nat @ ( produc1823638919063574929_nat_a @ X @ ( produc8795196974146716930_nat_a @ Xa @ Xb ) ) )
% 6.92/7.26 => ~ ( ( ( ( X = zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc9178034014595674355it_nat @ Xb ) ) )
% 6.92/7.26 & ( ( X != zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc3714732129343117170it_nat @ ( Xa @ Xb ) @ ( iterat4993027441371875583it_nat @ ( minus_7197305767214868737atural @ X @ one_one_Code_natural ) @ Xa ) ) ) ) )
% 6.92/7.26 => ~ ( accp_P7857408453303007510_nat_a @ iterat3051942729801024412it_nat @ ( produc1823638919063574929_nat_a @ X @ ( produc8795196974146716930_nat_a @ Xa @ Xb ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.pelims
% 6.92/7.26 thf(fact_7333_iterate_Opelims,axiom,
% 6.92/7.26 ! [X: code_natural,Xa: code_natural > produc7822875418678951345atural > produc5835291356934675326atural,Xb: code_natural,Y: produc7822875418678951345atural > produc5835291356934675326atural] :
% 6.92/7.26 ( ( ( iterat8892046348760725948atural @ X @ Xa @ Xb )
% 6.92/7.26 = Y )
% 6.92/7.26 => ( ( accp_P9117636446167716760atural @ iterat8136814461032266713atural @ ( produc7296465590736685127atural @ X @ ( produc2044891599319335296atural @ Xa @ Xb ) ) )
% 6.92/7.26 => ~ ( ( ( ( X = zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc6639722614265839536atural @ Xb ) ) )
% 6.92/7.26 & ( ( X != zero_z2226904508553997617atural )
% 6.92/7.26 => ( Y
% 6.92/7.26 = ( produc5538323210962509403atural @ ( Xa @ Xb ) @ ( iterat8892046348760725948atural @ ( minus_7197305767214868737atural @ X @ one_one_Code_natural ) @ Xa ) ) ) ) )
% 6.92/7.26 => ~ ( accp_P9117636446167716760atural @ iterat8136814461032266713atural @ ( produc7296465590736685127atural @ X @ ( produc2044891599319335296atural @ Xa @ Xb ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % iterate.pelims
% 6.92/7.26 thf(fact_7334_the__elem__eq,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat] :
% 6.92/7.26 ( ( the_el221668144340439132at_nat @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 6.92/7.26 = X ) ).
% 6.92/7.26
% 6.92/7.26 % the_elem_eq
% 6.92/7.26 thf(fact_7335_the__elem__eq,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat] :
% 6.92/7.26 ( ( the_el2281957884133575798at_nat @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 6.92/7.26 = X ) ).
% 6.92/7.26
% 6.92/7.26 % the_elem_eq
% 6.92/7.26 thf(fact_7336_the__elem__eq,axiom,
% 6.92/7.26 ! [X: $o] :
% 6.92/7.26 ( ( the_elem_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 6.92/7.26 = X ) ).
% 6.92/7.26
% 6.92/7.26 % the_elem_eq
% 6.92/7.26 thf(fact_7337_the__elem__eq,axiom,
% 6.92/7.26 ! [X: nat] :
% 6.92/7.26 ( ( the_elem_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 6.92/7.26 = X ) ).
% 6.92/7.26
% 6.92/7.26 % the_elem_eq
% 6.92/7.26 thf(fact_7338_the__elem__eq,axiom,
% 6.92/7.26 ! [X: int] :
% 6.92/7.26 ( ( the_elem_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 6.92/7.26 = X ) ).
% 6.92/7.26
% 6.92/7.26 % the_elem_eq
% 6.92/7.26 thf(fact_7339_inc__shift__def,axiom,
% 6.92/7.26 ( inc_shift
% 6.92/7.26 = ( ^ [V2: code_natural,K3: code_natural] : ( if_Code_natural @ ( V2 = K3 ) @ one_one_Code_natural @ ( plus_p4538020629002901425atural @ K3 @ one_one_Code_natural ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % inc_shift_def
% 6.92/7.26 thf(fact_7340_divmod__step__integer__def,axiom,
% 6.92/7.26 ( unique4921790084139445826nteger
% 6.92/7.26 = ( ^ [L2: num] :
% 6.92/7.26 ( produc6916734918728496179nteger
% 6.92/7.26 @ ^ [Q8: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q8 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q8 ) @ R5 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % divmod_step_integer_def
% 6.92/7.26 thf(fact_7341_xor__nonnegative__int__iff,axiom,
% 6.92/7.26 ! [K2: int,L: int] :
% 6.92/7.26 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K2 @ L ) )
% 6.92/7.26 = ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.26 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_nonnegative_int_iff
% 6.92/7.26 thf(fact_7342_xor__negative__int__iff,axiom,
% 6.92/7.26 ! [K2: int,L: int] :
% 6.92/7.26 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K2 @ L ) @ zero_zero_int )
% 6.92/7.26 = ( ( ord_less_int @ K2 @ zero_zero_int )
% 6.92/7.26 != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_negative_int_iff
% 6.92/7.26 thf(fact_7343_less__eq__integer__code_I1_J,axiom,
% 6.92/7.26 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 6.92/7.26
% 6.92/7.26 % less_eq_integer_code(1)
% 6.92/7.26 thf(fact_7344_plus__integer__code_I2_J,axiom,
% 6.92/7.26 ! [L: code_integer] :
% 6.92/7.26 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L )
% 6.92/7.26 = L ) ).
% 6.92/7.26
% 6.92/7.26 % plus_integer_code(2)
% 6.92/7.26 thf(fact_7345_plus__integer__code_I1_J,axiom,
% 6.92/7.26 ! [K2: code_integer] :
% 6.92/7.26 ( ( plus_p5714425477246183910nteger @ K2 @ zero_z3403309356797280102nteger )
% 6.92/7.26 = K2 ) ).
% 6.92/7.26
% 6.92/7.26 % plus_integer_code(1)
% 6.92/7.26 thf(fact_7346_sgn__integer__code,axiom,
% 6.92/7.26 ( sgn_sgn_Code_integer
% 6.92/7.26 = ( ^ [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 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % sgn_integer_code
% 6.92/7.26 thf(fact_7347_XOR__lower,axiom,
% 6.92/7.26 ! [X: int,Y: int] :
% 6.92/7.26 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.26 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.26 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % XOR_lower
% 6.92/7.26 thf(fact_7348_bit__nat__iff,axiom,
% 6.92/7.26 ! [K2: int,N2: nat] :
% 6.92/7.26 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K2 ) @ N2 )
% 6.92/7.26 = ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.26 & ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % bit_nat_iff
% 6.92/7.26 thf(fact_7349_XOR__upper,axiom,
% 6.92/7.26 ! [X: int,N2: nat,Y: int] :
% 6.92/7.26 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.26 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.26 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 6.92/7.26 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % XOR_upper
% 6.92/7.26 thf(fact_7350_xor__int__rec,axiom,
% 6.92/7.26 ( bit_se6526347334894502574or_int
% 6.92/7.26 = ( ^ [K3: int,L2: int] :
% 6.92/7.26 ( plus_plus_int
% 6.92/7.26 @ ( zero_n2684676970156552555ol_int
% 6.92/7.26 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 6.92/7.26 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 6.92/7.26 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_int_rec
% 6.92/7.26 thf(fact_7351_integer__of__int__code,axiom,
% 6.92/7.26 ( code_integer_of_int
% 6.92/7.26 = ( ^ [K3: int] :
% 6.92/7.26 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 6.92/7.26 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 6.92/7.26 @ ( if_Code_integer
% 6.92/7.26 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 6.92/7.26 = zero_zero_int )
% 6.92/7.26 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 6.92/7.26 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % integer_of_int_code
% 6.92/7.26 thf(fact_7352_xor__int__unfold,axiom,
% 6.92/7.26 ( bit_se6526347334894502574or_int
% 6.92/7.26 = ( ^ [K3: int,L2: int] :
% 6.92/7.26 ( if_int
% 6.92/7.26 @ ( K3
% 6.92/7.26 = ( uminus_uminus_int @ one_one_int ) )
% 6.92/7.26 @ ( bit_ri7919022796975470100ot_int @ L2 )
% 6.92/7.26 @ ( if_int
% 6.92/7.26 @ ( L2
% 6.92/7.26 = ( uminus_uminus_int @ one_one_int ) )
% 6.92/7.26 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 6.92/7.26 @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % xor_int_unfold
% 6.92/7.26 thf(fact_7353_is__singleton__the__elem,axiom,
% 6.92/7.26 ( is_sin2937591304547752795at_nat
% 6.92/7.26 = ( ^ [A6: set_Pr4329608150637261639at_nat] :
% 6.92/7.26 ( A6
% 6.92/7.26 = ( insert9069300056098147895at_nat @ ( the_el221668144340439132at_nat @ A6 ) @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singleton_the_elem
% 6.92/7.26 thf(fact_7354_is__singleton__the__elem,axiom,
% 6.92/7.26 ( is_sin2850979758926227957at_nat
% 6.92/7.26 = ( ^ [A6: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( A6
% 6.92/7.26 = ( insert8211810215607154385at_nat @ ( the_el2281957884133575798at_nat @ A6 ) @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singleton_the_elem
% 6.92/7.26 thf(fact_7355_is__singleton__the__elem,axiom,
% 6.92/7.26 ( is_singleton_o
% 6.92/7.26 = ( ^ [A6: set_o] :
% 6.92/7.26 ( A6
% 6.92/7.26 = ( insert_o @ ( the_elem_o @ A6 ) @ bot_bot_set_o ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singleton_the_elem
% 6.92/7.26 thf(fact_7356_is__singleton__the__elem,axiom,
% 6.92/7.26 ( is_singleton_nat
% 6.92/7.26 = ( ^ [A6: set_nat] :
% 6.92/7.26 ( A6
% 6.92/7.26 = ( insert_nat @ ( the_elem_nat @ A6 ) @ bot_bot_set_nat ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singleton_the_elem
% 6.92/7.26 thf(fact_7357_is__singleton__the__elem,axiom,
% 6.92/7.26 ( is_singleton_int
% 6.92/7.26 = ( ^ [A6: set_int] :
% 6.92/7.26 ( A6
% 6.92/7.26 = ( insert_int @ ( the_elem_int @ A6 ) @ bot_bot_set_int ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singleton_the_elem
% 6.92/7.26 thf(fact_7358_integer__of__num_I3_J,axiom,
% 6.92/7.26 ! [N2: num] :
% 6.92/7.26 ( ( code_integer_of_num @ ( bit1 @ N2 ) )
% 6.92/7.26 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) @ one_one_Code_integer ) ) ).
% 6.92/7.26
% 6.92/7.26 % integer_of_num(3)
% 6.92/7.26 thf(fact_7359_take__bit__num__code,axiom,
% 6.92/7.26 ( bit_take_bit_num
% 6.92/7.26 = ( ^ [N: nat,M3: num] :
% 6.92/7.26 ( produc478579273971653890on_num
% 6.92/7.26 @ ^ [A5: nat,X4: num] :
% 6.92/7.26 ( case_nat_option_num @ none_num
% 6.92/7.26 @ ^ [O: nat] :
% 6.92/7.26 ( case_num_option_num @ ( some_num @ one )
% 6.92/7.26 @ ^ [P7: num] :
% 6.92/7.26 ( case_o6005452278849405969um_num @ none_num
% 6.92/7.26 @ ^ [Q8: num] : ( some_num @ ( bit0 @ Q8 ) )
% 6.92/7.26 @ ( bit_take_bit_num @ O @ P7 ) )
% 6.92/7.26 @ ^ [P7: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P7 ) ) )
% 6.92/7.26 @ X4 )
% 6.92/7.26 @ A5 )
% 6.92/7.26 @ ( product_Pair_nat_num @ N @ M3 ) ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % take_bit_num_code
% 6.92/7.26 thf(fact_7360_is__singletonI,axiom,
% 6.92/7.26 ! [X: produc3843707927480180839at_nat] : ( is_sin2937591304547752795at_nat @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singletonI
% 6.92/7.26 thf(fact_7361_is__singletonI,axiom,
% 6.92/7.26 ! [X: product_prod_nat_nat] : ( is_sin2850979758926227957at_nat @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singletonI
% 6.92/7.26 thf(fact_7362_is__singletonI,axiom,
% 6.92/7.26 ! [X: $o] : ( is_singleton_o @ ( insert_o @ X @ bot_bot_set_o ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singletonI
% 6.92/7.26 thf(fact_7363_is__singletonI,axiom,
% 6.92/7.26 ! [X: nat] : ( is_singleton_nat @ ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singletonI
% 6.92/7.26 thf(fact_7364_is__singletonI,axiom,
% 6.92/7.26 ! [X: int] : ( is_singleton_int @ ( insert_int @ X @ bot_bot_set_int ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singletonI
% 6.92/7.26 thf(fact_7365_case__nat__numeral,axiom,
% 6.92/7.26 ! [A: option_num,F: nat > option_num,V: num] :
% 6.92/7.26 ( ( case_nat_option_num @ A @ F @ ( numeral_numeral_nat @ V ) )
% 6.92/7.26 = ( F @ ( pred_numeral @ V ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % case_nat_numeral
% 6.92/7.26 thf(fact_7366_case__nat__numeral,axiom,
% 6.92/7.26 ! [A: nat,F: nat > nat,V: num] :
% 6.92/7.26 ( ( case_nat_nat @ A @ F @ ( numeral_numeral_nat @ V ) )
% 6.92/7.26 = ( F @ ( pred_numeral @ V ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % case_nat_numeral
% 6.92/7.26 thf(fact_7367_case__nat__numeral,axiom,
% 6.92/7.26 ! [A: $o,F: nat > $o,V: num] :
% 6.92/7.26 ( ( case_nat_o @ A @ F @ ( numeral_numeral_nat @ V ) )
% 6.92/7.26 = ( F @ ( pred_numeral @ V ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % case_nat_numeral
% 6.92/7.26 thf(fact_7368_not__nonnegative__int__iff,axiom,
% 6.92/7.26 ! [K2: int] :
% 6.92/7.26 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K2 ) )
% 6.92/7.26 = ( ord_less_int @ K2 @ zero_zero_int ) ) ).
% 6.92/7.26
% 6.92/7.26 % not_nonnegative_int_iff
% 6.92/7.26 thf(fact_7369_not__negative__int__iff,axiom,
% 6.92/7.26 ! [K2: int] :
% 6.92/7.26 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K2 ) @ zero_zero_int )
% 6.92/7.26 = ( ord_less_eq_int @ zero_zero_int @ K2 ) ) ).
% 6.92/7.26
% 6.92/7.26 % not_negative_int_iff
% 6.92/7.26 thf(fact_7370_case__nat__add__eq__if,axiom,
% 6.92/7.26 ! [A: option_num,F: nat > option_num,V: num,N2: nat] :
% 6.92/7.26 ( ( case_nat_option_num @ A @ F @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 6.92/7.26 = ( F @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N2 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % case_nat_add_eq_if
% 6.92/7.26 thf(fact_7371_case__nat__add__eq__if,axiom,
% 6.92/7.26 ! [A: nat,F: nat > nat,V: num,N2: nat] :
% 6.92/7.26 ( ( case_nat_nat @ A @ F @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 6.92/7.26 = ( F @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N2 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % case_nat_add_eq_if
% 6.92/7.26 thf(fact_7372_case__nat__add__eq__if,axiom,
% 6.92/7.26 ! [A: $o,F: nat > $o,V: num,N2: nat] :
% 6.92/7.26 ( ( case_nat_o @ A @ F @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 6.92/7.26 = ( F @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N2 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % case_nat_add_eq_if
% 6.92/7.26 thf(fact_7373_abs__integer__code,axiom,
% 6.92/7.26 ( abs_abs_Code_integer
% 6.92/7.26 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K3 ) @ K3 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % abs_integer_code
% 6.92/7.26 thf(fact_7374_less__integer__code_I1_J,axiom,
% 6.92/7.26 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 6.92/7.26
% 6.92/7.26 % less_integer_code(1)
% 6.92/7.26 thf(fact_7375_less__integer_Oabs__eq,axiom,
% 6.92/7.26 ! [Xa: int,X: int] :
% 6.92/7.26 ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 6.92/7.26 = ( ord_less_int @ Xa @ X ) ) ).
% 6.92/7.26
% 6.92/7.26 % less_integer.abs_eq
% 6.92/7.26 thf(fact_7376_nat_Ocase__distrib,axiom,
% 6.92/7.26 ! [H: option_num > option_num,F1: option_num,F2: nat > option_num,Nat: nat] :
% 6.92/7.26 ( ( H @ ( case_nat_option_num @ F1 @ F2 @ Nat ) )
% 6.92/7.26 = ( case_nat_option_num @ ( H @ F1 )
% 6.92/7.26 @ ^ [X4: nat] : ( H @ ( F2 @ X4 ) )
% 6.92/7.26 @ Nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % nat.case_distrib
% 6.92/7.26 thf(fact_7377_nat_Ocase__distrib,axiom,
% 6.92/7.26 ! [H: option_num > nat,F1: option_num,F2: nat > option_num,Nat: nat] :
% 6.92/7.26 ( ( H @ ( case_nat_option_num @ F1 @ F2 @ Nat ) )
% 6.92/7.26 = ( case_nat_nat @ ( H @ F1 )
% 6.92/7.26 @ ^ [X4: nat] : ( H @ ( F2 @ X4 ) )
% 6.92/7.26 @ Nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % nat.case_distrib
% 6.92/7.26 thf(fact_7378_nat_Ocase__distrib,axiom,
% 6.92/7.26 ! [H: option_num > $o,F1: option_num,F2: nat > option_num,Nat: nat] :
% 6.92/7.26 ( ( H @ ( case_nat_option_num @ F1 @ F2 @ Nat ) )
% 6.92/7.26 = ( case_nat_o @ ( H @ F1 )
% 6.92/7.26 @ ^ [X4: nat] : ( H @ ( F2 @ X4 ) )
% 6.92/7.26 @ Nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % nat.case_distrib
% 6.92/7.26 thf(fact_7379_nat_Ocase__distrib,axiom,
% 6.92/7.26 ! [H: nat > option_num,F1: nat,F2: nat > nat,Nat: nat] :
% 6.92/7.26 ( ( H @ ( case_nat_nat @ F1 @ F2 @ Nat ) )
% 6.92/7.26 = ( case_nat_option_num @ ( H @ F1 )
% 6.92/7.26 @ ^ [X4: nat] : ( H @ ( F2 @ X4 ) )
% 6.92/7.26 @ Nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % nat.case_distrib
% 6.92/7.26 thf(fact_7380_nat_Ocase__distrib,axiom,
% 6.92/7.26 ! [H: nat > nat,F1: nat,F2: nat > nat,Nat: nat] :
% 6.92/7.26 ( ( H @ ( case_nat_nat @ F1 @ F2 @ Nat ) )
% 6.92/7.26 = ( case_nat_nat @ ( H @ F1 )
% 6.92/7.26 @ ^ [X4: nat] : ( H @ ( F2 @ X4 ) )
% 6.92/7.26 @ Nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % nat.case_distrib
% 6.92/7.26 thf(fact_7381_nat_Ocase__distrib,axiom,
% 6.92/7.26 ! [H: nat > $o,F1: nat,F2: nat > nat,Nat: nat] :
% 6.92/7.26 ( ( H @ ( case_nat_nat @ F1 @ F2 @ Nat ) )
% 6.92/7.26 = ( case_nat_o @ ( H @ F1 )
% 6.92/7.26 @ ^ [X4: nat] : ( H @ ( F2 @ X4 ) )
% 6.92/7.26 @ Nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % nat.case_distrib
% 6.92/7.26 thf(fact_7382_nat_Ocase__distrib,axiom,
% 6.92/7.26 ! [H: $o > option_num,F1: $o,F2: nat > $o,Nat: nat] :
% 6.92/7.26 ( ( H @ ( case_nat_o @ F1 @ F2 @ Nat ) )
% 6.92/7.26 = ( case_nat_option_num @ ( H @ F1 )
% 6.92/7.26 @ ^ [X4: nat] : ( H @ ( F2 @ X4 ) )
% 6.92/7.26 @ Nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % nat.case_distrib
% 6.92/7.26 thf(fact_7383_nat_Ocase__distrib,axiom,
% 6.92/7.26 ! [H: $o > nat,F1: $o,F2: nat > $o,Nat: nat] :
% 6.92/7.26 ( ( H @ ( case_nat_o @ F1 @ F2 @ Nat ) )
% 6.92/7.26 = ( case_nat_nat @ ( H @ F1 )
% 6.92/7.26 @ ^ [X4: nat] : ( H @ ( F2 @ X4 ) )
% 6.92/7.26 @ Nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % nat.case_distrib
% 6.92/7.26 thf(fact_7384_nat_Ocase__distrib,axiom,
% 6.92/7.26 ! [H: $o > $o,F1: $o,F2: nat > $o,Nat: nat] :
% 6.92/7.26 ( ( H @ ( case_nat_o @ F1 @ F2 @ Nat ) )
% 6.92/7.26 = ( case_nat_o @ ( H @ F1 )
% 6.92/7.26 @ ^ [X4: nat] : ( H @ ( F2 @ X4 ) )
% 6.92/7.26 @ Nat ) ) ).
% 6.92/7.26
% 6.92/7.26 % nat.case_distrib
% 6.92/7.26 thf(fact_7385_num_Ocase__distrib,axiom,
% 6.92/7.26 ! [H: option_num > option_num,F1: option_num,F2: num > option_num,F32: num > option_num,Num: num] :
% 6.92/7.26 ( ( H @ ( case_num_option_num @ F1 @ F2 @ F32 @ Num ) )
% 6.92/7.26 = ( case_num_option_num @ ( H @ F1 )
% 6.92/7.26 @ ^ [X4: num] : ( H @ ( F2 @ X4 ) )
% 6.92/7.26 @ ^ [X4: num] : ( H @ ( F32 @ X4 ) )
% 6.92/7.26 @ Num ) ) ).
% 6.92/7.26
% 6.92/7.26 % num.case_distrib
% 6.92/7.26 thf(fact_7386_old_Onat_Osimps_I4_J,axiom,
% 6.92/7.26 ! [F1: option_num,F2: nat > option_num] :
% 6.92/7.26 ( ( case_nat_option_num @ F1 @ F2 @ zero_zero_nat )
% 6.92/7.26 = F1 ) ).
% 6.92/7.26
% 6.92/7.26 % old.nat.simps(4)
% 6.92/7.26 thf(fact_7387_old_Onat_Osimps_I4_J,axiom,
% 6.92/7.26 ! [F1: nat,F2: nat > nat] :
% 6.92/7.26 ( ( case_nat_nat @ F1 @ F2 @ zero_zero_nat )
% 6.92/7.26 = F1 ) ).
% 6.92/7.26
% 6.92/7.26 % old.nat.simps(4)
% 6.92/7.26 thf(fact_7388_old_Onat_Osimps_I4_J,axiom,
% 6.92/7.26 ! [F1: $o,F2: nat > $o] :
% 6.92/7.26 ( ( case_nat_o @ F1 @ F2 @ zero_zero_nat )
% 6.92/7.26 = F1 ) ).
% 6.92/7.26
% 6.92/7.26 % old.nat.simps(4)
% 6.92/7.26 thf(fact_7389_old_Onat_Osimps_I5_J,axiom,
% 6.92/7.26 ! [F1: option_num,F2: nat > option_num,X2: nat] :
% 6.92/7.26 ( ( case_nat_option_num @ F1 @ F2 @ ( suc @ X2 ) )
% 6.92/7.26 = ( F2 @ X2 ) ) ).
% 6.92/7.26
% 6.92/7.26 % old.nat.simps(5)
% 6.92/7.26 thf(fact_7390_old_Onat_Osimps_I5_J,axiom,
% 6.92/7.26 ! [F1: nat,F2: nat > nat,X2: nat] :
% 6.92/7.26 ( ( case_nat_nat @ F1 @ F2 @ ( suc @ X2 ) )
% 6.92/7.26 = ( F2 @ X2 ) ) ).
% 6.92/7.26
% 6.92/7.26 % old.nat.simps(5)
% 6.92/7.26 thf(fact_7391_old_Onat_Osimps_I5_J,axiom,
% 6.92/7.26 ! [F1: $o,F2: nat > $o,X2: nat] :
% 6.92/7.26 ( ( case_nat_o @ F1 @ F2 @ ( suc @ X2 ) )
% 6.92/7.26 = ( F2 @ X2 ) ) ).
% 6.92/7.26
% 6.92/7.26 % old.nat.simps(5)
% 6.92/7.26 thf(fact_7392_not__add__distrib,axiom,
% 6.92/7.26 ! [A: int,B: int] :
% 6.92/7.26 ( ( bit_ri7919022796975470100ot_int @ ( plus_plus_int @ A @ B ) )
% 6.92/7.26 = ( minus_minus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 6.92/7.26
% 6.92/7.26 % not_add_distrib
% 6.92/7.26 thf(fact_7393_not__diff__distrib,axiom,
% 6.92/7.26 ! [A: int,B: int] :
% 6.92/7.26 ( ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A @ B ) )
% 6.92/7.26 = ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 6.92/7.26
% 6.92/7.26 % not_diff_distrib
% 6.92/7.26 thf(fact_7394_plus__integer_Oabs__eq,axiom,
% 6.92/7.26 ! [Xa: int,X: int] :
% 6.92/7.26 ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 6.92/7.26 = ( code_integer_of_int @ ( plus_plus_int @ Xa @ X ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % plus_integer.abs_eq
% 6.92/7.26 thf(fact_7395_less__eq__integer_Oabs__eq,axiom,
% 6.92/7.26 ! [Xa: int,X: int] :
% 6.92/7.26 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 6.92/7.26 = ( ord_less_eq_int @ Xa @ X ) ) ).
% 6.92/7.26
% 6.92/7.26 % less_eq_integer.abs_eq
% 6.92/7.26 thf(fact_7396_verit__eq__simplify_I17_J,axiom,
% 6.92/7.26 ! [F1: option_num,F2: num > option_num,F32: num > option_num,X2: num] :
% 6.92/7.26 ( ( case_num_option_num @ F1 @ F2 @ F32 @ ( bit0 @ X2 ) )
% 6.92/7.26 = ( F2 @ X2 ) ) ).
% 6.92/7.26
% 6.92/7.26 % verit_eq_simplify(17)
% 6.92/7.26 thf(fact_7397_verit__eq__simplify_I16_J,axiom,
% 6.92/7.26 ! [F1: option_num,F2: num > option_num,F32: num > option_num] :
% 6.92/7.26 ( ( case_num_option_num @ F1 @ F2 @ F32 @ one )
% 6.92/7.26 = F1 ) ).
% 6.92/7.26
% 6.92/7.26 % verit_eq_simplify(16)
% 6.92/7.26 thf(fact_7398_verit__eq__simplify_I18_J,axiom,
% 6.92/7.26 ! [F1: option_num,F2: num > option_num,F32: num > option_num,X32: num] :
% 6.92/7.26 ( ( case_num_option_num @ F1 @ F2 @ F32 @ ( bit1 @ X32 ) )
% 6.92/7.26 = ( F32 @ X32 ) ) ).
% 6.92/7.26
% 6.92/7.26 % verit_eq_simplify(18)
% 6.92/7.26 thf(fact_7399_is__singletonI_H,axiom,
% 6.92/7.26 ! [A4: set_se6260736226359567993nt_int] :
% 6.92/7.26 ( ( A4 != bot_bo1488462491386950373nt_int )
% 6.92/7.26 => ( ! [X3: set_Pr958786334691620121nt_int,Y3: set_Pr958786334691620121nt_int] :
% 6.92/7.26 ( ( member2340774599025711042nt_int @ X3 @ A4 )
% 6.92/7.26 => ( ( member2340774599025711042nt_int @ Y3 @ A4 )
% 6.92/7.26 => ( X3 = Y3 ) ) )
% 6.92/7.26 => ( is_sin6299389887212142093nt_int @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singletonI'
% 6.92/7.26 thf(fact_7400_is__singletonI_H,axiom,
% 6.92/7.26 ! [A4: set_set_nat] :
% 6.92/7.26 ( ( A4 != bot_bot_set_set_nat )
% 6.92/7.26 => ( ! [X3: set_nat,Y3: set_nat] :
% 6.92/7.26 ( ( member_set_nat @ X3 @ A4 )
% 6.92/7.26 => ( ( member_set_nat @ Y3 @ A4 )
% 6.92/7.26 => ( X3 = Y3 ) ) )
% 6.92/7.26 => ( is_singleton_set_nat @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singletonI'
% 6.92/7.26 thf(fact_7401_is__singletonI_H,axiom,
% 6.92/7.26 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.26 ( ( A4 != bot_bo2099793752762293965at_nat )
% 6.92/7.26 => ( ! [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 6.92/7.26 ( ( member8440522571783428010at_nat @ X3 @ A4 )
% 6.92/7.26 => ( ( member8440522571783428010at_nat @ Y3 @ A4 )
% 6.92/7.26 => ( X3 = Y3 ) ) )
% 6.92/7.26 => ( is_sin2850979758926227957at_nat @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singletonI'
% 6.92/7.26 thf(fact_7402_is__singletonI_H,axiom,
% 6.92/7.26 ! [A4: set_o] :
% 6.92/7.26 ( ( A4 != bot_bot_set_o )
% 6.92/7.26 => ( ! [X3: $o,Y3: $o] :
% 6.92/7.26 ( ( member_o @ X3 @ A4 )
% 6.92/7.26 => ( ( member_o @ Y3 @ A4 )
% 6.92/7.26 => ( X3 = Y3 ) ) )
% 6.92/7.26 => ( is_singleton_o @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singletonI'
% 6.92/7.26 thf(fact_7403_is__singletonI_H,axiom,
% 6.92/7.26 ! [A4: set_nat] :
% 6.92/7.26 ( ( A4 != bot_bot_set_nat )
% 6.92/7.26 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.26 ( ( member_nat @ X3 @ A4 )
% 6.92/7.26 => ( ( member_nat @ Y3 @ A4 )
% 6.92/7.26 => ( X3 = Y3 ) ) )
% 6.92/7.26 => ( is_singleton_nat @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singletonI'
% 6.92/7.26 thf(fact_7404_is__singletonI_H,axiom,
% 6.92/7.26 ! [A4: set_int] :
% 6.92/7.26 ( ( A4 != bot_bot_set_int )
% 6.92/7.26 => ( ! [X3: int,Y3: int] :
% 6.92/7.26 ( ( member_int @ X3 @ A4 )
% 6.92/7.26 => ( ( member_int @ Y3 @ A4 )
% 6.92/7.26 => ( X3 = Y3 ) ) )
% 6.92/7.26 => ( is_singleton_int @ A4 ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % is_singletonI'
% 6.92/7.26 thf(fact_7405_minus__eq__not__plus__1,axiom,
% 6.92/7.26 ( uminus1351360451143612070nteger
% 6.92/7.26 = ( ^ [A5: code_integer] : ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A5 ) @ one_one_Code_integer ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % minus_eq_not_plus_1
% 6.92/7.26 thf(fact_7406_minus__eq__not__plus__1,axiom,
% 6.92/7.26 ( uminus_uminus_int
% 6.92/7.26 = ( ^ [A5: int] : ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A5 ) @ one_one_int ) ) ) ).
% 6.92/7.26
% 6.92/7.26 % minus_eq_not_plus_1
% 6.92/7.26 thf(fact_7407_nth__Cons,axiom,
% 6.92/7.26 ! [X: int,Xs: list_int,N2: nat] :
% 6.92/7.26 ( ( nth_int @ ( cons_int @ X @ Xs ) @ N2 )
% 6.92/7.26 = ( case_nat_int @ X @ ( nth_int @ Xs ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % nth_Cons
% 6.92/7.27 thf(fact_7408_nth__Cons,axiom,
% 6.92/7.27 ! [X: option_num,Xs: list_option_num,N2: nat] :
% 6.92/7.27 ( ( nth_option_num @ ( cons_option_num @ X @ Xs ) @ N2 )
% 6.92/7.27 = ( case_nat_option_num @ X @ ( nth_option_num @ Xs ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % nth_Cons
% 6.92/7.27 thf(fact_7409_nth__Cons,axiom,
% 6.92/7.27 ! [X: nat,Xs: list_nat,N2: nat] :
% 6.92/7.27 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N2 )
% 6.92/7.27 = ( case_nat_nat @ X @ ( nth_nat @ Xs ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % nth_Cons
% 6.92/7.27 thf(fact_7410_nth__Cons,axiom,
% 6.92/7.27 ! [X: $o,Xs: list_o,N2: nat] :
% 6.92/7.27 ( ( nth_o @ ( cons_o @ X @ Xs ) @ N2 )
% 6.92/7.27 = ( case_nat_o @ X @ ( nth_o @ Xs ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % nth_Cons
% 6.92/7.27 thf(fact_7411_take__bit__not__mask__eq__0,axiom,
% 6.92/7.27 ! [M: nat,N2: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( bit_se1745604003318907178nteger @ M @ ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N2 ) ) )
% 6.92/7.27 = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.27
% 6.92/7.27 % take_bit_not_mask_eq_0
% 6.92/7.27 thf(fact_7412_take__bit__not__mask__eq__0,axiom,
% 6.92/7.27 ! [M: nat,N2: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) )
% 6.92/7.27 = zero_zero_int ) ) ).
% 6.92/7.27
% 6.92/7.27 % take_bit_not_mask_eq_0
% 6.92/7.27 thf(fact_7413_is__singleton__def,axiom,
% 6.92/7.27 ( is_sin2937591304547752795at_nat
% 6.92/7.27 = ( ^ [A6: set_Pr4329608150637261639at_nat] :
% 6.92/7.27 ? [X4: produc3843707927480180839at_nat] :
% 6.92/7.27 ( A6
% 6.92/7.27 = ( insert9069300056098147895at_nat @ X4 @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % is_singleton_def
% 6.92/7.27 thf(fact_7414_is__singleton__def,axiom,
% 6.92/7.27 ( is_sin2850979758926227957at_nat
% 6.92/7.27 = ( ^ [A6: set_Pr1261947904930325089at_nat] :
% 6.92/7.27 ? [X4: product_prod_nat_nat] :
% 6.92/7.27 ( A6
% 6.92/7.27 = ( insert8211810215607154385at_nat @ X4 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % is_singleton_def
% 6.92/7.27 thf(fact_7415_is__singleton__def,axiom,
% 6.92/7.27 ( is_singleton_o
% 6.92/7.27 = ( ^ [A6: set_o] :
% 6.92/7.27 ? [X4: $o] :
% 6.92/7.27 ( A6
% 6.92/7.27 = ( insert_o @ X4 @ bot_bot_set_o ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % is_singleton_def
% 6.92/7.27 thf(fact_7416_is__singleton__def,axiom,
% 6.92/7.27 ( is_singleton_nat
% 6.92/7.27 = ( ^ [A6: set_nat] :
% 6.92/7.27 ? [X4: nat] :
% 6.92/7.27 ( A6
% 6.92/7.27 = ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % is_singleton_def
% 6.92/7.27 thf(fact_7417_is__singleton__def,axiom,
% 6.92/7.27 ( is_singleton_int
% 6.92/7.27 = ( ^ [A6: set_int] :
% 6.92/7.27 ? [X4: int] :
% 6.92/7.27 ( A6
% 6.92/7.27 = ( insert_int @ X4 @ bot_bot_set_int ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % is_singleton_def
% 6.92/7.27 thf(fact_7418_is__singletonE,axiom,
% 6.92/7.27 ! [A4: set_Pr4329608150637261639at_nat] :
% 6.92/7.27 ( ( is_sin2937591304547752795at_nat @ A4 )
% 6.92/7.27 => ~ ! [X3: produc3843707927480180839at_nat] :
% 6.92/7.27 ( A4
% 6.92/7.27 != ( insert9069300056098147895at_nat @ X3 @ bot_bo228742789529271731at_nat ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % is_singletonE
% 6.92/7.27 thf(fact_7419_is__singletonE,axiom,
% 6.92/7.27 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.92/7.27 ( ( is_sin2850979758926227957at_nat @ A4 )
% 6.92/7.27 => ~ ! [X3: product_prod_nat_nat] :
% 6.92/7.27 ( A4
% 6.92/7.27 != ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % is_singletonE
% 6.92/7.27 thf(fact_7420_is__singletonE,axiom,
% 6.92/7.27 ! [A4: set_o] :
% 6.92/7.27 ( ( is_singleton_o @ A4 )
% 6.92/7.27 => ~ ! [X3: $o] :
% 6.92/7.27 ( A4
% 6.92/7.27 != ( insert_o @ X3 @ bot_bot_set_o ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % is_singletonE
% 6.92/7.27 thf(fact_7421_is__singletonE,axiom,
% 6.92/7.27 ! [A4: set_nat] :
% 6.92/7.27 ( ( is_singleton_nat @ A4 )
% 6.92/7.27 => ~ ! [X3: nat] :
% 6.92/7.27 ( A4
% 6.92/7.27 != ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % is_singletonE
% 6.92/7.27 thf(fact_7422_is__singletonE,axiom,
% 6.92/7.27 ! [A4: set_int] :
% 6.92/7.27 ( ( is_singleton_int @ A4 )
% 6.92/7.27 => ~ ! [X3: int] :
% 6.92/7.27 ( A4
% 6.92/7.27 != ( insert_int @ X3 @ bot_bot_set_int ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % is_singletonE
% 6.92/7.27 thf(fact_7423_integer__of__num_I2_J,axiom,
% 6.92/7.27 ! [N2: num] :
% 6.92/7.27 ( ( code_integer_of_num @ ( bit0 @ N2 ) )
% 6.92/7.27 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % integer_of_num(2)
% 6.92/7.27 thf(fact_7424_int__numeral__not__and__num,axiom,
% 6.92/7.27 ! [M: num,N2: num] :
% 6.92/7.27 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 6.92/7.27 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N2 @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % int_numeral_not_and_num
% 6.92/7.27 thf(fact_7425_int__numeral__and__not__num,axiom,
% 6.92/7.27 ! [M: num,N2: num] :
% 6.92/7.27 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.92/7.27 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % int_numeral_and_not_num
% 6.92/7.27 thf(fact_7426_and__not__numerals_I8_J,axiom,
% 6.92/7.27 ! [M: num,N2: num] :
% 6.92/7.27 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 6.92/7.27 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % and_not_numerals(8)
% 6.92/7.27 thf(fact_7427_not__int__rec,axiom,
% 6.92/7.27 ( bit_ri7919022796975470100ot_int
% 6.92/7.27 = ( ^ [K3: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % not_int_rec
% 6.92/7.27 thf(fact_7428_num__of__integer__code,axiom,
% 6.92/7.27 ( code_num_of_integer
% 6.92/7.27 = ( ^ [K3: code_integer] :
% 6.92/7.27 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 6.92/7.27 @ ( produc7336495610019696514er_num
% 6.92/7.27 @ ^ [L2: code_integer,J: code_integer] : ( if_num @ ( J = 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 ) )
% 6.92/7.27 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % num_of_integer_code
% 6.92/7.27 thf(fact_7429_int__of__integer__code,axiom,
% 6.92/7.27 ( code_int_of_integer
% 6.92/7.27 = ( ^ [K3: code_integer] :
% 6.92/7.27 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 6.92/7.27 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 6.92/7.27 @ ( produc1553301316500091796er_int
% 6.92/7.27 @ ^ [L2: code_integer,J: code_integer] : ( if_int @ ( J = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ one_one_int ) )
% 6.92/7.27 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % int_of_integer_code
% 6.92/7.27 thf(fact_7430_nat_Osplit__sels_I2_J,axiom,
% 6.92/7.27 ! [P2: option_num > $o,F1: option_num,F2: nat > option_num,Nat: nat] :
% 6.92/7.27 ( ( P2 @ ( case_nat_option_num @ F1 @ F2 @ Nat ) )
% 6.92/7.27 = ( ~ ( ( ( Nat = zero_zero_nat )
% 6.92/7.27 & ~ ( P2 @ F1 ) )
% 6.92/7.27 | ( ( Nat
% 6.92/7.27 = ( suc @ ( pred @ Nat ) ) )
% 6.92/7.27 & ~ ( P2 @ ( F2 @ ( pred @ Nat ) ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % nat.split_sels(2)
% 6.92/7.27 thf(fact_7431_nat_Osplit__sels_I2_J,axiom,
% 6.92/7.27 ! [P2: nat > $o,F1: nat,F2: nat > nat,Nat: nat] :
% 6.92/7.27 ( ( P2 @ ( case_nat_nat @ F1 @ F2 @ Nat ) )
% 6.92/7.27 = ( ~ ( ( ( Nat = zero_zero_nat )
% 6.92/7.27 & ~ ( P2 @ F1 ) )
% 6.92/7.27 | ( ( Nat
% 6.92/7.27 = ( suc @ ( pred @ Nat ) ) )
% 6.92/7.27 & ~ ( P2 @ ( F2 @ ( pred @ Nat ) ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % nat.split_sels(2)
% 6.92/7.27 thf(fact_7432_nat_Osplit__sels_I2_J,axiom,
% 6.92/7.27 ! [P2: $o > $o,F1: $o,F2: nat > $o,Nat: nat] :
% 6.92/7.27 ( ( P2 @ ( case_nat_o @ F1 @ F2 @ Nat ) )
% 6.92/7.27 = ( ~ ( ( ( Nat = zero_zero_nat )
% 6.92/7.27 & ~ ( P2 @ F1 ) )
% 6.92/7.27 | ( ( Nat
% 6.92/7.27 = ( suc @ ( pred @ Nat ) ) )
% 6.92/7.27 & ~ ( P2 @ ( F2 @ ( pred @ Nat ) ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % nat.split_sels(2)
% 6.92/7.27 thf(fact_7433_nat_Osplit__sels_I1_J,axiom,
% 6.92/7.27 ! [P2: option_num > $o,F1: option_num,F2: nat > option_num,Nat: nat] :
% 6.92/7.27 ( ( P2 @ ( case_nat_option_num @ F1 @ F2 @ Nat ) )
% 6.92/7.27 = ( ( ( Nat = zero_zero_nat )
% 6.92/7.27 => ( P2 @ F1 ) )
% 6.92/7.27 & ( ( Nat
% 6.92/7.27 = ( suc @ ( pred @ Nat ) ) )
% 6.92/7.27 => ( P2 @ ( F2 @ ( pred @ Nat ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % nat.split_sels(1)
% 6.92/7.27 thf(fact_7434_nat_Osplit__sels_I1_J,axiom,
% 6.92/7.27 ! [P2: nat > $o,F1: nat,F2: nat > nat,Nat: nat] :
% 6.92/7.27 ( ( P2 @ ( case_nat_nat @ F1 @ F2 @ Nat ) )
% 6.92/7.27 = ( ( ( Nat = zero_zero_nat )
% 6.92/7.27 => ( P2 @ F1 ) )
% 6.92/7.27 & ( ( Nat
% 6.92/7.27 = ( suc @ ( pred @ Nat ) ) )
% 6.92/7.27 => ( P2 @ ( F2 @ ( pred @ Nat ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % nat.split_sels(1)
% 6.92/7.27 thf(fact_7435_nat_Osplit__sels_I1_J,axiom,
% 6.92/7.27 ! [P2: $o > $o,F1: $o,F2: nat > $o,Nat: nat] :
% 6.92/7.27 ( ( P2 @ ( case_nat_o @ F1 @ F2 @ Nat ) )
% 6.92/7.27 = ( ( ( Nat = zero_zero_nat )
% 6.92/7.27 => ( P2 @ F1 ) )
% 6.92/7.27 & ( ( Nat
% 6.92/7.27 = ( suc @ ( pred @ Nat ) ) )
% 6.92/7.27 => ( P2 @ ( F2 @ ( pred @ Nat ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % nat.split_sels(1)
% 6.92/7.27 thf(fact_7436_mask__eq__sum__exp__nat,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( suc @ zero_zero_nat ) )
% 6.92/7.27 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.27 @ ( collect_nat
% 6.92/7.27 @ ^ [Q8: nat] : ( ord_less_nat @ Q8 @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % mask_eq_sum_exp_nat
% 6.92/7.27 thf(fact_7437_of__int__sum,axiom,
% 6.92/7.27 ! [F: int > int,A4: set_int] :
% 6.92/7.27 ( ( ring_1_of_int_rat @ ( groups4538972089207619220nt_int @ F @ A4 ) )
% 6.92/7.27 = ( groups3906332499630173760nt_rat
% 6.92/7.27 @ ^ [X4: int] : ( ring_1_of_int_rat @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % of_int_sum
% 6.92/7.27 thf(fact_7438_of__int__sum,axiom,
% 6.92/7.27 ! [F: int > int,A4: set_int] :
% 6.92/7.27 ( ( ring_1_of_int_int @ ( groups4538972089207619220nt_int @ F @ A4 ) )
% 6.92/7.27 = ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [X4: int] : ( ring_1_of_int_int @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % of_int_sum
% 6.92/7.27 thf(fact_7439_plus__integer_Orep__eq,axiom,
% 6.92/7.27 ! [X: code_integer,Xa: code_integer] :
% 6.92/7.27 ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X @ Xa ) )
% 6.92/7.27 = ( plus_plus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % plus_integer.rep_eq
% 6.92/7.27 thf(fact_7440_of__nat__sum,axiom,
% 6.92/7.27 ! [F: int > nat,A4: set_int] :
% 6.92/7.27 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A4 ) )
% 6.92/7.27 = ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [X4: int] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % of_nat_sum
% 6.92/7.27 thf(fact_7441_of__nat__sum,axiom,
% 6.92/7.27 ! [F: nat > nat,A4: set_nat] :
% 6.92/7.27 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A4 ) )
% 6.92/7.27 = ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [X4: nat] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % of_nat_sum
% 6.92/7.27 thf(fact_7442_of__nat__sum,axiom,
% 6.92/7.27 ! [F: nat > nat,A4: set_nat] :
% 6.92/7.27 ( ( semiri4939895301339042750nteger @ ( groups3542108847815614940at_nat @ F @ A4 ) )
% 6.92/7.27 = ( groups7501900531339628137nteger
% 6.92/7.27 @ ^ [X4: nat] : ( semiri4939895301339042750nteger @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % of_nat_sum
% 6.92/7.27 thf(fact_7443_of__nat__sum,axiom,
% 6.92/7.27 ! [F: nat > nat,A4: set_nat] :
% 6.92/7.27 ( ( semiri1316708129612266289at_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) )
% 6.92/7.27 = ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [X4: nat] : ( semiri1316708129612266289at_nat @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % of_nat_sum
% 6.92/7.27 thf(fact_7444_pred__def,axiom,
% 6.92/7.27 ( pred
% 6.92/7.27 = ( case_nat_nat @ zero_zero_nat
% 6.92/7.27 @ ^ [X23: nat] : X23 ) ) ).
% 6.92/7.27
% 6.92/7.27 % pred_def
% 6.92/7.27 thf(fact_7445_mod__sum__eq,axiom,
% 6.92/7.27 ! [F: nat > nat,A: nat,A4: set_nat] :
% 6.92/7.27 ( ( modulo_modulo_nat
% 6.92/7.27 @ ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] : ( modulo_modulo_nat @ ( F @ I ) @ A )
% 6.92/7.27 @ A4 )
% 6.92/7.27 @ A )
% 6.92/7.27 = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ A ) ) ).
% 6.92/7.27
% 6.92/7.27 % mod_sum_eq
% 6.92/7.27 thf(fact_7446_mod__sum__eq,axiom,
% 6.92/7.27 ! [F: int > int,A: int,A4: set_int] :
% 6.92/7.27 ( ( modulo_modulo_int
% 6.92/7.27 @ ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [I: int] : ( modulo_modulo_int @ ( F @ I ) @ A )
% 6.92/7.27 @ A4 )
% 6.92/7.27 @ A )
% 6.92/7.27 = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A4 ) @ A ) ) ).
% 6.92/7.27
% 6.92/7.27 % mod_sum_eq
% 6.92/7.27 thf(fact_7447_nat_Odisc__eq__case_I2_J,axiom,
% 6.92/7.27 ! [Nat: nat] :
% 6.92/7.27 ( ( Nat != zero_zero_nat )
% 6.92/7.27 = ( case_nat_o @ $false
% 6.92/7.27 @ ^ [Uu2: nat] : $true
% 6.92/7.27 @ Nat ) ) ).
% 6.92/7.27
% 6.92/7.27 % nat.disc_eq_case(2)
% 6.92/7.27 thf(fact_7448_nat_Odisc__eq__case_I1_J,axiom,
% 6.92/7.27 ! [Nat: nat] :
% 6.92/7.27 ( ( Nat = zero_zero_nat )
% 6.92/7.27 = ( case_nat_o @ $true
% 6.92/7.27 @ ^ [Uu2: nat] : $false
% 6.92/7.27 @ Nat ) ) ).
% 6.92/7.27
% 6.92/7.27 % nat.disc_eq_case(1)
% 6.92/7.27 thf(fact_7449_integer__less__iff,axiom,
% 6.92/7.27 ( ord_le6747313008572928689nteger
% 6.92/7.27 = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % integer_less_iff
% 6.92/7.27 thf(fact_7450_less__integer_Orep__eq,axiom,
% 6.92/7.27 ( ord_le6747313008572928689nteger
% 6.92/7.27 = ( ^ [X4: code_integer,Xa2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % less_integer.rep_eq
% 6.92/7.27 thf(fact_7451_int__of__integer__less__iff,axiom,
% 6.92/7.27 ! [X: code_integer,Y: code_integer] :
% 6.92/7.27 ( ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Y ) )
% 6.92/7.27 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ).
% 6.92/7.27
% 6.92/7.27 % int_of_integer_less_iff
% 6.92/7.27 thf(fact_7452_integer__less__eq__iff,axiom,
% 6.92/7.27 ( ord_le3102999989581377725nteger
% 6.92/7.27 = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % integer_less_eq_iff
% 6.92/7.27 thf(fact_7453_less__eq__integer_Orep__eq,axiom,
% 6.92/7.27 ( ord_le3102999989581377725nteger
% 6.92/7.27 = ( ^ [X4: code_integer,Xa2: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % less_eq_integer.rep_eq
% 6.92/7.27 thf(fact_7454_sum__power__add,axiom,
% 6.92/7.27 ! [X: rat,M: nat,I5: set_nat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [I: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M @ I ) )
% 6.92/7.27 @ I5 )
% 6.92/7.27 = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_power_add
% 6.92/7.27 thf(fact_7455_sum__power__add,axiom,
% 6.92/7.27 ! [X: int,M: nat,I5: set_nat] :
% 6.92/7.27 ( ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [I: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M @ I ) )
% 6.92/7.27 @ I5 )
% 6.92/7.27 = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_power_add
% 6.92/7.27 thf(fact_7456_less__eq__nat_Osimps_I2_J,axiom,
% 6.92/7.27 ! [M: nat,N2: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 6.92/7.27 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % less_eq_nat.simps(2)
% 6.92/7.27 thf(fact_7457_diff__Suc,axiom,
% 6.92/7.27 ! [M: nat,N2: nat] :
% 6.92/7.27 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 6.92/7.27 = ( case_nat_nat @ zero_zero_nat
% 6.92/7.27 @ ^ [K3: nat] : K3
% 6.92/7.27 @ ( minus_minus_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % diff_Suc
% 6.92/7.27 thf(fact_7458_bit__numeral__rec_I1_J,axiom,
% 6.92/7.27 ! [W2: num,N2: nat] :
% 6.92/7.27 ( ( bit_se8040316288895769887atural @ ( numera5444537566228673987atural @ ( bit0 @ W2 ) ) @ N2 )
% 6.92/7.27 = ( case_nat_o @ $false @ ( bit_se8040316288895769887atural @ ( numera5444537566228673987atural @ W2 ) ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % bit_numeral_rec(1)
% 6.92/7.27 thf(fact_7459_bit__numeral__rec_I1_J,axiom,
% 6.92/7.27 ! [W2: num,N2: nat] :
% 6.92/7.27 ( ( bit_se9216721137139052372nteger @ ( numera6620942414471956472nteger @ ( bit0 @ W2 ) ) @ N2 )
% 6.92/7.27 = ( case_nat_o @ $false @ ( bit_se9216721137139052372nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % bit_numeral_rec(1)
% 6.92/7.27 thf(fact_7460_bit__numeral__rec_I1_J,axiom,
% 6.92/7.27 ! [W2: num,N2: nat] :
% 6.92/7.27 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) @ N2 )
% 6.92/7.27 = ( case_nat_o @ $false @ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W2 ) ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % bit_numeral_rec(1)
% 6.92/7.27 thf(fact_7461_bit__numeral__rec_I1_J,axiom,
% 6.92/7.27 ! [W2: num,N2: nat] :
% 6.92/7.27 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) @ N2 )
% 6.92/7.27 = ( case_nat_o @ $false @ ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W2 ) ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % bit_numeral_rec(1)
% 6.92/7.27 thf(fact_7462_bit__numeral__rec_I2_J,axiom,
% 6.92/7.27 ! [W2: num,N2: nat] :
% 6.92/7.27 ( ( bit_se8040316288895769887atural @ ( numera5444537566228673987atural @ ( bit1 @ W2 ) ) @ N2 )
% 6.92/7.27 = ( case_nat_o @ $true @ ( bit_se8040316288895769887atural @ ( numera5444537566228673987atural @ W2 ) ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % bit_numeral_rec(2)
% 6.92/7.27 thf(fact_7463_bit__numeral__rec_I2_J,axiom,
% 6.92/7.27 ! [W2: num,N2: nat] :
% 6.92/7.27 ( ( bit_se9216721137139052372nteger @ ( numera6620942414471956472nteger @ ( bit1 @ W2 ) ) @ N2 )
% 6.92/7.27 = ( case_nat_o @ $true @ ( bit_se9216721137139052372nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % bit_numeral_rec(2)
% 6.92/7.27 thf(fact_7464_bit__numeral__rec_I2_J,axiom,
% 6.92/7.27 ! [W2: num,N2: nat] :
% 6.92/7.27 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ W2 ) ) @ N2 )
% 6.92/7.27 = ( case_nat_o @ $true @ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W2 ) ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % bit_numeral_rec(2)
% 6.92/7.27 thf(fact_7465_bit__numeral__rec_I2_J,axiom,
% 6.92/7.27 ! [W2: num,N2: nat] :
% 6.92/7.27 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) @ N2 )
% 6.92/7.27 = ( case_nat_o @ $true @ ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W2 ) ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % bit_numeral_rec(2)
% 6.92/7.27 thf(fact_7466_mask__eq__sum__exp,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int )
% 6.92/7.27 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 6.92/7.27 @ ( collect_nat
% 6.92/7.27 @ ^ [Q8: nat] : ( ord_less_nat @ Q8 @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % mask_eq_sum_exp
% 6.92/7.27 thf(fact_7467_mask__eq__sum__exp,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_natural )
% 6.92/7.27 = ( groups6325495683096345652atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 6.92/7.27 @ ( collect_nat
% 6.92/7.27 @ ^ [Q8: nat] : ( ord_less_nat @ Q8 @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % mask_eq_sum_exp
% 6.92/7.27 thf(fact_7468_mask__eq__sum__exp,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer )
% 6.92/7.27 = ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 6.92/7.27 @ ( collect_nat
% 6.92/7.27 @ ^ [Q8: nat] : ( ord_less_nat @ Q8 @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % mask_eq_sum_exp
% 6.92/7.27 thf(fact_7469_mask__eq__sum__exp,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat )
% 6.92/7.27 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.27 @ ( collect_nat
% 6.92/7.27 @ ^ [Q8: nat] : ( ord_less_nat @ Q8 @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % mask_eq_sum_exp
% 6.92/7.27 thf(fact_7470_sum__abs__ge__zero,axiom,
% 6.92/7.27 ! [F: int > int,A4: set_int] :
% 6.92/7.27 ( ord_less_eq_int @ zero_zero_int
% 6.92/7.27 @ ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [I: int] : ( abs_abs_int @ ( F @ I ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_abs_ge_zero
% 6.92/7.27 thf(fact_7471_sum__abs,axiom,
% 6.92/7.27 ! [F: int > int,A4: set_int] :
% 6.92/7.27 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A4 ) )
% 6.92/7.27 @ ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [I: int] : ( abs_abs_int @ ( F @ I ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_abs
% 6.92/7.27 thf(fact_7472_convex__sum__bound__le,axiom,
% 6.92/7.27 ! [I5: set_o,X: $o > code_integer,A: $o > code_integer,B: code_integer,Delta: code_integer] :
% 6.92/7.27 ( ! [I3: $o] :
% 6.92/7.27 ( ( member_o @ I3 @ I5 )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 6.92/7.27 => ( ( ( groups4406642042086082107nteger @ X @ I5 )
% 6.92/7.27 = one_one_Code_integer )
% 6.92/7.27 => ( ! [I3: $o] :
% 6.92/7.27 ( ( member_o @ I3 @ I5 )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 6.92/7.27 => ( ord_le3102999989581377725nteger
% 6.92/7.27 @ ( abs_abs_Code_integer
% 6.92/7.27 @ ( minus_8373710615458151222nteger
% 6.92/7.27 @ ( groups4406642042086082107nteger
% 6.92/7.27 @ ^ [I: $o] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 6.92/7.27 @ I5 )
% 6.92/7.27 @ B ) )
% 6.92/7.27 @ Delta ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % convex_sum_bound_le
% 6.92/7.27 thf(fact_7473_convex__sum__bound__le,axiom,
% 6.92/7.27 ! [I5: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 6.92/7.27 ( ! [I3: nat] :
% 6.92/7.27 ( ( member_nat @ I3 @ I5 )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 6.92/7.27 => ( ( ( groups7501900531339628137nteger @ X @ I5 )
% 6.92/7.27 = one_one_Code_integer )
% 6.92/7.27 => ( ! [I3: nat] :
% 6.92/7.27 ( ( member_nat @ I3 @ I5 )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 6.92/7.27 => ( ord_le3102999989581377725nteger
% 6.92/7.27 @ ( abs_abs_Code_integer
% 6.92/7.27 @ ( minus_8373710615458151222nteger
% 6.92/7.27 @ ( groups7501900531339628137nteger
% 6.92/7.27 @ ^ [I: nat] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 6.92/7.27 @ I5 )
% 6.92/7.27 @ B ) )
% 6.92/7.27 @ Delta ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % convex_sum_bound_le
% 6.92/7.27 thf(fact_7474_convex__sum__bound__le,axiom,
% 6.92/7.27 ! [I5: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 6.92/7.27 ( ! [I3: int] :
% 6.92/7.27 ( ( member_int @ I3 @ I5 )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 6.92/7.27 => ( ( ( groups7873554091576472773nteger @ X @ I5 )
% 6.92/7.27 = one_one_Code_integer )
% 6.92/7.27 => ( ! [I3: int] :
% 6.92/7.27 ( ( member_int @ I3 @ I5 )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 6.92/7.27 => ( ord_le3102999989581377725nteger
% 6.92/7.27 @ ( abs_abs_Code_integer
% 6.92/7.27 @ ( minus_8373710615458151222nteger
% 6.92/7.27 @ ( groups7873554091576472773nteger
% 6.92/7.27 @ ^ [I: int] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 6.92/7.27 @ I5 )
% 6.92/7.27 @ B ) )
% 6.92/7.27 @ Delta ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % convex_sum_bound_le
% 6.92/7.27 thf(fact_7475_convex__sum__bound__le,axiom,
% 6.92/7.27 ! [I5: set_o,X: $o > rat,A: $o > rat,B: rat,Delta: rat] :
% 6.92/7.27 ( ! [I3: $o] :
% 6.92/7.27 ( ( member_o @ I3 @ I5 )
% 6.92/7.27 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 6.92/7.27 => ( ( ( groups7872700643590313910_o_rat @ X @ I5 )
% 6.92/7.27 = one_one_rat )
% 6.92/7.27 => ( ! [I3: $o] :
% 6.92/7.27 ( ( member_o @ I3 @ I5 )
% 6.92/7.27 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 6.92/7.27 => ( ord_less_eq_rat
% 6.92/7.27 @ ( abs_abs_rat
% 6.92/7.27 @ ( minus_minus_rat
% 6.92/7.27 @ ( groups7872700643590313910_o_rat
% 6.92/7.27 @ ^ [I: $o] : ( times_times_rat @ ( A @ I ) @ ( X @ I ) )
% 6.92/7.27 @ I5 )
% 6.92/7.27 @ B ) )
% 6.92/7.27 @ Delta ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % convex_sum_bound_le
% 6.92/7.27 thf(fact_7476_convex__sum__bound__le,axiom,
% 6.92/7.27 ! [I5: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 6.92/7.27 ( ! [I3: nat] :
% 6.92/7.27 ( ( member_nat @ I3 @ I5 )
% 6.92/7.27 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 6.92/7.27 => ( ( ( groups2906978787729119204at_rat @ X @ I5 )
% 6.92/7.27 = one_one_rat )
% 6.92/7.27 => ( ! [I3: nat] :
% 6.92/7.27 ( ( member_nat @ I3 @ I5 )
% 6.92/7.27 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 6.92/7.27 => ( ord_less_eq_rat
% 6.92/7.27 @ ( abs_abs_rat
% 6.92/7.27 @ ( minus_minus_rat
% 6.92/7.27 @ ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( X @ I ) )
% 6.92/7.27 @ I5 )
% 6.92/7.27 @ B ) )
% 6.92/7.27 @ Delta ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % convex_sum_bound_le
% 6.92/7.27 thf(fact_7477_convex__sum__bound__le,axiom,
% 6.92/7.27 ! [I5: set_int,X: int > rat,A: int > rat,B: rat,Delta: rat] :
% 6.92/7.27 ( ! [I3: int] :
% 6.92/7.27 ( ( member_int @ I3 @ I5 )
% 6.92/7.27 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 6.92/7.27 => ( ( ( groups3906332499630173760nt_rat @ X @ I5 )
% 6.92/7.27 = one_one_rat )
% 6.92/7.27 => ( ! [I3: int] :
% 6.92/7.27 ( ( member_int @ I3 @ I5 )
% 6.92/7.27 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 6.92/7.27 => ( ord_less_eq_rat
% 6.92/7.27 @ ( abs_abs_rat
% 6.92/7.27 @ ( minus_minus_rat
% 6.92/7.27 @ ( groups3906332499630173760nt_rat
% 6.92/7.27 @ ^ [I: int] : ( times_times_rat @ ( A @ I ) @ ( X @ I ) )
% 6.92/7.27 @ I5 )
% 6.92/7.27 @ B ) )
% 6.92/7.27 @ Delta ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % convex_sum_bound_le
% 6.92/7.27 thf(fact_7478_convex__sum__bound__le,axiom,
% 6.92/7.27 ! [I5: set_o,X: $o > int,A: $o > int,B: int,Delta: int] :
% 6.92/7.27 ( ! [I3: $o] :
% 6.92/7.27 ( ( member_o @ I3 @ I5 )
% 6.92/7.27 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I3 ) ) )
% 6.92/7.27 => ( ( ( groups8505340233167759370_o_int @ X @ I5 )
% 6.92/7.27 = one_one_int )
% 6.92/7.27 => ( ! [I3: $o] :
% 6.92/7.27 ( ( member_o @ I3 @ I5 )
% 6.92/7.27 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 6.92/7.27 => ( ord_less_eq_int
% 6.92/7.27 @ ( abs_abs_int
% 6.92/7.27 @ ( minus_minus_int
% 6.92/7.27 @ ( groups8505340233167759370_o_int
% 6.92/7.27 @ ^ [I: $o] : ( times_times_int @ ( A @ I ) @ ( X @ I ) )
% 6.92/7.27 @ I5 )
% 6.92/7.27 @ B ) )
% 6.92/7.27 @ Delta ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % convex_sum_bound_le
% 6.92/7.27 thf(fact_7479_convex__sum__bound__le,axiom,
% 6.92/7.27 ! [I5: set_nat,X: nat > int,A: nat > int,B: int,Delta: int] :
% 6.92/7.27 ( ! [I3: nat] :
% 6.92/7.27 ( ( member_nat @ I3 @ I5 )
% 6.92/7.27 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I3 ) ) )
% 6.92/7.27 => ( ( ( groups3539618377306564664at_int @ X @ I5 )
% 6.92/7.27 = one_one_int )
% 6.92/7.27 => ( ! [I3: nat] :
% 6.92/7.27 ( ( member_nat @ I3 @ I5 )
% 6.92/7.27 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 6.92/7.27 => ( ord_less_eq_int
% 6.92/7.27 @ ( abs_abs_int
% 6.92/7.27 @ ( minus_minus_int
% 6.92/7.27 @ ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( X @ I ) )
% 6.92/7.27 @ I5 )
% 6.92/7.27 @ B ) )
% 6.92/7.27 @ Delta ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % convex_sum_bound_le
% 6.92/7.27 thf(fact_7480_convex__sum__bound__le,axiom,
% 6.92/7.27 ! [I5: set_int,X: int > int,A: int > int,B: int,Delta: int] :
% 6.92/7.27 ( ! [I3: int] :
% 6.92/7.27 ( ( member_int @ I3 @ I5 )
% 6.92/7.27 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I3 ) ) )
% 6.92/7.27 => ( ( ( groups4538972089207619220nt_int @ X @ I5 )
% 6.92/7.27 = one_one_int )
% 6.92/7.27 => ( ! [I3: int] :
% 6.92/7.27 ( ( member_int @ I3 @ I5 )
% 6.92/7.27 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 6.92/7.27 => ( ord_less_eq_int
% 6.92/7.27 @ ( abs_abs_int
% 6.92/7.27 @ ( minus_minus_int
% 6.92/7.27 @ ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [I: int] : ( times_times_int @ ( A @ I ) @ ( X @ I ) )
% 6.92/7.27 @ I5 )
% 6.92/7.27 @ B ) )
% 6.92/7.27 @ Delta ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % convex_sum_bound_le
% 6.92/7.27 thf(fact_7481_convex__sum__bound__le,axiom,
% 6.92/7.27 ! [I5: set_set_nat,X: set_nat > code_integer,A: set_nat > code_integer,B: code_integer,Delta: code_integer] :
% 6.92/7.27 ( ! [I3: set_nat] :
% 6.92/7.27 ( ( member_set_nat @ I3 @ I5 )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 6.92/7.27 => ( ( ( groups9190459664516455967nteger @ X @ I5 )
% 6.92/7.27 = one_one_Code_integer )
% 6.92/7.27 => ( ! [I3: set_nat] :
% 6.92/7.27 ( ( member_set_nat @ I3 @ I5 )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 6.92/7.27 => ( ord_le3102999989581377725nteger
% 6.92/7.27 @ ( abs_abs_Code_integer
% 6.92/7.27 @ ( minus_8373710615458151222nteger
% 6.92/7.27 @ ( groups9190459664516455967nteger
% 6.92/7.27 @ ^ [I: set_nat] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 6.92/7.27 @ I5 )
% 6.92/7.27 @ B ) )
% 6.92/7.27 @ Delta ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % convex_sum_bound_le
% 6.92/7.27 thf(fact_7482_abs__sum__abs,axiom,
% 6.92/7.27 ! [F: int > int,A4: set_int] :
% 6.92/7.27 ( ( abs_abs_int
% 6.92/7.27 @ ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [A5: int] : ( abs_abs_int @ ( F @ A5 ) )
% 6.92/7.27 @ A4 ) )
% 6.92/7.27 = ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [A5: int] : ( abs_abs_int @ ( F @ A5 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % abs_sum_abs
% 6.92/7.27 thf(fact_7483_sum_Oneutral__const,axiom,
% 6.92/7.27 ! [A4: set_nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [Uu2: nat] : zero_zero_nat
% 6.92/7.27 @ A4 )
% 6.92/7.27 = zero_zero_nat ) ).
% 6.92/7.27
% 6.92/7.27 % sum.neutral_const
% 6.92/7.27 thf(fact_7484_sum_Oneutral__const,axiom,
% 6.92/7.27 ! [A4: set_int] :
% 6.92/7.27 ( ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [Uu2: int] : zero_zero_int
% 6.92/7.27 @ A4 )
% 6.92/7.27 = zero_zero_int ) ).
% 6.92/7.27
% 6.92/7.27 % sum.neutral_const
% 6.92/7.27 thf(fact_7485_int__sum,axiom,
% 6.92/7.27 ! [F: int > nat,A4: set_int] :
% 6.92/7.27 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A4 ) )
% 6.92/7.27 = ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [X4: int] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % int_sum
% 6.92/7.27 thf(fact_7486_int__sum,axiom,
% 6.92/7.27 ! [F: nat > nat,A4: set_nat] :
% 6.92/7.27 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A4 ) )
% 6.92/7.27 = ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [X4: nat] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % int_sum
% 6.92/7.27 thf(fact_7487_sum_Oswap,axiom,
% 6.92/7.27 ! [G: nat > nat > nat,B5: set_nat,A4: set_nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] : ( groups3542108847815614940at_nat @ ( G @ I ) @ B5 )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [J: nat] :
% 6.92/7.27 ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] : ( G @ I @ J )
% 6.92/7.27 @ A4 )
% 6.92/7.27 @ B5 ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.swap
% 6.92/7.27 thf(fact_7488_sum_Oswap,axiom,
% 6.92/7.27 ! [G: int > int > int,B5: set_int,A4: set_int] :
% 6.92/7.27 ( ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [I: int] : ( groups4538972089207619220nt_int @ ( G @ I ) @ B5 )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [J: int] :
% 6.92/7.27 ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [I: int] : ( G @ I @ J )
% 6.92/7.27 @ A4 )
% 6.92/7.27 @ B5 ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.swap
% 6.92/7.27 thf(fact_7489_sum__mono,axiom,
% 6.92/7.27 ! [K5: set_o,F: $o > rat,G: $o > rat] :
% 6.92/7.27 ( ! [I3: $o] :
% 6.92/7.27 ( ( member_o @ I3 @ K5 )
% 6.92/7.27 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.27 => ( ord_less_eq_rat @ ( groups7872700643590313910_o_rat @ F @ K5 ) @ ( groups7872700643590313910_o_rat @ G @ K5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_mono
% 6.92/7.27 thf(fact_7490_sum__mono,axiom,
% 6.92/7.27 ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 6.92/7.27 ( ! [I3: nat] :
% 6.92/7.27 ( ( member_nat @ I3 @ K5 )
% 6.92/7.27 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.27 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_mono
% 6.92/7.27 thf(fact_7491_sum__mono,axiom,
% 6.92/7.27 ! [K5: set_int,F: int > rat,G: int > rat] :
% 6.92/7.27 ( ! [I3: int] :
% 6.92/7.27 ( ( member_int @ I3 @ K5 )
% 6.92/7.27 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.27 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_mono
% 6.92/7.27 thf(fact_7492_sum__mono,axiom,
% 6.92/7.27 ! [K5: set_o,F: $o > nat,G: $o > nat] :
% 6.92/7.27 ( ! [I3: $o] :
% 6.92/7.27 ( ( member_o @ I3 @ K5 )
% 6.92/7.27 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.27 => ( ord_less_eq_nat @ ( groups8507830703676809646_o_nat @ F @ K5 ) @ ( groups8507830703676809646_o_nat @ G @ K5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_mono
% 6.92/7.27 thf(fact_7493_sum__mono,axiom,
% 6.92/7.27 ! [K5: set_int,F: int > nat,G: int > nat] :
% 6.92/7.27 ( ! [I3: int] :
% 6.92/7.27 ( ( member_int @ I3 @ K5 )
% 6.92/7.27 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.27 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_mono
% 6.92/7.27 thf(fact_7494_sum__mono,axiom,
% 6.92/7.27 ! [K5: set_o,F: $o > int,G: $o > int] :
% 6.92/7.27 ( ! [I3: $o] :
% 6.92/7.27 ( ( member_o @ I3 @ K5 )
% 6.92/7.27 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.27 => ( ord_less_eq_int @ ( groups8505340233167759370_o_int @ F @ K5 ) @ ( groups8505340233167759370_o_int @ G @ K5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_mono
% 6.92/7.27 thf(fact_7495_sum__mono,axiom,
% 6.92/7.27 ! [K5: set_nat,F: nat > int,G: nat > int] :
% 6.92/7.27 ( ! [I3: nat] :
% 6.92/7.27 ( ( member_nat @ I3 @ K5 )
% 6.92/7.27 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.27 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_mono
% 6.92/7.27 thf(fact_7496_sum__mono,axiom,
% 6.92/7.27 ! [K5: set_nat,F: nat > nat,G: nat > nat] :
% 6.92/7.27 ( ! [I3: nat] :
% 6.92/7.27 ( ( member_nat @ I3 @ K5 )
% 6.92/7.27 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.27 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ K5 ) @ ( groups3542108847815614940at_nat @ G @ K5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_mono
% 6.92/7.27 thf(fact_7497_sum__mono,axiom,
% 6.92/7.27 ! [K5: set_int,F: int > int,G: int > int] :
% 6.92/7.27 ( ! [I3: int] :
% 6.92/7.27 ( ( member_int @ I3 @ K5 )
% 6.92/7.27 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.27 => ( ord_less_eq_int @ ( groups4538972089207619220nt_int @ F @ K5 ) @ ( groups4538972089207619220nt_int @ G @ K5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_mono
% 6.92/7.27 thf(fact_7498_sum__mono,axiom,
% 6.92/7.27 ! [K5: set_set_nat,F: set_nat > rat,G: set_nat > rat] :
% 6.92/7.27 ( ! [I3: set_nat] :
% 6.92/7.27 ( ( member_set_nat @ I3 @ K5 )
% 6.92/7.27 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.27 => ( ord_less_eq_rat @ ( groups7659867448343625626at_rat @ F @ K5 ) @ ( groups7659867448343625626at_rat @ G @ K5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_mono
% 6.92/7.27 thf(fact_7499_sum_Odistrib,axiom,
% 6.92/7.27 ! [G: nat > nat,H: nat > nat,A4: set_nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [X4: nat] : ( plus_plus_nat @ ( G @ X4 ) @ ( H @ X4 ) )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A4 ) @ ( groups3542108847815614940at_nat @ H @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.distrib
% 6.92/7.27 thf(fact_7500_sum_Odistrib,axiom,
% 6.92/7.27 ! [G: int > int,H: int > int,A4: set_int] :
% 6.92/7.27 ( ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [X4: int] : ( plus_plus_int @ ( G @ X4 ) @ ( H @ X4 ) )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A4 ) @ ( groups4538972089207619220nt_int @ H @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.distrib
% 6.92/7.27 thf(fact_7501_sum__product,axiom,
% 6.92/7.27 ! [F: nat > nat,A4: set_nat,G: nat > nat,B5: set_nat] :
% 6.92/7.27 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( groups3542108847815614940at_nat @ G @ B5 ) )
% 6.92/7.27 = ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] :
% 6.92/7.27 ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [J: nat] : ( times_times_nat @ ( F @ I ) @ ( G @ J ) )
% 6.92/7.27 @ B5 )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_product
% 6.92/7.27 thf(fact_7502_sum__product,axiom,
% 6.92/7.27 ! [F: int > int,A4: set_int,G: int > int,B5: set_int] :
% 6.92/7.27 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A4 ) @ ( groups4538972089207619220nt_int @ G @ B5 ) )
% 6.92/7.27 = ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [I: int] :
% 6.92/7.27 ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [J: int] : ( times_times_int @ ( F @ I ) @ ( G @ J ) )
% 6.92/7.27 @ B5 )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_product
% 6.92/7.27 thf(fact_7503_sum__distrib__right,axiom,
% 6.92/7.27 ! [F: nat > nat,A4: set_nat,R2: nat] :
% 6.92/7.27 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ R2 )
% 6.92/7.27 = ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [N: nat] : ( times_times_nat @ ( F @ N ) @ R2 )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_distrib_right
% 6.92/7.27 thf(fact_7504_sum__distrib__right,axiom,
% 6.92/7.27 ! [F: int > int,A4: set_int,R2: int] :
% 6.92/7.27 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A4 ) @ R2 )
% 6.92/7.27 = ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [N: int] : ( times_times_int @ ( F @ N ) @ R2 )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_distrib_right
% 6.92/7.27 thf(fact_7505_sum__distrib__left,axiom,
% 6.92/7.27 ! [R2: nat,F: nat > nat,A4: set_nat] :
% 6.92/7.27 ( ( times_times_nat @ R2 @ ( groups3542108847815614940at_nat @ F @ A4 ) )
% 6.92/7.27 = ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [N: nat] : ( times_times_nat @ R2 @ ( F @ N ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_distrib_left
% 6.92/7.27 thf(fact_7506_sum__distrib__left,axiom,
% 6.92/7.27 ! [R2: int,F: int > int,A4: set_int] :
% 6.92/7.27 ( ( times_times_int @ R2 @ ( groups4538972089207619220nt_int @ F @ A4 ) )
% 6.92/7.27 = ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [N: int] : ( times_times_int @ R2 @ ( F @ N ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_distrib_left
% 6.92/7.27 thf(fact_7507_sum__subtractf,axiom,
% 6.92/7.27 ! [F: int > int,G: int > int,A4: set_int] :
% 6.92/7.27 ( ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [X4: int] : ( minus_minus_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A4 ) @ ( groups4538972089207619220nt_int @ G @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_subtractf
% 6.92/7.27 thf(fact_7508_sum__negf,axiom,
% 6.92/7.27 ! [F: int > int,A4: set_int] :
% 6.92/7.27 ( ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [X4: int] : ( uminus_uminus_int @ ( F @ X4 ) )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( uminus_uminus_int @ ( groups4538972089207619220nt_int @ F @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_negf
% 6.92/7.27 thf(fact_7509_sum__nonpos,axiom,
% 6.92/7.27 ! [A4: set_o,F: $o > code_integer] :
% 6.92/7.27 ( ! [X3: $o] :
% 6.92/7.27 ( ( member_o @ X3 @ A4 )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ zero_z3403309356797280102nteger ) )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ ( groups4406642042086082107nteger @ F @ A4 ) @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonpos
% 6.92/7.27 thf(fact_7510_sum__nonpos,axiom,
% 6.92/7.27 ! [A4: set_nat,F: nat > code_integer] :
% 6.92/7.27 ( ! [X3: nat] :
% 6.92/7.27 ( ( member_nat @ X3 @ A4 )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ zero_z3403309356797280102nteger ) )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ ( groups7501900531339628137nteger @ F @ A4 ) @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonpos
% 6.92/7.27 thf(fact_7511_sum__nonpos,axiom,
% 6.92/7.27 ! [A4: set_int,F: int > code_integer] :
% 6.92/7.27 ( ! [X3: int] :
% 6.92/7.27 ( ( member_int @ X3 @ A4 )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ zero_z3403309356797280102nteger ) )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ ( groups7873554091576472773nteger @ F @ A4 ) @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonpos
% 6.92/7.27 thf(fact_7512_sum__nonpos,axiom,
% 6.92/7.27 ! [A4: set_o,F: $o > rat] :
% 6.92/7.27 ( ! [X3: $o] :
% 6.92/7.27 ( ( member_o @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 6.92/7.27 => ( ord_less_eq_rat @ ( groups7872700643590313910_o_rat @ F @ A4 ) @ zero_zero_rat ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonpos
% 6.92/7.27 thf(fact_7513_sum__nonpos,axiom,
% 6.92/7.27 ! [A4: set_nat,F: nat > rat] :
% 6.92/7.27 ( ! [X3: nat] :
% 6.92/7.27 ( ( member_nat @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 6.92/7.27 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ zero_zero_rat ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonpos
% 6.92/7.27 thf(fact_7514_sum__nonpos,axiom,
% 6.92/7.27 ! [A4: set_int,F: int > rat] :
% 6.92/7.27 ( ! [X3: int] :
% 6.92/7.27 ( ( member_int @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 6.92/7.27 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) @ zero_zero_rat ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonpos
% 6.92/7.27 thf(fact_7515_sum__nonpos,axiom,
% 6.92/7.27 ! [A4: set_o,F: $o > nat] :
% 6.92/7.27 ( ! [X3: $o] :
% 6.92/7.27 ( ( member_o @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 6.92/7.27 => ( ord_less_eq_nat @ ( groups8507830703676809646_o_nat @ F @ A4 ) @ zero_zero_nat ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonpos
% 6.92/7.27 thf(fact_7516_sum__nonpos,axiom,
% 6.92/7.27 ! [A4: set_int,F: int > nat] :
% 6.92/7.27 ( ! [X3: int] :
% 6.92/7.27 ( ( member_int @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 6.92/7.27 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ zero_zero_nat ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonpos
% 6.92/7.27 thf(fact_7517_sum__nonpos,axiom,
% 6.92/7.27 ! [A4: set_o,F: $o > int] :
% 6.92/7.27 ( ! [X3: $o] :
% 6.92/7.27 ( ( member_o @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_int @ ( F @ X3 ) @ zero_zero_int ) )
% 6.92/7.27 => ( ord_less_eq_int @ ( groups8505340233167759370_o_int @ F @ A4 ) @ zero_zero_int ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonpos
% 6.92/7.27 thf(fact_7518_sum__nonpos,axiom,
% 6.92/7.27 ! [A4: set_nat,F: nat > int] :
% 6.92/7.27 ( ! [X3: nat] :
% 6.92/7.27 ( ( member_nat @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_int @ ( F @ X3 ) @ zero_zero_int ) )
% 6.92/7.27 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ A4 ) @ zero_zero_int ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonpos
% 6.92/7.27 thf(fact_7519_sum__nonneg,axiom,
% 6.92/7.27 ! [A4: set_o,F: $o > code_integer] :
% 6.92/7.27 ( ! [X3: $o] :
% 6.92/7.27 ( ( member_o @ X3 @ A4 )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( groups4406642042086082107nteger @ F @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonneg
% 6.92/7.27 thf(fact_7520_sum__nonneg,axiom,
% 6.92/7.27 ! [A4: set_nat,F: nat > code_integer] :
% 6.92/7.27 ( ! [X3: nat] :
% 6.92/7.27 ( ( member_nat @ X3 @ A4 )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( groups7501900531339628137nteger @ F @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonneg
% 6.92/7.27 thf(fact_7521_sum__nonneg,axiom,
% 6.92/7.27 ! [A4: set_int,F: int > code_integer] :
% 6.92/7.27 ( ! [X3: int] :
% 6.92/7.27 ( ( member_int @ X3 @ A4 )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( groups7873554091576472773nteger @ F @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonneg
% 6.92/7.27 thf(fact_7522_sum__nonneg,axiom,
% 6.92/7.27 ! [A4: set_o,F: $o > rat] :
% 6.92/7.27 ( ! [X3: $o] :
% 6.92/7.27 ( ( member_o @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups7872700643590313910_o_rat @ F @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonneg
% 6.92/7.27 thf(fact_7523_sum__nonneg,axiom,
% 6.92/7.27 ! [A4: set_nat,F: nat > rat] :
% 6.92/7.27 ( ! [X3: nat] :
% 6.92/7.27 ( ( member_nat @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonneg
% 6.92/7.27 thf(fact_7524_sum__nonneg,axiom,
% 6.92/7.27 ! [A4: set_int,F: int > rat] :
% 6.92/7.27 ( ! [X3: int] :
% 6.92/7.27 ( ( member_int @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonneg
% 6.92/7.27 thf(fact_7525_sum__nonneg,axiom,
% 6.92/7.27 ! [A4: set_o,F: $o > nat] :
% 6.92/7.27 ( ! [X3: $o] :
% 6.92/7.27 ( ( member_o @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups8507830703676809646_o_nat @ F @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonneg
% 6.92/7.27 thf(fact_7526_sum__nonneg,axiom,
% 6.92/7.27 ! [A4: set_int,F: int > nat] :
% 6.92/7.27 ( ! [X3: int] :
% 6.92/7.27 ( ( member_int @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonneg
% 6.92/7.27 thf(fact_7527_sum__nonneg,axiom,
% 6.92/7.27 ! [A4: set_o,F: $o > int] :
% 6.92/7.27 ( ! [X3: $o] :
% 6.92/7.27 ( ( member_o @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ord_less_eq_int @ zero_zero_int @ ( groups8505340233167759370_o_int @ F @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonneg
% 6.92/7.27 thf(fact_7528_sum__nonneg,axiom,
% 6.92/7.27 ! [A4: set_nat,F: nat > int] :
% 6.92/7.27 ( ! [X3: nat] :
% 6.92/7.27 ( ( member_nat @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ord_less_eq_int @ zero_zero_int @ ( groups3539618377306564664at_int @ F @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_nonneg
% 6.92/7.27 thf(fact_7529_sum__subtractf__nat,axiom,
% 6.92/7.27 ! [A4: set_o,G: $o > nat,F: $o > nat] :
% 6.92/7.27 ( ! [X3: $o] :
% 6.92/7.27 ( ( member_o @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ( groups8507830703676809646_o_nat
% 6.92/7.27 @ ^ [X4: $o] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( minus_minus_nat @ ( groups8507830703676809646_o_nat @ F @ A4 ) @ ( groups8507830703676809646_o_nat @ G @ A4 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_subtractf_nat
% 6.92/7.27 thf(fact_7530_sum__subtractf__nat,axiom,
% 6.92/7.27 ! [A4: set_se6260736226359567993nt_int,G: set_Pr958786334691620121nt_int > nat,F: set_Pr958786334691620121nt_int > nat] :
% 6.92/7.27 ( ! [X3: set_Pr958786334691620121nt_int] :
% 6.92/7.27 ( ( member2340774599025711042nt_int @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ( groups185207323561075247nt_nat
% 6.92/7.27 @ ^ [X4: set_Pr958786334691620121nt_int] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( minus_minus_nat @ ( groups185207323561075247nt_nat @ F @ A4 ) @ ( groups185207323561075247nt_nat @ G @ A4 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_subtractf_nat
% 6.92/7.27 thf(fact_7531_sum__subtractf__nat,axiom,
% 6.92/7.27 ! [A4: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 6.92/7.27 ( ! [X3: set_nat] :
% 6.92/7.27 ( ( member_set_nat @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ( groups8294997508430121362at_nat
% 6.92/7.27 @ ^ [X4: set_nat] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A4 ) @ ( groups8294997508430121362at_nat @ G @ A4 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_subtractf_nat
% 6.92/7.27 thf(fact_7532_sum__subtractf__nat,axiom,
% 6.92/7.27 ! [A4: set_int,G: int > nat,F: int > nat] :
% 6.92/7.27 ( ! [X3: int] :
% 6.92/7.27 ( ( member_int @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ( groups4541462559716669496nt_nat
% 6.92/7.27 @ ^ [X4: int] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ G @ A4 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_subtractf_nat
% 6.92/7.27 thf(fact_7533_sum__subtractf__nat,axiom,
% 6.92/7.27 ! [A4: set_nat,G: nat > nat,F: nat > nat] :
% 6.92/7.27 ( ! [X3: nat] :
% 6.92/7.27 ( ( member_nat @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [X4: nat] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( groups3542108847815614940at_nat @ G @ A4 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_subtractf_nat
% 6.92/7.27 thf(fact_7534_sum__comp__morphism,axiom,
% 6.92/7.27 ! [H: nat > code_integer,G: nat > nat,A4: set_nat] :
% 6.92/7.27 ( ( ( H @ zero_zero_nat )
% 6.92/7.27 = zero_z3403309356797280102nteger )
% 6.92/7.27 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.27 ( ( H @ ( plus_plus_nat @ X3 @ Y3 ) )
% 6.92/7.27 = ( plus_p5714425477246183910nteger @ ( H @ X3 ) @ ( H @ Y3 ) ) )
% 6.92/7.27 => ( ( groups7501900531339628137nteger @ ( comp_n3898172953802868194er_nat @ H @ G ) @ A4 )
% 6.92/7.27 = ( H @ ( groups3542108847815614940at_nat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_comp_morphism
% 6.92/7.27 thf(fact_7535_sum__comp__morphism,axiom,
% 6.92/7.27 ! [H: nat > rat,G: nat > nat,A4: set_nat] :
% 6.92/7.27 ( ( ( H @ zero_zero_nat )
% 6.92/7.27 = zero_zero_rat )
% 6.92/7.27 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.27 ( ( H @ ( plus_plus_nat @ X3 @ Y3 ) )
% 6.92/7.27 = ( plus_plus_rat @ ( H @ X3 ) @ ( H @ Y3 ) ) )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ ( comp_nat_rat_nat @ H @ G ) @ A4 )
% 6.92/7.27 = ( H @ ( groups3542108847815614940at_nat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_comp_morphism
% 6.92/7.27 thf(fact_7536_sum__comp__morphism,axiom,
% 6.92/7.27 ! [H: nat > int,G: nat > nat,A4: set_nat] :
% 6.92/7.27 ( ( ( H @ zero_zero_nat )
% 6.92/7.27 = zero_zero_int )
% 6.92/7.27 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.27 ( ( H @ ( plus_plus_nat @ X3 @ Y3 ) )
% 6.92/7.27 = ( plus_plus_int @ ( H @ X3 ) @ ( H @ Y3 ) ) )
% 6.92/7.27 => ( ( groups3539618377306564664at_int @ ( comp_nat_int_nat @ H @ G ) @ A4 )
% 6.92/7.27 = ( H @ ( groups3542108847815614940at_nat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_comp_morphism
% 6.92/7.27 thf(fact_7537_sum__comp__morphism,axiom,
% 6.92/7.27 ! [H: int > code_integer,G: int > int,A4: set_int] :
% 6.92/7.27 ( ( ( H @ zero_zero_int )
% 6.92/7.27 = zero_z3403309356797280102nteger )
% 6.92/7.27 => ( ! [X3: int,Y3: int] :
% 6.92/7.27 ( ( H @ ( plus_plus_int @ X3 @ Y3 ) )
% 6.92/7.27 = ( plus_p5714425477246183910nteger @ ( H @ X3 ) @ ( H @ Y3 ) ) )
% 6.92/7.27 => ( ( groups7873554091576472773nteger @ ( comp_i1585864551200866970er_int @ H @ G ) @ A4 )
% 6.92/7.27 = ( H @ ( groups4538972089207619220nt_int @ G @ A4 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_comp_morphism
% 6.92/7.27 thf(fact_7538_sum__comp__morphism,axiom,
% 6.92/7.27 ! [H: int > rat,G: int > int,A4: set_int] :
% 6.92/7.27 ( ( ( H @ zero_zero_int )
% 6.92/7.27 = zero_zero_rat )
% 6.92/7.27 => ( ! [X3: int,Y3: int] :
% 6.92/7.27 ( ( H @ ( plus_plus_int @ X3 @ Y3 ) )
% 6.92/7.27 = ( plus_plus_rat @ ( H @ X3 ) @ ( H @ Y3 ) ) )
% 6.92/7.27 => ( ( groups3906332499630173760nt_rat @ ( comp_int_rat_int @ H @ G ) @ A4 )
% 6.92/7.27 = ( H @ ( groups4538972089207619220nt_int @ G @ A4 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_comp_morphism
% 6.92/7.27 thf(fact_7539_sum__comp__morphism,axiom,
% 6.92/7.27 ! [H: int > nat,G: int > int,A4: set_int] :
% 6.92/7.27 ( ( ( H @ zero_zero_int )
% 6.92/7.27 = zero_zero_nat )
% 6.92/7.27 => ( ! [X3: int,Y3: int] :
% 6.92/7.27 ( ( H @ ( plus_plus_int @ X3 @ Y3 ) )
% 6.92/7.27 = ( plus_plus_nat @ ( H @ X3 ) @ ( H @ Y3 ) ) )
% 6.92/7.27 => ( ( groups4541462559716669496nt_nat @ ( comp_int_nat_int @ H @ G ) @ A4 )
% 6.92/7.27 = ( H @ ( groups4538972089207619220nt_int @ G @ A4 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_comp_morphism
% 6.92/7.27 thf(fact_7540_sum__comp__morphism,axiom,
% 6.92/7.27 ! [H: code_integer > nat,G: nat > code_integer,A4: set_nat] :
% 6.92/7.27 ( ( ( H @ zero_z3403309356797280102nteger )
% 6.92/7.27 = zero_zero_nat )
% 6.92/7.27 => ( ! [X3: code_integer,Y3: code_integer] :
% 6.92/7.27 ( ( H @ ( plus_p5714425477246183910nteger @ X3 @ Y3 ) )
% 6.92/7.27 = ( plus_plus_nat @ ( H @ X3 ) @ ( H @ Y3 ) ) )
% 6.92/7.27 => ( ( groups3542108847815614940at_nat @ ( comp_C4049556595663050210at_nat @ H @ G ) @ A4 )
% 6.92/7.27 = ( H @ ( groups7501900531339628137nteger @ G @ A4 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_comp_morphism
% 6.92/7.27 thf(fact_7541_sum__comp__morphism,axiom,
% 6.92/7.27 ! [H: rat > nat,G: nat > rat,A4: set_nat] :
% 6.92/7.27 ( ( ( H @ zero_zero_rat )
% 6.92/7.27 = zero_zero_nat )
% 6.92/7.27 => ( ! [X3: rat,Y3: rat] :
% 6.92/7.27 ( ( H @ ( plus_plus_rat @ X3 @ Y3 ) )
% 6.92/7.27 = ( plus_plus_nat @ ( H @ X3 ) @ ( H @ Y3 ) ) )
% 6.92/7.27 => ( ( groups3542108847815614940at_nat @ ( comp_rat_nat_nat @ H @ G ) @ A4 )
% 6.92/7.27 = ( H @ ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_comp_morphism
% 6.92/7.27 thf(fact_7542_sum__comp__morphism,axiom,
% 6.92/7.27 ! [H: int > nat,G: nat > int,A4: set_nat] :
% 6.92/7.27 ( ( ( H @ zero_zero_int )
% 6.92/7.27 = zero_zero_nat )
% 6.92/7.27 => ( ! [X3: int,Y3: int] :
% 6.92/7.27 ( ( H @ ( plus_plus_int @ X3 @ Y3 ) )
% 6.92/7.27 = ( plus_plus_nat @ ( H @ X3 ) @ ( H @ Y3 ) ) )
% 6.92/7.27 => ( ( groups3542108847815614940at_nat @ ( comp_int_nat_nat @ H @ G ) @ A4 )
% 6.92/7.27 = ( H @ ( groups3539618377306564664at_int @ G @ A4 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_comp_morphism
% 6.92/7.27 thf(fact_7543_sum__comp__morphism,axiom,
% 6.92/7.27 ! [H: nat > nat,G: nat > nat,A4: set_nat] :
% 6.92/7.27 ( ( ( H @ zero_zero_nat )
% 6.92/7.27 = zero_zero_nat )
% 6.92/7.27 => ( ! [X3: nat,Y3: nat] :
% 6.92/7.27 ( ( H @ ( plus_plus_nat @ X3 @ Y3 ) )
% 6.92/7.27 = ( plus_plus_nat @ ( H @ X3 ) @ ( H @ Y3 ) ) )
% 6.92/7.27 => ( ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ H @ G ) @ A4 )
% 6.92/7.27 = ( H @ ( groups3542108847815614940at_nat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_comp_morphism
% 6.92/7.27 thf(fact_7544_sum__SucD,axiom,
% 6.92/7.27 ! [F: nat > nat,A4: set_nat,N2: nat] :
% 6.92/7.27 ( ( ( groups3542108847815614940at_nat @ F @ A4 )
% 6.92/7.27 = ( suc @ N2 ) )
% 6.92/7.27 => ? [X3: nat] :
% 6.92/7.27 ( ( member_nat @ X3 @ A4 )
% 6.92/7.27 & ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_SucD
% 6.92/7.27 thf(fact_7545_nat__of__integer__code,axiom,
% 6.92/7.27 ( code_nat_of_integer
% 6.92/7.27 = ( ^ [K3: code_integer] :
% 6.92/7.27 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 6.92/7.27 @ ( produc1555791787009142072er_nat
% 6.92/7.27 @ ^ [L2: code_integer,J: code_integer] : ( if_nat @ ( J = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ one_one_nat ) )
% 6.92/7.27 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % nat_of_integer_code
% 6.92/7.27 thf(fact_7546_choose__odd__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.27 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 6.92/7.27 @ ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [I: nat] :
% 6.92/7.27 ( if_rat
% 6.92/7.27 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I )
% 6.92/7.27 @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I ) )
% 6.92/7.27 @ zero_zero_rat )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) )
% 6.92/7.27 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_odd_sum
% 6.92/7.27 thf(fact_7547_choose__odd__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.27 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 6.92/7.27 @ ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [I: nat] :
% 6.92/7.27 ( if_int
% 6.92/7.27 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I )
% 6.92/7.27 @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I ) )
% 6.92/7.27 @ zero_zero_int )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) )
% 6.92/7.27 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_odd_sum
% 6.92/7.27 thf(fact_7548_choose__odd__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.27 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 6.92/7.27 @ ( groups7501900531339628137nteger
% 6.92/7.27 @ ^ [I: nat] :
% 6.92/7.27 ( if_Code_integer
% 6.92/7.27 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I )
% 6.92/7.27 @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I ) )
% 6.92/7.27 @ zero_z3403309356797280102nteger )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) )
% 6.92/7.27 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_odd_sum
% 6.92/7.27 thf(fact_7549_choose__even__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.27 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 6.92/7.27 @ ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [I: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I ) ) @ zero_zero_rat )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) )
% 6.92/7.27 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_even_sum
% 6.92/7.27 thf(fact_7550_choose__even__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.27 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 6.92/7.27 @ ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [I: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I ) ) @ zero_zero_int )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) )
% 6.92/7.27 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_even_sum
% 6.92/7.27 thf(fact_7551_choose__even__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.27 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 6.92/7.27 @ ( groups7501900531339628137nteger
% 6.92/7.27 @ ^ [I: nat] : ( if_Code_integer @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I ) ) @ zero_z3403309356797280102nteger )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) )
% 6.92/7.27 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_even_sum
% 6.92/7.27 thf(fact_7552_gbinomial__partial__row__sum,axiom,
% 6.92/7.27 ! [A: rat,M: nat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ M ) )
% 6.92/7.27 = ( 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 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gbinomial_partial_row_sum
% 6.92/7.27 thf(fact_7553_sum__gp,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,X: rat] :
% 6.92/7.27 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = zero_zero_rat ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( ( X = one_one_rat )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 6.92/7.27 & ( ( X != one_one_rat )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_gp
% 6.92/7.27 thf(fact_7554_Icc__eq__Icc,axiom,
% 6.92/7.27 ! [L: set_int,H: set_int,L4: set_int,H5: set_int] :
% 6.92/7.27 ( ( ( set_or370866239135849197et_int @ L @ H )
% 6.92/7.27 = ( set_or370866239135849197et_int @ L4 @ H5 ) )
% 6.92/7.27 = ( ( ( L = L4 )
% 6.92/7.27 & ( H = H5 ) )
% 6.92/7.27 | ( ~ ( ord_less_eq_set_int @ L @ H )
% 6.92/7.27 & ~ ( ord_less_eq_set_int @ L4 @ H5 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Icc_eq_Icc
% 6.92/7.27 thf(fact_7555_Icc__eq__Icc,axiom,
% 6.92/7.27 ! [L: rat,H: rat,L4: rat,H5: rat] :
% 6.92/7.27 ( ( ( set_or633870826150836451st_rat @ L @ H )
% 6.92/7.27 = ( set_or633870826150836451st_rat @ L4 @ H5 ) )
% 6.92/7.27 = ( ( ( L = L4 )
% 6.92/7.27 & ( H = H5 ) )
% 6.92/7.27 | ( ~ ( ord_less_eq_rat @ L @ H )
% 6.92/7.27 & ~ ( ord_less_eq_rat @ L4 @ H5 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Icc_eq_Icc
% 6.92/7.27 thf(fact_7556_Icc__eq__Icc,axiom,
% 6.92/7.27 ! [L: num,H: num,L4: num,H5: num] :
% 6.92/7.27 ( ( ( set_or7049704709247886629st_num @ L @ H )
% 6.92/7.27 = ( set_or7049704709247886629st_num @ L4 @ H5 ) )
% 6.92/7.27 = ( ( ( L = L4 )
% 6.92/7.27 & ( H = H5 ) )
% 6.92/7.27 | ( ~ ( ord_less_eq_num @ L @ H )
% 6.92/7.27 & ~ ( ord_less_eq_num @ L4 @ H5 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Icc_eq_Icc
% 6.92/7.27 thf(fact_7557_Icc__eq__Icc,axiom,
% 6.92/7.27 ! [L: nat,H: nat,L4: nat,H5: nat] :
% 6.92/7.27 ( ( ( set_or1269000886237332187st_nat @ L @ H )
% 6.92/7.27 = ( set_or1269000886237332187st_nat @ L4 @ H5 ) )
% 6.92/7.27 = ( ( ( L = L4 )
% 6.92/7.27 & ( H = H5 ) )
% 6.92/7.27 | ( ~ ( ord_less_eq_nat @ L @ H )
% 6.92/7.27 & ~ ( ord_less_eq_nat @ L4 @ H5 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Icc_eq_Icc
% 6.92/7.27 thf(fact_7558_Icc__eq__Icc,axiom,
% 6.92/7.27 ! [L: int,H: int,L4: int,H5: int] :
% 6.92/7.27 ( ( ( set_or1266510415728281911st_int @ L @ H )
% 6.92/7.27 = ( set_or1266510415728281911st_int @ L4 @ H5 ) )
% 6.92/7.27 = ( ( ( L = L4 )
% 6.92/7.27 & ( H = H5 ) )
% 6.92/7.27 | ( ~ ( ord_less_eq_int @ L @ H )
% 6.92/7.27 & ~ ( ord_less_eq_int @ L4 @ H5 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Icc_eq_Icc
% 6.92/7.27 thf(fact_7559_Icc__eq__Icc,axiom,
% 6.92/7.27 ! [L: code_integer,H: code_integer,L4: code_integer,H5: code_integer] :
% 6.92/7.27 ( ( ( set_or189985376899183464nteger @ L @ H )
% 6.92/7.27 = ( set_or189985376899183464nteger @ L4 @ H5 ) )
% 6.92/7.27 = ( ( ( L = L4 )
% 6.92/7.27 & ( H = H5 ) )
% 6.92/7.27 | ( ~ ( ord_le3102999989581377725nteger @ L @ H )
% 6.92/7.27 & ~ ( ord_le3102999989581377725nteger @ L4 @ H5 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Icc_eq_Icc
% 6.92/7.27 thf(fact_7560_atLeastAtMost__iff,axiom,
% 6.92/7.27 ! [I2: $o,L: $o,U: $o] :
% 6.92/7.27 ( ( member_o @ I2 @ ( set_or8904488021354931149Most_o @ L @ U ) )
% 6.92/7.27 = ( ( ord_less_eq_o @ L @ I2 )
% 6.92/7.27 & ( ord_less_eq_o @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastAtMost_iff
% 6.92/7.27 thf(fact_7561_atLeastAtMost__iff,axiom,
% 6.92/7.27 ! [I2: set_Pr958786334691620121nt_int,L: set_Pr958786334691620121nt_int,U: set_Pr958786334691620121nt_int] :
% 6.92/7.27 ( ( member2340774599025711042nt_int @ I2 @ ( set_or2481441762145802318nt_int @ L @ U ) )
% 6.92/7.27 = ( ( ord_le2843351958646193337nt_int @ L @ I2 )
% 6.92/7.27 & ( ord_le2843351958646193337nt_int @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastAtMost_iff
% 6.92/7.27 thf(fact_7562_atLeastAtMost__iff,axiom,
% 6.92/7.27 ! [I2: set_nat,L: set_nat,U: set_nat] :
% 6.92/7.27 ( ( member_set_nat @ I2 @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 6.92/7.27 = ( ( ord_less_eq_set_nat @ L @ I2 )
% 6.92/7.27 & ( ord_less_eq_set_nat @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastAtMost_iff
% 6.92/7.27 thf(fact_7563_atLeastAtMost__iff,axiom,
% 6.92/7.27 ! [I2: set_int,L: set_int,U: set_int] :
% 6.92/7.27 ( ( member_set_int @ I2 @ ( set_or370866239135849197et_int @ L @ U ) )
% 6.92/7.27 = ( ( ord_less_eq_set_int @ L @ I2 )
% 6.92/7.27 & ( ord_less_eq_set_int @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastAtMost_iff
% 6.92/7.27 thf(fact_7564_atLeastAtMost__iff,axiom,
% 6.92/7.27 ! [I2: rat,L: rat,U: rat] :
% 6.92/7.27 ( ( member_rat @ I2 @ ( set_or633870826150836451st_rat @ L @ U ) )
% 6.92/7.27 = ( ( ord_less_eq_rat @ L @ I2 )
% 6.92/7.27 & ( ord_less_eq_rat @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastAtMost_iff
% 6.92/7.27 thf(fact_7565_atLeastAtMost__iff,axiom,
% 6.92/7.27 ! [I2: num,L: num,U: num] :
% 6.92/7.27 ( ( member_num @ I2 @ ( set_or7049704709247886629st_num @ L @ U ) )
% 6.92/7.27 = ( ( ord_less_eq_num @ L @ I2 )
% 6.92/7.27 & ( ord_less_eq_num @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastAtMost_iff
% 6.92/7.27 thf(fact_7566_atLeastAtMost__iff,axiom,
% 6.92/7.27 ! [I2: nat,L: nat,U: nat] :
% 6.92/7.27 ( ( member_nat @ I2 @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 6.92/7.27 = ( ( ord_less_eq_nat @ L @ I2 )
% 6.92/7.27 & ( ord_less_eq_nat @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastAtMost_iff
% 6.92/7.27 thf(fact_7567_atLeastAtMost__iff,axiom,
% 6.92/7.27 ! [I2: int,L: int,U: int] :
% 6.92/7.27 ( ( member_int @ I2 @ ( set_or1266510415728281911st_int @ L @ U ) )
% 6.92/7.27 = ( ( ord_less_eq_int @ L @ I2 )
% 6.92/7.27 & ( ord_less_eq_int @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastAtMost_iff
% 6.92/7.27 thf(fact_7568_atLeastAtMost__iff,axiom,
% 6.92/7.27 ! [I2: code_integer,L: code_integer,U: code_integer] :
% 6.92/7.27 ( ( member_Code_integer @ I2 @ ( set_or189985376899183464nteger @ L @ U ) )
% 6.92/7.27 = ( ( ord_le3102999989581377725nteger @ L @ I2 )
% 6.92/7.27 & ( ord_le3102999989581377725nteger @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastAtMost_iff
% 6.92/7.27 thf(fact_7569_atMost__iff,axiom,
% 6.92/7.27 ! [I2: $o,K2: $o] :
% 6.92/7.27 ( ( member_o @ I2 @ ( set_ord_atMost_o @ K2 ) )
% 6.92/7.27 = ( ord_less_eq_o @ I2 @ K2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_iff
% 6.92/7.27 thf(fact_7570_atMost__iff,axiom,
% 6.92/7.27 ! [I2: set_Pr958786334691620121nt_int,K2: set_Pr958786334691620121nt_int] :
% 6.92/7.27 ( ( member2340774599025711042nt_int @ I2 @ ( set_or2459421552957432928nt_int @ K2 ) )
% 6.92/7.27 = ( ord_le2843351958646193337nt_int @ I2 @ K2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_iff
% 6.92/7.27 thf(fact_7571_atMost__iff,axiom,
% 6.92/7.27 ! [I2: set_nat,K2: set_nat] :
% 6.92/7.27 ( ( member_set_nat @ I2 @ ( set_or4236626031148496127et_nat @ K2 ) )
% 6.92/7.27 = ( ord_less_eq_set_nat @ I2 @ K2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_iff
% 6.92/7.27 thf(fact_7572_atMost__iff,axiom,
% 6.92/7.27 ! [I2: set_int,K2: set_int] :
% 6.92/7.27 ( ( member_set_int @ I2 @ ( set_or58775011639299419et_int @ K2 ) )
% 6.92/7.27 = ( ord_less_eq_set_int @ I2 @ K2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_iff
% 6.92/7.27 thf(fact_7573_atMost__iff,axiom,
% 6.92/7.27 ! [I2: rat,K2: rat] :
% 6.92/7.27 ( ( member_rat @ I2 @ ( set_ord_atMost_rat @ K2 ) )
% 6.92/7.27 = ( ord_less_eq_rat @ I2 @ K2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_iff
% 6.92/7.27 thf(fact_7574_atMost__iff,axiom,
% 6.92/7.27 ! [I2: num,K2: num] :
% 6.92/7.27 ( ( member_num @ I2 @ ( set_ord_atMost_num @ K2 ) )
% 6.92/7.27 = ( ord_less_eq_num @ I2 @ K2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_iff
% 6.92/7.27 thf(fact_7575_atMost__iff,axiom,
% 6.92/7.27 ! [I2: nat,K2: nat] :
% 6.92/7.27 ( ( member_nat @ I2 @ ( set_ord_atMost_nat @ K2 ) )
% 6.92/7.27 = ( ord_less_eq_nat @ I2 @ K2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_iff
% 6.92/7.27 thf(fact_7576_atMost__iff,axiom,
% 6.92/7.27 ! [I2: int,K2: int] :
% 6.92/7.27 ( ( member_int @ I2 @ ( set_ord_atMost_int @ K2 ) )
% 6.92/7.27 = ( ord_less_eq_int @ I2 @ K2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_iff
% 6.92/7.27 thf(fact_7577_atLeastatMost__empty__iff,axiom,
% 6.92/7.27 ! [A: $o,B: $o] :
% 6.92/7.27 ( ( ( set_or8904488021354931149Most_o @ A @ B )
% 6.92/7.27 = bot_bot_set_o )
% 6.92/7.27 = ( ~ ( ord_less_eq_o @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty_iff
% 6.92/7.27 thf(fact_7578_atLeastatMost__empty__iff,axiom,
% 6.92/7.27 ! [A: set_int,B: set_int] :
% 6.92/7.27 ( ( ( set_or370866239135849197et_int @ A @ B )
% 6.92/7.27 = bot_bot_set_set_int )
% 6.92/7.27 = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty_iff
% 6.92/7.27 thf(fact_7579_atLeastatMost__empty__iff,axiom,
% 6.92/7.27 ! [A: rat,B: rat] :
% 6.92/7.27 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 6.92/7.27 = bot_bot_set_rat )
% 6.92/7.27 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty_iff
% 6.92/7.27 thf(fact_7580_atLeastatMost__empty__iff,axiom,
% 6.92/7.27 ! [A: num,B: num] :
% 6.92/7.27 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 6.92/7.27 = bot_bot_set_num )
% 6.92/7.27 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty_iff
% 6.92/7.27 thf(fact_7581_atLeastatMost__empty__iff,axiom,
% 6.92/7.27 ! [A: nat,B: nat] :
% 6.92/7.27 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 6.92/7.27 = bot_bot_set_nat )
% 6.92/7.27 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty_iff
% 6.92/7.27 thf(fact_7582_atLeastatMost__empty__iff,axiom,
% 6.92/7.27 ! [A: int,B: int] :
% 6.92/7.27 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 6.92/7.27 = bot_bot_set_int )
% 6.92/7.27 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty_iff
% 6.92/7.27 thf(fact_7583_atLeastatMost__empty__iff,axiom,
% 6.92/7.27 ! [A: code_integer,B: code_integer] :
% 6.92/7.27 ( ( ( set_or189985376899183464nteger @ A @ B )
% 6.92/7.27 = bot_bo3990330152332043303nteger )
% 6.92/7.27 = ( ~ ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty_iff
% 6.92/7.27 thf(fact_7584_atLeastatMost__empty__iff2,axiom,
% 6.92/7.27 ! [A: $o,B: $o] :
% 6.92/7.27 ( ( bot_bot_set_o
% 6.92/7.27 = ( set_or8904488021354931149Most_o @ A @ B ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_o @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty_iff2
% 6.92/7.27 thf(fact_7585_atLeastatMost__empty__iff2,axiom,
% 6.92/7.27 ! [A: set_int,B: set_int] :
% 6.92/7.27 ( ( bot_bot_set_set_int
% 6.92/7.27 = ( set_or370866239135849197et_int @ A @ B ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty_iff2
% 6.92/7.27 thf(fact_7586_atLeastatMost__empty__iff2,axiom,
% 6.92/7.27 ! [A: rat,B: rat] :
% 6.92/7.27 ( ( bot_bot_set_rat
% 6.92/7.27 = ( set_or633870826150836451st_rat @ A @ B ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty_iff2
% 6.92/7.27 thf(fact_7587_atLeastatMost__empty__iff2,axiom,
% 6.92/7.27 ! [A: num,B: num] :
% 6.92/7.27 ( ( bot_bot_set_num
% 6.92/7.27 = ( set_or7049704709247886629st_num @ A @ B ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty_iff2
% 6.92/7.27 thf(fact_7588_atLeastatMost__empty__iff2,axiom,
% 6.92/7.27 ! [A: nat,B: nat] :
% 6.92/7.27 ( ( bot_bot_set_nat
% 6.92/7.27 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty_iff2
% 6.92/7.27 thf(fact_7589_atLeastatMost__empty__iff2,axiom,
% 6.92/7.27 ! [A: int,B: int] :
% 6.92/7.27 ( ( bot_bot_set_int
% 6.92/7.27 = ( set_or1266510415728281911st_int @ A @ B ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty_iff2
% 6.92/7.27 thf(fact_7590_atLeastatMost__empty__iff2,axiom,
% 6.92/7.27 ! [A: code_integer,B: code_integer] :
% 6.92/7.27 ( ( bot_bo3990330152332043303nteger
% 6.92/7.27 = ( set_or189985376899183464nteger @ A @ B ) )
% 6.92/7.27 = ( ~ ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty_iff2
% 6.92/7.27 thf(fact_7591_atLeastatMost__empty,axiom,
% 6.92/7.27 ! [B: $o,A: $o] :
% 6.92/7.27 ( ( ord_less_o @ B @ A )
% 6.92/7.27 => ( ( set_or8904488021354931149Most_o @ A @ B )
% 6.92/7.27 = bot_bot_set_o ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty
% 6.92/7.27 thf(fact_7592_atLeastatMost__empty,axiom,
% 6.92/7.27 ! [B: assn,A: assn] :
% 6.92/7.27 ( ( ord_less_assn @ B @ A )
% 6.92/7.27 => ( ( set_or7959216805967363635t_assn @ A @ B )
% 6.92/7.27 = bot_bot_set_assn ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty
% 6.92/7.27 thf(fact_7593_atLeastatMost__empty,axiom,
% 6.92/7.27 ! [B: rat,A: rat] :
% 6.92/7.27 ( ( ord_less_rat @ B @ A )
% 6.92/7.27 => ( ( set_or633870826150836451st_rat @ A @ B )
% 6.92/7.27 = bot_bot_set_rat ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty
% 6.92/7.27 thf(fact_7594_atLeastatMost__empty,axiom,
% 6.92/7.27 ! [B: num,A: num] :
% 6.92/7.27 ( ( ord_less_num @ B @ A )
% 6.92/7.27 => ( ( set_or7049704709247886629st_num @ A @ B )
% 6.92/7.27 = bot_bot_set_num ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty
% 6.92/7.27 thf(fact_7595_atLeastatMost__empty,axiom,
% 6.92/7.27 ! [B: nat,A: nat] :
% 6.92/7.27 ( ( ord_less_nat @ B @ A )
% 6.92/7.27 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 6.92/7.27 = bot_bot_set_nat ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty
% 6.92/7.27 thf(fact_7596_atLeastatMost__empty,axiom,
% 6.92/7.27 ! [B: int,A: int] :
% 6.92/7.27 ( ( ord_less_int @ B @ A )
% 6.92/7.27 => ( ( set_or1266510415728281911st_int @ A @ B )
% 6.92/7.27 = bot_bot_set_int ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty
% 6.92/7.27 thf(fact_7597_atLeastatMost__empty,axiom,
% 6.92/7.27 ! [B: code_integer,A: code_integer] :
% 6.92/7.27 ( ( ord_le6747313008572928689nteger @ B @ A )
% 6.92/7.27 => ( ( set_or189985376899183464nteger @ A @ B )
% 6.92/7.27 = bot_bo3990330152332043303nteger ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_empty
% 6.92/7.27 thf(fact_7598_atLeastatMost__subset__iff,axiom,
% 6.92/7.27 ! [A: set_int,B: set_int,C2: set_int,D2: set_int] :
% 6.92/7.27 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C2 @ D2 ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 6.92/7.27 | ( ( ord_less_eq_set_int @ C2 @ A )
% 6.92/7.27 & ( ord_less_eq_set_int @ B @ D2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_subset_iff
% 6.92/7.27 thf(fact_7599_atLeastatMost__subset__iff,axiom,
% 6.92/7.27 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.27 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C2 @ D2 ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_rat @ A @ B )
% 6.92/7.27 | ( ( ord_less_eq_rat @ C2 @ A )
% 6.92/7.27 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_subset_iff
% 6.92/7.27 thf(fact_7600_atLeastatMost__subset__iff,axiom,
% 6.92/7.27 ! [A: num,B: num,C2: num,D2: num] :
% 6.92/7.27 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C2 @ D2 ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_num @ A @ B )
% 6.92/7.27 | ( ( ord_less_eq_num @ C2 @ A )
% 6.92/7.27 & ( ord_less_eq_num @ B @ D2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_subset_iff
% 6.92/7.27 thf(fact_7601_atLeastatMost__subset__iff,axiom,
% 6.92/7.27 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.27 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C2 @ D2 ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_nat @ A @ B )
% 6.92/7.27 | ( ( ord_less_eq_nat @ C2 @ A )
% 6.92/7.27 & ( ord_less_eq_nat @ B @ D2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_subset_iff
% 6.92/7.27 thf(fact_7602_atLeastatMost__subset__iff,axiom,
% 6.92/7.27 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.27 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C2 @ D2 ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_int @ A @ B )
% 6.92/7.27 | ( ( ord_less_eq_int @ C2 @ A )
% 6.92/7.27 & ( ord_less_eq_int @ B @ D2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_subset_iff
% 6.92/7.27 thf(fact_7603_atLeastatMost__subset__iff,axiom,
% 6.92/7.27 ! [A: code_integer,B: code_integer,C2: code_integer,D2: code_integer] :
% 6.92/7.27 ( ( ord_le7084787975880047091nteger @ ( set_or189985376899183464nteger @ A @ B ) @ ( set_or189985376899183464nteger @ C2 @ D2 ) )
% 6.92/7.27 = ( ~ ( ord_le3102999989581377725nteger @ A @ B )
% 6.92/7.27 | ( ( ord_le3102999989581377725nteger @ C2 @ A )
% 6.92/7.27 & ( ord_le3102999989581377725nteger @ B @ D2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_subset_iff
% 6.92/7.27 thf(fact_7604_atMost__subset__iff,axiom,
% 6.92/7.27 ! [X: set_int,Y: set_int] :
% 6.92/7.27 ( ( ord_le4403425263959731960et_int @ ( set_or58775011639299419et_int @ X ) @ ( set_or58775011639299419et_int @ Y ) )
% 6.92/7.27 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_subset_iff
% 6.92/7.27 thf(fact_7605_atMost__subset__iff,axiom,
% 6.92/7.27 ! [X: rat,Y: rat] :
% 6.92/7.27 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X ) @ ( set_ord_atMost_rat @ Y ) )
% 6.92/7.27 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_subset_iff
% 6.92/7.27 thf(fact_7606_atMost__subset__iff,axiom,
% 6.92/7.27 ! [X: num,Y: num] :
% 6.92/7.27 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X ) @ ( set_ord_atMost_num @ Y ) )
% 6.92/7.27 = ( ord_less_eq_num @ X @ Y ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_subset_iff
% 6.92/7.27 thf(fact_7607_atMost__subset__iff,axiom,
% 6.92/7.27 ! [X: nat,Y: nat] :
% 6.92/7.27 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X ) @ ( set_ord_atMost_nat @ Y ) )
% 6.92/7.27 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_subset_iff
% 6.92/7.27 thf(fact_7608_atMost__subset__iff,axiom,
% 6.92/7.27 ! [X: int,Y: int] :
% 6.92/7.27 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X ) @ ( set_ord_atMost_int @ Y ) )
% 6.92/7.27 = ( ord_less_eq_int @ X @ Y ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_subset_iff
% 6.92/7.27 thf(fact_7609_Icc__subset__Iic__iff,axiom,
% 6.92/7.27 ! [L: set_int,H: set_int,H5: set_int] :
% 6.92/7.27 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ L @ H ) @ ( set_or58775011639299419et_int @ H5 ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_set_int @ L @ H )
% 6.92/7.27 | ( ord_less_eq_set_int @ H @ H5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Icc_subset_Iic_iff
% 6.92/7.27 thf(fact_7610_Icc__subset__Iic__iff,axiom,
% 6.92/7.27 ! [L: rat,H: rat,H5: rat] :
% 6.92/7.27 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H ) @ ( set_ord_atMost_rat @ H5 ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_rat @ L @ H )
% 6.92/7.27 | ( ord_less_eq_rat @ H @ H5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Icc_subset_Iic_iff
% 6.92/7.27 thf(fact_7611_Icc__subset__Iic__iff,axiom,
% 6.92/7.27 ! [L: num,H: num,H5: num] :
% 6.92/7.27 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H ) @ ( set_ord_atMost_num @ H5 ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_num @ L @ H )
% 6.92/7.27 | ( ord_less_eq_num @ H @ H5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Icc_subset_Iic_iff
% 6.92/7.27 thf(fact_7612_Icc__subset__Iic__iff,axiom,
% 6.92/7.27 ! [L: nat,H: nat,H5: nat] :
% 6.92/7.27 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H ) @ ( set_ord_atMost_nat @ H5 ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_nat @ L @ H )
% 6.92/7.27 | ( ord_less_eq_nat @ H @ H5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Icc_subset_Iic_iff
% 6.92/7.27 thf(fact_7613_Icc__subset__Iic__iff,axiom,
% 6.92/7.27 ! [L: int,H: int,H5: int] :
% 6.92/7.27 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H ) @ ( set_ord_atMost_int @ H5 ) )
% 6.92/7.27 = ( ~ ( ord_less_eq_int @ L @ H )
% 6.92/7.27 | ( ord_less_eq_int @ H @ H5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Icc_subset_Iic_iff
% 6.92/7.27 thf(fact_7614_Icc__subset__Iic__iff,axiom,
% 6.92/7.27 ! [L: code_integer,H: code_integer,H5: code_integer] :
% 6.92/7.27 ( ( ord_le7084787975880047091nteger @ ( set_or189985376899183464nteger @ L @ H ) @ ( set_or9101266186257409494nteger @ H5 ) )
% 6.92/7.27 = ( ~ ( ord_le3102999989581377725nteger @ L @ H )
% 6.92/7.27 | ( ord_le3102999989581377725nteger @ H @ H5 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Icc_subset_Iic_iff
% 6.92/7.27 thf(fact_7615_sum_OatMost__Suc,axiom,
% 6.92/7.27 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 6.92/7.27 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atMost_Suc
% 6.92/7.27 thf(fact_7616_sum_OatMost__Suc,axiom,
% 6.92/7.27 ! [G: nat > rat,N2: nat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atMost_Suc
% 6.92/7.27 thf(fact_7617_sum_OatMost__Suc,axiom,
% 6.92/7.27 ! [G: nat > int,N2: nat] :
% 6.92/7.27 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atMost_Suc
% 6.92/7.27 thf(fact_7618_sum_OatMost__Suc,axiom,
% 6.92/7.27 ! [G: nat > nat,N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atMost_Suc
% 6.92/7.27 thf(fact_7619_nat__of__integer__non__positive,axiom,
% 6.92/7.27 ! [K2: code_integer] :
% 6.92/7.27 ( ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger )
% 6.92/7.27 => ( ( code_nat_of_integer @ K2 )
% 6.92/7.27 = zero_zero_nat ) ) ).
% 6.92/7.27
% 6.92/7.27 % nat_of_integer_non_positive
% 6.92/7.27 thf(fact_7620_sum_Ocl__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > code_integer] :
% 6.92/7.27 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = zero_z3403309356797280102nteger ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.cl_ivl_Suc
% 6.92/7.27 thf(fact_7621_sum_Ocl__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > multis2468970476368604999at_nat] :
% 6.92/7.27 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = zero_z1048942125864253310at_nat ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.cl_ivl_Suc
% 6.92/7.27 thf(fact_7622_sum_Ocl__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > rat] :
% 6.92/7.27 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = zero_zero_rat ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.cl_ivl_Suc
% 6.92/7.27 thf(fact_7623_sum_Ocl__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > int] :
% 6.92/7.27 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = zero_zero_int ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.cl_ivl_Suc
% 6.92/7.27 thf(fact_7624_sum_Ocl__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > nat] :
% 6.92/7.27 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = zero_zero_nat ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.cl_ivl_Suc
% 6.92/7.27 thf(fact_7625_not__Iic__le__Icc,axiom,
% 6.92/7.27 ! [H: int,L4: int,H5: int] :
% 6.92/7.27 ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H ) @ ( set_or1266510415728281911st_int @ L4 @ H5 ) ) ).
% 6.92/7.27
% 6.92/7.27 % not_Iic_le_Icc
% 6.92/7.27 thf(fact_7626_atMost__def,axiom,
% 6.92/7.27 ( set_or2459421552957432928nt_int
% 6.92/7.27 = ( ^ [U3: set_Pr958786334691620121nt_int] :
% 6.92/7.27 ( collec5210948495886036740nt_int
% 6.92/7.27 @ ^ [X4: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ X4 @ U3 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_def
% 6.92/7.27 thf(fact_7627_atMost__def,axiom,
% 6.92/7.27 ( set_or4236626031148496127et_nat
% 6.92/7.27 = ( ^ [U3: set_nat] :
% 6.92/7.27 ( collect_set_nat
% 6.92/7.27 @ ^ [X4: set_nat] : ( ord_less_eq_set_nat @ X4 @ U3 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_def
% 6.92/7.27 thf(fact_7628_atMost__def,axiom,
% 6.92/7.27 ( set_or58775011639299419et_int
% 6.92/7.27 = ( ^ [U3: set_int] :
% 6.92/7.27 ( collect_set_int
% 6.92/7.27 @ ^ [X4: set_int] : ( ord_less_eq_set_int @ X4 @ U3 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_def
% 6.92/7.27 thf(fact_7629_atMost__def,axiom,
% 6.92/7.27 ( set_ord_atMost_rat
% 6.92/7.27 = ( ^ [U3: rat] :
% 6.92/7.27 ( collect_rat
% 6.92/7.27 @ ^ [X4: rat] : ( ord_less_eq_rat @ X4 @ U3 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_def
% 6.92/7.27 thf(fact_7630_atMost__def,axiom,
% 6.92/7.27 ( set_ord_atMost_num
% 6.92/7.27 = ( ^ [U3: num] :
% 6.92/7.27 ( collect_num
% 6.92/7.27 @ ^ [X4: num] : ( ord_less_eq_num @ X4 @ U3 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_def
% 6.92/7.27 thf(fact_7631_atMost__def,axiom,
% 6.92/7.27 ( set_ord_atMost_nat
% 6.92/7.27 = ( ^ [U3: nat] :
% 6.92/7.27 ( collect_nat
% 6.92/7.27 @ ^ [X4: nat] : ( ord_less_eq_nat @ X4 @ U3 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_def
% 6.92/7.27 thf(fact_7632_atMost__def,axiom,
% 6.92/7.27 ( set_ord_atMost_int
% 6.92/7.27 = ( ^ [U3: int] :
% 6.92/7.27 ( collect_int
% 6.92/7.27 @ ^ [X4: int] : ( ord_less_eq_int @ X4 @ U3 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atMost_def
% 6.92/7.27 thf(fact_7633_ivl__disj__un__two__touch_I4_J,axiom,
% 6.92/7.27 ! [L: rat,M: rat,U: rat] :
% 6.92/7.27 ( ( ord_less_eq_rat @ L @ M )
% 6.92/7.27 => ( ( ord_less_eq_rat @ M @ U )
% 6.92/7.27 => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M ) @ ( set_or633870826150836451st_rat @ M @ U ) )
% 6.92/7.27 = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ivl_disj_un_two_touch(4)
% 6.92/7.27 thf(fact_7634_ivl__disj__un__two__touch_I4_J,axiom,
% 6.92/7.27 ! [L: num,M: num,U: num] :
% 6.92/7.27 ( ( ord_less_eq_num @ L @ M )
% 6.92/7.27 => ( ( ord_less_eq_num @ M @ U )
% 6.92/7.27 => ( ( sup_sup_set_num @ ( set_or7049704709247886629st_num @ L @ M ) @ ( set_or7049704709247886629st_num @ M @ U ) )
% 6.92/7.27 = ( set_or7049704709247886629st_num @ L @ U ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ivl_disj_un_two_touch(4)
% 6.92/7.27 thf(fact_7635_ivl__disj__un__two__touch_I4_J,axiom,
% 6.92/7.27 ! [L: nat,M: nat,U: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ L @ M )
% 6.92/7.27 => ( ( ord_less_eq_nat @ M @ U )
% 6.92/7.27 => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M ) @ ( set_or1269000886237332187st_nat @ M @ U ) )
% 6.92/7.27 = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ivl_disj_un_two_touch(4)
% 6.92/7.27 thf(fact_7636_ivl__disj__un__two__touch_I4_J,axiom,
% 6.92/7.27 ! [L: int,M: int,U: int] :
% 6.92/7.27 ( ( ord_less_eq_int @ L @ M )
% 6.92/7.27 => ( ( ord_less_eq_int @ M @ U )
% 6.92/7.27 => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M ) @ ( set_or1266510415728281911st_int @ M @ U ) )
% 6.92/7.27 = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ivl_disj_un_two_touch(4)
% 6.92/7.27 thf(fact_7637_ivl__disj__un__two__touch_I4_J,axiom,
% 6.92/7.27 ! [L: code_integer,M: code_integer,U: code_integer] :
% 6.92/7.27 ( ( ord_le3102999989581377725nteger @ L @ M )
% 6.92/7.27 => ( ( ord_le3102999989581377725nteger @ M @ U )
% 6.92/7.27 => ( ( sup_su848401254843788991nteger @ ( set_or189985376899183464nteger @ L @ M ) @ ( set_or189985376899183464nteger @ M @ U ) )
% 6.92/7.27 = ( set_or189985376899183464nteger @ L @ U ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ivl_disj_un_two_touch(4)
% 6.92/7.27 thf(fact_7638_ex__nat__less,axiom,
% 6.92/7.27 ! [N2: nat,P2: nat > $o] :
% 6.92/7.27 ( ( ? [M3: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M3 @ N2 )
% 6.92/7.27 & ( P2 @ M3 ) ) )
% 6.92/7.27 = ( ? [X4: nat] :
% 6.92/7.27 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.27 & ( P2 @ X4 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ex_nat_less
% 6.92/7.27 thf(fact_7639_all__nat__less,axiom,
% 6.92/7.27 ! [N2: nat,P2: nat > $o] :
% 6.92/7.27 ( ( ! [M3: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M3 @ N2 )
% 6.92/7.27 => ( P2 @ M3 ) ) )
% 6.92/7.27 = ( ! [X4: nat] :
% 6.92/7.27 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.27 => ( P2 @ X4 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % all_nat_less
% 6.92/7.27 thf(fact_7640_sum_OatLeastAtMost__shift__bounds,axiom,
% 6.92/7.27 ! [G: nat > nat,M: nat,K2: nat,N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K2 ) @ ( plus_plus_nat @ N2 @ K2 ) ) )
% 6.92/7.27 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ K2 ) ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeastAtMost_shift_bounds
% 6.92/7.27 thf(fact_7641_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 6.92/7.27 ! [G: nat > nat,M: nat,N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.shift_bounds_cl_Suc_ivl
% 6.92/7.27 thf(fact_7642_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 6.92/7.27 ! [G: nat > nat,M: nat,K2: nat,N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K2 ) @ ( plus_plus_nat @ N2 @ K2 ) ) )
% 6.92/7.27 = ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( plus_plus_nat @ I @ K2 ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.shift_bounds_cl_nat_ivl
% 6.92/7.27 thf(fact_7643_sum__power__shift,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,X: rat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_power_shift
% 6.92/7.27 thf(fact_7644_sum__power__shift,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,X: int] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_power_shift
% 6.92/7.27 thf(fact_7645_atLeastatMost__psubset__iff,axiom,
% 6.92/7.27 ! [A: assn,B: assn,C2: assn,D2: assn] :
% 6.92/7.27 ( ( ord_less_set_assn @ ( set_or7959216805967363635t_assn @ A @ B ) @ ( set_or7959216805967363635t_assn @ C2 @ D2 ) )
% 6.92/7.27 = ( ( ~ ( ord_less_eq_assn @ A @ B )
% 6.92/7.27 | ( ( ord_less_eq_assn @ C2 @ A )
% 6.92/7.27 & ( ord_less_eq_assn @ B @ D2 )
% 6.92/7.27 & ( ( ord_less_assn @ C2 @ A )
% 6.92/7.27 | ( ord_less_assn @ B @ D2 ) ) ) )
% 6.92/7.27 & ( ord_less_eq_assn @ C2 @ D2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_psubset_iff
% 6.92/7.27 thf(fact_7646_atLeastatMost__psubset__iff,axiom,
% 6.92/7.27 ! [A: set_int,B: set_int,C2: set_int,D2: set_int] :
% 6.92/7.27 ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C2 @ D2 ) )
% 6.92/7.27 = ( ( ~ ( ord_less_eq_set_int @ A @ B )
% 6.92/7.27 | ( ( ord_less_eq_set_int @ C2 @ A )
% 6.92/7.27 & ( ord_less_eq_set_int @ B @ D2 )
% 6.92/7.27 & ( ( ord_less_set_int @ C2 @ A )
% 6.92/7.27 | ( ord_less_set_int @ B @ D2 ) ) ) )
% 6.92/7.27 & ( ord_less_eq_set_int @ C2 @ D2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_psubset_iff
% 6.92/7.27 thf(fact_7647_atLeastatMost__psubset__iff,axiom,
% 6.92/7.27 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.27 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C2 @ D2 ) )
% 6.92/7.27 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 6.92/7.27 | ( ( ord_less_eq_rat @ C2 @ A )
% 6.92/7.27 & ( ord_less_eq_rat @ B @ D2 )
% 6.92/7.27 & ( ( ord_less_rat @ C2 @ A )
% 6.92/7.27 | ( ord_less_rat @ B @ D2 ) ) ) )
% 6.92/7.27 & ( ord_less_eq_rat @ C2 @ D2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_psubset_iff
% 6.92/7.27 thf(fact_7648_atLeastatMost__psubset__iff,axiom,
% 6.92/7.27 ! [A: num,B: num,C2: num,D2: num] :
% 6.92/7.27 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C2 @ D2 ) )
% 6.92/7.27 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 6.92/7.27 | ( ( ord_less_eq_num @ C2 @ A )
% 6.92/7.27 & ( ord_less_eq_num @ B @ D2 )
% 6.92/7.27 & ( ( ord_less_num @ C2 @ A )
% 6.92/7.27 | ( ord_less_num @ B @ D2 ) ) ) )
% 6.92/7.27 & ( ord_less_eq_num @ C2 @ D2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_psubset_iff
% 6.92/7.27 thf(fact_7649_atLeastatMost__psubset__iff,axiom,
% 6.92/7.27 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.27 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C2 @ D2 ) )
% 6.92/7.27 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 6.92/7.27 | ( ( ord_less_eq_nat @ C2 @ A )
% 6.92/7.27 & ( ord_less_eq_nat @ B @ D2 )
% 6.92/7.27 & ( ( ord_less_nat @ C2 @ A )
% 6.92/7.27 | ( ord_less_nat @ B @ D2 ) ) ) )
% 6.92/7.27 & ( ord_less_eq_nat @ C2 @ D2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_psubset_iff
% 6.92/7.27 thf(fact_7650_atLeastatMost__psubset__iff,axiom,
% 6.92/7.27 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.27 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C2 @ D2 ) )
% 6.92/7.27 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 6.92/7.27 | ( ( ord_less_eq_int @ C2 @ A )
% 6.92/7.27 & ( ord_less_eq_int @ B @ D2 )
% 6.92/7.27 & ( ( ord_less_int @ C2 @ A )
% 6.92/7.27 | ( ord_less_int @ B @ D2 ) ) ) )
% 6.92/7.27 & ( ord_less_eq_int @ C2 @ D2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_psubset_iff
% 6.92/7.27 thf(fact_7651_atLeastatMost__psubset__iff,axiom,
% 6.92/7.27 ! [A: code_integer,B: code_integer,C2: code_integer,D2: code_integer] :
% 6.92/7.27 ( ( ord_le1307284697595431911nteger @ ( set_or189985376899183464nteger @ A @ B ) @ ( set_or189985376899183464nteger @ C2 @ D2 ) )
% 6.92/7.27 = ( ( ~ ( ord_le3102999989581377725nteger @ A @ B )
% 6.92/7.27 | ( ( ord_le3102999989581377725nteger @ C2 @ A )
% 6.92/7.27 & ( ord_le3102999989581377725nteger @ B @ D2 )
% 6.92/7.27 & ( ( ord_le6747313008572928689nteger @ C2 @ A )
% 6.92/7.27 | ( ord_le6747313008572928689nteger @ B @ D2 ) ) ) )
% 6.92/7.27 & ( ord_le3102999989581377725nteger @ C2 @ D2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastatMost_psubset_iff
% 6.92/7.27 thf(fact_7652_Icc__eq__insert__lb__nat,axiom,
% 6.92/7.27 ! [M: nat,N2: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( set_or1269000886237332187st_nat @ M @ N2 )
% 6.92/7.27 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Icc_eq_insert_lb_nat
% 6.92/7.27 thf(fact_7653_atLeastAtMostSuc__conv,axiom,
% 6.92/7.27 ! [M: nat,N2: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 6.92/7.27 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) )
% 6.92/7.27 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastAtMostSuc_conv
% 6.92/7.27 thf(fact_7654_atLeastAtMost__insertL,axiom,
% 6.92/7.27 ! [M: nat,N2: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 6.92/7.27 = ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastAtMost_insertL
% 6.92/7.27 thf(fact_7655_sum_OatLeastAtMost__rev,axiom,
% 6.92/7.27 ! [G: nat > nat,N2: nat,M: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 6.92/7.27 = ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeastAtMost_rev
% 6.92/7.27 thf(fact_7656_sum__choose__upper,axiom,
% 6.92/7.27 ! [M: nat,N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.27 = ( binomial @ ( suc @ N2 ) @ ( suc @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_choose_upper
% 6.92/7.27 thf(fact_7657_sum_OatLeast0__atMost__Suc__shift,axiom,
% 6.92/7.27 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 6.92/7.27 ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat ) @ ( groups6857163185585827899at_nat @ ( comp_n8698576032424989604at_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeast0_atMost_Suc_shift
% 6.92/7.27 thf(fact_7658_sum_OatLeast0__atMost__Suc__shift,axiom,
% 6.92/7.27 ! [G: nat > rat,N2: nat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_rat @ ( G @ zero_zero_nat ) @ ( groups2906978787729119204at_rat @ ( comp_nat_rat_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeast0_atMost_Suc_shift
% 6.92/7.27 thf(fact_7659_sum_OatLeast0__atMost__Suc__shift,axiom,
% 6.92/7.27 ! [G: nat > int,N2: nat] :
% 6.92/7.27 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_int @ ( G @ zero_zero_nat ) @ ( groups3539618377306564664at_int @ ( comp_nat_int_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeast0_atMost_Suc_shift
% 6.92/7.27 thf(fact_7660_sum_OatLeast0__atMost__Suc__shift,axiom,
% 6.92/7.27 ! [G: nat > nat,N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_nat @ ( G @ zero_zero_nat ) @ ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeast0_atMost_Suc_shift
% 6.92/7.27 thf(fact_7661_sum_OatLeast0__atMost__Suc,axiom,
% 6.92/7.27 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 6.92/7.27 ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeast0_atMost_Suc
% 6.92/7.27 thf(fact_7662_sum_OatLeast0__atMost__Suc,axiom,
% 6.92/7.27 ! [G: nat > rat,N2: nat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeast0_atMost_Suc
% 6.92/7.27 thf(fact_7663_sum_OatLeast0__atMost__Suc,axiom,
% 6.92/7.27 ! [G: nat > int,N2: nat] :
% 6.92/7.27 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeast0_atMost_Suc
% 6.92/7.27 thf(fact_7664_sum_OatLeast0__atMost__Suc,axiom,
% 6.92/7.27 ! [G: nat > nat,N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeast0_atMost_Suc
% 6.92/7.27 thf(fact_7665_sum_Onat__ivl__Suc_H,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 6.92/7.27 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_p7104986032573967614at_nat @ ( G @ ( suc @ N2 ) ) @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.nat_ivl_Suc'
% 6.92/7.27 thf(fact_7666_sum_Onat__ivl__Suc_H,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > rat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_rat @ ( G @ ( suc @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.nat_ivl_Suc'
% 6.92/7.27 thf(fact_7667_sum_Onat__ivl__Suc_H,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > int] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 6.92/7.27 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_int @ ( G @ ( suc @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.nat_ivl_Suc'
% 6.92/7.27 thf(fact_7668_sum_Onat__ivl__Suc_H,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 6.92/7.27 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_nat @ ( G @ ( suc @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.nat_ivl_Suc'
% 6.92/7.27 thf(fact_7669_sum_OatLeast__Suc__atMost,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( plus_p7104986032573967614at_nat @ ( G @ M ) @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeast_Suc_atMost
% 6.92/7.27 thf(fact_7670_sum_OatLeast__Suc__atMost,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > rat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeast_Suc_atMost
% 6.92/7.27 thf(fact_7671_sum_OatLeast__Suc__atMost,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > int] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeast_Suc_atMost
% 6.92/7.27 thf(fact_7672_sum_OatLeast__Suc__atMost,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeast_Suc_atMost
% 6.92/7.27 thf(fact_7673_sum_OatMost__Suc__shift,axiom,
% 6.92/7.27 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 6.92/7.27 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat )
% 6.92/7.27 @ ( groups6857163185585827899at_nat
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atMost_Suc_shift
% 6.92/7.27 thf(fact_7674_sum_OatMost__Suc__shift,axiom,
% 6.92/7.27 ! [G: nat > rat,N2: nat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 6.92/7.27 @ ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atMost_Suc_shift
% 6.92/7.27 thf(fact_7675_sum_OatMost__Suc__shift,axiom,
% 6.92/7.27 ! [G: nat > int,N2: nat] :
% 6.92/7.27 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 6.92/7.27 @ ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atMost_Suc_shift
% 6.92/7.27 thf(fact_7676_sum_OatMost__Suc__shift,axiom,
% 6.92/7.27 ! [G: nat > nat,N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 6.92/7.27 @ ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atMost_Suc_shift
% 6.92/7.27 thf(fact_7677_sum__telescope,axiom,
% 6.92/7.27 ! [F: nat > rat,I2: nat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [I: nat] : ( minus_minus_rat @ ( F @ I ) @ ( F @ ( suc @ I ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ I2 ) )
% 6.92/7.27 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_telescope
% 6.92/7.27 thf(fact_7678_sum__telescope,axiom,
% 6.92/7.27 ! [F: nat > int,I2: nat] :
% 6.92/7.27 ( ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [I: nat] : ( minus_minus_int @ ( F @ I ) @ ( F @ ( suc @ I ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ I2 ) )
% 6.92/7.27 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_telescope
% 6.92/7.27 thf(fact_7679_sum_OSuc__reindex__ivl,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_p7104986032573967614at_nat @ ( G @ M )
% 6.92/7.27 @ ( groups6857163185585827899at_nat
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.Suc_reindex_ivl
% 6.92/7.27 thf(fact_7680_sum_OSuc__reindex__ivl,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > rat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_rat @ ( G @ M )
% 6.92/7.27 @ ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.Suc_reindex_ivl
% 6.92/7.27 thf(fact_7681_sum_OSuc__reindex__ivl,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > int] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_int @ ( G @ M )
% 6.92/7.27 @ ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.Suc_reindex_ivl
% 6.92/7.27 thf(fact_7682_sum_OSuc__reindex__ivl,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_nat @ ( G @ M )
% 6.92/7.27 @ ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.Suc_reindex_ivl
% 6.92/7.27 thf(fact_7683_sum__Suc__diff,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,F: nat > rat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [I: nat] : ( minus_minus_rat @ ( F @ ( suc @ I ) ) @ ( F @ I ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_Suc_diff
% 6.92/7.27 thf(fact_7684_sum__Suc__diff,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,F: nat > int] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 6.92/7.27 => ( ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [I: nat] : ( minus_minus_int @ ( F @ ( suc @ I ) ) @ ( F @ I ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_Suc_diff
% 6.92/7.27 thf(fact_7685_sum_OatLeast__atMost__pred__shift,axiom,
% 6.92/7.27 ! [G: nat > nat,M: nat,N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ( comp_nat_nat_nat @ G
% 6.92/7.27 @ ^ [N: nat] : ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeast_atMost_pred_shift
% 6.92/7.27 thf(fact_7686_sum__choose__lower,axiom,
% 6.92/7.27 ! [R2: nat,N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K3 ) @ K3 )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.27 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N2 ) ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_choose_lower
% 6.92/7.27 thf(fact_7687_choose__rising__sum_I1_J,axiom,
% 6.92/7.27 ! [N2: nat,M: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [J: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J ) @ N2 )
% 6.92/7.27 @ ( set_ord_atMost_nat @ M ) )
% 6.92/7.27 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_rising_sum(1)
% 6.92/7.27 thf(fact_7688_choose__rising__sum_I2_J,axiom,
% 6.92/7.27 ! [N2: nat,M: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [J: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J ) @ N2 )
% 6.92/7.27 @ ( set_ord_atMost_nat @ M ) )
% 6.92/7.27 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ M ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_rising_sum(2)
% 6.92/7.27 thf(fact_7689_sum__atLeastAtMost__code,axiom,
% 6.92/7.27 ! [F: nat > code_integer,A: nat,B: nat] :
% 6.92/7.27 ( ( groups7501900531339628137nteger @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 6.92/7.27 = ( set_fo1084959871951514735nteger
% 6.92/7.27 @ ^ [A5: nat] : ( plus_p5714425477246183910nteger @ ( F @ A5 ) )
% 6.92/7.27 @ A
% 6.92/7.27 @ B
% 6.92/7.27 @ zero_z3403309356797280102nteger ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_atLeastAtMost_code
% 6.92/7.27 thf(fact_7690_sum__atLeastAtMost__code,axiom,
% 6.92/7.27 ! [F: nat > multis2468970476368604999at_nat,A: nat,B: nat] :
% 6.92/7.27 ( ( groups6857163185585827899at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 6.92/7.27 = ( set_fo4497565046347964853at_nat
% 6.92/7.27 @ ^ [A5: nat] : ( plus_p7104986032573967614at_nat @ ( F @ A5 ) )
% 6.92/7.27 @ A
% 6.92/7.27 @ B
% 6.92/7.27 @ zero_z1048942125864253310at_nat ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_atLeastAtMost_code
% 6.92/7.27 thf(fact_7691_sum__atLeastAtMost__code,axiom,
% 6.92/7.27 ! [F: nat > rat,A: nat,B: nat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 6.92/7.27 = ( set_fo1949268297981939178at_rat
% 6.92/7.27 @ ^ [A5: nat] : ( plus_plus_rat @ ( F @ A5 ) )
% 6.92/7.27 @ A
% 6.92/7.27 @ B
% 6.92/7.27 @ zero_zero_rat ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_atLeastAtMost_code
% 6.92/7.27 thf(fact_7692_sum__atLeastAtMost__code,axiom,
% 6.92/7.27 ! [F: nat > int,A: nat,B: nat] :
% 6.92/7.27 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 6.92/7.27 = ( set_fo2581907887559384638at_int
% 6.92/7.27 @ ^ [A5: nat] : ( plus_plus_int @ ( F @ A5 ) )
% 6.92/7.27 @ A
% 6.92/7.27 @ B
% 6.92/7.27 @ zero_zero_int ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_atLeastAtMost_code
% 6.92/7.27 thf(fact_7693_sum__atLeastAtMost__code,axiom,
% 6.92/7.27 ! [F: nat > nat,A: nat,B: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 6.92/7.27 = ( set_fo2584398358068434914at_nat
% 6.92/7.27 @ ^ [A5: nat] : ( plus_plus_nat @ ( F @ A5 ) )
% 6.92/7.27 @ A
% 6.92/7.27 @ B
% 6.92/7.27 @ zero_zero_nat ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_atLeastAtMost_code
% 6.92/7.27 thf(fact_7694_sum_Oub__add__nat,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > multis2468970476368604999at_nat,P3: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 6.92/7.27 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 6.92/7.27 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.ub_add_nat
% 6.92/7.27 thf(fact_7695_sum_Oub__add__nat,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > rat,P3: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 6.92/7.27 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.ub_add_nat
% 6.92/7.27 thf(fact_7696_sum_Oub__add__nat,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > int,P3: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 6.92/7.27 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 6.92/7.27 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.ub_add_nat
% 6.92/7.27 thf(fact_7697_sum_Oub__add__nat,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > nat,P3: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 6.92/7.27 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 6.92/7.27 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.ub_add_nat
% 6.92/7.27 thf(fact_7698_sum_OatLeastAtMost__shift__0,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ M ) ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.atLeastAtMost_shift_0
% 6.92/7.27 thf(fact_7699_gbinomial__parallel__sum,axiom,
% 6.92/7.27 ! [A: rat,N2: nat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [K3: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K3 ) ) @ K3 )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.27 = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % gbinomial_parallel_sum
% 6.92/7.27 thf(fact_7700_sum_Otriangle__reindex__eq,axiom,
% 6.92/7.27 ! [G: nat > nat > nat,N2: nat] :
% 6.92/7.27 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 6.92/7.27 @ ( collec3392354462482085612at_nat
% 6.92/7.27 @ ( produc6081775807080527818_nat_o
% 6.92/7.27 @ ^ [I: nat,J: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I @ J ) @ N2 ) ) ) )
% 6.92/7.27 = ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [K3: nat] :
% 6.92/7.27 ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] : ( G @ I @ ( minus_minus_nat @ K3 @ I ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ K3 ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.triangle_reindex_eq
% 6.92/7.27 thf(fact_7701_sum__choose__diagonal,axiom,
% 6.92/7.27 ! [M: nat,N2: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N2 @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ M ) )
% 6.92/7.27 = ( binomial @ ( suc @ N2 ) @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_choose_diagonal
% 6.92/7.27 thf(fact_7702_vandermonde,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,R2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N2 @ ( minus_minus_nat @ R2 @ K3 ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ R2 ) )
% 6.92/7.27 = ( binomial @ ( plus_plus_nat @ M @ N2 ) @ R2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % vandermonde
% 6.92/7.27 thf(fact_7703_sum__gp__basic,axiom,
% 6.92/7.27 ! [X: code_integer,N2: nat] :
% 6.92/7.27 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 6.92/7.27 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_gp_basic
% 6.92/7.27 thf(fact_7704_sum__gp__basic,axiom,
% 6.92/7.27 ! [X: rat,N2: nat] :
% 6.92/7.27 ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 6.92/7.27 = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_gp_basic
% 6.92/7.27 thf(fact_7705_sum__gp__basic,axiom,
% 6.92/7.27 ! [X: int,N2: nat] :
% 6.92/7.27 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 6.92/7.27 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ ( suc @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_gp_basic
% 6.92/7.27 thf(fact_7706_sum__natinterval__diff,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,F: nat > code_integer] :
% 6.92/7.27 ( ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups7501900531339628137nteger
% 6.92/7.27 @ ^ [K3: nat] : ( minus_8373710615458151222nteger @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( minus_8373710615458151222nteger @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 6.92/7.27 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups7501900531339628137nteger
% 6.92/7.27 @ ^ [K3: nat] : ( minus_8373710615458151222nteger @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = zero_z3403309356797280102nteger ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_natinterval_diff
% 6.92/7.27 thf(fact_7707_sum__natinterval__diff,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,F: nat > rat] :
% 6.92/7.27 ( ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 6.92/7.27 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = zero_zero_rat ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_natinterval_diff
% 6.92/7.27 thf(fact_7708_sum__natinterval__diff,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,F: nat > int] :
% 6.92/7.27 ( ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 6.92/7.27 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = zero_zero_int ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_natinterval_diff
% 6.92/7.27 thf(fact_7709_sum__telescope_H_H,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,F: nat > rat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 6.92/7.27 = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_telescope''
% 6.92/7.27 thf(fact_7710_sum__telescope_H_H,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,F: nat > int] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 6.92/7.27 = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_telescope''
% 6.92/7.27 thf(fact_7711_choose__row__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat @ ( binomial @ N2 ) @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.27 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_row_sum
% 6.92/7.27 thf(fact_7712_binomial,axiom,
% 6.92/7.27 ! [A: nat,B: nat,N2: nat] :
% 6.92/7.27 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 6.92/7.27 = ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [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 ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % binomial
% 6.92/7.27 thf(fact_7713_sum_Oin__pairs__0,axiom,
% 6.92/7.27 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 6.92/7.27 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 6.92/7.27 = ( groups6857163185585827899at_nat
% 6.92/7.27 @ ^ [I: nat] : ( plus_p7104986032573967614at_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.in_pairs_0
% 6.92/7.27 thf(fact_7714_sum_Oin__pairs__0,axiom,
% 6.92/7.27 ! [G: nat > rat,N2: nat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 6.92/7.27 = ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [I: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.in_pairs_0
% 6.92/7.27 thf(fact_7715_sum_Oin__pairs__0,axiom,
% 6.92/7.27 ! [G: nat > int,N2: nat] :
% 6.92/7.27 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 6.92/7.27 = ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [I: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.in_pairs_0
% 6.92/7.27 thf(fact_7716_sum_Oin__pairs__0,axiom,
% 6.92/7.27 ! [G: nat > nat,N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 6.92/7.27 = ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.in_pairs_0
% 6.92/7.27 thf(fact_7717_nat__of__integer__less__iff,axiom,
% 6.92/7.27 ! [X: code_integer,Y: code_integer] :
% 6.92/7.27 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 6.92/7.27 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 6.92/7.27 => ( ( ord_less_nat @ ( code_nat_of_integer @ X ) @ ( code_nat_of_integer @ Y ) )
% 6.92/7.27 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % nat_of_integer_less_iff
% 6.92/7.27 thf(fact_7718_gbinomial__sum__lower__neg,axiom,
% 6.92/7.27 ! [A: rat,M: nat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ M ) )
% 6.92/7.27 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gbinomial_sum_lower_neg
% 6.92/7.27 thf(fact_7719_binomial__ring,axiom,
% 6.92/7.27 ! [A: rat,B: rat,N2: nat] :
% 6.92/7.27 ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 6.92/7.27 = ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [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 ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % binomial_ring
% 6.92/7.27 thf(fact_7720_binomial__ring,axiom,
% 6.92/7.27 ! [A: int,B: int,N2: nat] :
% 6.92/7.27 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 6.92/7.27 = ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [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 ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % binomial_ring
% 6.92/7.27 thf(fact_7721_binomial__ring,axiom,
% 6.92/7.27 ! [A: code_integer,B: code_integer,N2: nat] :
% 6.92/7.27 ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N2 )
% 6.92/7.27 = ( groups7501900531339628137nteger
% 6.92/7.27 @ ^ [K3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ K3 ) ) @ ( power_8256067586552552935nteger @ A @ K3 ) ) @ ( power_8256067586552552935nteger @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % binomial_ring
% 6.92/7.27 thf(fact_7722_binomial__ring,axiom,
% 6.92/7.27 ! [A: nat,B: nat,N2: nat] :
% 6.92/7.27 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 6.92/7.27 = ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [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 ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % binomial_ring
% 6.92/7.27 thf(fact_7723_sum__gp__multiplied,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,X: code_integer] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 6.92/7.27 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ ( suc @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_gp_multiplied
% 6.92/7.27 thf(fact_7724_sum__gp__multiplied,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,X: rat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 6.92/7.27 = ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_gp_multiplied
% 6.92/7.27 thf(fact_7725_sum__gp__multiplied,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,X: int] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 6.92/7.27 = ( minus_minus_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ ( suc @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_gp_multiplied
% 6.92/7.27 thf(fact_7726_pochhammer__binomial__sum,axiom,
% 6.92/7.27 ! [A: rat,B: rat,N2: nat] :
% 6.92/7.27 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 6.92/7.27 = ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [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 ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % pochhammer_binomial_sum
% 6.92/7.27 thf(fact_7727_pochhammer__binomial__sum,axiom,
% 6.92/7.27 ! [A: int,B: int,N2: nat] :
% 6.92/7.27 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 6.92/7.27 = ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [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 ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % pochhammer_binomial_sum
% 6.92/7.27 thf(fact_7728_pochhammer__binomial__sum,axiom,
% 6.92/7.27 ! [A: code_integer,B: code_integer,N2: nat] :
% 6.92/7.27 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N2 )
% 6.92/7.27 = ( groups7501900531339628137nteger
% 6.92/7.27 @ ^ [K3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ K3 ) ) @ ( comm_s8582702949713902594nteger @ A @ K3 ) ) @ ( comm_s8582702949713902594nteger @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % pochhammer_binomial_sum
% 6.92/7.27 thf(fact_7729_sum_Oin__pairs,axiom,
% 6.92/7.27 ! [G: nat > multis2468970476368604999at_nat,M: nat,N2: nat] :
% 6.92/7.27 ( ( 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 ) ) ) )
% 6.92/7.27 = ( groups6857163185585827899at_nat
% 6.92/7.27 @ ^ [I: nat] : ( plus_p7104986032573967614at_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.in_pairs
% 6.92/7.27 thf(fact_7730_sum_Oin__pairs,axiom,
% 6.92/7.27 ! [G: nat > rat,M: nat,N2: nat] :
% 6.92/7.27 ( ( 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 ) ) ) )
% 6.92/7.27 = ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [I: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.in_pairs
% 6.92/7.27 thf(fact_7731_sum_Oin__pairs,axiom,
% 6.92/7.27 ! [G: nat > int,M: nat,N2: nat] :
% 6.92/7.27 ( ( 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 ) ) ) )
% 6.92/7.27 = ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [I: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.in_pairs
% 6.92/7.27 thf(fact_7732_sum_Oin__pairs,axiom,
% 6.92/7.27 ! [G: nat > nat,M: nat,N2: nat] :
% 6.92/7.27 ( ( 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 ) ) ) )
% 6.92/7.27 = ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.in_pairs
% 6.92/7.27 thf(fact_7733_choose__square__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N2 @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.27 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_square_sum
% 6.92/7.27 thf(fact_7734_sum_Ozero__middle,axiom,
% 6.92/7.27 ! [P3: nat,K2: nat,G: nat > code_integer,H: nat > code_integer] :
% 6.92/7.27 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 6.92/7.27 => ( ( ord_less_eq_nat @ K2 @ P3 )
% 6.92/7.27 => ( ( groups7501900531339628137nteger
% 6.92/7.27 @ ^ [J: nat] : ( if_Code_integer @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( if_Code_integer @ ( J = K2 ) @ zero_z3403309356797280102nteger @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ P3 ) )
% 6.92/7.27 = ( groups7501900531339628137nteger
% 6.92/7.27 @ ^ [J: nat] : ( if_Code_integer @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( H @ J ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.zero_middle
% 6.92/7.27 thf(fact_7735_sum_Ozero__middle,axiom,
% 6.92/7.27 ! [P3: nat,K2: nat,G: nat > multis2468970476368604999at_nat,H: nat > multis2468970476368604999at_nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 6.92/7.27 => ( ( ord_less_eq_nat @ K2 @ P3 )
% 6.92/7.27 => ( ( groups6857163185585827899at_nat
% 6.92/7.27 @ ^ [J: nat] : ( if_mul8430962117462786573at_nat @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( if_mul8430962117462786573at_nat @ ( J = K2 ) @ zero_z1048942125864253310at_nat @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ P3 ) )
% 6.92/7.27 = ( groups6857163185585827899at_nat
% 6.92/7.27 @ ^ [J: nat] : ( if_mul8430962117462786573at_nat @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( H @ J ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.zero_middle
% 6.92/7.27 thf(fact_7736_sum_Ozero__middle,axiom,
% 6.92/7.27 ! [P3: nat,K2: nat,G: nat > rat,H: nat > rat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 6.92/7.27 => ( ( ord_less_eq_nat @ K2 @ P3 )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [J: nat] : ( if_rat @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( if_rat @ ( J = K2 ) @ zero_zero_rat @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ P3 ) )
% 6.92/7.27 = ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [J: nat] : ( if_rat @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( H @ J ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.zero_middle
% 6.92/7.27 thf(fact_7737_sum_Ozero__middle,axiom,
% 6.92/7.27 ! [P3: nat,K2: nat,G: nat > int,H: nat > int] :
% 6.92/7.27 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 6.92/7.27 => ( ( ord_less_eq_nat @ K2 @ P3 )
% 6.92/7.27 => ( ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( if_int @ ( J = K2 ) @ zero_zero_int @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ P3 ) )
% 6.92/7.27 = ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( H @ J ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.zero_middle
% 6.92/7.27 thf(fact_7738_sum_Ozero__middle,axiom,
% 6.92/7.27 ! [P3: nat,K2: nat,G: nat > nat,H: nat > nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 6.92/7.27 => ( ( ord_less_eq_nat @ K2 @ P3 )
% 6.92/7.27 => ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( if_nat @ ( J = K2 ) @ zero_zero_nat @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ P3 ) )
% 6.92/7.27 = ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( H @ J ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.zero_middle
% 6.92/7.27 thf(fact_7739_gbinomial__partial__sum__poly,axiom,
% 6.92/7.27 ! [M: nat,A: rat,X: rat,Y: rat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [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 ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ M ) )
% 6.92/7.27 = ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [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 ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gbinomial_partial_sum_poly
% 6.92/7.27 thf(fact_7740_gbinomial__sum__up__index,axiom,
% 6.92/7.27 ! [K2: nat,N2: nat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [J: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J ) @ K2 )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.27 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gbinomial_sum_up_index
% 6.92/7.27 thf(fact_7741_gauss__sum__nat,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [X4: nat] : X4
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.27 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gauss_sum_nat
% 6.92/7.27 thf(fact_7742_sum__gp0,axiom,
% 6.92/7.27 ! [X: rat,N2: nat] :
% 6.92/7.27 ( ( ( X = one_one_rat )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.27 = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 6.92/7.27 & ( ( X != one_one_rat )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.27 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_gp0
% 6.92/7.27 thf(fact_7743_gbinomial__partial__sum__poly__xpos,axiom,
% 6.92/7.27 ! [M: nat,A: rat,X: rat,Y: rat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [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 ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ M ) )
% 6.92/7.27 = ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [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 ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gbinomial_partial_sum_poly_xpos
% 6.92/7.27 thf(fact_7744_choose__alternating__linear__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( N2 != one_one_nat )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [I: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I ) @ ( semiri681578069525770553at_rat @ I ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.27 = zero_zero_rat ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_alternating_linear_sum
% 6.92/7.27 thf(fact_7745_choose__alternating__linear__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( N2 != one_one_nat )
% 6.92/7.27 => ( ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [I: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I ) @ ( semiri1314217659103216013at_int @ I ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.27 = zero_zero_int ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_alternating_linear_sum
% 6.92/7.27 thf(fact_7746_choose__alternating__linear__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( N2 != one_one_nat )
% 6.92/7.27 => ( ( groups7501900531339628137nteger
% 6.92/7.27 @ ^ [I: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I ) @ ( semiri4939895301339042750nteger @ I ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.27 = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_alternating_linear_sum
% 6.92/7.27 thf(fact_7747_gbinomial__sum__nat__pow2,axiom,
% 6.92/7.27 ! [M: nat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [K3: nat] : ( divide_divide_rat @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ K3 ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ M ) )
% 6.92/7.27 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ M ) ) ).
% 6.92/7.27
% 6.92/7.27 % gbinomial_sum_nat_pow2
% 6.92/7.27 thf(fact_7748_double__arith__series,axiom,
% 6.92/7.27 ! [A: rat,D2: rat,N2: nat] :
% 6.92/7.27 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 6.92/7.27 @ ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [I: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I ) @ D2 ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 6.92/7.27 = ( 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 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % double_arith_series
% 6.92/7.27 thf(fact_7749_double__arith__series,axiom,
% 6.92/7.27 ! [A: code_natural,D2: code_natural,N2: nat] :
% 6.92/7.27 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) )
% 6.92/7.27 @ ( groups6325495683096345652atural
% 6.92/7.27 @ ^ [I: nat] : ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ I ) @ D2 ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 6.92/7.27 = ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ D2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % double_arith_series
% 6.92/7.27 thf(fact_7750_double__arith__series,axiom,
% 6.92/7.27 ! [A: int,D2: int,N2: nat] :
% 6.92/7.27 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 6.92/7.27 @ ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [I: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I ) @ D2 ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 6.92/7.27 = ( 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 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % double_arith_series
% 6.92/7.27 thf(fact_7751_double__arith__series,axiom,
% 6.92/7.27 ! [A: code_integer,D2: code_integer,N2: nat] :
% 6.92/7.27 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 6.92/7.27 @ ( groups7501900531339628137nteger
% 6.92/7.27 @ ^ [I: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I ) @ D2 ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 6.92/7.27 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % double_arith_series
% 6.92/7.27 thf(fact_7752_double__arith__series,axiom,
% 6.92/7.27 ! [A: nat,D2: nat,N2: nat] :
% 6.92/7.27 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 6.92/7.27 @ ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I ) @ D2 ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 6.92/7.27 = ( 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 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % double_arith_series
% 6.92/7.27 thf(fact_7753_double__gauss__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 6.92/7.27 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % double_gauss_sum
% 6.92/7.27 thf(fact_7754_double__gauss__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 6.92/7.27 = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % double_gauss_sum
% 6.92/7.27 thf(fact_7755_double__gauss__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 6.92/7.27 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % double_gauss_sum
% 6.92/7.27 thf(fact_7756_double__gauss__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 6.92/7.27 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % double_gauss_sum
% 6.92/7.27 thf(fact_7757_double__gauss__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 6.92/7.27 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % double_gauss_sum
% 6.92/7.27 thf(fact_7758_binomial__r__part__sum,axiom,
% 6.92/7.27 ! [M: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 6.92/7.27 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % binomial_r_part_sum
% 6.92/7.27 thf(fact_7759_choose__linear__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] : ( times_times_nat @ I @ ( binomial @ N2 @ I ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.27 = ( times_times_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_linear_sum
% 6.92/7.27 thf(fact_7760_arith__series__nat,axiom,
% 6.92/7.27 ! [A: nat,D2: nat,N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I @ D2 ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.27 = ( 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 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % arith_series_nat
% 6.92/7.27 thf(fact_7761_Sum__Icc__nat,axiom,
% 6.92/7.27 ! [M: nat,N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [X4: nat] : X4
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( 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 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Sum_Icc_nat
% 6.92/7.27 thf(fact_7762_choose__alternating__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [I: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.27 = zero_zero_rat ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_alternating_sum
% 6.92/7.27 thf(fact_7763_choose__alternating__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.27 => ( ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [I: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.27 = zero_zero_int ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_alternating_sum
% 6.92/7.27 thf(fact_7764_choose__alternating__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.92/7.27 => ( ( groups7501900531339628137nteger
% 6.92/7.27 @ ^ [I: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I ) ) )
% 6.92/7.27 @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.27 = zero_z3403309356797280102nteger ) ) ).
% 6.92/7.27
% 6.92/7.27 % choose_alternating_sum
% 6.92/7.27 thf(fact_7765_double__gauss__sum__from__Suc__0,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 6.92/7.27 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % double_gauss_sum_from_Suc_0
% 6.92/7.27 thf(fact_7766_double__gauss__sum__from__Suc__0,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 6.92/7.27 = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % double_gauss_sum_from_Suc_0
% 6.92/7.27 thf(fact_7767_double__gauss__sum__from__Suc__0,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 6.92/7.27 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % double_gauss_sum_from_Suc_0
% 6.92/7.27 thf(fact_7768_double__gauss__sum__from__Suc__0,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 6.92/7.27 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % double_gauss_sum_from_Suc_0
% 6.92/7.27 thf(fact_7769_double__gauss__sum__from__Suc__0,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 6.92/7.27 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % double_gauss_sum_from_Suc_0
% 6.92/7.27 thf(fact_7770_arith__series,axiom,
% 6.92/7.27 ! [A: code_natural,D2: code_natural,N2: nat] :
% 6.92/7.27 ( ( groups6325495683096345652atural
% 6.92/7.27 @ ^ [I: nat] : ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ I ) @ D2 ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.27 = ( 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 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % arith_series
% 6.92/7.27 thf(fact_7771_arith__series,axiom,
% 6.92/7.27 ! [A: int,D2: int,N2: nat] :
% 6.92/7.27 ( ( groups3539618377306564664at_int
% 6.92/7.27 @ ^ [I: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I ) @ D2 ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.27 = ( 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 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % arith_series
% 6.92/7.27 thf(fact_7772_arith__series,axiom,
% 6.92/7.27 ! [A: code_integer,D2: code_integer,N2: nat] :
% 6.92/7.27 ( ( groups7501900531339628137nteger
% 6.92/7.27 @ ^ [I: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I ) @ D2 ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.27 = ( 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 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % arith_series
% 6.92/7.27 thf(fact_7773_arith__series,axiom,
% 6.92/7.27 ! [A: nat,D2: nat,N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I ) @ D2 ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.27 = ( 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 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % arith_series
% 6.92/7.27 thf(fact_7774_gauss__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.27 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gauss_sum
% 6.92/7.27 thf(fact_7775_gauss__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.27 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gauss_sum
% 6.92/7.27 thf(fact_7776_gauss__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.27 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gauss_sum
% 6.92/7.27 thf(fact_7777_gauss__sum,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.27 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gauss_sum
% 6.92/7.27 thf(fact_7778_sum__gp__offset,axiom,
% 6.92/7.27 ! [X: rat,M: nat,N2: nat] :
% 6.92/7.27 ( ( ( X = one_one_rat )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) )
% 6.92/7.27 & ( ( X != one_one_rat )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 6.92/7.27 = ( 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 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_gp_offset
% 6.92/7.27 thf(fact_7779_gauss__sum__from__Suc__0,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 6.92/7.27 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gauss_sum_from_Suc_0
% 6.92/7.27 thf(fact_7780_gauss__sum__from__Suc__0,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 6.92/7.27 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gauss_sum_from_Suc_0
% 6.92/7.27 thf(fact_7781_gauss__sum__from__Suc__0,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 6.92/7.27 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gauss_sum_from_Suc_0
% 6.92/7.27 thf(fact_7782_gauss__sum__from__Suc__0,axiom,
% 6.92/7.27 ! [N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 6.92/7.27 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gauss_sum_from_Suc_0
% 6.92/7.27 thf(fact_7783_gchoose__row__sum__weighted,axiom,
% 6.92/7.27 ! [R2: rat,M: nat] :
% 6.92/7.27 ( ( groups2906978787729119204at_rat
% 6.92/7.27 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R2 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 6.92/7.27 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R2 @ ( suc @ M ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gchoose_row_sum_weighted
% 6.92/7.27 thf(fact_7784_gbinomial__r__part__sum,axiom,
% 6.92/7.27 ! [M: nat] :
% 6.92/7.27 ( ( 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 ) )
% 6.92/7.27 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % gbinomial_r_part_sum
% 6.92/7.27 thf(fact_7785_pochhammer__times__pochhammer__half,axiom,
% 6.92/7.27 ! [Z3: rat,N2: nat] :
% 6.92/7.27 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z3 @ ( suc @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( groups73079841787564623at_rat
% 6.92/7.27 @ ^ [K3: nat] : ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % pochhammer_times_pochhammer_half
% 6.92/7.27 thf(fact_7786_divmod__integer__eq__cases,axiom,
% 6.92/7.27 ( code_divmod_integer
% 6.92/7.27 = ( ^ [K3: code_integer,L2: code_integer] :
% 6.92/7.27 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 6.92/7.27 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 6.92/7.27 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 6.92/7.27 @ ( if_Pro6119634080678213985nteger
% 6.92/7.27 @ ( ( sgn_sgn_Code_integer @ K3 )
% 6.92/7.27 = ( sgn_sgn_Code_integer @ L2 ) )
% 6.92/7.27 @ ( code_divmod_abs @ K3 @ L2 )
% 6.92/7.27 @ ( produc6916734918728496179nteger
% 6.92/7.27 @ ^ [R5: code_integer,S5: code_integer] : ( if_Pro6119634080678213985nteger @ ( S5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S5 ) ) )
% 6.92/7.27 @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % divmod_integer_eq_cases
% 6.92/7.27 thf(fact_7787_Sum__Icc__int,axiom,
% 6.92/7.27 ! [M: int,N2: int] :
% 6.92/7.27 ( ( ord_less_eq_int @ M @ N2 )
% 6.92/7.27 => ( ( groups4538972089207619220nt_int
% 6.92/7.27 @ ^ [X4: int] : X4
% 6.92/7.27 @ ( set_or1266510415728281911st_int @ M @ N2 ) )
% 6.92/7.27 = ( 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 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Sum_Icc_int
% 6.92/7.27 thf(fact_7788_Sum__Ico__nat,axiom,
% 6.92/7.27 ! [M: nat,N2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat
% 6.92/7.27 @ ^ [X4: nat] : X4
% 6.92/7.27 @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 6.92/7.27 = ( 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 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % Sum_Ico_nat
% 6.92/7.27 thf(fact_7789_sum__power2,axiom,
% 6.92/7.27 ! [K2: nat] :
% 6.92/7.27 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K2 ) )
% 6.92/7.27 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) @ one_one_nat ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum_power2
% 6.92/7.27 thf(fact_7790_of__nat__id,axiom,
% 6.92/7.27 ( semiri1316708129612266289at_nat
% 6.92/7.27 = ( ^ [N: nat] : N ) ) ).
% 6.92/7.27
% 6.92/7.27 % of_nat_id
% 6.92/7.27 thf(fact_7791_apsnd__conv,axiom,
% 6.92/7.27 ! [F: int > int,X: int,Y: int] :
% 6.92/7.27 ( ( produc4463282112584876420nt_int @ F @ ( product_Pair_int_int @ X @ Y ) )
% 6.92/7.27 = ( product_Pair_int_int @ X @ ( F @ Y ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % apsnd_conv
% 6.92/7.27 thf(fact_7792_apsnd__conv,axiom,
% 6.92/7.27 ! [F: produc3658429121746597890et_nat > produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 6.92/7.27 ( ( produc8750854537940449737_nat_o @ F @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 6.92/7.27 = ( produc5001842942810119800et_nat @ X @ ( F @ Y ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % apsnd_conv
% 6.92/7.27 thf(fact_7793_apsnd__conv,axiom,
% 6.92/7.27 ! [F: produc3658429121746597890et_nat > produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 6.92/7.27 ( ( produc7714581247149323085_nat_o @ F @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 6.92/7.27 = ( produc2245416461498447860et_nat @ X @ ( F @ Y ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % apsnd_conv
% 6.92/7.27 thf(fact_7794_apsnd__conv,axiom,
% 6.92/7.27 ! [F: produc3925858234332021118et_nat > produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 6.92/7.27 ( ( produc1515462096303866701_nat_o @ F @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 6.92/7.27 = ( produc5001842942810119800et_nat @ X @ ( F @ Y ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % apsnd_conv
% 6.92/7.27 thf(fact_7795_apsnd__conv,axiom,
% 6.92/7.27 ! [F: produc3925858234332021118et_nat > produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 6.92/7.27 ( ( produc969530845752564945_nat_o @ F @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 6.92/7.27 = ( produc2245416461498447860et_nat @ X @ ( F @ Y ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % apsnd_conv
% 6.92/7.27 thf(fact_7796_apsnd__conv,axiom,
% 6.92/7.27 ! [F: produc6653097349344004940it_nat > produc6653097349344004940it_nat,X: b,Y: produc6653097349344004940it_nat] :
% 6.92/7.27 ( ( produc701890989253350759_nat_b @ F @ ( produc4082563078715348724it_nat @ X @ Y ) )
% 6.92/7.27 = ( produc4082563078715348724it_nat @ X @ ( F @ Y ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % apsnd_conv
% 6.92/7.27 thf(fact_7797_apsnd__conv,axiom,
% 6.92/7.27 ! [F: produc6653097349344004940it_nat > produc6653097349344004940it_nat,X: a,Y: produc6653097349344004940it_nat] :
% 6.92/7.27 ( ( produc701890989253350758_nat_a @ F @ ( produc9178034014595674355it_nat @ X @ Y ) )
% 6.92/7.27 = ( produc9178034014595674355it_nat @ X @ ( F @ Y ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % apsnd_conv
% 6.92/7.27 thf(fact_7798_apsnd__conv,axiom,
% 6.92/7.27 ! [F: code_integer > code_integer,X: code_integer,Y: code_integer] :
% 6.92/7.27 ( ( produc6499014454317279255nteger @ F @ ( produc1086072967326762835nteger @ X @ Y ) )
% 6.92/7.27 = ( produc1086072967326762835nteger @ X @ ( F @ Y ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % apsnd_conv
% 6.92/7.27 thf(fact_7799_prod_Oneutral__const,axiom,
% 6.92/7.27 ! [A4: set_nat] :
% 6.92/7.27 ( ( groups708209901874060359at_nat
% 6.92/7.27 @ ^ [Uu2: nat] : one_one_nat
% 6.92/7.27 @ A4 )
% 6.92/7.27 = one_one_nat ) ).
% 6.92/7.27
% 6.92/7.27 % prod.neutral_const
% 6.92/7.27 thf(fact_7800_prod_Oneutral__const,axiom,
% 6.92/7.27 ! [A4: set_nat] :
% 6.92/7.27 ( ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [Uu2: nat] : one_one_int
% 6.92/7.27 @ A4 )
% 6.92/7.27 = one_one_int ) ).
% 6.92/7.27
% 6.92/7.27 % prod.neutral_const
% 6.92/7.27 thf(fact_7801_prod_Oneutral__const,axiom,
% 6.92/7.27 ! [A4: set_int] :
% 6.92/7.27 ( ( groups1705073143266064639nt_int
% 6.92/7.27 @ ^ [Uu2: int] : one_one_int
% 6.92/7.27 @ A4 )
% 6.92/7.27 = one_one_int ) ).
% 6.92/7.27
% 6.92/7.27 % prod.neutral_const
% 6.92/7.27 thf(fact_7802_of__nat__prod,axiom,
% 6.92/7.27 ! [F: int > nat,A4: set_int] :
% 6.92/7.27 ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A4 ) )
% 6.92/7.27 = ( groups1705073143266064639nt_int
% 6.92/7.27 @ ^ [X4: int] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % of_nat_prod
% 6.92/7.27 thf(fact_7803_of__nat__prod,axiom,
% 6.92/7.27 ! [F: nat > nat,A4: set_nat] :
% 6.92/7.27 ( ( semiri4939895301339042750nteger @ ( groups708209901874060359at_nat @ F @ A4 ) )
% 6.92/7.27 = ( groups3455450783089532116nteger
% 6.92/7.27 @ ^ [X4: nat] : ( semiri4939895301339042750nteger @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % of_nat_prod
% 6.92/7.27 thf(fact_7804_of__nat__prod,axiom,
% 6.92/7.27 ! [F: nat > nat,A4: set_nat] :
% 6.92/7.27 ( ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ F @ A4 ) )
% 6.92/7.27 = ( groups708209901874060359at_nat
% 6.92/7.27 @ ^ [X4: nat] : ( semiri1316708129612266289at_nat @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % of_nat_prod
% 6.92/7.27 thf(fact_7805_of__nat__prod,axiom,
% 6.92/7.27 ! [F: nat > nat,A4: set_nat] :
% 6.92/7.27 ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A4 ) )
% 6.92/7.27 = ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [X4: nat] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % of_nat_prod
% 6.92/7.27 thf(fact_7806_of__int__prod,axiom,
% 6.92/7.27 ! [F: nat > int,A4: set_nat] :
% 6.92/7.27 ( ( ring_1_of_int_rat @ ( groups705719431365010083at_int @ F @ A4 ) )
% 6.92/7.27 = ( groups73079841787564623at_rat
% 6.92/7.27 @ ^ [X4: nat] : ( ring_1_of_int_rat @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % of_int_prod
% 6.92/7.27 thf(fact_7807_of__int__prod,axiom,
% 6.92/7.27 ! [F: nat > int,A4: set_nat] :
% 6.92/7.27 ( ( ring_1_of_int_int @ ( groups705719431365010083at_int @ F @ A4 ) )
% 6.92/7.27 = ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [X4: nat] : ( ring_1_of_int_int @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % of_int_prod
% 6.92/7.27 thf(fact_7808_of__int__prod,axiom,
% 6.92/7.27 ! [F: int > int,A4: set_int] :
% 6.92/7.27 ( ( ring_1_of_int_rat @ ( groups1705073143266064639nt_int @ F @ A4 ) )
% 6.92/7.27 = ( groups1072433553688619179nt_rat
% 6.92/7.27 @ ^ [X4: int] : ( ring_1_of_int_rat @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % of_int_prod
% 6.92/7.27 thf(fact_7809_of__int__prod,axiom,
% 6.92/7.27 ! [F: int > int,A4: set_int] :
% 6.92/7.27 ( ( ring_1_of_int_int @ ( groups1705073143266064639nt_int @ F @ A4 ) )
% 6.92/7.27 = ( groups1705073143266064639nt_int
% 6.92/7.27 @ ^ [X4: int] : ( ring_1_of_int_int @ ( F @ X4 ) )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % of_int_prod
% 6.92/7.27 thf(fact_7810_atLeastLessThan__iff,axiom,
% 6.92/7.27 ! [I2: $o,L: $o,U: $o] :
% 6.92/7.27 ( ( member_o @ I2 @ ( set_or7139685690850216873Than_o @ L @ U ) )
% 6.92/7.27 = ( ( ord_less_eq_o @ L @ I2 )
% 6.92/7.27 & ( ord_less_o @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_iff
% 6.92/7.27 thf(fact_7811_atLeastLessThan__iff,axiom,
% 6.92/7.27 ! [I2: set_Pr958786334691620121nt_int,L: set_Pr958786334691620121nt_int,U: set_Pr958786334691620121nt_int] :
% 6.92/7.27 ( ( member2340774599025711042nt_int @ I2 @ ( set_or2826562449856406570nt_int @ L @ U ) )
% 6.92/7.27 = ( ( ord_le2843351958646193337nt_int @ L @ I2 )
% 6.92/7.27 & ( ord_le7563427860532173253nt_int @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_iff
% 6.92/7.27 thf(fact_7812_atLeastLessThan__iff,axiom,
% 6.92/7.27 ! [I2: set_nat,L: set_nat,U: set_nat] :
% 6.92/7.27 ( ( member_set_nat @ I2 @ ( set_or3540276404033026485et_nat @ L @ U ) )
% 6.92/7.27 = ( ( ord_less_eq_set_nat @ L @ I2 )
% 6.92/7.27 & ( ord_less_set_nat @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_iff
% 6.92/7.27 thf(fact_7813_atLeastLessThan__iff,axiom,
% 6.92/7.27 ! [I2: assn,L: assn,U: assn] :
% 6.92/7.27 ( ( member_assn @ I2 @ ( set_or5523502641901747543n_assn @ L @ U ) )
% 6.92/7.27 = ( ( ord_less_eq_assn @ L @ I2 )
% 6.92/7.27 & ( ord_less_assn @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_iff
% 6.92/7.27 thf(fact_7814_atLeastLessThan__iff,axiom,
% 6.92/7.27 ! [I2: set_int,L: set_int,U: set_int] :
% 6.92/7.27 ( ( member_set_int @ I2 @ ( set_or8585797421378605585et_int @ L @ U ) )
% 6.92/7.27 = ( ( ord_less_eq_set_int @ L @ I2 )
% 6.92/7.27 & ( ord_less_set_int @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_iff
% 6.92/7.27 thf(fact_7815_atLeastLessThan__iff,axiom,
% 6.92/7.27 ! [I2: rat,L: rat,U: rat] :
% 6.92/7.27 ( ( member_rat @ I2 @ ( set_or4029947393144176647an_rat @ L @ U ) )
% 6.92/7.27 = ( ( ord_less_eq_rat @ L @ I2 )
% 6.92/7.27 & ( ord_less_rat @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_iff
% 6.92/7.27 thf(fact_7816_atLeastLessThan__iff,axiom,
% 6.92/7.27 ! [I2: num,L: num,U: num] :
% 6.92/7.27 ( ( member_num @ I2 @ ( set_or1222409239386451017an_num @ L @ U ) )
% 6.92/7.27 = ( ( ord_less_eq_num @ L @ I2 )
% 6.92/7.27 & ( ord_less_num @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_iff
% 6.92/7.27 thf(fact_7817_atLeastLessThan__iff,axiom,
% 6.92/7.27 ! [I2: nat,L: nat,U: nat] :
% 6.92/7.27 ( ( member_nat @ I2 @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 6.92/7.27 = ( ( ord_less_eq_nat @ L @ I2 )
% 6.92/7.27 & ( ord_less_nat @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_iff
% 6.92/7.27 thf(fact_7818_atLeastLessThan__iff,axiom,
% 6.92/7.27 ! [I2: code_integer,L: code_integer,U: code_integer] :
% 6.92/7.27 ( ( member_Code_integer @ I2 @ ( set_or8404916559141939852nteger @ L @ U ) )
% 6.92/7.27 = ( ( ord_le3102999989581377725nteger @ L @ I2 )
% 6.92/7.27 & ( ord_le6747313008572928689nteger @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_iff
% 6.92/7.27 thf(fact_7819_atLeastLessThan__iff,axiom,
% 6.92/7.27 ! [I2: int,L: int,U: int] :
% 6.92/7.27 ( ( member_int @ I2 @ ( set_or4662586982721622107an_int @ L @ U ) )
% 6.92/7.27 = ( ( ord_less_eq_int @ L @ I2 )
% 6.92/7.27 & ( ord_less_int @ I2 @ U ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_iff
% 6.92/7.27 thf(fact_7820_atLeastLessThan__empty,axiom,
% 6.92/7.27 ! [B: $o,A: $o] :
% 6.92/7.27 ( ( ord_less_eq_o @ B @ A )
% 6.92/7.27 => ( ( set_or7139685690850216873Than_o @ A @ B )
% 6.92/7.27 = bot_bot_set_o ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty
% 6.92/7.27 thf(fact_7821_atLeastLessThan__empty,axiom,
% 6.92/7.27 ! [B: set_int,A: set_int] :
% 6.92/7.27 ( ( ord_less_eq_set_int @ B @ A )
% 6.92/7.27 => ( ( set_or8585797421378605585et_int @ A @ B )
% 6.92/7.27 = bot_bot_set_set_int ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty
% 6.92/7.27 thf(fact_7822_atLeastLessThan__empty,axiom,
% 6.92/7.27 ! [B: rat,A: rat] :
% 6.92/7.27 ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.27 => ( ( set_or4029947393144176647an_rat @ A @ B )
% 6.92/7.27 = bot_bot_set_rat ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty
% 6.92/7.27 thf(fact_7823_atLeastLessThan__empty,axiom,
% 6.92/7.27 ! [B: num,A: num] :
% 6.92/7.27 ( ( ord_less_eq_num @ B @ A )
% 6.92/7.27 => ( ( set_or1222409239386451017an_num @ A @ B )
% 6.92/7.27 = bot_bot_set_num ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty
% 6.92/7.27 thf(fact_7824_atLeastLessThan__empty,axiom,
% 6.92/7.27 ! [B: nat,A: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.27 => ( ( set_or4665077453230672383an_nat @ A @ B )
% 6.92/7.27 = bot_bot_set_nat ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty
% 6.92/7.27 thf(fact_7825_atLeastLessThan__empty,axiom,
% 6.92/7.27 ! [B: code_integer,A: code_integer] :
% 6.92/7.27 ( ( ord_le3102999989581377725nteger @ B @ A )
% 6.92/7.27 => ( ( set_or8404916559141939852nteger @ A @ B )
% 6.92/7.27 = bot_bo3990330152332043303nteger ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty
% 6.92/7.27 thf(fact_7826_atLeastLessThan__empty,axiom,
% 6.92/7.27 ! [B: int,A: int] :
% 6.92/7.27 ( ( ord_less_eq_int @ B @ A )
% 6.92/7.27 => ( ( set_or4662586982721622107an_int @ A @ B )
% 6.92/7.27 = bot_bot_set_int ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty
% 6.92/7.27 thf(fact_7827_atLeastLessThan__empty__iff2,axiom,
% 6.92/7.27 ! [A: $o,B: $o] :
% 6.92/7.27 ( ( bot_bot_set_o
% 6.92/7.27 = ( set_or7139685690850216873Than_o @ A @ B ) )
% 6.92/7.27 = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty_iff2
% 6.92/7.27 thf(fact_7828_atLeastLessThan__empty__iff2,axiom,
% 6.92/7.27 ! [A: assn,B: assn] :
% 6.92/7.27 ( ( bot_bot_set_assn
% 6.92/7.27 = ( set_or5523502641901747543n_assn @ A @ B ) )
% 6.92/7.27 = ( ~ ( ord_less_assn @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty_iff2
% 6.92/7.27 thf(fact_7829_atLeastLessThan__empty__iff2,axiom,
% 6.92/7.27 ! [A: rat,B: rat] :
% 6.92/7.27 ( ( bot_bot_set_rat
% 6.92/7.27 = ( set_or4029947393144176647an_rat @ A @ B ) )
% 6.92/7.27 = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty_iff2
% 6.92/7.27 thf(fact_7830_atLeastLessThan__empty__iff2,axiom,
% 6.92/7.27 ! [A: num,B: num] :
% 6.92/7.27 ( ( bot_bot_set_num
% 6.92/7.27 = ( set_or1222409239386451017an_num @ A @ B ) )
% 6.92/7.27 = ( ~ ( ord_less_num @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty_iff2
% 6.92/7.27 thf(fact_7831_atLeastLessThan__empty__iff2,axiom,
% 6.92/7.27 ! [A: nat,B: nat] :
% 6.92/7.27 ( ( bot_bot_set_nat
% 6.92/7.27 = ( set_or4665077453230672383an_nat @ A @ B ) )
% 6.92/7.27 = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty_iff2
% 6.92/7.27 thf(fact_7832_atLeastLessThan__empty__iff2,axiom,
% 6.92/7.27 ! [A: code_integer,B: code_integer] :
% 6.92/7.27 ( ( bot_bo3990330152332043303nteger
% 6.92/7.27 = ( set_or8404916559141939852nteger @ A @ B ) )
% 6.92/7.27 = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty_iff2
% 6.92/7.27 thf(fact_7833_atLeastLessThan__empty__iff2,axiom,
% 6.92/7.27 ! [A: int,B: int] :
% 6.92/7.27 ( ( bot_bot_set_int
% 6.92/7.27 = ( set_or4662586982721622107an_int @ A @ B ) )
% 6.92/7.27 = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty_iff2
% 6.92/7.27 thf(fact_7834_atLeastLessThan__empty__iff,axiom,
% 6.92/7.27 ! [A: $o,B: $o] :
% 6.92/7.27 ( ( ( set_or7139685690850216873Than_o @ A @ B )
% 6.92/7.27 = bot_bot_set_o )
% 6.92/7.27 = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty_iff
% 6.92/7.27 thf(fact_7835_atLeastLessThan__empty__iff,axiom,
% 6.92/7.27 ! [A: assn,B: assn] :
% 6.92/7.27 ( ( ( set_or5523502641901747543n_assn @ A @ B )
% 6.92/7.27 = bot_bot_set_assn )
% 6.92/7.27 = ( ~ ( ord_less_assn @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty_iff
% 6.92/7.27 thf(fact_7836_atLeastLessThan__empty__iff,axiom,
% 6.92/7.27 ! [A: rat,B: rat] :
% 6.92/7.27 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 6.92/7.27 = bot_bot_set_rat )
% 6.92/7.27 = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty_iff
% 6.92/7.27 thf(fact_7837_atLeastLessThan__empty__iff,axiom,
% 6.92/7.27 ! [A: num,B: num] :
% 6.92/7.27 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 6.92/7.27 = bot_bot_set_num )
% 6.92/7.27 = ( ~ ( ord_less_num @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty_iff
% 6.92/7.27 thf(fact_7838_atLeastLessThan__empty__iff,axiom,
% 6.92/7.27 ! [A: nat,B: nat] :
% 6.92/7.27 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 6.92/7.27 = bot_bot_set_nat )
% 6.92/7.27 = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty_iff
% 6.92/7.27 thf(fact_7839_atLeastLessThan__empty__iff,axiom,
% 6.92/7.27 ! [A: code_integer,B: code_integer] :
% 6.92/7.27 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 6.92/7.27 = bot_bo3990330152332043303nteger )
% 6.92/7.27 = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty_iff
% 6.92/7.27 thf(fact_7840_atLeastLessThan__empty__iff,axiom,
% 6.92/7.27 ! [A: int,B: int] :
% 6.92/7.27 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 6.92/7.27 = bot_bot_set_int )
% 6.92/7.27 = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_empty_iff
% 6.92/7.27 thf(fact_7841_ivl__subset,axiom,
% 6.92/7.27 ! [I2: rat,J2: rat,M: rat,N2: rat] :
% 6.92/7.27 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ I2 @ J2 ) @ ( set_or4029947393144176647an_rat @ M @ N2 ) )
% 6.92/7.27 = ( ( ord_less_eq_rat @ J2 @ I2 )
% 6.92/7.27 | ( ( ord_less_eq_rat @ M @ I2 )
% 6.92/7.27 & ( ord_less_eq_rat @ J2 @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ivl_subset
% 6.92/7.27 thf(fact_7842_ivl__subset,axiom,
% 6.92/7.27 ! [I2: num,J2: num,M: num,N2: num] :
% 6.92/7.27 ( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ I2 @ J2 ) @ ( set_or1222409239386451017an_num @ M @ N2 ) )
% 6.92/7.27 = ( ( ord_less_eq_num @ J2 @ I2 )
% 6.92/7.27 | ( ( ord_less_eq_num @ M @ I2 )
% 6.92/7.27 & ( ord_less_eq_num @ J2 @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ivl_subset
% 6.92/7.27 thf(fact_7843_ivl__subset,axiom,
% 6.92/7.27 ! [I2: nat,J2: nat,M: nat,N2: nat] :
% 6.92/7.27 ( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J2 ) @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 6.92/7.27 = ( ( ord_less_eq_nat @ J2 @ I2 )
% 6.92/7.27 | ( ( ord_less_eq_nat @ M @ I2 )
% 6.92/7.27 & ( ord_less_eq_nat @ J2 @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ivl_subset
% 6.92/7.27 thf(fact_7844_ivl__subset,axiom,
% 6.92/7.27 ! [I2: code_integer,J2: code_integer,M: code_integer,N2: code_integer] :
% 6.92/7.27 ( ( ord_le7084787975880047091nteger @ ( set_or8404916559141939852nteger @ I2 @ J2 ) @ ( set_or8404916559141939852nteger @ M @ N2 ) )
% 6.92/7.27 = ( ( ord_le3102999989581377725nteger @ J2 @ I2 )
% 6.92/7.27 | ( ( ord_le3102999989581377725nteger @ M @ I2 )
% 6.92/7.27 & ( ord_le3102999989581377725nteger @ J2 @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ivl_subset
% 6.92/7.27 thf(fact_7845_ivl__subset,axiom,
% 6.92/7.27 ! [I2: int,J2: int,M: int,N2: int] :
% 6.92/7.27 ( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ I2 @ J2 ) @ ( set_or4662586982721622107an_int @ M @ N2 ) )
% 6.92/7.27 = ( ( ord_less_eq_int @ J2 @ I2 )
% 6.92/7.27 | ( ( ord_less_eq_int @ M @ I2 )
% 6.92/7.27 & ( ord_less_eq_int @ J2 @ N2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ivl_subset
% 6.92/7.27 thf(fact_7846_ivl__diff,axiom,
% 6.92/7.27 ! [I2: rat,N2: rat,M: rat] :
% 6.92/7.27 ( ( ord_less_eq_rat @ I2 @ N2 )
% 6.92/7.27 => ( ( minus_minus_set_rat @ ( set_or4029947393144176647an_rat @ I2 @ M ) @ ( set_or4029947393144176647an_rat @ I2 @ N2 ) )
% 6.92/7.27 = ( set_or4029947393144176647an_rat @ N2 @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ivl_diff
% 6.92/7.27 thf(fact_7847_ivl__diff,axiom,
% 6.92/7.27 ! [I2: num,N2: num,M: num] :
% 6.92/7.27 ( ( ord_less_eq_num @ I2 @ N2 )
% 6.92/7.27 => ( ( minus_minus_set_num @ ( set_or1222409239386451017an_num @ I2 @ M ) @ ( set_or1222409239386451017an_num @ I2 @ N2 ) )
% 6.92/7.27 = ( set_or1222409239386451017an_num @ N2 @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ivl_diff
% 6.92/7.27 thf(fact_7848_ivl__diff,axiom,
% 6.92/7.27 ! [I2: nat,N2: nat,M: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ I2 @ N2 )
% 6.92/7.27 => ( ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ M ) @ ( set_or4665077453230672383an_nat @ I2 @ N2 ) )
% 6.92/7.27 = ( set_or4665077453230672383an_nat @ N2 @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ivl_diff
% 6.92/7.27 thf(fact_7849_ivl__diff,axiom,
% 6.92/7.27 ! [I2: code_integer,N2: code_integer,M: code_integer] :
% 6.92/7.27 ( ( ord_le3102999989581377725nteger @ I2 @ N2 )
% 6.92/7.27 => ( ( minus_2355218937544613996nteger @ ( set_or8404916559141939852nteger @ I2 @ M ) @ ( set_or8404916559141939852nteger @ I2 @ N2 ) )
% 6.92/7.27 = ( set_or8404916559141939852nteger @ N2 @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ivl_diff
% 6.92/7.27 thf(fact_7850_ivl__diff,axiom,
% 6.92/7.27 ! [I2: int,N2: int,M: int] :
% 6.92/7.27 ( ( ord_less_eq_int @ I2 @ N2 )
% 6.92/7.27 => ( ( minus_minus_set_int @ ( set_or4662586982721622107an_int @ I2 @ M ) @ ( set_or4662586982721622107an_int @ I2 @ N2 ) )
% 6.92/7.27 = ( set_or4662586982721622107an_int @ N2 @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % ivl_diff
% 6.92/7.27 thf(fact_7851_sum_Oop__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > code_integer] :
% 6.92/7.27 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = zero_z3403309356797280102nteger ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.op_ivl_Suc
% 6.92/7.27 thf(fact_7852_sum_Oop__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > multis2468970476368604999at_nat] :
% 6.92/7.27 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = zero_z1048942125864253310at_nat ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.op_ivl_Suc
% 6.92/7.27 thf(fact_7853_sum_Oop__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > rat] :
% 6.92/7.27 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = zero_zero_rat ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.op_ivl_Suc
% 6.92/7.27 thf(fact_7854_sum_Oop__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > int] :
% 6.92/7.27 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = zero_zero_int ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.op_ivl_Suc
% 6.92/7.27 thf(fact_7855_sum_Oop__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > nat] :
% 6.92/7.27 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = zero_zero_nat ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % sum.op_ivl_Suc
% 6.92/7.27 thf(fact_7856_prod_Ocl__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > code_integer] :
% 6.92/7.27 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = one_one_Code_integer ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.cl_ivl_Suc
% 6.92/7.27 thf(fact_7857_prod_Ocl__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > assn] :
% 6.92/7.27 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = one_one_assn ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.cl_ivl_Suc
% 6.92/7.27 thf(fact_7858_prod_Ocl__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > rat] :
% 6.92/7.27 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = one_one_rat ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.cl_ivl_Suc
% 6.92/7.27 thf(fact_7859_prod_Ocl__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > nat] :
% 6.92/7.27 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = one_one_nat ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.cl_ivl_Suc
% 6.92/7.27 thf(fact_7860_prod_Ocl__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > int] :
% 6.92/7.27 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = one_one_int ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 6.92/7.27 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.cl_ivl_Suc
% 6.92/7.27 thf(fact_7861_prod_Oop__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > code_integer] :
% 6.92/7.27 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = one_one_Code_integer ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.op_ivl_Suc
% 6.92/7.27 thf(fact_7862_prod_Oop__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > assn] :
% 6.92/7.27 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = one_one_assn ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.op_ivl_Suc
% 6.92/7.27 thf(fact_7863_prod_Oop__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > rat] :
% 6.92/7.27 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = one_one_rat ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.op_ivl_Suc
% 6.92/7.27 thf(fact_7864_prod_Oop__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > nat] :
% 6.92/7.27 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = one_one_nat ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.op_ivl_Suc
% 6.92/7.27 thf(fact_7865_prod_Oop__ivl__Suc,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > int] :
% 6.92/7.27 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = one_one_int ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.op_ivl_Suc
% 6.92/7.27 thf(fact_7866_prod_Oshift__bounds__nat__ivl,axiom,
% 6.92/7.27 ! [G: nat > nat,M: nat,K2: nat,N2: nat] :
% 6.92/7.27 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K2 ) @ ( plus_plus_nat @ N2 @ K2 ) ) )
% 6.92/7.27 = ( groups708209901874060359at_nat
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( plus_plus_nat @ I @ K2 ) )
% 6.92/7.27 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.shift_bounds_nat_ivl
% 6.92/7.27 thf(fact_7867_prod_Oshift__bounds__nat__ivl,axiom,
% 6.92/7.27 ! [G: nat > int,M: nat,K2: nat,N2: nat] :
% 6.92/7.27 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K2 ) @ ( plus_plus_nat @ N2 @ K2 ) ) )
% 6.92/7.27 = ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( plus_plus_nat @ I @ K2 ) )
% 6.92/7.27 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.shift_bounds_nat_ivl
% 6.92/7.27 thf(fact_7868_prod_OatLeastLessThan__shift__bounds,axiom,
% 6.92/7.27 ! [G: nat > nat,M: nat,K2: nat,N2: nat] :
% 6.92/7.27 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K2 ) @ ( plus_plus_nat @ N2 @ K2 ) ) )
% 6.92/7.27 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ K2 ) ) @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeastLessThan_shift_bounds
% 6.92/7.27 thf(fact_7869_prod_OatLeastLessThan__shift__bounds,axiom,
% 6.92/7.27 ! [G: nat > int,M: nat,K2: nat,N2: nat] :
% 6.92/7.27 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K2 ) @ ( plus_plus_nat @ N2 @ K2 ) ) )
% 6.92/7.27 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ ( plus_plus_nat @ K2 ) ) @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeastLessThan_shift_bounds
% 6.92/7.27 thf(fact_7870_prod_OatLeastLessThan__concat,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,P3: nat,G: nat > assn] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 6.92/7.27 => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 6.92/7.27 = ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeastLessThan_concat
% 6.92/7.27 thf(fact_7871_prod_OatLeastLessThan__concat,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,P3: nat,G: nat > rat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 6.92/7.27 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 6.92/7.27 = ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeastLessThan_concat
% 6.92/7.27 thf(fact_7872_prod_OatLeastLessThan__concat,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,P3: nat,G: nat > nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 6.92/7.27 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 6.92/7.27 = ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeastLessThan_concat
% 6.92/7.27 thf(fact_7873_prod_OatLeastLessThan__concat,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,P3: nat,G: nat > int] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 6.92/7.27 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 6.92/7.27 = ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeastLessThan_concat
% 6.92/7.27 thf(fact_7874_prod_Oshift__bounds__Suc__ivl,axiom,
% 6.92/7.27 ! [G: nat > nat,M: nat,N2: nat] :
% 6.92/7.27 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( groups708209901874060359at_nat
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.27 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.shift_bounds_Suc_ivl
% 6.92/7.27 thf(fact_7875_prod_Oshift__bounds__Suc__ivl,axiom,
% 6.92/7.27 ! [G: nat > int,M: nat,N2: nat] :
% 6.92/7.27 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.27 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.shift_bounds_Suc_ivl
% 6.92/7.27 thf(fact_7876_atLeastLessThan__eq__iff,axiom,
% 6.92/7.27 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.27 ( ( ord_less_rat @ A @ B )
% 6.92/7.27 => ( ( ord_less_rat @ C2 @ D2 )
% 6.92/7.27 => ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 6.92/7.27 = ( set_or4029947393144176647an_rat @ C2 @ D2 ) )
% 6.92/7.27 = ( ( A = C2 )
% 6.92/7.27 & ( B = D2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_eq_iff
% 6.92/7.27 thf(fact_7877_atLeastLessThan__eq__iff,axiom,
% 6.92/7.27 ! [A: num,B: num,C2: num,D2: num] :
% 6.92/7.27 ( ( ord_less_num @ A @ B )
% 6.92/7.27 => ( ( ord_less_num @ C2 @ D2 )
% 6.92/7.27 => ( ( ( set_or1222409239386451017an_num @ A @ B )
% 6.92/7.27 = ( set_or1222409239386451017an_num @ C2 @ D2 ) )
% 6.92/7.27 = ( ( A = C2 )
% 6.92/7.27 & ( B = D2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_eq_iff
% 6.92/7.27 thf(fact_7878_atLeastLessThan__eq__iff,axiom,
% 6.92/7.27 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.27 ( ( ord_less_nat @ A @ B )
% 6.92/7.27 => ( ( ord_less_nat @ C2 @ D2 )
% 6.92/7.27 => ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 6.92/7.27 = ( set_or4665077453230672383an_nat @ C2 @ D2 ) )
% 6.92/7.27 = ( ( A = C2 )
% 6.92/7.27 & ( B = D2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_eq_iff
% 6.92/7.27 thf(fact_7879_atLeastLessThan__eq__iff,axiom,
% 6.92/7.27 ! [A: code_integer,B: code_integer,C2: code_integer,D2: code_integer] :
% 6.92/7.27 ( ( ord_le6747313008572928689nteger @ A @ B )
% 6.92/7.27 => ( ( ord_le6747313008572928689nteger @ C2 @ D2 )
% 6.92/7.27 => ( ( ( set_or8404916559141939852nteger @ A @ B )
% 6.92/7.27 = ( set_or8404916559141939852nteger @ C2 @ D2 ) )
% 6.92/7.27 = ( ( A = C2 )
% 6.92/7.27 & ( B = D2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_eq_iff
% 6.92/7.27 thf(fact_7880_atLeastLessThan__eq__iff,axiom,
% 6.92/7.27 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.27 ( ( ord_less_int @ A @ B )
% 6.92/7.27 => ( ( ord_less_int @ C2 @ D2 )
% 6.92/7.27 => ( ( ( set_or4662586982721622107an_int @ A @ B )
% 6.92/7.27 = ( set_or4662586982721622107an_int @ C2 @ D2 ) )
% 6.92/7.27 = ( ( A = C2 )
% 6.92/7.27 & ( B = D2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_eq_iff
% 6.92/7.27 thf(fact_7881_atLeastLessThan__inj_I1_J,axiom,
% 6.92/7.27 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.27 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 6.92/7.27 = ( set_or4029947393144176647an_rat @ C2 @ D2 ) )
% 6.92/7.27 => ( ( ord_less_rat @ A @ B )
% 6.92/7.27 => ( ( ord_less_rat @ C2 @ D2 )
% 6.92/7.27 => ( A = C2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_inj(1)
% 6.92/7.27 thf(fact_7882_atLeastLessThan__inj_I1_J,axiom,
% 6.92/7.27 ! [A: num,B: num,C2: num,D2: num] :
% 6.92/7.27 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 6.92/7.27 = ( set_or1222409239386451017an_num @ C2 @ D2 ) )
% 6.92/7.27 => ( ( ord_less_num @ A @ B )
% 6.92/7.27 => ( ( ord_less_num @ C2 @ D2 )
% 6.92/7.27 => ( A = C2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_inj(1)
% 6.92/7.27 thf(fact_7883_atLeastLessThan__inj_I1_J,axiom,
% 6.92/7.27 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.27 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 6.92/7.27 = ( set_or4665077453230672383an_nat @ C2 @ D2 ) )
% 6.92/7.27 => ( ( ord_less_nat @ A @ B )
% 6.92/7.27 => ( ( ord_less_nat @ C2 @ D2 )
% 6.92/7.27 => ( A = C2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_inj(1)
% 6.92/7.27 thf(fact_7884_atLeastLessThan__inj_I1_J,axiom,
% 6.92/7.27 ! [A: code_integer,B: code_integer,C2: code_integer,D2: code_integer] :
% 6.92/7.27 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 6.92/7.27 = ( set_or8404916559141939852nteger @ C2 @ D2 ) )
% 6.92/7.27 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 6.92/7.27 => ( ( ord_le6747313008572928689nteger @ C2 @ D2 )
% 6.92/7.27 => ( A = C2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_inj(1)
% 6.92/7.27 thf(fact_7885_atLeastLessThan__inj_I1_J,axiom,
% 6.92/7.27 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.27 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 6.92/7.27 = ( set_or4662586982721622107an_int @ C2 @ D2 ) )
% 6.92/7.27 => ( ( ord_less_int @ A @ B )
% 6.92/7.27 => ( ( ord_less_int @ C2 @ D2 )
% 6.92/7.27 => ( A = C2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_inj(1)
% 6.92/7.27 thf(fact_7886_atLeastLessThan__inj_I2_J,axiom,
% 6.92/7.27 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.27 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 6.92/7.27 = ( set_or4029947393144176647an_rat @ C2 @ D2 ) )
% 6.92/7.27 => ( ( ord_less_rat @ A @ B )
% 6.92/7.27 => ( ( ord_less_rat @ C2 @ D2 )
% 6.92/7.27 => ( B = D2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_inj(2)
% 6.92/7.27 thf(fact_7887_atLeastLessThan__inj_I2_J,axiom,
% 6.92/7.27 ! [A: num,B: num,C2: num,D2: num] :
% 6.92/7.27 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 6.92/7.27 = ( set_or1222409239386451017an_num @ C2 @ D2 ) )
% 6.92/7.27 => ( ( ord_less_num @ A @ B )
% 6.92/7.27 => ( ( ord_less_num @ C2 @ D2 )
% 6.92/7.27 => ( B = D2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_inj(2)
% 6.92/7.27 thf(fact_7888_atLeastLessThan__inj_I2_J,axiom,
% 6.92/7.27 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.27 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 6.92/7.27 = ( set_or4665077453230672383an_nat @ C2 @ D2 ) )
% 6.92/7.27 => ( ( ord_less_nat @ A @ B )
% 6.92/7.27 => ( ( ord_less_nat @ C2 @ D2 )
% 6.92/7.27 => ( B = D2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_inj(2)
% 6.92/7.27 thf(fact_7889_atLeastLessThan__inj_I2_J,axiom,
% 6.92/7.27 ! [A: code_integer,B: code_integer,C2: code_integer,D2: code_integer] :
% 6.92/7.27 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 6.92/7.27 = ( set_or8404916559141939852nteger @ C2 @ D2 ) )
% 6.92/7.27 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 6.92/7.27 => ( ( ord_le6747313008572928689nteger @ C2 @ D2 )
% 6.92/7.27 => ( B = D2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_inj(2)
% 6.92/7.27 thf(fact_7890_atLeastLessThan__inj_I2_J,axiom,
% 6.92/7.27 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.27 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 6.92/7.27 = ( set_or4662586982721622107an_int @ C2 @ D2 ) )
% 6.92/7.27 => ( ( ord_less_int @ A @ B )
% 6.92/7.27 => ( ( ord_less_int @ C2 @ D2 )
% 6.92/7.27 => ( B = D2 ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % atLeastLessThan_inj(2)
% 6.92/7.27 thf(fact_7891_prod_Oivl__cong,axiom,
% 6.92/7.27 ! [A: nat,C2: nat,B: nat,D2: nat,G: nat > nat,H: nat > nat] :
% 6.92/7.27 ( ( A = C2 )
% 6.92/7.27 => ( ( B = D2 )
% 6.92/7.27 => ( ! [X3: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ C2 @ X3 )
% 6.92/7.27 => ( ( ord_less_nat @ X3 @ D2 )
% 6.92/7.27 => ( ( G @ X3 )
% 6.92/7.27 = ( H @ X3 ) ) ) )
% 6.92/7.27 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 6.92/7.27 = ( groups708209901874060359at_nat @ H @ ( set_or4665077453230672383an_nat @ C2 @ D2 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.ivl_cong
% 6.92/7.27 thf(fact_7892_prod_Oivl__cong,axiom,
% 6.92/7.27 ! [A: nat,C2: nat,B: nat,D2: nat,G: nat > int,H: nat > int] :
% 6.92/7.27 ( ( A = C2 )
% 6.92/7.27 => ( ( B = D2 )
% 6.92/7.27 => ( ! [X3: nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ C2 @ X3 )
% 6.92/7.27 => ( ( ord_less_nat @ X3 @ D2 )
% 6.92/7.27 => ( ( G @ X3 )
% 6.92/7.27 = ( H @ X3 ) ) ) )
% 6.92/7.27 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 6.92/7.27 = ( groups705719431365010083at_int @ H @ ( set_or4665077453230672383an_nat @ C2 @ D2 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.ivl_cong
% 6.92/7.27 thf(fact_7893_prod_Oivl__cong,axiom,
% 6.92/7.27 ! [A: int,C2: int,B: int,D2: int,G: int > int,H: int > int] :
% 6.92/7.27 ( ( A = C2 )
% 6.92/7.27 => ( ( B = D2 )
% 6.92/7.27 => ( ! [X3: int] :
% 6.92/7.27 ( ( ord_less_eq_int @ C2 @ X3 )
% 6.92/7.27 => ( ( ord_less_int @ X3 @ D2 )
% 6.92/7.27 => ( ( G @ X3 )
% 6.92/7.27 = ( H @ X3 ) ) ) )
% 6.92/7.27 => ( ( groups1705073143266064639nt_int @ G @ ( set_or4662586982721622107an_int @ A @ B ) )
% 6.92/7.27 = ( groups1705073143266064639nt_int @ H @ ( set_or4662586982721622107an_int @ C2 @ D2 ) ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.ivl_cong
% 6.92/7.27 thf(fact_7894_prod_Oswap,axiom,
% 6.92/7.27 ! [G: nat > nat > nat,B5: set_nat,A4: set_nat] :
% 6.92/7.27 ( ( groups708209901874060359at_nat
% 6.92/7.27 @ ^ [I: nat] : ( groups708209901874060359at_nat @ ( G @ I ) @ B5 )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( groups708209901874060359at_nat
% 6.92/7.27 @ ^ [J: nat] :
% 6.92/7.27 ( groups708209901874060359at_nat
% 6.92/7.27 @ ^ [I: nat] : ( G @ I @ J )
% 6.92/7.27 @ A4 )
% 6.92/7.27 @ B5 ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.swap
% 6.92/7.27 thf(fact_7895_prod_Oswap,axiom,
% 6.92/7.27 ! [G: nat > nat > int,B5: set_nat,A4: set_nat] :
% 6.92/7.27 ( ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [I: nat] : ( groups705719431365010083at_int @ ( G @ I ) @ B5 )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [J: nat] :
% 6.92/7.27 ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [I: nat] : ( G @ I @ J )
% 6.92/7.27 @ A4 )
% 6.92/7.27 @ B5 ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.swap
% 6.92/7.27 thf(fact_7896_prod_Oswap,axiom,
% 6.92/7.27 ! [G: nat > int > int,B5: set_int,A4: set_nat] :
% 6.92/7.27 ( ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [I: nat] : ( groups1705073143266064639nt_int @ ( G @ I ) @ B5 )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( groups1705073143266064639nt_int
% 6.92/7.27 @ ^ [J: int] :
% 6.92/7.27 ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [I: nat] : ( G @ I @ J )
% 6.92/7.27 @ A4 )
% 6.92/7.27 @ B5 ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.swap
% 6.92/7.27 thf(fact_7897_prod_Oswap,axiom,
% 6.92/7.27 ! [G: int > nat > int,B5: set_nat,A4: set_int] :
% 6.92/7.27 ( ( groups1705073143266064639nt_int
% 6.92/7.27 @ ^ [I: int] : ( groups705719431365010083at_int @ ( G @ I ) @ B5 )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [J: nat] :
% 6.92/7.27 ( groups1705073143266064639nt_int
% 6.92/7.27 @ ^ [I: int] : ( G @ I @ J )
% 6.92/7.27 @ A4 )
% 6.92/7.27 @ B5 ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.swap
% 6.92/7.27 thf(fact_7898_prod_Oswap,axiom,
% 6.92/7.27 ! [G: int > int > int,B5: set_int,A4: set_int] :
% 6.92/7.27 ( ( groups1705073143266064639nt_int
% 6.92/7.27 @ ^ [I: int] : ( groups1705073143266064639nt_int @ ( G @ I ) @ B5 )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( groups1705073143266064639nt_int
% 6.92/7.27 @ ^ [J: int] :
% 6.92/7.27 ( groups1705073143266064639nt_int
% 6.92/7.27 @ ^ [I: int] : ( G @ I @ J )
% 6.92/7.27 @ A4 )
% 6.92/7.27 @ B5 ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.swap
% 6.92/7.27 thf(fact_7899_prod_Odistrib,axiom,
% 6.92/7.27 ! [G: nat > nat,H: nat > nat,A4: set_nat] :
% 6.92/7.27 ( ( groups708209901874060359at_nat
% 6.92/7.27 @ ^ [X4: nat] : ( times_times_nat @ ( G @ X4 ) @ ( H @ X4 ) )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A4 ) @ ( groups708209901874060359at_nat @ H @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.distrib
% 6.92/7.27 thf(fact_7900_prod_Odistrib,axiom,
% 6.92/7.27 ! [G: nat > int,H: nat > int,A4: set_nat] :
% 6.92/7.27 ( ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [X4: nat] : ( times_times_int @ ( G @ X4 ) @ ( H @ X4 ) )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( times_times_int @ ( groups705719431365010083at_int @ G @ A4 ) @ ( groups705719431365010083at_int @ H @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.distrib
% 6.92/7.27 thf(fact_7901_prod_Odistrib,axiom,
% 6.92/7.27 ! [G: int > int,H: int > int,A4: set_int] :
% 6.92/7.27 ( ( groups1705073143266064639nt_int
% 6.92/7.27 @ ^ [X4: int] : ( times_times_int @ ( G @ X4 ) @ ( H @ X4 ) )
% 6.92/7.27 @ A4 )
% 6.92/7.27 = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A4 ) @ ( groups1705073143266064639nt_int @ H @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.distrib
% 6.92/7.27 thf(fact_7902_prod_OatLeast__Suc__lessThan,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > assn] :
% 6.92/7.27 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 6.92/7.27 = ( times_times_assn @ ( G @ M ) @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeast_Suc_lessThan
% 6.92/7.27 thf(fact_7903_prod_OatLeast__Suc__lessThan,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > rat] :
% 6.92/7.27 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 6.92/7.27 = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeast_Suc_lessThan
% 6.92/7.27 thf(fact_7904_prod_OatLeast__Suc__lessThan,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > nat] :
% 6.92/7.27 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 6.92/7.27 = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeast_Suc_lessThan
% 6.92/7.27 thf(fact_7905_prod_OatLeast__Suc__lessThan,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > int] :
% 6.92/7.27 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 6.92/7.27 = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeast_Suc_lessThan
% 6.92/7.27 thf(fact_7906_prod_OatLeastLessThan__Suc,axiom,
% 6.92/7.27 ! [A: nat,B: nat,G: nat > assn] :
% 6.92/7.27 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.27 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 6.92/7.27 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeastLessThan_Suc
% 6.92/7.27 thf(fact_7907_prod_OatLeastLessThan__Suc,axiom,
% 6.92/7.27 ! [A: nat,B: nat,G: nat > rat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.27 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 6.92/7.27 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeastLessThan_Suc
% 6.92/7.27 thf(fact_7908_prod_OatLeastLessThan__Suc,axiom,
% 6.92/7.27 ! [A: nat,B: nat,G: nat > nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.27 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 6.92/7.27 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeastLessThan_Suc
% 6.92/7.27 thf(fact_7909_prod_OatLeastLessThan__Suc,axiom,
% 6.92/7.27 ! [A: nat,B: nat,G: nat > int] :
% 6.92/7.27 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.27 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 6.92/7.27 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeastLessThan_Suc
% 6.92/7.27 thf(fact_7910_prod__power__distrib,axiom,
% 6.92/7.27 ! [F: nat > nat,A4: set_nat,N2: nat] :
% 6.92/7.27 ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A4 ) @ N2 )
% 6.92/7.27 = ( groups708209901874060359at_nat
% 6.92/7.27 @ ^ [X4: nat] : ( power_power_nat @ ( F @ X4 ) @ N2 )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_power_distrib
% 6.92/7.27 thf(fact_7911_prod__power__distrib,axiom,
% 6.92/7.27 ! [F: nat > int,A4: set_nat,N2: nat] :
% 6.92/7.27 ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A4 ) @ N2 )
% 6.92/7.27 = ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [X4: nat] : ( power_power_int @ ( F @ X4 ) @ N2 )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_power_distrib
% 6.92/7.27 thf(fact_7912_prod__power__distrib,axiom,
% 6.92/7.27 ! [F: int > int,A4: set_int,N2: nat] :
% 6.92/7.27 ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A4 ) @ N2 )
% 6.92/7.27 = ( groups1705073143266064639nt_int
% 6.92/7.27 @ ^ [X4: int] : ( power_power_int @ ( F @ X4 ) @ N2 )
% 6.92/7.27 @ A4 ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_power_distrib
% 6.92/7.27 thf(fact_7913_prod_OatLeastLessThan__shift__0,axiom,
% 6.92/7.27 ! [G: nat > nat,M: nat,N2: nat] :
% 6.92/7.27 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 6.92/7.27 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ M ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeastLessThan_shift_0
% 6.92/7.27 thf(fact_7914_prod_OatLeastLessThan__shift__0,axiom,
% 6.92/7.27 ! [G: nat > int,M: nat,N2: nat] :
% 6.92/7.27 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 6.92/7.27 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ ( plus_plus_nat @ M ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeastLessThan_shift_0
% 6.92/7.27 thf(fact_7915_mod__prod__eq,axiom,
% 6.92/7.27 ! [F: nat > nat,A: nat,A4: set_nat] :
% 6.92/7.27 ( ( modulo_modulo_nat
% 6.92/7.27 @ ( groups708209901874060359at_nat
% 6.92/7.27 @ ^ [I: nat] : ( modulo_modulo_nat @ ( F @ I ) @ A )
% 6.92/7.27 @ A4 )
% 6.92/7.27 @ A )
% 6.92/7.27 = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A4 ) @ A ) ) ).
% 6.92/7.27
% 6.92/7.27 % mod_prod_eq
% 6.92/7.27 thf(fact_7916_mod__prod__eq,axiom,
% 6.92/7.27 ! [F: nat > int,A: int,A4: set_nat] :
% 6.92/7.27 ( ( modulo_modulo_int
% 6.92/7.27 @ ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [I: nat] : ( modulo_modulo_int @ ( F @ I ) @ A )
% 6.92/7.27 @ A4 )
% 6.92/7.27 @ A )
% 6.92/7.27 = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A4 ) @ A ) ) ).
% 6.92/7.27
% 6.92/7.27 % mod_prod_eq
% 6.92/7.27 thf(fact_7917_mod__prod__eq,axiom,
% 6.92/7.27 ! [F: int > int,A: int,A4: set_int] :
% 6.92/7.27 ( ( modulo_modulo_int
% 6.92/7.27 @ ( groups1705073143266064639nt_int
% 6.92/7.27 @ ^ [I: int] : ( modulo_modulo_int @ ( F @ I ) @ A )
% 6.92/7.27 @ A4 )
% 6.92/7.27 @ A )
% 6.92/7.27 = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A4 ) @ A ) ) ).
% 6.92/7.27
% 6.92/7.27 % mod_prod_eq
% 6.92/7.27 thf(fact_7918_prod_Olast__plus,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > assn] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( times_times_assn @ ( G @ N2 ) @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.last_plus
% 6.92/7.27 thf(fact_7919_prod_Olast__plus,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > rat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( times_times_rat @ ( G @ N2 ) @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.last_plus
% 6.92/7.27 thf(fact_7920_prod_Olast__plus,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > nat] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( times_times_nat @ ( G @ N2 ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.last_plus
% 6.92/7.27 thf(fact_7921_prod_Olast__plus,axiom,
% 6.92/7.27 ! [M: nat,N2: nat,G: nat > int] :
% 6.92/7.27 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.27 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = ( times_times_int @ ( G @ N2 ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.last_plus
% 6.92/7.27 thf(fact_7922_prod_OatLeast__lessThan__pred__shift,axiom,
% 6.92/7.27 ! [G: nat > nat,M: nat,N2: nat] :
% 6.92/7.27 ( ( groups708209901874060359at_nat
% 6.92/7.27 @ ( comp_nat_nat_nat @ G
% 6.92/7.27 @ ^ [N: nat] : ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 6.92/7.27 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeast_lessThan_pred_shift
% 6.92/7.27 thf(fact_7923_prod_OatLeast__lessThan__pred__shift,axiom,
% 6.92/7.27 ! [G: nat > int,M: nat,N2: nat] :
% 6.92/7.27 ( ( groups705719431365010083at_int
% 6.92/7.27 @ ( comp_nat_int_nat @ G
% 6.92/7.27 @ ^ [N: nat] : ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 6.92/7.27 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 6.92/7.27 = ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeast_lessThan_pred_shift
% 6.92/7.27 thf(fact_7924_prod_OatLeastLessThan__rev,axiom,
% 6.92/7.27 ! [G: nat > nat,N2: nat,M: nat] :
% 6.92/7.27 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M ) )
% 6.92/7.27 = ( groups708209901874060359at_nat
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ ( suc @ I ) ) )
% 6.92/7.27 @ ( set_or4665077453230672383an_nat @ N2 @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeastLessThan_rev
% 6.92/7.27 thf(fact_7925_prod_OatLeastLessThan__rev,axiom,
% 6.92/7.27 ! [G: nat > int,N2: nat,M: nat] :
% 6.92/7.27 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ M ) )
% 6.92/7.27 = ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [I: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ ( suc @ I ) ) )
% 6.92/7.27 @ ( set_or4665077453230672383an_nat @ N2 @ M ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.atLeastLessThan_rev
% 6.92/7.27 thf(fact_7926_prod_Onested__swap,axiom,
% 6.92/7.27 ! [A: nat > nat > nat,N2: nat] :
% 6.92/7.27 ( ( groups708209901874060359at_nat
% 6.92/7.27 @ ^ [I: nat] : ( groups708209901874060359at_nat @ ( A @ I ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.27 = ( groups708209901874060359at_nat
% 6.92/7.27 @ ^ [J: nat] :
% 6.92/7.27 ( groups708209901874060359at_nat
% 6.92/7.27 @ ^ [I: nat] : ( A @ I @ J )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N2 ) )
% 6.92/7.27 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.nested_swap
% 6.92/7.27 thf(fact_7927_prod_Onested__swap,axiom,
% 6.92/7.27 ! [A: nat > nat > int,N2: nat] :
% 6.92/7.27 ( ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [I: nat] : ( groups705719431365010083at_int @ ( A @ I ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I ) )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.27 = ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [J: nat] :
% 6.92/7.27 ( groups705719431365010083at_int
% 6.92/7.27 @ ^ [I: nat] : ( A @ I @ J )
% 6.92/7.27 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N2 ) )
% 6.92/7.27 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod.nested_swap
% 6.92/7.27 thf(fact_7928_apsnd__compose,axiom,
% 6.92/7.27 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 6.92/7.27 ( ( produc9020447175693601247nteger @ F @ ( produc6499014454317279255nteger @ G @ X ) )
% 6.92/7.27 = ( produc9020447175693601247nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ X ) ) ).
% 6.92/7.27
% 6.92/7.27 % apsnd_compose
% 6.92/7.27 thf(fact_7929_apsnd__compose,axiom,
% 6.92/7.27 ! [F: code_integer > code_integer,G: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 6.92/7.27 ( ( produc6499014454317279255nteger @ F @ ( produc6499014454317279255nteger @ G @ X ) )
% 6.92/7.27 = ( produc6499014454317279255nteger @ ( comp_C7449957260575251196nteger @ F @ G ) @ X ) ) ).
% 6.92/7.27
% 6.92/7.27 % apsnd_compose
% 6.92/7.27 thf(fact_7930_prod__nonneg,axiom,
% 6.92/7.27 ! [A4: set_nat,F: nat > nat] :
% 6.92/7.27 ( ! [X3: nat] :
% 6.92/7.27 ( ( member_nat @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_nonneg
% 6.92/7.27 thf(fact_7931_prod__nonneg,axiom,
% 6.92/7.27 ! [A4: set_nat,F: nat > int] :
% 6.92/7.27 ( ! [X3: nat] :
% 6.92/7.27 ( ( member_nat @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_nonneg
% 6.92/7.27 thf(fact_7932_prod__nonneg,axiom,
% 6.92/7.27 ! [A4: set_int,F: int > int] :
% 6.92/7.27 ( ! [X3: int] :
% 6.92/7.27 ( ( member_int @ X3 @ A4 )
% 6.92/7.27 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 6.92/7.27 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_nonneg
% 6.92/7.27 thf(fact_7933_prod__mono,axiom,
% 6.92/7.27 ! [A4: set_o,F: $o > code_integer,G: $o > code_integer] :
% 6.92/7.27 ( ! [I3: $o] :
% 6.92/7.27 ( ( member_o @ I3 @ A4 )
% 6.92/7.27 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 6.92/7.27 & ( ord_le3102999989581377725nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ ( groups7694694392188491536nteger @ F @ A4 ) @ ( groups7694694392188491536nteger @ G @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_mono
% 6.92/7.27 thf(fact_7934_prod__mono,axiom,
% 6.92/7.27 ! [A4: set_nat,F: nat > code_integer,G: nat > code_integer] :
% 6.92/7.27 ( ! [I3: nat] :
% 6.92/7.27 ( ( member_nat @ I3 @ A4 )
% 6.92/7.27 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 6.92/7.27 & ( ord_le3102999989581377725nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F @ A4 ) @ ( groups3455450783089532116nteger @ G @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_mono
% 6.92/7.27 thf(fact_7935_prod__mono,axiom,
% 6.92/7.27 ! [A4: set_int,F: int > code_integer,G: int > code_integer] :
% 6.92/7.27 ( ! [I3: int] :
% 6.92/7.27 ( ( member_int @ I3 @ A4 )
% 6.92/7.27 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 6.92/7.27 & ( ord_le3102999989581377725nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.92/7.27 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F @ A4 ) @ ( groups3827104343326376752nteger @ G @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_mono
% 6.92/7.27 thf(fact_7936_prod__mono,axiom,
% 6.92/7.27 ! [A4: set_o,F: $o > rat,G: $o > rat] :
% 6.92/7.27 ( ! [I3: $o] :
% 6.92/7.27 ( ( member_o @ I3 @ A4 )
% 6.92/7.27 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 6.92/7.27 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.92/7.27 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A4 ) @ ( groups2869687844427037835_o_rat @ G @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_mono
% 6.92/7.27 thf(fact_7937_prod__mono,axiom,
% 6.92/7.27 ! [A4: set_nat,F: nat > rat,G: nat > rat] :
% 6.92/7.27 ( ! [I3: nat] :
% 6.92/7.27 ( ( member_nat @ I3 @ A4 )
% 6.92/7.27 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 6.92/7.27 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.92/7.27 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A4 ) @ ( groups73079841787564623at_rat @ G @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_mono
% 6.92/7.27 thf(fact_7938_prod__mono,axiom,
% 6.92/7.27 ! [A4: set_int,F: int > rat,G: int > rat] :
% 6.92/7.27 ( ! [I3: int] :
% 6.92/7.27 ( ( member_int @ I3 @ A4 )
% 6.92/7.27 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 6.92/7.27 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.92/7.27 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A4 ) @ ( groups1072433553688619179nt_rat @ G @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_mono
% 6.92/7.27 thf(fact_7939_prod__mono,axiom,
% 6.92/7.27 ! [A4: set_o,F: $o > nat,G: $o > nat] :
% 6.92/7.27 ( ! [I3: $o] :
% 6.92/7.27 ( ( member_o @ I3 @ A4 )
% 6.92/7.27 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 6.92/7.27 & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.92/7.27 => ( ord_less_eq_nat @ ( groups3504817904513533571_o_nat @ F @ A4 ) @ ( groups3504817904513533571_o_nat @ G @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_mono
% 6.92/7.27 thf(fact_7940_prod__mono,axiom,
% 6.92/7.27 ! [A4: set_int,F: int > nat,G: int > nat] :
% 6.92/7.27 ( ! [I3: int] :
% 6.92/7.27 ( ( member_int @ I3 @ A4 )
% 6.92/7.27 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 6.92/7.27 & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.92/7.27 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A4 ) @ ( groups1707563613775114915nt_nat @ G @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_mono
% 6.92/7.27 thf(fact_7941_prod__mono,axiom,
% 6.92/7.27 ! [A4: set_o,F: $o > int,G: $o > int] :
% 6.92/7.27 ( ! [I3: $o] :
% 6.92/7.27 ( ( member_o @ I3 @ A4 )
% 6.92/7.27 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) )
% 6.92/7.27 & ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.92/7.27 => ( ord_less_eq_int @ ( groups3502327434004483295_o_int @ F @ A4 ) @ ( groups3502327434004483295_o_int @ G @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_mono
% 6.92/7.27 thf(fact_7942_prod__mono,axiom,
% 6.92/7.27 ! [A4: set_nat,F: nat > nat,G: nat > nat] :
% 6.92/7.27 ( ! [I3: nat] :
% 6.92/7.27 ( ( member_nat @ I3 @ A4 )
% 6.92/7.27 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 6.92/7.27 & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.92/7.27 => ( ord_less_eq_nat @ ( groups708209901874060359at_nat @ F @ A4 ) @ ( groups708209901874060359at_nat @ G @ A4 ) ) ) ).
% 6.92/7.27
% 6.92/7.27 % prod_mono
% 6.92/7.27 thf(fact_7943_prod_Ohead__if,axiom,
% 6.92/7.27 ! [N2: nat,M: nat,G: nat > code_integer] :
% 6.92/7.27 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.27 = one_one_Code_integer ) )
% 6.92/7.27 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.27 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.head_if
% 6.92/7.28 thf(fact_7944_prod_Ohead__if,axiom,
% 6.92/7.28 ! [N2: nat,M: nat,G: nat > assn] :
% 6.92/7.28 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = one_one_assn ) )
% 6.92/7.28 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.head_if
% 6.92/7.28 thf(fact_7945_prod_Ohead__if,axiom,
% 6.92/7.28 ! [N2: nat,M: nat,G: nat > rat] :
% 6.92/7.28 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = one_one_rat ) )
% 6.92/7.28 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.head_if
% 6.92/7.28 thf(fact_7946_prod_Ohead__if,axiom,
% 6.92/7.28 ! [N2: nat,M: nat,G: nat > nat] :
% 6.92/7.28 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = one_one_nat ) )
% 6.92/7.28 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.head_if
% 6.92/7.28 thf(fact_7947_prod_Ohead__if,axiom,
% 6.92/7.28 ! [N2: nat,M: nat,G: nat > int] :
% 6.92/7.28 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = one_one_int ) )
% 6.92/7.28 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.head_if
% 6.92/7.28 thf(fact_7948_prod__pos,axiom,
% 6.92/7.28 ! [A4: set_nat,F: nat > nat] :
% 6.92/7.28 ( ! [X3: nat] :
% 6.92/7.28 ( ( member_nat @ X3 @ A4 )
% 6.92/7.28 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 6.92/7.28 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A4 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_pos
% 6.92/7.28 thf(fact_7949_prod__pos,axiom,
% 6.92/7.28 ! [A4: set_nat,F: nat > int] :
% 6.92/7.28 ( ! [X3: nat] :
% 6.92/7.28 ( ( member_nat @ X3 @ A4 )
% 6.92/7.28 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 6.92/7.28 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A4 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_pos
% 6.92/7.28 thf(fact_7950_prod__pos,axiom,
% 6.92/7.28 ! [A4: set_int,F: int > int] :
% 6.92/7.28 ( ! [X3: int] :
% 6.92/7.28 ( ( member_int @ X3 @ A4 )
% 6.92/7.28 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 6.92/7.28 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A4 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_pos
% 6.92/7.28 thf(fact_7951_prod__ge__1,axiom,
% 6.92/7.28 ! [A4: set_o,F: $o > code_integer] :
% 6.92/7.28 ( ! [X3: $o] :
% 6.92/7.28 ( ( member_o @ X3 @ A4 )
% 6.92/7.28 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X3 ) ) )
% 6.92/7.28 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F @ A4 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_ge_1
% 6.92/7.28 thf(fact_7952_prod__ge__1,axiom,
% 6.92/7.28 ! [A4: set_nat,F: nat > code_integer] :
% 6.92/7.28 ( ! [X3: nat] :
% 6.92/7.28 ( ( member_nat @ X3 @ A4 )
% 6.92/7.28 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X3 ) ) )
% 6.92/7.28 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F @ A4 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_ge_1
% 6.92/7.28 thf(fact_7953_prod__ge__1,axiom,
% 6.92/7.28 ! [A4: set_int,F: int > code_integer] :
% 6.92/7.28 ( ! [X3: int] :
% 6.92/7.28 ( ( member_int @ X3 @ A4 )
% 6.92/7.28 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X3 ) ) )
% 6.92/7.28 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F @ A4 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_ge_1
% 6.92/7.28 thf(fact_7954_prod__ge__1,axiom,
% 6.92/7.28 ! [A4: set_o,F: $o > rat] :
% 6.92/7.28 ( ! [X3: $o] :
% 6.92/7.28 ( ( member_o @ X3 @ A4 )
% 6.92/7.28 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 6.92/7.28 => ( ord_less_eq_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ A4 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_ge_1
% 6.92/7.28 thf(fact_7955_prod__ge__1,axiom,
% 6.92/7.28 ! [A4: set_nat,F: nat > rat] :
% 6.92/7.28 ( ! [X3: nat] :
% 6.92/7.28 ( ( member_nat @ X3 @ A4 )
% 6.92/7.28 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 6.92/7.28 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A4 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_ge_1
% 6.92/7.28 thf(fact_7956_prod__ge__1,axiom,
% 6.92/7.28 ! [A4: set_int,F: int > rat] :
% 6.92/7.28 ( ! [X3: int] :
% 6.92/7.28 ( ( member_int @ X3 @ A4 )
% 6.92/7.28 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 6.92/7.28 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A4 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_ge_1
% 6.92/7.28 thf(fact_7957_prod__ge__1,axiom,
% 6.92/7.28 ! [A4: set_o,F: $o > nat] :
% 6.92/7.28 ( ! [X3: $o] :
% 6.92/7.28 ( ( member_o @ X3 @ A4 )
% 6.92/7.28 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 6.92/7.28 => ( ord_less_eq_nat @ one_one_nat @ ( groups3504817904513533571_o_nat @ F @ A4 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_ge_1
% 6.92/7.28 thf(fact_7958_prod__ge__1,axiom,
% 6.92/7.28 ! [A4: set_int,F: int > nat] :
% 6.92/7.28 ( ! [X3: int] :
% 6.92/7.28 ( ( member_int @ X3 @ A4 )
% 6.92/7.28 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 6.92/7.28 => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A4 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_ge_1
% 6.92/7.28 thf(fact_7959_prod__ge__1,axiom,
% 6.92/7.28 ! [A4: set_o,F: $o > int] :
% 6.92/7.28 ( ! [X3: $o] :
% 6.92/7.28 ( ( member_o @ X3 @ A4 )
% 6.92/7.28 => ( ord_less_eq_int @ one_one_int @ ( F @ X3 ) ) )
% 6.92/7.28 => ( ord_less_eq_int @ one_one_int @ ( groups3502327434004483295_o_int @ F @ A4 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_ge_1
% 6.92/7.28 thf(fact_7960_prod__ge__1,axiom,
% 6.92/7.28 ! [A4: set_nat,F: nat > nat] :
% 6.92/7.28 ( ! [X3: nat] :
% 6.92/7.28 ( ( member_nat @ X3 @ A4 )
% 6.92/7.28 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 6.92/7.28 => ( ord_less_eq_nat @ one_one_nat @ ( groups708209901874060359at_nat @ F @ A4 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_ge_1
% 6.92/7.28 thf(fact_7961_atLeastLessThan__subset__iff,axiom,
% 6.92/7.28 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.28 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ A @ B ) @ ( set_or4029947393144176647an_rat @ C2 @ D2 ) )
% 6.92/7.28 => ( ( ord_less_eq_rat @ B @ A )
% 6.92/7.28 | ( ( ord_less_eq_rat @ C2 @ A )
% 6.92/7.28 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastLessThan_subset_iff
% 6.92/7.28 thf(fact_7962_atLeastLessThan__subset__iff,axiom,
% 6.92/7.28 ! [A: num,B: num,C2: num,D2: num] :
% 6.92/7.28 ( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ A @ B ) @ ( set_or1222409239386451017an_num @ C2 @ D2 ) )
% 6.92/7.28 => ( ( ord_less_eq_num @ B @ A )
% 6.92/7.28 | ( ( ord_less_eq_num @ C2 @ A )
% 6.92/7.28 & ( ord_less_eq_num @ B @ D2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastLessThan_subset_iff
% 6.92/7.28 thf(fact_7963_atLeastLessThan__subset__iff,axiom,
% 6.92/7.28 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.28 ( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ A @ B ) @ ( set_or4665077453230672383an_nat @ C2 @ D2 ) )
% 6.92/7.28 => ( ( ord_less_eq_nat @ B @ A )
% 6.92/7.28 | ( ( ord_less_eq_nat @ C2 @ A )
% 6.92/7.28 & ( ord_less_eq_nat @ B @ D2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastLessThan_subset_iff
% 6.92/7.28 thf(fact_7964_atLeastLessThan__subset__iff,axiom,
% 6.92/7.28 ! [A: code_integer,B: code_integer,C2: code_integer,D2: code_integer] :
% 6.92/7.28 ( ( ord_le7084787975880047091nteger @ ( set_or8404916559141939852nteger @ A @ B ) @ ( set_or8404916559141939852nteger @ C2 @ D2 ) )
% 6.92/7.28 => ( ( ord_le3102999989581377725nteger @ B @ A )
% 6.92/7.28 | ( ( ord_le3102999989581377725nteger @ C2 @ A )
% 6.92/7.28 & ( ord_le3102999989581377725nteger @ B @ D2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastLessThan_subset_iff
% 6.92/7.28 thf(fact_7965_atLeastLessThan__subset__iff,axiom,
% 6.92/7.28 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.28 ( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ A @ B ) @ ( set_or4662586982721622107an_int @ C2 @ D2 ) )
% 6.92/7.28 => ( ( ord_less_eq_int @ B @ A )
% 6.92/7.28 | ( ( ord_less_eq_int @ C2 @ A )
% 6.92/7.28 & ( ord_less_eq_int @ B @ D2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastLessThan_subset_iff
% 6.92/7.28 thf(fact_7966_prod_OatLeastAtMost__shift__bounds,axiom,
% 6.92/7.28 ! [G: nat > nat,M: nat,K2: nat,N2: nat] :
% 6.92/7.28 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K2 ) @ ( plus_plus_nat @ N2 @ K2 ) ) )
% 6.92/7.28 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ K2 ) ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeastAtMost_shift_bounds
% 6.92/7.28 thf(fact_7967_prod_OatLeastAtMost__shift__bounds,axiom,
% 6.92/7.28 ! [G: nat > int,M: nat,K2: nat,N2: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K2 ) @ ( plus_plus_nat @ N2 @ K2 ) ) )
% 6.92/7.28 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ ( plus_plus_nat @ K2 ) ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeastAtMost_shift_bounds
% 6.92/7.28 thf(fact_7968_ivl__disj__un__two_I3_J,axiom,
% 6.92/7.28 ! [L: rat,M: rat,U: rat] :
% 6.92/7.28 ( ( ord_less_eq_rat @ L @ M )
% 6.92/7.28 => ( ( ord_less_eq_rat @ M @ U )
% 6.92/7.28 => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ M ) @ ( set_or4029947393144176647an_rat @ M @ U ) )
% 6.92/7.28 = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_two(3)
% 6.92/7.28 thf(fact_7969_ivl__disj__un__two_I3_J,axiom,
% 6.92/7.28 ! [L: num,M: num,U: num] :
% 6.92/7.28 ( ( ord_less_eq_num @ L @ M )
% 6.92/7.28 => ( ( ord_less_eq_num @ M @ U )
% 6.92/7.28 => ( ( sup_sup_set_num @ ( set_or1222409239386451017an_num @ L @ M ) @ ( set_or1222409239386451017an_num @ M @ U ) )
% 6.92/7.28 = ( set_or1222409239386451017an_num @ L @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_two(3)
% 6.92/7.28 thf(fact_7970_ivl__disj__un__two_I3_J,axiom,
% 6.92/7.28 ! [L: nat,M: nat,U: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ L @ M )
% 6.92/7.28 => ( ( ord_less_eq_nat @ M @ U )
% 6.92/7.28 => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ M ) @ ( set_or4665077453230672383an_nat @ M @ U ) )
% 6.92/7.28 = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_two(3)
% 6.92/7.28 thf(fact_7971_ivl__disj__un__two_I3_J,axiom,
% 6.92/7.28 ! [L: code_integer,M: code_integer,U: code_integer] :
% 6.92/7.28 ( ( ord_le3102999989581377725nteger @ L @ M )
% 6.92/7.28 => ( ( ord_le3102999989581377725nteger @ M @ U )
% 6.92/7.28 => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ M ) @ ( set_or8404916559141939852nteger @ M @ U ) )
% 6.92/7.28 = ( set_or8404916559141939852nteger @ L @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_two(3)
% 6.92/7.28 thf(fact_7972_ivl__disj__un__two_I3_J,axiom,
% 6.92/7.28 ! [L: int,M: int,U: int] :
% 6.92/7.28 ( ( ord_less_eq_int @ L @ M )
% 6.92/7.28 => ( ( ord_less_eq_int @ M @ U )
% 6.92/7.28 => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ M ) @ ( set_or4662586982721622107an_int @ M @ U ) )
% 6.92/7.28 = ( set_or4662586982721622107an_int @ L @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_two(3)
% 6.92/7.28 thf(fact_7973_all__nat__less__eq,axiom,
% 6.92/7.28 ! [N2: nat,P2: nat > $o] :
% 6.92/7.28 ( ( ! [M3: nat] :
% 6.92/7.28 ( ( ord_less_nat @ M3 @ N2 )
% 6.92/7.28 => ( P2 @ M3 ) ) )
% 6.92/7.28 = ( ! [X4: nat] :
% 6.92/7.28 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.28 => ( P2 @ X4 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % all_nat_less_eq
% 6.92/7.28 thf(fact_7974_ex__nat__less__eq,axiom,
% 6.92/7.28 ! [N2: nat,P2: nat > $o] :
% 6.92/7.28 ( ( ? [M3: nat] :
% 6.92/7.28 ( ( ord_less_nat @ M3 @ N2 )
% 6.92/7.28 & ( P2 @ M3 ) ) )
% 6.92/7.28 = ( ? [X4: nat] :
% 6.92/7.28 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.28 & ( P2 @ X4 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ex_nat_less_eq
% 6.92/7.28 thf(fact_7975_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat,M: nat] :
% 6.92/7.28 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M ) )
% 6.92/7.28 = ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeastLessThan_rev_at_least_Suc_atMost
% 6.92/7.28 thf(fact_7976_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 6.92/7.28 ! [G: nat > int,N2: nat,M: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ M ) )
% 6.92/7.28 = ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeastLessThan_rev_at_least_Suc_atMost
% 6.92/7.28 thf(fact_7977_pochhammer__prod,axiom,
% 6.92/7.28 ( comm_s4028243227959126397er_rat
% 6.92/7.28 = ( ^ [A5: rat,N: nat] :
% 6.92/7.28 ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ I ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_prod
% 6.92/7.28 thf(fact_7978_pochhammer__prod,axiom,
% 6.92/7.28 ( comm_s8582702949713902594nteger
% 6.92/7.28 = ( ^ [A5: code_integer,N: nat] :
% 6.92/7.28 ( groups3455450783089532116nteger
% 6.92/7.28 @ ^ [I: nat] : ( plus_p5714425477246183910nteger @ A5 @ ( semiri4939895301339042750nteger @ I ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_prod
% 6.92/7.28 thf(fact_7979_pochhammer__prod,axiom,
% 6.92/7.28 ( comm_s4663373288045622133er_nat
% 6.92/7.28 = ( ^ [A5: nat,N: nat] :
% 6.92/7.28 ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ I ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_prod
% 6.92/7.28 thf(fact_7980_pochhammer__prod,axiom,
% 6.92/7.28 ( comm_s4660882817536571857er_int
% 6.92/7.28 = ( ^ [A5: int,N: nat] :
% 6.92/7.28 ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ I ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_prod
% 6.92/7.28 thf(fact_7981_fact__prod__rev,axiom,
% 6.92/7.28 ( semiri1406184849735516958ct_int
% 6.92/7.28 = ( ^ [N: nat] : ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ ( minus_minus_nat @ N ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % fact_prod_rev
% 6.92/7.28 thf(fact_7982_fact__prod__rev,axiom,
% 6.92/7.28 ( semiri3624122377584611663nteger
% 6.92/7.28 = ( ^ [N: nat] : ( semiri4939895301339042750nteger @ ( groups708209901874060359at_nat @ ( minus_minus_nat @ N ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % fact_prod_rev
% 6.92/7.28 thf(fact_7983_fact__prod__rev,axiom,
% 6.92/7.28 ( semiri1408675320244567234ct_nat
% 6.92/7.28 = ( ^ [N: nat] : ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ ( minus_minus_nat @ N ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % fact_prod_rev
% 6.92/7.28 thf(fact_7984_sum_OatLeastLessThan__shift__bounds,axiom,
% 6.92/7.28 ! [G: nat > nat,M: nat,K2: nat,N2: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K2 ) @ ( plus_plus_nat @ N2 @ K2 ) ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ K2 ) ) @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeastLessThan_shift_bounds
% 6.92/7.28 thf(fact_7985_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 6.92/7.28 ! [G: nat > nat,M: nat,N2: nat] :
% 6.92/7.28 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.shift_bounds_cl_Suc_ivl
% 6.92/7.28 thf(fact_7986_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 6.92/7.28 ! [G: nat > int,M: nat,N2: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.shift_bounds_cl_Suc_ivl
% 6.92/7.28 thf(fact_7987_power__sum,axiom,
% 6.92/7.28 ! [C2: nat,F: nat > nat,A4: set_nat] :
% 6.92/7.28 ( ( power_power_nat @ C2 @ ( groups3542108847815614940at_nat @ F @ A4 ) )
% 6.92/7.28 = ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [A5: nat] : ( power_power_nat @ C2 @ ( F @ A5 ) )
% 6.92/7.28 @ A4 ) ) ).
% 6.92/7.28
% 6.92/7.28 % power_sum
% 6.92/7.28 thf(fact_7988_power__sum,axiom,
% 6.92/7.28 ! [C2: int,F: nat > nat,A4: set_nat] :
% 6.92/7.28 ( ( power_power_int @ C2 @ ( groups3542108847815614940at_nat @ F @ A4 ) )
% 6.92/7.28 = ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [A5: nat] : ( power_power_int @ C2 @ ( F @ A5 ) )
% 6.92/7.28 @ A4 ) ) ).
% 6.92/7.28
% 6.92/7.28 % power_sum
% 6.92/7.28 thf(fact_7989_power__sum,axiom,
% 6.92/7.28 ! [C2: int,F: int > nat,A4: set_int] :
% 6.92/7.28 ( ( power_power_int @ C2 @ ( groups4541462559716669496nt_nat @ F @ A4 ) )
% 6.92/7.28 = ( groups1705073143266064639nt_int
% 6.92/7.28 @ ^ [A5: int] : ( power_power_int @ C2 @ ( F @ A5 ) )
% 6.92/7.28 @ A4 ) ) ).
% 6.92/7.28
% 6.92/7.28 % power_sum
% 6.92/7.28 thf(fact_7990_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 6.92/7.28 ! [G: nat > nat,M: nat,K2: nat,N2: nat] :
% 6.92/7.28 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K2 ) @ ( plus_plus_nat @ N2 @ K2 ) ) )
% 6.92/7.28 = ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( plus_plus_nat @ I @ K2 ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.shift_bounds_cl_nat_ivl
% 6.92/7.28 thf(fact_7991_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 6.92/7.28 ! [G: nat > int,M: nat,K2: nat,N2: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K2 ) @ ( plus_plus_nat @ N2 @ K2 ) ) )
% 6.92/7.28 = ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( plus_plus_nat @ I @ K2 ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.shift_bounds_cl_nat_ivl
% 6.92/7.28 thf(fact_7992_sum_Oshift__bounds__Suc__ivl,axiom,
% 6.92/7.28 ! [G: nat > nat,M: nat,N2: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.shift_bounds_Suc_ivl
% 6.92/7.28 thf(fact_7993_sum_Oshift__bounds__nat__ivl,axiom,
% 6.92/7.28 ! [G: nat > nat,M: nat,K2: nat,N2: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K2 ) @ ( plus_plus_nat @ N2 @ K2 ) ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( plus_plus_nat @ I @ K2 ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.shift_bounds_nat_ivl
% 6.92/7.28 thf(fact_7994_prod__le__1,axiom,
% 6.92/7.28 ! [A4: set_o,F: $o > code_integer] :
% 6.92/7.28 ( ! [X3: $o] :
% 6.92/7.28 ( ( member_o @ X3 @ A4 )
% 6.92/7.28 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) )
% 6.92/7.28 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ one_one_Code_integer ) ) )
% 6.92/7.28 => ( ord_le3102999989581377725nteger @ ( groups7694694392188491536nteger @ F @ A4 ) @ one_one_Code_integer ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_le_1
% 6.92/7.28 thf(fact_7995_prod__le__1,axiom,
% 6.92/7.28 ! [A4: set_nat,F: nat > code_integer] :
% 6.92/7.28 ( ! [X3: nat] :
% 6.92/7.28 ( ( member_nat @ X3 @ A4 )
% 6.92/7.28 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) )
% 6.92/7.28 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ one_one_Code_integer ) ) )
% 6.92/7.28 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F @ A4 ) @ one_one_Code_integer ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_le_1
% 6.92/7.28 thf(fact_7996_prod__le__1,axiom,
% 6.92/7.28 ! [A4: set_int,F: int > code_integer] :
% 6.92/7.28 ( ! [X3: int] :
% 6.92/7.28 ( ( member_int @ X3 @ A4 )
% 6.92/7.28 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) )
% 6.92/7.28 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ one_one_Code_integer ) ) )
% 6.92/7.28 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F @ A4 ) @ one_one_Code_integer ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_le_1
% 6.92/7.28 thf(fact_7997_prod__le__1,axiom,
% 6.92/7.28 ! [A4: set_o,F: $o > rat] :
% 6.92/7.28 ( ! [X3: $o] :
% 6.92/7.28 ( ( member_o @ X3 @ A4 )
% 6.92/7.28 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 6.92/7.28 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 6.92/7.28 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A4 ) @ one_one_rat ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_le_1
% 6.92/7.28 thf(fact_7998_prod__le__1,axiom,
% 6.92/7.28 ! [A4: set_nat,F: nat > rat] :
% 6.92/7.28 ( ! [X3: nat] :
% 6.92/7.28 ( ( member_nat @ X3 @ A4 )
% 6.92/7.28 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 6.92/7.28 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 6.92/7.28 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A4 ) @ one_one_rat ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_le_1
% 6.92/7.28 thf(fact_7999_prod__le__1,axiom,
% 6.92/7.28 ! [A4: set_int,F: int > rat] :
% 6.92/7.28 ( ! [X3: int] :
% 6.92/7.28 ( ( member_int @ X3 @ A4 )
% 6.92/7.28 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 6.92/7.28 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 6.92/7.28 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A4 ) @ one_one_rat ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_le_1
% 6.92/7.28 thf(fact_8000_prod__le__1,axiom,
% 6.92/7.28 ! [A4: set_o,F: $o > nat] :
% 6.92/7.28 ( ! [X3: $o] :
% 6.92/7.28 ( ( member_o @ X3 @ A4 )
% 6.92/7.28 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 6.92/7.28 & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 6.92/7.28 => ( ord_less_eq_nat @ ( groups3504817904513533571_o_nat @ F @ A4 ) @ one_one_nat ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_le_1
% 6.92/7.28 thf(fact_8001_prod__le__1,axiom,
% 6.92/7.28 ! [A4: set_int,F: int > nat] :
% 6.92/7.28 ( ! [X3: int] :
% 6.92/7.28 ( ( member_int @ X3 @ A4 )
% 6.92/7.28 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 6.92/7.28 & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 6.92/7.28 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A4 ) @ one_one_nat ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_le_1
% 6.92/7.28 thf(fact_8002_prod__le__1,axiom,
% 6.92/7.28 ! [A4: set_o,F: $o > int] :
% 6.92/7.28 ( ! [X3: $o] :
% 6.92/7.28 ( ( member_o @ X3 @ A4 )
% 6.92/7.28 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) )
% 6.92/7.28 & ( ord_less_eq_int @ ( F @ X3 ) @ one_one_int ) ) )
% 6.92/7.28 => ( ord_less_eq_int @ ( groups3502327434004483295_o_int @ F @ A4 ) @ one_one_int ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_le_1
% 6.92/7.28 thf(fact_8003_prod__le__1,axiom,
% 6.92/7.28 ! [A4: set_nat,F: nat > nat] :
% 6.92/7.28 ( ! [X3: nat] :
% 6.92/7.28 ( ( member_nat @ X3 @ A4 )
% 6.92/7.28 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 6.92/7.28 & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 6.92/7.28 => ( ord_less_eq_nat @ ( groups708209901874060359at_nat @ F @ A4 ) @ one_one_nat ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_le_1
% 6.92/7.28 thf(fact_8004_fact__split,axiom,
% 6.92/7.28 ! [K2: nat,N2: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.28 => ( ( semiri773545260158071498ct_rat @ N2 )
% 6.92/7.28 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N2 @ K2 ) @ N2 ) ) ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ K2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % fact_split
% 6.92/7.28 thf(fact_8005_fact__split,axiom,
% 6.92/7.28 ! [K2: nat,N2: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.28 => ( ( semiri1406184849735516958ct_int @ N2 )
% 6.92/7.28 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N2 @ K2 ) @ N2 ) ) ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ K2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % fact_split
% 6.92/7.28 thf(fact_8006_fact__split,axiom,
% 6.92/7.28 ! [K2: nat,N2: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.28 => ( ( semiri3624122377584611663nteger @ N2 )
% 6.92/7.28 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N2 @ K2 ) @ N2 ) ) ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ K2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % fact_split
% 6.92/7.28 thf(fact_8007_fact__split,axiom,
% 6.92/7.28 ! [K2: nat,N2: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.28 => ( ( semiri1408675320244567234ct_nat @ N2 )
% 6.92/7.28 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N2 @ K2 ) @ N2 ) ) ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % fact_split
% 6.92/7.28 thf(fact_8008_sum_Oivl__cong,axiom,
% 6.92/7.28 ! [A: nat,C2: nat,B: nat,D2: nat,G: nat > nat,H: nat > nat] :
% 6.92/7.28 ( ( A = C2 )
% 6.92/7.28 => ( ( B = D2 )
% 6.92/7.28 => ( ! [X3: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ C2 @ X3 )
% 6.92/7.28 => ( ( ord_less_nat @ X3 @ D2 )
% 6.92/7.28 => ( ( G @ X3 )
% 6.92/7.28 = ( H @ X3 ) ) ) )
% 6.92/7.28 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat @ H @ ( set_or4665077453230672383an_nat @ C2 @ D2 ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.ivl_cong
% 6.92/7.28 thf(fact_8009_sum_Oivl__cong,axiom,
% 6.92/7.28 ! [A: int,C2: int,B: int,D2: int,G: int > int,H: int > int] :
% 6.92/7.28 ( ( A = C2 )
% 6.92/7.28 => ( ( B = D2 )
% 6.92/7.28 => ( ! [X3: int] :
% 6.92/7.28 ( ( ord_less_eq_int @ C2 @ X3 )
% 6.92/7.28 => ( ( ord_less_int @ X3 @ D2 )
% 6.92/7.28 => ( ( G @ X3 )
% 6.92/7.28 = ( H @ X3 ) ) ) )
% 6.92/7.28 => ( ( groups4538972089207619220nt_int @ G @ ( set_or4662586982721622107an_int @ A @ B ) )
% 6.92/7.28 = ( groups4538972089207619220nt_int @ H @ ( set_or4662586982721622107an_int @ C2 @ D2 ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.ivl_cong
% 6.92/7.28 thf(fact_8010_gbinomial__altdef__of__nat,axiom,
% 6.92/7.28 ( gbinomial_rat
% 6.92/7.28 = ( ^ [A5: rat,K3: nat] :
% 6.92/7.28 ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( divide_divide_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ I ) ) @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ K3 @ I ) ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K3 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % gbinomial_altdef_of_nat
% 6.92/7.28 thf(fact_8011_binomial__altdef__of__nat,axiom,
% 6.92/7.28 ! [K2: nat,N2: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ K2 @ N2 )
% 6.92/7.28 => ( ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K2 ) )
% 6.92/7.28 = ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I ) ) @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ K2 @ I ) ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % binomial_altdef_of_nat
% 6.92/7.28 thf(fact_8012_ivl__disj__un__two_I7_J,axiom,
% 6.92/7.28 ! [L: rat,M: rat,U: rat] :
% 6.92/7.28 ( ( ord_less_eq_rat @ L @ M )
% 6.92/7.28 => ( ( ord_less_eq_rat @ M @ U )
% 6.92/7.28 => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ M ) @ ( set_or633870826150836451st_rat @ M @ U ) )
% 6.92/7.28 = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_two(7)
% 6.92/7.28 thf(fact_8013_ivl__disj__un__two_I7_J,axiom,
% 6.92/7.28 ! [L: num,M: num,U: num] :
% 6.92/7.28 ( ( ord_less_eq_num @ L @ M )
% 6.92/7.28 => ( ( ord_less_eq_num @ M @ U )
% 6.92/7.28 => ( ( sup_sup_set_num @ ( set_or1222409239386451017an_num @ L @ M ) @ ( set_or7049704709247886629st_num @ M @ U ) )
% 6.92/7.28 = ( set_or7049704709247886629st_num @ L @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_two(7)
% 6.92/7.28 thf(fact_8014_ivl__disj__un__two_I7_J,axiom,
% 6.92/7.28 ! [L: nat,M: nat,U: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ L @ M )
% 6.92/7.28 => ( ( ord_less_eq_nat @ M @ U )
% 6.92/7.28 => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ M ) @ ( set_or1269000886237332187st_nat @ M @ U ) )
% 6.92/7.28 = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_two(7)
% 6.92/7.28 thf(fact_8015_ivl__disj__un__two_I7_J,axiom,
% 6.92/7.28 ! [L: code_integer,M: code_integer,U: code_integer] :
% 6.92/7.28 ( ( ord_le3102999989581377725nteger @ L @ M )
% 6.92/7.28 => ( ( ord_le3102999989581377725nteger @ M @ U )
% 6.92/7.28 => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ M ) @ ( set_or189985376899183464nteger @ M @ U ) )
% 6.92/7.28 = ( set_or189985376899183464nteger @ L @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_two(7)
% 6.92/7.28 thf(fact_8016_ivl__disj__un__two_I7_J,axiom,
% 6.92/7.28 ! [L: int,M: int,U: int] :
% 6.92/7.28 ( ( ord_less_eq_int @ L @ M )
% 6.92/7.28 => ( ( ord_less_eq_int @ M @ U )
% 6.92/7.28 => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ M ) @ ( set_or1266510415728281911st_int @ M @ U ) )
% 6.92/7.28 = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_two(7)
% 6.92/7.28 thf(fact_8017_gbinomial__mult__fact,axiom,
% 6.92/7.28 ! [K2: nat,A: rat] :
% 6.92/7.28 ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( gbinomial_rat @ A @ K2 ) )
% 6.92/7.28 = ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % gbinomial_mult_fact
% 6.92/7.28 thf(fact_8018_gbinomial__mult__fact_H,axiom,
% 6.92/7.28 ! [A: rat,K2: nat] :
% 6.92/7.28 ( ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ ( semiri773545260158071498ct_rat @ K2 ) )
% 6.92/7.28 = ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % gbinomial_mult_fact'
% 6.92/7.28 thf(fact_8019_gbinomial__prod__rev,axiom,
% 6.92/7.28 ( gbinom7368847122466276068atural
% 6.92/7.28 = ( ^ [A5: code_natural,K3: nat] :
% 6.92/7.28 ( divide5121882707175180666atural
% 6.92/7.28 @ ( groups2279045934846249631atural
% 6.92/7.28 @ ^ [I: nat] : ( minus_7197305767214868737atural @ A5 @ ( semiri3763490453095760265atural @ I ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K3 ) )
% 6.92/7.28 @ ( semiri2447717529341329178atural @ K3 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % gbinomial_prod_rev
% 6.92/7.28 thf(fact_8020_gbinomial__prod__rev,axiom,
% 6.92/7.28 ( gbinomial_rat
% 6.92/7.28 = ( ^ [A5: rat,K3: nat] :
% 6.92/7.28 ( divide_divide_rat
% 6.92/7.28 @ ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ I ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K3 ) )
% 6.92/7.28 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % gbinomial_prod_rev
% 6.92/7.28 thf(fact_8021_gbinomial__prod__rev,axiom,
% 6.92/7.28 ( gbinom8545251970709558553nteger
% 6.92/7.28 = ( ^ [A5: code_integer,K3: nat] :
% 6.92/7.28 ( divide6298287555418463151nteger
% 6.92/7.28 @ ( groups3455450783089532116nteger
% 6.92/7.28 @ ^ [I: nat] : ( minus_8373710615458151222nteger @ A5 @ ( semiri4939895301339042750nteger @ I ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K3 ) )
% 6.92/7.28 @ ( semiri3624122377584611663nteger @ K3 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % gbinomial_prod_rev
% 6.92/7.28 thf(fact_8022_gbinomial__prod__rev,axiom,
% 6.92/7.28 ( gbinomial_nat
% 6.92/7.28 = ( ^ [A5: nat,K3: nat] :
% 6.92/7.28 ( divide_divide_nat
% 6.92/7.28 @ ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( minus_minus_nat @ A5 @ ( semiri1316708129612266289at_nat @ I ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K3 ) )
% 6.92/7.28 @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % gbinomial_prod_rev
% 6.92/7.28 thf(fact_8023_gbinomial__prod__rev,axiom,
% 6.92/7.28 ( gbinomial_int
% 6.92/7.28 = ( ^ [A5: int,K3: nat] :
% 6.92/7.28 ( divide_divide_int
% 6.92/7.28 @ ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( minus_minus_int @ A5 @ ( semiri1314217659103216013at_int @ I ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K3 ) )
% 6.92/7.28 @ ( semiri1406184849735516958ct_int @ K3 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % gbinomial_prod_rev
% 6.92/7.28 thf(fact_8024_sum_OatLeastLessThan__concat,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,P3: nat,G: nat > multis2468970476368604999at_nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 6.92/7.28 => ( ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 6.92/7.28 = ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeastLessThan_concat
% 6.92/7.28 thf(fact_8025_sum_OatLeastLessThan__concat,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,P3: nat,G: nat > rat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 6.92/7.28 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 6.92/7.28 = ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeastLessThan_concat
% 6.92/7.28 thf(fact_8026_sum_OatLeastLessThan__concat,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,P3: nat,G: nat > int] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 6.92/7.28 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 6.92/7.28 = ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeastLessThan_concat
% 6.92/7.28 thf(fact_8027_sum_OatLeastLessThan__concat,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,P3: nat,G: nat > nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 6.92/7.28 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeastLessThan_concat
% 6.92/7.28 thf(fact_8028_sum__diff__nat__ivl,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,P3: nat,F: nat > rat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 6.92/7.28 => ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) )
% 6.92/7.28 = ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_diff_nat_ivl
% 6.92/7.28 thf(fact_8029_sum__diff__nat__ivl,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,P3: nat,F: nat > int] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 6.92/7.28 => ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) )
% 6.92/7.28 = ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_diff_nat_ivl
% 6.92/7.28 thf(fact_8030_bset_I1_J,axiom,
% 6.92/7.28 ! [D4: int,B5: set_int,P2: int > $o,Q2: int > $o] :
% 6.92/7.28 ( ! [X3: int] :
% 6.92/7.28 ( ! [Xa3: int] :
% 6.92/7.28 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb2: int] :
% 6.92/7.28 ( ( member_int @ Xb2 @ B5 )
% 6.92/7.28 => ( X3
% 6.92/7.28 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 6.92/7.28 => ( ( P2 @ X3 )
% 6.92/7.28 => ( P2 @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 6.92/7.28 => ( ! [X3: int] :
% 6.92/7.28 ( ! [Xa3: int] :
% 6.92/7.28 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb2: int] :
% 6.92/7.28 ( ( member_int @ Xb2 @ B5 )
% 6.92/7.28 => ( X3
% 6.92/7.28 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 6.92/7.28 => ( ( Q2 @ X3 )
% 6.92/7.28 => ( Q2 @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ B5 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( plus_plus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( ( P2 @ X6 )
% 6.92/7.28 & ( Q2 @ X6 ) )
% 6.92/7.28 => ( ( P2 @ ( minus_minus_int @ X6 @ D4 ) )
% 6.92/7.28 & ( Q2 @ ( minus_minus_int @ X6 @ D4 ) ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % bset(1)
% 6.92/7.28 thf(fact_8031_bset_I2_J,axiom,
% 6.92/7.28 ! [D4: int,B5: set_int,P2: int > $o,Q2: int > $o] :
% 6.92/7.28 ( ! [X3: int] :
% 6.92/7.28 ( ! [Xa3: int] :
% 6.92/7.28 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb2: int] :
% 6.92/7.28 ( ( member_int @ Xb2 @ B5 )
% 6.92/7.28 => ( X3
% 6.92/7.28 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 6.92/7.28 => ( ( P2 @ X3 )
% 6.92/7.28 => ( P2 @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 6.92/7.28 => ( ! [X3: int] :
% 6.92/7.28 ( ! [Xa3: int] :
% 6.92/7.28 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb2: int] :
% 6.92/7.28 ( ( member_int @ Xb2 @ B5 )
% 6.92/7.28 => ( X3
% 6.92/7.28 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 6.92/7.28 => ( ( Q2 @ X3 )
% 6.92/7.28 => ( Q2 @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ B5 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( plus_plus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( ( P2 @ X6 )
% 6.92/7.28 | ( Q2 @ X6 ) )
% 6.92/7.28 => ( ( P2 @ ( minus_minus_int @ X6 @ D4 ) )
% 6.92/7.28 | ( Q2 @ ( minus_minus_int @ X6 @ D4 ) ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % bset(2)
% 6.92/7.28 thf(fact_8032_aset_I1_J,axiom,
% 6.92/7.28 ! [D4: int,A4: set_int,P2: int > $o,Q2: int > $o] :
% 6.92/7.28 ( ! [X3: int] :
% 6.92/7.28 ( ! [Xa3: int] :
% 6.92/7.28 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb2: int] :
% 6.92/7.28 ( ( member_int @ Xb2 @ A4 )
% 6.92/7.28 => ( X3
% 6.92/7.28 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 6.92/7.28 => ( ( P2 @ X3 )
% 6.92/7.28 => ( P2 @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 6.92/7.28 => ( ! [X3: int] :
% 6.92/7.28 ( ! [Xa3: int] :
% 6.92/7.28 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb2: int] :
% 6.92/7.28 ( ( member_int @ Xb2 @ A4 )
% 6.92/7.28 => ( X3
% 6.92/7.28 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 6.92/7.28 => ( ( Q2 @ X3 )
% 6.92/7.28 => ( Q2 @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ A4 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( minus_minus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( ( P2 @ X6 )
% 6.92/7.28 & ( Q2 @ X6 ) )
% 6.92/7.28 => ( ( P2 @ ( plus_plus_int @ X6 @ D4 ) )
% 6.92/7.28 & ( Q2 @ ( plus_plus_int @ X6 @ D4 ) ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % aset(1)
% 6.92/7.28 thf(fact_8033_aset_I2_J,axiom,
% 6.92/7.28 ! [D4: int,A4: set_int,P2: int > $o,Q2: int > $o] :
% 6.92/7.28 ( ! [X3: int] :
% 6.92/7.28 ( ! [Xa3: int] :
% 6.92/7.28 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb2: int] :
% 6.92/7.28 ( ( member_int @ Xb2 @ A4 )
% 6.92/7.28 => ( X3
% 6.92/7.28 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 6.92/7.28 => ( ( P2 @ X3 )
% 6.92/7.28 => ( P2 @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 6.92/7.28 => ( ! [X3: int] :
% 6.92/7.28 ( ! [Xa3: int] :
% 6.92/7.28 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb2: int] :
% 6.92/7.28 ( ( member_int @ Xb2 @ A4 )
% 6.92/7.28 => ( X3
% 6.92/7.28 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 6.92/7.28 => ( ( Q2 @ X3 )
% 6.92/7.28 => ( Q2 @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ A4 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( minus_minus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( ( P2 @ X6 )
% 6.92/7.28 | ( Q2 @ X6 ) )
% 6.92/7.28 => ( ( P2 @ ( plus_plus_int @ X6 @ D4 ) )
% 6.92/7.28 | ( Q2 @ ( plus_plus_int @ X6 @ D4 ) ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % aset(2)
% 6.92/7.28 thf(fact_8034_atLeastLessThan__add__Un,axiom,
% 6.92/7.28 ! [I2: nat,J2: nat,K2: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.92/7.28 => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J2 @ K2 ) )
% 6.92/7.28 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J2 ) @ ( set_or4665077453230672383an_nat @ J2 @ ( plus_plus_nat @ J2 @ K2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastLessThan_add_Un
% 6.92/7.28 thf(fact_8035_prod_OatLeastAtMost__rev,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat,M: nat] :
% 6.92/7.28 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 6.92/7.28 = ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeastAtMost_rev
% 6.92/7.28 thf(fact_8036_prod_OatLeastAtMost__rev,axiom,
% 6.92/7.28 ! [G: nat > int,N2: nat,M: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 6.92/7.28 = ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeastAtMost_rev
% 6.92/7.28 thf(fact_8037_prod_OatLeast__Suc__atMost,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > assn] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( times_times_assn @ ( G @ M ) @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeast_Suc_atMost
% 6.92/7.28 thf(fact_8038_prod_OatLeast__Suc__atMost,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > rat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeast_Suc_atMost
% 6.92/7.28 thf(fact_8039_prod_OatLeast__Suc__atMost,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeast_Suc_atMost
% 6.92/7.28 thf(fact_8040_prod_OatLeast__Suc__atMost,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > int] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeast_Suc_atMost
% 6.92/7.28 thf(fact_8041_prod_Onat__ivl__Suc_H,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > assn] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 6.92/7.28 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_assn @ ( G @ ( suc @ N2 ) ) @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.nat_ivl_Suc'
% 6.92/7.28 thf(fact_8042_prod_Onat__ivl__Suc_H,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > rat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 6.92/7.28 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_rat @ ( G @ ( suc @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.nat_ivl_Suc'
% 6.92/7.28 thf(fact_8043_prod_Onat__ivl__Suc_H,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 6.92/7.28 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_nat @ ( G @ ( suc @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.nat_ivl_Suc'
% 6.92/7.28 thf(fact_8044_prod_Onat__ivl__Suc_H,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > int] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 6.92/7.28 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_int @ ( G @ ( suc @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.nat_ivl_Suc'
% 6.92/7.28 thf(fact_8045_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 6.92/7.28 ! [A: assn,B: assn,C2: assn,D2: assn] :
% 6.92/7.28 ( ( ord_less_eq_set_assn @ ( set_or7959216805967363635t_assn @ A @ B ) @ ( set_or5523502641901747543n_assn @ C2 @ D2 ) )
% 6.92/7.28 = ( ( ord_less_eq_assn @ A @ B )
% 6.92/7.28 => ( ( ord_less_eq_assn @ C2 @ A )
% 6.92/7.28 & ( ord_less_assn @ B @ D2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 6.92/7.28 thf(fact_8046_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 6.92/7.28 ! [A: set_int,B: set_int,C2: set_int,D2: set_int] :
% 6.92/7.28 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or8585797421378605585et_int @ C2 @ D2 ) )
% 6.92/7.28 = ( ( ord_less_eq_set_int @ A @ B )
% 6.92/7.28 => ( ( ord_less_eq_set_int @ C2 @ A )
% 6.92/7.28 & ( ord_less_set_int @ B @ D2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 6.92/7.28 thf(fact_8047_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 6.92/7.28 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.28 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or4029947393144176647an_rat @ C2 @ D2 ) )
% 6.92/7.28 = ( ( ord_less_eq_rat @ A @ B )
% 6.92/7.28 => ( ( ord_less_eq_rat @ C2 @ A )
% 6.92/7.28 & ( ord_less_rat @ B @ D2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 6.92/7.28 thf(fact_8048_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 6.92/7.28 ! [A: num,B: num,C2: num,D2: num] :
% 6.92/7.28 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or1222409239386451017an_num @ C2 @ D2 ) )
% 6.92/7.28 = ( ( ord_less_eq_num @ A @ B )
% 6.92/7.28 => ( ( ord_less_eq_num @ C2 @ A )
% 6.92/7.28 & ( ord_less_num @ B @ D2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 6.92/7.28 thf(fact_8049_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 6.92/7.28 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.28 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or4665077453230672383an_nat @ C2 @ D2 ) )
% 6.92/7.28 = ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.28 => ( ( ord_less_eq_nat @ C2 @ A )
% 6.92/7.28 & ( ord_less_nat @ B @ D2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 6.92/7.28 thf(fact_8050_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 6.92/7.28 ! [A: code_integer,B: code_integer,C2: code_integer,D2: code_integer] :
% 6.92/7.28 ( ( ord_le7084787975880047091nteger @ ( set_or189985376899183464nteger @ A @ B ) @ ( set_or8404916559141939852nteger @ C2 @ D2 ) )
% 6.92/7.28 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 6.92/7.28 => ( ( ord_le3102999989581377725nteger @ C2 @ A )
% 6.92/7.28 & ( ord_le6747313008572928689nteger @ B @ D2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 6.92/7.28 thf(fact_8051_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 6.92/7.28 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.28 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or4662586982721622107an_int @ C2 @ D2 ) )
% 6.92/7.28 = ( ( ord_less_eq_int @ A @ B )
% 6.92/7.28 => ( ( ord_less_eq_int @ C2 @ A )
% 6.92/7.28 & ( ord_less_int @ B @ D2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 6.92/7.28 thf(fact_8052_atLeastLessThan__subseteq__atLeastAtMost__iff,axiom,
% 6.92/7.28 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.28 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C2 @ D2 ) )
% 6.92/7.28 = ( ( ord_less_rat @ A @ B )
% 6.92/7.28 => ( ( ord_less_eq_rat @ C2 @ A )
% 6.92/7.28 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastLessThan_subseteq_atLeastAtMost_iff
% 6.92/7.28 thf(fact_8053_ivl__disj__un__two__touch_I2_J,axiom,
% 6.92/7.28 ! [L: rat,M: rat,U: rat] :
% 6.92/7.28 ( ( ord_less_eq_rat @ L @ M )
% 6.92/7.28 => ( ( ord_less_rat @ M @ U )
% 6.92/7.28 => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M ) @ ( set_or4029947393144176647an_rat @ M @ U ) )
% 6.92/7.28 = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_two_touch(2)
% 6.92/7.28 thf(fact_8054_ivl__disj__un__two__touch_I2_J,axiom,
% 6.92/7.28 ! [L: num,M: num,U: num] :
% 6.92/7.28 ( ( ord_less_eq_num @ L @ M )
% 6.92/7.28 => ( ( ord_less_num @ M @ U )
% 6.92/7.28 => ( ( sup_sup_set_num @ ( set_or7049704709247886629st_num @ L @ M ) @ ( set_or1222409239386451017an_num @ M @ U ) )
% 6.92/7.28 = ( set_or1222409239386451017an_num @ L @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_two_touch(2)
% 6.92/7.28 thf(fact_8055_ivl__disj__un__two__touch_I2_J,axiom,
% 6.92/7.28 ! [L: nat,M: nat,U: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ L @ M )
% 6.92/7.28 => ( ( ord_less_nat @ M @ U )
% 6.92/7.28 => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M ) @ ( set_or4665077453230672383an_nat @ M @ U ) )
% 6.92/7.28 = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_two_touch(2)
% 6.92/7.28 thf(fact_8056_ivl__disj__un__two__touch_I2_J,axiom,
% 6.92/7.28 ! [L: code_integer,M: code_integer,U: code_integer] :
% 6.92/7.28 ( ( ord_le3102999989581377725nteger @ L @ M )
% 6.92/7.28 => ( ( ord_le6747313008572928689nteger @ M @ U )
% 6.92/7.28 => ( ( sup_su848401254843788991nteger @ ( set_or189985376899183464nteger @ L @ M ) @ ( set_or8404916559141939852nteger @ M @ U ) )
% 6.92/7.28 = ( set_or8404916559141939852nteger @ L @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_two_touch(2)
% 6.92/7.28 thf(fact_8057_ivl__disj__un__two__touch_I2_J,axiom,
% 6.92/7.28 ! [L: int,M: int,U: int] :
% 6.92/7.28 ( ( ord_less_eq_int @ L @ M )
% 6.92/7.28 => ( ( ord_less_int @ M @ U )
% 6.92/7.28 => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M ) @ ( set_or4662586982721622107an_int @ M @ U ) )
% 6.92/7.28 = ( set_or4662586982721622107an_int @ L @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_two_touch(2)
% 6.92/7.28 thf(fact_8058_sum_OatLeast0__lessThan__Suc,axiom,
% 6.92/7.28 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 6.92/7.28 ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeast0_lessThan_Suc
% 6.92/7.28 thf(fact_8059_sum_OatLeast0__lessThan__Suc,axiom,
% 6.92/7.28 ! [G: nat > rat,N2: nat] :
% 6.92/7.28 ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeast0_lessThan_Suc
% 6.92/7.28 thf(fact_8060_sum_OatLeast0__lessThan__Suc,axiom,
% 6.92/7.28 ! [G: nat > int,N2: nat] :
% 6.92/7.28 ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeast0_lessThan_Suc
% 6.92/7.28 thf(fact_8061_sum_OatLeast0__lessThan__Suc,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeast0_lessThan_Suc
% 6.92/7.28 thf(fact_8062_sum_OatLeast0__lessThan__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 6.92/7.28 ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat ) @ ( groups6857163185585827899at_nat @ ( comp_n8698576032424989604at_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeast0_lessThan_Suc_shift
% 6.92/7.28 thf(fact_8063_sum_OatLeast0__lessThan__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > rat,N2: nat] :
% 6.92/7.28 ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_plus_rat @ ( G @ zero_zero_nat ) @ ( groups2906978787729119204at_rat @ ( comp_nat_rat_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeast0_lessThan_Suc_shift
% 6.92/7.28 thf(fact_8064_sum_OatLeast0__lessThan__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > int,N2: nat] :
% 6.92/7.28 ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_plus_int @ ( G @ zero_zero_nat ) @ ( groups3539618377306564664at_int @ ( comp_nat_int_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeast0_lessThan_Suc_shift
% 6.92/7.28 thf(fact_8065_sum_OatLeast0__lessThan__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_plus_nat @ ( G @ zero_zero_nat ) @ ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ suc ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeast0_lessThan_Suc_shift
% 6.92/7.28 thf(fact_8066_sum_OatLeast__Suc__lessThan,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 6.92/7.28 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 6.92/7.28 = ( plus_p7104986032573967614at_nat @ ( G @ M ) @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeast_Suc_lessThan
% 6.92/7.28 thf(fact_8067_sum_OatLeast__Suc__lessThan,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > rat] :
% 6.92/7.28 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 6.92/7.28 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeast_Suc_lessThan
% 6.92/7.28 thf(fact_8068_sum_OatLeast__Suc__lessThan,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > int] :
% 6.92/7.28 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 6.92/7.28 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeast_Suc_lessThan
% 6.92/7.28 thf(fact_8069_sum_OatLeast__Suc__lessThan,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > nat] :
% 6.92/7.28 ( ( ord_less_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 6.92/7.28 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeast_Suc_lessThan
% 6.92/7.28 thf(fact_8070_sum_OatLeastLessThan__Suc,axiom,
% 6.92/7.28 ! [A: nat,B: nat,G: nat > multis2468970476368604999at_nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.28 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 6.92/7.28 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeastLessThan_Suc
% 6.92/7.28 thf(fact_8071_sum_OatLeastLessThan__Suc,axiom,
% 6.92/7.28 ! [A: nat,B: nat,G: nat > rat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 6.92/7.28 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeastLessThan_Suc
% 6.92/7.28 thf(fact_8072_sum_OatLeastLessThan__Suc,axiom,
% 6.92/7.28 ! [A: nat,B: nat,G: nat > int] :
% 6.92/7.28 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.28 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 6.92/7.28 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeastLessThan_Suc
% 6.92/7.28 thf(fact_8073_sum_OatLeastLessThan__Suc,axiom,
% 6.92/7.28 ! [A: nat,B: nat,G: nat > nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ A @ B )
% 6.92/7.28 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 6.92/7.28 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeastLessThan_Suc
% 6.92/7.28 thf(fact_8074_sum_OatLeastLessThan__shift__0,axiom,
% 6.92/7.28 ! [G: nat > nat,M: nat,N2: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ M ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeastLessThan_shift_0
% 6.92/7.28 thf(fact_8075_sum_Olast__plus,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( plus_p7104986032573967614at_nat @ ( G @ N2 ) @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.last_plus
% 6.92/7.28 thf(fact_8076_sum_Olast__plus,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > rat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( plus_plus_rat @ ( G @ N2 ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.last_plus
% 6.92/7.28 thf(fact_8077_sum_Olast__plus,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > int] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( plus_plus_int @ ( G @ N2 ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.last_plus
% 6.92/7.28 thf(fact_8078_sum_Olast__plus,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( plus_plus_nat @ ( G @ N2 ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.last_plus
% 6.92/7.28 thf(fact_8079_aset_I10_J,axiom,
% 6.92/7.28 ! [D2: int,D4: int,A4: set_int,T6: int] :
% 6.92/7.28 ( ( dvd_dvd_int @ D2 @ D4 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ A4 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( minus_minus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ T6 ) )
% 6.92/7.28 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X6 @ D4 ) @ T6 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % aset(10)
% 6.92/7.28 thf(fact_8080_aset_I9_J,axiom,
% 6.92/7.28 ! [D2: int,D4: int,A4: set_int,T6: int] :
% 6.92/7.28 ( ( dvd_dvd_int @ D2 @ D4 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ A4 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( minus_minus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ T6 ) )
% 6.92/7.28 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X6 @ D4 ) @ T6 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % aset(9)
% 6.92/7.28 thf(fact_8081_bset_I10_J,axiom,
% 6.92/7.28 ! [D2: int,D4: int,B5: set_int,T6: int] :
% 6.92/7.28 ( ( dvd_dvd_int @ D2 @ D4 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ B5 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( plus_plus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ T6 ) )
% 6.92/7.28 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ D4 ) @ T6 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % bset(10)
% 6.92/7.28 thf(fact_8082_bset_I9_J,axiom,
% 6.92/7.28 ! [D2: int,D4: int,B5: set_int,T6: int] :
% 6.92/7.28 ( ( dvd_dvd_int @ D2 @ D4 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ B5 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( plus_plus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ T6 ) )
% 6.92/7.28 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ D4 ) @ T6 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % bset(9)
% 6.92/7.28 thf(fact_8083_prod_OSuc__reindex__ivl,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > assn] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_assn @ ( G @ M )
% 6.92/7.28 @ ( groups6906906614972039071t_assn
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.Suc_reindex_ivl
% 6.92/7.28 thf(fact_8084_prod_OSuc__reindex__ivl,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > rat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_rat @ ( G @ M )
% 6.92/7.28 @ ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.Suc_reindex_ivl
% 6.92/7.28 thf(fact_8085_prod_OSuc__reindex__ivl,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_nat @ ( G @ M )
% 6.92/7.28 @ ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.Suc_reindex_ivl
% 6.92/7.28 thf(fact_8086_prod_OSuc__reindex__ivl,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > int] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_int @ ( G @ M )
% 6.92/7.28 @ ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.Suc_reindex_ivl
% 6.92/7.28 thf(fact_8087_atLeastAtMostPlus1__int__conv,axiom,
% 6.92/7.28 ! [M: int,N2: int] :
% 6.92/7.28 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 6.92/7.28 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 6.92/7.28 = ( insert_int @ ( plus_plus_int @ one_one_int @ N2 ) @ ( set_or1266510415728281911st_int @ M @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastAtMostPlus1_int_conv
% 6.92/7.28 thf(fact_8088_prod_OatMost__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > assn,N2: nat] :
% 6.92/7.28 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_assn @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups6906906614972039071t_assn
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atMost_Suc_shift
% 6.92/7.28 thf(fact_8089_prod_OatMost__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > rat,N2: nat] :
% 6.92/7.28 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_rat @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atMost_Suc_shift
% 6.92/7.28 thf(fact_8090_prod_OatMost__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_nat @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atMost_Suc_shift
% 6.92/7.28 thf(fact_8091_prod_OatMost__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > int,N2: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_int @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atMost_Suc_shift
% 6.92/7.28 thf(fact_8092_prod_OatLeast__atMost__pred__shift,axiom,
% 6.92/7.28 ! [G: nat > nat,M: nat,N2: nat] :
% 6.92/7.28 ( ( groups708209901874060359at_nat
% 6.92/7.28 @ ( comp_nat_nat_nat @ G
% 6.92/7.28 @ ^ [N: nat] : ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeast_atMost_pred_shift
% 6.92/7.28 thf(fact_8093_prod_OatLeast__atMost__pred__shift,axiom,
% 6.92/7.28 ! [G: nat > int,M: nat,N2: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int
% 6.92/7.28 @ ( comp_nat_int_nat @ G
% 6.92/7.28 @ ^ [N: nat] : ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeast_atMost_pred_shift
% 6.92/7.28 thf(fact_8094_atLeastLessThanSuc,axiom,
% 6.92/7.28 ! [M: nat,N2: nat] :
% 6.92/7.28 ( ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 6.92/7.28 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) )
% 6.92/7.28 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 6.92/7.28 = bot_bot_set_nat ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastLessThanSuc
% 6.92/7.28 thf(fact_8095_fact__prod,axiom,
% 6.92/7.28 ( semiri1406184849735516958ct_int
% 6.92/7.28 = ( ^ [N: nat] :
% 6.92/7.28 ( semiri1314217659103216013at_int
% 6.92/7.28 @ ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [X4: nat] : X4
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % fact_prod
% 6.92/7.28 thf(fact_8096_fact__prod,axiom,
% 6.92/7.28 ( semiri3624122377584611663nteger
% 6.92/7.28 = ( ^ [N: nat] :
% 6.92/7.28 ( semiri4939895301339042750nteger
% 6.92/7.28 @ ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [X4: nat] : X4
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % fact_prod
% 6.92/7.28 thf(fact_8097_fact__prod,axiom,
% 6.92/7.28 ( semiri1408675320244567234ct_nat
% 6.92/7.28 = ( ^ [N: nat] :
% 6.92/7.28 ( semiri1316708129612266289at_nat
% 6.92/7.28 @ ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [X4: nat] : X4
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % fact_prod
% 6.92/7.28 thf(fact_8098_sum__Suc__diff_H,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,F: nat > rat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [I: nat] : ( minus_minus_rat @ ( F @ ( suc @ I ) ) @ ( F @ I ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 6.92/7.28 = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_Suc_diff'
% 6.92/7.28 thf(fact_8099_sum__Suc__diff_H,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,F: nat > int] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups3539618377306564664at_int
% 6.92/7.28 @ ^ [I: nat] : ( minus_minus_int @ ( F @ ( suc @ I ) ) @ ( F @ I ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 6.92/7.28 = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_Suc_diff'
% 6.92/7.28 thf(fact_8100_sum_OatLeast__lessThan__pred__shift,axiom,
% 6.92/7.28 ! [G: nat > nat,M: nat,N2: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat
% 6.92/7.28 @ ( comp_nat_nat_nat @ G
% 6.92/7.28 @ ^ [N: nat] : ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeast_lessThan_pred_shift
% 6.92/7.28 thf(fact_8101_sum_OatLeastLessThan__rev,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat,M: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ ( suc @ I ) ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ N2 @ M ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeastLessThan_rev
% 6.92/7.28 thf(fact_8102_sum_Onested__swap,axiom,
% 6.92/7.28 ! [A: nat > nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [I: nat] : ( groups3542108847815614940at_nat @ ( A @ I ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [J: nat] :
% 6.92/7.28 ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [I: nat] : ( A @ I @ J )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N2 ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.nested_swap
% 6.92/7.28 thf(fact_8103_prod__atLeastAtMost__code,axiom,
% 6.92/7.28 ! [F: nat > code_integer,A: nat,B: nat] :
% 6.92/7.28 ( ( groups3455450783089532116nteger @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 6.92/7.28 = ( set_fo1084959871951514735nteger
% 6.92/7.28 @ ^ [A5: nat] : ( times_3573771949741848930nteger @ ( F @ A5 ) )
% 6.92/7.28 @ A
% 6.92/7.28 @ B
% 6.92/7.28 @ one_one_Code_integer ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_atLeastAtMost_code
% 6.92/7.28 thf(fact_8104_prod__atLeastAtMost__code,axiom,
% 6.92/7.28 ! [F: nat > assn,A: nat,B: nat] :
% 6.92/7.28 ( ( groups6906906614972039071t_assn @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 6.92/7.28 = ( set_fo1959793692361082170t_assn
% 6.92/7.28 @ ^ [A5: nat] : ( times_times_assn @ ( F @ A5 ) )
% 6.92/7.28 @ A
% 6.92/7.28 @ B
% 6.92/7.28 @ one_one_assn ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_atLeastAtMost_code
% 6.92/7.28 thf(fact_8105_prod__atLeastAtMost__code,axiom,
% 6.92/7.28 ! [F: nat > rat,A: nat,B: nat] :
% 6.92/7.28 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 6.92/7.28 = ( set_fo1949268297981939178at_rat
% 6.92/7.28 @ ^ [A5: nat] : ( times_times_rat @ ( F @ A5 ) )
% 6.92/7.28 @ A
% 6.92/7.28 @ B
% 6.92/7.28 @ one_one_rat ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_atLeastAtMost_code
% 6.92/7.28 thf(fact_8106_prod__atLeastAtMost__code,axiom,
% 6.92/7.28 ! [F: nat > nat,A: nat,B: nat] :
% 6.92/7.28 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 6.92/7.28 = ( set_fo2584398358068434914at_nat
% 6.92/7.28 @ ^ [A5: nat] : ( times_times_nat @ ( F @ A5 ) )
% 6.92/7.28 @ A
% 6.92/7.28 @ B
% 6.92/7.28 @ one_one_nat ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_atLeastAtMost_code
% 6.92/7.28 thf(fact_8107_prod__atLeastAtMost__code,axiom,
% 6.92/7.28 ! [F: nat > int,A: nat,B: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 6.92/7.28 = ( set_fo2581907887559384638at_int
% 6.92/7.28 @ ^ [A5: nat] : ( times_times_int @ ( F @ A5 ) )
% 6.92/7.28 @ A
% 6.92/7.28 @ B
% 6.92/7.28 @ one_one_int ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_atLeastAtMost_code
% 6.92/7.28 thf(fact_8108_prod_OatLeastAtMost__shift__0,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( groups708209901874060359at_nat @ ( comp_nat_nat_nat @ G @ ( plus_plus_nat @ M ) ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeastAtMost_shift_0
% 6.92/7.28 thf(fact_8109_prod_OatLeastAtMost__shift__0,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > int] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.28 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ ( plus_plus_nat @ M ) ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeastAtMost_shift_0
% 6.92/7.28 thf(fact_8110_prod_Oub__add__nat,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > assn,P3: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 6.92/7.28 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 6.92/7.28 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.ub_add_nat
% 6.92/7.28 thf(fact_8111_prod_Oub__add__nat,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > rat,P3: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 6.92/7.28 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 6.92/7.28 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.ub_add_nat
% 6.92/7.28 thf(fact_8112_prod_Oub__add__nat,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > nat,P3: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 6.92/7.28 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 6.92/7.28 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.ub_add_nat
% 6.92/7.28 thf(fact_8113_prod_Oub__add__nat,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,G: nat > int,P3: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 6.92/7.28 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 6.92/7.28 = ( 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 ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.ub_add_nat
% 6.92/7.28 thf(fact_8114_ivl__disj__un__singleton_I6_J,axiom,
% 6.92/7.28 ! [L: $o,U: $o] :
% 6.92/7.28 ( ( ord_less_eq_o @ L @ U )
% 6.92/7.28 => ( ( sup_sup_set_o @ ( set_or7139685690850216873Than_o @ L @ U ) @ ( insert_o @ U @ bot_bot_set_o ) )
% 6.92/7.28 = ( set_or8904488021354931149Most_o @ L @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_singleton(6)
% 6.92/7.28 thf(fact_8115_ivl__disj__un__singleton_I6_J,axiom,
% 6.92/7.28 ! [L: rat,U: rat] :
% 6.92/7.28 ( ( ord_less_eq_rat @ L @ U )
% 6.92/7.28 => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ U ) @ ( insert_rat @ U @ bot_bot_set_rat ) )
% 6.92/7.28 = ( set_or633870826150836451st_rat @ L @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_singleton(6)
% 6.92/7.28 thf(fact_8116_ivl__disj__un__singleton_I6_J,axiom,
% 6.92/7.28 ! [L: num,U: num] :
% 6.92/7.28 ( ( ord_less_eq_num @ L @ U )
% 6.92/7.28 => ( ( sup_sup_set_num @ ( set_or1222409239386451017an_num @ L @ U ) @ ( insert_num @ U @ bot_bot_set_num ) )
% 6.92/7.28 = ( set_or7049704709247886629st_num @ L @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_singleton(6)
% 6.92/7.28 thf(fact_8117_ivl__disj__un__singleton_I6_J,axiom,
% 6.92/7.28 ! [L: nat,U: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ L @ U )
% 6.92/7.28 => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ U ) @ ( insert_nat @ U @ bot_bot_set_nat ) )
% 6.92/7.28 = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_singleton(6)
% 6.92/7.28 thf(fact_8118_ivl__disj__un__singleton_I6_J,axiom,
% 6.92/7.28 ! [L: code_integer,U: code_integer] :
% 6.92/7.28 ( ( ord_le3102999989581377725nteger @ L @ U )
% 6.92/7.28 => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ U ) @ ( insert_Code_integer @ U @ bot_bo3990330152332043303nteger ) )
% 6.92/7.28 = ( set_or189985376899183464nteger @ L @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_singleton(6)
% 6.92/7.28 thf(fact_8119_ivl__disj__un__singleton_I6_J,axiom,
% 6.92/7.28 ! [L: int,U: int] :
% 6.92/7.28 ( ( ord_less_eq_int @ L @ U )
% 6.92/7.28 => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ U ) @ ( insert_int @ U @ bot_bot_set_int ) )
% 6.92/7.28 = ( set_or1266510415728281911st_int @ L @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_singleton(6)
% 6.92/7.28 thf(fact_8120_sum_Ohead__if,axiom,
% 6.92/7.28 ! [N2: nat,M: nat,G: nat > code_integer] :
% 6.92/7.28 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = zero_z3403309356797280102nteger ) )
% 6.92/7.28 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.head_if
% 6.92/7.28 thf(fact_8121_sum_Ohead__if,axiom,
% 6.92/7.28 ! [N2: nat,M: nat,G: nat > multis2468970476368604999at_nat] :
% 6.92/7.28 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = zero_z1048942125864253310at_nat ) )
% 6.92/7.28 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.head_if
% 6.92/7.28 thf(fact_8122_sum_Ohead__if,axiom,
% 6.92/7.28 ! [N2: nat,M: nat,G: nat > rat] :
% 6.92/7.28 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = zero_zero_rat ) )
% 6.92/7.28 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.head_if
% 6.92/7.28 thf(fact_8123_sum_Ohead__if,axiom,
% 6.92/7.28 ! [N2: nat,M: nat,G: nat > int] :
% 6.92/7.28 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = zero_zero_int ) )
% 6.92/7.28 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.head_if
% 6.92/7.28 thf(fact_8124_sum_Ohead__if,axiom,
% 6.92/7.28 ! [N2: nat,M: nat,G: nat > nat] :
% 6.92/7.28 ( ( ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = zero_zero_nat ) )
% 6.92/7.28 & ( ~ ( ord_less_nat @ N2 @ M )
% 6.92/7.28 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 6.92/7.28 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.head_if
% 6.92/7.28 thf(fact_8125_periodic__finite__ex,axiom,
% 6.92/7.28 ! [D2: int,P2: int > $o] :
% 6.92/7.28 ( ( ord_less_int @ zero_zero_int @ D2 )
% 6.92/7.28 => ( ! [X3: int,K: int] :
% 6.92/7.28 ( ( P2 @ X3 )
% 6.92/7.28 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D2 ) ) ) )
% 6.92/7.28 => ( ( ? [X11: int] : ( P2 @ X11 ) )
% 6.92/7.28 = ( ? [X4: int] :
% 6.92/7.28 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D2 ) )
% 6.92/7.28 & ( P2 @ X4 ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % periodic_finite_ex
% 6.92/7.28 thf(fact_8126_bset_I3_J,axiom,
% 6.92/7.28 ! [D4: int,T6: int,B5: set_int] :
% 6.92/7.28 ( ( ord_less_int @ zero_zero_int @ D4 )
% 6.92/7.28 => ( ( member_int @ ( minus_minus_int @ T6 @ one_one_int ) @ B5 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ B5 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( plus_plus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( X6 = T6 )
% 6.92/7.28 => ( ( minus_minus_int @ X6 @ D4 )
% 6.92/7.28 = T6 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % bset(3)
% 6.92/7.28 thf(fact_8127_bset_I4_J,axiom,
% 6.92/7.28 ! [D4: int,T6: int,B5: set_int] :
% 6.92/7.28 ( ( ord_less_int @ zero_zero_int @ D4 )
% 6.92/7.28 => ( ( member_int @ T6 @ B5 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ B5 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( plus_plus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( X6 != T6 )
% 6.92/7.28 => ( ( minus_minus_int @ X6 @ D4 )
% 6.92/7.28 != T6 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % bset(4)
% 6.92/7.28 thf(fact_8128_bset_I5_J,axiom,
% 6.92/7.28 ! [D4: int,B5: set_int,T6: int] :
% 6.92/7.28 ( ( ord_less_int @ zero_zero_int @ D4 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ B5 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( plus_plus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( ord_less_int @ X6 @ T6 )
% 6.92/7.28 => ( ord_less_int @ ( minus_minus_int @ X6 @ D4 ) @ T6 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % bset(5)
% 6.92/7.28 thf(fact_8129_bset_I7_J,axiom,
% 6.92/7.28 ! [D4: int,T6: int,B5: set_int] :
% 6.92/7.28 ( ( ord_less_int @ zero_zero_int @ D4 )
% 6.92/7.28 => ( ( member_int @ T6 @ B5 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ B5 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( plus_plus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( ord_less_int @ T6 @ X6 )
% 6.92/7.28 => ( ord_less_int @ T6 @ ( minus_minus_int @ X6 @ D4 ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % bset(7)
% 6.92/7.28 thf(fact_8130_aset_I3_J,axiom,
% 6.92/7.28 ! [D4: int,T6: int,A4: set_int] :
% 6.92/7.28 ( ( ord_less_int @ zero_zero_int @ D4 )
% 6.92/7.28 => ( ( member_int @ ( plus_plus_int @ T6 @ one_one_int ) @ A4 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ A4 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( minus_minus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( X6 = T6 )
% 6.92/7.28 => ( ( plus_plus_int @ X6 @ D4 )
% 6.92/7.28 = T6 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % aset(3)
% 6.92/7.28 thf(fact_8131_aset_I4_J,axiom,
% 6.92/7.28 ! [D4: int,T6: int,A4: set_int] :
% 6.92/7.28 ( ( ord_less_int @ zero_zero_int @ D4 )
% 6.92/7.28 => ( ( member_int @ T6 @ A4 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ A4 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( minus_minus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( X6 != T6 )
% 6.92/7.28 => ( ( plus_plus_int @ X6 @ D4 )
% 6.92/7.28 != T6 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % aset(4)
% 6.92/7.28 thf(fact_8132_aset_I5_J,axiom,
% 6.92/7.28 ! [D4: int,T6: int,A4: set_int] :
% 6.92/7.28 ( ( ord_less_int @ zero_zero_int @ D4 )
% 6.92/7.28 => ( ( member_int @ T6 @ A4 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ A4 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( minus_minus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( ord_less_int @ X6 @ T6 )
% 6.92/7.28 => ( ord_less_int @ ( plus_plus_int @ X6 @ D4 ) @ T6 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % aset(5)
% 6.92/7.28 thf(fact_8133_aset_I7_J,axiom,
% 6.92/7.28 ! [D4: int,A4: set_int,T6: int] :
% 6.92/7.28 ( ( ord_less_int @ zero_zero_int @ D4 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ A4 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( minus_minus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( ord_less_int @ T6 @ X6 )
% 6.92/7.28 => ( ord_less_int @ T6 @ ( plus_plus_int @ X6 @ D4 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % aset(7)
% 6.92/7.28 thf(fact_8134_atLeastLessThan__nat__numeral,axiom,
% 6.92/7.28 ! [M: nat,K2: num] :
% 6.92/7.28 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K2 ) )
% 6.92/7.28 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K2 ) )
% 6.92/7.28 = ( insert_nat @ ( pred_numeral @ K2 ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K2 ) ) ) ) )
% 6.92/7.28 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K2 ) )
% 6.92/7.28 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K2 ) )
% 6.92/7.28 = bot_bot_set_nat ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastLessThan_nat_numeral
% 6.92/7.28 thf(fact_8135_fact__eq__fact__times,axiom,
% 6.92/7.28 ! [N2: nat,M: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.28 => ( ( semiri1408675320244567234ct_nat @ M )
% 6.92/7.28 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N2 )
% 6.92/7.28 @ ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [X4: nat] : X4
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % fact_eq_fact_times
% 6.92/7.28 thf(fact_8136_sum_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat,M: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeastLessThan_rev_at_least_Suc_atMost
% 6.92/7.28 thf(fact_8137_simp__from__to,axiom,
% 6.92/7.28 ( set_or1266510415728281911st_int
% 6.92/7.28 = ( ^ [I: int,J: int] : ( if_set_int @ ( ord_less_int @ J @ I ) @ bot_bot_set_int @ ( insert_int @ I @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % simp_from_to
% 6.92/7.28 thf(fact_8138_aset_I8_J,axiom,
% 6.92/7.28 ! [D4: int,A4: set_int,T6: int] :
% 6.92/7.28 ( ( ord_less_int @ zero_zero_int @ D4 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ A4 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( minus_minus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( ord_less_eq_int @ T6 @ X6 )
% 6.92/7.28 => ( ord_less_eq_int @ T6 @ ( plus_plus_int @ X6 @ D4 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % aset(8)
% 6.92/7.28 thf(fact_8139_aset_I6_J,axiom,
% 6.92/7.28 ! [D4: int,T6: int,A4: set_int] :
% 6.92/7.28 ( ( ord_less_int @ zero_zero_int @ D4 )
% 6.92/7.28 => ( ( member_int @ ( plus_plus_int @ T6 @ one_one_int ) @ A4 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ A4 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( minus_minus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( ord_less_eq_int @ X6 @ T6 )
% 6.92/7.28 => ( ord_less_eq_int @ ( plus_plus_int @ X6 @ D4 ) @ T6 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % aset(6)
% 6.92/7.28 thf(fact_8140_bset_I8_J,axiom,
% 6.92/7.28 ! [D4: int,T6: int,B5: set_int] :
% 6.92/7.28 ( ( ord_less_int @ zero_zero_int @ D4 )
% 6.92/7.28 => ( ( member_int @ ( minus_minus_int @ T6 @ one_one_int ) @ B5 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ B5 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( plus_plus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( ord_less_eq_int @ T6 @ X6 )
% 6.92/7.28 => ( ord_less_eq_int @ T6 @ ( minus_minus_int @ X6 @ D4 ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % bset(8)
% 6.92/7.28 thf(fact_8141_bset_I6_J,axiom,
% 6.92/7.28 ! [D4: int,B5: set_int,T6: int] :
% 6.92/7.28 ( ( ord_less_int @ zero_zero_int @ D4 )
% 6.92/7.28 => ! [X6: int] :
% 6.92/7.28 ( ! [Xa4: int] :
% 6.92/7.28 ( ( member_int @ Xa4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb3: int] :
% 6.92/7.28 ( ( member_int @ Xb3 @ B5 )
% 6.92/7.28 => ( X6
% 6.92/7.28 != ( plus_plus_int @ Xb3 @ Xa4 ) ) ) )
% 6.92/7.28 => ( ( ord_less_eq_int @ X6 @ T6 )
% 6.92/7.28 => ( ord_less_eq_int @ ( minus_minus_int @ X6 @ D4 ) @ T6 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % bset(6)
% 6.92/7.28 thf(fact_8142_cpmi,axiom,
% 6.92/7.28 ! [D4: int,P2: int > $o,P6: int > $o,B5: set_int] :
% 6.92/7.28 ( ( ord_less_int @ zero_zero_int @ D4 )
% 6.92/7.28 => ( ? [Z6: int] :
% 6.92/7.28 ! [X3: int] :
% 6.92/7.28 ( ( ord_less_int @ X3 @ Z6 )
% 6.92/7.28 => ( ( P2 @ X3 )
% 6.92/7.28 = ( P6 @ X3 ) ) )
% 6.92/7.28 => ( ! [X3: int] :
% 6.92/7.28 ( ! [Xa3: int] :
% 6.92/7.28 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb2: int] :
% 6.92/7.28 ( ( member_int @ Xb2 @ B5 )
% 6.92/7.28 => ( X3
% 6.92/7.28 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 6.92/7.28 => ( ( P2 @ X3 )
% 6.92/7.28 => ( P2 @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 6.92/7.28 => ( ! [X3: int,K: int] :
% 6.92/7.28 ( ( P6 @ X3 )
% 6.92/7.28 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D4 ) ) ) )
% 6.92/7.28 => ( ( ? [X11: int] : ( P2 @ X11 ) )
% 6.92/7.28 = ( ? [X4: int] :
% 6.92/7.28 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 & ( P6 @ X4 ) )
% 6.92/7.28 | ? [X4: int] :
% 6.92/7.28 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 & ? [Y4: int] :
% 6.92/7.28 ( ( member_int @ Y4 @ B5 )
% 6.92/7.28 & ( P2 @ ( plus_plus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % cpmi
% 6.92/7.28 thf(fact_8143_cppi,axiom,
% 6.92/7.28 ! [D4: int,P2: int > $o,P6: int > $o,A4: set_int] :
% 6.92/7.28 ( ( ord_less_int @ zero_zero_int @ D4 )
% 6.92/7.28 => ( ? [Z6: int] :
% 6.92/7.28 ! [X3: int] :
% 6.92/7.28 ( ( ord_less_int @ Z6 @ X3 )
% 6.92/7.28 => ( ( P2 @ X3 )
% 6.92/7.28 = ( P6 @ X3 ) ) )
% 6.92/7.28 => ( ! [X3: int] :
% 6.92/7.28 ( ! [Xa3: int] :
% 6.92/7.28 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 => ! [Xb2: int] :
% 6.92/7.28 ( ( member_int @ Xb2 @ A4 )
% 6.92/7.28 => ( X3
% 6.92/7.28 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 6.92/7.28 => ( ( P2 @ X3 )
% 6.92/7.28 => ( P2 @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 6.92/7.28 => ( ! [X3: int,K: int] :
% 6.92/7.28 ( ( P6 @ X3 )
% 6.92/7.28 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D4 ) ) ) )
% 6.92/7.28 => ( ( ? [X11: int] : ( P2 @ X11 ) )
% 6.92/7.28 = ( ? [X4: int] :
% 6.92/7.28 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 & ( P6 @ X4 ) )
% 6.92/7.28 | ? [X4: int] :
% 6.92/7.28 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 6.92/7.28 & ? [Y4: int] :
% 6.92/7.28 ( ( member_int @ Y4 @ A4 )
% 6.92/7.28 & ( P2 @ ( minus_minus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % cppi
% 6.92/7.28 thf(fact_8144_pochhammer__Suc__prod,axiom,
% 6.92/7.28 ! [A: rat,N2: nat] :
% 6.92/7.28 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 6.92/7.28 = ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_Suc_prod
% 6.92/7.28 thf(fact_8145_pochhammer__Suc__prod,axiom,
% 6.92/7.28 ! [A: code_integer,N2: nat] :
% 6.92/7.28 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 6.92/7.28 = ( groups3455450783089532116nteger
% 6.92/7.28 @ ^ [I: nat] : ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_Suc_prod
% 6.92/7.28 thf(fact_8146_pochhammer__Suc__prod,axiom,
% 6.92/7.28 ! [A: nat,N2: nat] :
% 6.92/7.28 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 6.92/7.28 = ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_Suc_prod
% 6.92/7.28 thf(fact_8147_pochhammer__Suc__prod,axiom,
% 6.92/7.28 ! [A: int,N2: nat] :
% 6.92/7.28 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 6.92/7.28 = ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_Suc_prod
% 6.92/7.28 thf(fact_8148_pochhammer__prod__rev,axiom,
% 6.92/7.28 ( comm_s4028243227959126397er_rat
% 6.92/7.28 = ( ^ [A5: rat,N: nat] :
% 6.92/7.28 ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I ) ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_prod_rev
% 6.92/7.28 thf(fact_8149_pochhammer__prod__rev,axiom,
% 6.92/7.28 ( comm_s8582702949713902594nteger
% 6.92/7.28 = ( ^ [A5: code_integer,N: nat] :
% 6.92/7.28 ( groups3455450783089532116nteger
% 6.92/7.28 @ ^ [I: nat] : ( plus_p5714425477246183910nteger @ A5 @ ( semiri4939895301339042750nteger @ ( minus_minus_nat @ N @ I ) ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_prod_rev
% 6.92/7.28 thf(fact_8150_pochhammer__prod__rev,axiom,
% 6.92/7.28 ( comm_s4663373288045622133er_nat
% 6.92/7.28 = ( ^ [A5: nat,N: nat] :
% 6.92/7.28 ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I ) ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_prod_rev
% 6.92/7.28 thf(fact_8151_pochhammer__prod__rev,axiom,
% 6.92/7.28 ( comm_s4660882817536571857er_int
% 6.92/7.28 = ( ^ [A5: int,N: nat] :
% 6.92/7.28 ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I ) ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_prod_rev
% 6.92/7.28 thf(fact_8152_fact__div__fact,axiom,
% 6.92/7.28 ! [N2: nat,M: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ N2 @ M )
% 6.92/7.28 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) )
% 6.92/7.28 = ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [X4: nat] : X4
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % fact_div_fact
% 6.92/7.28 thf(fact_8153_prod_Oin__pairs,axiom,
% 6.92/7.28 ! [G: nat > assn,M: nat,N2: nat] :
% 6.92/7.28 ( ( 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 ) ) ) )
% 6.92/7.28 = ( groups6906906614972039071t_assn
% 6.92/7.28 @ ^ [I: nat] : ( times_times_assn @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.in_pairs
% 6.92/7.28 thf(fact_8154_prod_Oin__pairs,axiom,
% 6.92/7.28 ! [G: nat > rat,M: nat,N2: nat] :
% 6.92/7.28 ( ( 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 ) ) ) )
% 6.92/7.28 = ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.in_pairs
% 6.92/7.28 thf(fact_8155_prod_Oin__pairs,axiom,
% 6.92/7.28 ! [G: nat > nat,M: nat,N2: nat] :
% 6.92/7.28 ( ( 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 ) ) ) )
% 6.92/7.28 = ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.in_pairs
% 6.92/7.28 thf(fact_8156_prod_Oin__pairs,axiom,
% 6.92/7.28 ! [G: nat > int,M: nat,N2: nat] :
% 6.92/7.28 ( ( 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 ) ) ) )
% 6.92/7.28 = ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.in_pairs
% 6.92/7.28 thf(fact_8157_prod_Oin__pairs__0,axiom,
% 6.92/7.28 ! [G: nat > assn,N2: nat] :
% 6.92/7.28 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 6.92/7.28 = ( groups6906906614972039071t_assn
% 6.92/7.28 @ ^ [I: nat] : ( times_times_assn @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.in_pairs_0
% 6.92/7.28 thf(fact_8158_prod_Oin__pairs__0,axiom,
% 6.92/7.28 ! [G: nat > rat,N2: nat] :
% 6.92/7.28 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 6.92/7.28 = ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.in_pairs_0
% 6.92/7.28 thf(fact_8159_prod_Oin__pairs__0,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 6.92/7.28 = ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.in_pairs_0
% 6.92/7.28 thf(fact_8160_prod_Oin__pairs__0,axiom,
% 6.92/7.28 ! [G: nat > int,N2: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 6.92/7.28 = ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.in_pairs_0
% 6.92/7.28 thf(fact_8161_pochhammer__Suc__prod__rev,axiom,
% 6.92/7.28 ! [A: rat,N2: nat] :
% 6.92/7.28 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 6.92/7.28 = ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I ) ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_Suc_prod_rev
% 6.92/7.28 thf(fact_8162_pochhammer__Suc__prod__rev,axiom,
% 6.92/7.28 ! [A: code_integer,N2: nat] :
% 6.92/7.28 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 6.92/7.28 = ( groups3455450783089532116nteger
% 6.92/7.28 @ ^ [I: nat] : ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ ( minus_minus_nat @ N2 @ I ) ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_Suc_prod_rev
% 6.92/7.28 thf(fact_8163_pochhammer__Suc__prod__rev,axiom,
% 6.92/7.28 ! [A: nat,N2: nat] :
% 6.92/7.28 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 6.92/7.28 = ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I ) ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_Suc_prod_rev
% 6.92/7.28 thf(fact_8164_pochhammer__Suc__prod__rev,axiom,
% 6.92/7.28 ! [A: int,N2: nat] :
% 6.92/7.28 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 6.92/7.28 = ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I ) ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % pochhammer_Suc_prod_rev
% 6.92/7.28 thf(fact_8165_divmod__integer__code,axiom,
% 6.92/7.28 ( code_divmod_integer
% 6.92/7.28 = ( ^ [K3: code_integer,L2: code_integer] :
% 6.92/7.28 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 6.92/7.28 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L2 )
% 6.92/7.28 @ ( produc6916734918728496179nteger
% 6.92/7.28 @ ^ [R5: code_integer,S5: code_integer] : ( if_Pro6119634080678213985nteger @ ( S5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S5 ) ) )
% 6.92/7.28 @ ( code_divmod_abs @ K3 @ L2 ) ) )
% 6.92/7.28 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 6.92/7.28 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 6.92/7.28 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L2 )
% 6.92/7.28 @ ( produc6916734918728496179nteger
% 6.92/7.28 @ ^ [R5: code_integer,S5: code_integer] : ( if_Pro6119634080678213985nteger @ ( S5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S5 ) ) )
% 6.92/7.28 @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % divmod_integer_code
% 6.92/7.28 thf(fact_8166_horner__sum__eq__sum,axiom,
% 6.92/7.28 ( groups6853238114764508677at_rat
% 6.92/7.28 = ( ^ [F3: nat > rat,A5: rat,Xs3: list_nat] :
% 6.92/7.28 ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [N: nat] : ( times_times_rat @ ( F3 @ ( nth_nat @ Xs3 @ N ) ) @ ( power_power_rat @ A5 @ N ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs3 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % horner_sum_eq_sum
% 6.92/7.28 thf(fact_8167_horner__sum__eq__sum,axiom,
% 6.92/7.28 ( groups8483887719401441109_o_rat
% 6.92/7.28 = ( ^ [F3: $o > rat,A5: rat,Xs3: list_o] :
% 6.92/7.28 ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [N: nat] : ( times_times_rat @ ( F3 @ ( nth_o @ Xs3 @ N ) ) @ ( power_power_rat @ A5 @ N ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_o @ Xs3 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % horner_sum_eq_sum
% 6.92/7.28 thf(fact_8168_horner__sum__eq__sum,axiom,
% 6.92/7.28 ( groups7852591826665563233nt_rat
% 6.92/7.28 = ( ^ [F3: int > rat,A5: rat,Xs3: list_int] :
% 6.92/7.28 ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [N: nat] : ( times_times_rat @ ( F3 @ ( nth_int @ Xs3 @ N ) ) @ ( power_power_rat @ A5 @ N ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs3 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % horner_sum_eq_sum
% 6.92/7.28 thf(fact_8169_horner__sum__eq__sum,axiom,
% 6.92/7.28 ( groups7485877704341954137at_int
% 6.92/7.28 = ( ^ [F3: nat > int,A5: int,Xs3: list_nat] :
% 6.92/7.28 ( groups3539618377306564664at_int
% 6.92/7.28 @ ^ [N: nat] : ( times_times_int @ ( F3 @ ( nth_nat @ Xs3 @ N ) ) @ ( power_power_int @ A5 @ N ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs3 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % horner_sum_eq_sum
% 6.92/7.28 thf(fact_8170_horner__sum__eq__sum,axiom,
% 6.92/7.28 ( groups8485231416243008693nt_int
% 6.92/7.28 = ( ^ [F3: int > int,A5: int,Xs3: list_int] :
% 6.92/7.28 ( groups3539618377306564664at_int
% 6.92/7.28 @ ^ [N: nat] : ( times_times_int @ ( F3 @ ( nth_int @ Xs3 @ N ) ) @ ( power_power_int @ A5 @ N ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs3 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % horner_sum_eq_sum
% 6.92/7.28 thf(fact_8171_horner__sum__eq__sum,axiom,
% 6.92/7.28 ( groups7488368174851004413at_nat
% 6.92/7.28 = ( ^ [F3: nat > nat,A5: nat,Xs3: list_nat] :
% 6.92/7.28 ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [N: nat] : ( times_times_nat @ ( F3 @ ( nth_nat @ Xs3 @ N ) ) @ ( power_power_nat @ A5 @ N ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs3 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % horner_sum_eq_sum
% 6.92/7.28 thf(fact_8172_horner__sum__eq__sum,axiom,
% 6.92/7.28 ( groups9119017779487936845_o_nat
% 6.92/7.28 = ( ^ [F3: $o > nat,A5: nat,Xs3: list_o] :
% 6.92/7.28 ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [N: nat] : ( times_times_nat @ ( F3 @ ( nth_o @ Xs3 @ N ) ) @ ( power_power_nat @ A5 @ N ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_o @ Xs3 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % horner_sum_eq_sum
% 6.92/7.28 thf(fact_8173_horner__sum__eq__sum,axiom,
% 6.92/7.28 ( groups8487721886752058969nt_nat
% 6.92/7.28 = ( ^ [F3: int > nat,A5: nat,Xs3: list_int] :
% 6.92/7.28 ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [N: nat] : ( times_times_nat @ ( F3 @ ( nth_int @ Xs3 @ N ) ) @ ( power_power_nat @ A5 @ N ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs3 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % horner_sum_eq_sum
% 6.92/7.28 thf(fact_8174_horner__sum__eq__sum,axiom,
% 6.92/7.28 ( groups9116527308978886569_o_int
% 6.92/7.28 = ( ^ [F3: $o > int,A5: int,Xs3: list_o] :
% 6.92/7.28 ( groups3539618377306564664at_int
% 6.92/7.28 @ ^ [N: nat] : ( times_times_int @ ( F3 @ ( nth_o @ Xs3 @ N ) ) @ ( power_power_int @ A5 @ N ) )
% 6.92/7.28 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_o @ Xs3 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % horner_sum_eq_sum
% 6.92/7.28 thf(fact_8175_prod_Ozero__middle,axiom,
% 6.92/7.28 ! [P3: nat,K2: nat,G: nat > code_integer,H: nat > code_integer] :
% 6.92/7.28 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 6.92/7.28 => ( ( ord_less_eq_nat @ K2 @ P3 )
% 6.92/7.28 => ( ( groups3455450783089532116nteger
% 6.92/7.28 @ ^ [J: nat] : ( if_Code_integer @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( if_Code_integer @ ( J = K2 ) @ one_one_Code_integer @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ P3 ) )
% 6.92/7.28 = ( groups3455450783089532116nteger
% 6.92/7.28 @ ^ [J: nat] : ( if_Code_integer @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( H @ J ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.zero_middle
% 6.92/7.28 thf(fact_8176_prod_Ozero__middle,axiom,
% 6.92/7.28 ! [P3: nat,K2: nat,G: nat > assn,H: nat > assn] :
% 6.92/7.28 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 6.92/7.28 => ( ( ord_less_eq_nat @ K2 @ P3 )
% 6.92/7.28 => ( ( groups6906906614972039071t_assn
% 6.92/7.28 @ ^ [J: nat] : ( if_assn @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( if_assn @ ( J = K2 ) @ one_one_assn @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ P3 ) )
% 6.92/7.28 = ( groups6906906614972039071t_assn
% 6.92/7.28 @ ^ [J: nat] : ( if_assn @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( H @ J ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.zero_middle
% 6.92/7.28 thf(fact_8177_prod_Ozero__middle,axiom,
% 6.92/7.28 ! [P3: nat,K2: nat,G: nat > rat,H: nat > rat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 6.92/7.28 => ( ( ord_less_eq_nat @ K2 @ P3 )
% 6.92/7.28 => ( ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [J: nat] : ( if_rat @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( if_rat @ ( J = K2 ) @ one_one_rat @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ P3 ) )
% 6.92/7.28 = ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [J: nat] : ( if_rat @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( H @ J ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.zero_middle
% 6.92/7.28 thf(fact_8178_prod_Ozero__middle,axiom,
% 6.92/7.28 ! [P3: nat,K2: nat,G: nat > nat,H: nat > nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 6.92/7.28 => ( ( ord_less_eq_nat @ K2 @ P3 )
% 6.92/7.28 => ( ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( if_nat @ ( J = K2 ) @ one_one_nat @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ P3 ) )
% 6.92/7.28 = ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( H @ J ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.zero_middle
% 6.92/7.28 thf(fact_8179_prod_Ozero__middle,axiom,
% 6.92/7.28 ! [P3: nat,K2: nat,G: nat > int,H: nat > int] :
% 6.92/7.28 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 6.92/7.28 => ( ( ord_less_eq_nat @ K2 @ P3 )
% 6.92/7.28 => ( ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( if_int @ ( J = K2 ) @ one_one_int @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ P3 ) )
% 6.92/7.28 = ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G @ J ) @ ( H @ J ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.zero_middle
% 6.92/7.28 thf(fact_8180_gbinomial__Suc,axiom,
% 6.92/7.28 ! [A: code_natural,K2: nat] :
% 6.92/7.28 ( ( gbinom7368847122466276068atural @ A @ ( suc @ K2 ) )
% 6.92/7.28 = ( divide5121882707175180666atural
% 6.92/7.28 @ ( groups2279045934846249631atural
% 6.92/7.28 @ ^ [I: nat] : ( minus_7197305767214868737atural @ A @ ( semiri3763490453095760265atural @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 6.92/7.28 @ ( semiri2447717529341329178atural @ ( suc @ K2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % gbinomial_Suc
% 6.92/7.28 thf(fact_8181_gbinomial__Suc,axiom,
% 6.92/7.28 ! [A: rat,K2: nat] :
% 6.92/7.28 ( ( gbinomial_rat @ A @ ( suc @ K2 ) )
% 6.92/7.28 = ( divide_divide_rat
% 6.92/7.28 @ ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 6.92/7.28 @ ( semiri773545260158071498ct_rat @ ( suc @ K2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % gbinomial_Suc
% 6.92/7.28 thf(fact_8182_gbinomial__Suc,axiom,
% 6.92/7.28 ! [A: code_integer,K2: nat] :
% 6.92/7.28 ( ( gbinom8545251970709558553nteger @ A @ ( suc @ K2 ) )
% 6.92/7.28 = ( divide6298287555418463151nteger
% 6.92/7.28 @ ( groups3455450783089532116nteger
% 6.92/7.28 @ ^ [I: nat] : ( minus_8373710615458151222nteger @ A @ ( semiri4939895301339042750nteger @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 6.92/7.28 @ ( semiri3624122377584611663nteger @ ( suc @ K2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % gbinomial_Suc
% 6.92/7.28 thf(fact_8183_gbinomial__Suc,axiom,
% 6.92/7.28 ! [A: nat,K2: nat] :
% 6.92/7.28 ( ( gbinomial_nat @ A @ ( suc @ K2 ) )
% 6.92/7.28 = ( divide_divide_nat
% 6.92/7.28 @ ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 6.92/7.28 @ ( semiri1408675320244567234ct_nat @ ( suc @ K2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % gbinomial_Suc
% 6.92/7.28 thf(fact_8184_gbinomial__Suc,axiom,
% 6.92/7.28 ! [A: int,K2: nat] :
% 6.92/7.28 ( ( gbinomial_int @ A @ ( suc @ K2 ) )
% 6.92/7.28 = ( divide_divide_int
% 6.92/7.28 @ ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I ) )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 6.92/7.28 @ ( semiri1406184849735516958ct_int @ ( suc @ K2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % gbinomial_Suc
% 6.92/7.28 thf(fact_8185_bit__cut__integer__code,axiom,
% 6.92/7.28 ( code_bit_cut_integer
% 6.92/7.28 = ( ^ [K3: code_integer] :
% 6.92/7.28 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 6.92/7.28 @ ( produc9125791028180074456eger_o
% 6.92/7.28 @ ^ [R5: code_integer,S5: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S5 ) ) @ ( S5 = one_one_Code_integer ) )
% 6.92/7.28 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % bit_cut_integer_code
% 6.92/7.28 thf(fact_8186_natLess__def,axiom,
% 6.92/7.28 ( bNF_Ca8459412986667044542atLess
% 6.92/7.28 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % natLess_def
% 6.92/7.28 thf(fact_8187_sum_Otriangle__reindex,axiom,
% 6.92/7.28 ! [G: nat > nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 6.92/7.28 @ ( collec3392354462482085612at_nat
% 6.92/7.28 @ ( produc6081775807080527818_nat_o
% 6.92/7.28 @ ^ [I: nat,J: nat] : ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ N2 ) ) ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [K3: nat] :
% 6.92/7.28 ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ I @ ( minus_minus_nat @ K3 @ I ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ K3 ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.triangle_reindex
% 6.92/7.28 thf(fact_8188_prod__decode__aux_Osimps,axiom,
% 6.92/7.28 ( nat_prod_decode_aux
% 6.92/7.28 = ( ^ [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 ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_decode_aux.simps
% 6.92/7.28 thf(fact_8189_lessThan__iff,axiom,
% 6.92/7.28 ! [I2: $o,K2: $o] :
% 6.92/7.28 ( ( member_o @ I2 @ ( set_ord_lessThan_o @ K2 ) )
% 6.92/7.28 = ( ord_less_o @ I2 @ K2 ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_iff
% 6.92/7.28 thf(fact_8190_lessThan__iff,axiom,
% 6.92/7.28 ! [I2: set_Pr958786334691620121nt_int,K2: set_Pr958786334691620121nt_int] :
% 6.92/7.28 ( ( member2340774599025711042nt_int @ I2 @ ( set_or4940836740269066044nt_int @ K2 ) )
% 6.92/7.28 = ( ord_le7563427860532173253nt_int @ I2 @ K2 ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_iff
% 6.92/7.28 thf(fact_8191_lessThan__iff,axiom,
% 6.92/7.28 ! [I2: set_nat,K2: set_nat] :
% 6.92/7.28 ( ( member_set_nat @ I2 @ ( set_or890127255671739683et_nat @ K2 ) )
% 6.92/7.28 = ( ord_less_set_nat @ I2 @ K2 ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_iff
% 6.92/7.28 thf(fact_8192_lessThan__iff,axiom,
% 6.92/7.28 ! [I2: assn,K2: assn] :
% 6.92/7.28 ( ( member_assn @ I2 @ ( set_or7637083652282234053n_assn @ K2 ) )
% 6.92/7.28 = ( ord_less_assn @ I2 @ K2 ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_iff
% 6.92/7.28 thf(fact_8193_lessThan__iff,axiom,
% 6.92/7.28 ! [I2: rat,K2: rat] :
% 6.92/7.28 ( ( member_rat @ I2 @ ( set_ord_lessThan_rat @ K2 ) )
% 6.92/7.28 = ( ord_less_rat @ I2 @ K2 ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_iff
% 6.92/7.28 thf(fact_8194_lessThan__iff,axiom,
% 6.92/7.28 ! [I2: num,K2: num] :
% 6.92/7.28 ( ( member_num @ I2 @ ( set_ord_lessThan_num @ K2 ) )
% 6.92/7.28 = ( ord_less_num @ I2 @ K2 ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_iff
% 6.92/7.28 thf(fact_8195_lessThan__iff,axiom,
% 6.92/7.28 ! [I2: nat,K2: nat] :
% 6.92/7.28 ( ( member_nat @ I2 @ ( set_ord_lessThan_nat @ K2 ) )
% 6.92/7.28 = ( ord_less_nat @ I2 @ K2 ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_iff
% 6.92/7.28 thf(fact_8196_lessThan__iff,axiom,
% 6.92/7.28 ! [I2: int,K2: int] :
% 6.92/7.28 ( ( member_int @ I2 @ ( set_ord_lessThan_int @ K2 ) )
% 6.92/7.28 = ( ord_less_int @ I2 @ K2 ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_iff
% 6.92/7.28 thf(fact_8197_lessThan__subset__iff,axiom,
% 6.92/7.28 ! [X: rat,Y: rat] :
% 6.92/7.28 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y ) )
% 6.92/7.28 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_subset_iff
% 6.92/7.28 thf(fact_8198_lessThan__subset__iff,axiom,
% 6.92/7.28 ! [X: num,Y: num] :
% 6.92/7.28 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y ) )
% 6.92/7.28 = ( ord_less_eq_num @ X @ Y ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_subset_iff
% 6.92/7.28 thf(fact_8199_lessThan__subset__iff,axiom,
% 6.92/7.28 ! [X: nat,Y: nat] :
% 6.92/7.28 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 6.92/7.28 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_subset_iff
% 6.92/7.28 thf(fact_8200_lessThan__subset__iff,axiom,
% 6.92/7.28 ! [X: int,Y: int] :
% 6.92/7.28 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 6.92/7.28 = ( ord_less_eq_int @ X @ Y ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_subset_iff
% 6.92/7.28 thf(fact_8201_sum_OlessThan__Suc,axiom,
% 6.92/7.28 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 6.92/7.28 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.lessThan_Suc
% 6.92/7.28 thf(fact_8202_sum_OlessThan__Suc,axiom,
% 6.92/7.28 ! [G: nat > rat,N2: nat] :
% 6.92/7.28 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.lessThan_Suc
% 6.92/7.28 thf(fact_8203_sum_OlessThan__Suc,axiom,
% 6.92/7.28 ! [G: nat > int,N2: nat] :
% 6.92/7.28 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.lessThan_Suc
% 6.92/7.28 thf(fact_8204_sum_OlessThan__Suc,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.lessThan_Suc
% 6.92/7.28 thf(fact_8205_int__prod,axiom,
% 6.92/7.28 ! [F: int > nat,A4: set_int] :
% 6.92/7.28 ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A4 ) )
% 6.92/7.28 = ( groups1705073143266064639nt_int
% 6.92/7.28 @ ^ [X4: int] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 6.92/7.28 @ A4 ) ) ).
% 6.92/7.28
% 6.92/7.28 % int_prod
% 6.92/7.28 thf(fact_8206_int__prod,axiom,
% 6.92/7.28 ! [F: nat > nat,A4: set_nat] :
% 6.92/7.28 ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A4 ) )
% 6.92/7.28 = ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [X4: nat] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 6.92/7.28 @ A4 ) ) ).
% 6.92/7.28
% 6.92/7.28 % int_prod
% 6.92/7.28 thf(fact_8207_lessThan__def,axiom,
% 6.92/7.28 ( set_or4940836740269066044nt_int
% 6.92/7.28 = ( ^ [U3: set_Pr958786334691620121nt_int] :
% 6.92/7.28 ( collec5210948495886036740nt_int
% 6.92/7.28 @ ^ [X4: set_Pr958786334691620121nt_int] : ( ord_le7563427860532173253nt_int @ X4 @ U3 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_def
% 6.92/7.28 thf(fact_8208_lessThan__def,axiom,
% 6.92/7.28 ( set_or890127255671739683et_nat
% 6.92/7.28 = ( ^ [U3: set_nat] :
% 6.92/7.28 ( collect_set_nat
% 6.92/7.28 @ ^ [X4: set_nat] : ( ord_less_set_nat @ X4 @ U3 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_def
% 6.92/7.28 thf(fact_8209_lessThan__def,axiom,
% 6.92/7.28 ( set_or7637083652282234053n_assn
% 6.92/7.28 = ( ^ [U3: assn] :
% 6.92/7.28 ( collect_assn
% 6.92/7.28 @ ^ [X4: assn] : ( ord_less_assn @ X4 @ U3 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_def
% 6.92/7.28 thf(fact_8210_lessThan__def,axiom,
% 6.92/7.28 ( set_ord_lessThan_rat
% 6.92/7.28 = ( ^ [U3: rat] :
% 6.92/7.28 ( collect_rat
% 6.92/7.28 @ ^ [X4: rat] : ( ord_less_rat @ X4 @ U3 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_def
% 6.92/7.28 thf(fact_8211_lessThan__def,axiom,
% 6.92/7.28 ( set_ord_lessThan_num
% 6.92/7.28 = ( ^ [U3: num] :
% 6.92/7.28 ( collect_num
% 6.92/7.28 @ ^ [X4: num] : ( ord_less_num @ X4 @ U3 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_def
% 6.92/7.28 thf(fact_8212_lessThan__def,axiom,
% 6.92/7.28 ( set_ord_lessThan_nat
% 6.92/7.28 = ( ^ [U3: nat] :
% 6.92/7.28 ( collect_nat
% 6.92/7.28 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ U3 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_def
% 6.92/7.28 thf(fact_8213_lessThan__def,axiom,
% 6.92/7.28 ( set_ord_lessThan_int
% 6.92/7.28 = ( ^ [U3: int] :
% 6.92/7.28 ( collect_int
% 6.92/7.28 @ ^ [X4: int] : ( ord_less_int @ X4 @ U3 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_def
% 6.92/7.28 thf(fact_8214_lessThan__strict__subset__iff,axiom,
% 6.92/7.28 ! [M: rat,N2: rat] :
% 6.92/7.28 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N2 ) )
% 6.92/7.28 = ( ord_less_rat @ M @ N2 ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_strict_subset_iff
% 6.92/7.28 thf(fact_8215_lessThan__strict__subset__iff,axiom,
% 6.92/7.28 ! [M: num,N2: num] :
% 6.92/7.28 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N2 ) )
% 6.92/7.28 = ( ord_less_num @ M @ N2 ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_strict_subset_iff
% 6.92/7.28 thf(fact_8216_lessThan__strict__subset__iff,axiom,
% 6.92/7.28 ! [M: nat,N2: nat] :
% 6.92/7.28 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N2 ) )
% 6.92/7.28 = ( ord_less_nat @ M @ N2 ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_strict_subset_iff
% 6.92/7.28 thf(fact_8217_lessThan__strict__subset__iff,axiom,
% 6.92/7.28 ! [M: int,N2: int] :
% 6.92/7.28 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N2 ) )
% 6.92/7.28 = ( ord_less_int @ M @ N2 ) ) ).
% 6.92/7.28
% 6.92/7.28 % lessThan_strict_subset_iff
% 6.92/7.28 thf(fact_8218_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
% 6.92/7.28 ! [L: code_integer,U: code_integer] :
% 6.92/7.28 ( ( set_or8404916559141939852nteger @ L @ ( plus_p5714425477246183910nteger @ U @ one_one_Code_integer ) )
% 6.92/7.28 = ( set_or189985376899183464nteger @ L @ U ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastLessThanPlusOne_atLeastAtMost_integer
% 6.92/7.28 thf(fact_8219_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 6.92/7.28 ! [L: int,U: int] :
% 6.92/7.28 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 6.92/7.28 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 6.92/7.28
% 6.92/7.28 % atLeastLessThanPlusOne_atLeastAtMost_int
% 6.92/7.28 thf(fact_8220_sum_Onat__diff__reindex,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I ) ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.nat_diff_reindex
% 6.92/7.28 thf(fact_8221_prod_Onat__diff__reindex,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I ) ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) )
% 6.92/7.28 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.nat_diff_reindex
% 6.92/7.28 thf(fact_8222_prod_Onat__diff__reindex,axiom,
% 6.92/7.28 ! [G: nat > int,N2: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I ) ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) )
% 6.92/7.28 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.nat_diff_reindex
% 6.92/7.28 thf(fact_8223_prod__int__eq,axiom,
% 6.92/7.28 ! [I2: nat,J2: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ J2 ) )
% 6.92/7.28 = ( groups1705073143266064639nt_int
% 6.92/7.28 @ ^ [X4: int] : X4
% 6.92/7.28 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_int_eq
% 6.92/7.28 thf(fact_8224_ivl__disj__un__one_I2_J,axiom,
% 6.92/7.28 ! [L: rat,U: rat] :
% 6.92/7.28 ( ( ord_less_eq_rat @ L @ U )
% 6.92/7.28 => ( ( sup_sup_set_rat @ ( set_ord_lessThan_rat @ L ) @ ( set_or4029947393144176647an_rat @ L @ U ) )
% 6.92/7.28 = ( set_ord_lessThan_rat @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_one(2)
% 6.92/7.28 thf(fact_8225_ivl__disj__un__one_I2_J,axiom,
% 6.92/7.28 ! [L: num,U: num] :
% 6.92/7.28 ( ( ord_less_eq_num @ L @ U )
% 6.92/7.28 => ( ( sup_sup_set_num @ ( set_ord_lessThan_num @ L ) @ ( set_or1222409239386451017an_num @ L @ U ) )
% 6.92/7.28 = ( set_ord_lessThan_num @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_one(2)
% 6.92/7.28 thf(fact_8226_ivl__disj__un__one_I2_J,axiom,
% 6.92/7.28 ! [L: nat,U: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ L @ U )
% 6.92/7.28 => ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 6.92/7.28 = ( set_ord_lessThan_nat @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_one(2)
% 6.92/7.28 thf(fact_8227_ivl__disj__un__one_I2_J,axiom,
% 6.92/7.28 ! [L: code_integer,U: code_integer] :
% 6.92/7.28 ( ( ord_le3102999989581377725nteger @ L @ U )
% 6.92/7.28 => ( ( sup_su848401254843788991nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or8404916559141939852nteger @ L @ U ) )
% 6.92/7.28 = ( set_or5754767410780653050nteger @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_one(2)
% 6.92/7.28 thf(fact_8228_ivl__disj__un__one_I2_J,axiom,
% 6.92/7.28 ! [L: int,U: int] :
% 6.92/7.28 ( ( ord_less_eq_int @ L @ U )
% 6.92/7.28 => ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or4662586982721622107an_int @ L @ U ) )
% 6.92/7.28 = ( set_ord_lessThan_int @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_one(2)
% 6.92/7.28 thf(fact_8229_prod_Otriangle__reindex,axiom,
% 6.92/7.28 ! [G: nat > nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 6.92/7.28 @ ( collec3392354462482085612at_nat
% 6.92/7.28 @ ( produc6081775807080527818_nat_o
% 6.92/7.28 @ ^ [I: nat,J: nat] : ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ N2 ) ) ) )
% 6.92/7.28 = ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [K3: nat] :
% 6.92/7.28 ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ I @ ( minus_minus_nat @ K3 @ I ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ K3 ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.triangle_reindex
% 6.92/7.28 thf(fact_8230_prod_Otriangle__reindex,axiom,
% 6.92/7.28 ! [G: nat > nat > int,N2: nat] :
% 6.92/7.28 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 6.92/7.28 @ ( collec3392354462482085612at_nat
% 6.92/7.28 @ ( produc6081775807080527818_nat_o
% 6.92/7.28 @ ^ [I: nat,J: nat] : ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ N2 ) ) ) )
% 6.92/7.28 = ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [K3: nat] :
% 6.92/7.28 ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( G @ I @ ( minus_minus_nat @ K3 @ I ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ K3 ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.triangle_reindex
% 6.92/7.28 thf(fact_8231_Iic__subset__Iio__iff,axiom,
% 6.92/7.28 ! [A: rat,B: rat] :
% 6.92/7.28 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 6.92/7.28 = ( ord_less_rat @ A @ B ) ) ).
% 6.92/7.28
% 6.92/7.28 % Iic_subset_Iio_iff
% 6.92/7.28 thf(fact_8232_Iic__subset__Iio__iff,axiom,
% 6.92/7.28 ! [A: num,B: num] :
% 6.92/7.28 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 6.92/7.28 = ( ord_less_num @ A @ B ) ) ).
% 6.92/7.28
% 6.92/7.28 % Iic_subset_Iio_iff
% 6.92/7.28 thf(fact_8233_Iic__subset__Iio__iff,axiom,
% 6.92/7.28 ! [A: nat,B: nat] :
% 6.92/7.28 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 6.92/7.28 = ( ord_less_nat @ A @ B ) ) ).
% 6.92/7.28
% 6.92/7.28 % Iic_subset_Iio_iff
% 6.92/7.28 thf(fact_8234_Iic__subset__Iio__iff,axiom,
% 6.92/7.28 ! [A: int,B: int] :
% 6.92/7.28 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 6.92/7.28 = ( ord_less_int @ A @ B ) ) ).
% 6.92/7.28
% 6.92/7.28 % Iic_subset_Iio_iff
% 6.92/7.28 thf(fact_8235_sum__diff__distrib,axiom,
% 6.92/7.28 ! [Q2: int > nat,P2: int > nat,N2: int] :
% 6.92/7.28 ( ! [X3: int] : ( ord_less_eq_nat @ ( Q2 @ X3 ) @ ( P2 @ X3 ) )
% 6.92/7.28 => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P2 @ ( set_ord_lessThan_int @ N2 ) ) @ ( groups4541462559716669496nt_nat @ Q2 @ ( set_ord_lessThan_int @ N2 ) ) )
% 6.92/7.28 = ( groups4541462559716669496nt_nat
% 6.92/7.28 @ ^ [X4: int] : ( minus_minus_nat @ ( P2 @ X4 ) @ ( Q2 @ X4 ) )
% 6.92/7.28 @ ( set_ord_lessThan_int @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_diff_distrib
% 6.92/7.28 thf(fact_8236_sum__diff__distrib,axiom,
% 6.92/7.28 ! [Q2: nat > nat,P2: nat > nat,N2: nat] :
% 6.92/7.28 ( ! [X3: nat] : ( ord_less_eq_nat @ ( Q2 @ X3 ) @ ( P2 @ X3 ) )
% 6.92/7.28 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P2 @ ( set_ord_lessThan_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ Q2 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [X4: nat] : ( minus_minus_nat @ ( P2 @ X4 ) @ ( Q2 @ X4 ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_diff_distrib
% 6.92/7.28 thf(fact_8237_sum_OlessThan__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 6.92/7.28 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups6857163185585827899at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.lessThan_Suc_shift
% 6.92/7.28 thf(fact_8238_sum_OlessThan__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > rat,N2: nat] :
% 6.92/7.28 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.lessThan_Suc_shift
% 6.92/7.28 thf(fact_8239_sum_OlessThan__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > int,N2: nat] :
% 6.92/7.28 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups3539618377306564664at_int
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.lessThan_Suc_shift
% 6.92/7.28 thf(fact_8240_sum_OlessThan__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.lessThan_Suc_shift
% 6.92/7.28 thf(fact_8241_sum__lessThan__telescope_H,axiom,
% 6.92/7.28 ! [F: nat > rat,M: nat] :
% 6.92/7.28 ( ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [N: nat] : ( minus_minus_rat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ M ) )
% 6.92/7.28 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_lessThan_telescope'
% 6.92/7.28 thf(fact_8242_sum__lessThan__telescope_H,axiom,
% 6.92/7.28 ! [F: nat > int,M: nat] :
% 6.92/7.28 ( ( groups3539618377306564664at_int
% 6.92/7.28 @ ^ [N: nat] : ( minus_minus_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ M ) )
% 6.92/7.28 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_lessThan_telescope'
% 6.92/7.28 thf(fact_8243_sum__lessThan__telescope,axiom,
% 6.92/7.28 ! [F: nat > rat,M: nat] :
% 6.92/7.28 ( ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [N: nat] : ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ M ) )
% 6.92/7.28 = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_lessThan_telescope
% 6.92/7.28 thf(fact_8244_sum__lessThan__telescope,axiom,
% 6.92/7.28 ! [F: nat > int,M: nat] :
% 6.92/7.28 ( ( groups3539618377306564664at_int
% 6.92/7.28 @ ^ [N: nat] : ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ M ) )
% 6.92/7.28 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_lessThan_telescope
% 6.92/7.28 thf(fact_8245_prod_OlessThan__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > assn,N2: nat] :
% 6.92/7.28 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_assn @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups6906906614972039071t_assn
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.lessThan_Suc_shift
% 6.92/7.28 thf(fact_8246_prod_OlessThan__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > rat,N2: nat] :
% 6.92/7.28 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_rat @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.lessThan_Suc_shift
% 6.92/7.28 thf(fact_8247_prod_OlessThan__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_nat @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.lessThan_Suc_shift
% 6.92/7.28 thf(fact_8248_prod_OlessThan__Suc__shift,axiom,
% 6.92/7.28 ! [G: nat > int,N2: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_int @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.lessThan_Suc_shift
% 6.92/7.28 thf(fact_8249_sum_OatLeast1__atMost__eq,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atLeast1_atMost_eq
% 6.92/7.28 thf(fact_8250_prod_OatLeast1__atMost__eq,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 6.92/7.28 = ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeast1_atMost_eq
% 6.92/7.28 thf(fact_8251_prod_OatLeast1__atMost__eq,axiom,
% 6.92/7.28 ! [G: nat > int,N2: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 6.92/7.28 = ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atLeast1_atMost_eq
% 6.92/7.28 thf(fact_8252_sum__bounds__lt__plus1,axiom,
% 6.92/7.28 ! [F: nat > nat,Mm: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ Mm ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_bounds_lt_plus1
% 6.92/7.28 thf(fact_8253_prod__int__plus__eq,axiom,
% 6.92/7.28 ! [I2: nat,J2: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J2 ) ) )
% 6.92/7.28 = ( groups1705073143266064639nt_int
% 6.92/7.28 @ ^ [X4: int] : X4
% 6.92/7.28 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_int_plus_eq
% 6.92/7.28 thf(fact_8254_sum_Onat__group,axiom,
% 6.92/7.28 ! [G: nat > nat,K2: nat,N2: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [M3: nat] : ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M3 @ K2 ) @ ( plus_plus_nat @ ( times_times_nat @ M3 @ K2 ) @ K2 ) ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N2 @ K2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.nat_group
% 6.92/7.28 thf(fact_8255_prod_Onat__group,axiom,
% 6.92/7.28 ! [G: nat > nat,K2: nat,N2: nat] :
% 6.92/7.28 ( ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [M3: nat] : ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M3 @ K2 ) @ ( plus_plus_nat @ ( times_times_nat @ M3 @ K2 ) @ K2 ) ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) )
% 6.92/7.28 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N2 @ K2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.nat_group
% 6.92/7.28 thf(fact_8256_prod_Onat__group,axiom,
% 6.92/7.28 ! [G: nat > int,K2: nat,N2: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [M3: nat] : ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M3 @ K2 ) @ ( plus_plus_nat @ ( times_times_nat @ M3 @ K2 ) @ K2 ) ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) )
% 6.92/7.28 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N2 @ K2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.nat_group
% 6.92/7.28 thf(fact_8257_sum_Onested__swap_H,axiom,
% 6.92/7.28 ! [A: nat > nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [I: nat] : ( groups3542108847815614940at_nat @ ( A @ I ) @ ( set_ord_lessThan_nat @ I ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.28 = ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [J: nat] :
% 6.92/7.28 ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [I: nat] : ( A @ I @ J )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N2 ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.nested_swap'
% 6.92/7.28 thf(fact_8258_prod_Onested__swap_H,axiom,
% 6.92/7.28 ! [A: nat > nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( groups708209901874060359at_nat @ ( A @ I ) @ ( set_ord_lessThan_nat @ I ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.28 = ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [J: nat] :
% 6.92/7.28 ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( A @ I @ J )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N2 ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.nested_swap'
% 6.92/7.28 thf(fact_8259_prod_Onested__swap_H,axiom,
% 6.92/7.28 ! [A: nat > nat > int,N2: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( groups705719431365010083at_int @ ( A @ I ) @ ( set_ord_lessThan_nat @ I ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.28 = ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [J: nat] :
% 6.92/7.28 ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( A @ I @ J )
% 6.92/7.28 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N2 ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.nested_swap'
% 6.92/7.28 thf(fact_8260_Iio__Int__singleton,axiom,
% 6.92/7.28 ! [X: $o,K2: $o] :
% 6.92/7.28 ( ( ( ord_less_o @ X @ K2 )
% 6.92/7.28 => ( ( inf_inf_set_o @ ( set_ord_lessThan_o @ K2 ) @ ( insert_o @ X @ bot_bot_set_o ) )
% 6.92/7.28 = ( insert_o @ X @ bot_bot_set_o ) ) )
% 6.92/7.28 & ( ~ ( ord_less_o @ X @ K2 )
% 6.92/7.28 => ( ( inf_inf_set_o @ ( set_ord_lessThan_o @ K2 ) @ ( insert_o @ X @ bot_bot_set_o ) )
% 6.92/7.28 = bot_bot_set_o ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % Iio_Int_singleton
% 6.92/7.28 thf(fact_8261_Iio__Int__singleton,axiom,
% 6.92/7.28 ! [X: assn,K2: assn] :
% 6.92/7.28 ( ( ( ord_less_assn @ X @ K2 )
% 6.92/7.28 => ( ( inf_inf_set_assn @ ( set_or7637083652282234053n_assn @ K2 ) @ ( insert_assn @ X @ bot_bot_set_assn ) )
% 6.92/7.28 = ( insert_assn @ X @ bot_bot_set_assn ) ) )
% 6.92/7.28 & ( ~ ( ord_less_assn @ X @ K2 )
% 6.92/7.28 => ( ( inf_inf_set_assn @ ( set_or7637083652282234053n_assn @ K2 ) @ ( insert_assn @ X @ bot_bot_set_assn ) )
% 6.92/7.28 = bot_bot_set_assn ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % Iio_Int_singleton
% 6.92/7.28 thf(fact_8262_Iio__Int__singleton,axiom,
% 6.92/7.28 ! [X: rat,K2: rat] :
% 6.92/7.28 ( ( ( ord_less_rat @ X @ K2 )
% 6.92/7.28 => ( ( inf_inf_set_rat @ ( set_ord_lessThan_rat @ K2 ) @ ( insert_rat @ X @ bot_bot_set_rat ) )
% 6.92/7.28 = ( insert_rat @ X @ bot_bot_set_rat ) ) )
% 6.92/7.28 & ( ~ ( ord_less_rat @ X @ K2 )
% 6.92/7.28 => ( ( inf_inf_set_rat @ ( set_ord_lessThan_rat @ K2 ) @ ( insert_rat @ X @ bot_bot_set_rat ) )
% 6.92/7.28 = bot_bot_set_rat ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % Iio_Int_singleton
% 6.92/7.28 thf(fact_8263_Iio__Int__singleton,axiom,
% 6.92/7.28 ! [X: num,K2: num] :
% 6.92/7.28 ( ( ( ord_less_num @ X @ K2 )
% 6.92/7.28 => ( ( inf_inf_set_num @ ( set_ord_lessThan_num @ K2 ) @ ( insert_num @ X @ bot_bot_set_num ) )
% 6.92/7.28 = ( insert_num @ X @ bot_bot_set_num ) ) )
% 6.92/7.28 & ( ~ ( ord_less_num @ X @ K2 )
% 6.92/7.28 => ( ( inf_inf_set_num @ ( set_ord_lessThan_num @ K2 ) @ ( insert_num @ X @ bot_bot_set_num ) )
% 6.92/7.28 = bot_bot_set_num ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % Iio_Int_singleton
% 6.92/7.28 thf(fact_8264_Iio__Int__singleton,axiom,
% 6.92/7.28 ! [X: nat,K2: nat] :
% 6.92/7.28 ( ( ( ord_less_nat @ X @ K2 )
% 6.92/7.28 => ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ K2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 6.92/7.28 = ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 6.92/7.28 & ( ~ ( ord_less_nat @ X @ K2 )
% 6.92/7.28 => ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ K2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 6.92/7.28 = bot_bot_set_nat ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % Iio_Int_singleton
% 6.92/7.28 thf(fact_8265_Iio__Int__singleton,axiom,
% 6.92/7.28 ! [X: int,K2: int] :
% 6.92/7.28 ( ( ( ord_less_int @ X @ K2 )
% 6.92/7.28 => ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ K2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 6.92/7.28 = ( insert_int @ X @ bot_bot_set_int ) ) )
% 6.92/7.28 & ( ~ ( ord_less_int @ X @ K2 )
% 6.92/7.28 => ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ K2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 6.92/7.28 = bot_bot_set_int ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % Iio_Int_singleton
% 6.92/7.28 thf(fact_8266_ivl__disj__un__singleton_I2_J,axiom,
% 6.92/7.28 ! [U: $o] :
% 6.92/7.28 ( ( sup_sup_set_o @ ( set_ord_lessThan_o @ U ) @ ( insert_o @ U @ bot_bot_set_o ) )
% 6.92/7.28 = ( set_ord_atMost_o @ U ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_singleton(2)
% 6.92/7.28 thf(fact_8267_ivl__disj__un__singleton_I2_J,axiom,
% 6.92/7.28 ! [U: nat] :
% 6.92/7.28 ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ U ) @ ( insert_nat @ U @ bot_bot_set_nat ) )
% 6.92/7.28 = ( set_ord_atMost_nat @ U ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_singleton(2)
% 6.92/7.28 thf(fact_8268_ivl__disj__un__singleton_I2_J,axiom,
% 6.92/7.28 ! [U: int] :
% 6.92/7.28 ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ U ) @ ( insert_int @ U @ bot_bot_set_int ) )
% 6.92/7.28 = ( set_ord_atMost_int @ U ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_singleton(2)
% 6.92/7.28 thf(fact_8269_ivl__disj__un__one_I4_J,axiom,
% 6.92/7.28 ! [L: rat,U: rat] :
% 6.92/7.28 ( ( ord_less_eq_rat @ L @ U )
% 6.92/7.28 => ( ( sup_sup_set_rat @ ( set_ord_lessThan_rat @ L ) @ ( set_or633870826150836451st_rat @ L @ U ) )
% 6.92/7.28 = ( set_ord_atMost_rat @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_one(4)
% 6.92/7.28 thf(fact_8270_ivl__disj__un__one_I4_J,axiom,
% 6.92/7.28 ! [L: num,U: num] :
% 6.92/7.28 ( ( ord_less_eq_num @ L @ U )
% 6.92/7.28 => ( ( sup_sup_set_num @ ( set_ord_lessThan_num @ L ) @ ( set_or7049704709247886629st_num @ L @ U ) )
% 6.92/7.28 = ( set_ord_atMost_num @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_one(4)
% 6.92/7.28 thf(fact_8271_ivl__disj__un__one_I4_J,axiom,
% 6.92/7.28 ! [L: nat,U: nat] :
% 6.92/7.28 ( ( ord_less_eq_nat @ L @ U )
% 6.92/7.28 => ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 6.92/7.28 = ( set_ord_atMost_nat @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_one(4)
% 6.92/7.28 thf(fact_8272_ivl__disj__un__one_I4_J,axiom,
% 6.92/7.28 ! [L: int,U: int] :
% 6.92/7.28 ( ( ord_less_eq_int @ L @ U )
% 6.92/7.28 => ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 6.92/7.28 = ( set_ord_atMost_int @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_one(4)
% 6.92/7.28 thf(fact_8273_ivl__disj__un__one_I4_J,axiom,
% 6.92/7.28 ! [L: code_integer,U: code_integer] :
% 6.92/7.28 ( ( ord_le3102999989581377725nteger @ L @ U )
% 6.92/7.28 => ( ( sup_su848401254843788991nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or189985376899183464nteger @ L @ U ) )
% 6.92/7.28 = ( set_or9101266186257409494nteger @ U ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % ivl_disj_un_one(4)
% 6.92/7.28 thf(fact_8274_one__diff__power__eq,axiom,
% 6.92/7.28 ! [X: code_integer,N2: nat] :
% 6.92/7.28 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 6.92/7.28 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % one_diff_power_eq
% 6.92/7.28 thf(fact_8275_one__diff__power__eq,axiom,
% 6.92/7.28 ! [X: rat,N2: nat] :
% 6.92/7.28 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) )
% 6.92/7.28 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % one_diff_power_eq
% 6.92/7.28 thf(fact_8276_one__diff__power__eq,axiom,
% 6.92/7.28 ! [X: int,N2: nat] :
% 6.92/7.28 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 6.92/7.28 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % one_diff_power_eq
% 6.92/7.28 thf(fact_8277_power__diff__1__eq,axiom,
% 6.92/7.28 ! [X: code_integer,N2: nat] :
% 6.92/7.28 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ N2 ) @ one_one_Code_integer )
% 6.92/7.28 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % power_diff_1_eq
% 6.92/7.28 thf(fact_8278_power__diff__1__eq,axiom,
% 6.92/7.28 ! [X: rat,N2: nat] :
% 6.92/7.28 ( ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ one_one_rat )
% 6.92/7.28 = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % power_diff_1_eq
% 6.92/7.28 thf(fact_8279_power__diff__1__eq,axiom,
% 6.92/7.28 ! [X: int,N2: nat] :
% 6.92/7.28 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ one_one_int )
% 6.92/7.28 = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % power_diff_1_eq
% 6.92/7.28 thf(fact_8280_geometric__sum,axiom,
% 6.92/7.28 ! [X: rat,N2: nat] :
% 6.92/7.28 ( ( X != one_one_rat )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 6.92/7.28 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % geometric_sum
% 6.92/7.28 thf(fact_8281_sum_OatMost__shift,axiom,
% 6.92/7.28 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 6.92/7.28 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.28 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups6857163185585827899at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atMost_shift
% 6.92/7.28 thf(fact_8282_sum_OatMost__shift,axiom,
% 6.92/7.28 ! [G: nat > rat,N2: nat] :
% 6.92/7.28 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.28 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atMost_shift
% 6.92/7.28 thf(fact_8283_sum_OatMost__shift,axiom,
% 6.92/7.28 ! [G: nat > int,N2: nat] :
% 6.92/7.28 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.28 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups3539618377306564664at_int
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atMost_shift
% 6.92/7.28 thf(fact_8284_sum_OatMost__shift,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.28 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.atMost_shift
% 6.92/7.28 thf(fact_8285_prod_OatMost__shift,axiom,
% 6.92/7.28 ! [G: nat > assn,N2: nat] :
% 6.92/7.28 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.28 = ( times_times_assn @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups6906906614972039071t_assn
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atMost_shift
% 6.92/7.28 thf(fact_8286_prod_OatMost__shift,axiom,
% 6.92/7.28 ! [G: nat > rat,N2: nat] :
% 6.92/7.28 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.28 = ( times_times_rat @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atMost_shift
% 6.92/7.28 thf(fact_8287_prod_OatMost__shift,axiom,
% 6.92/7.28 ! [G: nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.28 = ( times_times_nat @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atMost_shift
% 6.92/7.28 thf(fact_8288_prod_OatMost__shift,axiom,
% 6.92/7.28 ! [G: nat > int,N2: nat] :
% 6.92/7.28 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 6.92/7.28 = ( times_times_int @ ( G @ zero_zero_nat )
% 6.92/7.28 @ ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( G @ ( suc @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.atMost_shift
% 6.92/7.28 thf(fact_8289_sum__gp__strict,axiom,
% 6.92/7.28 ! [X: rat,N2: nat] :
% 6.92/7.28 ( ( ( X = one_one_rat )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 6.92/7.28 = ( semiri681578069525770553at_rat @ N2 ) ) )
% 6.92/7.28 & ( ( X != one_one_rat )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 6.92/7.28 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_gp_strict
% 6.92/7.28 thf(fact_8290_power__diff__sumr2,axiom,
% 6.92/7.28 ! [X: rat,N2: nat,Y: rat] :
% 6.92/7.28 ( ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 6.92/7.28 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 6.92/7.28 @ ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [I: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I ) ) ) @ ( power_power_rat @ X @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % power_diff_sumr2
% 6.92/7.28 thf(fact_8291_power__diff__sumr2,axiom,
% 6.92/7.28 ! [X: int,N2: nat,Y: int] :
% 6.92/7.28 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 6.92/7.28 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 6.92/7.28 @ ( groups3539618377306564664at_int
% 6.92/7.28 @ ^ [I: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I ) ) ) @ ( power_power_int @ X @ I ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % power_diff_sumr2
% 6.92/7.28 thf(fact_8292_diff__power__eq__sum,axiom,
% 6.92/7.28 ! [X: rat,N2: nat,Y: rat] :
% 6.92/7.28 ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) @ ( power_power_rat @ Y @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 6.92/7.28 @ ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [P7: nat] : ( times_times_rat @ ( power_power_rat @ X @ P7 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ P7 ) ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % diff_power_eq_sum
% 6.92/7.28 thf(fact_8293_diff__power__eq__sum,axiom,
% 6.92/7.28 ! [X: int,N2: nat,Y: int] :
% 6.92/7.28 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N2 ) ) @ ( power_power_int @ Y @ ( suc @ N2 ) ) )
% 6.92/7.28 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 6.92/7.28 @ ( groups3539618377306564664at_int
% 6.92/7.28 @ ^ [P7: nat] : ( times_times_int @ ( power_power_int @ X @ P7 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ P7 ) ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % diff_power_eq_sum
% 6.92/7.28 thf(fact_8294_one__diff__power__eq_H,axiom,
% 6.92/7.28 ! [X: code_integer,N2: nat] :
% 6.92/7.28 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 6.92/7.28 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X )
% 6.92/7.28 @ ( groups7501900531339628137nteger
% 6.92/7.28 @ ^ [I: nat] : ( power_8256067586552552935nteger @ X @ ( minus_minus_nat @ N2 @ ( suc @ I ) ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % one_diff_power_eq'
% 6.92/7.28 thf(fact_8295_one__diff__power__eq_H,axiom,
% 6.92/7.28 ! [X: rat,N2: nat] :
% 6.92/7.28 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) )
% 6.92/7.28 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 6.92/7.28 @ ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [I: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N2 @ ( suc @ I ) ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % one_diff_power_eq'
% 6.92/7.28 thf(fact_8296_one__diff__power__eq_H,axiom,
% 6.92/7.28 ! [X: int,N2: nat] :
% 6.92/7.28 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 6.92/7.28 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 6.92/7.28 @ ( groups3539618377306564664at_int
% 6.92/7.28 @ ^ [I: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N2 @ ( suc @ I ) ) )
% 6.92/7.28 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % one_diff_power_eq'
% 6.92/7.28 thf(fact_8297_prod_Otriangle__reindex__eq,axiom,
% 6.92/7.28 ! [G: nat > nat > nat,N2: nat] :
% 6.92/7.28 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 6.92/7.28 @ ( collec3392354462482085612at_nat
% 6.92/7.28 @ ( produc6081775807080527818_nat_o
% 6.92/7.28 @ ^ [I: nat,J: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I @ J ) @ N2 ) ) ) )
% 6.92/7.28 = ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [K3: nat] :
% 6.92/7.28 ( groups708209901874060359at_nat
% 6.92/7.28 @ ^ [I: nat] : ( G @ I @ ( minus_minus_nat @ K3 @ I ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ K3 ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.triangle_reindex_eq
% 6.92/7.28 thf(fact_8298_prod_Otriangle__reindex__eq,axiom,
% 6.92/7.28 ! [G: nat > nat > int,N2: nat] :
% 6.92/7.28 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 6.92/7.28 @ ( collec3392354462482085612at_nat
% 6.92/7.28 @ ( produc6081775807080527818_nat_o
% 6.92/7.28 @ ^ [I: nat,J: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I @ J ) @ N2 ) ) ) )
% 6.92/7.28 = ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [K3: nat] :
% 6.92/7.28 ( groups705719431365010083at_int
% 6.92/7.28 @ ^ [I: nat] : ( G @ I @ ( minus_minus_nat @ K3 @ I ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ K3 ) )
% 6.92/7.28 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.triangle_reindex_eq
% 6.92/7.28 thf(fact_8299_prod__decode__aux_Oelims,axiom,
% 6.92/7.28 ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 6.92/7.28 ( ( ( nat_prod_decode_aux @ X @ Xa )
% 6.92/7.28 = Y )
% 6.92/7.28 => ( ( ( ord_less_eq_nat @ Xa @ X )
% 6.92/7.28 => ( Y
% 6.92/7.28 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 6.92/7.28 & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 6.92/7.28 => ( Y
% 6.92/7.28 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_decode_aux.elims
% 6.92/7.28 thf(fact_8300_prod__decode__aux_Opelims,axiom,
% 6.92/7.28 ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 6.92/7.28 ( ( ( nat_prod_decode_aux @ X @ Xa )
% 6.92/7.28 = Y )
% 6.92/7.28 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 6.92/7.28 => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X )
% 6.92/7.28 => ( Y
% 6.92/7.28 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 6.92/7.28 & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 6.92/7.28 => ( Y
% 6.92/7.28 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) )
% 6.92/7.28 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_decode_aux.pelims
% 6.92/7.28 thf(fact_8301_signed__take__bit__code,axiom,
% 6.92/7.28 ( bit_ri6519982836138164636nteger
% 6.92/7.28 = ( ^ [N: nat,A5: code_integer] : ( if_Code_integer @ ( bit_se9216721137139052372nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A5 ) @ N ) @ ( plus_p5714425477246183910nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A5 ) @ ( bit_se7788150548672797655nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) @ ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A5 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % signed_take_bit_code
% 6.92/7.28 thf(fact_8302_signed__take__bit__code,axiom,
% 6.92/7.28 ( bit_ri631733984087533419it_int
% 6.92/7.28 = ( ^ [N: nat,A5: int] : ( if_int @ ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A5 ) @ N ) @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A5 ) @ ( bit_se545348938243370406it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) ) ) @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A5 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % signed_take_bit_code
% 6.92/7.28 thf(fact_8303_sum__zero__power_H,axiom,
% 6.92/7.28 ! [A4: set_nat,C2: nat > rat,D2: nat > rat] :
% 6.92/7.28 ( ( ( ( finite_finite_nat @ A4 )
% 6.92/7.28 & ( member_nat @ zero_zero_nat @ A4 ) )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [I: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) ) @ ( D2 @ I ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( divide_divide_rat @ ( C2 @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 6.92/7.28 & ( ~ ( ( finite_finite_nat @ A4 )
% 6.92/7.28 & ( member_nat @ zero_zero_nat @ A4 ) )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [I: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) ) @ ( D2 @ I ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = zero_zero_rat ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_zero_power'
% 6.92/7.28 thf(fact_8304_or__int__rec,axiom,
% 6.92/7.28 ( bit_se1409905431419307370or_int
% 6.92/7.28 = ( ^ [K3: int,L2: int] :
% 6.92/7.28 ( plus_plus_int
% 6.92/7.28 @ ( zero_n2684676970156552555ol_int
% 6.92/7.28 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 6.92/7.28 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 6.92/7.28 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % or_int_rec
% 6.92/7.28 thf(fact_8305_execute__of__list,axiom,
% 6.92/7.28 ! [Xs: list_nat,H: heap_e7401611519738050253t_unit] :
% 6.92/7.28 ( ( heap_T2203789307644377761ay_nat @ ( array_of_list_nat @ Xs ) @ H )
% 6.92/7.28 = ( some_P8206036975937309155it_nat
% 6.92/7.28 @ ( produc8657510640128716596it_nat
% 6.92/7.28 @ ^ [R5: array_nat,H7: heap_e7401611519738050253t_unit] : ( produc4907525368653469954it_nat @ R5 @ ( produc584006145561248582it_nat @ H7 @ ( plus_plus_nat @ one_one_nat @ ( size_size_list_nat @ Xs ) ) ) )
% 6.92/7.28 @ ( array_alloc_nat @ Xs @ H ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % execute_of_list
% 6.92/7.28 thf(fact_8306_execute__of__list,axiom,
% 6.92/7.28 ! [Xs: list_o,H: heap_e7401611519738050253t_unit] :
% 6.92/7.28 ( ( heap_T8140152426084121245rray_o @ ( array_of_list_o @ Xs ) @ H )
% 6.92/7.28 = ( some_P3509045262911171395it_nat
% 6.92/7.28 @ ( produc5512802776183222702it_nat
% 6.92/7.28 @ ^ [R5: array_o,H7: heap_e7401611519738050253t_unit] : ( produc2890842502232952598it_nat @ R5 @ ( produc584006145561248582it_nat @ H7 @ ( plus_plus_nat @ one_one_nat @ ( size_size_list_o @ Xs ) ) ) )
% 6.92/7.28 @ ( array_alloc_o @ Xs @ H ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % execute_of_list
% 6.92/7.28 thf(fact_8307_execute__of__list,axiom,
% 6.92/7.28 ! [Xs: list_int,H: heap_e7401611519738050253t_unit] :
% 6.92/7.28 ( ( heap_T7249310324989956861ay_int @ ( array_of_list_int @ Xs ) @ H )
% 6.92/7.28 = ( some_P8650484732927216191it_nat
% 6.92/7.28 @ ( produc3016605123915955252it_nat
% 6.92/7.28 @ ^ [R5: array_int,H7: heap_e7401611519738050253t_unit] : ( produc5351973125643376990it_nat @ R5 @ ( produc584006145561248582it_nat @ H7 @ ( plus_plus_nat @ one_one_nat @ ( size_size_list_int @ Xs ) ) ) )
% 6.92/7.28 @ ( array_alloc_int @ Xs @ H ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % execute_of_list
% 6.92/7.28 thf(fact_8308_push__bit__nonnegative__int__iff,axiom,
% 6.92/7.28 ! [N2: nat,K2: int] :
% 6.92/7.28 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N2 @ K2 ) )
% 6.92/7.28 = ( ord_less_eq_int @ zero_zero_int @ K2 ) ) ).
% 6.92/7.28
% 6.92/7.28 % push_bit_nonnegative_int_iff
% 6.92/7.28 thf(fact_8309_push__bit__negative__int__iff,axiom,
% 6.92/7.28 ! [N2: nat,K2: int] :
% 6.92/7.28 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N2 @ K2 ) @ zero_zero_int )
% 6.92/7.28 = ( ord_less_int @ K2 @ zero_zero_int ) ) ).
% 6.92/7.28
% 6.92/7.28 % push_bit_negative_int_iff
% 6.92/7.28 thf(fact_8310_push__bit__push__bit,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,A: int] :
% 6.92/7.28 ( ( bit_se545348938243370406it_int @ M @ ( bit_se545348938243370406it_int @ N2 @ A ) )
% 6.92/7.28 = ( bit_se545348938243370406it_int @ ( plus_plus_nat @ M @ N2 ) @ A ) ) ).
% 6.92/7.28
% 6.92/7.28 % push_bit_push_bit
% 6.92/7.28 thf(fact_8311_push__bit__push__bit,axiom,
% 6.92/7.28 ! [M: nat,N2: nat,A: nat] :
% 6.92/7.28 ( ( bit_se547839408752420682it_nat @ M @ ( bit_se547839408752420682it_nat @ N2 @ A ) )
% 6.92/7.28 = ( bit_se547839408752420682it_nat @ ( plus_plus_nat @ M @ N2 ) @ A ) ) ).
% 6.92/7.28
% 6.92/7.28 % push_bit_push_bit
% 6.92/7.28 thf(fact_8312_infinite__Icc__iff,axiom,
% 6.92/7.28 ! [A: rat,B: rat] :
% 6.92/7.28 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 6.92/7.28 = ( ord_less_rat @ A @ B ) ) ).
% 6.92/7.28
% 6.92/7.28 % infinite_Icc_iff
% 6.92/7.28 thf(fact_8313_infinite__Ico__iff,axiom,
% 6.92/7.28 ! [A: rat,B: rat] :
% 6.92/7.28 ( ( ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A @ B ) ) )
% 6.92/7.28 = ( ord_less_rat @ A @ B ) ) ).
% 6.92/7.28
% 6.92/7.28 % infinite_Ico_iff
% 6.92/7.28 thf(fact_8314_or__nonnegative__int__iff,axiom,
% 6.92/7.28 ! [K2: int,L: int] :
% 6.92/7.28 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K2 @ L ) )
% 6.92/7.28 = ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 6.92/7.28 & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % or_nonnegative_int_iff
% 6.92/7.28 thf(fact_8315_or__negative__int__iff,axiom,
% 6.92/7.28 ! [K2: int,L: int] :
% 6.92/7.28 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K2 @ L ) @ zero_zero_int )
% 6.92/7.28 = ( ( ord_less_int @ K2 @ zero_zero_int )
% 6.92/7.28 | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % or_negative_int_iff
% 6.92/7.28 thf(fact_8316_sum_Odelta,axiom,
% 6.92/7.28 ! [S: set_o,A: $o,B: $o > code_integer] :
% 6.92/7.28 ( ( finite_finite_o @ S )
% 6.92/7.28 => ( ( ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups4406642042086082107nteger
% 6.92/7.28 @ ^ [K3: $o] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups4406642042086082107nteger
% 6.92/7.28 @ ^ [K3: $o] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_z3403309356797280102nteger ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta
% 6.92/7.28 thf(fact_8317_sum_Odelta,axiom,
% 6.92/7.28 ! [S: set_nat,A: nat,B: nat > code_integer] :
% 6.92/7.28 ( ( finite_finite_nat @ S )
% 6.92/7.28 => ( ( ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups7501900531339628137nteger
% 6.92/7.28 @ ^ [K3: nat] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups7501900531339628137nteger
% 6.92/7.28 @ ^ [K3: nat] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_z3403309356797280102nteger ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta
% 6.92/7.28 thf(fact_8318_sum_Odelta,axiom,
% 6.92/7.28 ! [S: set_int,A: int,B: int > code_integer] :
% 6.92/7.28 ( ( finite_finite_int @ S )
% 6.92/7.28 => ( ( ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups7873554091576472773nteger
% 6.92/7.28 @ ^ [K3: int] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups7873554091576472773nteger
% 6.92/7.28 @ ^ [K3: int] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_z3403309356797280102nteger ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta
% 6.92/7.28 thf(fact_8319_sum_Odelta,axiom,
% 6.92/7.28 ! [S: set_Code_integer,A: code_integer,B: code_integer > code_integer] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ S )
% 6.92/7.28 => ( ( ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups879477027807139574nteger
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups879477027807139574nteger
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_z3403309356797280102nteger ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta
% 6.92/7.28 thf(fact_8320_sum_Odelta,axiom,
% 6.92/7.28 ! [S: set_o,A: $o,B: $o > rat] :
% 6.92/7.28 ( ( finite_finite_o @ S )
% 6.92/7.28 => ( ( ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups7872700643590313910_o_rat
% 6.92/7.28 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups7872700643590313910_o_rat
% 6.92/7.28 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_zero_rat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta
% 6.92/7.28 thf(fact_8321_sum_Odelta,axiom,
% 6.92/7.28 ! [S: set_nat,A: nat,B: nat > rat] :
% 6.92/7.28 ( ( finite_finite_nat @ S )
% 6.92/7.28 => ( ( ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_zero_rat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta
% 6.92/7.28 thf(fact_8322_sum_Odelta,axiom,
% 6.92/7.28 ! [S: set_int,A: int,B: int > rat] :
% 6.92/7.28 ( ( finite_finite_int @ S )
% 6.92/7.28 => ( ( ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups3906332499630173760nt_rat
% 6.92/7.28 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups3906332499630173760nt_rat
% 6.92/7.28 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_zero_rat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta
% 6.92/7.28 thf(fact_8323_sum_Odelta,axiom,
% 6.92/7.28 ! [S: set_Code_integer,A: code_integer,B: code_integer > rat] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ S )
% 6.92/7.28 => ( ( ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups6602215022474089585er_rat
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups6602215022474089585er_rat
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_zero_rat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta
% 6.92/7.28 thf(fact_8324_sum_Odelta,axiom,
% 6.92/7.28 ! [S: set_o,A: $o,B: $o > nat] :
% 6.92/7.28 ( ( finite_finite_o @ S )
% 6.92/7.28 => ( ( ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups8507830703676809646_o_nat
% 6.92/7.28 @ ^ [K3: $o] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_nat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups8507830703676809646_o_nat
% 6.92/7.28 @ ^ [K3: $o] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_nat )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_zero_nat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta
% 6.92/7.28 thf(fact_8325_sum_Odelta,axiom,
% 6.92/7.28 ! [S: set_int,A: int,B: int > nat] :
% 6.92/7.28 ( ( finite_finite_int @ S )
% 6.92/7.28 => ( ( ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups4541462559716669496nt_nat
% 6.92/7.28 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_nat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups4541462559716669496nt_nat
% 6.92/7.28 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_nat )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_zero_nat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta
% 6.92/7.28 thf(fact_8326_sum_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_o,A: $o,B: $o > code_integer] :
% 6.92/7.28 ( ( finite_finite_o @ S )
% 6.92/7.28 => ( ( ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups4406642042086082107nteger
% 6.92/7.28 @ ^ [K3: $o] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups4406642042086082107nteger
% 6.92/7.28 @ ^ [K3: $o] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_z3403309356797280102nteger ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta'
% 6.92/7.28 thf(fact_8327_sum_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_nat,A: nat,B: nat > code_integer] :
% 6.92/7.28 ( ( finite_finite_nat @ S )
% 6.92/7.28 => ( ( ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups7501900531339628137nteger
% 6.92/7.28 @ ^ [K3: nat] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups7501900531339628137nteger
% 6.92/7.28 @ ^ [K3: nat] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_z3403309356797280102nteger ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta'
% 6.92/7.28 thf(fact_8328_sum_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_int,A: int,B: int > code_integer] :
% 6.92/7.28 ( ( finite_finite_int @ S )
% 6.92/7.28 => ( ( ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups7873554091576472773nteger
% 6.92/7.28 @ ^ [K3: int] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups7873554091576472773nteger
% 6.92/7.28 @ ^ [K3: int] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_z3403309356797280102nteger ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta'
% 6.92/7.28 thf(fact_8329_sum_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_Code_integer,A: code_integer,B: code_integer > code_integer] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ S )
% 6.92/7.28 => ( ( ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups879477027807139574nteger
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups879477027807139574nteger
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_z3403309356797280102nteger ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta'
% 6.92/7.28 thf(fact_8330_sum_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_o,A: $o,B: $o > rat] :
% 6.92/7.28 ( ( finite_finite_o @ S )
% 6.92/7.28 => ( ( ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups7872700643590313910_o_rat
% 6.92/7.28 @ ^ [K3: $o] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups7872700643590313910_o_rat
% 6.92/7.28 @ ^ [K3: $o] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_zero_rat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta'
% 6.92/7.28 thf(fact_8331_sum_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_nat,A: nat,B: nat > rat] :
% 6.92/7.28 ( ( finite_finite_nat @ S )
% 6.92/7.28 => ( ( ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_zero_rat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta'
% 6.92/7.28 thf(fact_8332_sum_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_int,A: int,B: int > rat] :
% 6.92/7.28 ( ( finite_finite_int @ S )
% 6.92/7.28 => ( ( ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups3906332499630173760nt_rat
% 6.92/7.28 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups3906332499630173760nt_rat
% 6.92/7.28 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_zero_rat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta'
% 6.92/7.28 thf(fact_8333_sum_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_Code_integer,A: code_integer,B: code_integer > rat] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ S )
% 6.92/7.28 => ( ( ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups6602215022474089585er_rat
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups6602215022474089585er_rat
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_zero_rat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta'
% 6.92/7.28 thf(fact_8334_sum_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_o,A: $o,B: $o > nat] :
% 6.92/7.28 ( ( finite_finite_o @ S )
% 6.92/7.28 => ( ( ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups8507830703676809646_o_nat
% 6.92/7.28 @ ^ [K3: $o] : ( if_nat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_nat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups8507830703676809646_o_nat
% 6.92/7.28 @ ^ [K3: $o] : ( if_nat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_nat )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_zero_nat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta'
% 6.92/7.28 thf(fact_8335_sum_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_int,A: int,B: int > nat] :
% 6.92/7.28 ( ( finite_finite_int @ S )
% 6.92/7.28 => ( ( ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups4541462559716669496nt_nat
% 6.92/7.28 @ ^ [K3: int] : ( if_nat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_nat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups4541462559716669496nt_nat
% 6.92/7.28 @ ^ [K3: int] : ( if_nat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_nat )
% 6.92/7.28 @ S )
% 6.92/7.28 = zero_zero_nat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.delta'
% 6.92/7.28 thf(fact_8336_prod_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_o,A: $o,B: $o > code_integer] :
% 6.92/7.28 ( ( finite_finite_o @ S )
% 6.92/7.28 => ( ( ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups7694694392188491536nteger
% 6.92/7.28 @ ^ [K3: $o] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups7694694392188491536nteger
% 6.92/7.28 @ ^ [K3: $o] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_Code_integer ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta'
% 6.92/7.28 thf(fact_8337_prod_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_nat,A: nat,B: nat > code_integer] :
% 6.92/7.28 ( ( finite_finite_nat @ S )
% 6.92/7.28 => ( ( ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups3455450783089532116nteger
% 6.92/7.28 @ ^ [K3: nat] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups3455450783089532116nteger
% 6.92/7.28 @ ^ [K3: nat] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_Code_integer ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta'
% 6.92/7.28 thf(fact_8338_prod_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_int,A: int,B: int > code_integer] :
% 6.92/7.28 ( ( finite_finite_int @ S )
% 6.92/7.28 => ( ( ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups3827104343326376752nteger
% 6.92/7.28 @ ^ [K3: int] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups3827104343326376752nteger
% 6.92/7.28 @ ^ [K3: int] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_Code_integer ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta'
% 6.92/7.28 thf(fact_8339_prod_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_Code_integer,A: code_integer,B: code_integer > code_integer] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ S )
% 6.92/7.28 => ( ( ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups3674199335183972705nteger
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups3674199335183972705nteger
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_Code_integer ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta'
% 6.92/7.28 thf(fact_8340_prod_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_o,A: $o,B: $o > assn] :
% 6.92/7.28 ( ( finite_finite_o @ S )
% 6.92/7.28 => ( ( ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups5301882518646026715o_assn
% 6.92/7.28 @ ^ [K3: $o] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups5301882518646026715o_assn
% 6.92/7.28 @ ^ [K3: $o] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_assn ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta'
% 6.92/7.28 thf(fact_8341_prod_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_nat,A: nat,B: nat > assn] :
% 6.92/7.28 ( ( finite_finite_nat @ S )
% 6.92/7.28 => ( ( ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups6906906614972039071t_assn
% 6.92/7.28 @ ^ [K3: nat] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups6906906614972039071t_assn
% 6.92/7.28 @ ^ [K3: nat] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_assn ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta'
% 6.92/7.28 thf(fact_8342_prod_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_int,A: int,B: int > assn] :
% 6.92/7.28 ( ( finite_finite_int @ S )
% 6.92/7.28 => ( ( ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups7882442080178216443t_assn
% 6.92/7.28 @ ^ [K3: int] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups7882442080178216443t_assn
% 6.92/7.28 @ ^ [K3: int] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_assn ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta'
% 6.92/7.28 thf(fact_8343_prod_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_Code_integer,A: code_integer,B: code_integer > assn] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ S )
% 6.92/7.28 => ( ( ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups1304777262505850412r_assn
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups1304777262505850412r_assn
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_assn ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta'
% 6.92/7.28 thf(fact_8344_prod_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_o,A: $o,B: $o > rat] :
% 6.92/7.28 ( ( finite_finite_o @ S )
% 6.92/7.28 => ( ( ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups2869687844427037835_o_rat
% 6.92/7.28 @ ^ [K3: $o] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups2869687844427037835_o_rat
% 6.92/7.28 @ ^ [K3: $o] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_rat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta'
% 6.92/7.28 thf(fact_8345_prod_Odelta_H,axiom,
% 6.92/7.28 ! [S: set_nat,A: nat,B: nat > rat] :
% 6.92/7.28 ( ( finite_finite_nat @ S )
% 6.92/7.28 => ( ( ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_rat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta'
% 6.92/7.28 thf(fact_8346_prod_Odelta,axiom,
% 6.92/7.28 ! [S: set_o,A: $o,B: $o > code_integer] :
% 6.92/7.28 ( ( finite_finite_o @ S )
% 6.92/7.28 => ( ( ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups7694694392188491536nteger
% 6.92/7.28 @ ^ [K3: $o] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups7694694392188491536nteger
% 6.92/7.28 @ ^ [K3: $o] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_Code_integer ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta
% 6.92/7.28 thf(fact_8347_prod_Odelta,axiom,
% 6.92/7.28 ! [S: set_nat,A: nat,B: nat > code_integer] :
% 6.92/7.28 ( ( finite_finite_nat @ S )
% 6.92/7.28 => ( ( ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups3455450783089532116nteger
% 6.92/7.28 @ ^ [K3: nat] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups3455450783089532116nteger
% 6.92/7.28 @ ^ [K3: nat] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_Code_integer ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta
% 6.92/7.28 thf(fact_8348_prod_Odelta,axiom,
% 6.92/7.28 ! [S: set_int,A: int,B: int > code_integer] :
% 6.92/7.28 ( ( finite_finite_int @ S )
% 6.92/7.28 => ( ( ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups3827104343326376752nteger
% 6.92/7.28 @ ^ [K3: int] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups3827104343326376752nteger
% 6.92/7.28 @ ^ [K3: int] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_Code_integer ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta
% 6.92/7.28 thf(fact_8349_prod_Odelta,axiom,
% 6.92/7.28 ! [S: set_Code_integer,A: code_integer,B: code_integer > code_integer] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ S )
% 6.92/7.28 => ( ( ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups3674199335183972705nteger
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups3674199335183972705nteger
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_Code_integer ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta
% 6.92/7.28 thf(fact_8350_prod_Odelta,axiom,
% 6.92/7.28 ! [S: set_o,A: $o,B: $o > assn] :
% 6.92/7.28 ( ( finite_finite_o @ S )
% 6.92/7.28 => ( ( ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups5301882518646026715o_assn
% 6.92/7.28 @ ^ [K3: $o] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups5301882518646026715o_assn
% 6.92/7.28 @ ^ [K3: $o] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_assn ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta
% 6.92/7.28 thf(fact_8351_prod_Odelta,axiom,
% 6.92/7.28 ! [S: set_nat,A: nat,B: nat > assn] :
% 6.92/7.28 ( ( finite_finite_nat @ S )
% 6.92/7.28 => ( ( ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups6906906614972039071t_assn
% 6.92/7.28 @ ^ [K3: nat] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups6906906614972039071t_assn
% 6.92/7.28 @ ^ [K3: nat] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_assn ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta
% 6.92/7.28 thf(fact_8352_prod_Odelta,axiom,
% 6.92/7.28 ! [S: set_int,A: int,B: int > assn] :
% 6.92/7.28 ( ( finite_finite_int @ S )
% 6.92/7.28 => ( ( ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups7882442080178216443t_assn
% 6.92/7.28 @ ^ [K3: int] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_int @ A @ S )
% 6.92/7.28 => ( ( groups7882442080178216443t_assn
% 6.92/7.28 @ ^ [K3: int] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_assn ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta
% 6.92/7.28 thf(fact_8353_prod_Odelta,axiom,
% 6.92/7.28 ! [S: set_Code_integer,A: code_integer,B: code_integer > assn] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ S )
% 6.92/7.28 => ( ( ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups1304777262505850412r_assn
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_Code_integer @ A @ S )
% 6.92/7.28 => ( ( groups1304777262505850412r_assn
% 6.92/7.28 @ ^ [K3: code_integer] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_assn ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta
% 6.92/7.28 thf(fact_8354_prod_Odelta,axiom,
% 6.92/7.28 ! [S: set_o,A: $o,B: $o > rat] :
% 6.92/7.28 ( ( finite_finite_o @ S )
% 6.92/7.28 => ( ( ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups2869687844427037835_o_rat
% 6.92/7.28 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_o @ A @ S )
% 6.92/7.28 => ( ( groups2869687844427037835_o_rat
% 6.92/7.28 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_rat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta
% 6.92/7.28 thf(fact_8355_prod_Odelta,axiom,
% 6.92/7.28 ! [S: set_nat,A: nat,B: nat > rat] :
% 6.92/7.28 ( ( finite_finite_nat @ S )
% 6.92/7.28 => ( ( ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = ( B @ A ) ) )
% 6.92/7.28 & ( ~ ( member_nat @ A @ S )
% 6.92/7.28 => ( ( groups73079841787564623at_rat
% 6.92/7.28 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 6.92/7.28 @ S )
% 6.92/7.28 = one_one_rat ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod.delta
% 6.92/7.28 thf(fact_8356_sum_Oinsert,axiom,
% 6.92/7.28 ! [A4: set_o,X: $o,G: $o > rat] :
% 6.92/7.28 ( ( finite_finite_o @ A4 )
% 6.92/7.28 => ( ~ ( member_o @ X @ A4 )
% 6.92/7.28 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A4 ) )
% 6.92/7.28 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.insert
% 6.92/7.28 thf(fact_8357_sum_Oinsert,axiom,
% 6.92/7.28 ! [A4: set_nat,X: nat,G: nat > rat] :
% 6.92/7.28 ( ( finite_finite_nat @ A4 )
% 6.92/7.28 => ( ~ ( member_nat @ X @ A4 )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A4 ) )
% 6.92/7.28 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.insert
% 6.92/7.28 thf(fact_8358_sum_Oinsert,axiom,
% 6.92/7.28 ! [A4: set_int,X: int,G: int > rat] :
% 6.92/7.28 ( ( finite_finite_int @ A4 )
% 6.92/7.28 => ( ~ ( member_int @ X @ A4 )
% 6.92/7.28 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A4 ) )
% 6.92/7.28 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.insert
% 6.92/7.28 thf(fact_8359_sum_Oinsert,axiom,
% 6.92/7.28 ! [A4: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.28 => ( ~ ( member_Code_integer @ X @ A4 )
% 6.92/7.28 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A4 ) )
% 6.92/7.28 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.insert
% 6.92/7.28 thf(fact_8360_sum_Oinsert,axiom,
% 6.92/7.28 ! [A4: set_o,X: $o,G: $o > nat] :
% 6.92/7.28 ( ( finite_finite_o @ A4 )
% 6.92/7.28 => ( ~ ( member_o @ X @ A4 )
% 6.92/7.28 => ( ( groups8507830703676809646_o_nat @ G @ ( insert_o @ X @ A4 ) )
% 6.92/7.28 = ( plus_plus_nat @ ( G @ X ) @ ( groups8507830703676809646_o_nat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.insert
% 6.92/7.28 thf(fact_8361_sum_Oinsert,axiom,
% 6.92/7.28 ! [A4: set_int,X: int,G: int > nat] :
% 6.92/7.28 ( ( finite_finite_int @ A4 )
% 6.92/7.28 => ( ~ ( member_int @ X @ A4 )
% 6.92/7.28 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A4 ) )
% 6.92/7.28 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.insert
% 6.92/7.28 thf(fact_8362_sum_Oinsert,axiom,
% 6.92/7.28 ! [A4: set_Code_integer,X: code_integer,G: code_integer > nat] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.28 => ( ~ ( member_Code_integer @ X @ A4 )
% 6.92/7.28 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X @ A4 ) )
% 6.92/7.28 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.insert
% 6.92/7.28 thf(fact_8363_sum_Oinsert,axiom,
% 6.92/7.28 ! [A4: set_o,X: $o,G: $o > int] :
% 6.92/7.28 ( ( finite_finite_o @ A4 )
% 6.92/7.28 => ( ~ ( member_o @ X @ A4 )
% 6.92/7.28 => ( ( groups8505340233167759370_o_int @ G @ ( insert_o @ X @ A4 ) )
% 6.92/7.28 = ( plus_plus_int @ ( G @ X ) @ ( groups8505340233167759370_o_int @ G @ A4 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.insert
% 6.92/7.28 thf(fact_8364_sum_Oinsert,axiom,
% 6.92/7.28 ! [A4: set_nat,X: nat,G: nat > int] :
% 6.92/7.28 ( ( finite_finite_nat @ A4 )
% 6.92/7.28 => ( ~ ( member_nat @ X @ A4 )
% 6.92/7.28 => ( ( groups3539618377306564664at_int @ G @ ( insert_nat @ X @ A4 ) )
% 6.92/7.28 = ( plus_plus_int @ ( G @ X ) @ ( groups3539618377306564664at_int @ G @ A4 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.insert
% 6.92/7.28 thf(fact_8365_sum_Oinsert,axiom,
% 6.92/7.28 ! [A4: set_Code_integer,X: code_integer,G: code_integer > int] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.28 => ( ~ ( member_Code_integer @ X @ A4 )
% 6.92/7.28 => ( ( groups7234854612051535045er_int @ G @ ( insert_Code_integer @ X @ A4 ) )
% 6.92/7.28 = ( plus_plus_int @ ( G @ X ) @ ( groups7234854612051535045er_int @ G @ A4 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.insert
% 6.92/7.28 thf(fact_8366_prod__pos__nat__iff,axiom,
% 6.92/7.28 ! [A4: set_int,F: int > nat] :
% 6.92/7.28 ( ( finite_finite_int @ A4 )
% 6.92/7.28 => ( ( ord_less_nat @ zero_zero_nat @ ( groups1707563613775114915nt_nat @ F @ A4 ) )
% 6.92/7.28 = ( ! [X4: int] :
% 6.92/7.28 ( ( member_int @ X4 @ A4 )
% 6.92/7.28 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_pos_nat_iff
% 6.92/7.28 thf(fact_8367_prod__pos__nat__iff,axiom,
% 6.92/7.28 ! [A4: set_Code_integer,F: code_integer > nat] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.28 => ( ( ord_less_nat @ zero_zero_nat @ ( groups3190895334310489300er_nat @ F @ A4 ) )
% 6.92/7.28 = ( ! [X4: code_integer] :
% 6.92/7.28 ( ( member_Code_integer @ X4 @ A4 )
% 6.92/7.28 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_pos_nat_iff
% 6.92/7.28 thf(fact_8368_prod__pos__nat__iff,axiom,
% 6.92/7.28 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 6.92/7.28 ( ( finite6177210948735845034at_nat @ A4 )
% 6.92/7.28 => ( ( ord_less_nat @ zero_zero_nat @ ( groups4077766827762148844at_nat @ F @ A4 ) )
% 6.92/7.28 = ( ! [X4: product_prod_nat_nat] :
% 6.92/7.28 ( ( member8440522571783428010at_nat @ X4 @ A4 )
% 6.92/7.28 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_pos_nat_iff
% 6.92/7.28 thf(fact_8369_prod__pos__nat__iff,axiom,
% 6.92/7.28 ! [A4: set_nat,F: nat > nat] :
% 6.92/7.28 ( ( finite_finite_nat @ A4 )
% 6.92/7.28 => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A4 ) )
% 6.92/7.28 = ( ! [X4: nat] :
% 6.92/7.28 ( ( member_nat @ X4 @ A4 )
% 6.92/7.28 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % prod_pos_nat_iff
% 6.92/7.28 thf(fact_8370_sum__of__bool__mult__eq,axiom,
% 6.92/7.28 ! [A4: set_int,P2: int > $o,F: int > rat] :
% 6.92/7.28 ( ( finite_finite_int @ A4 )
% 6.92/7.28 => ( ( groups3906332499630173760nt_rat
% 6.92/7.28 @ ^ [X4: int] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) @ ( F @ X4 ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups3906332499630173760nt_rat @ F @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_of_bool_mult_eq
% 6.92/7.28 thf(fact_8371_sum__of__bool__mult__eq,axiom,
% 6.92/7.28 ! [A4: set_Code_integer,P2: code_integer > $o,F: code_integer > rat] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.28 => ( ( groups6602215022474089585er_rat
% 6.92/7.28 @ ^ [X4: code_integer] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) @ ( F @ X4 ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups6602215022474089585er_rat @ F @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_of_bool_mult_eq
% 6.92/7.28 thf(fact_8372_sum__of__bool__mult__eq,axiom,
% 6.92/7.28 ! [A4: set_nat,P2: nat > $o,F: nat > rat] :
% 6.92/7.28 ( ( finite_finite_nat @ A4 )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [X4: nat] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) @ ( F @ X4 ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups2906978787729119204at_rat @ F @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_of_bool_mult_eq
% 6.92/7.28 thf(fact_8373_sum__of__bool__mult__eq,axiom,
% 6.92/7.28 ! [A4: set_int,P2: int > $o,F: int > nat] :
% 6.92/7.28 ( ( finite_finite_int @ A4 )
% 6.92/7.28 => ( ( groups4541462559716669496nt_nat
% 6.92/7.28 @ ^ [X4: int] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) @ ( F @ X4 ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups4541462559716669496nt_nat @ F @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_of_bool_mult_eq
% 6.92/7.28 thf(fact_8374_sum__of__bool__mult__eq,axiom,
% 6.92/7.28 ! [A4: set_Code_integer,P2: code_integer > $o,F: code_integer > nat] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.28 => ( ( groups7237345082560585321er_nat
% 6.92/7.28 @ ^ [X4: code_integer] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) @ ( F @ X4 ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups7237345082560585321er_nat @ F @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_of_bool_mult_eq
% 6.92/7.28 thf(fact_8375_sum__of__bool__mult__eq,axiom,
% 6.92/7.28 ! [A4: set_Code_integer,P2: code_integer > $o,F: code_integer > int] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.28 => ( ( groups7234854612051535045er_int
% 6.92/7.28 @ ^ [X4: code_integer] : ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( P2 @ X4 ) ) @ ( F @ X4 ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups7234854612051535045er_int @ F @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_of_bool_mult_eq
% 6.92/7.28 thf(fact_8376_sum__of__bool__mult__eq,axiom,
% 6.92/7.28 ! [A4: set_nat,P2: nat > $o,F: nat > int] :
% 6.92/7.28 ( ( finite_finite_nat @ A4 )
% 6.92/7.28 => ( ( groups3539618377306564664at_int
% 6.92/7.28 @ ^ [X4: nat] : ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( P2 @ X4 ) ) @ ( F @ X4 ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups3539618377306564664at_int @ F @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_of_bool_mult_eq
% 6.92/7.28 thf(fact_8377_sum__of__bool__mult__eq,axiom,
% 6.92/7.28 ! [A4: set_int,P2: int > $o,F: int > code_integer] :
% 6.92/7.28 ( ( finite_finite_int @ A4 )
% 6.92/7.28 => ( ( groups7873554091576472773nteger
% 6.92/7.28 @ ^ [X4: int] : ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( P2 @ X4 ) ) @ ( F @ X4 ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups7873554091576472773nteger @ F @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_of_bool_mult_eq
% 6.92/7.28 thf(fact_8378_sum__of__bool__mult__eq,axiom,
% 6.92/7.28 ! [A4: set_Code_integer,P2: code_integer > $o,F: code_integer > code_integer] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.28 => ( ( groups879477027807139574nteger
% 6.92/7.28 @ ^ [X4: code_integer] : ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( P2 @ X4 ) ) @ ( F @ X4 ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups879477027807139574nteger @ F @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_of_bool_mult_eq
% 6.92/7.28 thf(fact_8379_sum__of__bool__mult__eq,axiom,
% 6.92/7.28 ! [A4: set_nat,P2: nat > $o,F: nat > code_integer] :
% 6.92/7.28 ( ( finite_finite_nat @ A4 )
% 6.92/7.28 => ( ( groups7501900531339628137nteger
% 6.92/7.28 @ ^ [X4: nat] : ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( P2 @ X4 ) ) @ ( F @ X4 ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups7501900531339628137nteger @ F @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_of_bool_mult_eq
% 6.92/7.28 thf(fact_8380_sum__mult__of__bool__eq,axiom,
% 6.92/7.28 ! [A4: set_int,F: int > rat,P2: int > $o] :
% 6.92/7.28 ( ( finite_finite_int @ A4 )
% 6.92/7.28 => ( ( groups3906332499630173760nt_rat
% 6.92/7.28 @ ^ [X4: int] : ( times_times_rat @ ( F @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups3906332499630173760nt_rat @ F @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_mult_of_bool_eq
% 6.92/7.28 thf(fact_8381_sum__mult__of__bool__eq,axiom,
% 6.92/7.28 ! [A4: set_Code_integer,F: code_integer > rat,P2: code_integer > $o] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.28 => ( ( groups6602215022474089585er_rat
% 6.92/7.28 @ ^ [X4: code_integer] : ( times_times_rat @ ( F @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups6602215022474089585er_rat @ F @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_mult_of_bool_eq
% 6.92/7.28 thf(fact_8382_sum__mult__of__bool__eq,axiom,
% 6.92/7.28 ! [A4: set_nat,F: nat > rat,P2: nat > $o] :
% 6.92/7.28 ( ( finite_finite_nat @ A4 )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [X4: nat] : ( times_times_rat @ ( F @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups2906978787729119204at_rat @ F @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_mult_of_bool_eq
% 6.92/7.28 thf(fact_8383_sum__mult__of__bool__eq,axiom,
% 6.92/7.28 ! [A4: set_int,F: int > nat,P2: int > $o] :
% 6.92/7.28 ( ( finite_finite_int @ A4 )
% 6.92/7.28 => ( ( groups4541462559716669496nt_nat
% 6.92/7.28 @ ^ [X4: int] : ( times_times_nat @ ( F @ X4 ) @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups4541462559716669496nt_nat @ F @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_mult_of_bool_eq
% 6.92/7.28 thf(fact_8384_sum__mult__of__bool__eq,axiom,
% 6.92/7.28 ! [A4: set_Code_integer,F: code_integer > nat,P2: code_integer > $o] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.28 => ( ( groups7237345082560585321er_nat
% 6.92/7.28 @ ^ [X4: code_integer] : ( times_times_nat @ ( F @ X4 ) @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups7237345082560585321er_nat @ F @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_mult_of_bool_eq
% 6.92/7.28 thf(fact_8385_sum__mult__of__bool__eq,axiom,
% 6.92/7.28 ! [A4: set_Code_integer,F: code_integer > int,P2: code_integer > $o] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.28 => ( ( groups7234854612051535045er_int
% 6.92/7.28 @ ^ [X4: code_integer] : ( times_times_int @ ( F @ X4 ) @ ( zero_n2684676970156552555ol_int @ ( P2 @ X4 ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups7234854612051535045er_int @ F @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_mult_of_bool_eq
% 6.92/7.28 thf(fact_8386_sum__mult__of__bool__eq,axiom,
% 6.92/7.28 ! [A4: set_nat,F: nat > int,P2: nat > $o] :
% 6.92/7.28 ( ( finite_finite_nat @ A4 )
% 6.92/7.28 => ( ( groups3539618377306564664at_int
% 6.92/7.28 @ ^ [X4: nat] : ( times_times_int @ ( F @ X4 ) @ ( zero_n2684676970156552555ol_int @ ( P2 @ X4 ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups3539618377306564664at_int @ F @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_mult_of_bool_eq
% 6.92/7.28 thf(fact_8387_sum__mult__of__bool__eq,axiom,
% 6.92/7.28 ! [A4: set_int,F: int > code_integer,P2: int > $o] :
% 6.92/7.28 ( ( finite_finite_int @ A4 )
% 6.92/7.28 => ( ( groups7873554091576472773nteger
% 6.92/7.28 @ ^ [X4: int] : ( times_3573771949741848930nteger @ ( F @ X4 ) @ ( zero_n356916108424825756nteger @ ( P2 @ X4 ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups7873554091576472773nteger @ F @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_mult_of_bool_eq
% 6.92/7.28 thf(fact_8388_sum__mult__of__bool__eq,axiom,
% 6.92/7.28 ! [A4: set_Code_integer,F: code_integer > code_integer,P2: code_integer > $o] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.28 => ( ( groups879477027807139574nteger
% 6.92/7.28 @ ^ [X4: code_integer] : ( times_3573771949741848930nteger @ ( F @ X4 ) @ ( zero_n356916108424825756nteger @ ( P2 @ X4 ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups879477027807139574nteger @ F @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_mult_of_bool_eq
% 6.92/7.28 thf(fact_8389_sum__mult__of__bool__eq,axiom,
% 6.92/7.28 ! [A4: set_nat,F: nat > code_integer,P2: nat > $o] :
% 6.92/7.28 ( ( finite_finite_nat @ A4 )
% 6.92/7.28 => ( ( groups7501900531339628137nteger
% 6.92/7.28 @ ^ [X4: nat] : ( times_3573771949741848930nteger @ ( F @ X4 ) @ ( zero_n356916108424825756nteger @ ( P2 @ X4 ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups7501900531339628137nteger @ F @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_mult_of_bool_eq
% 6.92/7.28 thf(fact_8390_sum__zero__power,axiom,
% 6.92/7.28 ! [A4: set_nat,C2: nat > rat] :
% 6.92/7.28 ( ( ( ( finite_finite_nat @ A4 )
% 6.92/7.28 & ( member_nat @ zero_zero_nat @ A4 ) )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( C2 @ zero_zero_nat ) ) )
% 6.92/7.28 & ( ~ ( ( finite_finite_nat @ A4 )
% 6.92/7.28 & ( member_nat @ zero_zero_nat @ A4 ) )
% 6.92/7.28 => ( ( groups2906978787729119204at_rat
% 6.92/7.28 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = zero_zero_rat ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum_zero_power
% 6.92/7.28 thf(fact_8391_or__numerals_I4_J,axiom,
% 6.92/7.28 ! [X: num,Y: num] :
% 6.92/7.28 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 6.92/7.28 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % or_numerals(4)
% 6.92/7.28 thf(fact_8392_or__numerals_I4_J,axiom,
% 6.92/7.28 ! [X: num,Y: num] :
% 6.92/7.28 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 6.92/7.28 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % or_numerals(4)
% 6.92/7.28 thf(fact_8393_or__numerals_I4_J,axiom,
% 6.92/7.28 ! [X: num,Y: num] :
% 6.92/7.28 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 6.92/7.28 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % or_numerals(4)
% 6.92/7.28 thf(fact_8394_or__numerals_I4_J,axiom,
% 6.92/7.28 ! [X: num,Y: num] :
% 6.92/7.28 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 6.92/7.28 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % or_numerals(4)
% 6.92/7.28 thf(fact_8395_or__numerals_I6_J,axiom,
% 6.92/7.28 ! [X: num,Y: num] :
% 6.92/7.28 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 6.92/7.28 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % or_numerals(6)
% 6.92/7.28 thf(fact_8396_or__numerals_I6_J,axiom,
% 6.92/7.28 ! [X: num,Y: num] :
% 6.92/7.28 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 6.92/7.28 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % or_numerals(6)
% 6.92/7.28 thf(fact_8397_or__numerals_I6_J,axiom,
% 6.92/7.28 ! [X: num,Y: num] :
% 6.92/7.28 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 6.92/7.28 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % or_numerals(6)
% 6.92/7.28 thf(fact_8398_or__numerals_I6_J,axiom,
% 6.92/7.28 ! [X: num,Y: num] :
% 6.92/7.28 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 6.92/7.28 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % or_numerals(6)
% 6.92/7.28 thf(fact_8399_or__numerals_I7_J,axiom,
% 6.92/7.28 ! [X: num,Y: num] :
% 6.92/7.28 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 6.92/7.28 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % or_numerals(7)
% 6.92/7.28 thf(fact_8400_or__numerals_I7_J,axiom,
% 6.92/7.28 ! [X: num,Y: num] :
% 6.92/7.28 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 6.92/7.28 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % or_numerals(7)
% 6.92/7.28 thf(fact_8401_or__numerals_I7_J,axiom,
% 6.92/7.28 ! [X: num,Y: num] :
% 6.92/7.28 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 6.92/7.28 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % or_numerals(7)
% 6.92/7.28 thf(fact_8402_or__numerals_I7_J,axiom,
% 6.92/7.28 ! [X: num,Y: num] :
% 6.92/7.28 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 6.92/7.28 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % or_numerals(7)
% 6.92/7.28 thf(fact_8403_bounded__nat__set__is__finite,axiom,
% 6.92/7.28 ! [N7: set_nat,N2: nat] :
% 6.92/7.28 ( ! [X3: nat] :
% 6.92/7.28 ( ( member_nat @ X3 @ N7 )
% 6.92/7.28 => ( ord_less_nat @ X3 @ N2 ) )
% 6.92/7.28 => ( finite_finite_nat @ N7 ) ) ).
% 6.92/7.28
% 6.92/7.28 % bounded_nat_set_is_finite
% 6.92/7.28 thf(fact_8404_finite__nat__set__iff__bounded,axiom,
% 6.92/7.28 ( finite_finite_nat
% 6.92/7.28 = ( ^ [N8: set_nat] :
% 6.92/7.28 ? [M3: nat] :
% 6.92/7.28 ! [X4: nat] :
% 6.92/7.28 ( ( member_nat @ X4 @ N8 )
% 6.92/7.28 => ( ord_less_nat @ X4 @ M3 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % finite_nat_set_iff_bounded
% 6.92/7.28 thf(fact_8405_push__bit__add,axiom,
% 6.92/7.28 ! [N2: nat,A: int,B: int] :
% 6.92/7.28 ( ( bit_se545348938243370406it_int @ N2 @ ( plus_plus_int @ A @ B ) )
% 6.92/7.28 = ( plus_plus_int @ ( bit_se545348938243370406it_int @ N2 @ A ) @ ( bit_se545348938243370406it_int @ N2 @ B ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % push_bit_add
% 6.92/7.28 thf(fact_8406_push__bit__add,axiom,
% 6.92/7.28 ! [N2: nat,A: nat,B: nat] :
% 6.92/7.28 ( ( bit_se547839408752420682it_nat @ N2 @ ( plus_plus_nat @ A @ B ) )
% 6.92/7.28 = ( plus_plus_nat @ ( bit_se547839408752420682it_nat @ N2 @ A ) @ ( bit_se547839408752420682it_nat @ N2 @ B ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % push_bit_add
% 6.92/7.28 thf(fact_8407_finite__if__eq__beyond__finite,axiom,
% 6.92/7.28 ! [S: set_Pr958786334691620121nt_int,S3: set_Pr958786334691620121nt_int] :
% 6.92/7.28 ( ( finite2998713641127702882nt_int @ S )
% 6.92/7.28 => ( finite8744585540193469122nt_int
% 6.92/7.28 @ ( collec5210948495886036740nt_int
% 6.92/7.28 @ ^ [S5: set_Pr958786334691620121nt_int] :
% 6.92/7.28 ( ( minus_1052850069191792384nt_int @ S5 @ S )
% 6.92/7.28 = ( minus_1052850069191792384nt_int @ S3 @ S ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % finite_if_eq_beyond_finite
% 6.92/7.28 thf(fact_8408_finite__if__eq__beyond__finite,axiom,
% 6.92/7.28 ! [S: set_nat,S3: set_nat] :
% 6.92/7.28 ( ( finite_finite_nat @ S )
% 6.92/7.28 => ( finite1152437895449049373et_nat
% 6.92/7.28 @ ( collect_set_nat
% 6.92/7.28 @ ^ [S5: set_nat] :
% 6.92/7.28 ( ( minus_minus_set_nat @ S5 @ S )
% 6.92/7.28 = ( minus_minus_set_nat @ S3 @ S ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % finite_if_eq_beyond_finite
% 6.92/7.28 thf(fact_8409_finite__if__eq__beyond__finite,axiom,
% 6.92/7.28 ! [S: set_int,S3: set_int] :
% 6.92/7.28 ( ( finite_finite_int @ S )
% 6.92/7.28 => ( finite6197958912794628473et_int
% 6.92/7.28 @ ( collect_set_int
% 6.92/7.28 @ ^ [S5: set_int] :
% 6.92/7.28 ( ( minus_minus_set_int @ S5 @ S )
% 6.92/7.28 = ( minus_minus_set_int @ S3 @ S ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % finite_if_eq_beyond_finite
% 6.92/7.28 thf(fact_8410_finite__if__eq__beyond__finite,axiom,
% 6.92/7.28 ! [S: set_Code_integer,S3: set_Code_integer] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ S )
% 6.92/7.28 => ( finite6931041176100689706nteger
% 6.92/7.28 @ ( collec574505750873337192nteger
% 6.92/7.28 @ ^ [S5: set_Code_integer] :
% 6.92/7.28 ( ( minus_2355218937544613996nteger @ S5 @ S )
% 6.92/7.28 = ( minus_2355218937544613996nteger @ S3 @ S ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % finite_if_eq_beyond_finite
% 6.92/7.28 thf(fact_8411_finite__if__eq__beyond__finite,axiom,
% 6.92/7.28 ! [S: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 6.92/7.28 ( ( finite6177210948735845034at_nat @ S )
% 6.92/7.28 => ( finite9047747110432174090at_nat
% 6.92/7.28 @ ( collec5514110066124741708at_nat
% 6.92/7.28 @ ^ [S5: set_Pr1261947904930325089at_nat] :
% 6.92/7.28 ( ( minus_1356011639430497352at_nat @ S5 @ S )
% 6.92/7.28 = ( minus_1356011639430497352at_nat @ S3 @ S ) ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % finite_if_eq_beyond_finite
% 6.92/7.28 thf(fact_8412_finite__nat__set__iff__bounded__le,axiom,
% 6.92/7.28 ( finite_finite_nat
% 6.92/7.28 = ( ^ [N8: set_nat] :
% 6.92/7.28 ? [M3: nat] :
% 6.92/7.28 ! [X4: nat] :
% 6.92/7.28 ( ( member_nat @ X4 @ N8 )
% 6.92/7.28 => ( ord_less_eq_nat @ X4 @ M3 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % finite_nat_set_iff_bounded_le
% 6.92/7.28 thf(fact_8413_finite__M__bounded__by__nat,axiom,
% 6.92/7.28 ! [P2: nat > $o,I2: nat] :
% 6.92/7.28 ( finite_finite_nat
% 6.92/7.28 @ ( collect_nat
% 6.92/7.28 @ ^ [K3: nat] :
% 6.92/7.28 ( ( P2 @ K3 )
% 6.92/7.28 & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % finite_M_bounded_by_nat
% 6.92/7.28 thf(fact_8414_finite__less__ub,axiom,
% 6.92/7.28 ! [F: nat > nat,U: nat] :
% 6.92/7.28 ( ! [N5: nat] : ( ord_less_eq_nat @ N5 @ ( F @ N5 ) )
% 6.92/7.28 => ( finite_finite_nat
% 6.92/7.28 @ ( collect_nat
% 6.92/7.28 @ ^ [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ U ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % finite_less_ub
% 6.92/7.28 thf(fact_8415_sum_Oswap__restrict,axiom,
% 6.92/7.28 ! [A4: set_o,B5: set_nat,G: $o > nat > nat,R3: $o > nat > $o] :
% 6.92/7.28 ( ( finite_finite_o @ A4 )
% 6.92/7.28 => ( ( finite_finite_nat @ B5 )
% 6.92/7.28 => ( ( groups8507830703676809646_o_nat
% 6.92/7.28 @ ^ [X4: $o] :
% 6.92/7.28 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 6.92/7.28 @ ( collect_nat
% 6.92/7.28 @ ^ [Y4: nat] :
% 6.92/7.28 ( ( member_nat @ Y4 @ B5 )
% 6.92/7.28 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [Y4: nat] :
% 6.92/7.28 ( groups8507830703676809646_o_nat
% 6.92/7.28 @ ^ [X4: $o] : ( G @ X4 @ Y4 )
% 6.92/7.28 @ ( collect_o
% 6.92/7.28 @ ^ [X4: $o] :
% 6.92/7.28 ( ( member_o @ X4 @ A4 )
% 6.92/7.28 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.28 @ B5 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.swap_restrict
% 6.92/7.28 thf(fact_8416_sum_Oswap__restrict,axiom,
% 6.92/7.28 ! [A4: set_int,B5: set_nat,G: int > nat > nat,R3: int > nat > $o] :
% 6.92/7.28 ( ( finite_finite_int @ A4 )
% 6.92/7.28 => ( ( finite_finite_nat @ B5 )
% 6.92/7.28 => ( ( groups4541462559716669496nt_nat
% 6.92/7.28 @ ^ [X4: int] :
% 6.92/7.28 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 6.92/7.28 @ ( collect_nat
% 6.92/7.28 @ ^ [Y4: nat] :
% 6.92/7.28 ( ( member_nat @ Y4 @ B5 )
% 6.92/7.28 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [Y4: nat] :
% 6.92/7.28 ( groups4541462559716669496nt_nat
% 6.92/7.28 @ ^ [X4: int] : ( G @ X4 @ Y4 )
% 6.92/7.28 @ ( collect_int
% 6.92/7.28 @ ^ [X4: int] :
% 6.92/7.28 ( ( member_int @ X4 @ A4 )
% 6.92/7.28 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.28 @ B5 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.swap_restrict
% 6.92/7.28 thf(fact_8417_sum_Oswap__restrict,axiom,
% 6.92/7.28 ! [A4: set_Code_integer,B5: set_nat,G: code_integer > nat > nat,R3: code_integer > nat > $o] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.28 => ( ( finite_finite_nat @ B5 )
% 6.92/7.28 => ( ( groups7237345082560585321er_nat
% 6.92/7.28 @ ^ [X4: code_integer] :
% 6.92/7.28 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 6.92/7.28 @ ( collect_nat
% 6.92/7.28 @ ^ [Y4: nat] :
% 6.92/7.28 ( ( member_nat @ Y4 @ B5 )
% 6.92/7.28 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups3542108847815614940at_nat
% 6.92/7.28 @ ^ [Y4: nat] :
% 6.92/7.28 ( groups7237345082560585321er_nat
% 6.92/7.28 @ ^ [X4: code_integer] : ( G @ X4 @ Y4 )
% 6.92/7.28 @ ( collect_Code_integer
% 6.92/7.28 @ ^ [X4: code_integer] :
% 6.92/7.28 ( ( member_Code_integer @ X4 @ A4 )
% 6.92/7.28 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.28 @ B5 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.swap_restrict
% 6.92/7.28 thf(fact_8418_sum_Oswap__restrict,axiom,
% 6.92/7.28 ! [A4: set_o,B5: set_int,G: $o > int > int,R3: $o > int > $o] :
% 6.92/7.28 ( ( finite_finite_o @ A4 )
% 6.92/7.28 => ( ( finite_finite_int @ B5 )
% 6.92/7.28 => ( ( groups8505340233167759370_o_int
% 6.92/7.28 @ ^ [X4: $o] :
% 6.92/7.28 ( groups4538972089207619220nt_int @ ( G @ X4 )
% 6.92/7.28 @ ( collect_int
% 6.92/7.28 @ ^ [Y4: int] :
% 6.92/7.28 ( ( member_int @ Y4 @ B5 )
% 6.92/7.28 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups4538972089207619220nt_int
% 6.92/7.28 @ ^ [Y4: int] :
% 6.92/7.28 ( groups8505340233167759370_o_int
% 6.92/7.28 @ ^ [X4: $o] : ( G @ X4 @ Y4 )
% 6.92/7.28 @ ( collect_o
% 6.92/7.28 @ ^ [X4: $o] :
% 6.92/7.28 ( ( member_o @ X4 @ A4 )
% 6.92/7.28 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.28 @ B5 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.swap_restrict
% 6.92/7.28 thf(fact_8419_sum_Oswap__restrict,axiom,
% 6.92/7.28 ! [A4: set_nat,B5: set_int,G: nat > int > int,R3: nat > int > $o] :
% 6.92/7.28 ( ( finite_finite_nat @ A4 )
% 6.92/7.28 => ( ( finite_finite_int @ B5 )
% 6.92/7.28 => ( ( groups3539618377306564664at_int
% 6.92/7.28 @ ^ [X4: nat] :
% 6.92/7.28 ( groups4538972089207619220nt_int @ ( G @ X4 )
% 6.92/7.28 @ ( collect_int
% 6.92/7.28 @ ^ [Y4: int] :
% 6.92/7.28 ( ( member_int @ Y4 @ B5 )
% 6.92/7.28 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups4538972089207619220nt_int
% 6.92/7.28 @ ^ [Y4: int] :
% 6.92/7.28 ( groups3539618377306564664at_int
% 6.92/7.28 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 6.92/7.28 @ ( collect_nat
% 6.92/7.28 @ ^ [X4: nat] :
% 6.92/7.28 ( ( member_nat @ X4 @ A4 )
% 6.92/7.28 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.28 @ B5 ) ) ) ) ).
% 6.92/7.28
% 6.92/7.28 % sum.swap_restrict
% 6.92/7.28 thf(fact_8420_sum_Oswap__restrict,axiom,
% 6.92/7.28 ! [A4: set_Code_integer,B5: set_int,G: code_integer > int > int,R3: code_integer > int > $o] :
% 6.92/7.28 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.28 => ( ( finite_finite_int @ B5 )
% 6.92/7.28 => ( ( groups7234854612051535045er_int
% 6.92/7.28 @ ^ [X4: code_integer] :
% 6.92/7.28 ( groups4538972089207619220nt_int @ ( G @ X4 )
% 6.92/7.28 @ ( collect_int
% 6.92/7.28 @ ^ [Y4: int] :
% 6.92/7.28 ( ( member_int @ Y4 @ B5 )
% 6.92/7.28 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.28 @ A4 )
% 6.92/7.28 = ( groups4538972089207619220nt_int
% 6.92/7.28 @ ^ [Y4: int] :
% 6.92/7.28 ( groups7234854612051535045er_int
% 6.92/7.28 @ ^ [X4: code_integer] : ( G @ X4 @ Y4 )
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X4 @ A4 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.swap_restrict
% 6.92/7.29 thf(fact_8421_sum_Oswap__restrict,axiom,
% 6.92/7.29 ! [A4: set_nat,B5: set_o,G: nat > $o > nat,R3: nat > $o > $o] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( finite_finite_o @ B5 )
% 6.92/7.29 => ( ( groups3542108847815614940at_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( groups8507830703676809646_o_nat @ ( G @ X4 )
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [Y4: $o] :
% 6.92/7.29 ( ( member_o @ Y4 @ B5 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ A4 )
% 6.92/7.29 = ( groups8507830703676809646_o_nat
% 6.92/7.29 @ ^ [Y4: $o] :
% 6.92/7.29 ( groups3542108847815614940at_nat
% 6.92/7.29 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( member_nat @ X4 @ A4 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.swap_restrict
% 6.92/7.29 thf(fact_8422_sum_Oswap__restrict,axiom,
% 6.92/7.29 ! [A4: set_nat,B5: set_int,G: nat > int > nat,R3: nat > int > $o] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( finite_finite_int @ B5 )
% 6.92/7.29 => ( ( groups3542108847815614940at_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( groups4541462559716669496nt_nat @ ( G @ X4 )
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [Y4: int] :
% 6.92/7.29 ( ( member_int @ Y4 @ B5 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ A4 )
% 6.92/7.29 = ( groups4541462559716669496nt_nat
% 6.92/7.29 @ ^ [Y4: int] :
% 6.92/7.29 ( groups3542108847815614940at_nat
% 6.92/7.29 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( member_nat @ X4 @ A4 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.swap_restrict
% 6.92/7.29 thf(fact_8423_sum_Oswap__restrict,axiom,
% 6.92/7.29 ! [A4: set_nat,B5: set_Code_integer,G: nat > code_integer > nat,R3: nat > code_integer > $o] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( finite6017078050557962740nteger @ B5 )
% 6.92/7.29 => ( ( groups3542108847815614940at_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( groups7237345082560585321er_nat @ ( G @ X4 )
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [Y4: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ Y4 @ B5 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ A4 )
% 6.92/7.29 = ( groups7237345082560585321er_nat
% 6.92/7.29 @ ^ [Y4: code_integer] :
% 6.92/7.29 ( groups3542108847815614940at_nat
% 6.92/7.29 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( member_nat @ X4 @ A4 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.swap_restrict
% 6.92/7.29 thf(fact_8424_sum_Oswap__restrict,axiom,
% 6.92/7.29 ! [A4: set_nat,B5: set_nat,G: nat > nat > nat,R3: nat > nat > $o] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( finite_finite_nat @ B5 )
% 6.92/7.29 => ( ( groups3542108847815614940at_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [Y4: nat] :
% 6.92/7.29 ( ( member_nat @ Y4 @ B5 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ A4 )
% 6.92/7.29 = ( groups3542108847815614940at_nat
% 6.92/7.29 @ ^ [Y4: nat] :
% 6.92/7.29 ( groups3542108847815614940at_nat
% 6.92/7.29 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( member_nat @ X4 @ A4 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.swap_restrict
% 6.92/7.29 thf(fact_8425_prod_Oswap__restrict,axiom,
% 6.92/7.29 ! [A4: set_o,B5: set_nat,G: $o > nat > nat,R3: $o > nat > $o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( finite_finite_nat @ B5 )
% 6.92/7.29 => ( ( groups3504817904513533571_o_nat
% 6.92/7.29 @ ^ [X4: $o] :
% 6.92/7.29 ( groups708209901874060359at_nat @ ( G @ X4 )
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [Y4: nat] :
% 6.92/7.29 ( ( member_nat @ Y4 @ B5 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ A4 )
% 6.92/7.29 = ( groups708209901874060359at_nat
% 6.92/7.29 @ ^ [Y4: nat] :
% 6.92/7.29 ( groups3504817904513533571_o_nat
% 6.92/7.29 @ ^ [X4: $o] : ( G @ X4 @ Y4 )
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [X4: $o] :
% 6.92/7.29 ( ( member_o @ X4 @ A4 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.swap_restrict
% 6.92/7.29 thf(fact_8426_prod_Oswap__restrict,axiom,
% 6.92/7.29 ! [A4: set_int,B5: set_nat,G: int > nat > nat,R3: int > nat > $o] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( finite_finite_nat @ B5 )
% 6.92/7.29 => ( ( groups1707563613775114915nt_nat
% 6.92/7.29 @ ^ [X4: int] :
% 6.92/7.29 ( groups708209901874060359at_nat @ ( G @ X4 )
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [Y4: nat] :
% 6.92/7.29 ( ( member_nat @ Y4 @ B5 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ A4 )
% 6.92/7.29 = ( groups708209901874060359at_nat
% 6.92/7.29 @ ^ [Y4: nat] :
% 6.92/7.29 ( groups1707563613775114915nt_nat
% 6.92/7.29 @ ^ [X4: int] : ( G @ X4 @ Y4 )
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] :
% 6.92/7.29 ( ( member_int @ X4 @ A4 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.swap_restrict
% 6.92/7.29 thf(fact_8427_prod_Oswap__restrict,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,B5: set_nat,G: code_integer > nat > nat,R3: code_integer > nat > $o] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( finite_finite_nat @ B5 )
% 6.92/7.29 => ( ( groups3190895334310489300er_nat
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( groups708209901874060359at_nat @ ( G @ X4 )
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [Y4: nat] :
% 6.92/7.29 ( ( member_nat @ Y4 @ B5 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ A4 )
% 6.92/7.29 = ( groups708209901874060359at_nat
% 6.92/7.29 @ ^ [Y4: nat] :
% 6.92/7.29 ( groups3190895334310489300er_nat
% 6.92/7.29 @ ^ [X4: code_integer] : ( G @ X4 @ Y4 )
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X4 @ A4 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.swap_restrict
% 6.92/7.29 thf(fact_8428_prod_Oswap__restrict,axiom,
% 6.92/7.29 ! [A4: set_o,B5: set_nat,G: $o > nat > int,R3: $o > nat > $o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( finite_finite_nat @ B5 )
% 6.92/7.29 => ( ( groups3502327434004483295_o_int
% 6.92/7.29 @ ^ [X4: $o] :
% 6.92/7.29 ( groups705719431365010083at_int @ ( G @ X4 )
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [Y4: nat] :
% 6.92/7.29 ( ( member_nat @ Y4 @ B5 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ A4 )
% 6.92/7.29 = ( groups705719431365010083at_int
% 6.92/7.29 @ ^ [Y4: nat] :
% 6.92/7.29 ( groups3502327434004483295_o_int
% 6.92/7.29 @ ^ [X4: $o] : ( G @ X4 @ Y4 )
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [X4: $o] :
% 6.92/7.29 ( ( member_o @ X4 @ A4 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.swap_restrict
% 6.92/7.29 thf(fact_8429_prod_Oswap__restrict,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,B5: set_nat,G: code_integer > nat > int,R3: code_integer > nat > $o] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( finite_finite_nat @ B5 )
% 6.92/7.29 => ( ( groups3188404863801439024er_int
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( groups705719431365010083at_int @ ( G @ X4 )
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [Y4: nat] :
% 6.92/7.29 ( ( member_nat @ Y4 @ B5 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ A4 )
% 6.92/7.29 = ( groups705719431365010083at_int
% 6.92/7.29 @ ^ [Y4: nat] :
% 6.92/7.29 ( groups3188404863801439024er_int
% 6.92/7.29 @ ^ [X4: code_integer] : ( G @ X4 @ Y4 )
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X4 @ A4 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.swap_restrict
% 6.92/7.29 thf(fact_8430_prod_Oswap__restrict,axiom,
% 6.92/7.29 ! [A4: set_o,B5: set_int,G: $o > int > int,R3: $o > int > $o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( finite_finite_int @ B5 )
% 6.92/7.29 => ( ( groups3502327434004483295_o_int
% 6.92/7.29 @ ^ [X4: $o] :
% 6.92/7.29 ( groups1705073143266064639nt_int @ ( G @ X4 )
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [Y4: int] :
% 6.92/7.29 ( ( member_int @ Y4 @ B5 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ A4 )
% 6.92/7.29 = ( groups1705073143266064639nt_int
% 6.92/7.29 @ ^ [Y4: int] :
% 6.92/7.29 ( groups3502327434004483295_o_int
% 6.92/7.29 @ ^ [X4: $o] : ( G @ X4 @ Y4 )
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [X4: $o] :
% 6.92/7.29 ( ( member_o @ X4 @ A4 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.swap_restrict
% 6.92/7.29 thf(fact_8431_prod_Oswap__restrict,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,B5: set_int,G: code_integer > int > int,R3: code_integer > int > $o] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( finite_finite_int @ B5 )
% 6.92/7.29 => ( ( groups3188404863801439024er_int
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( groups1705073143266064639nt_int @ ( G @ X4 )
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [Y4: int] :
% 6.92/7.29 ( ( member_int @ Y4 @ B5 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ A4 )
% 6.92/7.29 = ( groups1705073143266064639nt_int
% 6.92/7.29 @ ^ [Y4: int] :
% 6.92/7.29 ( groups3188404863801439024er_int
% 6.92/7.29 @ ^ [X4: code_integer] : ( G @ X4 @ Y4 )
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X4 @ A4 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.swap_restrict
% 6.92/7.29 thf(fact_8432_prod_Oswap__restrict,axiom,
% 6.92/7.29 ! [A4: set_nat,B5: set_o,G: nat > $o > nat,R3: nat > $o > $o] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( finite_finite_o @ B5 )
% 6.92/7.29 => ( ( groups708209901874060359at_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( groups3504817904513533571_o_nat @ ( G @ X4 )
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [Y4: $o] :
% 6.92/7.29 ( ( member_o @ Y4 @ B5 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ A4 )
% 6.92/7.29 = ( groups3504817904513533571_o_nat
% 6.92/7.29 @ ^ [Y4: $o] :
% 6.92/7.29 ( groups708209901874060359at_nat
% 6.92/7.29 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( member_nat @ X4 @ A4 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.swap_restrict
% 6.92/7.29 thf(fact_8433_prod_Oswap__restrict,axiom,
% 6.92/7.29 ! [A4: set_nat,B5: set_int,G: nat > int > nat,R3: nat > int > $o] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( finite_finite_int @ B5 )
% 6.92/7.29 => ( ( groups708209901874060359at_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( groups1707563613775114915nt_nat @ ( G @ X4 )
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [Y4: int] :
% 6.92/7.29 ( ( member_int @ Y4 @ B5 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ A4 )
% 6.92/7.29 = ( groups1707563613775114915nt_nat
% 6.92/7.29 @ ^ [Y4: int] :
% 6.92/7.29 ( groups708209901874060359at_nat
% 6.92/7.29 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( member_nat @ X4 @ A4 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.swap_restrict
% 6.92/7.29 thf(fact_8434_prod_Oswap__restrict,axiom,
% 6.92/7.29 ! [A4: set_nat,B5: set_Code_integer,G: nat > code_integer > nat,R3: nat > code_integer > $o] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( finite6017078050557962740nteger @ B5 )
% 6.92/7.29 => ( ( groups708209901874060359at_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( groups3190895334310489300er_nat @ ( G @ X4 )
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [Y4: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ Y4 @ B5 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ A4 )
% 6.92/7.29 = ( groups3190895334310489300er_nat
% 6.92/7.29 @ ^ [Y4: code_integer] :
% 6.92/7.29 ( groups708209901874060359at_nat
% 6.92/7.29 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( member_nat @ X4 @ A4 )
% 6.92/7.29 & ( R3 @ X4 @ Y4 ) ) ) )
% 6.92/7.29 @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.swap_restrict
% 6.92/7.29 thf(fact_8435_OR__lower,axiom,
% 6.92/7.29 ! [X: int,Y: int] :
% 6.92/7.29 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.92/7.29 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.92/7.29 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % OR_lower
% 6.92/7.29 thf(fact_8436_or__greater__eq,axiom,
% 6.92/7.29 ! [L: int,K2: int] :
% 6.92/7.29 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 6.92/7.29 => ( ord_less_eq_int @ K2 @ ( bit_se1409905431419307370or_int @ K2 @ L ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % or_greater_eq
% 6.92/7.29 thf(fact_8437_disjunctive__add,axiom,
% 6.92/7.29 ! [A: int,B: int] :
% 6.92/7.29 ( ! [N5: nat] :
% 6.92/7.29 ( ~ ( bit_se1146084159140164899it_int @ A @ N5 )
% 6.92/7.29 | ~ ( bit_se1146084159140164899it_int @ B @ N5 ) )
% 6.92/7.29 => ( ( plus_plus_int @ A @ B )
% 6.92/7.29 = ( bit_se1409905431419307370or_int @ A @ B ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % disjunctive_add
% 6.92/7.29 thf(fact_8438_disjunctive__add,axiom,
% 6.92/7.29 ! [A: nat,B: nat] :
% 6.92/7.29 ( ! [N5: nat] :
% 6.92/7.29 ( ~ ( bit_se1148574629649215175it_nat @ A @ N5 )
% 6.92/7.29 | ~ ( bit_se1148574629649215175it_nat @ B @ N5 ) )
% 6.92/7.29 => ( ( plus_plus_nat @ A @ B )
% 6.92/7.29 = ( bit_se1412395901928357646or_nat @ A @ B ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % disjunctive_add
% 6.92/7.29 thf(fact_8439_infinite__growing,axiom,
% 6.92/7.29 ! [X7: set_Code_integer] :
% 6.92/7.29 ( ( X7 != bot_bo3990330152332043303nteger )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ X7 )
% 6.92/7.29 => ? [Xa3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ Xa3 @ X7 )
% 6.92/7.29 & ( ord_le6747313008572928689nteger @ X3 @ Xa3 ) ) )
% 6.92/7.29 => ~ ( finite6017078050557962740nteger @ X7 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % infinite_growing
% 6.92/7.29 thf(fact_8440_infinite__growing,axiom,
% 6.92/7.29 ! [X7: set_o] :
% 6.92/7.29 ( ( X7 != bot_bot_set_o )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ X7 )
% 6.92/7.29 => ? [Xa3: $o] :
% 6.92/7.29 ( ( member_o @ Xa3 @ X7 )
% 6.92/7.29 & ( ord_less_o @ X3 @ Xa3 ) ) )
% 6.92/7.29 => ~ ( finite_finite_o @ X7 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % infinite_growing
% 6.92/7.29 thf(fact_8441_infinite__growing,axiom,
% 6.92/7.29 ! [X7: set_rat] :
% 6.92/7.29 ( ( X7 != bot_bot_set_rat )
% 6.92/7.29 => ( ! [X3: rat] :
% 6.92/7.29 ( ( member_rat @ X3 @ X7 )
% 6.92/7.29 => ? [Xa3: rat] :
% 6.92/7.29 ( ( member_rat @ Xa3 @ X7 )
% 6.92/7.29 & ( ord_less_rat @ X3 @ Xa3 ) ) )
% 6.92/7.29 => ~ ( finite_finite_rat @ X7 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % infinite_growing
% 6.92/7.29 thf(fact_8442_infinite__growing,axiom,
% 6.92/7.29 ! [X7: set_num] :
% 6.92/7.29 ( ( X7 != bot_bot_set_num )
% 6.92/7.29 => ( ! [X3: num] :
% 6.92/7.29 ( ( member_num @ X3 @ X7 )
% 6.92/7.29 => ? [Xa3: num] :
% 6.92/7.29 ( ( member_num @ Xa3 @ X7 )
% 6.92/7.29 & ( ord_less_num @ X3 @ Xa3 ) ) )
% 6.92/7.29 => ~ ( finite_finite_num @ X7 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % infinite_growing
% 6.92/7.29 thf(fact_8443_infinite__growing,axiom,
% 6.92/7.29 ! [X7: set_nat] :
% 6.92/7.29 ( ( X7 != bot_bot_set_nat )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ X7 )
% 6.92/7.29 => ? [Xa3: nat] :
% 6.92/7.29 ( ( member_nat @ Xa3 @ X7 )
% 6.92/7.29 & ( ord_less_nat @ X3 @ Xa3 ) ) )
% 6.92/7.29 => ~ ( finite_finite_nat @ X7 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % infinite_growing
% 6.92/7.29 thf(fact_8444_infinite__growing,axiom,
% 6.92/7.29 ! [X7: set_int] :
% 6.92/7.29 ( ( X7 != bot_bot_set_int )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ X7 )
% 6.92/7.29 => ? [Xa3: int] :
% 6.92/7.29 ( ( member_int @ Xa3 @ X7 )
% 6.92/7.29 & ( ord_less_int @ X3 @ Xa3 ) ) )
% 6.92/7.29 => ~ ( finite_finite_int @ X7 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % infinite_growing
% 6.92/7.29 thf(fact_8445_ex__min__if__finite,axiom,
% 6.92/7.29 ! [S: set_Code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ S )
% 6.92/7.29 => ( ( S != bot_bo3990330152332043303nteger )
% 6.92/7.29 => ? [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ S )
% 6.92/7.29 & ~ ? [Xa3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ Xa3 @ S )
% 6.92/7.29 & ( ord_le6747313008572928689nteger @ Xa3 @ X3 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % ex_min_if_finite
% 6.92/7.29 thf(fact_8446_ex__min__if__finite,axiom,
% 6.92/7.29 ! [S: set_o] :
% 6.92/7.29 ( ( finite_finite_o @ S )
% 6.92/7.29 => ( ( S != bot_bot_set_o )
% 6.92/7.29 => ? [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ S )
% 6.92/7.29 & ~ ? [Xa3: $o] :
% 6.92/7.29 ( ( member_o @ Xa3 @ S )
% 6.92/7.29 & ( ord_less_o @ Xa3 @ X3 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % ex_min_if_finite
% 6.92/7.29 thf(fact_8447_ex__min__if__finite,axiom,
% 6.92/7.29 ! [S: set_assn] :
% 6.92/7.29 ( ( finite_finite_assn @ S )
% 6.92/7.29 => ( ( S != bot_bot_set_assn )
% 6.92/7.29 => ? [X3: assn] :
% 6.92/7.29 ( ( member_assn @ X3 @ S )
% 6.92/7.29 & ~ ? [Xa3: assn] :
% 6.92/7.29 ( ( member_assn @ Xa3 @ S )
% 6.92/7.29 & ( ord_less_assn @ Xa3 @ X3 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % ex_min_if_finite
% 6.92/7.29 thf(fact_8448_ex__min__if__finite,axiom,
% 6.92/7.29 ! [S: set_rat] :
% 6.92/7.29 ( ( finite_finite_rat @ S )
% 6.92/7.29 => ( ( S != bot_bot_set_rat )
% 6.92/7.29 => ? [X3: rat] :
% 6.92/7.29 ( ( member_rat @ X3 @ S )
% 6.92/7.29 & ~ ? [Xa3: rat] :
% 6.92/7.29 ( ( member_rat @ Xa3 @ S )
% 6.92/7.29 & ( ord_less_rat @ Xa3 @ X3 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % ex_min_if_finite
% 6.92/7.29 thf(fact_8449_ex__min__if__finite,axiom,
% 6.92/7.29 ! [S: set_num] :
% 6.92/7.29 ( ( finite_finite_num @ S )
% 6.92/7.29 => ( ( S != bot_bot_set_num )
% 6.92/7.29 => ? [X3: num] :
% 6.92/7.29 ( ( member_num @ X3 @ S )
% 6.92/7.29 & ~ ? [Xa3: num] :
% 6.92/7.29 ( ( member_num @ Xa3 @ S )
% 6.92/7.29 & ( ord_less_num @ Xa3 @ X3 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % ex_min_if_finite
% 6.92/7.29 thf(fact_8450_ex__min__if__finite,axiom,
% 6.92/7.29 ! [S: set_nat] :
% 6.92/7.29 ( ( finite_finite_nat @ S )
% 6.92/7.29 => ( ( S != bot_bot_set_nat )
% 6.92/7.29 => ? [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ S )
% 6.92/7.29 & ~ ? [Xa3: nat] :
% 6.92/7.29 ( ( member_nat @ Xa3 @ S )
% 6.92/7.29 & ( ord_less_nat @ Xa3 @ X3 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % ex_min_if_finite
% 6.92/7.29 thf(fact_8451_ex__min__if__finite,axiom,
% 6.92/7.29 ! [S: set_int] :
% 6.92/7.29 ( ( finite_finite_int @ S )
% 6.92/7.29 => ( ( S != bot_bot_set_int )
% 6.92/7.29 => ? [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ S )
% 6.92/7.29 & ~ ? [Xa3: int] :
% 6.92/7.29 ( ( member_int @ Xa3 @ S )
% 6.92/7.29 & ( ord_less_int @ Xa3 @ X3 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % ex_min_if_finite
% 6.92/7.29 thf(fact_8452_plus__and__or,axiom,
% 6.92/7.29 ! [X: int,Y: int] :
% 6.92/7.29 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ ( bit_se1409905431419307370or_int @ X @ Y ) )
% 6.92/7.29 = ( plus_plus_int @ X @ Y ) ) ).
% 6.92/7.29
% 6.92/7.29 % plus_and_or
% 6.92/7.29 thf(fact_8453_sum__mono__inv,axiom,
% 6.92/7.29 ! [F: $o > rat,I5: set_o,G: $o > rat,I2: $o] :
% 6.92/7.29 ( ( ( groups7872700643590313910_o_rat @ F @ I5 )
% 6.92/7.29 = ( groups7872700643590313910_o_rat @ G @ I5 ) )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.29 => ( ( member_o @ I2 @ I5 )
% 6.92/7.29 => ( ( finite_finite_o @ I5 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = ( G @ I2 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_mono_inv
% 6.92/7.29 thf(fact_8454_sum__mono__inv,axiom,
% 6.92/7.29 ! [F: nat > rat,I5: set_nat,G: nat > rat,I2: nat] :
% 6.92/7.29 ( ( ( groups2906978787729119204at_rat @ F @ I5 )
% 6.92/7.29 = ( groups2906978787729119204at_rat @ G @ I5 ) )
% 6.92/7.29 => ( ! [I3: nat] :
% 6.92/7.29 ( ( member_nat @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.29 => ( ( member_nat @ I2 @ I5 )
% 6.92/7.29 => ( ( finite_finite_nat @ I5 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = ( G @ I2 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_mono_inv
% 6.92/7.29 thf(fact_8455_sum__mono__inv,axiom,
% 6.92/7.29 ! [F: int > rat,I5: set_int,G: int > rat,I2: int] :
% 6.92/7.29 ( ( ( groups3906332499630173760nt_rat @ F @ I5 )
% 6.92/7.29 = ( groups3906332499630173760nt_rat @ G @ I5 ) )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.29 => ( ( member_int @ I2 @ I5 )
% 6.92/7.29 => ( ( finite_finite_int @ I5 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = ( G @ I2 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_mono_inv
% 6.92/7.29 thf(fact_8456_sum__mono__inv,axiom,
% 6.92/7.29 ! [F: code_integer > rat,I5: set_Code_integer,G: code_integer > rat,I2: code_integer] :
% 6.92/7.29 ( ( ( groups6602215022474089585er_rat @ F @ I5 )
% 6.92/7.29 = ( groups6602215022474089585er_rat @ G @ I5 ) )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.29 => ( ( member_Code_integer @ I2 @ I5 )
% 6.92/7.29 => ( ( finite6017078050557962740nteger @ I5 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = ( G @ I2 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_mono_inv
% 6.92/7.29 thf(fact_8457_sum__mono__inv,axiom,
% 6.92/7.29 ! [F: $o > nat,I5: set_o,G: $o > nat,I2: $o] :
% 6.92/7.29 ( ( ( groups8507830703676809646_o_nat @ F @ I5 )
% 6.92/7.29 = ( groups8507830703676809646_o_nat @ G @ I5 ) )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.29 => ( ( member_o @ I2 @ I5 )
% 6.92/7.29 => ( ( finite_finite_o @ I5 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = ( G @ I2 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_mono_inv
% 6.92/7.29 thf(fact_8458_sum__mono__inv,axiom,
% 6.92/7.29 ! [F: int > nat,I5: set_int,G: int > nat,I2: int] :
% 6.92/7.29 ( ( ( groups4541462559716669496nt_nat @ F @ I5 )
% 6.92/7.29 = ( groups4541462559716669496nt_nat @ G @ I5 ) )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.29 => ( ( member_int @ I2 @ I5 )
% 6.92/7.29 => ( ( finite_finite_int @ I5 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = ( G @ I2 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_mono_inv
% 6.92/7.29 thf(fact_8459_sum__mono__inv,axiom,
% 6.92/7.29 ! [F: code_integer > nat,I5: set_Code_integer,G: code_integer > nat,I2: code_integer] :
% 6.92/7.29 ( ( ( groups7237345082560585321er_nat @ F @ I5 )
% 6.92/7.29 = ( groups7237345082560585321er_nat @ G @ I5 ) )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.29 => ( ( member_Code_integer @ I2 @ I5 )
% 6.92/7.29 => ( ( finite6017078050557962740nteger @ I5 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = ( G @ I2 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_mono_inv
% 6.92/7.29 thf(fact_8460_sum__mono__inv,axiom,
% 6.92/7.29 ! [F: $o > int,I5: set_o,G: $o > int,I2: $o] :
% 6.92/7.29 ( ( ( groups8505340233167759370_o_int @ F @ I5 )
% 6.92/7.29 = ( groups8505340233167759370_o_int @ G @ I5 ) )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.29 => ( ( member_o @ I2 @ I5 )
% 6.92/7.29 => ( ( finite_finite_o @ I5 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = ( G @ I2 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_mono_inv
% 6.92/7.29 thf(fact_8461_sum__mono__inv,axiom,
% 6.92/7.29 ! [F: nat > int,I5: set_nat,G: nat > int,I2: nat] :
% 6.92/7.29 ( ( ( groups3539618377306564664at_int @ F @ I5 )
% 6.92/7.29 = ( groups3539618377306564664at_int @ G @ I5 ) )
% 6.92/7.29 => ( ! [I3: nat] :
% 6.92/7.29 ( ( member_nat @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.29 => ( ( member_nat @ I2 @ I5 )
% 6.92/7.29 => ( ( finite_finite_nat @ I5 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = ( G @ I2 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_mono_inv
% 6.92/7.29 thf(fact_8462_sum__mono__inv,axiom,
% 6.92/7.29 ! [F: code_integer > int,I5: set_Code_integer,G: code_integer > int,I2: code_integer] :
% 6.92/7.29 ( ( ( groups7234854612051535045er_int @ F @ I5 )
% 6.92/7.29 = ( groups7234854612051535045er_int @ G @ I5 ) )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 6.92/7.29 => ( ( member_Code_integer @ I2 @ I5 )
% 6.92/7.29 => ( ( finite6017078050557962740nteger @ I5 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = ( G @ I2 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_mono_inv
% 6.92/7.29 thf(fact_8463_infinite__Icc,axiom,
% 6.92/7.29 ! [A: rat,B: rat] :
% 6.92/7.29 ( ( ord_less_rat @ A @ B )
% 6.92/7.29 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % infinite_Icc
% 6.92/7.29 thf(fact_8464_infinite__Ico,axiom,
% 6.92/7.29 ! [A: rat,B: rat] :
% 6.92/7.29 ( ( ord_less_rat @ A @ B )
% 6.92/7.29 => ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A @ B ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % infinite_Ico
% 6.92/7.29 thf(fact_8465_push__bit__take__bit,axiom,
% 6.92/7.29 ! [M: nat,N2: nat,A: int] :
% 6.92/7.29 ( ( bit_se545348938243370406it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 6.92/7.29 = ( bit_se2923211474154528505it_int @ ( plus_plus_nat @ M @ N2 ) @ ( bit_se545348938243370406it_int @ M @ A ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % push_bit_take_bit
% 6.92/7.29 thf(fact_8466_push__bit__take__bit,axiom,
% 6.92/7.29 ! [M: nat,N2: nat,A: nat] :
% 6.92/7.29 ( ( bit_se547839408752420682it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 6.92/7.29 = ( bit_se2925701944663578781it_nat @ ( plus_plus_nat @ M @ N2 ) @ ( bit_se547839408752420682it_nat @ M @ A ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % push_bit_take_bit
% 6.92/7.29 thf(fact_8467_sum_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_o,X: $o > code_integer,Y: $o > code_integer] :
% 6.92/7.29 ( ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != zero_z3403309356797280102nteger ) ) ) )
% 6.92/7.29 => ( ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != zero_z3403309356797280102nteger ) ) ) )
% 6.92/7.29 => ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( plus_p5714425477246183910nteger @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.finite_Collect_op
% 6.92/7.29 thf(fact_8468_sum_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_nat,X: nat > code_integer,Y: nat > code_integer] :
% 6.92/7.29 ( ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != zero_z3403309356797280102nteger ) ) ) )
% 6.92/7.29 => ( ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != zero_z3403309356797280102nteger ) ) ) )
% 6.92/7.29 => ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( plus_p5714425477246183910nteger @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.finite_Collect_op
% 6.92/7.29 thf(fact_8469_sum_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_int,X: int > code_integer,Y: int > code_integer] :
% 6.92/7.29 ( ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [I: int] :
% 6.92/7.29 ( ( member_int @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != zero_z3403309356797280102nteger ) ) ) )
% 6.92/7.29 => ( ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [I: int] :
% 6.92/7.29 ( ( member_int @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != zero_z3403309356797280102nteger ) ) ) )
% 6.92/7.29 => ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [I: int] :
% 6.92/7.29 ( ( member_int @ I @ I5 )
% 6.92/7.29 & ( ( plus_p5714425477246183910nteger @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.finite_Collect_op
% 6.92/7.29 thf(fact_8470_sum_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_Code_integer,X: code_integer > code_integer,Y: code_integer > code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [I: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != zero_z3403309356797280102nteger ) ) ) )
% 6.92/7.29 => ( ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [I: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != zero_z3403309356797280102nteger ) ) ) )
% 6.92/7.29 => ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [I: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I @ I5 )
% 6.92/7.29 & ( ( plus_p5714425477246183910nteger @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.finite_Collect_op
% 6.92/7.29 thf(fact_8471_sum_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_o,X: $o > rat,Y: $o > rat] :
% 6.92/7.29 ( ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != zero_zero_rat ) ) ) )
% 6.92/7.29 => ( ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != zero_zero_rat ) ) ) )
% 6.92/7.29 => ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( plus_plus_rat @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.finite_Collect_op
% 6.92/7.29 thf(fact_8472_sum_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_nat,X: nat > rat,Y: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != zero_zero_rat ) ) ) )
% 6.92/7.29 => ( ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != zero_zero_rat ) ) ) )
% 6.92/7.29 => ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( plus_plus_rat @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.finite_Collect_op
% 6.92/7.29 thf(fact_8473_sum_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_int,X: int > rat,Y: int > rat] :
% 6.92/7.29 ( ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [I: int] :
% 6.92/7.29 ( ( member_int @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != zero_zero_rat ) ) ) )
% 6.92/7.29 => ( ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [I: int] :
% 6.92/7.29 ( ( member_int @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != zero_zero_rat ) ) ) )
% 6.92/7.29 => ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [I: int] :
% 6.92/7.29 ( ( member_int @ I @ I5 )
% 6.92/7.29 & ( ( plus_plus_rat @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.finite_Collect_op
% 6.92/7.29 thf(fact_8474_sum_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_Code_integer,X: code_integer > rat,Y: code_integer > rat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [I: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != zero_zero_rat ) ) ) )
% 6.92/7.29 => ( ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [I: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != zero_zero_rat ) ) ) )
% 6.92/7.29 => ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [I: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I @ I5 )
% 6.92/7.29 & ( ( plus_plus_rat @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.finite_Collect_op
% 6.92/7.29 thf(fact_8475_sum_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_o,X: $o > nat,Y: $o > nat] :
% 6.92/7.29 ( ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != zero_zero_nat ) ) ) )
% 6.92/7.29 => ( ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != zero_zero_nat ) ) ) )
% 6.92/7.29 => ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( plus_plus_nat @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != zero_zero_nat ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.finite_Collect_op
% 6.92/7.29 thf(fact_8476_sum_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_nat,X: nat > nat,Y: nat > nat] :
% 6.92/7.29 ( ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != zero_zero_nat ) ) ) )
% 6.92/7.29 => ( ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != zero_zero_nat ) ) ) )
% 6.92/7.29 => ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( plus_plus_nat @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != zero_zero_nat ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.finite_Collect_op
% 6.92/7.29 thf(fact_8477_prod_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_o,X: $o > code_integer,Y: $o > code_integer] :
% 6.92/7.29 ( ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != one_one_Code_integer ) ) ) )
% 6.92/7.29 => ( ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != one_one_Code_integer ) ) ) )
% 6.92/7.29 => ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != one_one_Code_integer ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.finite_Collect_op
% 6.92/7.29 thf(fact_8478_prod_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_nat,X: nat > code_integer,Y: nat > code_integer] :
% 6.92/7.29 ( ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != one_one_Code_integer ) ) ) )
% 6.92/7.29 => ( ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != one_one_Code_integer ) ) ) )
% 6.92/7.29 => ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != one_one_Code_integer ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.finite_Collect_op
% 6.92/7.29 thf(fact_8479_prod_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_int,X: int > code_integer,Y: int > code_integer] :
% 6.92/7.29 ( ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [I: int] :
% 6.92/7.29 ( ( member_int @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != one_one_Code_integer ) ) ) )
% 6.92/7.29 => ( ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [I: int] :
% 6.92/7.29 ( ( member_int @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != one_one_Code_integer ) ) ) )
% 6.92/7.29 => ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [I: int] :
% 6.92/7.29 ( ( member_int @ I @ I5 )
% 6.92/7.29 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != one_one_Code_integer ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.finite_Collect_op
% 6.92/7.29 thf(fact_8480_prod_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_Code_integer,X: code_integer > code_integer,Y: code_integer > code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [I: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != one_one_Code_integer ) ) ) )
% 6.92/7.29 => ( ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [I: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != one_one_Code_integer ) ) ) )
% 6.92/7.29 => ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [I: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I @ I5 )
% 6.92/7.29 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != one_one_Code_integer ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.finite_Collect_op
% 6.92/7.29 thf(fact_8481_prod_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_o,X: $o > assn,Y: $o > assn] :
% 6.92/7.29 ( ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != one_one_assn ) ) ) )
% 6.92/7.29 => ( ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != one_one_assn ) ) ) )
% 6.92/7.29 => ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( times_times_assn @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != one_one_assn ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.finite_Collect_op
% 6.92/7.29 thf(fact_8482_prod_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_nat,X: nat > assn,Y: nat > assn] :
% 6.92/7.29 ( ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != one_one_assn ) ) ) )
% 6.92/7.29 => ( ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != one_one_assn ) ) ) )
% 6.92/7.29 => ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( times_times_assn @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != one_one_assn ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.finite_Collect_op
% 6.92/7.29 thf(fact_8483_prod_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_int,X: int > assn,Y: int > assn] :
% 6.92/7.29 ( ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [I: int] :
% 6.92/7.29 ( ( member_int @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != one_one_assn ) ) ) )
% 6.92/7.29 => ( ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [I: int] :
% 6.92/7.29 ( ( member_int @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != one_one_assn ) ) ) )
% 6.92/7.29 => ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [I: int] :
% 6.92/7.29 ( ( member_int @ I @ I5 )
% 6.92/7.29 & ( ( times_times_assn @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != one_one_assn ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.finite_Collect_op
% 6.92/7.29 thf(fact_8484_prod_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_Code_integer,X: code_integer > assn,Y: code_integer > assn] :
% 6.92/7.29 ( ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [I: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != one_one_assn ) ) ) )
% 6.92/7.29 => ( ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [I: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != one_one_assn ) ) ) )
% 6.92/7.29 => ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [I: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I @ I5 )
% 6.92/7.29 & ( ( times_times_assn @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != one_one_assn ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.finite_Collect_op
% 6.92/7.29 thf(fact_8485_prod_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_o,X: $o > rat,Y: $o > rat] :
% 6.92/7.29 ( ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != one_one_rat ) ) ) )
% 6.92/7.29 => ( ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != one_one_rat ) ) ) )
% 6.92/7.29 => ( finite_finite_o
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [I: $o] :
% 6.92/7.29 ( ( member_o @ I @ I5 )
% 6.92/7.29 & ( ( times_times_rat @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != one_one_rat ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.finite_Collect_op
% 6.92/7.29 thf(fact_8486_prod_Ofinite__Collect__op,axiom,
% 6.92/7.29 ! [I5: set_nat,X: nat > rat,Y: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( X @ I )
% 6.92/7.29 != one_one_rat ) ) ) )
% 6.92/7.29 => ( ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( Y @ I )
% 6.92/7.29 != one_one_rat ) ) ) )
% 6.92/7.29 => ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [I: nat] :
% 6.92/7.29 ( ( member_nat @ I @ I5 )
% 6.92/7.29 & ( ( times_times_rat @ ( X @ I ) @ ( Y @ I ) )
% 6.92/7.29 != one_one_rat ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.finite_Collect_op
% 6.92/7.29 thf(fact_8487_sum_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_o,G: $o > code_integer,P2: $o > $o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( groups4406642042086082107nteger @ G
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [X4: $o] :
% 6.92/7.29 ( ( member_o @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups4406642042086082107nteger
% 6.92/7.29 @ ^ [X4: $o] : ( if_Code_integer @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_z3403309356797280102nteger )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_filter
% 6.92/7.29 thf(fact_8488_sum_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_nat,G: nat > code_integer,P2: nat > $o] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( groups7501900531339628137nteger @ G
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( member_nat @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups7501900531339628137nteger
% 6.92/7.29 @ ^ [X4: nat] : ( if_Code_integer @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_z3403309356797280102nteger )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_filter
% 6.92/7.29 thf(fact_8489_sum_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > code_integer,P2: int > $o] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups7873554091576472773nteger @ G
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] :
% 6.92/7.29 ( ( member_int @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups7873554091576472773nteger
% 6.92/7.29 @ ^ [X4: int] : ( if_Code_integer @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_z3403309356797280102nteger )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_filter
% 6.92/7.29 thf(fact_8490_sum_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > code_integer,P2: code_integer > $o] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups879477027807139574nteger @ G
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups879477027807139574nteger
% 6.92/7.29 @ ^ [X4: code_integer] : ( if_Code_integer @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_z3403309356797280102nteger )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_filter
% 6.92/7.29 thf(fact_8491_sum_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_o,G: $o > rat,P2: $o > $o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( groups7872700643590313910_o_rat @ G
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [X4: $o] :
% 6.92/7.29 ( ( member_o @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups7872700643590313910_o_rat
% 6.92/7.29 @ ^ [X4: $o] : ( if_rat @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_rat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_filter
% 6.92/7.29 thf(fact_8492_sum_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_nat,G: nat > rat,P2: nat > $o] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( groups2906978787729119204at_rat @ G
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( member_nat @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups2906978787729119204at_rat
% 6.92/7.29 @ ^ [X4: nat] : ( if_rat @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_rat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_filter
% 6.92/7.29 thf(fact_8493_sum_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > rat,P2: int > $o] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups3906332499630173760nt_rat @ G
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] :
% 6.92/7.29 ( ( member_int @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups3906332499630173760nt_rat
% 6.92/7.29 @ ^ [X4: int] : ( if_rat @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_rat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_filter
% 6.92/7.29 thf(fact_8494_sum_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > rat,P2: code_integer > $o] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups6602215022474089585er_rat @ G
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups6602215022474089585er_rat
% 6.92/7.29 @ ^ [X4: code_integer] : ( if_rat @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_rat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_filter
% 6.92/7.29 thf(fact_8495_sum_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_o,G: $o > nat,P2: $o > $o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( groups8507830703676809646_o_nat @ G
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [X4: $o] :
% 6.92/7.29 ( ( member_o @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups8507830703676809646_o_nat
% 6.92/7.29 @ ^ [X4: $o] : ( if_nat @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_nat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_filter
% 6.92/7.29 thf(fact_8496_sum_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > nat,P2: int > $o] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups4541462559716669496nt_nat @ G
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] :
% 6.92/7.29 ( ( member_int @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups4541462559716669496nt_nat
% 6.92/7.29 @ ^ [X4: int] : ( if_nat @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_nat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_filter
% 6.92/7.29 thf(fact_8497_filter__preserves__multiset,axiom,
% 6.92/7.29 ! [M6: list_nat > nat,P2: list_nat > $o] :
% 6.92/7.29 ( ( finite8100373058378681591st_nat
% 6.92/7.29 @ ( collect_list_nat
% 6.92/7.29 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite8100373058378681591st_nat
% 6.92/7.29 @ ( collect_list_nat
% 6.92/7.29 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M6 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % filter_preserves_multiset
% 6.92/7.29 thf(fact_8498_filter__preserves__multiset,axiom,
% 6.92/7.29 ! [M6: set_Pr958786334691620121nt_int > nat,P2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.29 ( ( finite8744585540193469122nt_int
% 6.92/7.29 @ ( collec5210948495886036740nt_int
% 6.92/7.29 @ ^ [X4: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite8744585540193469122nt_int
% 6.92/7.29 @ ( collec5210948495886036740nt_int
% 6.92/7.29 @ ^ [X4: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M6 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % filter_preserves_multiset
% 6.92/7.29 thf(fact_8499_filter__preserves__multiset,axiom,
% 6.92/7.29 ! [M6: set_nat > nat,P2: set_nat > $o] :
% 6.92/7.29 ( ( finite1152437895449049373et_nat
% 6.92/7.29 @ ( collect_set_nat
% 6.92/7.29 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite1152437895449049373et_nat
% 6.92/7.29 @ ( collect_set_nat
% 6.92/7.29 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M6 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % filter_preserves_multiset
% 6.92/7.29 thf(fact_8500_filter__preserves__multiset,axiom,
% 6.92/7.29 ! [M6: nat > nat,P2: nat > $o] :
% 6.92/7.29 ( ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M6 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % filter_preserves_multiset
% 6.92/7.29 thf(fact_8501_filter__preserves__multiset,axiom,
% 6.92/7.29 ! [M6: int > nat,P2: int > $o] :
% 6.92/7.29 ( ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M6 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % filter_preserves_multiset
% 6.92/7.29 thf(fact_8502_filter__preserves__multiset,axiom,
% 6.92/7.29 ! [M6: code_integer > nat,P2: code_integer > $o] :
% 6.92/7.29 ( ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M6 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % filter_preserves_multiset
% 6.92/7.29 thf(fact_8503_filter__preserves__multiset,axiom,
% 6.92/7.29 ! [M6: product_prod_nat_nat > nat,P2: product_prod_nat_nat > $o] :
% 6.92/7.29 ( ( finite6177210948735845034at_nat
% 6.92/7.29 @ ( collec3392354462482085612at_nat
% 6.92/7.29 @ ^ [X4: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite6177210948735845034at_nat
% 6.92/7.29 @ ( collec3392354462482085612at_nat
% 6.92/7.29 @ ^ [X4: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M6 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % filter_preserves_multiset
% 6.92/7.29 thf(fact_8504_prod_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_o,G: $o > code_integer,P2: $o > $o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( groups7694694392188491536nteger @ G
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [X4: $o] :
% 6.92/7.29 ( ( member_o @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups7694694392188491536nteger
% 6.92/7.29 @ ^ [X4: $o] : ( if_Code_integer @ ( P2 @ X4 ) @ ( G @ X4 ) @ one_one_Code_integer )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_filter
% 6.92/7.29 thf(fact_8505_prod_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_nat,G: nat > code_integer,P2: nat > $o] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( groups3455450783089532116nteger @ G
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( member_nat @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups3455450783089532116nteger
% 6.92/7.29 @ ^ [X4: nat] : ( if_Code_integer @ ( P2 @ X4 ) @ ( G @ X4 ) @ one_one_Code_integer )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_filter
% 6.92/7.29 thf(fact_8506_prod_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > code_integer,P2: int > $o] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups3827104343326376752nteger @ G
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] :
% 6.92/7.29 ( ( member_int @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups3827104343326376752nteger
% 6.92/7.29 @ ^ [X4: int] : ( if_Code_integer @ ( P2 @ X4 ) @ ( G @ X4 ) @ one_one_Code_integer )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_filter
% 6.92/7.29 thf(fact_8507_prod_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > code_integer,P2: code_integer > $o] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups3674199335183972705nteger @ G
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups3674199335183972705nteger
% 6.92/7.29 @ ^ [X4: code_integer] : ( if_Code_integer @ ( P2 @ X4 ) @ ( G @ X4 ) @ one_one_Code_integer )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_filter
% 6.92/7.29 thf(fact_8508_prod_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_o,G: $o > assn,P2: $o > $o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( groups5301882518646026715o_assn @ G
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [X4: $o] :
% 6.92/7.29 ( ( member_o @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups5301882518646026715o_assn
% 6.92/7.29 @ ^ [X4: $o] : ( if_assn @ ( P2 @ X4 ) @ ( G @ X4 ) @ one_one_assn )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_filter
% 6.92/7.29 thf(fact_8509_prod_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_nat,G: nat > assn,P2: nat > $o] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( groups6906906614972039071t_assn @ G
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( member_nat @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups6906906614972039071t_assn
% 6.92/7.29 @ ^ [X4: nat] : ( if_assn @ ( P2 @ X4 ) @ ( G @ X4 ) @ one_one_assn )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_filter
% 6.92/7.29 thf(fact_8510_prod_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > assn,P2: int > $o] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups7882442080178216443t_assn @ G
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] :
% 6.92/7.29 ( ( member_int @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups7882442080178216443t_assn
% 6.92/7.29 @ ^ [X4: int] : ( if_assn @ ( P2 @ X4 ) @ ( G @ X4 ) @ one_one_assn )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_filter
% 6.92/7.29 thf(fact_8511_prod_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > assn,P2: code_integer > $o] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups1304777262505850412r_assn @ G
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups1304777262505850412r_assn
% 6.92/7.29 @ ^ [X4: code_integer] : ( if_assn @ ( P2 @ X4 ) @ ( G @ X4 ) @ one_one_assn )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_filter
% 6.92/7.29 thf(fact_8512_prod_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_o,G: $o > rat,P2: $o > $o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( groups2869687844427037835_o_rat @ G
% 6.92/7.29 @ ( collect_o
% 6.92/7.29 @ ^ [X4: $o] :
% 6.92/7.29 ( ( member_o @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups2869687844427037835_o_rat
% 6.92/7.29 @ ^ [X4: $o] : ( if_rat @ ( P2 @ X4 ) @ ( G @ X4 ) @ one_one_rat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_filter
% 6.92/7.29 thf(fact_8513_prod_Ointer__filter,axiom,
% 6.92/7.29 ! [A4: set_nat,G: nat > rat,P2: nat > $o] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( groups73079841787564623at_rat @ G
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( member_nat @ X4 @ A4 )
% 6.92/7.29 & ( P2 @ X4 ) ) ) )
% 6.92/7.29 = ( groups73079841787564623at_rat
% 6.92/7.29 @ ^ [X4: nat] : ( if_rat @ ( P2 @ X4 ) @ ( G @ X4 ) @ one_one_rat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_filter
% 6.92/7.29 thf(fact_8514_finite__int__segment,axiom,
% 6.92/7.29 ! [A: rat,B: rat] :
% 6.92/7.29 ( finite_finite_rat
% 6.92/7.29 @ ( collect_rat
% 6.92/7.29 @ ^ [X4: rat] :
% 6.92/7.29 ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 6.92/7.29 & ( ord_less_eq_rat @ A @ X4 )
% 6.92/7.29 & ( ord_less_eq_rat @ X4 @ B ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_int_segment
% 6.92/7.29 thf(fact_8515_sum__nonneg__eq__0__iff,axiom,
% 6.92/7.29 ! [A4: set_o,F: $o > code_integer] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ A4 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( ( groups4406642042086082107nteger @ F @ A4 )
% 6.92/7.29 = zero_z3403309356797280102nteger )
% 6.92/7.29 = ( ! [X4: $o] :
% 6.92/7.29 ( ( member_o @ X4 @ A4 )
% 6.92/7.29 => ( ( F @ X4 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_eq_0_iff
% 6.92/7.29 thf(fact_8516_sum__nonneg__eq__0__iff,axiom,
% 6.92/7.29 ! [A4: set_nat,F: nat > code_integer] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ A4 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( ( groups7501900531339628137nteger @ F @ A4 )
% 6.92/7.29 = zero_z3403309356797280102nteger )
% 6.92/7.29 = ( ! [X4: nat] :
% 6.92/7.29 ( ( member_nat @ X4 @ A4 )
% 6.92/7.29 => ( ( F @ X4 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_eq_0_iff
% 6.92/7.29 thf(fact_8517_sum__nonneg__eq__0__iff,axiom,
% 6.92/7.29 ! [A4: set_int,F: int > code_integer] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ A4 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( ( groups7873554091576472773nteger @ F @ A4 )
% 6.92/7.29 = zero_z3403309356797280102nteger )
% 6.92/7.29 = ( ! [X4: int] :
% 6.92/7.29 ( ( member_int @ X4 @ A4 )
% 6.92/7.29 => ( ( F @ X4 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_eq_0_iff
% 6.92/7.29 thf(fact_8518_sum__nonneg__eq__0__iff,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,F: code_integer > code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ A4 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( ( groups879477027807139574nteger @ F @ A4 )
% 6.92/7.29 = zero_z3403309356797280102nteger )
% 6.92/7.29 = ( ! [X4: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X4 @ A4 )
% 6.92/7.29 => ( ( F @ X4 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_eq_0_iff
% 6.92/7.29 thf(fact_8519_sum__nonneg__eq__0__iff,axiom,
% 6.92/7.29 ! [A4: set_o,F: $o > rat] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( ( groups7872700643590313910_o_rat @ F @ A4 )
% 6.92/7.29 = zero_zero_rat )
% 6.92/7.29 = ( ! [X4: $o] :
% 6.92/7.29 ( ( member_o @ X4 @ A4 )
% 6.92/7.29 => ( ( F @ X4 )
% 6.92/7.29 = zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_eq_0_iff
% 6.92/7.29 thf(fact_8520_sum__nonneg__eq__0__iff,axiom,
% 6.92/7.29 ! [A4: set_nat,F: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( ( groups2906978787729119204at_rat @ F @ A4 )
% 6.92/7.29 = zero_zero_rat )
% 6.92/7.29 = ( ! [X4: nat] :
% 6.92/7.29 ( ( member_nat @ X4 @ A4 )
% 6.92/7.29 => ( ( F @ X4 )
% 6.92/7.29 = zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_eq_0_iff
% 6.92/7.29 thf(fact_8521_sum__nonneg__eq__0__iff,axiom,
% 6.92/7.29 ! [A4: set_int,F: int > rat] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( ( groups3906332499630173760nt_rat @ F @ A4 )
% 6.92/7.29 = zero_zero_rat )
% 6.92/7.29 = ( ! [X4: int] :
% 6.92/7.29 ( ( member_int @ X4 @ A4 )
% 6.92/7.29 => ( ( F @ X4 )
% 6.92/7.29 = zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_eq_0_iff
% 6.92/7.29 thf(fact_8522_sum__nonneg__eq__0__iff,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,F: code_integer > rat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( ( groups6602215022474089585er_rat @ F @ A4 )
% 6.92/7.29 = zero_zero_rat )
% 6.92/7.29 = ( ! [X4: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X4 @ A4 )
% 6.92/7.29 => ( ( F @ X4 )
% 6.92/7.29 = zero_zero_rat ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_eq_0_iff
% 6.92/7.29 thf(fact_8523_sum__nonneg__eq__0__iff,axiom,
% 6.92/7.29 ! [A4: set_o,F: $o > nat] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( ( groups8507830703676809646_o_nat @ F @ A4 )
% 6.92/7.29 = zero_zero_nat )
% 6.92/7.29 = ( ! [X4: $o] :
% 6.92/7.29 ( ( member_o @ X4 @ A4 )
% 6.92/7.29 => ( ( F @ X4 )
% 6.92/7.29 = zero_zero_nat ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_eq_0_iff
% 6.92/7.29 thf(fact_8524_sum__nonneg__eq__0__iff,axiom,
% 6.92/7.29 ! [A4: set_int,F: int > nat] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( ( groups4541462559716669496nt_nat @ F @ A4 )
% 6.92/7.29 = zero_zero_nat )
% 6.92/7.29 = ( ! [X4: int] :
% 6.92/7.29 ( ( member_int @ X4 @ A4 )
% 6.92/7.29 => ( ( F @ X4 )
% 6.92/7.29 = zero_zero_nat ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_eq_0_iff
% 6.92/7.29 thf(fact_8525_sum__le__included,axiom,
% 6.92/7.29 ! [S2: set_nat,T6: set_nat,G: nat > code_integer,I2: nat > nat,F: nat > code_integer] :
% 6.92/7.29 ( ( finite_finite_nat @ S2 )
% 6.92/7.29 => ( ( finite_finite_nat @ T6 )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ T6 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ S2 )
% 6.92/7.29 => ? [Xa3: nat] :
% 6.92/7.29 ( ( member_nat @ Xa3 @ T6 )
% 6.92/7.29 & ( ( I2 @ Xa3 )
% 6.92/7.29 = X3 )
% 6.92/7.29 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa3 ) ) ) )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ ( groups7501900531339628137nteger @ F @ S2 ) @ ( groups7501900531339628137nteger @ G @ T6 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_le_included
% 6.92/7.29 thf(fact_8526_sum__le__included,axiom,
% 6.92/7.29 ! [S2: set_nat,T6: set_int,G: int > code_integer,I2: int > nat,F: nat > code_integer] :
% 6.92/7.29 ( ( finite_finite_nat @ S2 )
% 6.92/7.29 => ( ( finite_finite_int @ T6 )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ T6 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ S2 )
% 6.92/7.29 => ? [Xa3: int] :
% 6.92/7.29 ( ( member_int @ Xa3 @ T6 )
% 6.92/7.29 & ( ( I2 @ Xa3 )
% 6.92/7.29 = X3 )
% 6.92/7.29 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa3 ) ) ) )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ ( groups7501900531339628137nteger @ F @ S2 ) @ ( groups7873554091576472773nteger @ G @ T6 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_le_included
% 6.92/7.29 thf(fact_8527_sum__le__included,axiom,
% 6.92/7.29 ! [S2: set_nat,T6: set_Code_integer,G: code_integer > code_integer,I2: code_integer > nat,F: nat > code_integer] :
% 6.92/7.29 ( ( finite_finite_nat @ S2 )
% 6.92/7.29 => ( ( finite6017078050557962740nteger @ T6 )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ T6 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ S2 )
% 6.92/7.29 => ? [Xa3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ Xa3 @ T6 )
% 6.92/7.29 & ( ( I2 @ Xa3 )
% 6.92/7.29 = X3 )
% 6.92/7.29 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa3 ) ) ) )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ ( groups7501900531339628137nteger @ F @ S2 ) @ ( groups879477027807139574nteger @ G @ T6 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_le_included
% 6.92/7.29 thf(fact_8528_sum__le__included,axiom,
% 6.92/7.29 ! [S2: set_int,T6: set_nat,G: nat > code_integer,I2: nat > int,F: int > code_integer] :
% 6.92/7.29 ( ( finite_finite_int @ S2 )
% 6.92/7.29 => ( ( finite_finite_nat @ T6 )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ T6 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ S2 )
% 6.92/7.29 => ? [Xa3: nat] :
% 6.92/7.29 ( ( member_nat @ Xa3 @ T6 )
% 6.92/7.29 & ( ( I2 @ Xa3 )
% 6.92/7.29 = X3 )
% 6.92/7.29 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa3 ) ) ) )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ ( groups7873554091576472773nteger @ F @ S2 ) @ ( groups7501900531339628137nteger @ G @ T6 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_le_included
% 6.92/7.29 thf(fact_8529_sum__le__included,axiom,
% 6.92/7.29 ! [S2: set_int,T6: set_int,G: int > code_integer,I2: int > int,F: int > code_integer] :
% 6.92/7.29 ( ( finite_finite_int @ S2 )
% 6.92/7.29 => ( ( finite_finite_int @ T6 )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ T6 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ S2 )
% 6.92/7.29 => ? [Xa3: int] :
% 6.92/7.29 ( ( member_int @ Xa3 @ T6 )
% 6.92/7.29 & ( ( I2 @ Xa3 )
% 6.92/7.29 = X3 )
% 6.92/7.29 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa3 ) ) ) )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ ( groups7873554091576472773nteger @ F @ S2 ) @ ( groups7873554091576472773nteger @ G @ T6 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_le_included
% 6.92/7.29 thf(fact_8530_sum__le__included,axiom,
% 6.92/7.29 ! [S2: set_int,T6: set_Code_integer,G: code_integer > code_integer,I2: code_integer > int,F: int > code_integer] :
% 6.92/7.29 ( ( finite_finite_int @ S2 )
% 6.92/7.29 => ( ( finite6017078050557962740nteger @ T6 )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ T6 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ S2 )
% 6.92/7.29 => ? [Xa3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ Xa3 @ T6 )
% 6.92/7.29 & ( ( I2 @ Xa3 )
% 6.92/7.29 = X3 )
% 6.92/7.29 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa3 ) ) ) )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ ( groups7873554091576472773nteger @ F @ S2 ) @ ( groups879477027807139574nteger @ G @ T6 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_le_included
% 6.92/7.29 thf(fact_8531_sum__le__included,axiom,
% 6.92/7.29 ! [S2: set_Code_integer,T6: set_nat,G: nat > code_integer,I2: nat > code_integer,F: code_integer > code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ S2 )
% 6.92/7.29 => ( ( finite_finite_nat @ T6 )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ T6 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ S2 )
% 6.92/7.29 => ? [Xa3: nat] :
% 6.92/7.29 ( ( member_nat @ Xa3 @ T6 )
% 6.92/7.29 & ( ( I2 @ Xa3 )
% 6.92/7.29 = X3 )
% 6.92/7.29 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa3 ) ) ) )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ ( groups879477027807139574nteger @ F @ S2 ) @ ( groups7501900531339628137nteger @ G @ T6 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_le_included
% 6.92/7.29 thf(fact_8532_sum__le__included,axiom,
% 6.92/7.29 ! [S2: set_Code_integer,T6: set_int,G: int > code_integer,I2: int > code_integer,F: code_integer > code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ S2 )
% 6.92/7.29 => ( ( finite_finite_int @ T6 )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ T6 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ S2 )
% 6.92/7.29 => ? [Xa3: int] :
% 6.92/7.29 ( ( member_int @ Xa3 @ T6 )
% 6.92/7.29 & ( ( I2 @ Xa3 )
% 6.92/7.29 = X3 )
% 6.92/7.29 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa3 ) ) ) )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ ( groups879477027807139574nteger @ F @ S2 ) @ ( groups7873554091576472773nteger @ G @ T6 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_le_included
% 6.92/7.29 thf(fact_8533_sum__le__included,axiom,
% 6.92/7.29 ! [S2: set_Code_integer,T6: set_Code_integer,G: code_integer > code_integer,I2: code_integer > code_integer,F: code_integer > code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ S2 )
% 6.92/7.29 => ( ( finite6017078050557962740nteger @ T6 )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ T6 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ S2 )
% 6.92/7.29 => ? [Xa3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ Xa3 @ T6 )
% 6.92/7.29 & ( ( I2 @ Xa3 )
% 6.92/7.29 = X3 )
% 6.92/7.29 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa3 ) ) ) )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ ( groups879477027807139574nteger @ F @ S2 ) @ ( groups879477027807139574nteger @ G @ T6 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_le_included
% 6.92/7.29 thf(fact_8534_sum__le__included,axiom,
% 6.92/7.29 ! [S2: set_nat,T6: set_nat,G: nat > rat,I2: nat > nat,F: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat @ S2 )
% 6.92/7.29 => ( ( finite_finite_nat @ T6 )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ T6 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ S2 )
% 6.92/7.29 => ? [Xa3: nat] :
% 6.92/7.29 ( ( member_nat @ Xa3 @ T6 )
% 6.92/7.29 & ( ( I2 @ Xa3 )
% 6.92/7.29 = X3 )
% 6.92/7.29 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa3 ) ) ) )
% 6.92/7.29 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S2 ) @ ( groups2906978787729119204at_rat @ G @ T6 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_le_included
% 6.92/7.29 thf(fact_8535_finite__ranking__induct,axiom,
% 6.92/7.29 ! [S: set_Code_integer,P2: set_Code_integer > $o,F: code_integer > rat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ S )
% 6.92/7.29 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 6.92/7.29 => ( ! [X3: code_integer,S8: set_Code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ S8 )
% 6.92/7.29 => ( ! [Y5: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ Y5 @ S8 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( P2 @ S8 )
% 6.92/7.29 => ( P2 @ ( insert_Code_integer @ X3 @ S8 ) ) ) ) )
% 6.92/7.29 => ( P2 @ S ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_ranking_induct
% 6.92/7.29 thf(fact_8536_finite__ranking__induct,axiom,
% 6.92/7.29 ! [S: set_o,P2: set_o > $o,F: $o > rat] :
% 6.92/7.29 ( ( finite_finite_o @ S )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_o )
% 6.92/7.29 => ( ! [X3: $o,S8: set_o] :
% 6.92/7.29 ( ( finite_finite_o @ S8 )
% 6.92/7.29 => ( ! [Y5: $o] :
% 6.92/7.29 ( ( member_o @ Y5 @ S8 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( P2 @ S8 )
% 6.92/7.29 => ( P2 @ ( insert_o @ X3 @ S8 ) ) ) ) )
% 6.92/7.29 => ( P2 @ S ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_ranking_induct
% 6.92/7.29 thf(fact_8537_finite__ranking__induct,axiom,
% 6.92/7.29 ! [S: set_nat,P2: set_nat > $o,F: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat @ S )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_nat )
% 6.92/7.29 => ( ! [X3: nat,S8: set_nat] :
% 6.92/7.29 ( ( finite_finite_nat @ S8 )
% 6.92/7.29 => ( ! [Y5: nat] :
% 6.92/7.29 ( ( member_nat @ Y5 @ S8 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( P2 @ S8 )
% 6.92/7.29 => ( P2 @ ( insert_nat @ X3 @ S8 ) ) ) ) )
% 6.92/7.29 => ( P2 @ S ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_ranking_induct
% 6.92/7.29 thf(fact_8538_finite__ranking__induct,axiom,
% 6.92/7.29 ! [S: set_int,P2: set_int > $o,F: int > rat] :
% 6.92/7.29 ( ( finite_finite_int @ S )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_int )
% 6.92/7.29 => ( ! [X3: int,S8: set_int] :
% 6.92/7.29 ( ( finite_finite_int @ S8 )
% 6.92/7.29 => ( ! [Y5: int] :
% 6.92/7.29 ( ( member_int @ Y5 @ S8 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( P2 @ S8 )
% 6.92/7.29 => ( P2 @ ( insert_int @ X3 @ S8 ) ) ) ) )
% 6.92/7.29 => ( P2 @ S ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_ranking_induct
% 6.92/7.29 thf(fact_8539_finite__ranking__induct,axiom,
% 6.92/7.29 ! [S: set_Code_integer,P2: set_Code_integer > $o,F: code_integer > num] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ S )
% 6.92/7.29 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 6.92/7.29 => ( ! [X3: code_integer,S8: set_Code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ S8 )
% 6.92/7.29 => ( ! [Y5: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ Y5 @ S8 )
% 6.92/7.29 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( P2 @ S8 )
% 6.92/7.29 => ( P2 @ ( insert_Code_integer @ X3 @ S8 ) ) ) ) )
% 6.92/7.29 => ( P2 @ S ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_ranking_induct
% 6.92/7.29 thf(fact_8540_finite__ranking__induct,axiom,
% 6.92/7.29 ! [S: set_o,P2: set_o > $o,F: $o > num] :
% 6.92/7.29 ( ( finite_finite_o @ S )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_o )
% 6.92/7.29 => ( ! [X3: $o,S8: set_o] :
% 6.92/7.29 ( ( finite_finite_o @ S8 )
% 6.92/7.29 => ( ! [Y5: $o] :
% 6.92/7.29 ( ( member_o @ Y5 @ S8 )
% 6.92/7.29 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( P2 @ S8 )
% 6.92/7.29 => ( P2 @ ( insert_o @ X3 @ S8 ) ) ) ) )
% 6.92/7.29 => ( P2 @ S ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_ranking_induct
% 6.92/7.29 thf(fact_8541_finite__ranking__induct,axiom,
% 6.92/7.29 ! [S: set_nat,P2: set_nat > $o,F: nat > num] :
% 6.92/7.29 ( ( finite_finite_nat @ S )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_nat )
% 6.92/7.29 => ( ! [X3: nat,S8: set_nat] :
% 6.92/7.29 ( ( finite_finite_nat @ S8 )
% 6.92/7.29 => ( ! [Y5: nat] :
% 6.92/7.29 ( ( member_nat @ Y5 @ S8 )
% 6.92/7.29 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( P2 @ S8 )
% 6.92/7.29 => ( P2 @ ( insert_nat @ X3 @ S8 ) ) ) ) )
% 6.92/7.29 => ( P2 @ S ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_ranking_induct
% 6.92/7.29 thf(fact_8542_finite__ranking__induct,axiom,
% 6.92/7.29 ! [S: set_int,P2: set_int > $o,F: int > num] :
% 6.92/7.29 ( ( finite_finite_int @ S )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_int )
% 6.92/7.29 => ( ! [X3: int,S8: set_int] :
% 6.92/7.29 ( ( finite_finite_int @ S8 )
% 6.92/7.29 => ( ! [Y5: int] :
% 6.92/7.29 ( ( member_int @ Y5 @ S8 )
% 6.92/7.29 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( P2 @ S8 )
% 6.92/7.29 => ( P2 @ ( insert_int @ X3 @ S8 ) ) ) ) )
% 6.92/7.29 => ( P2 @ S ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_ranking_induct
% 6.92/7.29 thf(fact_8543_finite__ranking__induct,axiom,
% 6.92/7.29 ! [S: set_Code_integer,P2: set_Code_integer > $o,F: code_integer > nat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ S )
% 6.92/7.29 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 6.92/7.29 => ( ! [X3: code_integer,S8: set_Code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ S8 )
% 6.92/7.29 => ( ! [Y5: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ Y5 @ S8 )
% 6.92/7.29 => ( ord_less_eq_nat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( P2 @ S8 )
% 6.92/7.29 => ( P2 @ ( insert_Code_integer @ X3 @ S8 ) ) ) ) )
% 6.92/7.29 => ( P2 @ S ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_ranking_induct
% 6.92/7.29 thf(fact_8544_finite__ranking__induct,axiom,
% 6.92/7.29 ! [S: set_o,P2: set_o > $o,F: $o > nat] :
% 6.92/7.29 ( ( finite_finite_o @ S )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_o )
% 6.92/7.29 => ( ! [X3: $o,S8: set_o] :
% 6.92/7.29 ( ( finite_finite_o @ S8 )
% 6.92/7.29 => ( ! [Y5: $o] :
% 6.92/7.29 ( ( member_o @ Y5 @ S8 )
% 6.92/7.29 => ( ord_less_eq_nat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 6.92/7.29 => ( ( P2 @ S8 )
% 6.92/7.29 => ( P2 @ ( insert_o @ X3 @ S8 ) ) ) ) )
% 6.92/7.29 => ( P2 @ S ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_ranking_induct
% 6.92/7.29 thf(fact_8545_sum__strict__mono__ex1,axiom,
% 6.92/7.29 ! [A4: set_nat,F: nat > rat,G: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ? [X6: nat] :
% 6.92/7.29 ( ( member_nat @ X6 @ A4 )
% 6.92/7.29 & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 6.92/7.29 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono_ex1
% 6.92/7.29 thf(fact_8546_sum__strict__mono__ex1,axiom,
% 6.92/7.29 ! [A4: set_int,F: int > rat,G: int > rat] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ? [X6: int] :
% 6.92/7.29 ( ( member_int @ X6 @ A4 )
% 6.92/7.29 & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 6.92/7.29 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) @ ( groups3906332499630173760nt_rat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono_ex1
% 6.92/7.29 thf(fact_8547_sum__strict__mono__ex1,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,F: code_integer > rat,G: code_integer > rat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ? [X6: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X6 @ A4 )
% 6.92/7.29 & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 6.92/7.29 => ( ord_less_rat @ ( groups6602215022474089585er_rat @ F @ A4 ) @ ( groups6602215022474089585er_rat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono_ex1
% 6.92/7.29 thf(fact_8548_sum__strict__mono__ex1,axiom,
% 6.92/7.29 ! [A4: set_int,F: int > nat,G: int > nat] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ? [X6: int] :
% 6.92/7.29 ( ( member_int @ X6 @ A4 )
% 6.92/7.29 & ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 6.92/7.29 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono_ex1
% 6.92/7.29 thf(fact_8549_sum__strict__mono__ex1,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,F: code_integer > nat,G: code_integer > nat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ? [X6: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X6 @ A4 )
% 6.92/7.29 & ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 6.92/7.29 => ( ord_less_nat @ ( groups7237345082560585321er_nat @ F @ A4 ) @ ( groups7237345082560585321er_nat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono_ex1
% 6.92/7.29 thf(fact_8550_sum__strict__mono__ex1,axiom,
% 6.92/7.29 ! [A4: set_nat,F: nat > int,G: nat > int] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ? [X6: nat] :
% 6.92/7.29 ( ( member_nat @ X6 @ A4 )
% 6.92/7.29 & ( ord_less_int @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 6.92/7.29 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A4 ) @ ( groups3539618377306564664at_int @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono_ex1
% 6.92/7.29 thf(fact_8551_sum__strict__mono__ex1,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,F: code_integer > int,G: code_integer > int] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ? [X6: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X6 @ A4 )
% 6.92/7.29 & ( ord_less_int @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 6.92/7.29 => ( ord_less_int @ ( groups7234854612051535045er_int @ F @ A4 ) @ ( groups7234854612051535045er_int @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono_ex1
% 6.92/7.29 thf(fact_8552_sum__strict__mono__ex1,axiom,
% 6.92/7.29 ! [A4: set_nat,F: nat > nat,G: nat > nat] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ? [X6: nat] :
% 6.92/7.29 ( ( member_nat @ X6 @ A4 )
% 6.92/7.29 & ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 6.92/7.29 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( groups3542108847815614940at_nat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono_ex1
% 6.92/7.29 thf(fact_8553_sum__strict__mono__ex1,axiom,
% 6.92/7.29 ! [A4: set_int,F: int > int,G: int > int] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ? [X6: int] :
% 6.92/7.29 ( ( member_int @ X6 @ A4 )
% 6.92/7.29 & ( ord_less_int @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 6.92/7.29 => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A4 ) @ ( groups4538972089207619220nt_int @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono_ex1
% 6.92/7.29 thf(fact_8554_sum__strict__mono__ex1,axiom,
% 6.92/7.29 ! [A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > rat,G: product_prod_nat_nat > rat] :
% 6.92/7.29 ( ( finite6177210948735845034at_nat @ A4 )
% 6.92/7.29 => ( ! [X3: product_prod_nat_nat] :
% 6.92/7.29 ( ( member8440522571783428010at_nat @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ? [X6: product_prod_nat_nat] :
% 6.92/7.29 ( ( member8440522571783428010at_nat @ X6 @ A4 )
% 6.92/7.29 & ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 6.92/7.29 => ( ord_less_rat @ ( groups342789780944988191at_rat @ F @ A4 ) @ ( groups342789780944988191at_rat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono_ex1
% 6.92/7.29 thf(fact_8555_finite__linorder__max__induct,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,P2: set_Code_integer > $o] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 6.92/7.29 => ( ! [B3: code_integer,A9: set_Code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A9 )
% 6.92/7.29 => ( ! [X6: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X6 @ A9 )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ X6 @ B3 ) )
% 6.92/7.29 => ( ( P2 @ A9 )
% 6.92/7.29 => ( P2 @ ( insert_Code_integer @ B3 @ A9 ) ) ) ) )
% 6.92/7.29 => ( P2 @ A4 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_linorder_max_induct
% 6.92/7.29 thf(fact_8556_finite__linorder__max__induct,axiom,
% 6.92/7.29 ! [A4: set_o,P2: set_o > $o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_o )
% 6.92/7.29 => ( ! [B3: $o,A9: set_o] :
% 6.92/7.29 ( ( finite_finite_o @ A9 )
% 6.92/7.29 => ( ! [X6: $o] :
% 6.92/7.29 ( ( member_o @ X6 @ A9 )
% 6.92/7.29 => ( ord_less_o @ X6 @ B3 ) )
% 6.92/7.29 => ( ( P2 @ A9 )
% 6.92/7.29 => ( P2 @ ( insert_o @ B3 @ A9 ) ) ) ) )
% 6.92/7.29 => ( P2 @ A4 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_linorder_max_induct
% 6.92/7.29 thf(fact_8557_finite__linorder__max__induct,axiom,
% 6.92/7.29 ! [A4: set_rat,P2: set_rat > $o] :
% 6.92/7.29 ( ( finite_finite_rat @ A4 )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_rat )
% 6.92/7.29 => ( ! [B3: rat,A9: set_rat] :
% 6.92/7.29 ( ( finite_finite_rat @ A9 )
% 6.92/7.29 => ( ! [X6: rat] :
% 6.92/7.29 ( ( member_rat @ X6 @ A9 )
% 6.92/7.29 => ( ord_less_rat @ X6 @ B3 ) )
% 6.92/7.29 => ( ( P2 @ A9 )
% 6.92/7.29 => ( P2 @ ( insert_rat @ B3 @ A9 ) ) ) ) )
% 6.92/7.29 => ( P2 @ A4 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_linorder_max_induct
% 6.92/7.29 thf(fact_8558_finite__linorder__max__induct,axiom,
% 6.92/7.29 ! [A4: set_num,P2: set_num > $o] :
% 6.92/7.29 ( ( finite_finite_num @ A4 )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_num )
% 6.92/7.29 => ( ! [B3: num,A9: set_num] :
% 6.92/7.29 ( ( finite_finite_num @ A9 )
% 6.92/7.29 => ( ! [X6: num] :
% 6.92/7.29 ( ( member_num @ X6 @ A9 )
% 6.92/7.29 => ( ord_less_num @ X6 @ B3 ) )
% 6.92/7.29 => ( ( P2 @ A9 )
% 6.92/7.29 => ( P2 @ ( insert_num @ B3 @ A9 ) ) ) ) )
% 6.92/7.29 => ( P2 @ A4 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_linorder_max_induct
% 6.92/7.29 thf(fact_8559_finite__linorder__max__induct,axiom,
% 6.92/7.29 ! [A4: set_nat,P2: set_nat > $o] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_nat )
% 6.92/7.29 => ( ! [B3: nat,A9: set_nat] :
% 6.92/7.29 ( ( finite_finite_nat @ A9 )
% 6.92/7.29 => ( ! [X6: nat] :
% 6.92/7.29 ( ( member_nat @ X6 @ A9 )
% 6.92/7.29 => ( ord_less_nat @ X6 @ B3 ) )
% 6.92/7.29 => ( ( P2 @ A9 )
% 6.92/7.29 => ( P2 @ ( insert_nat @ B3 @ A9 ) ) ) ) )
% 6.92/7.29 => ( P2 @ A4 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_linorder_max_induct
% 6.92/7.29 thf(fact_8560_finite__linorder__max__induct,axiom,
% 6.92/7.29 ! [A4: set_int,P2: set_int > $o] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_int )
% 6.92/7.29 => ( ! [B3: int,A9: set_int] :
% 6.92/7.29 ( ( finite_finite_int @ A9 )
% 6.92/7.29 => ( ! [X6: int] :
% 6.92/7.29 ( ( member_int @ X6 @ A9 )
% 6.92/7.29 => ( ord_less_int @ X6 @ B3 ) )
% 6.92/7.29 => ( ( P2 @ A9 )
% 6.92/7.29 => ( P2 @ ( insert_int @ B3 @ A9 ) ) ) ) )
% 6.92/7.29 => ( P2 @ A4 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_linorder_max_induct
% 6.92/7.29 thf(fact_8561_finite__linorder__min__induct,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,P2: set_Code_integer > $o] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 6.92/7.29 => ( ! [B3: code_integer,A9: set_Code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A9 )
% 6.92/7.29 => ( ! [X6: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X6 @ A9 )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ B3 @ X6 ) )
% 6.92/7.29 => ( ( P2 @ A9 )
% 6.92/7.29 => ( P2 @ ( insert_Code_integer @ B3 @ A9 ) ) ) ) )
% 6.92/7.29 => ( P2 @ A4 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_linorder_min_induct
% 6.92/7.29 thf(fact_8562_finite__linorder__min__induct,axiom,
% 6.92/7.29 ! [A4: set_o,P2: set_o > $o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_o )
% 6.92/7.29 => ( ! [B3: $o,A9: set_o] :
% 6.92/7.29 ( ( finite_finite_o @ A9 )
% 6.92/7.29 => ( ! [X6: $o] :
% 6.92/7.29 ( ( member_o @ X6 @ A9 )
% 6.92/7.29 => ( ord_less_o @ B3 @ X6 ) )
% 6.92/7.29 => ( ( P2 @ A9 )
% 6.92/7.29 => ( P2 @ ( insert_o @ B3 @ A9 ) ) ) ) )
% 6.92/7.29 => ( P2 @ A4 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_linorder_min_induct
% 6.92/7.29 thf(fact_8563_finite__linorder__min__induct,axiom,
% 6.92/7.29 ! [A4: set_rat,P2: set_rat > $o] :
% 6.92/7.29 ( ( finite_finite_rat @ A4 )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_rat )
% 6.92/7.29 => ( ! [B3: rat,A9: set_rat] :
% 6.92/7.29 ( ( finite_finite_rat @ A9 )
% 6.92/7.29 => ( ! [X6: rat] :
% 6.92/7.29 ( ( member_rat @ X6 @ A9 )
% 6.92/7.29 => ( ord_less_rat @ B3 @ X6 ) )
% 6.92/7.29 => ( ( P2 @ A9 )
% 6.92/7.29 => ( P2 @ ( insert_rat @ B3 @ A9 ) ) ) ) )
% 6.92/7.29 => ( P2 @ A4 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_linorder_min_induct
% 6.92/7.29 thf(fact_8564_finite__linorder__min__induct,axiom,
% 6.92/7.29 ! [A4: set_num,P2: set_num > $o] :
% 6.92/7.29 ( ( finite_finite_num @ A4 )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_num )
% 6.92/7.29 => ( ! [B3: num,A9: set_num] :
% 6.92/7.29 ( ( finite_finite_num @ A9 )
% 6.92/7.29 => ( ! [X6: num] :
% 6.92/7.29 ( ( member_num @ X6 @ A9 )
% 6.92/7.29 => ( ord_less_num @ B3 @ X6 ) )
% 6.92/7.29 => ( ( P2 @ A9 )
% 6.92/7.29 => ( P2 @ ( insert_num @ B3 @ A9 ) ) ) ) )
% 6.92/7.29 => ( P2 @ A4 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_linorder_min_induct
% 6.92/7.29 thf(fact_8565_finite__linorder__min__induct,axiom,
% 6.92/7.29 ! [A4: set_nat,P2: set_nat > $o] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_nat )
% 6.92/7.29 => ( ! [B3: nat,A9: set_nat] :
% 6.92/7.29 ( ( finite_finite_nat @ A9 )
% 6.92/7.29 => ( ! [X6: nat] :
% 6.92/7.29 ( ( member_nat @ X6 @ A9 )
% 6.92/7.29 => ( ord_less_nat @ B3 @ X6 ) )
% 6.92/7.29 => ( ( P2 @ A9 )
% 6.92/7.29 => ( P2 @ ( insert_nat @ B3 @ A9 ) ) ) ) )
% 6.92/7.29 => ( P2 @ A4 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_linorder_min_induct
% 6.92/7.29 thf(fact_8566_finite__linorder__min__induct,axiom,
% 6.92/7.29 ! [A4: set_int,P2: set_int > $o] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( P2 @ bot_bot_set_int )
% 6.92/7.29 => ( ! [B3: int,A9: set_int] :
% 6.92/7.29 ( ( finite_finite_int @ A9 )
% 6.92/7.29 => ( ! [X6: int] :
% 6.92/7.29 ( ( member_int @ X6 @ A9 )
% 6.92/7.29 => ( ord_less_int @ B3 @ X6 ) )
% 6.92/7.29 => ( ( P2 @ A9 )
% 6.92/7.29 => ( P2 @ ( insert_int @ B3 @ A9 ) ) ) ) )
% 6.92/7.29 => ( P2 @ A4 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_linorder_min_induct
% 6.92/7.29 thf(fact_8567_sum_Orelated,axiom,
% 6.92/7.29 ! [R3: code_integer > code_integer > $o,S: set_nat,H: nat > code_integer,G: nat > code_integer] :
% 6.92/7.29 ( ( R3 @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 6.92/7.29 => ( ! [X13: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 6.92/7.29 ( ( ( R3 @ X13 @ X22 )
% 6.92/7.29 & ( R3 @ Y12 @ Y22 ) )
% 6.92/7.29 => ( R3 @ ( plus_p5714425477246183910nteger @ X13 @ Y12 ) @ ( plus_p5714425477246183910nteger @ X22 @ Y22 ) ) )
% 6.92/7.29 => ( ( finite_finite_nat @ S )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ S )
% 6.92/7.29 => ( R3 @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( R3 @ ( groups7501900531339628137nteger @ H @ S ) @ ( groups7501900531339628137nteger @ G @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.related
% 6.92/7.29 thf(fact_8568_sum_Orelated,axiom,
% 6.92/7.29 ! [R3: code_integer > code_integer > $o,S: set_int,H: int > code_integer,G: int > code_integer] :
% 6.92/7.29 ( ( R3 @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 6.92/7.29 => ( ! [X13: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 6.92/7.29 ( ( ( R3 @ X13 @ X22 )
% 6.92/7.29 & ( R3 @ Y12 @ Y22 ) )
% 6.92/7.29 => ( R3 @ ( plus_p5714425477246183910nteger @ X13 @ Y12 ) @ ( plus_p5714425477246183910nteger @ X22 @ Y22 ) ) )
% 6.92/7.29 => ( ( finite_finite_int @ S )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ S )
% 6.92/7.29 => ( R3 @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( R3 @ ( groups7873554091576472773nteger @ H @ S ) @ ( groups7873554091576472773nteger @ G @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.related
% 6.92/7.29 thf(fact_8569_sum_Orelated,axiom,
% 6.92/7.29 ! [R3: code_integer > code_integer > $o,S: set_Code_integer,H: code_integer > code_integer,G: code_integer > code_integer] :
% 6.92/7.29 ( ( R3 @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 6.92/7.29 => ( ! [X13: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 6.92/7.29 ( ( ( R3 @ X13 @ X22 )
% 6.92/7.29 & ( R3 @ Y12 @ Y22 ) )
% 6.92/7.29 => ( R3 @ ( plus_p5714425477246183910nteger @ X13 @ Y12 ) @ ( plus_p5714425477246183910nteger @ X22 @ Y22 ) ) )
% 6.92/7.29 => ( ( finite6017078050557962740nteger @ S )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ S )
% 6.92/7.29 => ( R3 @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( R3 @ ( groups879477027807139574nteger @ H @ S ) @ ( groups879477027807139574nteger @ G @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.related
% 6.92/7.29 thf(fact_8570_sum_Orelated,axiom,
% 6.92/7.29 ! [R3: rat > rat > $o,S: set_nat,H: nat > rat,G: nat > rat] :
% 6.92/7.29 ( ( R3 @ zero_zero_rat @ zero_zero_rat )
% 6.92/7.29 => ( ! [X13: rat,Y12: rat,X22: rat,Y22: rat] :
% 6.92/7.29 ( ( ( R3 @ X13 @ X22 )
% 6.92/7.29 & ( R3 @ Y12 @ Y22 ) )
% 6.92/7.29 => ( R3 @ ( plus_plus_rat @ X13 @ Y12 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 6.92/7.29 => ( ( finite_finite_nat @ S )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ S )
% 6.92/7.29 => ( R3 @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( R3 @ ( groups2906978787729119204at_rat @ H @ S ) @ ( groups2906978787729119204at_rat @ G @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.related
% 6.92/7.29 thf(fact_8571_sum_Orelated,axiom,
% 6.92/7.29 ! [R3: rat > rat > $o,S: set_int,H: int > rat,G: int > rat] :
% 6.92/7.29 ( ( R3 @ zero_zero_rat @ zero_zero_rat )
% 6.92/7.29 => ( ! [X13: rat,Y12: rat,X22: rat,Y22: rat] :
% 6.92/7.29 ( ( ( R3 @ X13 @ X22 )
% 6.92/7.29 & ( R3 @ Y12 @ Y22 ) )
% 6.92/7.29 => ( R3 @ ( plus_plus_rat @ X13 @ Y12 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 6.92/7.29 => ( ( finite_finite_int @ S )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ S )
% 6.92/7.29 => ( R3 @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( R3 @ ( groups3906332499630173760nt_rat @ H @ S ) @ ( groups3906332499630173760nt_rat @ G @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.related
% 6.92/7.29 thf(fact_8572_sum_Orelated,axiom,
% 6.92/7.29 ! [R3: rat > rat > $o,S: set_Code_integer,H: code_integer > rat,G: code_integer > rat] :
% 6.92/7.29 ( ( R3 @ zero_zero_rat @ zero_zero_rat )
% 6.92/7.29 => ( ! [X13: rat,Y12: rat,X22: rat,Y22: rat] :
% 6.92/7.29 ( ( ( R3 @ X13 @ X22 )
% 6.92/7.29 & ( R3 @ Y12 @ Y22 ) )
% 6.92/7.29 => ( R3 @ ( plus_plus_rat @ X13 @ Y12 ) @ ( plus_plus_rat @ X22 @ Y22 ) ) )
% 6.92/7.29 => ( ( finite6017078050557962740nteger @ S )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ S )
% 6.92/7.29 => ( R3 @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( R3 @ ( groups6602215022474089585er_rat @ H @ S ) @ ( groups6602215022474089585er_rat @ G @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.related
% 6.92/7.29 thf(fact_8573_sum_Orelated,axiom,
% 6.92/7.29 ! [R3: nat > nat > $o,S: set_int,H: int > nat,G: int > nat] :
% 6.92/7.29 ( ( R3 @ zero_zero_nat @ zero_zero_nat )
% 6.92/7.29 => ( ! [X13: nat,Y12: nat,X22: nat,Y22: nat] :
% 6.92/7.29 ( ( ( R3 @ X13 @ X22 )
% 6.92/7.29 & ( R3 @ Y12 @ Y22 ) )
% 6.92/7.29 => ( R3 @ ( plus_plus_nat @ X13 @ Y12 ) @ ( plus_plus_nat @ X22 @ Y22 ) ) )
% 6.92/7.29 => ( ( finite_finite_int @ S )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ S )
% 6.92/7.29 => ( R3 @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( R3 @ ( groups4541462559716669496nt_nat @ H @ S ) @ ( groups4541462559716669496nt_nat @ G @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.related
% 6.92/7.29 thf(fact_8574_sum_Orelated,axiom,
% 6.92/7.29 ! [R3: nat > nat > $o,S: set_Code_integer,H: code_integer > nat,G: code_integer > nat] :
% 6.92/7.29 ( ( R3 @ zero_zero_nat @ zero_zero_nat )
% 6.92/7.29 => ( ! [X13: nat,Y12: nat,X22: nat,Y22: nat] :
% 6.92/7.29 ( ( ( R3 @ X13 @ X22 )
% 6.92/7.29 & ( R3 @ Y12 @ Y22 ) )
% 6.92/7.29 => ( R3 @ ( plus_plus_nat @ X13 @ Y12 ) @ ( plus_plus_nat @ X22 @ Y22 ) ) )
% 6.92/7.29 => ( ( finite6017078050557962740nteger @ S )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ S )
% 6.92/7.29 => ( R3 @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( R3 @ ( groups7237345082560585321er_nat @ H @ S ) @ ( groups7237345082560585321er_nat @ G @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.related
% 6.92/7.29 thf(fact_8575_sum_Orelated,axiom,
% 6.92/7.29 ! [R3: int > int > $o,S: set_nat,H: nat > int,G: nat > int] :
% 6.92/7.29 ( ( R3 @ zero_zero_int @ zero_zero_int )
% 6.92/7.29 => ( ! [X13: int,Y12: int,X22: int,Y22: int] :
% 6.92/7.29 ( ( ( R3 @ X13 @ X22 )
% 6.92/7.29 & ( R3 @ Y12 @ Y22 ) )
% 6.92/7.29 => ( R3 @ ( plus_plus_int @ X13 @ Y12 ) @ ( plus_plus_int @ X22 @ Y22 ) ) )
% 6.92/7.29 => ( ( finite_finite_nat @ S )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ S )
% 6.92/7.29 => ( R3 @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( R3 @ ( groups3539618377306564664at_int @ H @ S ) @ ( groups3539618377306564664at_int @ G @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.related
% 6.92/7.29 thf(fact_8576_sum_Orelated,axiom,
% 6.92/7.29 ! [R3: int > int > $o,S: set_Code_integer,H: code_integer > int,G: code_integer > int] :
% 6.92/7.29 ( ( R3 @ zero_zero_int @ zero_zero_int )
% 6.92/7.29 => ( ! [X13: int,Y12: int,X22: int,Y22: int] :
% 6.92/7.29 ( ( ( R3 @ X13 @ X22 )
% 6.92/7.29 & ( R3 @ Y12 @ Y22 ) )
% 6.92/7.29 => ( R3 @ ( plus_plus_int @ X13 @ Y12 ) @ ( plus_plus_int @ X22 @ Y22 ) ) )
% 6.92/7.29 => ( ( finite6017078050557962740nteger @ S )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ S )
% 6.92/7.29 => ( R3 @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( R3 @ ( groups7234854612051535045er_int @ H @ S ) @ ( groups7234854612051535045er_int @ G @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.related
% 6.92/7.29 thf(fact_8577_sum__strict__mono,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,F: code_integer > rat,G: code_integer > rat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( A4 != bot_bo3990330152332043303nteger )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ ( groups6602215022474089585er_rat @ F @ A4 ) @ ( groups6602215022474089585er_rat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono
% 6.92/7.29 thf(fact_8578_sum__strict__mono,axiom,
% 6.92/7.29 ! [A4: set_o,F: $o > rat,G: $o > rat] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( A4 != bot_bot_set_o )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ ( groups7872700643590313910_o_rat @ F @ A4 ) @ ( groups7872700643590313910_o_rat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono
% 6.92/7.29 thf(fact_8579_sum__strict__mono,axiom,
% 6.92/7.29 ! [A4: set_nat,F: nat > rat,G: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( A4 != bot_bot_set_nat )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono
% 6.92/7.29 thf(fact_8580_sum__strict__mono,axiom,
% 6.92/7.29 ! [A4: set_int,F: int > rat,G: int > rat] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( A4 != bot_bot_set_int )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) @ ( groups3906332499630173760nt_rat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono
% 6.92/7.29 thf(fact_8581_sum__strict__mono,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,F: code_integer > nat,G: code_integer > nat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( A4 != bot_bo3990330152332043303nteger )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ord_less_nat @ ( groups7237345082560585321er_nat @ F @ A4 ) @ ( groups7237345082560585321er_nat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono
% 6.92/7.29 thf(fact_8582_sum__strict__mono,axiom,
% 6.92/7.29 ! [A4: set_o,F: $o > nat,G: $o > nat] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( A4 != bot_bot_set_o )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ord_less_nat @ ( groups8507830703676809646_o_nat @ F @ A4 ) @ ( groups8507830703676809646_o_nat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono
% 6.92/7.29 thf(fact_8583_sum__strict__mono,axiom,
% 6.92/7.29 ! [A4: set_int,F: int > nat,G: int > nat] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( A4 != bot_bot_set_int )
% 6.92/7.29 => ( ! [X3: int] :
% 6.92/7.29 ( ( member_int @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono
% 6.92/7.29 thf(fact_8584_sum__strict__mono,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,F: code_integer > int,G: code_integer > int] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( A4 != bot_bo3990330152332043303nteger )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ord_less_int @ ( groups7234854612051535045er_int @ F @ A4 ) @ ( groups7234854612051535045er_int @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono
% 6.92/7.29 thf(fact_8585_sum__strict__mono,axiom,
% 6.92/7.29 ! [A4: set_o,F: $o > int,G: $o > int] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( A4 != bot_bot_set_o )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ord_less_int @ ( groups8505340233167759370_o_int @ F @ A4 ) @ ( groups8505340233167759370_o_int @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono
% 6.92/7.29 thf(fact_8586_sum__strict__mono,axiom,
% 6.92/7.29 ! [A4: set_nat,F: nat > int,G: nat > int] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( A4 != bot_bot_set_nat )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ A4 )
% 6.92/7.29 => ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 6.92/7.29 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A4 ) @ ( groups3539618377306564664at_int @ G @ A4 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_strict_mono
% 6.92/7.29 thf(fact_8587_sum_Oinsert__if,axiom,
% 6.92/7.29 ! [A4: set_o,X: $o,G: $o > rat] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( ( member_o @ X @ A4 )
% 6.92/7.29 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A4 ) )
% 6.92/7.29 = ( groups7872700643590313910_o_rat @ G @ A4 ) ) )
% 6.92/7.29 & ( ~ ( member_o @ X @ A4 )
% 6.92/7.29 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A4 ) )
% 6.92/7.29 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ A4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.insert_if
% 6.92/7.29 thf(fact_8588_sum_Oinsert__if,axiom,
% 6.92/7.29 ! [A4: set_nat,X: nat,G: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( ( member_nat @ X @ A4 )
% 6.92/7.29 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A4 ) )
% 6.92/7.29 = ( groups2906978787729119204at_rat @ G @ A4 ) ) )
% 6.92/7.29 & ( ~ ( member_nat @ X @ A4 )
% 6.92/7.29 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A4 ) )
% 6.92/7.29 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.insert_if
% 6.92/7.29 thf(fact_8589_sum_Oinsert__if,axiom,
% 6.92/7.29 ! [A4: set_int,X: int,G: int > rat] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( ( member_int @ X @ A4 )
% 6.92/7.29 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A4 ) )
% 6.92/7.29 = ( groups3906332499630173760nt_rat @ G @ A4 ) ) )
% 6.92/7.29 & ( ~ ( member_int @ X @ A4 )
% 6.92/7.29 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A4 ) )
% 6.92/7.29 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.insert_if
% 6.92/7.29 thf(fact_8590_sum_Oinsert__if,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( ( member_Code_integer @ X @ A4 )
% 6.92/7.29 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A4 ) )
% 6.92/7.29 = ( groups6602215022474089585er_rat @ G @ A4 ) ) )
% 6.92/7.29 & ( ~ ( member_Code_integer @ X @ A4 )
% 6.92/7.29 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A4 ) )
% 6.92/7.29 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ A4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.insert_if
% 6.92/7.29 thf(fact_8591_sum_Oinsert__if,axiom,
% 6.92/7.29 ! [A4: set_o,X: $o,G: $o > nat] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( ( member_o @ X @ A4 )
% 6.92/7.29 => ( ( groups8507830703676809646_o_nat @ G @ ( insert_o @ X @ A4 ) )
% 6.92/7.29 = ( groups8507830703676809646_o_nat @ G @ A4 ) ) )
% 6.92/7.29 & ( ~ ( member_o @ X @ A4 )
% 6.92/7.29 => ( ( groups8507830703676809646_o_nat @ G @ ( insert_o @ X @ A4 ) )
% 6.92/7.29 = ( plus_plus_nat @ ( G @ X ) @ ( groups8507830703676809646_o_nat @ G @ A4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.insert_if
% 6.92/7.29 thf(fact_8592_sum_Oinsert__if,axiom,
% 6.92/7.29 ! [A4: set_int,X: int,G: int > nat] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( ( member_int @ X @ A4 )
% 6.92/7.29 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A4 ) )
% 6.92/7.29 = ( groups4541462559716669496nt_nat @ G @ A4 ) ) )
% 6.92/7.29 & ( ~ ( member_int @ X @ A4 )
% 6.92/7.29 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A4 ) )
% 6.92/7.29 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.insert_if
% 6.92/7.29 thf(fact_8593_sum_Oinsert__if,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,X: code_integer,G: code_integer > nat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( ( member_Code_integer @ X @ A4 )
% 6.92/7.29 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X @ A4 ) )
% 6.92/7.29 = ( groups7237345082560585321er_nat @ G @ A4 ) ) )
% 6.92/7.29 & ( ~ ( member_Code_integer @ X @ A4 )
% 6.92/7.29 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X @ A4 ) )
% 6.92/7.29 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ A4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.insert_if
% 6.92/7.29 thf(fact_8594_sum_Oinsert__if,axiom,
% 6.92/7.29 ! [A4: set_o,X: $o,G: $o > int] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( ( member_o @ X @ A4 )
% 6.92/7.29 => ( ( groups8505340233167759370_o_int @ G @ ( insert_o @ X @ A4 ) )
% 6.92/7.29 = ( groups8505340233167759370_o_int @ G @ A4 ) ) )
% 6.92/7.29 & ( ~ ( member_o @ X @ A4 )
% 6.92/7.29 => ( ( groups8505340233167759370_o_int @ G @ ( insert_o @ X @ A4 ) )
% 6.92/7.29 = ( plus_plus_int @ ( G @ X ) @ ( groups8505340233167759370_o_int @ G @ A4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.insert_if
% 6.92/7.29 thf(fact_8595_sum_Oinsert__if,axiom,
% 6.92/7.29 ! [A4: set_nat,X: nat,G: nat > int] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( ( member_nat @ X @ A4 )
% 6.92/7.29 => ( ( groups3539618377306564664at_int @ G @ ( insert_nat @ X @ A4 ) )
% 6.92/7.29 = ( groups3539618377306564664at_int @ G @ A4 ) ) )
% 6.92/7.29 & ( ~ ( member_nat @ X @ A4 )
% 6.92/7.29 => ( ( groups3539618377306564664at_int @ G @ ( insert_nat @ X @ A4 ) )
% 6.92/7.29 = ( plus_plus_int @ ( G @ X ) @ ( groups3539618377306564664at_int @ G @ A4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.insert_if
% 6.92/7.29 thf(fact_8596_sum_Oinsert__if,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,X: code_integer,G: code_integer > int] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( ( member_Code_integer @ X @ A4 )
% 6.92/7.29 => ( ( groups7234854612051535045er_int @ G @ ( insert_Code_integer @ X @ A4 ) )
% 6.92/7.29 = ( groups7234854612051535045er_int @ G @ A4 ) ) )
% 6.92/7.29 & ( ~ ( member_Code_integer @ X @ A4 )
% 6.92/7.29 => ( ( groups7234854612051535045er_int @ G @ ( insert_Code_integer @ X @ A4 ) )
% 6.92/7.29 = ( plus_plus_int @ ( G @ X ) @ ( groups7234854612051535045er_int @ G @ A4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.insert_if
% 6.92/7.29 thf(fact_8597_bit__push__bit__iff__int,axiom,
% 6.92/7.29 ! [M: nat,K2: int,N2: nat] :
% 6.92/7.29 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K2 ) @ N2 )
% 6.92/7.29 = ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.29 & ( bit_se1146084159140164899it_int @ K2 @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % bit_push_bit_iff_int
% 6.92/7.29 thf(fact_8598_prod__dvd__prod__subset,axiom,
% 6.92/7.29 ! [B5: set_Code_integer,A4: set_Code_integer,F: code_integer > nat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ B5 )
% 6.92/7.29 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.92/7.29 => ( dvd_dvd_nat @ ( groups3190895334310489300er_nat @ F @ A4 ) @ ( groups3190895334310489300er_nat @ F @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset
% 6.92/7.29 thf(fact_8599_prod__dvd__prod__subset,axiom,
% 6.92/7.29 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 6.92/7.29 ( ( finite6177210948735845034at_nat @ B5 )
% 6.92/7.29 => ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 6.92/7.29 => ( dvd_dvd_nat @ ( groups4077766827762148844at_nat @ F @ A4 ) @ ( groups4077766827762148844at_nat @ F @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset
% 6.92/7.29 thf(fact_8600_prod__dvd__prod__subset,axiom,
% 6.92/7.29 ! [B5: set_Code_integer,A4: set_Code_integer,F: code_integer > int] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ B5 )
% 6.92/7.29 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.92/7.29 => ( dvd_dvd_int @ ( groups3188404863801439024er_int @ F @ A4 ) @ ( groups3188404863801439024er_int @ F @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset
% 6.92/7.29 thf(fact_8601_prod__dvd__prod__subset,axiom,
% 6.92/7.29 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > int] :
% 6.92/7.29 ( ( finite6177210948735845034at_nat @ B5 )
% 6.92/7.29 => ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 6.92/7.29 => ( dvd_dvd_int @ ( groups4075276357253098568at_int @ F @ A4 ) @ ( groups4075276357253098568at_int @ F @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset
% 6.92/7.29 thf(fact_8602_prod__dvd__prod__subset,axiom,
% 6.92/7.29 ! [B5: set_int,A4: set_int,F: int > nat] :
% 6.92/7.29 ( ( finite_finite_int @ B5 )
% 6.92/7.29 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.29 => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A4 ) @ ( groups1707563613775114915nt_nat @ F @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset
% 6.92/7.29 thf(fact_8603_prod__dvd__prod__subset,axiom,
% 6.92/7.29 ! [B5: set_nat,A4: set_nat,F: nat > nat] :
% 6.92/7.29 ( ( finite_finite_nat @ B5 )
% 6.92/7.29 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.92/7.29 => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A4 ) @ ( groups708209901874060359at_nat @ F @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset
% 6.92/7.29 thf(fact_8604_prod__dvd__prod__subset,axiom,
% 6.92/7.29 ! [B5: set_nat,A4: set_nat,F: nat > int] :
% 6.92/7.29 ( ( finite_finite_nat @ B5 )
% 6.92/7.29 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.92/7.29 => ( dvd_dvd_int @ ( groups705719431365010083at_int @ F @ A4 ) @ ( groups705719431365010083at_int @ F @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset
% 6.92/7.29 thf(fact_8605_prod__dvd__prod__subset,axiom,
% 6.92/7.29 ! [B5: set_int,A4: set_int,F: int > int] :
% 6.92/7.29 ( ( finite_finite_int @ B5 )
% 6.92/7.29 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.29 => ( dvd_dvd_int @ ( groups1705073143266064639nt_int @ F @ A4 ) @ ( groups1705073143266064639nt_int @ F @ B5 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset
% 6.92/7.29 thf(fact_8606_prod__dvd__prod__subset2,axiom,
% 6.92/7.29 ! [B5: set_o,A4: set_o,F: $o > nat,G: $o > nat] :
% 6.92/7.29 ( ( finite_finite_o @ B5 )
% 6.92/7.29 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.92/7.29 => ( ! [A3: $o] :
% 6.92/7.29 ( ( member_o @ A3 @ A4 )
% 6.92/7.29 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 6.92/7.29 => ( dvd_dvd_nat @ ( groups3504817904513533571_o_nat @ F @ A4 ) @ ( groups3504817904513533571_o_nat @ G @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset2
% 6.92/7.29 thf(fact_8607_prod__dvd__prod__subset2,axiom,
% 6.92/7.29 ! [B5: set_Code_integer,A4: set_Code_integer,F: code_integer > nat,G: code_integer > nat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ B5 )
% 6.92/7.29 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.92/7.29 => ( ! [A3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ A3 @ A4 )
% 6.92/7.29 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 6.92/7.29 => ( dvd_dvd_nat @ ( groups3190895334310489300er_nat @ F @ A4 ) @ ( groups3190895334310489300er_nat @ G @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset2
% 6.92/7.29 thf(fact_8608_prod__dvd__prod__subset2,axiom,
% 6.92/7.29 ! [B5: set_o,A4: set_o,F: $o > int,G: $o > int] :
% 6.92/7.29 ( ( finite_finite_o @ B5 )
% 6.92/7.29 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.92/7.29 => ( ! [A3: $o] :
% 6.92/7.29 ( ( member_o @ A3 @ A4 )
% 6.92/7.29 => ( dvd_dvd_int @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 6.92/7.29 => ( dvd_dvd_int @ ( groups3502327434004483295_o_int @ F @ A4 ) @ ( groups3502327434004483295_o_int @ G @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset2
% 6.92/7.29 thf(fact_8609_prod__dvd__prod__subset2,axiom,
% 6.92/7.29 ! [B5: set_Code_integer,A4: set_Code_integer,F: code_integer > int,G: code_integer > int] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ B5 )
% 6.92/7.29 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.92/7.29 => ( ! [A3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ A3 @ A4 )
% 6.92/7.29 => ( dvd_dvd_int @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 6.92/7.29 => ( dvd_dvd_int @ ( groups3188404863801439024er_int @ F @ A4 ) @ ( groups3188404863801439024er_int @ G @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset2
% 6.92/7.29 thf(fact_8610_prod__dvd__prod__subset2,axiom,
% 6.92/7.29 ! [B5: set_int,A4: set_int,F: int > nat,G: int > nat] :
% 6.92/7.29 ( ( finite_finite_int @ B5 )
% 6.92/7.29 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.29 => ( ! [A3: int] :
% 6.92/7.29 ( ( member_int @ A3 @ A4 )
% 6.92/7.29 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 6.92/7.29 => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A4 ) @ ( groups1707563613775114915nt_nat @ G @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset2
% 6.92/7.29 thf(fact_8611_prod__dvd__prod__subset2,axiom,
% 6.92/7.29 ! [B5: set_nat,A4: set_nat,F: nat > nat,G: nat > nat] :
% 6.92/7.29 ( ( finite_finite_nat @ B5 )
% 6.92/7.29 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.92/7.29 => ( ! [A3: nat] :
% 6.92/7.29 ( ( member_nat @ A3 @ A4 )
% 6.92/7.29 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 6.92/7.29 => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A4 ) @ ( groups708209901874060359at_nat @ G @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset2
% 6.92/7.29 thf(fact_8612_prod__dvd__prod__subset2,axiom,
% 6.92/7.29 ! [B5: set_nat,A4: set_nat,F: nat > int,G: nat > int] :
% 6.92/7.29 ( ( finite_finite_nat @ B5 )
% 6.92/7.29 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.92/7.29 => ( ! [A3: nat] :
% 6.92/7.29 ( ( member_nat @ A3 @ A4 )
% 6.92/7.29 => ( dvd_dvd_int @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 6.92/7.29 => ( dvd_dvd_int @ ( groups705719431365010083at_int @ F @ A4 ) @ ( groups705719431365010083at_int @ G @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset2
% 6.92/7.29 thf(fact_8613_prod__dvd__prod__subset2,axiom,
% 6.92/7.29 ! [B5: set_int,A4: set_int,F: int > int,G: int > int] :
% 6.92/7.29 ( ( finite_finite_int @ B5 )
% 6.92/7.29 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.92/7.29 => ( ! [A3: int] :
% 6.92/7.29 ( ( member_int @ A3 @ A4 )
% 6.92/7.29 => ( dvd_dvd_int @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 6.92/7.29 => ( dvd_dvd_int @ ( groups1705073143266064639nt_int @ F @ A4 ) @ ( groups1705073143266064639nt_int @ G @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset2
% 6.92/7.29 thf(fact_8614_prod__dvd__prod__subset2,axiom,
% 6.92/7.29 ! [B5: set_set_nat,A4: set_set_nat,F: set_nat > nat,G: set_nat > nat] :
% 6.92/7.29 ( ( finite1152437895449049373et_nat @ B5 )
% 6.92/7.29 => ( ( ord_le6893508408891458716et_nat @ A4 @ B5 )
% 6.92/7.29 => ( ! [A3: set_nat] :
% 6.92/7.29 ( ( member_set_nat @ A3 @ A4 )
% 6.92/7.29 => ( dvd_dvd_nat @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 6.92/7.29 => ( dvd_dvd_nat @ ( groups4248547760180025341at_nat @ F @ A4 ) @ ( groups4248547760180025341at_nat @ G @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset2
% 6.92/7.29 thf(fact_8615_prod__dvd__prod__subset2,axiom,
% 6.92/7.29 ! [B5: set_set_nat,A4: set_set_nat,F: set_nat > int,G: set_nat > int] :
% 6.92/7.29 ( ( finite1152437895449049373et_nat @ B5 )
% 6.92/7.29 => ( ( ord_le6893508408891458716et_nat @ A4 @ B5 )
% 6.92/7.29 => ( ! [A3: set_nat] :
% 6.92/7.29 ( ( member_set_nat @ A3 @ A4 )
% 6.92/7.29 => ( dvd_dvd_int @ ( F @ A3 ) @ ( G @ A3 ) ) )
% 6.92/7.29 => ( dvd_dvd_int @ ( groups4246057289670975065at_int @ F @ A4 ) @ ( groups4246057289670975065at_int @ G @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod_dvd_prod_subset2
% 6.92/7.29 thf(fact_8616_concat__bit__eq,axiom,
% 6.92/7.29 ( bit_concat_bit
% 6.92/7.29 = ( ^ [N: nat,K3: int,L2: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ K3 ) @ ( bit_se545348938243370406it_int @ N @ L2 ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % concat_bit_eq
% 6.92/7.29 thf(fact_8617_bit__push__bit__iff__nat,axiom,
% 6.92/7.29 ! [M: nat,Q6: nat,N2: nat] :
% 6.92/7.29 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q6 ) @ N2 )
% 6.92/7.29 = ( ( ord_less_eq_nat @ M @ N2 )
% 6.92/7.29 & ( bit_se1148574629649215175it_nat @ Q6 @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % bit_push_bit_iff_nat
% 6.92/7.29 thf(fact_8618_sum__nonneg__leq__bound,axiom,
% 6.92/7.29 ! [S2: set_o,F: $o > code_integer,B5: code_integer,I2: $o] :
% 6.92/7.29 ( ( finite_finite_o @ S2 )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ S2 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups4406642042086082107nteger @ F @ S2 )
% 6.92/7.29 = B5 )
% 6.92/7.29 => ( ( member_o @ I2 @ S2 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_leq_bound
% 6.92/7.29 thf(fact_8619_sum__nonneg__leq__bound,axiom,
% 6.92/7.29 ! [S2: set_nat,F: nat > code_integer,B5: code_integer,I2: nat] :
% 6.92/7.29 ( ( finite_finite_nat @ S2 )
% 6.92/7.29 => ( ! [I3: nat] :
% 6.92/7.29 ( ( member_nat @ I3 @ S2 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups7501900531339628137nteger @ F @ S2 )
% 6.92/7.29 = B5 )
% 6.92/7.29 => ( ( member_nat @ I2 @ S2 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_leq_bound
% 6.92/7.29 thf(fact_8620_sum__nonneg__leq__bound,axiom,
% 6.92/7.29 ! [S2: set_int,F: int > code_integer,B5: code_integer,I2: int] :
% 6.92/7.29 ( ( finite_finite_int @ S2 )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ S2 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups7873554091576472773nteger @ F @ S2 )
% 6.92/7.29 = B5 )
% 6.92/7.29 => ( ( member_int @ I2 @ S2 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_leq_bound
% 6.92/7.29 thf(fact_8621_sum__nonneg__leq__bound,axiom,
% 6.92/7.29 ! [S2: set_Code_integer,F: code_integer > code_integer,B5: code_integer,I2: code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ S2 )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ S2 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups879477027807139574nteger @ F @ S2 )
% 6.92/7.29 = B5 )
% 6.92/7.29 => ( ( member_Code_integer @ I2 @ S2 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_leq_bound
% 6.92/7.29 thf(fact_8622_sum__nonneg__leq__bound,axiom,
% 6.92/7.29 ! [S2: set_o,F: $o > rat,B5: rat,I2: $o] :
% 6.92/7.29 ( ( finite_finite_o @ S2 )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ S2 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups7872700643590313910_o_rat @ F @ S2 )
% 6.92/7.29 = B5 )
% 6.92/7.29 => ( ( member_o @ I2 @ S2 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_leq_bound
% 6.92/7.29 thf(fact_8623_sum__nonneg__leq__bound,axiom,
% 6.92/7.29 ! [S2: set_nat,F: nat > rat,B5: rat,I2: nat] :
% 6.92/7.29 ( ( finite_finite_nat @ S2 )
% 6.92/7.29 => ( ! [I3: nat] :
% 6.92/7.29 ( ( member_nat @ I3 @ S2 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 6.92/7.29 = B5 )
% 6.92/7.29 => ( ( member_nat @ I2 @ S2 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_leq_bound
% 6.92/7.29 thf(fact_8624_sum__nonneg__leq__bound,axiom,
% 6.92/7.29 ! [S2: set_int,F: int > rat,B5: rat,I2: int] :
% 6.92/7.29 ( ( finite_finite_int @ S2 )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ S2 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 6.92/7.29 = B5 )
% 6.92/7.29 => ( ( member_int @ I2 @ S2 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_leq_bound
% 6.92/7.29 thf(fact_8625_sum__nonneg__leq__bound,axiom,
% 6.92/7.29 ! [S2: set_Code_integer,F: code_integer > rat,B5: rat,I2: code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ S2 )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ S2 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups6602215022474089585er_rat @ F @ S2 )
% 6.92/7.29 = B5 )
% 6.92/7.29 => ( ( member_Code_integer @ I2 @ S2 )
% 6.92/7.29 => ( ord_less_eq_rat @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_leq_bound
% 6.92/7.29 thf(fact_8626_sum__nonneg__leq__bound,axiom,
% 6.92/7.29 ! [S2: set_o,F: $o > nat,B5: nat,I2: $o] :
% 6.92/7.29 ( ( finite_finite_o @ S2 )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ S2 )
% 6.92/7.29 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups8507830703676809646_o_nat @ F @ S2 )
% 6.92/7.29 = B5 )
% 6.92/7.29 => ( ( member_o @ I2 @ S2 )
% 6.92/7.29 => ( ord_less_eq_nat @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_leq_bound
% 6.92/7.29 thf(fact_8627_sum__nonneg__leq__bound,axiom,
% 6.92/7.29 ! [S2: set_int,F: int > nat,B5: nat,I2: int] :
% 6.92/7.29 ( ( finite_finite_int @ S2 )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ S2 )
% 6.92/7.29 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups4541462559716669496nt_nat @ F @ S2 )
% 6.92/7.29 = B5 )
% 6.92/7.29 => ( ( member_int @ I2 @ S2 )
% 6.92/7.29 => ( ord_less_eq_nat @ ( F @ I2 ) @ B5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_leq_bound
% 6.92/7.29 thf(fact_8628_sum__nonneg__0,axiom,
% 6.92/7.29 ! [S2: set_o,F: $o > code_integer,I2: $o] :
% 6.92/7.29 ( ( finite_finite_o @ S2 )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ S2 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups4406642042086082107nteger @ F @ S2 )
% 6.92/7.29 = zero_z3403309356797280102nteger )
% 6.92/7.29 => ( ( member_o @ I2 @ S2 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_0
% 6.92/7.29 thf(fact_8629_sum__nonneg__0,axiom,
% 6.92/7.29 ! [S2: set_nat,F: nat > code_integer,I2: nat] :
% 6.92/7.29 ( ( finite_finite_nat @ S2 )
% 6.92/7.29 => ( ! [I3: nat] :
% 6.92/7.29 ( ( member_nat @ I3 @ S2 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups7501900531339628137nteger @ F @ S2 )
% 6.92/7.29 = zero_z3403309356797280102nteger )
% 6.92/7.29 => ( ( member_nat @ I2 @ S2 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_0
% 6.92/7.29 thf(fact_8630_sum__nonneg__0,axiom,
% 6.92/7.29 ! [S2: set_int,F: int > code_integer,I2: int] :
% 6.92/7.29 ( ( finite_finite_int @ S2 )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ S2 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups7873554091576472773nteger @ F @ S2 )
% 6.92/7.29 = zero_z3403309356797280102nteger )
% 6.92/7.29 => ( ( member_int @ I2 @ S2 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_0
% 6.92/7.29 thf(fact_8631_sum__nonneg__0,axiom,
% 6.92/7.29 ! [S2: set_Code_integer,F: code_integer > code_integer,I2: code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ S2 )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ S2 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups879477027807139574nteger @ F @ S2 )
% 6.92/7.29 = zero_z3403309356797280102nteger )
% 6.92/7.29 => ( ( member_Code_integer @ I2 @ S2 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_0
% 6.92/7.29 thf(fact_8632_sum__nonneg__0,axiom,
% 6.92/7.29 ! [S2: set_o,F: $o > rat,I2: $o] :
% 6.92/7.29 ( ( finite_finite_o @ S2 )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ S2 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups7872700643590313910_o_rat @ F @ S2 )
% 6.92/7.29 = zero_zero_rat )
% 6.92/7.29 => ( ( member_o @ I2 @ S2 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = zero_zero_rat ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_0
% 6.92/7.29 thf(fact_8633_sum__nonneg__0,axiom,
% 6.92/7.29 ! [S2: set_nat,F: nat > rat,I2: nat] :
% 6.92/7.29 ( ( finite_finite_nat @ S2 )
% 6.92/7.29 => ( ! [I3: nat] :
% 6.92/7.29 ( ( member_nat @ I3 @ S2 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 6.92/7.29 = zero_zero_rat )
% 6.92/7.29 => ( ( member_nat @ I2 @ S2 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = zero_zero_rat ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_0
% 6.92/7.29 thf(fact_8634_sum__nonneg__0,axiom,
% 6.92/7.29 ! [S2: set_int,F: int > rat,I2: int] :
% 6.92/7.29 ( ( finite_finite_int @ S2 )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ S2 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 6.92/7.29 = zero_zero_rat )
% 6.92/7.29 => ( ( member_int @ I2 @ S2 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = zero_zero_rat ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_0
% 6.92/7.29 thf(fact_8635_sum__nonneg__0,axiom,
% 6.92/7.29 ! [S2: set_Code_integer,F: code_integer > rat,I2: code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ S2 )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ S2 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups6602215022474089585er_rat @ F @ S2 )
% 6.92/7.29 = zero_zero_rat )
% 6.92/7.29 => ( ( member_Code_integer @ I2 @ S2 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = zero_zero_rat ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_0
% 6.92/7.29 thf(fact_8636_sum__nonneg__0,axiom,
% 6.92/7.29 ! [S2: set_o,F: $o > nat,I2: $o] :
% 6.92/7.29 ( ( finite_finite_o @ S2 )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ S2 )
% 6.92/7.29 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups8507830703676809646_o_nat @ F @ S2 )
% 6.92/7.29 = zero_zero_nat )
% 6.92/7.29 => ( ( member_o @ I2 @ S2 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = zero_zero_nat ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_0
% 6.92/7.29 thf(fact_8637_sum__nonneg__0,axiom,
% 6.92/7.29 ! [S2: set_int,F: int > nat,I2: int] :
% 6.92/7.29 ( ( finite_finite_int @ S2 )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ S2 )
% 6.92/7.29 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ( ( groups4541462559716669496nt_nat @ F @ S2 )
% 6.92/7.29 = zero_zero_nat )
% 6.92/7.29 => ( ( member_int @ I2 @ S2 )
% 6.92/7.29 => ( ( F @ I2 )
% 6.92/7.29 = zero_zero_nat ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_nonneg_0
% 6.92/7.29 thf(fact_8638_add__mset__in__multiset,axiom,
% 6.92/7.29 ! [M6: list_nat > nat,A: list_nat] :
% 6.92/7.29 ( ( finite8100373058378681591st_nat
% 6.92/7.29 @ ( collect_list_nat
% 6.92/7.29 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite8100373058378681591st_nat
% 6.92/7.29 @ ( collect_list_nat
% 6.92/7.29 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M6 @ X4 ) ) @ ( M6 @ X4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % add_mset_in_multiset
% 6.92/7.29 thf(fact_8639_add__mset__in__multiset,axiom,
% 6.92/7.29 ! [M6: set_Pr958786334691620121nt_int > nat,A: set_Pr958786334691620121nt_int] :
% 6.92/7.29 ( ( finite8744585540193469122nt_int
% 6.92/7.29 @ ( collec5210948495886036740nt_int
% 6.92/7.29 @ ^ [X4: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite8744585540193469122nt_int
% 6.92/7.29 @ ( collec5210948495886036740nt_int
% 6.92/7.29 @ ^ [X4: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M6 @ X4 ) ) @ ( M6 @ X4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % add_mset_in_multiset
% 6.92/7.29 thf(fact_8640_add__mset__in__multiset,axiom,
% 6.92/7.29 ! [M6: set_nat > nat,A: set_nat] :
% 6.92/7.29 ( ( finite1152437895449049373et_nat
% 6.92/7.29 @ ( collect_set_nat
% 6.92/7.29 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite1152437895449049373et_nat
% 6.92/7.29 @ ( collect_set_nat
% 6.92/7.29 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M6 @ X4 ) ) @ ( M6 @ X4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % add_mset_in_multiset
% 6.92/7.29 thf(fact_8641_add__mset__in__multiset,axiom,
% 6.92/7.29 ! [M6: nat > nat,A: nat] :
% 6.92/7.29 ( ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M6 @ X4 ) ) @ ( M6 @ X4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % add_mset_in_multiset
% 6.92/7.29 thf(fact_8642_add__mset__in__multiset,axiom,
% 6.92/7.29 ! [M6: int > nat,A: int] :
% 6.92/7.29 ( ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M6 @ X4 ) ) @ ( M6 @ X4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % add_mset_in_multiset
% 6.92/7.29 thf(fact_8643_add__mset__in__multiset,axiom,
% 6.92/7.29 ! [M6: code_integer > nat,A: code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M6 @ X4 ) ) @ ( M6 @ X4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % add_mset_in_multiset
% 6.92/7.29 thf(fact_8644_add__mset__in__multiset,axiom,
% 6.92/7.29 ! [M6: product_prod_nat_nat > nat,A: product_prod_nat_nat] :
% 6.92/7.29 ( ( finite6177210948735845034at_nat
% 6.92/7.29 @ ( collec3392354462482085612at_nat
% 6.92/7.29 @ ^ [X4: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite6177210948735845034at_nat
% 6.92/7.29 @ ( collec3392354462482085612at_nat
% 6.92/7.29 @ ^ [X4: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M6 @ X4 ) ) @ ( M6 @ X4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % add_mset_in_multiset
% 6.92/7.29 thf(fact_8645_sum_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_o,G: $o > code_integer,B5: set_o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( groups4406642042086082107nteger @ G @ ( inf_inf_set_o @ A4 @ B5 ) )
% 6.92/7.29 = ( groups4406642042086082107nteger
% 6.92/7.29 @ ^ [X4: $o] : ( if_Code_integer @ ( member_o @ X4 @ B5 ) @ ( G @ X4 ) @ zero_z3403309356797280102nteger )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_restrict
% 6.92/7.29 thf(fact_8646_sum_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > code_integer,B5: set_int] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups7873554091576472773nteger @ G @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.92/7.29 = ( groups7873554091576472773nteger
% 6.92/7.29 @ ^ [X4: int] : ( if_Code_integer @ ( member_int @ X4 @ B5 ) @ ( G @ X4 ) @ zero_z3403309356797280102nteger )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_restrict
% 6.92/7.29 thf(fact_8647_sum_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > code_integer,B5: set_Code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups879477027807139574nteger @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) )
% 6.92/7.29 = ( groups879477027807139574nteger
% 6.92/7.29 @ ^ [X4: code_integer] : ( if_Code_integer @ ( member_Code_integer @ X4 @ B5 ) @ ( G @ X4 ) @ zero_z3403309356797280102nteger )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_restrict
% 6.92/7.29 thf(fact_8648_sum_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_o,G: $o > rat,B5: set_o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( groups7872700643590313910_o_rat @ G @ ( inf_inf_set_o @ A4 @ B5 ) )
% 6.92/7.29 = ( groups7872700643590313910_o_rat
% 6.92/7.29 @ ^ [X4: $o] : ( if_rat @ ( member_o @ X4 @ B5 ) @ ( G @ X4 ) @ zero_zero_rat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_restrict
% 6.92/7.29 thf(fact_8649_sum_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > rat,B5: set_int] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups3906332499630173760nt_rat @ G @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.92/7.29 = ( groups3906332499630173760nt_rat
% 6.92/7.29 @ ^ [X4: int] : ( if_rat @ ( member_int @ X4 @ B5 ) @ ( G @ X4 ) @ zero_zero_rat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_restrict
% 6.92/7.29 thf(fact_8650_sum_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > rat,B5: set_Code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups6602215022474089585er_rat @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) )
% 6.92/7.29 = ( groups6602215022474089585er_rat
% 6.92/7.29 @ ^ [X4: code_integer] : ( if_rat @ ( member_Code_integer @ X4 @ B5 ) @ ( G @ X4 ) @ zero_zero_rat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_restrict
% 6.92/7.29 thf(fact_8651_sum_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_o,G: $o > nat,B5: set_o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( groups8507830703676809646_o_nat @ G @ ( inf_inf_set_o @ A4 @ B5 ) )
% 6.92/7.29 = ( groups8507830703676809646_o_nat
% 6.92/7.29 @ ^ [X4: $o] : ( if_nat @ ( member_o @ X4 @ B5 ) @ ( G @ X4 ) @ zero_zero_nat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_restrict
% 6.92/7.29 thf(fact_8652_sum_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > nat,B5: set_int] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups4541462559716669496nt_nat @ G @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.92/7.29 = ( groups4541462559716669496nt_nat
% 6.92/7.29 @ ^ [X4: int] : ( if_nat @ ( member_int @ X4 @ B5 ) @ ( G @ X4 ) @ zero_zero_nat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_restrict
% 6.92/7.29 thf(fact_8653_sum_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > nat,B5: set_Code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups7237345082560585321er_nat @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) )
% 6.92/7.29 = ( groups7237345082560585321er_nat
% 6.92/7.29 @ ^ [X4: code_integer] : ( if_nat @ ( member_Code_integer @ X4 @ B5 ) @ ( G @ X4 ) @ zero_zero_nat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_restrict
% 6.92/7.29 thf(fact_8654_sum_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_o,G: $o > int,B5: set_o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( groups8505340233167759370_o_int @ G @ ( inf_inf_set_o @ A4 @ B5 ) )
% 6.92/7.29 = ( groups8505340233167759370_o_int
% 6.92/7.29 @ ^ [X4: $o] : ( if_int @ ( member_o @ X4 @ B5 ) @ ( G @ X4 ) @ zero_zero_int )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.inter_restrict
% 6.92/7.29 thf(fact_8655_sum_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_nat,G: nat > code_integer] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( groups7501900531339628137nteger @ G
% 6.92/7.29 @ ( minus_minus_set_nat @ A4
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) ) ) )
% 6.92/7.29 = ( groups7501900531339628137nteger @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.setdiff_irrelevant
% 6.92/7.29 thf(fact_8656_sum_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > code_integer] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups7873554091576472773nteger @ G
% 6.92/7.29 @ ( minus_minus_set_int @ A4
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) ) ) )
% 6.92/7.29 = ( groups7873554091576472773nteger @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.setdiff_irrelevant
% 6.92/7.29 thf(fact_8657_sum_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups879477027807139574nteger @ G
% 6.92/7.29 @ ( minus_2355218937544613996nteger @ A4
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) ) ) )
% 6.92/7.29 = ( groups879477027807139574nteger @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.setdiff_irrelevant
% 6.92/7.29 thf(fact_8658_sum_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_nat,G: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( groups2906978787729119204at_rat @ G
% 6.92/7.29 @ ( minus_minus_set_nat @ A4
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = zero_zero_rat ) ) ) )
% 6.92/7.29 = ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.setdiff_irrelevant
% 6.92/7.29 thf(fact_8659_sum_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > rat] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups3906332499630173760nt_rat @ G
% 6.92/7.29 @ ( minus_minus_set_int @ A4
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = zero_zero_rat ) ) ) )
% 6.92/7.29 = ( groups3906332499630173760nt_rat @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.setdiff_irrelevant
% 6.92/7.29 thf(fact_8660_sum_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > rat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups6602215022474089585er_rat @ G
% 6.92/7.29 @ ( minus_2355218937544613996nteger @ A4
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = zero_zero_rat ) ) ) )
% 6.92/7.29 = ( groups6602215022474089585er_rat @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.setdiff_irrelevant
% 6.92/7.29 thf(fact_8661_sum_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > nat] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups4541462559716669496nt_nat @ G
% 6.92/7.29 @ ( minus_minus_set_int @ A4
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = zero_zero_nat ) ) ) )
% 6.92/7.29 = ( groups4541462559716669496nt_nat @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.setdiff_irrelevant
% 6.92/7.29 thf(fact_8662_sum_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > nat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups7237345082560585321er_nat @ G
% 6.92/7.29 @ ( minus_2355218937544613996nteger @ A4
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = zero_zero_nat ) ) ) )
% 6.92/7.29 = ( groups7237345082560585321er_nat @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.setdiff_irrelevant
% 6.92/7.29 thf(fact_8663_sum_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_nat,G: nat > int] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( groups3539618377306564664at_int @ G
% 6.92/7.29 @ ( minus_minus_set_nat @ A4
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = zero_zero_int ) ) ) )
% 6.92/7.29 = ( groups3539618377306564664at_int @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.setdiff_irrelevant
% 6.92/7.29 thf(fact_8664_sum_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > int] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups7234854612051535045er_int @ G
% 6.92/7.29 @ ( minus_2355218937544613996nteger @ A4
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = zero_zero_int ) ) ) )
% 6.92/7.29 = ( groups7234854612051535045er_int @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.setdiff_irrelevant
% 6.92/7.29 thf(fact_8665_diff__preserves__multiset,axiom,
% 6.92/7.29 ! [M6: list_nat > nat,N7: list_nat > nat] :
% 6.92/7.29 ( ( finite8100373058378681591st_nat
% 6.92/7.29 @ ( collect_list_nat
% 6.92/7.29 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite8100373058378681591st_nat
% 6.92/7.29 @ ( collect_list_nat
% 6.92/7.29 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M6 @ X4 ) @ ( N7 @ X4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % diff_preserves_multiset
% 6.92/7.29 thf(fact_8666_diff__preserves__multiset,axiom,
% 6.92/7.29 ! [M6: set_Pr958786334691620121nt_int > nat,N7: set_Pr958786334691620121nt_int > nat] :
% 6.92/7.29 ( ( finite8744585540193469122nt_int
% 6.92/7.29 @ ( collec5210948495886036740nt_int
% 6.92/7.29 @ ^ [X4: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite8744585540193469122nt_int
% 6.92/7.29 @ ( collec5210948495886036740nt_int
% 6.92/7.29 @ ^ [X4: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M6 @ X4 ) @ ( N7 @ X4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % diff_preserves_multiset
% 6.92/7.29 thf(fact_8667_diff__preserves__multiset,axiom,
% 6.92/7.29 ! [M6: set_nat > nat,N7: set_nat > nat] :
% 6.92/7.29 ( ( finite1152437895449049373et_nat
% 6.92/7.29 @ ( collect_set_nat
% 6.92/7.29 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite1152437895449049373et_nat
% 6.92/7.29 @ ( collect_set_nat
% 6.92/7.29 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M6 @ X4 ) @ ( N7 @ X4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % diff_preserves_multiset
% 6.92/7.29 thf(fact_8668_diff__preserves__multiset,axiom,
% 6.92/7.29 ! [M6: nat > nat,N7: nat > nat] :
% 6.92/7.29 ( ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M6 @ X4 ) @ ( N7 @ X4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % diff_preserves_multiset
% 6.92/7.29 thf(fact_8669_diff__preserves__multiset,axiom,
% 6.92/7.29 ! [M6: int > nat,N7: int > nat] :
% 6.92/7.29 ( ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite_finite_int
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M6 @ X4 ) @ ( N7 @ X4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % diff_preserves_multiset
% 6.92/7.29 thf(fact_8670_diff__preserves__multiset,axiom,
% 6.92/7.29 ! [M6: code_integer > nat,N7: code_integer > nat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite6017078050557962740nteger
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M6 @ X4 ) @ ( N7 @ X4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % diff_preserves_multiset
% 6.92/7.29 thf(fact_8671_diff__preserves__multiset,axiom,
% 6.92/7.29 ! [M6: product_prod_nat_nat > nat,N7: product_prod_nat_nat > nat] :
% 6.92/7.29 ( ( finite6177210948735845034at_nat
% 6.92/7.29 @ ( collec3392354462482085612at_nat
% 6.92/7.29 @ ^ [X4: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 6.92/7.29 => ( finite6177210948735845034at_nat
% 6.92/7.29 @ ( collec3392354462482085612at_nat
% 6.92/7.29 @ ^ [X4: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M6 @ X4 ) @ ( N7 @ X4 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % diff_preserves_multiset
% 6.92/7.29 thf(fact_8672_prod_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_o,G: $o > code_integer,B5: set_o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( groups7694694392188491536nteger @ G @ ( inf_inf_set_o @ A4 @ B5 ) )
% 6.92/7.29 = ( groups7694694392188491536nteger
% 6.92/7.29 @ ^ [X4: $o] : ( if_Code_integer @ ( member_o @ X4 @ B5 ) @ ( G @ X4 ) @ one_one_Code_integer )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_restrict
% 6.92/7.29 thf(fact_8673_prod_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > code_integer,B5: set_int] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups3827104343326376752nteger @ G @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.92/7.29 = ( groups3827104343326376752nteger
% 6.92/7.29 @ ^ [X4: int] : ( if_Code_integer @ ( member_int @ X4 @ B5 ) @ ( G @ X4 ) @ one_one_Code_integer )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_restrict
% 6.92/7.29 thf(fact_8674_prod_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > code_integer,B5: set_Code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups3674199335183972705nteger @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) )
% 6.92/7.29 = ( groups3674199335183972705nteger
% 6.92/7.29 @ ^ [X4: code_integer] : ( if_Code_integer @ ( member_Code_integer @ X4 @ B5 ) @ ( G @ X4 ) @ one_one_Code_integer )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_restrict
% 6.92/7.29 thf(fact_8675_prod_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_o,G: $o > assn,B5: set_o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( groups5301882518646026715o_assn @ G @ ( inf_inf_set_o @ A4 @ B5 ) )
% 6.92/7.29 = ( groups5301882518646026715o_assn
% 6.92/7.29 @ ^ [X4: $o] : ( if_assn @ ( member_o @ X4 @ B5 ) @ ( G @ X4 ) @ one_one_assn )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_restrict
% 6.92/7.29 thf(fact_8676_prod_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > assn,B5: set_int] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups7882442080178216443t_assn @ G @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.92/7.29 = ( groups7882442080178216443t_assn
% 6.92/7.29 @ ^ [X4: int] : ( if_assn @ ( member_int @ X4 @ B5 ) @ ( G @ X4 ) @ one_one_assn )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_restrict
% 6.92/7.29 thf(fact_8677_prod_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > assn,B5: set_Code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups1304777262505850412r_assn @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) )
% 6.92/7.29 = ( groups1304777262505850412r_assn
% 6.92/7.29 @ ^ [X4: code_integer] : ( if_assn @ ( member_Code_integer @ X4 @ B5 ) @ ( G @ X4 ) @ one_one_assn )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_restrict
% 6.92/7.29 thf(fact_8678_prod_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_o,G: $o > rat,B5: set_o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( groups2869687844427037835_o_rat @ G @ ( inf_inf_set_o @ A4 @ B5 ) )
% 6.92/7.29 = ( groups2869687844427037835_o_rat
% 6.92/7.29 @ ^ [X4: $o] : ( if_rat @ ( member_o @ X4 @ B5 ) @ ( G @ X4 ) @ one_one_rat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_restrict
% 6.92/7.29 thf(fact_8679_prod_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > rat,B5: set_int] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups1072433553688619179nt_rat @ G @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.92/7.29 = ( groups1072433553688619179nt_rat
% 6.92/7.29 @ ^ [X4: int] : ( if_rat @ ( member_int @ X4 @ B5 ) @ ( G @ X4 ) @ one_one_rat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_restrict
% 6.92/7.29 thf(fact_8680_prod_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > rat,B5: set_Code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups2555765274223993564er_rat @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) )
% 6.92/7.29 = ( groups2555765274223993564er_rat
% 6.92/7.29 @ ^ [X4: code_integer] : ( if_rat @ ( member_Code_integer @ X4 @ B5 ) @ ( G @ X4 ) @ one_one_rat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_restrict
% 6.92/7.29 thf(fact_8681_prod_Ointer__restrict,axiom,
% 6.92/7.29 ! [A4: set_o,G: $o > nat,B5: set_o] :
% 6.92/7.29 ( ( finite_finite_o @ A4 )
% 6.92/7.29 => ( ( groups3504817904513533571_o_nat @ G @ ( inf_inf_set_o @ A4 @ B5 ) )
% 6.92/7.29 = ( groups3504817904513533571_o_nat
% 6.92/7.29 @ ^ [X4: $o] : ( if_nat @ ( member_o @ X4 @ B5 ) @ ( G @ X4 ) @ one_one_nat )
% 6.92/7.29 @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.inter_restrict
% 6.92/7.29 thf(fact_8682_prod_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_nat,G: nat > code_integer] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( groups3455450783089532116nteger @ G
% 6.92/7.29 @ ( minus_minus_set_nat @ A4
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = one_one_Code_integer ) ) ) )
% 6.92/7.29 = ( groups3455450783089532116nteger @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.setdiff_irrelevant
% 6.92/7.29 thf(fact_8683_prod_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > code_integer] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups3827104343326376752nteger @ G
% 6.92/7.29 @ ( minus_minus_set_int @ A4
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = one_one_Code_integer ) ) ) )
% 6.92/7.29 = ( groups3827104343326376752nteger @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.setdiff_irrelevant
% 6.92/7.29 thf(fact_8684_prod_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups3674199335183972705nteger @ G
% 6.92/7.29 @ ( minus_2355218937544613996nteger @ A4
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = one_one_Code_integer ) ) ) )
% 6.92/7.29 = ( groups3674199335183972705nteger @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.setdiff_irrelevant
% 6.92/7.29 thf(fact_8685_prod_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_nat,G: nat > assn] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( groups6906906614972039071t_assn @ G
% 6.92/7.29 @ ( minus_minus_set_nat @ A4
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = one_one_assn ) ) ) )
% 6.92/7.29 = ( groups6906906614972039071t_assn @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.setdiff_irrelevant
% 6.92/7.29 thf(fact_8686_prod_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > assn] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups7882442080178216443t_assn @ G
% 6.92/7.29 @ ( minus_minus_set_int @ A4
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = one_one_assn ) ) ) )
% 6.92/7.29 = ( groups7882442080178216443t_assn @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.setdiff_irrelevant
% 6.92/7.29 thf(fact_8687_prod_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > assn] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups1304777262505850412r_assn @ G
% 6.92/7.29 @ ( minus_2355218937544613996nteger @ A4
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = one_one_assn ) ) ) )
% 6.92/7.29 = ( groups1304777262505850412r_assn @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.setdiff_irrelevant
% 6.92/7.29 thf(fact_8688_prod_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_nat,G: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat @ A4 )
% 6.92/7.29 => ( ( groups73079841787564623at_rat @ G
% 6.92/7.29 @ ( minus_minus_set_nat @ A4
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [X4: nat] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = one_one_rat ) ) ) )
% 6.92/7.29 = ( groups73079841787564623at_rat @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.setdiff_irrelevant
% 6.92/7.29 thf(fact_8689_prod_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > rat] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups1072433553688619179nt_rat @ G
% 6.92/7.29 @ ( minus_minus_set_int @ A4
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = one_one_rat ) ) ) )
% 6.92/7.29 = ( groups1072433553688619179nt_rat @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.setdiff_irrelevant
% 6.92/7.29 thf(fact_8690_prod_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_Code_integer,G: code_integer > rat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ A4 )
% 6.92/7.29 => ( ( groups2555765274223993564er_rat @ G
% 6.92/7.29 @ ( minus_2355218937544613996nteger @ A4
% 6.92/7.29 @ ( collect_Code_integer
% 6.92/7.29 @ ^ [X4: code_integer] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = one_one_rat ) ) ) )
% 6.92/7.29 = ( groups2555765274223993564er_rat @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.setdiff_irrelevant
% 6.92/7.29 thf(fact_8691_prod_Osetdiff__irrelevant,axiom,
% 6.92/7.29 ! [A4: set_int,G: int > nat] :
% 6.92/7.29 ( ( finite_finite_int @ A4 )
% 6.92/7.29 => ( ( groups1707563613775114915nt_nat @ G
% 6.92/7.29 @ ( minus_minus_set_int @ A4
% 6.92/7.29 @ ( collect_int
% 6.92/7.29 @ ^ [X4: int] :
% 6.92/7.29 ( ( G @ X4 )
% 6.92/7.29 = one_one_nat ) ) ) )
% 6.92/7.29 = ( groups1707563613775114915nt_nat @ G @ A4 ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % prod.setdiff_irrelevant
% 6.92/7.29 thf(fact_8692_finite__divisors__nat,axiom,
% 6.92/7.29 ! [M: nat] :
% 6.92/7.29 ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.92/7.29 => ( finite_finite_nat
% 6.92/7.29 @ ( collect_nat
% 6.92/7.29 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_divisors_nat
% 6.92/7.29 thf(fact_8693_subset__eq__atLeast0__atMost__finite,axiom,
% 6.92/7.29 ! [N7: set_nat,N2: nat] :
% 6.92/7.29 ( ( ord_less_eq_set_nat @ N7 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.29 => ( finite_finite_nat @ N7 ) ) ).
% 6.92/7.29
% 6.92/7.29 % subset_eq_atLeast0_atMost_finite
% 6.92/7.29 thf(fact_8694_subset__eq__atLeast0__lessThan__finite,axiom,
% 6.92/7.29 ! [N7: set_nat,N2: nat] :
% 6.92/7.29 ( ( ord_less_eq_set_nat @ N7 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 6.92/7.29 => ( finite_finite_nat @ N7 ) ) ).
% 6.92/7.29
% 6.92/7.29 % subset_eq_atLeast0_lessThan_finite
% 6.92/7.29 thf(fact_8695_finite__abs__int__segment,axiom,
% 6.92/7.29 ! [A: rat] :
% 6.92/7.29 ( finite_finite_rat
% 6.92/7.29 @ ( collect_rat
% 6.92/7.29 @ ^ [K3: rat] :
% 6.92/7.29 ( ( member_rat @ K3 @ ring_1_Ints_rat )
% 6.92/7.29 & ( ord_less_eq_rat @ ( abs_abs_rat @ K3 ) @ A ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % finite_abs_int_segment
% 6.92/7.29 thf(fact_8696_sum__pos2,axiom,
% 6.92/7.29 ! [I5: set_o,I2: $o,F: $o > code_integer] :
% 6.92/7.29 ( ( finite_finite_o @ I5 )
% 6.92/7.29 => ( ( member_o @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ I5 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups4406642042086082107nteger @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos2
% 6.92/7.29 thf(fact_8697_sum__pos2,axiom,
% 6.92/7.29 ! [I5: set_nat,I2: nat,F: nat > code_integer] :
% 6.92/7.29 ( ( finite_finite_nat @ I5 )
% 6.92/7.29 => ( ( member_nat @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: nat] :
% 6.92/7.29 ( ( member_nat @ I3 @ I5 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups7501900531339628137nteger @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos2
% 6.92/7.29 thf(fact_8698_sum__pos2,axiom,
% 6.92/7.29 ! [I5: set_int,I2: int,F: int > code_integer] :
% 6.92/7.29 ( ( finite_finite_int @ I5 )
% 6.92/7.29 => ( ( member_int @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ I5 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups7873554091576472773nteger @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos2
% 6.92/7.29 thf(fact_8699_sum__pos2,axiom,
% 6.92/7.29 ! [I5: set_Code_integer,I2: code_integer,F: code_integer > code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ I5 )
% 6.92/7.29 => ( ( member_Code_integer @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ I5 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups879477027807139574nteger @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos2
% 6.92/7.29 thf(fact_8700_sum__pos2,axiom,
% 6.92/7.29 ! [I5: set_o,I2: $o,F: $o > rat] :
% 6.92/7.29 ( ( finite_finite_o @ I5 )
% 6.92/7.29 => ( ( member_o @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ zero_zero_rat @ ( groups7872700643590313910_o_rat @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos2
% 6.92/7.29 thf(fact_8701_sum__pos2,axiom,
% 6.92/7.29 ! [I5: set_nat,I2: nat,F: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat @ I5 )
% 6.92/7.29 => ( ( member_nat @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: nat] :
% 6.92/7.29 ( ( member_nat @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos2
% 6.92/7.29 thf(fact_8702_sum__pos2,axiom,
% 6.92/7.29 ! [I5: set_int,I2: int,F: int > rat] :
% 6.92/7.29 ( ( finite_finite_int @ I5 )
% 6.92/7.29 => ( ( member_int @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos2
% 6.92/7.29 thf(fact_8703_sum__pos2,axiom,
% 6.92/7.29 ! [I5: set_Code_integer,I2: code_integer,F: code_integer > rat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ I5 )
% 6.92/7.29 => ( ( member_Code_integer @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ zero_zero_rat @ ( groups6602215022474089585er_rat @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos2
% 6.92/7.29 thf(fact_8704_sum__pos2,axiom,
% 6.92/7.29 ! [I5: set_o,I2: $o,F: $o > nat] :
% 6.92/7.29 ( ( finite_finite_o @ I5 )
% 6.92/7.29 => ( ( member_o @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_nat @ zero_zero_nat @ ( groups8507830703676809646_o_nat @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos2
% 6.92/7.29 thf(fact_8705_sum__pos2,axiom,
% 6.92/7.29 ! [I5: set_int,I2: int,F: int > nat] :
% 6.92/7.29 ( ( finite_finite_int @ I5 )
% 6.92/7.29 => ( ( member_int @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos2
% 6.92/7.29 thf(fact_8706_sum__pos,axiom,
% 6.92/7.29 ! [I5: set_Code_integer,F: code_integer > code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bo3990330152332043303nteger )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ I5 )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups879477027807139574nteger @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos
% 6.92/7.29 thf(fact_8707_sum__pos,axiom,
% 6.92/7.29 ! [I5: set_o,F: $o > code_integer] :
% 6.92/7.29 ( ( finite_finite_o @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bot_set_o )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ I5 )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups4406642042086082107nteger @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos
% 6.92/7.29 thf(fact_8708_sum__pos,axiom,
% 6.92/7.29 ! [I5: set_nat,F: nat > code_integer] :
% 6.92/7.29 ( ( finite_finite_nat @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bot_set_nat )
% 6.92/7.29 => ( ! [I3: nat] :
% 6.92/7.29 ( ( member_nat @ I3 @ I5 )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups7501900531339628137nteger @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos
% 6.92/7.29 thf(fact_8709_sum__pos,axiom,
% 6.92/7.29 ! [I5: set_int,F: int > code_integer] :
% 6.92/7.29 ( ( finite_finite_int @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bot_set_int )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ I5 )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups7873554091576472773nteger @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos
% 6.92/7.29 thf(fact_8710_sum__pos,axiom,
% 6.92/7.29 ! [I5: set_Code_integer,F: code_integer > rat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bo3990330152332043303nteger )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ zero_zero_rat @ ( groups6602215022474089585er_rat @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos
% 6.92/7.29 thf(fact_8711_sum__pos,axiom,
% 6.92/7.29 ! [I5: set_o,F: $o > rat] :
% 6.92/7.29 ( ( finite_finite_o @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bot_set_o )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ zero_zero_rat @ ( groups7872700643590313910_o_rat @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos
% 6.92/7.29 thf(fact_8712_sum__pos,axiom,
% 6.92/7.29 ! [I5: set_nat,F: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bot_set_nat )
% 6.92/7.29 => ( ! [I3: nat] :
% 6.92/7.29 ( ( member_nat @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos
% 6.92/7.29 thf(fact_8713_sum__pos,axiom,
% 6.92/7.29 ! [I5: set_int,F: int > rat] :
% 6.92/7.29 ( ( finite_finite_int @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bot_set_int )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos
% 6.92/7.29 thf(fact_8714_sum__pos,axiom,
% 6.92/7.29 ! [I5: set_Code_integer,F: code_integer > nat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bo3990330152332043303nteger )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_nat @ zero_zero_nat @ ( groups7237345082560585321er_nat @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos
% 6.92/7.29 thf(fact_8715_sum__pos,axiom,
% 6.92/7.29 ! [I5: set_o,F: $o > nat] :
% 6.92/7.29 ( ( finite_finite_o @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bot_set_o )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_nat @ zero_zero_nat @ ( groups8507830703676809646_o_nat @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum_pos
% 6.92/7.29 thf(fact_8716_less__1__prod2,axiom,
% 6.92/7.29 ! [I5: set_o,I2: $o,F: $o > code_integer] :
% 6.92/7.29 ( ( finite_finite_o @ I5 )
% 6.92/7.29 => ( ( member_o @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ I5 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod2
% 6.92/7.29 thf(fact_8717_less__1__prod2,axiom,
% 6.92/7.29 ! [I5: set_nat,I2: nat,F: nat > code_integer] :
% 6.92/7.29 ( ( finite_finite_nat @ I5 )
% 6.92/7.29 => ( ( member_nat @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: nat] :
% 6.92/7.29 ( ( member_nat @ I3 @ I5 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod2
% 6.92/7.29 thf(fact_8718_less__1__prod2,axiom,
% 6.92/7.29 ! [I5: set_int,I2: int,F: int > code_integer] :
% 6.92/7.29 ( ( finite_finite_int @ I5 )
% 6.92/7.29 => ( ( member_int @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ I5 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod2
% 6.92/7.29 thf(fact_8719_less__1__prod2,axiom,
% 6.92/7.29 ! [I5: set_Code_integer,I2: code_integer,F: code_integer > code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ I5 )
% 6.92/7.29 => ( ( member_Code_integer @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ I5 )
% 6.92/7.29 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3674199335183972705nteger @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod2
% 6.92/7.29 thf(fact_8720_less__1__prod2,axiom,
% 6.92/7.29 ! [I5: set_o,I2: $o,F: $o > rat] :
% 6.92/7.29 ( ( finite_finite_o @ I5 )
% 6.92/7.29 => ( ( member_o @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod2
% 6.92/7.29 thf(fact_8721_less__1__prod2,axiom,
% 6.92/7.29 ! [I5: set_nat,I2: nat,F: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat @ I5 )
% 6.92/7.29 => ( ( member_nat @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: nat] :
% 6.92/7.29 ( ( member_nat @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod2
% 6.92/7.29 thf(fact_8722_less__1__prod2,axiom,
% 6.92/7.29 ! [I5: set_int,I2: int,F: int > rat] :
% 6.92/7.29 ( ( finite_finite_int @ I5 )
% 6.92/7.29 => ( ( member_int @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod2
% 6.92/7.29 thf(fact_8723_less__1__prod2,axiom,
% 6.92/7.29 ! [I5: set_Code_integer,I2: code_integer,F: code_integer > rat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ I5 )
% 6.92/7.29 => ( ( member_Code_integer @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ one_one_rat @ ( groups2555765274223993564er_rat @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod2
% 6.92/7.29 thf(fact_8724_less__1__prod2,axiom,
% 6.92/7.29 ! [I5: set_o,I2: $o,F: $o > int] :
% 6.92/7.29 ( ( finite_finite_o @ I5 )
% 6.92/7.29 => ( ( member_o @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_int @ one_one_int @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_int @ one_one_int @ ( groups3502327434004483295_o_int @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod2
% 6.92/7.29 thf(fact_8725_less__1__prod2,axiom,
% 6.92/7.29 ! [I5: set_Code_integer,I2: code_integer,F: code_integer > int] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ I5 )
% 6.92/7.29 => ( ( member_Code_integer @ I2 @ I5 )
% 6.92/7.29 => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_eq_int @ one_one_int @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_int @ one_one_int @ ( groups3188404863801439024er_int @ F @ I5 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod2
% 6.92/7.29 thf(fact_8726_less__1__prod,axiom,
% 6.92/7.29 ! [I5: set_Code_integer,F: code_integer > code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bo3990330152332043303nteger )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ I5 )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3674199335183972705nteger @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod
% 6.92/7.29 thf(fact_8727_less__1__prod,axiom,
% 6.92/7.29 ! [I5: set_o,F: $o > code_integer] :
% 6.92/7.29 ( ( finite_finite_o @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bot_set_o )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ I5 )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod
% 6.92/7.29 thf(fact_8728_less__1__prod,axiom,
% 6.92/7.29 ! [I5: set_nat,F: nat > code_integer] :
% 6.92/7.29 ( ( finite_finite_nat @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bot_set_nat )
% 6.92/7.29 => ( ! [I3: nat] :
% 6.92/7.29 ( ( member_nat @ I3 @ I5 )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod
% 6.92/7.29 thf(fact_8729_less__1__prod,axiom,
% 6.92/7.29 ! [I5: set_int,F: int > code_integer] :
% 6.92/7.29 ( ( finite_finite_int @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bot_set_int )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ I5 )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod
% 6.92/7.29 thf(fact_8730_less__1__prod,axiom,
% 6.92/7.29 ! [I5: set_Code_integer,F: code_integer > rat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bo3990330152332043303nteger )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ one_one_rat @ ( groups2555765274223993564er_rat @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod
% 6.92/7.29 thf(fact_8731_less__1__prod,axiom,
% 6.92/7.29 ! [I5: set_o,F: $o > rat] :
% 6.92/7.29 ( ( finite_finite_o @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bot_set_o )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod
% 6.92/7.29 thf(fact_8732_less__1__prod,axiom,
% 6.92/7.29 ! [I5: set_nat,F: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bot_set_nat )
% 6.92/7.29 => ( ! [I3: nat] :
% 6.92/7.29 ( ( member_nat @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod
% 6.92/7.29 thf(fact_8733_less__1__prod,axiom,
% 6.92/7.29 ! [I5: set_int,F: int > rat] :
% 6.92/7.29 ( ( finite_finite_int @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bot_set_int )
% 6.92/7.29 => ( ! [I3: int] :
% 6.92/7.29 ( ( member_int @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod
% 6.92/7.29 thf(fact_8734_less__1__prod,axiom,
% 6.92/7.29 ! [I5: set_Code_integer,F: code_integer > int] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bo3990330152332043303nteger )
% 6.92/7.29 => ( ! [I3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_int @ one_one_int @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_int @ one_one_int @ ( groups3188404863801439024er_int @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod
% 6.92/7.29 thf(fact_8735_less__1__prod,axiom,
% 6.92/7.29 ! [I5: set_o,F: $o > int] :
% 6.92/7.29 ( ( finite_finite_o @ I5 )
% 6.92/7.29 => ( ( I5 != bot_bot_set_o )
% 6.92/7.29 => ( ! [I3: $o] :
% 6.92/7.29 ( ( member_o @ I3 @ I5 )
% 6.92/7.29 => ( ord_less_int @ one_one_int @ ( F @ I3 ) ) )
% 6.92/7.29 => ( ord_less_int @ one_one_int @ ( groups3502327434004483295_o_int @ F @ I5 ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % less_1_prod
% 6.92/7.29 thf(fact_8736_sum_Omono__neutral__cong__right,axiom,
% 6.92/7.29 ! [T7: set_o,S: set_o,G: $o > code_integer,H: $o > code_integer] :
% 6.92/7.29 ( ( finite_finite_o @ T7 )
% 6.92/7.29 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups4406642042086082107nteger @ G @ T7 )
% 6.92/7.29 = ( groups4406642042086082107nteger @ H @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_right
% 6.92/7.29 thf(fact_8737_sum_Omono__neutral__cong__right,axiom,
% 6.92/7.29 ! [T7: set_nat,S: set_nat,G: nat > code_integer,H: nat > code_integer] :
% 6.92/7.29 ( ( finite_finite_nat @ T7 )
% 6.92/7.29 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups7501900531339628137nteger @ G @ T7 )
% 6.92/7.29 = ( groups7501900531339628137nteger @ H @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_right
% 6.92/7.29 thf(fact_8738_sum_Omono__neutral__cong__right,axiom,
% 6.92/7.29 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > code_integer,H: code_integer > code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ T7 )
% 6.92/7.29 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups879477027807139574nteger @ G @ T7 )
% 6.92/7.29 = ( groups879477027807139574nteger @ H @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_right
% 6.92/7.29 thf(fact_8739_sum_Omono__neutral__cong__right,axiom,
% 6.92/7.29 ! [T7: set_o,S: set_o,G: $o > rat,H: $o > rat] :
% 6.92/7.29 ( ( finite_finite_o @ T7 )
% 6.92/7.29 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = zero_zero_rat ) )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups7872700643590313910_o_rat @ G @ T7 )
% 6.92/7.29 = ( groups7872700643590313910_o_rat @ H @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_right
% 6.92/7.29 thf(fact_8740_sum_Omono__neutral__cong__right,axiom,
% 6.92/7.29 ! [T7: set_nat,S: set_nat,G: nat > rat,H: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat @ T7 )
% 6.92/7.29 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = zero_zero_rat ) )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups2906978787729119204at_rat @ G @ T7 )
% 6.92/7.29 = ( groups2906978787729119204at_rat @ H @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_right
% 6.92/7.29 thf(fact_8741_sum_Omono__neutral__cong__right,axiom,
% 6.92/7.29 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > rat,H: code_integer > rat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ T7 )
% 6.92/7.29 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = zero_zero_rat ) )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups6602215022474089585er_rat @ G @ T7 )
% 6.92/7.29 = ( groups6602215022474089585er_rat @ H @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_right
% 6.92/7.29 thf(fact_8742_sum_Omono__neutral__cong__right,axiom,
% 6.92/7.29 ! [T7: set_o,S: set_o,G: $o > nat,H: $o > nat] :
% 6.92/7.29 ( ( finite_finite_o @ T7 )
% 6.92/7.29 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = zero_zero_nat ) )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups8507830703676809646_o_nat @ G @ T7 )
% 6.92/7.29 = ( groups8507830703676809646_o_nat @ H @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_right
% 6.92/7.29 thf(fact_8743_sum_Omono__neutral__cong__right,axiom,
% 6.92/7.29 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > nat,H: code_integer > nat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ T7 )
% 6.92/7.29 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = zero_zero_nat ) )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups7237345082560585321er_nat @ G @ T7 )
% 6.92/7.29 = ( groups7237345082560585321er_nat @ H @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_right
% 6.92/7.29 thf(fact_8744_sum_Omono__neutral__cong__right,axiom,
% 6.92/7.29 ! [T7: set_o,S: set_o,G: $o > int,H: $o > int] :
% 6.92/7.29 ( ( finite_finite_o @ T7 )
% 6.92/7.29 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = zero_zero_int ) )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups8505340233167759370_o_int @ G @ T7 )
% 6.92/7.29 = ( groups8505340233167759370_o_int @ H @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_right
% 6.92/7.29 thf(fact_8745_sum_Omono__neutral__cong__right,axiom,
% 6.92/7.29 ! [T7: set_nat,S: set_nat,G: nat > int,H: nat > int] :
% 6.92/7.29 ( ( finite_finite_nat @ T7 )
% 6.92/7.29 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = zero_zero_int ) )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups3539618377306564664at_int @ G @ T7 )
% 6.92/7.29 = ( groups3539618377306564664at_int @ H @ S ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_right
% 6.92/7.29 thf(fact_8746_sum_Omono__neutral__cong__left,axiom,
% 6.92/7.29 ! [T7: set_o,S: set_o,H: $o > code_integer,G: $o > code_integer] :
% 6.92/7.29 ( ( finite_finite_o @ T7 )
% 6.92/7.29 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.92/7.29 => ( ( H @ X3 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups4406642042086082107nteger @ G @ S )
% 6.92/7.29 = ( groups4406642042086082107nteger @ H @ T7 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_left
% 6.92/7.29 thf(fact_8747_sum_Omono__neutral__cong__left,axiom,
% 6.92/7.29 ! [T7: set_nat,S: set_nat,H: nat > code_integer,G: nat > code_integer] :
% 6.92/7.29 ( ( finite_finite_nat @ T7 )
% 6.92/7.29 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.92/7.29 => ( ( H @ X3 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups7501900531339628137nteger @ G @ S )
% 6.92/7.29 = ( groups7501900531339628137nteger @ H @ T7 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_left
% 6.92/7.29 thf(fact_8748_sum_Omono__neutral__cong__left,axiom,
% 6.92/7.29 ! [T7: set_Code_integer,S: set_Code_integer,H: code_integer > code_integer,G: code_integer > code_integer] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ T7 )
% 6.92/7.29 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.92/7.29 => ( ( H @ X3 )
% 6.92/7.29 = zero_z3403309356797280102nteger ) )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups879477027807139574nteger @ G @ S )
% 6.92/7.29 = ( groups879477027807139574nteger @ H @ T7 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_left
% 6.92/7.29 thf(fact_8749_sum_Omono__neutral__cong__left,axiom,
% 6.92/7.29 ! [T7: set_o,S: set_o,H: $o > rat,G: $o > rat] :
% 6.92/7.29 ( ( finite_finite_o @ T7 )
% 6.92/7.29 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.92/7.29 => ( ( H @ X3 )
% 6.92/7.29 = zero_zero_rat ) )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups7872700643590313910_o_rat @ G @ S )
% 6.92/7.29 = ( groups7872700643590313910_o_rat @ H @ T7 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_left
% 6.92/7.29 thf(fact_8750_sum_Omono__neutral__cong__left,axiom,
% 6.92/7.29 ! [T7: set_nat,S: set_nat,H: nat > rat,G: nat > rat] :
% 6.92/7.29 ( ( finite_finite_nat @ T7 )
% 6.92/7.29 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.92/7.29 => ( ( H @ X3 )
% 6.92/7.29 = zero_zero_rat ) )
% 6.92/7.29 => ( ! [X3: nat] :
% 6.92/7.29 ( ( member_nat @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups2906978787729119204at_rat @ G @ S )
% 6.92/7.29 = ( groups2906978787729119204at_rat @ H @ T7 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_left
% 6.92/7.29 thf(fact_8751_sum_Omono__neutral__cong__left,axiom,
% 6.92/7.29 ! [T7: set_Code_integer,S: set_Code_integer,H: code_integer > rat,G: code_integer > rat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ T7 )
% 6.92/7.29 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.92/7.29 => ( ( H @ X3 )
% 6.92/7.29 = zero_zero_rat ) )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups6602215022474089585er_rat @ G @ S )
% 6.92/7.29 = ( groups6602215022474089585er_rat @ H @ T7 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_left
% 6.92/7.29 thf(fact_8752_sum_Omono__neutral__cong__left,axiom,
% 6.92/7.29 ! [T7: set_o,S: set_o,H: $o > nat,G: $o > nat] :
% 6.92/7.29 ( ( finite_finite_o @ T7 )
% 6.92/7.29 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.92/7.29 => ( ( H @ X3 )
% 6.92/7.29 = zero_zero_nat ) )
% 6.92/7.29 => ( ! [X3: $o] :
% 6.92/7.29 ( ( member_o @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups8507830703676809646_o_nat @ G @ S )
% 6.92/7.29 = ( groups8507830703676809646_o_nat @ H @ T7 ) ) ) ) ) ) ).
% 6.92/7.29
% 6.92/7.29 % sum.mono_neutral_cong_left
% 6.92/7.29 thf(fact_8753_sum_Omono__neutral__cong__left,axiom,
% 6.92/7.29 ! [T7: set_Code_integer,S: set_Code_integer,H: code_integer > nat,G: code_integer > nat] :
% 6.92/7.29 ( ( finite6017078050557962740nteger @ T7 )
% 6.92/7.29 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.92/7.29 => ( ( H @ X3 )
% 6.92/7.29 = zero_zero_nat ) )
% 6.92/7.29 => ( ! [X3: code_integer] :
% 6.92/7.29 ( ( member_Code_integer @ X3 @ S )
% 6.92/7.29 => ( ( G @ X3 )
% 6.92/7.29 = ( H @ X3 ) ) )
% 6.92/7.29 => ( ( groups7237345082560585321er_nat @ G @ S )
% 6.94/7.29 = ( groups7237345082560585321er_nat @ H @ T7 ) ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_cong_left
% 6.94/7.29 thf(fact_8754_sum_Omono__neutral__cong__left,axiom,
% 6.94/7.29 ! [T7: set_o,S: set_o,H: $o > int,G: $o > int] :
% 6.94/7.29 ( ( finite_finite_o @ T7 )
% 6.94/7.29 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.94/7.29 => ( ! [X3: $o] :
% 6.94/7.29 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.94/7.29 => ( ( H @ X3 )
% 6.94/7.29 = zero_zero_int ) )
% 6.94/7.29 => ( ! [X3: $o] :
% 6.94/7.29 ( ( member_o @ X3 @ S )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = ( H @ X3 ) ) )
% 6.94/7.29 => ( ( groups8505340233167759370_o_int @ G @ S )
% 6.94/7.29 = ( groups8505340233167759370_o_int @ H @ T7 ) ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_cong_left
% 6.94/7.29 thf(fact_8755_sum_Omono__neutral__cong__left,axiom,
% 6.94/7.29 ! [T7: set_nat,S: set_nat,H: nat > int,G: nat > int] :
% 6.94/7.29 ( ( finite_finite_nat @ T7 )
% 6.94/7.29 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.29 => ( ! [X3: nat] :
% 6.94/7.29 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.29 => ( ( H @ X3 )
% 6.94/7.29 = zero_zero_int ) )
% 6.94/7.29 => ( ! [X3: nat] :
% 6.94/7.29 ( ( member_nat @ X3 @ S )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = ( H @ X3 ) ) )
% 6.94/7.29 => ( ( groups3539618377306564664at_int @ G @ S )
% 6.94/7.29 = ( groups3539618377306564664at_int @ H @ T7 ) ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_cong_left
% 6.94/7.29 thf(fact_8756_sum_Omono__neutral__right,axiom,
% 6.94/7.29 ! [T7: set_nat,S: set_nat,G: nat > code_integer] :
% 6.94/7.29 ( ( finite_finite_nat @ T7 )
% 6.94/7.29 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.29 => ( ! [X3: nat] :
% 6.94/7.29 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_z3403309356797280102nteger ) )
% 6.94/7.29 => ( ( groups7501900531339628137nteger @ G @ T7 )
% 6.94/7.29 = ( groups7501900531339628137nteger @ G @ S ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_right
% 6.94/7.29 thf(fact_8757_sum_Omono__neutral__right,axiom,
% 6.94/7.29 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > code_integer] :
% 6.94/7.29 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.29 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.29 => ( ! [X3: code_integer] :
% 6.94/7.29 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_z3403309356797280102nteger ) )
% 6.94/7.29 => ( ( groups879477027807139574nteger @ G @ T7 )
% 6.94/7.29 = ( groups879477027807139574nteger @ G @ S ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_right
% 6.94/7.29 thf(fact_8758_sum_Omono__neutral__right,axiom,
% 6.94/7.29 ! [T7: set_nat,S: set_nat,G: nat > rat] :
% 6.94/7.29 ( ( finite_finite_nat @ T7 )
% 6.94/7.29 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.29 => ( ! [X3: nat] :
% 6.94/7.29 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_zero_rat ) )
% 6.94/7.29 => ( ( groups2906978787729119204at_rat @ G @ T7 )
% 6.94/7.29 = ( groups2906978787729119204at_rat @ G @ S ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_right
% 6.94/7.29 thf(fact_8759_sum_Omono__neutral__right,axiom,
% 6.94/7.29 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > rat] :
% 6.94/7.29 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.29 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.29 => ( ! [X3: code_integer] :
% 6.94/7.29 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_zero_rat ) )
% 6.94/7.29 => ( ( groups6602215022474089585er_rat @ G @ T7 )
% 6.94/7.29 = ( groups6602215022474089585er_rat @ G @ S ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_right
% 6.94/7.29 thf(fact_8760_sum_Omono__neutral__right,axiom,
% 6.94/7.29 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > nat] :
% 6.94/7.29 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.29 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.29 => ( ! [X3: code_integer] :
% 6.94/7.29 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_zero_nat ) )
% 6.94/7.29 => ( ( groups7237345082560585321er_nat @ G @ T7 )
% 6.94/7.29 = ( groups7237345082560585321er_nat @ G @ S ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_right
% 6.94/7.29 thf(fact_8761_sum_Omono__neutral__right,axiom,
% 6.94/7.29 ! [T7: set_nat,S: set_nat,G: nat > int] :
% 6.94/7.29 ( ( finite_finite_nat @ T7 )
% 6.94/7.29 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.29 => ( ! [X3: nat] :
% 6.94/7.29 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_zero_int ) )
% 6.94/7.29 => ( ( groups3539618377306564664at_int @ G @ T7 )
% 6.94/7.29 = ( groups3539618377306564664at_int @ G @ S ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_right
% 6.94/7.29 thf(fact_8762_sum_Omono__neutral__right,axiom,
% 6.94/7.29 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > int] :
% 6.94/7.29 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.29 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.29 => ( ! [X3: code_integer] :
% 6.94/7.29 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_zero_int ) )
% 6.94/7.29 => ( ( groups7234854612051535045er_int @ G @ T7 )
% 6.94/7.29 = ( groups7234854612051535045er_int @ G @ S ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_right
% 6.94/7.29 thf(fact_8763_sum_Omono__neutral__right,axiom,
% 6.94/7.29 ! [T7: set_int,S: set_int,G: int > code_integer] :
% 6.94/7.29 ( ( finite_finite_int @ T7 )
% 6.94/7.29 => ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.29 => ( ! [X3: int] :
% 6.94/7.29 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_z3403309356797280102nteger ) )
% 6.94/7.29 => ( ( groups7873554091576472773nteger @ G @ T7 )
% 6.94/7.29 = ( groups7873554091576472773nteger @ G @ S ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_right
% 6.94/7.29 thf(fact_8764_sum_Omono__neutral__right,axiom,
% 6.94/7.29 ! [T7: set_int,S: set_int,G: int > rat] :
% 6.94/7.29 ( ( finite_finite_int @ T7 )
% 6.94/7.29 => ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.29 => ( ! [X3: int] :
% 6.94/7.29 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_zero_rat ) )
% 6.94/7.29 => ( ( groups3906332499630173760nt_rat @ G @ T7 )
% 6.94/7.29 = ( groups3906332499630173760nt_rat @ G @ S ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_right
% 6.94/7.29 thf(fact_8765_sum_Omono__neutral__right,axiom,
% 6.94/7.29 ! [T7: set_int,S: set_int,G: int > nat] :
% 6.94/7.29 ( ( finite_finite_int @ T7 )
% 6.94/7.29 => ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.29 => ( ! [X3: int] :
% 6.94/7.29 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_zero_nat ) )
% 6.94/7.29 => ( ( groups4541462559716669496nt_nat @ G @ T7 )
% 6.94/7.29 = ( groups4541462559716669496nt_nat @ G @ S ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_right
% 6.94/7.29 thf(fact_8766_sum_Omono__neutral__left,axiom,
% 6.94/7.29 ! [T7: set_nat,S: set_nat,G: nat > code_integer] :
% 6.94/7.29 ( ( finite_finite_nat @ T7 )
% 6.94/7.29 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.29 => ( ! [X3: nat] :
% 6.94/7.29 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_z3403309356797280102nteger ) )
% 6.94/7.29 => ( ( groups7501900531339628137nteger @ G @ S )
% 6.94/7.29 = ( groups7501900531339628137nteger @ G @ T7 ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_left
% 6.94/7.29 thf(fact_8767_sum_Omono__neutral__left,axiom,
% 6.94/7.29 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > code_integer] :
% 6.94/7.29 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.29 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.29 => ( ! [X3: code_integer] :
% 6.94/7.29 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_z3403309356797280102nteger ) )
% 6.94/7.29 => ( ( groups879477027807139574nteger @ G @ S )
% 6.94/7.29 = ( groups879477027807139574nteger @ G @ T7 ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_left
% 6.94/7.29 thf(fact_8768_sum_Omono__neutral__left,axiom,
% 6.94/7.29 ! [T7: set_nat,S: set_nat,G: nat > rat] :
% 6.94/7.29 ( ( finite_finite_nat @ T7 )
% 6.94/7.29 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.29 => ( ! [X3: nat] :
% 6.94/7.29 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_zero_rat ) )
% 6.94/7.29 => ( ( groups2906978787729119204at_rat @ G @ S )
% 6.94/7.29 = ( groups2906978787729119204at_rat @ G @ T7 ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_left
% 6.94/7.29 thf(fact_8769_sum_Omono__neutral__left,axiom,
% 6.94/7.29 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > rat] :
% 6.94/7.29 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.29 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.29 => ( ! [X3: code_integer] :
% 6.94/7.29 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_zero_rat ) )
% 6.94/7.29 => ( ( groups6602215022474089585er_rat @ G @ S )
% 6.94/7.29 = ( groups6602215022474089585er_rat @ G @ T7 ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_left
% 6.94/7.29 thf(fact_8770_sum_Omono__neutral__left,axiom,
% 6.94/7.29 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > nat] :
% 6.94/7.29 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.29 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.29 => ( ! [X3: code_integer] :
% 6.94/7.29 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_zero_nat ) )
% 6.94/7.29 => ( ( groups7237345082560585321er_nat @ G @ S )
% 6.94/7.29 = ( groups7237345082560585321er_nat @ G @ T7 ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_left
% 6.94/7.29 thf(fact_8771_sum_Omono__neutral__left,axiom,
% 6.94/7.29 ! [T7: set_nat,S: set_nat,G: nat > int] :
% 6.94/7.29 ( ( finite_finite_nat @ T7 )
% 6.94/7.29 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.29 => ( ! [X3: nat] :
% 6.94/7.29 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_zero_int ) )
% 6.94/7.29 => ( ( groups3539618377306564664at_int @ G @ S )
% 6.94/7.29 = ( groups3539618377306564664at_int @ G @ T7 ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_left
% 6.94/7.29 thf(fact_8772_sum_Omono__neutral__left,axiom,
% 6.94/7.29 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > int] :
% 6.94/7.29 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.29 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.29 => ( ! [X3: code_integer] :
% 6.94/7.29 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_zero_int ) )
% 6.94/7.29 => ( ( groups7234854612051535045er_int @ G @ S )
% 6.94/7.29 = ( groups7234854612051535045er_int @ G @ T7 ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_left
% 6.94/7.29 thf(fact_8773_sum_Omono__neutral__left,axiom,
% 6.94/7.29 ! [T7: set_int,S: set_int,G: int > code_integer] :
% 6.94/7.29 ( ( finite_finite_int @ T7 )
% 6.94/7.29 => ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.29 => ( ! [X3: int] :
% 6.94/7.29 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_z3403309356797280102nteger ) )
% 6.94/7.29 => ( ( groups7873554091576472773nteger @ G @ S )
% 6.94/7.29 = ( groups7873554091576472773nteger @ G @ T7 ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_left
% 6.94/7.29 thf(fact_8774_sum_Omono__neutral__left,axiom,
% 6.94/7.29 ! [T7: set_int,S: set_int,G: int > rat] :
% 6.94/7.29 ( ( finite_finite_int @ T7 )
% 6.94/7.29 => ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.29 => ( ! [X3: int] :
% 6.94/7.29 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_zero_rat ) )
% 6.94/7.29 => ( ( groups3906332499630173760nt_rat @ G @ S )
% 6.94/7.29 = ( groups3906332499630173760nt_rat @ G @ T7 ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_left
% 6.94/7.29 thf(fact_8775_sum_Omono__neutral__left,axiom,
% 6.94/7.29 ! [T7: set_int,S: set_int,G: int > nat] :
% 6.94/7.29 ( ( finite_finite_int @ T7 )
% 6.94/7.29 => ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.29 => ( ! [X3: int] :
% 6.94/7.29 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.29 => ( ( G @ X3 )
% 6.94/7.29 = zero_zero_nat ) )
% 6.94/7.29 => ( ( groups4541462559716669496nt_nat @ G @ S )
% 6.94/7.29 = ( groups4541462559716669496nt_nat @ G @ T7 ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.mono_neutral_left
% 6.94/7.29 thf(fact_8776_sum_Osame__carrierI,axiom,
% 6.94/7.29 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > code_integer,H: $o > code_integer] :
% 6.94/7.29 ( ( finite_finite_o @ C4 )
% 6.94/7.29 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.29 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.29 => ( ! [A3: $o] :
% 6.94/7.29 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.29 => ( ( G @ A3 )
% 6.94/7.29 = zero_z3403309356797280102nteger ) )
% 6.94/7.29 => ( ! [B3: $o] :
% 6.94/7.29 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.29 => ( ( H @ B3 )
% 6.94/7.29 = zero_z3403309356797280102nteger ) )
% 6.94/7.29 => ( ( ( groups4406642042086082107nteger @ G @ C4 )
% 6.94/7.29 = ( groups4406642042086082107nteger @ H @ C4 ) )
% 6.94/7.29 => ( ( groups4406642042086082107nteger @ G @ A4 )
% 6.94/7.29 = ( groups4406642042086082107nteger @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.same_carrierI
% 6.94/7.29 thf(fact_8777_sum_Osame__carrierI,axiom,
% 6.94/7.29 ! [C4: set_nat,A4: set_nat,B5: set_nat,G: nat > code_integer,H: nat > code_integer] :
% 6.94/7.29 ( ( finite_finite_nat @ C4 )
% 6.94/7.29 => ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.94/7.29 => ( ( ord_less_eq_set_nat @ B5 @ C4 )
% 6.94/7.29 => ( ! [A3: nat] :
% 6.94/7.29 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C4 @ A4 ) )
% 6.94/7.29 => ( ( G @ A3 )
% 6.94/7.29 = zero_z3403309356797280102nteger ) )
% 6.94/7.29 => ( ! [B3: nat] :
% 6.94/7.29 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ C4 @ B5 ) )
% 6.94/7.29 => ( ( H @ B3 )
% 6.94/7.29 = zero_z3403309356797280102nteger ) )
% 6.94/7.29 => ( ( ( groups7501900531339628137nteger @ G @ C4 )
% 6.94/7.29 = ( groups7501900531339628137nteger @ H @ C4 ) )
% 6.94/7.29 => ( ( groups7501900531339628137nteger @ G @ A4 )
% 6.94/7.29 = ( groups7501900531339628137nteger @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.same_carrierI
% 6.94/7.29 thf(fact_8778_sum_Osame__carrierI,axiom,
% 6.94/7.29 ! [C4: set_Code_integer,A4: set_Code_integer,B5: set_Code_integer,G: code_integer > code_integer,H: code_integer > code_integer] :
% 6.94/7.29 ( ( finite6017078050557962740nteger @ C4 )
% 6.94/7.29 => ( ( ord_le7084787975880047091nteger @ A4 @ C4 )
% 6.94/7.29 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 6.94/7.29 => ( ! [A3: code_integer] :
% 6.94/7.29 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A4 ) )
% 6.94/7.29 => ( ( G @ A3 )
% 6.94/7.29 = zero_z3403309356797280102nteger ) )
% 6.94/7.29 => ( ! [B3: code_integer] :
% 6.94/7.29 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 6.94/7.29 => ( ( H @ B3 )
% 6.94/7.29 = zero_z3403309356797280102nteger ) )
% 6.94/7.29 => ( ( ( groups879477027807139574nteger @ G @ C4 )
% 6.94/7.29 = ( groups879477027807139574nteger @ H @ C4 ) )
% 6.94/7.29 => ( ( groups879477027807139574nteger @ G @ A4 )
% 6.94/7.29 = ( groups879477027807139574nteger @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.same_carrierI
% 6.94/7.29 thf(fact_8779_sum_Osame__carrierI,axiom,
% 6.94/7.29 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > rat,H: $o > rat] :
% 6.94/7.29 ( ( finite_finite_o @ C4 )
% 6.94/7.29 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.29 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.29 => ( ! [A3: $o] :
% 6.94/7.29 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.29 => ( ( G @ A3 )
% 6.94/7.29 = zero_zero_rat ) )
% 6.94/7.29 => ( ! [B3: $o] :
% 6.94/7.29 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.29 => ( ( H @ B3 )
% 6.94/7.29 = zero_zero_rat ) )
% 6.94/7.29 => ( ( ( groups7872700643590313910_o_rat @ G @ C4 )
% 6.94/7.29 = ( groups7872700643590313910_o_rat @ H @ C4 ) )
% 6.94/7.29 => ( ( groups7872700643590313910_o_rat @ G @ A4 )
% 6.94/7.29 = ( groups7872700643590313910_o_rat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.same_carrierI
% 6.94/7.29 thf(fact_8780_sum_Osame__carrierI,axiom,
% 6.94/7.29 ! [C4: set_nat,A4: set_nat,B5: set_nat,G: nat > rat,H: nat > rat] :
% 6.94/7.29 ( ( finite_finite_nat @ C4 )
% 6.94/7.29 => ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.94/7.29 => ( ( ord_less_eq_set_nat @ B5 @ C4 )
% 6.94/7.29 => ( ! [A3: nat] :
% 6.94/7.29 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C4 @ A4 ) )
% 6.94/7.29 => ( ( G @ A3 )
% 6.94/7.29 = zero_zero_rat ) )
% 6.94/7.29 => ( ! [B3: nat] :
% 6.94/7.29 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ C4 @ B5 ) )
% 6.94/7.29 => ( ( H @ B3 )
% 6.94/7.29 = zero_zero_rat ) )
% 6.94/7.29 => ( ( ( groups2906978787729119204at_rat @ G @ C4 )
% 6.94/7.29 = ( groups2906978787729119204at_rat @ H @ C4 ) )
% 6.94/7.29 => ( ( groups2906978787729119204at_rat @ G @ A4 )
% 6.94/7.29 = ( groups2906978787729119204at_rat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.same_carrierI
% 6.94/7.29 thf(fact_8781_sum_Osame__carrierI,axiom,
% 6.94/7.29 ! [C4: set_Code_integer,A4: set_Code_integer,B5: set_Code_integer,G: code_integer > rat,H: code_integer > rat] :
% 6.94/7.29 ( ( finite6017078050557962740nteger @ C4 )
% 6.94/7.29 => ( ( ord_le7084787975880047091nteger @ A4 @ C4 )
% 6.94/7.29 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 6.94/7.29 => ( ! [A3: code_integer] :
% 6.94/7.29 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A4 ) )
% 6.94/7.29 => ( ( G @ A3 )
% 6.94/7.29 = zero_zero_rat ) )
% 6.94/7.29 => ( ! [B3: code_integer] :
% 6.94/7.29 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 6.94/7.29 => ( ( H @ B3 )
% 6.94/7.29 = zero_zero_rat ) )
% 6.94/7.29 => ( ( ( groups6602215022474089585er_rat @ G @ C4 )
% 6.94/7.29 = ( groups6602215022474089585er_rat @ H @ C4 ) )
% 6.94/7.29 => ( ( groups6602215022474089585er_rat @ G @ A4 )
% 6.94/7.29 = ( groups6602215022474089585er_rat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.29
% 6.94/7.29 % sum.same_carrierI
% 6.94/7.29 thf(fact_8782_sum_Osame__carrierI,axiom,
% 6.94/7.29 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > nat,H: $o > nat] :
% 6.94/7.29 ( ( finite_finite_o @ C4 )
% 6.94/7.29 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.29 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.29 => ( ! [A3: $o] :
% 6.94/7.29 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.29 => ( ( G @ A3 )
% 6.94/7.29 = zero_zero_nat ) )
% 6.94/7.29 => ( ! [B3: $o] :
% 6.94/7.29 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.29 => ( ( H @ B3 )
% 6.94/7.29 = zero_zero_nat ) )
% 6.94/7.29 => ( ( ( groups8507830703676809646_o_nat @ G @ C4 )
% 6.94/7.29 = ( groups8507830703676809646_o_nat @ H @ C4 ) )
% 6.94/7.29 => ( ( groups8507830703676809646_o_nat @ G @ A4 )
% 6.94/7.30 = ( groups8507830703676809646_o_nat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.same_carrierI
% 6.94/7.30 thf(fact_8783_sum_Osame__carrierI,axiom,
% 6.94/7.30 ! [C4: set_Code_integer,A4: set_Code_integer,B5: set_Code_integer,G: code_integer > nat,H: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = zero_zero_nat ) )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = zero_zero_nat ) )
% 6.94/7.30 => ( ( ( groups7237345082560585321er_nat @ G @ C4 )
% 6.94/7.30 = ( groups7237345082560585321er_nat @ H @ C4 ) )
% 6.94/7.30 => ( ( groups7237345082560585321er_nat @ G @ A4 )
% 6.94/7.30 = ( groups7237345082560585321er_nat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.same_carrierI
% 6.94/7.30 thf(fact_8784_sum_Osame__carrierI,axiom,
% 6.94/7.30 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > int,H: $o > int] :
% 6.94/7.30 ( ( finite_finite_o @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = zero_zero_int ) )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = zero_zero_int ) )
% 6.94/7.30 => ( ( ( groups8505340233167759370_o_int @ G @ C4 )
% 6.94/7.30 = ( groups8505340233167759370_o_int @ H @ C4 ) )
% 6.94/7.30 => ( ( groups8505340233167759370_o_int @ G @ A4 )
% 6.94/7.30 = ( groups8505340233167759370_o_int @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.same_carrierI
% 6.94/7.30 thf(fact_8785_sum_Osame__carrierI,axiom,
% 6.94/7.30 ! [C4: set_nat,A4: set_nat,B5: set_nat,G: nat > int,H: nat > int] :
% 6.94/7.30 ( ( finite_finite_nat @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: nat] :
% 6.94/7.30 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = zero_zero_int ) )
% 6.94/7.30 => ( ! [B3: nat] :
% 6.94/7.30 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = zero_zero_int ) )
% 6.94/7.30 => ( ( ( groups3539618377306564664at_int @ G @ C4 )
% 6.94/7.30 = ( groups3539618377306564664at_int @ H @ C4 ) )
% 6.94/7.30 => ( ( groups3539618377306564664at_int @ G @ A4 )
% 6.94/7.30 = ( groups3539618377306564664at_int @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.same_carrierI
% 6.94/7.30 thf(fact_8786_sum_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > code_integer,H: $o > code_integer] :
% 6.94/7.30 ( ( finite_finite_o @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = zero_z3403309356797280102nteger ) )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = zero_z3403309356797280102nteger ) )
% 6.94/7.30 => ( ( ( groups4406642042086082107nteger @ G @ A4 )
% 6.94/7.30 = ( groups4406642042086082107nteger @ H @ B5 ) )
% 6.94/7.30 = ( ( groups4406642042086082107nteger @ G @ C4 )
% 6.94/7.30 = ( groups4406642042086082107nteger @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.same_carrier
% 6.94/7.30 thf(fact_8787_sum_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_nat,A4: set_nat,B5: set_nat,G: nat > code_integer,H: nat > code_integer] :
% 6.94/7.30 ( ( finite_finite_nat @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: nat] :
% 6.94/7.30 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = zero_z3403309356797280102nteger ) )
% 6.94/7.30 => ( ! [B3: nat] :
% 6.94/7.30 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = zero_z3403309356797280102nteger ) )
% 6.94/7.30 => ( ( ( groups7501900531339628137nteger @ G @ A4 )
% 6.94/7.30 = ( groups7501900531339628137nteger @ H @ B5 ) )
% 6.94/7.30 = ( ( groups7501900531339628137nteger @ G @ C4 )
% 6.94/7.30 = ( groups7501900531339628137nteger @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.same_carrier
% 6.94/7.30 thf(fact_8788_sum_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_Code_integer,A4: set_Code_integer,B5: set_Code_integer,G: code_integer > code_integer,H: code_integer > code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = zero_z3403309356797280102nteger ) )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = zero_z3403309356797280102nteger ) )
% 6.94/7.30 => ( ( ( groups879477027807139574nteger @ G @ A4 )
% 6.94/7.30 = ( groups879477027807139574nteger @ H @ B5 ) )
% 6.94/7.30 = ( ( groups879477027807139574nteger @ G @ C4 )
% 6.94/7.30 = ( groups879477027807139574nteger @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.same_carrier
% 6.94/7.30 thf(fact_8789_sum_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > rat,H: $o > rat] :
% 6.94/7.30 ( ( finite_finite_o @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = zero_zero_rat ) )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = zero_zero_rat ) )
% 6.94/7.30 => ( ( ( groups7872700643590313910_o_rat @ G @ A4 )
% 6.94/7.30 = ( groups7872700643590313910_o_rat @ H @ B5 ) )
% 6.94/7.30 = ( ( groups7872700643590313910_o_rat @ G @ C4 )
% 6.94/7.30 = ( groups7872700643590313910_o_rat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.same_carrier
% 6.94/7.30 thf(fact_8790_sum_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_nat,A4: set_nat,B5: set_nat,G: nat > rat,H: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: nat] :
% 6.94/7.30 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = zero_zero_rat ) )
% 6.94/7.30 => ( ! [B3: nat] :
% 6.94/7.30 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = zero_zero_rat ) )
% 6.94/7.30 => ( ( ( groups2906978787729119204at_rat @ G @ A4 )
% 6.94/7.30 = ( groups2906978787729119204at_rat @ H @ B5 ) )
% 6.94/7.30 = ( ( groups2906978787729119204at_rat @ G @ C4 )
% 6.94/7.30 = ( groups2906978787729119204at_rat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.same_carrier
% 6.94/7.30 thf(fact_8791_sum_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_Code_integer,A4: set_Code_integer,B5: set_Code_integer,G: code_integer > rat,H: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = zero_zero_rat ) )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = zero_zero_rat ) )
% 6.94/7.30 => ( ( ( groups6602215022474089585er_rat @ G @ A4 )
% 6.94/7.30 = ( groups6602215022474089585er_rat @ H @ B5 ) )
% 6.94/7.30 = ( ( groups6602215022474089585er_rat @ G @ C4 )
% 6.94/7.30 = ( groups6602215022474089585er_rat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.same_carrier
% 6.94/7.30 thf(fact_8792_sum_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > nat,H: $o > nat] :
% 6.94/7.30 ( ( finite_finite_o @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = zero_zero_nat ) )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = zero_zero_nat ) )
% 6.94/7.30 => ( ( ( groups8507830703676809646_o_nat @ G @ A4 )
% 6.94/7.30 = ( groups8507830703676809646_o_nat @ H @ B5 ) )
% 6.94/7.30 = ( ( groups8507830703676809646_o_nat @ G @ C4 )
% 6.94/7.30 = ( groups8507830703676809646_o_nat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.same_carrier
% 6.94/7.30 thf(fact_8793_sum_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_Code_integer,A4: set_Code_integer,B5: set_Code_integer,G: code_integer > nat,H: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = zero_zero_nat ) )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = zero_zero_nat ) )
% 6.94/7.30 => ( ( ( groups7237345082560585321er_nat @ G @ A4 )
% 6.94/7.30 = ( groups7237345082560585321er_nat @ H @ B5 ) )
% 6.94/7.30 = ( ( groups7237345082560585321er_nat @ G @ C4 )
% 6.94/7.30 = ( groups7237345082560585321er_nat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.same_carrier
% 6.94/7.30 thf(fact_8794_sum_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > int,H: $o > int] :
% 6.94/7.30 ( ( finite_finite_o @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = zero_zero_int ) )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = zero_zero_int ) )
% 6.94/7.30 => ( ( ( groups8505340233167759370_o_int @ G @ A4 )
% 6.94/7.30 = ( groups8505340233167759370_o_int @ H @ B5 ) )
% 6.94/7.30 = ( ( groups8505340233167759370_o_int @ G @ C4 )
% 6.94/7.30 = ( groups8505340233167759370_o_int @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.same_carrier
% 6.94/7.30 thf(fact_8795_sum_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_nat,A4: set_nat,B5: set_nat,G: nat > int,H: nat > int] :
% 6.94/7.30 ( ( finite_finite_nat @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: nat] :
% 6.94/7.30 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = zero_zero_int ) )
% 6.94/7.30 => ( ! [B3: nat] :
% 6.94/7.30 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = zero_zero_int ) )
% 6.94/7.30 => ( ( ( groups3539618377306564664at_int @ G @ A4 )
% 6.94/7.30 = ( groups3539618377306564664at_int @ H @ B5 ) )
% 6.94/7.30 = ( ( groups3539618377306564664at_int @ G @ C4 )
% 6.94/7.30 = ( groups3539618377306564664at_int @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.same_carrier
% 6.94/7.30 thf(fact_8796_sum_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_nat,A4: set_nat,G: nat > rat] :
% 6.94/7.30 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups2906978787729119204at_rat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups2906978787729119204at_rat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.subset_diff
% 6.94/7.30 thf(fact_8797_sum_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,G: code_integer > rat] :
% 6.94/7.30 ( ( ord_le7084787975880047091nteger @ B5 @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups6602215022474089585er_rat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups6602215022474089585er_rat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.subset_diff
% 6.94/7.30 thf(fact_8798_sum_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,G: code_integer > nat] :
% 6.94/7.30 ( ( ord_le7084787975880047091nteger @ B5 @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups7237345082560585321er_nat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups7237345082560585321er_nat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.subset_diff
% 6.94/7.30 thf(fact_8799_sum_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_nat,A4: set_nat,G: nat > int] :
% 6.94/7.30 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups3539618377306564664at_int @ G @ A4 )
% 6.94/7.30 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups3539618377306564664at_int @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.subset_diff
% 6.94/7.30 thf(fact_8800_sum_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,G: code_integer > int] :
% 6.94/7.30 ( ( ord_le7084787975880047091nteger @ B5 @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups7234854612051535045er_int @ G @ A4 )
% 6.94/7.30 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups7234854612051535045er_int @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.subset_diff
% 6.94/7.30 thf(fact_8801_sum_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_int,A4: set_int,G: int > rat] :
% 6.94/7.30 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups3906332499630173760nt_rat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups3906332499630173760nt_rat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.subset_diff
% 6.94/7.30 thf(fact_8802_sum_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_int,A4: set_int,G: int > nat] :
% 6.94/7.30 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups4541462559716669496nt_nat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups4541462559716669496nt_nat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.subset_diff
% 6.94/7.30 thf(fact_8803_sum_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_nat,A4: set_nat,G: nat > nat] :
% 6.94/7.30 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups3542108847815614940at_nat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups3542108847815614940at_nat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.subset_diff
% 6.94/7.30 thf(fact_8804_sum_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_int,A4: set_int,G: int > int] :
% 6.94/7.30 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups4538972089207619220nt_int @ G @ A4 )
% 6.94/7.30 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups4538972089207619220nt_int @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.subset_diff
% 6.94/7.30 thf(fact_8805_sum_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > rat] :
% 6.94/7.30 ( ( ord_le3146513528884898305at_nat @ B5 @ A4 )
% 6.94/7.30 => ( ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.30 => ( ( groups342789780944988191at_rat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) @ ( groups342789780944988191at_rat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.subset_diff
% 6.94/7.30 thf(fact_8806_sum__diff,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,F: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 6.94/7.30 => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ ( groups2906978787729119204at_rat @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_diff
% 6.94/7.30 thf(fact_8807_sum__diff,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,F: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ B5 @ A4 )
% 6.94/7.30 => ( ( groups6602215022474089585er_rat @ F @ ( minus_2355218937544613996nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_rat @ ( groups6602215022474089585er_rat @ F @ A4 ) @ ( groups6602215022474089585er_rat @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_diff
% 6.94/7.30 thf(fact_8808_sum__diff,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,F: nat > int] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 6.94/7.30 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A4 ) @ ( groups3539618377306564664at_int @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_diff
% 6.94/7.30 thf(fact_8809_sum__diff,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,F: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ B5 @ A4 )
% 6.94/7.30 => ( ( groups7234854612051535045er_int @ F @ ( minus_2355218937544613996nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_int @ ( groups7234854612051535045er_int @ F @ A4 ) @ ( groups7234854612051535045er_int @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_diff
% 6.94/7.30 thf(fact_8810_sum__diff,axiom,
% 6.94/7.30 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > rat] :
% 6.94/7.30 ( ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.30 => ( ( ord_le3146513528884898305at_nat @ B5 @ A4 )
% 6.94/7.30 => ( ( groups342789780944988191at_rat @ F @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_rat @ ( groups342789780944988191at_rat @ F @ A4 ) @ ( groups342789780944988191at_rat @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_diff
% 6.94/7.30 thf(fact_8811_sum__diff,axiom,
% 6.94/7.30 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > int] :
% 6.94/7.30 ( ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.30 => ( ( ord_le3146513528884898305at_nat @ B5 @ A4 )
% 6.94/7.30 => ( ( groups975429370522433651at_int @ F @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_int @ ( groups975429370522433651at_int @ F @ A4 ) @ ( groups975429370522433651at_int @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_diff
% 6.94/7.30 thf(fact_8812_sum__diff,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,F: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_set_int @ B5 @ A4 )
% 6.94/7.30 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) @ ( groups3906332499630173760nt_rat @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_diff
% 6.94/7.30 thf(fact_8813_sum__diff,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,F: int > int] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_set_int @ B5 @ A4 )
% 6.94/7.30 => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A4 ) @ ( groups4538972089207619220nt_int @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_diff
% 6.94/7.30 thf(fact_8814_prod_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_nat,A4: set_nat,G: nat > assn] :
% 6.94/7.30 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups6906906614972039071t_assn @ G @ A4 )
% 6.94/7.30 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups6906906614972039071t_assn @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.subset_diff
% 6.94/7.30 thf(fact_8815_prod_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,G: code_integer > assn] :
% 6.94/7.30 ( ( ord_le7084787975880047091nteger @ B5 @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups1304777262505850412r_assn @ G @ A4 )
% 6.94/7.30 = ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups1304777262505850412r_assn @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.subset_diff
% 6.94/7.30 thf(fact_8816_prod_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_nat,A4: set_nat,G: nat > rat] :
% 6.94/7.30 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups73079841787564623at_rat @ G @ A4 )
% 6.94/7.30 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups73079841787564623at_rat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.subset_diff
% 6.94/7.30 thf(fact_8817_prod_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,G: code_integer > rat] :
% 6.94/7.30 ( ( ord_le7084787975880047091nteger @ B5 @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups2555765274223993564er_rat @ G @ A4 )
% 6.94/7.30 = ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups2555765274223993564er_rat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.subset_diff
% 6.94/7.30 thf(fact_8818_prod_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,G: code_integer > nat] :
% 6.94/7.30 ( ( ord_le7084787975880047091nteger @ B5 @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups3190895334310489300er_nat @ G @ A4 )
% 6.94/7.30 = ( times_times_nat @ ( groups3190895334310489300er_nat @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups3190895334310489300er_nat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.subset_diff
% 6.94/7.30 thf(fact_8819_prod_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,G: code_integer > int] :
% 6.94/7.30 ( ( ord_le7084787975880047091nteger @ B5 @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups3188404863801439024er_int @ G @ A4 )
% 6.94/7.30 = ( times_times_int @ ( groups3188404863801439024er_int @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups3188404863801439024er_int @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.subset_diff
% 6.94/7.30 thf(fact_8820_prod_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_int,A4: set_int,G: int > assn] :
% 6.94/7.30 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups7882442080178216443t_assn @ G @ A4 )
% 6.94/7.30 = ( times_times_assn @ ( groups7882442080178216443t_assn @ G @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups7882442080178216443t_assn @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.subset_diff
% 6.94/7.30 thf(fact_8821_prod_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_int,A4: set_int,G: int > rat] :
% 6.94/7.30 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups1072433553688619179nt_rat @ G @ A4 )
% 6.94/7.30 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.subset_diff
% 6.94/7.30 thf(fact_8822_prod_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_int,A4: set_int,G: int > nat] :
% 6.94/7.30 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups1707563613775114915nt_nat @ G @ A4 )
% 6.94/7.30 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1707563613775114915nt_nat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.subset_diff
% 6.94/7.30 thf(fact_8823_prod_Osubset__diff,axiom,
% 6.94/7.30 ! [B5: set_nat,A4: set_nat,G: nat > nat] :
% 6.94/7.30 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups708209901874060359at_nat @ G @ A4 )
% 6.94/7.30 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups708209901874060359at_nat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.subset_diff
% 6.94/7.30 thf(fact_8824_prod_Omono__neutral__cong__right,axiom,
% 6.94/7.30 ! [T7: set_o,S: set_o,G: $o > code_integer,H: $o > code_integer] :
% 6.94/7.30 ( ( finite_finite_o @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups7694694392188491536nteger @ G @ T7 )
% 6.94/7.30 = ( groups7694694392188491536nteger @ H @ S ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_right
% 6.94/7.30 thf(fact_8825_prod_Omono__neutral__cong__right,axiom,
% 6.94/7.30 ! [T7: set_nat,S: set_nat,G: nat > code_integer,H: nat > code_integer] :
% 6.94/7.30 ( ( finite_finite_nat @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups3455450783089532116nteger @ G @ T7 )
% 6.94/7.30 = ( groups3455450783089532116nteger @ H @ S ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_right
% 6.94/7.30 thf(fact_8826_prod_Omono__neutral__cong__right,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > code_integer,H: code_integer > code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups3674199335183972705nteger @ G @ T7 )
% 6.94/7.30 = ( groups3674199335183972705nteger @ H @ S ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_right
% 6.94/7.30 thf(fact_8827_prod_Omono__neutral__cong__right,axiom,
% 6.94/7.30 ! [T7: set_o,S: set_o,G: $o > assn,H: $o > assn] :
% 6.94/7.30 ( ( finite_finite_o @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups5301882518646026715o_assn @ G @ T7 )
% 6.94/7.30 = ( groups5301882518646026715o_assn @ H @ S ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_right
% 6.94/7.30 thf(fact_8828_prod_Omono__neutral__cong__right,axiom,
% 6.94/7.30 ! [T7: set_nat,S: set_nat,G: nat > assn,H: nat > assn] :
% 6.94/7.30 ( ( finite_finite_nat @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups6906906614972039071t_assn @ G @ T7 )
% 6.94/7.30 = ( groups6906906614972039071t_assn @ H @ S ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_right
% 6.94/7.30 thf(fact_8829_prod_Omono__neutral__cong__right,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > assn,H: code_integer > assn] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups1304777262505850412r_assn @ G @ T7 )
% 6.94/7.30 = ( groups1304777262505850412r_assn @ H @ S ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_right
% 6.94/7.30 thf(fact_8830_prod_Omono__neutral__cong__right,axiom,
% 6.94/7.30 ! [T7: set_o,S: set_o,G: $o > rat,H: $o > rat] :
% 6.94/7.30 ( ( finite_finite_o @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups2869687844427037835_o_rat @ G @ T7 )
% 6.94/7.30 = ( groups2869687844427037835_o_rat @ H @ S ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_right
% 6.94/7.30 thf(fact_8831_prod_Omono__neutral__cong__right,axiom,
% 6.94/7.30 ! [T7: set_nat,S: set_nat,G: nat > rat,H: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups73079841787564623at_rat @ G @ T7 )
% 6.94/7.30 = ( groups73079841787564623at_rat @ H @ S ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_right
% 6.94/7.30 thf(fact_8832_prod_Omono__neutral__cong__right,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > rat,H: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups2555765274223993564er_rat @ G @ T7 )
% 6.94/7.30 = ( groups2555765274223993564er_rat @ H @ S ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_right
% 6.94/7.30 thf(fact_8833_prod_Omono__neutral__cong__right,axiom,
% 6.94/7.30 ! [T7: set_o,S: set_o,G: $o > nat,H: $o > nat] :
% 6.94/7.30 ( ( finite_finite_o @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_nat ) )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups3504817904513533571_o_nat @ G @ T7 )
% 6.94/7.30 = ( groups3504817904513533571_o_nat @ H @ S ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_right
% 6.94/7.30 thf(fact_8834_prod_Omono__neutral__cong__left,axiom,
% 6.94/7.30 ! [T7: set_o,S: set_o,H: $o > code_integer,G: $o > code_integer] :
% 6.94/7.30 ( ( finite_finite_o @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.94/7.30 => ( ( H @ X3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups7694694392188491536nteger @ G @ S )
% 6.94/7.30 = ( groups7694694392188491536nteger @ H @ T7 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_left
% 6.94/7.30 thf(fact_8835_prod_Omono__neutral__cong__left,axiom,
% 6.94/7.30 ! [T7: set_nat,S: set_nat,H: nat > code_integer,G: nat > code_integer] :
% 6.94/7.30 ( ( finite_finite_nat @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.30 => ( ( H @ X3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups3455450783089532116nteger @ G @ S )
% 6.94/7.30 = ( groups3455450783089532116nteger @ H @ T7 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_left
% 6.94/7.30 thf(fact_8836_prod_Omono__neutral__cong__left,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,H: code_integer > code_integer,G: code_integer > code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( H @ X3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups3674199335183972705nteger @ G @ S )
% 6.94/7.30 = ( groups3674199335183972705nteger @ H @ T7 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_left
% 6.94/7.30 thf(fact_8837_prod_Omono__neutral__cong__left,axiom,
% 6.94/7.30 ! [T7: set_o,S: set_o,H: $o > assn,G: $o > assn] :
% 6.94/7.30 ( ( finite_finite_o @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.94/7.30 => ( ( H @ X3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups5301882518646026715o_assn @ G @ S )
% 6.94/7.30 = ( groups5301882518646026715o_assn @ H @ T7 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_left
% 6.94/7.30 thf(fact_8838_prod_Omono__neutral__cong__left,axiom,
% 6.94/7.30 ! [T7: set_nat,S: set_nat,H: nat > assn,G: nat > assn] :
% 6.94/7.30 ( ( finite_finite_nat @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.30 => ( ( H @ X3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups6906906614972039071t_assn @ G @ S )
% 6.94/7.30 = ( groups6906906614972039071t_assn @ H @ T7 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_left
% 6.94/7.30 thf(fact_8839_prod_Omono__neutral__cong__left,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,H: code_integer > assn,G: code_integer > assn] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( H @ X3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups1304777262505850412r_assn @ G @ S )
% 6.94/7.30 = ( groups1304777262505850412r_assn @ H @ T7 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_left
% 6.94/7.30 thf(fact_8840_prod_Omono__neutral__cong__left,axiom,
% 6.94/7.30 ! [T7: set_o,S: set_o,H: $o > rat,G: $o > rat] :
% 6.94/7.30 ( ( finite_finite_o @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.94/7.30 => ( ( H @ X3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups2869687844427037835_o_rat @ G @ S )
% 6.94/7.30 = ( groups2869687844427037835_o_rat @ H @ T7 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_left
% 6.94/7.30 thf(fact_8841_prod_Omono__neutral__cong__left,axiom,
% 6.94/7.30 ! [T7: set_nat,S: set_nat,H: nat > rat,G: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.30 => ( ( H @ X3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups73079841787564623at_rat @ G @ S )
% 6.94/7.30 = ( groups73079841787564623at_rat @ H @ T7 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_left
% 6.94/7.30 thf(fact_8842_prod_Omono__neutral__cong__left,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,H: code_integer > rat,G: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( H @ X3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups2555765274223993564er_rat @ G @ S )
% 6.94/7.30 = ( groups2555765274223993564er_rat @ H @ T7 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_left
% 6.94/7.30 thf(fact_8843_prod_Omono__neutral__cong__left,axiom,
% 6.94/7.30 ! [T7: set_o,S: set_o,H: $o > nat,G: $o > nat] :
% 6.94/7.30 ( ( finite_finite_o @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ S @ T7 )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.94/7.30 => ( ( H @ X3 )
% 6.94/7.30 = one_one_nat ) )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ S )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = ( H @ X3 ) ) )
% 6.94/7.30 => ( ( groups3504817904513533571_o_nat @ G @ S )
% 6.94/7.30 = ( groups3504817904513533571_o_nat @ H @ T7 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_cong_left
% 6.94/7.30 thf(fact_8844_prod_Omono__neutral__right,axiom,
% 6.94/7.30 ! [T7: set_nat,S: set_nat,G: nat > code_integer] :
% 6.94/7.30 ( ( finite_finite_nat @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ( groups3455450783089532116nteger @ G @ T7 )
% 6.94/7.30 = ( groups3455450783089532116nteger @ G @ S ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_right
% 6.94/7.30 thf(fact_8845_prod_Omono__neutral__right,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ( groups3674199335183972705nteger @ G @ T7 )
% 6.94/7.30 = ( groups3674199335183972705nteger @ G @ S ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_right
% 6.94/7.30 thf(fact_8846_prod_Omono__neutral__right,axiom,
% 6.94/7.30 ! [T7: set_nat,S: set_nat,G: nat > assn] :
% 6.94/7.30 ( ( finite_finite_nat @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ( groups6906906614972039071t_assn @ G @ T7 )
% 6.94/7.30 = ( groups6906906614972039071t_assn @ G @ S ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_right
% 6.94/7.30 thf(fact_8847_prod_Omono__neutral__right,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > assn] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ( groups1304777262505850412r_assn @ G @ T7 )
% 6.94/7.30 = ( groups1304777262505850412r_assn @ G @ S ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_right
% 6.94/7.30 thf(fact_8848_prod_Omono__neutral__right,axiom,
% 6.94/7.30 ! [T7: set_nat,S: set_nat,G: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ( groups73079841787564623at_rat @ G @ T7 )
% 6.94/7.30 = ( groups73079841787564623at_rat @ G @ S ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_right
% 6.94/7.30 thf(fact_8849_prod_Omono__neutral__right,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ( groups2555765274223993564er_rat @ G @ T7 )
% 6.94/7.30 = ( groups2555765274223993564er_rat @ G @ S ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_right
% 6.94/7.30 thf(fact_8850_prod_Omono__neutral__right,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_nat ) )
% 6.94/7.30 => ( ( groups3190895334310489300er_nat @ G @ T7 )
% 6.94/7.30 = ( groups3190895334310489300er_nat @ G @ S ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_right
% 6.94/7.30 thf(fact_8851_prod_Omono__neutral__right,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_int ) )
% 6.94/7.30 => ( ( groups3188404863801439024er_int @ G @ T7 )
% 6.94/7.30 = ( groups3188404863801439024er_int @ G @ S ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_right
% 6.94/7.30 thf(fact_8852_prod_Omono__neutral__right,axiom,
% 6.94/7.30 ! [T7: set_int,S: set_int,G: int > code_integer] :
% 6.94/7.30 ( ( finite_finite_int @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ( groups3827104343326376752nteger @ G @ T7 )
% 6.94/7.30 = ( groups3827104343326376752nteger @ G @ S ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_right
% 6.94/7.30 thf(fact_8853_prod_Omono__neutral__right,axiom,
% 6.94/7.30 ! [T7: set_int,S: set_int,G: int > assn] :
% 6.94/7.30 ( ( finite_finite_int @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ( groups7882442080178216443t_assn @ G @ T7 )
% 6.94/7.30 = ( groups7882442080178216443t_assn @ G @ S ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_right
% 6.94/7.30 thf(fact_8854_prod_Omono__neutral__left,axiom,
% 6.94/7.30 ! [T7: set_nat,S: set_nat,G: nat > code_integer] :
% 6.94/7.30 ( ( finite_finite_nat @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ( groups3455450783089532116nteger @ G @ S )
% 6.94/7.30 = ( groups3455450783089532116nteger @ G @ T7 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_left
% 6.94/7.30 thf(fact_8855_prod_Omono__neutral__left,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ( groups3674199335183972705nteger @ G @ S )
% 6.94/7.30 = ( groups3674199335183972705nteger @ G @ T7 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_left
% 6.94/7.30 thf(fact_8856_prod_Omono__neutral__left,axiom,
% 6.94/7.30 ! [T7: set_nat,S: set_nat,G: nat > assn] :
% 6.94/7.30 ( ( finite_finite_nat @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ( groups6906906614972039071t_assn @ G @ S )
% 6.94/7.30 = ( groups6906906614972039071t_assn @ G @ T7 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_left
% 6.94/7.30 thf(fact_8857_prod_Omono__neutral__left,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > assn] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ( groups1304777262505850412r_assn @ G @ S )
% 6.94/7.30 = ( groups1304777262505850412r_assn @ G @ T7 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_left
% 6.94/7.30 thf(fact_8858_prod_Omono__neutral__left,axiom,
% 6.94/7.30 ! [T7: set_nat,S: set_nat,G: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ( groups73079841787564623at_rat @ G @ S )
% 6.94/7.30 = ( groups73079841787564623at_rat @ G @ T7 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_left
% 6.94/7.30 thf(fact_8859_prod_Omono__neutral__left,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ( groups2555765274223993564er_rat @ G @ S )
% 6.94/7.30 = ( groups2555765274223993564er_rat @ G @ T7 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_left
% 6.94/7.30 thf(fact_8860_prod_Omono__neutral__left,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_nat ) )
% 6.94/7.30 => ( ( groups3190895334310489300er_nat @ G @ S )
% 6.94/7.30 = ( groups3190895334310489300er_nat @ G @ T7 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_left
% 6.94/7.30 thf(fact_8861_prod_Omono__neutral__left,axiom,
% 6.94/7.30 ! [T7: set_Code_integer,S: set_Code_integer,G: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_int ) )
% 6.94/7.30 => ( ( groups3188404863801439024er_int @ G @ S )
% 6.94/7.30 = ( groups3188404863801439024er_int @ G @ T7 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_left
% 6.94/7.30 thf(fact_8862_prod_Omono__neutral__left,axiom,
% 6.94/7.30 ! [T7: set_int,S: set_int,G: int > code_integer] :
% 6.94/7.30 ( ( finite_finite_int @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ( groups3827104343326376752nteger @ G @ S )
% 6.94/7.30 = ( groups3827104343326376752nteger @ G @ T7 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_left
% 6.94/7.30 thf(fact_8863_prod_Omono__neutral__left,axiom,
% 6.94/7.30 ! [T7: set_int,S: set_int,G: int > assn] :
% 6.94/7.30 ( ( finite_finite_int @ T7 )
% 6.94/7.30 => ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ( groups7882442080178216443t_assn @ G @ S )
% 6.94/7.30 = ( groups7882442080178216443t_assn @ G @ T7 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.mono_neutral_left
% 6.94/7.30 thf(fact_8864_prod_Osame__carrierI,axiom,
% 6.94/7.30 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > code_integer,H: $o > code_integer] :
% 6.94/7.30 ( ( finite_finite_o @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ( ( groups7694694392188491536nteger @ G @ C4 )
% 6.94/7.30 = ( groups7694694392188491536nteger @ H @ C4 ) )
% 6.94/7.30 => ( ( groups7694694392188491536nteger @ G @ A4 )
% 6.94/7.30 = ( groups7694694392188491536nteger @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrierI
% 6.94/7.30 thf(fact_8865_prod_Osame__carrierI,axiom,
% 6.94/7.30 ! [C4: set_nat,A4: set_nat,B5: set_nat,G: nat > code_integer,H: nat > code_integer] :
% 6.94/7.30 ( ( finite_finite_nat @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: nat] :
% 6.94/7.30 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ! [B3: nat] :
% 6.94/7.30 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ( ( groups3455450783089532116nteger @ G @ C4 )
% 6.94/7.30 = ( groups3455450783089532116nteger @ H @ C4 ) )
% 6.94/7.30 => ( ( groups3455450783089532116nteger @ G @ A4 )
% 6.94/7.30 = ( groups3455450783089532116nteger @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrierI
% 6.94/7.30 thf(fact_8866_prod_Osame__carrierI,axiom,
% 6.94/7.30 ! [C4: set_Code_integer,A4: set_Code_integer,B5: set_Code_integer,G: code_integer > code_integer,H: code_integer > code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ( ( groups3674199335183972705nteger @ G @ C4 )
% 6.94/7.30 = ( groups3674199335183972705nteger @ H @ C4 ) )
% 6.94/7.30 => ( ( groups3674199335183972705nteger @ G @ A4 )
% 6.94/7.30 = ( groups3674199335183972705nteger @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrierI
% 6.94/7.30 thf(fact_8867_prod_Osame__carrierI,axiom,
% 6.94/7.30 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > assn,H: $o > assn] :
% 6.94/7.30 ( ( finite_finite_o @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ( ( groups5301882518646026715o_assn @ G @ C4 )
% 6.94/7.30 = ( groups5301882518646026715o_assn @ H @ C4 ) )
% 6.94/7.30 => ( ( groups5301882518646026715o_assn @ G @ A4 )
% 6.94/7.30 = ( groups5301882518646026715o_assn @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrierI
% 6.94/7.30 thf(fact_8868_prod_Osame__carrierI,axiom,
% 6.94/7.30 ! [C4: set_nat,A4: set_nat,B5: set_nat,G: nat > assn,H: nat > assn] :
% 6.94/7.30 ( ( finite_finite_nat @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: nat] :
% 6.94/7.30 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ! [B3: nat] :
% 6.94/7.30 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ( ( groups6906906614972039071t_assn @ G @ C4 )
% 6.94/7.30 = ( groups6906906614972039071t_assn @ H @ C4 ) )
% 6.94/7.30 => ( ( groups6906906614972039071t_assn @ G @ A4 )
% 6.94/7.30 = ( groups6906906614972039071t_assn @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrierI
% 6.94/7.30 thf(fact_8869_prod_Osame__carrierI,axiom,
% 6.94/7.30 ! [C4: set_Code_integer,A4: set_Code_integer,B5: set_Code_integer,G: code_integer > assn,H: code_integer > assn] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ( ( groups1304777262505850412r_assn @ G @ C4 )
% 6.94/7.30 = ( groups1304777262505850412r_assn @ H @ C4 ) )
% 6.94/7.30 => ( ( groups1304777262505850412r_assn @ G @ A4 )
% 6.94/7.30 = ( groups1304777262505850412r_assn @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrierI
% 6.94/7.30 thf(fact_8870_prod_Osame__carrierI,axiom,
% 6.94/7.30 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > rat,H: $o > rat] :
% 6.94/7.30 ( ( finite_finite_o @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ( ( groups2869687844427037835_o_rat @ G @ C4 )
% 6.94/7.30 = ( groups2869687844427037835_o_rat @ H @ C4 ) )
% 6.94/7.30 => ( ( groups2869687844427037835_o_rat @ G @ A4 )
% 6.94/7.30 = ( groups2869687844427037835_o_rat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrierI
% 6.94/7.30 thf(fact_8871_prod_Osame__carrierI,axiom,
% 6.94/7.30 ! [C4: set_nat,A4: set_nat,B5: set_nat,G: nat > rat,H: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: nat] :
% 6.94/7.30 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ! [B3: nat] :
% 6.94/7.30 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ( ( groups73079841787564623at_rat @ G @ C4 )
% 6.94/7.30 = ( groups73079841787564623at_rat @ H @ C4 ) )
% 6.94/7.30 => ( ( groups73079841787564623at_rat @ G @ A4 )
% 6.94/7.30 = ( groups73079841787564623at_rat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrierI
% 6.94/7.30 thf(fact_8872_prod_Osame__carrierI,axiom,
% 6.94/7.30 ! [C4: set_Code_integer,A4: set_Code_integer,B5: set_Code_integer,G: code_integer > rat,H: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ( ( groups2555765274223993564er_rat @ G @ C4 )
% 6.94/7.30 = ( groups2555765274223993564er_rat @ H @ C4 ) )
% 6.94/7.30 => ( ( groups2555765274223993564er_rat @ G @ A4 )
% 6.94/7.30 = ( groups2555765274223993564er_rat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrierI
% 6.94/7.30 thf(fact_8873_prod_Osame__carrierI,axiom,
% 6.94/7.30 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > nat,H: $o > nat] :
% 6.94/7.30 ( ( finite_finite_o @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_nat ) )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_nat ) )
% 6.94/7.30 => ( ( ( groups3504817904513533571_o_nat @ G @ C4 )
% 6.94/7.30 = ( groups3504817904513533571_o_nat @ H @ C4 ) )
% 6.94/7.30 => ( ( groups3504817904513533571_o_nat @ G @ A4 )
% 6.94/7.30 = ( groups3504817904513533571_o_nat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrierI
% 6.94/7.30 thf(fact_8874_prod_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > code_integer,H: $o > code_integer] :
% 6.94/7.30 ( ( finite_finite_o @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ( ( groups7694694392188491536nteger @ G @ A4 )
% 6.94/7.30 = ( groups7694694392188491536nteger @ H @ B5 ) )
% 6.94/7.30 = ( ( groups7694694392188491536nteger @ G @ C4 )
% 6.94/7.30 = ( groups7694694392188491536nteger @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrier
% 6.94/7.30 thf(fact_8875_prod_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_nat,A4: set_nat,B5: set_nat,G: nat > code_integer,H: nat > code_integer] :
% 6.94/7.30 ( ( finite_finite_nat @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: nat] :
% 6.94/7.30 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ! [B3: nat] :
% 6.94/7.30 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ( ( groups3455450783089532116nteger @ G @ A4 )
% 6.94/7.30 = ( groups3455450783089532116nteger @ H @ B5 ) )
% 6.94/7.30 = ( ( groups3455450783089532116nteger @ G @ C4 )
% 6.94/7.30 = ( groups3455450783089532116nteger @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrier
% 6.94/7.30 thf(fact_8876_prod_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_Code_integer,A4: set_Code_integer,B5: set_Code_integer,G: code_integer > code_integer,H: code_integer > code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ( ( groups3674199335183972705nteger @ G @ A4 )
% 6.94/7.30 = ( groups3674199335183972705nteger @ H @ B5 ) )
% 6.94/7.30 = ( ( groups3674199335183972705nteger @ G @ C4 )
% 6.94/7.30 = ( groups3674199335183972705nteger @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrier
% 6.94/7.30 thf(fact_8877_prod_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > assn,H: $o > assn] :
% 6.94/7.30 ( ( finite_finite_o @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ( ( groups5301882518646026715o_assn @ G @ A4 )
% 6.94/7.30 = ( groups5301882518646026715o_assn @ H @ B5 ) )
% 6.94/7.30 = ( ( groups5301882518646026715o_assn @ G @ C4 )
% 6.94/7.30 = ( groups5301882518646026715o_assn @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrier
% 6.94/7.30 thf(fact_8878_prod_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_nat,A4: set_nat,B5: set_nat,G: nat > assn,H: nat > assn] :
% 6.94/7.30 ( ( finite_finite_nat @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: nat] :
% 6.94/7.30 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ! [B3: nat] :
% 6.94/7.30 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ( ( groups6906906614972039071t_assn @ G @ A4 )
% 6.94/7.30 = ( groups6906906614972039071t_assn @ H @ B5 ) )
% 6.94/7.30 = ( ( groups6906906614972039071t_assn @ G @ C4 )
% 6.94/7.30 = ( groups6906906614972039071t_assn @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrier
% 6.94/7.30 thf(fact_8879_prod_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_Code_integer,A4: set_Code_integer,B5: set_Code_integer,G: code_integer > assn,H: code_integer > assn] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ( ( groups1304777262505850412r_assn @ G @ A4 )
% 6.94/7.30 = ( groups1304777262505850412r_assn @ H @ B5 ) )
% 6.94/7.30 = ( ( groups1304777262505850412r_assn @ G @ C4 )
% 6.94/7.30 = ( groups1304777262505850412r_assn @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrier
% 6.94/7.30 thf(fact_8880_prod_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > rat,H: $o > rat] :
% 6.94/7.30 ( ( finite_finite_o @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ( ( groups2869687844427037835_o_rat @ G @ A4 )
% 6.94/7.30 = ( groups2869687844427037835_o_rat @ H @ B5 ) )
% 6.94/7.30 = ( ( groups2869687844427037835_o_rat @ G @ C4 )
% 6.94/7.30 = ( groups2869687844427037835_o_rat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrier
% 6.94/7.30 thf(fact_8881_prod_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_nat,A4: set_nat,B5: set_nat,G: nat > rat,H: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: nat] :
% 6.94/7.30 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ! [B3: nat] :
% 6.94/7.30 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ( ( groups73079841787564623at_rat @ G @ A4 )
% 6.94/7.30 = ( groups73079841787564623at_rat @ H @ B5 ) )
% 6.94/7.30 = ( ( groups73079841787564623at_rat @ G @ C4 )
% 6.94/7.30 = ( groups73079841787564623at_rat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrier
% 6.94/7.30 thf(fact_8882_prod_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_Code_integer,A4: set_Code_integer,B5: set_Code_integer,G: code_integer > rat,H: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ( ( groups2555765274223993564er_rat @ G @ A4 )
% 6.94/7.30 = ( groups2555765274223993564er_rat @ H @ B5 ) )
% 6.94/7.30 = ( ( groups2555765274223993564er_rat @ G @ C4 )
% 6.94/7.30 = ( groups2555765274223993564er_rat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrier
% 6.94/7.30 thf(fact_8883_prod_Osame__carrier,axiom,
% 6.94/7.30 ! [C4: set_o,A4: set_o,B5: set_o,G: $o > nat,H: $o > nat] :
% 6.94/7.30 ( ( finite_finite_o @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ C4 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ B5 @ C4 )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ ( minus_minus_set_o @ C4 @ A4 ) )
% 6.94/7.30 => ( ( G @ A3 )
% 6.94/7.30 = one_one_nat ) )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ C4 @ B5 ) )
% 6.94/7.30 => ( ( H @ B3 )
% 6.94/7.30 = one_one_nat ) )
% 6.94/7.30 => ( ( ( groups3504817904513533571_o_nat @ G @ A4 )
% 6.94/7.30 = ( groups3504817904513533571_o_nat @ H @ B5 ) )
% 6.94/7.30 = ( ( groups3504817904513533571_o_nat @ G @ C4 )
% 6.94/7.30 = ( groups3504817904513533571_o_nat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.same_carrier
% 6.94/7.30 thf(fact_8884_sum_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( groups3906332499630173760nt_rat @ G @ ( inf_inf_set_int @ A4 @ B5 ) ) )
% 6.94/7.30 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ A4 ) @ ( groups3906332499630173760nt_rat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter
% 6.94/7.30 thf(fact_8885_sum_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) ) @ ( groups6602215022474089585er_rat @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) )
% 6.94/7.30 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ A4 ) @ ( groups6602215022474089585er_rat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter
% 6.94/7.30 thf(fact_8886_sum_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > nat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( groups4541462559716669496nt_nat @ G @ ( inf_inf_set_int @ A4 @ B5 ) ) )
% 6.94/7.30 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ A4 ) @ ( groups4541462559716669496nt_nat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter
% 6.94/7.30 thf(fact_8887_sum_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) ) @ ( groups7237345082560585321er_nat @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) )
% 6.94/7.30 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ A4 ) @ ( groups7237345082560585321er_nat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter
% 6.94/7.30 thf(fact_8888_sum_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) ) @ ( groups7234854612051535045er_int @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) )
% 6.94/7.30 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ A4 ) @ ( groups7234854612051535045er_int @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter
% 6.94/7.30 thf(fact_8889_sum_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( groups2906978787729119204at_rat @ G @ ( inf_inf_set_nat @ A4 @ B5 ) ) )
% 6.94/7.30 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ A4 ) @ ( groups2906978787729119204at_rat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter
% 6.94/7.30 thf(fact_8890_sum_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > int] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( groups3539618377306564664at_int @ G @ ( inf_inf_set_nat @ A4 @ B5 ) ) )
% 6.94/7.30 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ A4 ) @ ( groups3539618377306564664at_int @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter
% 6.94/7.30 thf(fact_8891_sum_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > nat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( groups3542108847815614940at_nat @ G @ ( inf_inf_set_nat @ A4 @ B5 ) ) )
% 6.94/7.30 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A4 ) @ ( groups3542108847815614940at_nat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter
% 6.94/7.30 thf(fact_8892_sum_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > int] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( groups4538972089207619220nt_int @ G @ ( inf_inf_set_int @ A4 @ B5 ) ) )
% 6.94/7.30 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A4 ) @ ( groups4538972089207619220nt_int @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter
% 6.94/7.30 thf(fact_8893_sum_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > rat] :
% 6.94/7.30 ( ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.30 => ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.30 => ( ( plus_plus_rat @ ( groups342789780944988191at_rat @ G @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) ) @ ( groups342789780944988191at_rat @ G @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) )
% 6.94/7.30 = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G @ A4 ) @ ( groups342789780944988191at_rat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter
% 6.94/7.30 thf(fact_8894_sum_OInt__Diff,axiom,
% 6.94/7.30 ! [A4: set_int,G: int > rat,B5: set_int] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups3906332499630173760nt_rat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.Int_Diff
% 6.94/7.30 thf(fact_8895_sum_OInt__Diff,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,G: code_integer > rat,B5: set_Code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups6602215022474089585er_rat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.Int_Diff
% 6.94/7.30 thf(fact_8896_sum_OInt__Diff,axiom,
% 6.94/7.30 ! [A4: set_int,G: int > nat,B5: set_int] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups4541462559716669496nt_nat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.Int_Diff
% 6.94/7.30 thf(fact_8897_sum_OInt__Diff,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,G: code_integer > nat,B5: set_Code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups7237345082560585321er_nat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.Int_Diff
% 6.94/7.30 thf(fact_8898_sum_OInt__Diff,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,G: code_integer > int,B5: set_Code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups7234854612051535045er_int @ G @ A4 )
% 6.94/7.30 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.Int_Diff
% 6.94/7.30 thf(fact_8899_sum_OInt__Diff,axiom,
% 6.94/7.30 ! [A4: set_nat,G: nat > rat,B5: set_nat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups2906978787729119204at_rat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.Int_Diff
% 6.94/7.30 thf(fact_8900_sum_OInt__Diff,axiom,
% 6.94/7.30 ! [A4: set_nat,G: nat > int,B5: set_nat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups3539618377306564664at_int @ G @ A4 )
% 6.94/7.30 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.Int_Diff
% 6.94/7.30 thf(fact_8901_sum_OInt__Diff,axiom,
% 6.94/7.30 ! [A4: set_nat,G: nat > nat,B5: set_nat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups3542108847815614940at_nat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( groups3542108847815614940at_nat @ G @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.Int_Diff
% 6.94/7.30 thf(fact_8902_sum_OInt__Diff,axiom,
% 6.94/7.30 ! [A4: set_int,G: int > int,B5: set_int] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups4538972089207619220nt_int @ G @ A4 )
% 6.94/7.30 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.Int_Diff
% 6.94/7.30 thf(fact_8903_sum_OInt__Diff,axiom,
% 6.94/7.30 ! [A4: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > rat,B5: set_Pr1261947904930325089at_nat] :
% 6.94/7.30 ( ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.30 => ( ( groups342789780944988191at_rat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) @ ( groups342789780944988191at_rat @ G @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.Int_Diff
% 6.94/7.30 thf(fact_8904_prod_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > assn] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( times_times_assn @ ( groups7882442080178216443t_assn @ G @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( groups7882442080178216443t_assn @ G @ ( inf_inf_set_int @ A4 @ B5 ) ) )
% 6.94/7.30 = ( times_times_assn @ ( groups7882442080178216443t_assn @ G @ A4 ) @ ( groups7882442080178216443t_assn @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter
% 6.94/7.30 thf(fact_8905_prod_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > assn] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) ) @ ( groups1304777262505850412r_assn @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) )
% 6.94/7.30 = ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ A4 ) @ ( groups1304777262505850412r_assn @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter
% 6.94/7.30 thf(fact_8906_prod_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > assn] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( groups6906906614972039071t_assn @ G @ ( inf_inf_set_nat @ A4 @ B5 ) ) )
% 6.94/7.30 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ A4 ) @ ( groups6906906614972039071t_assn @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter
% 6.94/7.30 thf(fact_8907_prod_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ G @ ( inf_inf_set_int @ A4 @ B5 ) ) )
% 6.94/7.30 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ A4 ) @ ( groups1072433553688619179nt_rat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter
% 6.94/7.30 thf(fact_8908_prod_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) ) @ ( groups2555765274223993564er_rat @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) )
% 6.94/7.30 = ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ A4 ) @ ( groups2555765274223993564er_rat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter
% 6.94/7.30 thf(fact_8909_prod_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( groups73079841787564623at_rat @ G @ ( inf_inf_set_nat @ A4 @ B5 ) ) )
% 6.94/7.30 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ A4 ) @ ( groups73079841787564623at_rat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter
% 6.94/7.30 thf(fact_8910_prod_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > nat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( groups1707563613775114915nt_nat @ G @ ( inf_inf_set_int @ A4 @ B5 ) ) )
% 6.94/7.30 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ A4 ) @ ( groups1707563613775114915nt_nat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter
% 6.94/7.30 thf(fact_8911_prod_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( times_times_nat @ ( groups3190895334310489300er_nat @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) ) @ ( groups3190895334310489300er_nat @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) )
% 6.94/7.30 = ( times_times_nat @ ( groups3190895334310489300er_nat @ G @ A4 ) @ ( groups3190895334310489300er_nat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter
% 6.94/7.30 thf(fact_8912_prod_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( times_times_int @ ( groups3188404863801439024er_int @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) ) @ ( groups3188404863801439024er_int @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) )
% 6.94/7.30 = ( times_times_int @ ( groups3188404863801439024er_int @ G @ A4 ) @ ( groups3188404863801439024er_int @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter
% 6.94/7.30 thf(fact_8913_prod_Ounion__inter,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > nat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( groups708209901874060359at_nat @ G @ ( inf_inf_set_nat @ A4 @ B5 ) ) )
% 6.94/7.30 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A4 ) @ ( groups708209901874060359at_nat @ G @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter
% 6.94/7.30 thf(fact_8914_sum__diff__nat,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,F: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ B5 @ A4 )
% 6.94/7.30 => ( ( groups7237345082560585321er_nat @ F @ ( minus_2355218937544613996nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_nat @ ( groups7237345082560585321er_nat @ F @ A4 ) @ ( groups7237345082560585321er_nat @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_diff_nat
% 6.94/7.30 thf(fact_8915_sum__diff__nat,axiom,
% 6.94/7.30 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 6.94/7.30 ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.30 => ( ( ord_le3146513528884898305at_nat @ B5 @ A4 )
% 6.94/7.30 => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A4 ) @ ( groups977919841031483927at_nat @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_diff_nat
% 6.94/7.30 thf(fact_8916_sum__diff__nat,axiom,
% 6.94/7.30 ! [B5: set_int,A4: set_int,F: int > nat] :
% 6.94/7.30 ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_int @ B5 @ A4 )
% 6.94/7.30 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_diff_nat
% 6.94/7.30 thf(fact_8917_sum__diff__nat,axiom,
% 6.94/7.30 ! [B5: set_nat,A4: set_nat,F: nat > nat] :
% 6.94/7.30 ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 6.94/7.30 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( groups3542108847815614940at_nat @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_diff_nat
% 6.94/7.30 thf(fact_8918_push__bit__mask__eq,axiom,
% 6.94/7.30 ! [M: nat,N2: nat] :
% 6.94/7.30 ( ( bit_se545348938243370406it_int @ M @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 6.94/7.30 = ( bit_se725231765392027082nd_int @ ( bit_se2000444600071755411sk_int @ ( plus_plus_nat @ N2 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ M ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % push_bit_mask_eq
% 6.94/7.30 thf(fact_8919_sum_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_int,P2: int > $o,H: int > rat,G: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups3906332499630173760nt_rat
% 6.94/7.30 @ ^ [X4: int] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ H @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) @ ( groups3906332499630173760nt_rat @ G @ ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.If_cases
% 6.94/7.30 thf(fact_8920_sum_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,P2: code_integer > $o,H: code_integer > rat,G: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups6602215022474089585er_rat
% 6.94/7.30 @ ^ [X4: code_integer] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ H @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) @ ( groups6602215022474089585er_rat @ G @ ( inf_in1364745209274528805nteger @ A4 @ ( uminus804700908173204444nteger @ ( collect_Code_integer @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.If_cases
% 6.94/7.30 thf(fact_8921_sum_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_int,P2: int > $o,H: int > nat,G: int > nat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups4541462559716669496nt_nat
% 6.94/7.30 @ ^ [X4: int] : ( if_nat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ H @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) @ ( groups4541462559716669496nt_nat @ G @ ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.If_cases
% 6.94/7.30 thf(fact_8922_sum_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,P2: code_integer > $o,H: code_integer > nat,G: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups7237345082560585321er_nat
% 6.94/7.30 @ ^ [X4: code_integer] : ( if_nat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ H @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) @ ( groups7237345082560585321er_nat @ G @ ( inf_in1364745209274528805nteger @ A4 @ ( uminus804700908173204444nteger @ ( collect_Code_integer @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.If_cases
% 6.94/7.30 thf(fact_8923_sum_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,P2: code_integer > $o,H: code_integer > int,G: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups7234854612051535045er_int
% 6.94/7.30 @ ^ [X4: code_integer] : ( if_int @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( plus_plus_int @ ( groups7234854612051535045er_int @ H @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) @ ( groups7234854612051535045er_int @ G @ ( inf_in1364745209274528805nteger @ A4 @ ( uminus804700908173204444nteger @ ( collect_Code_integer @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.If_cases
% 6.94/7.30 thf(fact_8924_sum_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_nat,P2: nat > $o,H: nat > rat,G: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups2906978787729119204at_rat
% 6.94/7.30 @ ^ [X4: nat] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ H @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) @ ( groups2906978787729119204at_rat @ G @ ( inf_inf_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.If_cases
% 6.94/7.30 thf(fact_8925_sum_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_nat,P2: nat > $o,H: nat > int,G: nat > int] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups3539618377306564664at_int
% 6.94/7.30 @ ^ [X4: nat] : ( if_int @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( plus_plus_int @ ( groups3539618377306564664at_int @ H @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) @ ( groups3539618377306564664at_int @ G @ ( inf_inf_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.If_cases
% 6.94/7.30 thf(fact_8926_sum_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_nat,P2: nat > $o,H: nat > nat,G: nat > nat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups3542108847815614940at_nat
% 6.94/7.30 @ ^ [X4: nat] : ( if_nat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ H @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) @ ( groups3542108847815614940at_nat @ G @ ( inf_inf_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.If_cases
% 6.94/7.30 thf(fact_8927_sum_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_int,P2: int > $o,H: int > int,G: int > int] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups4538972089207619220nt_int
% 6.94/7.30 @ ^ [X4: int] : ( if_int @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ H @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) @ ( groups4538972089207619220nt_int @ G @ ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.If_cases
% 6.94/7.30 thf(fact_8928_sum_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_list_nat,P2: list_nat > $o,H: list_nat > rat,G: list_nat > rat] :
% 6.94/7.30 ( ( finite8100373058378681591st_nat @ A4 )
% 6.94/7.30 => ( ( groups3760926236672600436at_rat
% 6.94/7.30 @ ^ [X4: list_nat] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( groups3760926236672600436at_rat @ H @ ( inf_inf_set_list_nat @ A4 @ ( collect_list_nat @ P2 ) ) ) @ ( groups3760926236672600436at_rat @ G @ ( inf_inf_set_list_nat @ A4 @ ( uminus3195874150345416415st_nat @ ( collect_list_nat @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.If_cases
% 6.94/7.30 thf(fact_8929_prod_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_int,P2: int > $o,H: int > assn,G: int > assn] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups7882442080178216443t_assn
% 6.94/7.30 @ ^ [X4: int] : ( if_assn @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( times_times_assn @ ( groups7882442080178216443t_assn @ H @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) @ ( groups7882442080178216443t_assn @ G @ ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.If_cases
% 6.94/7.30 thf(fact_8930_prod_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,P2: code_integer > $o,H: code_integer > assn,G: code_integer > assn] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups1304777262505850412r_assn
% 6.94/7.30 @ ^ [X4: code_integer] : ( if_assn @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( times_times_assn @ ( groups1304777262505850412r_assn @ H @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) @ ( groups1304777262505850412r_assn @ G @ ( inf_in1364745209274528805nteger @ A4 @ ( uminus804700908173204444nteger @ ( collect_Code_integer @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.If_cases
% 6.94/7.30 thf(fact_8931_prod_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_nat,P2: nat > $o,H: nat > assn,G: nat > assn] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups6906906614972039071t_assn
% 6.94/7.30 @ ^ [X4: nat] : ( if_assn @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( times_times_assn @ ( groups6906906614972039071t_assn @ H @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) @ ( groups6906906614972039071t_assn @ G @ ( inf_inf_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.If_cases
% 6.94/7.30 thf(fact_8932_prod_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_int,P2: int > $o,H: int > rat,G: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups1072433553688619179nt_rat
% 6.94/7.30 @ ^ [X4: int] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ H @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) @ ( groups1072433553688619179nt_rat @ G @ ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.If_cases
% 6.94/7.30 thf(fact_8933_prod_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,P2: code_integer > $o,H: code_integer > rat,G: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups2555765274223993564er_rat
% 6.94/7.30 @ ^ [X4: code_integer] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( times_times_rat @ ( groups2555765274223993564er_rat @ H @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) @ ( groups2555765274223993564er_rat @ G @ ( inf_in1364745209274528805nteger @ A4 @ ( uminus804700908173204444nteger @ ( collect_Code_integer @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.If_cases
% 6.94/7.30 thf(fact_8934_prod_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_nat,P2: nat > $o,H: nat > rat,G: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups73079841787564623at_rat
% 6.94/7.30 @ ^ [X4: nat] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( times_times_rat @ ( groups73079841787564623at_rat @ H @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) @ ( groups73079841787564623at_rat @ G @ ( inf_inf_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.If_cases
% 6.94/7.30 thf(fact_8935_prod_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_int,P2: int > $o,H: int > nat,G: int > nat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups1707563613775114915nt_nat
% 6.94/7.30 @ ^ [X4: int] : ( if_nat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ H @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) @ ( groups1707563613775114915nt_nat @ G @ ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.If_cases
% 6.94/7.30 thf(fact_8936_prod_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,P2: code_integer > $o,H: code_integer > nat,G: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups3190895334310489300er_nat
% 6.94/7.30 @ ^ [X4: code_integer] : ( if_nat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( times_times_nat @ ( groups3190895334310489300er_nat @ H @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) @ ( groups3190895334310489300er_nat @ G @ ( inf_in1364745209274528805nteger @ A4 @ ( uminus804700908173204444nteger @ ( collect_Code_integer @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.If_cases
% 6.94/7.30 thf(fact_8937_prod_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,P2: code_integer > $o,H: code_integer > int,G: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups3188404863801439024er_int
% 6.94/7.30 @ ^ [X4: code_integer] : ( if_int @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( times_times_int @ ( groups3188404863801439024er_int @ H @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) @ ( groups3188404863801439024er_int @ G @ ( inf_in1364745209274528805nteger @ A4 @ ( uminus804700908173204444nteger @ ( collect_Code_integer @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.If_cases
% 6.94/7.30 thf(fact_8938_prod_OIf__cases,axiom,
% 6.94/7.30 ! [A4: set_nat,P2: nat > $o,H: nat > nat,G: nat > nat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups708209901874060359at_nat
% 6.94/7.30 @ ^ [X4: nat] : ( if_nat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 6.94/7.30 @ A4 )
% 6.94/7.30 = ( times_times_nat @ ( groups708209901874060359at_nat @ H @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) @ ( groups708209901874060359at_nat @ G @ ( inf_inf_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.If_cases
% 6.94/7.30 thf(fact_8939_prod__mono__strict,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,F: code_integer > code_integer,G: code_integer > code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ! [I3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ I3 @ A4 )
% 6.94/7.30 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 6.94/7.30 & ( ord_le6747313008572928689nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.94/7.30 => ( ( A4 != bot_bo3990330152332043303nteger )
% 6.94/7.30 => ( ord_le6747313008572928689nteger @ ( groups3674199335183972705nteger @ F @ A4 ) @ ( groups3674199335183972705nteger @ G @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono_strict
% 6.94/7.30 thf(fact_8940_prod__mono__strict,axiom,
% 6.94/7.30 ! [A4: set_o,F: $o > code_integer,G: $o > code_integer] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ! [I3: $o] :
% 6.94/7.30 ( ( member_o @ I3 @ A4 )
% 6.94/7.30 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 6.94/7.30 & ( ord_le6747313008572928689nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.94/7.30 => ( ( A4 != bot_bot_set_o )
% 6.94/7.30 => ( ord_le6747313008572928689nteger @ ( groups7694694392188491536nteger @ F @ A4 ) @ ( groups7694694392188491536nteger @ G @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono_strict
% 6.94/7.30 thf(fact_8941_prod__mono__strict,axiom,
% 6.94/7.30 ! [A4: set_nat,F: nat > code_integer,G: nat > code_integer] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ! [I3: nat] :
% 6.94/7.30 ( ( member_nat @ I3 @ A4 )
% 6.94/7.30 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 6.94/7.30 & ( ord_le6747313008572928689nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.94/7.30 => ( ( A4 != bot_bot_set_nat )
% 6.94/7.30 => ( ord_le6747313008572928689nteger @ ( groups3455450783089532116nteger @ F @ A4 ) @ ( groups3455450783089532116nteger @ G @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono_strict
% 6.94/7.30 thf(fact_8942_prod__mono__strict,axiom,
% 6.94/7.30 ! [A4: set_int,F: int > code_integer,G: int > code_integer] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ! [I3: int] :
% 6.94/7.30 ( ( member_int @ I3 @ A4 )
% 6.94/7.30 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 6.94/7.30 & ( ord_le6747313008572928689nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.94/7.30 => ( ( A4 != bot_bot_set_int )
% 6.94/7.30 => ( ord_le6747313008572928689nteger @ ( groups3827104343326376752nteger @ F @ A4 ) @ ( groups3827104343326376752nteger @ G @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono_strict
% 6.94/7.30 thf(fact_8943_prod__mono__strict,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,F: code_integer > rat,G: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ! [I3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ I3 @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 6.94/7.30 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.94/7.30 => ( ( A4 != bot_bo3990330152332043303nteger )
% 6.94/7.30 => ( ord_less_rat @ ( groups2555765274223993564er_rat @ F @ A4 ) @ ( groups2555765274223993564er_rat @ G @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono_strict
% 6.94/7.30 thf(fact_8944_prod__mono__strict,axiom,
% 6.94/7.30 ! [A4: set_o,F: $o > rat,G: $o > rat] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ! [I3: $o] :
% 6.94/7.30 ( ( member_o @ I3 @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 6.94/7.30 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.94/7.30 => ( ( A4 != bot_bot_set_o )
% 6.94/7.30 => ( ord_less_rat @ ( groups2869687844427037835_o_rat @ F @ A4 ) @ ( groups2869687844427037835_o_rat @ G @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono_strict
% 6.94/7.30 thf(fact_8945_prod__mono__strict,axiom,
% 6.94/7.30 ! [A4: set_nat,F: nat > rat,G: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ! [I3: nat] :
% 6.94/7.30 ( ( member_nat @ I3 @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 6.94/7.30 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.94/7.30 => ( ( A4 != bot_bot_set_nat )
% 6.94/7.30 => ( ord_less_rat @ ( groups73079841787564623at_rat @ F @ A4 ) @ ( groups73079841787564623at_rat @ G @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono_strict
% 6.94/7.30 thf(fact_8946_prod__mono__strict,axiom,
% 6.94/7.30 ! [A4: set_int,F: int > rat,G: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ! [I3: int] :
% 6.94/7.30 ( ( member_int @ I3 @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 6.94/7.30 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.94/7.30 => ( ( A4 != bot_bot_set_int )
% 6.94/7.30 => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F @ A4 ) @ ( groups1072433553688619179nt_rat @ G @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono_strict
% 6.94/7.30 thf(fact_8947_prod__mono__strict,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,F: code_integer > nat,G: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ! [I3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ I3 @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 6.94/7.30 & ( ord_less_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.94/7.30 => ( ( A4 != bot_bo3990330152332043303nteger )
% 6.94/7.30 => ( ord_less_nat @ ( groups3190895334310489300er_nat @ F @ A4 ) @ ( groups3190895334310489300er_nat @ G @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono_strict
% 6.94/7.30 thf(fact_8948_prod__mono__strict,axiom,
% 6.94/7.30 ! [A4: set_o,F: $o > nat,G: $o > nat] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ! [I3: $o] :
% 6.94/7.30 ( ( member_o @ I3 @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 6.94/7.30 & ( ord_less_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 6.94/7.30 => ( ( A4 != bot_bot_set_o )
% 6.94/7.30 => ( ord_less_nat @ ( groups3504817904513533571_o_nat @ F @ A4 ) @ ( groups3504817904513533571_o_nat @ G @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono_strict
% 6.94/7.30 thf(fact_8949_sum__mono2,axiom,
% 6.94/7.30 ! [B5: set_o,A4: set_o,F: $o > code_integer] :
% 6.94/7.30 ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ ( groups4406642042086082107nteger @ F @ A4 ) @ ( groups4406642042086082107nteger @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_mono2
% 6.94/7.30 thf(fact_8950_sum__mono2,axiom,
% 6.94/7.30 ! [B5: set_nat,A4: set_nat,F: nat > code_integer] :
% 6.94/7.30 ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: nat] :
% 6.94/7.30 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ ( groups7501900531339628137nteger @ F @ A4 ) @ ( groups7501900531339628137nteger @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_mono2
% 6.94/7.30 thf(fact_8951_sum__mono2,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,F: code_integer > code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ ( groups879477027807139574nteger @ F @ A4 ) @ ( groups879477027807139574nteger @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_mono2
% 6.94/7.30 thf(fact_8952_sum__mono2,axiom,
% 6.94/7.30 ! [B5: set_o,A4: set_o,F: $o > rat] :
% 6.94/7.30 ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ord_less_eq_rat @ ( groups7872700643590313910_o_rat @ F @ A4 ) @ ( groups7872700643590313910_o_rat @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_mono2
% 6.94/7.30 thf(fact_8953_sum__mono2,axiom,
% 6.94/7.30 ! [B5: set_nat,A4: set_nat,F: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: nat] :
% 6.94/7.30 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ ( groups2906978787729119204at_rat @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_mono2
% 6.94/7.30 thf(fact_8954_sum__mono2,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,F: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ord_less_eq_rat @ ( groups6602215022474089585er_rat @ F @ A4 ) @ ( groups6602215022474089585er_rat @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_mono2
% 6.94/7.30 thf(fact_8955_sum__mono2,axiom,
% 6.94/7.30 ! [B5: set_o,A4: set_o,F: $o > nat] :
% 6.94/7.30 ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ord_less_eq_nat @ ( groups8507830703676809646_o_nat @ F @ A4 ) @ ( groups8507830703676809646_o_nat @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_mono2
% 6.94/7.30 thf(fact_8956_sum__mono2,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,F: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ord_less_eq_nat @ ( groups7237345082560585321er_nat @ F @ A4 ) @ ( groups7237345082560585321er_nat @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_mono2
% 6.94/7.30 thf(fact_8957_sum__mono2,axiom,
% 6.94/7.30 ! [B5: set_o,A4: set_o,F: $o > int] :
% 6.94/7.30 ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ord_less_eq_int @ ( groups8505340233167759370_o_int @ F @ A4 ) @ ( groups8505340233167759370_o_int @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_mono2
% 6.94/7.30 thf(fact_8958_sum__mono2,axiom,
% 6.94/7.30 ! [B5: set_nat,A4: set_nat,F: nat > int] :
% 6.94/7.30 ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: nat] :
% 6.94/7.30 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ A4 ) @ ( groups3539618377306564664at_int @ F @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_mono2
% 6.94/7.30 thf(fact_8959_sum_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > code_integer] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = zero_z3403309356797280102nteger ) )
% 6.94/7.30 => ( ( groups7873554091576472773nteger @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_p5714425477246183910nteger @ ( groups7873554091576472773nteger @ G @ A4 ) @ ( groups7873554091576472773nteger @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter_neutral
% 6.94/7.30 thf(fact_8960_sum_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = zero_z3403309356797280102nteger ) )
% 6.94/7.30 => ( ( groups879477027807139574nteger @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_p5714425477246183910nteger @ ( groups879477027807139574nteger @ G @ A4 ) @ ( groups879477027807139574nteger @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter_neutral
% 6.94/7.30 thf(fact_8961_sum_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = zero_zero_rat ) )
% 6.94/7.30 => ( ( groups3906332499630173760nt_rat @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ A4 ) @ ( groups3906332499630173760nt_rat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter_neutral
% 6.94/7.30 thf(fact_8962_sum_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = zero_zero_rat ) )
% 6.94/7.30 => ( ( groups6602215022474089585er_rat @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ A4 ) @ ( groups6602215022474089585er_rat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter_neutral
% 6.94/7.30 thf(fact_8963_sum_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > nat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = zero_zero_nat ) )
% 6.94/7.30 => ( ( groups4541462559716669496nt_nat @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ A4 ) @ ( groups4541462559716669496nt_nat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter_neutral
% 6.94/7.30 thf(fact_8964_sum_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = zero_zero_nat ) )
% 6.94/7.30 => ( ( groups7237345082560585321er_nat @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ A4 ) @ ( groups7237345082560585321er_nat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter_neutral
% 6.94/7.30 thf(fact_8965_sum_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = zero_zero_int ) )
% 6.94/7.30 => ( ( groups7234854612051535045er_int @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ A4 ) @ ( groups7234854612051535045er_int @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter_neutral
% 6.94/7.30 thf(fact_8966_sum_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > code_integer] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = zero_z3403309356797280102nteger ) )
% 6.94/7.30 => ( ( groups7501900531339628137nteger @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G @ A4 ) @ ( groups7501900531339628137nteger @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter_neutral
% 6.94/7.30 thf(fact_8967_sum_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = zero_zero_rat ) )
% 6.94/7.30 => ( ( groups2906978787729119204at_rat @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ A4 ) @ ( groups2906978787729119204at_rat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter_neutral
% 6.94/7.30 thf(fact_8968_sum_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > int] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = zero_zero_int ) )
% 6.94/7.30 => ( ( groups3539618377306564664at_int @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ A4 ) @ ( groups3539618377306564664at_int @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_inter_neutral
% 6.94/7.30 thf(fact_8969_sum_Oinsert__remove,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,G: code_integer > rat,X: code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A4 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.insert_remove
% 6.94/7.30 thf(fact_8970_sum_Oinsert__remove,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,G: code_integer > nat,X: code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X @ A4 ) )
% 6.94/7.30 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.insert_remove
% 6.94/7.30 thf(fact_8971_sum_Oinsert__remove,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,G: code_integer > int,X: code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( groups7234854612051535045er_int @ G @ ( insert_Code_integer @ X @ A4 ) )
% 6.94/7.30 = ( plus_plus_int @ ( G @ X ) @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.insert_remove
% 6.94/7.30 thf(fact_8972_sum_Oinsert__remove,axiom,
% 6.94/7.30 ! [A4: set_o,G: $o > rat,X: $o] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A4 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.insert_remove
% 6.94/7.30 thf(fact_8973_sum_Oinsert__remove,axiom,
% 6.94/7.30 ! [A4: set_o,G: $o > nat,X: $o] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( groups8507830703676809646_o_nat @ G @ ( insert_o @ X @ A4 ) )
% 6.94/7.30 = ( plus_plus_nat @ ( G @ X ) @ ( groups8507830703676809646_o_nat @ G @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.insert_remove
% 6.94/7.30 thf(fact_8974_sum_Oinsert__remove,axiom,
% 6.94/7.30 ! [A4: set_o,G: $o > int,X: $o] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( groups8505340233167759370_o_int @ G @ ( insert_o @ X @ A4 ) )
% 6.94/7.30 = ( plus_plus_int @ ( G @ X ) @ ( groups8505340233167759370_o_int @ G @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.insert_remove
% 6.94/7.30 thf(fact_8975_sum_Oinsert__remove,axiom,
% 6.94/7.30 ! [A4: set_nat,G: nat > rat,X: nat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A4 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.insert_remove
% 6.94/7.30 thf(fact_8976_sum_Oinsert__remove,axiom,
% 6.94/7.30 ! [A4: set_nat,G: nat > int,X: nat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( groups3539618377306564664at_int @ G @ ( insert_nat @ X @ A4 ) )
% 6.94/7.30 = ( plus_plus_int @ ( G @ X ) @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.insert_remove
% 6.94/7.30 thf(fact_8977_sum_Oinsert__remove,axiom,
% 6.94/7.30 ! [A4: set_int,G: int > rat,X: int] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A4 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.insert_remove
% 6.94/7.30 thf(fact_8978_sum_Oinsert__remove,axiom,
% 6.94/7.30 ! [A4: set_int,G: int > nat,X: int] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A4 ) )
% 6.94/7.30 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.insert_remove
% 6.94/7.30 thf(fact_8979_sum_Oremove,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( member_Code_integer @ X @ A4 )
% 6.94/7.30 => ( ( groups6602215022474089585er_rat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.remove
% 6.94/7.30 thf(fact_8980_sum_Oremove,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,X: code_integer,G: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( member_Code_integer @ X @ A4 )
% 6.94/7.30 => ( ( groups7237345082560585321er_nat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.remove
% 6.94/7.30 thf(fact_8981_sum_Oremove,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,X: code_integer,G: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( member_Code_integer @ X @ A4 )
% 6.94/7.30 => ( ( groups7234854612051535045er_int @ G @ A4 )
% 6.94/7.30 = ( plus_plus_int @ ( G @ X ) @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.remove
% 6.94/7.30 thf(fact_8982_sum_Oremove,axiom,
% 6.94/7.30 ! [A4: set_o,X: $o,G: $o > rat] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( member_o @ X @ A4 )
% 6.94/7.30 => ( ( groups7872700643590313910_o_rat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.remove
% 6.94/7.30 thf(fact_8983_sum_Oremove,axiom,
% 6.94/7.30 ! [A4: set_o,X: $o,G: $o > nat] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( member_o @ X @ A4 )
% 6.94/7.30 => ( ( groups8507830703676809646_o_nat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_nat @ ( G @ X ) @ ( groups8507830703676809646_o_nat @ G @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.remove
% 6.94/7.30 thf(fact_8984_sum_Oremove,axiom,
% 6.94/7.30 ! [A4: set_o,X: $o,G: $o > int] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( member_o @ X @ A4 )
% 6.94/7.30 => ( ( groups8505340233167759370_o_int @ G @ A4 )
% 6.94/7.30 = ( plus_plus_int @ ( G @ X ) @ ( groups8505340233167759370_o_int @ G @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.remove
% 6.94/7.30 thf(fact_8985_sum_Oremove,axiom,
% 6.94/7.30 ! [A4: set_nat,X: nat,G: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( member_nat @ X @ A4 )
% 6.94/7.30 => ( ( groups2906978787729119204at_rat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.remove
% 6.94/7.30 thf(fact_8986_sum_Oremove,axiom,
% 6.94/7.30 ! [A4: set_nat,X: nat,G: nat > int] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( member_nat @ X @ A4 )
% 6.94/7.30 => ( ( groups3539618377306564664at_int @ G @ A4 )
% 6.94/7.30 = ( plus_plus_int @ ( G @ X ) @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.remove
% 6.94/7.30 thf(fact_8987_sum_Oremove,axiom,
% 6.94/7.30 ! [A4: set_int,X: int,G: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( member_int @ X @ A4 )
% 6.94/7.30 => ( ( groups3906332499630173760nt_rat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.remove
% 6.94/7.30 thf(fact_8988_sum_Oremove,axiom,
% 6.94/7.30 ! [A4: set_int,X: int,G: int > nat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( member_int @ X @ A4 )
% 6.94/7.30 => ( ( groups4541462559716669496nt_nat @ G @ A4 )
% 6.94/7.30 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.remove
% 6.94/7.30 thf(fact_8989_sum__Un,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,F: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( groups3906332499630173760nt_rat @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_rat @ ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) @ ( groups3906332499630173760nt_rat @ F @ B5 ) ) @ ( groups3906332499630173760nt_rat @ F @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un
% 6.94/7.30 thf(fact_8990_sum__Un,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,F: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( groups6602215022474089585er_rat @ F @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_rat @ ( plus_plus_rat @ ( groups6602215022474089585er_rat @ F @ A4 ) @ ( groups6602215022474089585er_rat @ F @ B5 ) ) @ ( groups6602215022474089585er_rat @ F @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un
% 6.94/7.30 thf(fact_8991_sum__Un,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,F: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( groups2906978787729119204at_rat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_rat @ ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ ( groups2906978787729119204at_rat @ F @ B5 ) ) @ ( groups2906978787729119204at_rat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un
% 6.94/7.30 thf(fact_8992_sum__Un,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,F: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( groups7234854612051535045er_int @ F @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_int @ ( plus_plus_int @ ( groups7234854612051535045er_int @ F @ A4 ) @ ( groups7234854612051535045er_int @ F @ B5 ) ) @ ( groups7234854612051535045er_int @ F @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un
% 6.94/7.30 thf(fact_8993_sum__Un,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,F: nat > int] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( groups3539618377306564664at_int @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_int @ ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ A4 ) @ ( groups3539618377306564664at_int @ F @ B5 ) ) @ ( groups3539618377306564664at_int @ F @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un
% 6.94/7.30 thf(fact_8994_sum__Un,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,F: int > int] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( groups4538972089207619220nt_int @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_int @ ( plus_plus_int @ ( groups4538972089207619220nt_int @ F @ A4 ) @ ( groups4538972089207619220nt_int @ F @ B5 ) ) @ ( groups4538972089207619220nt_int @ F @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un
% 6.94/7.30 thf(fact_8995_sum__Un,axiom,
% 6.94/7.30 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > rat] :
% 6.94/7.30 ( ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.30 => ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.30 => ( ( groups342789780944988191at_rat @ F @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_rat @ ( plus_plus_rat @ ( groups342789780944988191at_rat @ F @ A4 ) @ ( groups342789780944988191at_rat @ F @ B5 ) ) @ ( groups342789780944988191at_rat @ F @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un
% 6.94/7.30 thf(fact_8996_sum__Un,axiom,
% 6.94/7.30 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > int] :
% 6.94/7.30 ( ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.30 => ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.30 => ( ( groups975429370522433651at_int @ F @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_int @ ( plus_plus_int @ ( groups975429370522433651at_int @ F @ A4 ) @ ( groups975429370522433651at_int @ F @ B5 ) ) @ ( groups975429370522433651at_int @ F @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un
% 6.94/7.30 thf(fact_8997_sum__Un,axiom,
% 6.94/7.30 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,F: produc4166570645942440679at_nat > rat] :
% 6.94/7.30 ( ( finite1918287321285529104at_nat @ A4 )
% 6.94/7.30 => ( ( finite1918287321285529104at_nat @ B5 )
% 6.94/7.30 => ( ( groups6424767709179651461at_rat @ F @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_rat @ ( plus_plus_rat @ ( groups6424767709179651461at_rat @ F @ A4 ) @ ( groups6424767709179651461at_rat @ F @ B5 ) ) @ ( groups6424767709179651461at_rat @ F @ ( inf_in1697001100524423349at_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un
% 6.94/7.30 thf(fact_8998_sum__Un,axiom,
% 6.94/7.30 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > rat] :
% 6.94/7.30 ( ( finite4343798906461161616at_nat @ A4 )
% 6.94/7.30 => ( ( finite4343798906461161616at_nat @ B5 )
% 6.94/7.30 => ( ( groups3225780264831618053at_rat @ F @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_rat @ ( plus_plus_rat @ ( groups3225780264831618053at_rat @ F @ A4 ) @ ( groups3225780264831618053at_rat @ F @ B5 ) ) @ ( groups3225780264831618053at_rat @ F @ ( inf_in7913087082777306421at_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un
% 6.94/7.30 thf(fact_8999_sum_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ( inf_in1364745209274528805nteger @ A4 @ B5 )
% 6.94/7.30 = bot_bo3990330152332043303nteger )
% 6.94/7.30 => ( ( groups6602215022474089585er_rat @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ A4 ) @ ( groups6602215022474089585er_rat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_disjoint
% 6.94/7.30 thf(fact_9000_sum_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ( inf_in1364745209274528805nteger @ A4 @ B5 )
% 6.94/7.30 = bot_bo3990330152332043303nteger )
% 6.94/7.30 => ( ( groups7237345082560585321er_nat @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ A4 ) @ ( groups7237345082560585321er_nat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_disjoint
% 6.94/7.30 thf(fact_9001_sum_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ( inf_in1364745209274528805nteger @ A4 @ B5 )
% 6.94/7.30 = bot_bo3990330152332043303nteger )
% 6.94/7.30 => ( ( groups7234854612051535045er_int @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ A4 ) @ ( groups7234854612051535045er_int @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_disjoint
% 6.94/7.30 thf(fact_9002_sum_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_o,B5: set_o,G: $o > rat] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ( inf_inf_set_o @ A4 @ B5 )
% 6.94/7.30 = bot_bot_set_o )
% 6.94/7.30 => ( ( groups7872700643590313910_o_rat @ G @ ( sup_sup_set_o @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( groups7872700643590313910_o_rat @ G @ A4 ) @ ( groups7872700643590313910_o_rat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_disjoint
% 6.94/7.30 thf(fact_9003_sum_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_o,B5: set_o,G: $o > nat] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ( inf_inf_set_o @ A4 @ B5 )
% 6.94/7.30 = bot_bot_set_o )
% 6.94/7.30 => ( ( groups8507830703676809646_o_nat @ G @ ( sup_sup_set_o @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_nat @ ( groups8507830703676809646_o_nat @ G @ A4 ) @ ( groups8507830703676809646_o_nat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_disjoint
% 6.94/7.30 thf(fact_9004_sum_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_o,B5: set_o,G: $o > int] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ( inf_inf_set_o @ A4 @ B5 )
% 6.94/7.30 = bot_bot_set_o )
% 6.94/7.30 => ( ( groups8505340233167759370_o_int @ G @ ( sup_sup_set_o @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_int @ ( groups8505340233167759370_o_int @ G @ A4 ) @ ( groups8505340233167759370_o_int @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_disjoint
% 6.94/7.30 thf(fact_9005_sum_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( ( inf_inf_set_nat @ A4 @ B5 )
% 6.94/7.30 = bot_bot_set_nat )
% 6.94/7.30 => ( ( groups2906978787729119204at_rat @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ A4 ) @ ( groups2906978787729119204at_rat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_disjoint
% 6.94/7.30 thf(fact_9006_sum_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > int] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( ( inf_inf_set_nat @ A4 @ B5 )
% 6.94/7.30 = bot_bot_set_nat )
% 6.94/7.30 => ( ( groups3539618377306564664at_int @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ A4 ) @ ( groups3539618377306564664at_int @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_disjoint
% 6.94/7.30 thf(fact_9007_sum_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( ( inf_inf_set_int @ A4 @ B5 )
% 6.94/7.30 = bot_bot_set_int )
% 6.94/7.30 => ( ( groups3906332499630173760nt_rat @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ A4 ) @ ( groups3906332499630173760nt_rat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_disjoint
% 6.94/7.30 thf(fact_9008_sum_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > nat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( ( inf_inf_set_int @ A4 @ B5 )
% 6.94/7.30 = bot_bot_set_int )
% 6.94/7.30 => ( ( groups4541462559716669496nt_nat @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ A4 ) @ ( groups4541462559716669496nt_nat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_disjoint
% 6.94/7.30 thf(fact_9009_prod_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > code_integer] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ( groups3827104343326376752nteger @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G @ A4 ) @ ( groups3827104343326376752nteger @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter_neutral
% 6.94/7.30 thf(fact_9010_prod_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ( groups3674199335183972705nteger @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( times_3573771949741848930nteger @ ( groups3674199335183972705nteger @ G @ A4 ) @ ( groups3674199335183972705nteger @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter_neutral
% 6.94/7.30 thf(fact_9011_prod_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > code_integer] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_Code_integer ) )
% 6.94/7.30 => ( ( groups3455450783089532116nteger @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ A4 ) @ ( groups3455450783089532116nteger @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter_neutral
% 6.94/7.30 thf(fact_9012_prod_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > assn] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ( groups7882442080178216443t_assn @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_assn @ ( groups7882442080178216443t_assn @ G @ A4 ) @ ( groups7882442080178216443t_assn @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter_neutral
% 6.94/7.30 thf(fact_9013_prod_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > assn] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ( groups1304777262505850412r_assn @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ A4 ) @ ( groups1304777262505850412r_assn @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter_neutral
% 6.94/7.30 thf(fact_9014_prod_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > assn] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_assn ) )
% 6.94/7.30 => ( ( groups6906906614972039071t_assn @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ A4 ) @ ( groups6906906614972039071t_assn @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter_neutral
% 6.94/7.30 thf(fact_9015_prod_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ( groups1072433553688619179nt_rat @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ A4 ) @ ( groups1072433553688619179nt_rat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter_neutral
% 6.94/7.30 thf(fact_9016_prod_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ( groups2555765274223993564er_rat @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ A4 ) @ ( groups2555765274223993564er_rat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter_neutral
% 6.94/7.30 thf(fact_9017_prod_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_rat ) )
% 6.94/7.30 => ( ( groups73079841787564623at_rat @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ A4 ) @ ( groups73079841787564623at_rat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter_neutral
% 6.94/7.30 thf(fact_9018_prod_Ounion__inter__neutral,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > nat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.94/7.30 => ( ( G @ X3 )
% 6.94/7.30 = one_one_nat ) )
% 6.94/7.30 => ( ( groups1707563613775114915nt_nat @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ A4 ) @ ( groups1707563613775114915nt_nat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_inter_neutral
% 6.94/7.30 thf(fact_9019_prod_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > assn] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ( inf_in1364745209274528805nteger @ A4 @ B5 )
% 6.94/7.30 = bot_bo3990330152332043303nteger )
% 6.94/7.30 => ( ( groups1304777262505850412r_assn @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ A4 ) @ ( groups1304777262505850412r_assn @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_disjoint
% 6.94/7.30 thf(fact_9020_prod_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_o,B5: set_o,G: $o > assn] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ( inf_inf_set_o @ A4 @ B5 )
% 6.94/7.30 = bot_bot_set_o )
% 6.94/7.30 => ( ( groups5301882518646026715o_assn @ G @ ( sup_sup_set_o @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_assn @ ( groups5301882518646026715o_assn @ G @ A4 ) @ ( groups5301882518646026715o_assn @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_disjoint
% 6.94/7.30 thf(fact_9021_prod_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > assn] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( ( inf_inf_set_nat @ A4 @ B5 )
% 6.94/7.30 = bot_bot_set_nat )
% 6.94/7.30 => ( ( groups6906906614972039071t_assn @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ A4 ) @ ( groups6906906614972039071t_assn @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_disjoint
% 6.94/7.30 thf(fact_9022_prod_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > assn] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( ( inf_inf_set_int @ A4 @ B5 )
% 6.94/7.30 = bot_bot_set_int )
% 6.94/7.30 => ( ( groups7882442080178216443t_assn @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_assn @ ( groups7882442080178216443t_assn @ G @ A4 ) @ ( groups7882442080178216443t_assn @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_disjoint
% 6.94/7.30 thf(fact_9023_prod_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ( inf_in1364745209274528805nteger @ A4 @ B5 )
% 6.94/7.30 = bot_bo3990330152332043303nteger )
% 6.94/7.30 => ( ( groups2555765274223993564er_rat @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ A4 ) @ ( groups2555765274223993564er_rat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_disjoint
% 6.94/7.30 thf(fact_9024_prod_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_o,B5: set_o,G: $o > rat] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ( inf_inf_set_o @ A4 @ B5 )
% 6.94/7.30 = bot_bot_set_o )
% 6.94/7.30 => ( ( groups2869687844427037835_o_rat @ G @ ( sup_sup_set_o @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_rat @ ( groups2869687844427037835_o_rat @ G @ A4 ) @ ( groups2869687844427037835_o_rat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_disjoint
% 6.94/7.30 thf(fact_9025_prod_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( ( inf_inf_set_nat @ A4 @ B5 )
% 6.94/7.30 = bot_bot_set_nat )
% 6.94/7.30 => ( ( groups73079841787564623at_rat @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ A4 ) @ ( groups73079841787564623at_rat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_disjoint
% 6.94/7.30 thf(fact_9026_prod_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( ( inf_inf_set_int @ A4 @ B5 )
% 6.94/7.30 = bot_bot_set_int )
% 6.94/7.30 => ( ( groups1072433553688619179nt_rat @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ A4 ) @ ( groups1072433553688619179nt_rat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_disjoint
% 6.94/7.30 thf(fact_9027_prod_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ( inf_in1364745209274528805nteger @ A4 @ B5 )
% 6.94/7.30 = bot_bo3990330152332043303nteger )
% 6.94/7.30 => ( ( groups3190895334310489300er_nat @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_nat @ ( groups3190895334310489300er_nat @ G @ A4 ) @ ( groups3190895334310489300er_nat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_disjoint
% 6.94/7.30 thf(fact_9028_prod_Ounion__disjoint,axiom,
% 6.94/7.30 ! [A4: set_o,B5: set_o,G: $o > nat] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ( inf_inf_set_o @ A4 @ B5 )
% 6.94/7.30 = bot_bot_set_o )
% 6.94/7.30 => ( ( groups3504817904513533571_o_nat @ G @ ( sup_sup_set_o @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_nat @ ( groups3504817904513533571_o_nat @ G @ A4 ) @ ( groups3504817904513533571_o_nat @ G @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_disjoint
% 6.94/7.30 thf(fact_9029_sum_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( groups3906332499630173760nt_rat @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups3906332499630173760nt_rat @ G @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_diff2
% 6.94/7.30 thf(fact_9030_sum_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( groups6602215022474089585er_rat @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ B5 @ A4 ) ) ) @ ( groups6602215022474089585er_rat @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_diff2
% 6.94/7.30 thf(fact_9031_sum_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > nat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( groups4541462559716669496nt_nat @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups4541462559716669496nt_nat @ G @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_diff2
% 6.94/7.30 thf(fact_9032_sum_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( groups7237345082560585321er_nat @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ B5 @ A4 ) ) ) @ ( groups7237345082560585321er_nat @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_diff2
% 6.94/7.30 thf(fact_9033_sum_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( groups7234854612051535045er_int @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_int @ ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ B5 @ A4 ) ) ) @ ( groups7234854612051535045er_int @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_diff2
% 6.94/7.30 thf(fact_9034_sum_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( groups2906978787729119204at_rat @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups2906978787729119204at_rat @ G @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_diff2
% 6.94/7.30 thf(fact_9035_sum_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > int] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( groups3539618377306564664at_int @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_int @ ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups3539618377306564664at_int @ G @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_diff2
% 6.94/7.30 thf(fact_9036_sum_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > nat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( groups3542108847815614940at_nat @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups3542108847815614940at_nat @ G @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups3542108847815614940at_nat @ G @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_diff2
% 6.94/7.30 thf(fact_9037_sum_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > int] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( groups4538972089207619220nt_int @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_int @ ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups4538972089207619220nt_int @ G @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_diff2
% 6.94/7.30 thf(fact_9038_sum_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > rat] :
% 6.94/7.30 ( ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.30 => ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.30 => ( ( groups342789780944988191at_rat @ G @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups342789780944988191at_rat @ G @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) @ ( groups342789780944988191at_rat @ G @ ( minus_1356011639430497352at_nat @ B5 @ A4 ) ) ) @ ( groups342789780944988191at_rat @ G @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.union_diff2
% 6.94/7.30 thf(fact_9039_sum__Un2,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,F: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 => ( ( groups3906332499630173760nt_rat @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups3906332499630173760nt_rat @ F @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un2
% 6.94/7.30 thf(fact_9040_sum__Un2,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,F: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 => ( ( groups6602215022474089585er_rat @ F @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups6602215022474089585er_rat @ F @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups6602215022474089585er_rat @ F @ ( minus_2355218937544613996nteger @ B5 @ A4 ) ) ) @ ( groups6602215022474089585er_rat @ F @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un2
% 6.94/7.30 thf(fact_9041_sum__Un2,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,F: int > nat] :
% 6.94/7.30 ( ( finite_finite_int @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 => ( ( groups4541462559716669496nt_nat @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups4541462559716669496nt_nat @ F @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un2
% 6.94/7.30 thf(fact_9042_sum__Un2,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,F: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 => ( ( groups7237345082560585321er_nat @ F @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups7237345082560585321er_nat @ F @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups7237345082560585321er_nat @ F @ ( minus_2355218937544613996nteger @ B5 @ A4 ) ) ) @ ( groups7237345082560585321er_nat @ F @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un2
% 6.94/7.30 thf(fact_9043_sum__Un2,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,F: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 => ( ( groups7234854612051535045er_int @ F @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_int @ ( plus_plus_int @ ( groups7234854612051535045er_int @ F @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups7234854612051535045er_int @ F @ ( minus_2355218937544613996nteger @ B5 @ A4 ) ) ) @ ( groups7234854612051535045er_int @ F @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un2
% 6.94/7.30 thf(fact_9044_sum__Un2,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,F: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 => ( ( groups2906978787729119204at_rat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups2906978787729119204at_rat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un2
% 6.94/7.30 thf(fact_9045_sum__Un2,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,F: nat > int] :
% 6.94/7.30 ( ( finite_finite_nat @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 => ( ( groups3539618377306564664at_int @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_int @ ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups3539618377306564664at_int @ F @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un2
% 6.94/7.30 thf(fact_9046_sum__Un2,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,F: nat > nat] :
% 6.94/7.30 ( ( finite_finite_nat @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 => ( ( groups3542108847815614940at_nat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups3542108847815614940at_nat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un2
% 6.94/7.30 thf(fact_9047_sum__Un2,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,F: int > int] :
% 6.94/7.30 ( ( finite_finite_int @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 => ( ( groups4538972089207619220nt_int @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_int @ ( plus_plus_int @ ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups4538972089207619220nt_int @ F @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un2
% 6.94/7.30 thf(fact_9048_sum__Un2,axiom,
% 6.94/7.30 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > rat] :
% 6.94/7.30 ( ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) )
% 6.94/7.30 => ( ( groups342789780944988191at_rat @ F @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups342789780944988191at_rat @ F @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) @ ( groups342789780944988191at_rat @ F @ ( minus_1356011639430497352at_nat @ B5 @ A4 ) ) ) @ ( groups342789780944988191at_rat @ F @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un2
% 6.94/7.30 thf(fact_9049_prod_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > assn] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( groups7882442080178216443t_assn @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_assn @ ( times_times_assn @ ( groups7882442080178216443t_assn @ G @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups7882442080178216443t_assn @ G @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups7882442080178216443t_assn @ G @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_diff2
% 6.94/7.30 thf(fact_9050_prod_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > assn] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( groups1304777262505850412r_assn @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_assn @ ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ B5 @ A4 ) ) ) @ ( groups1304777262505850412r_assn @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_diff2
% 6.94/7.30 thf(fact_9051_prod_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > assn] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( groups6906906614972039071t_assn @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_assn @ ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups6906906614972039071t_assn @ G @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups6906906614972039071t_assn @ G @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_diff2
% 6.94/7.30 thf(fact_9052_prod_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( groups1072433553688619179nt_rat @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_rat @ ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups1072433553688619179nt_rat @ G @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_diff2
% 6.94/7.30 thf(fact_9053_prod_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( groups2555765274223993564er_rat @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_rat @ ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ B5 @ A4 ) ) ) @ ( groups2555765274223993564er_rat @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_diff2
% 6.94/7.30 thf(fact_9054_prod_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( groups73079841787564623at_rat @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_rat @ ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups73079841787564623at_rat @ G @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_diff2
% 6.94/7.30 thf(fact_9055_prod_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,G: int > nat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( groups1707563613775114915nt_nat @ G @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_nat @ ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups1707563613775114915nt_nat @ G @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_diff2
% 6.94/7.30 thf(fact_9056_prod_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( groups3190895334310489300er_nat @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_nat @ ( times_times_nat @ ( groups3190895334310489300er_nat @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups3190895334310489300er_nat @ G @ ( minus_2355218937544613996nteger @ B5 @ A4 ) ) ) @ ( groups3190895334310489300er_nat @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_diff2
% 6.94/7.30 thf(fact_9057_prod_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,G: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( groups3188404863801439024er_int @ G @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_int @ ( times_times_int @ ( groups3188404863801439024er_int @ G @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( groups3188404863801439024er_int @ G @ ( minus_2355218937544613996nteger @ B5 @ A4 ) ) ) @ ( groups3188404863801439024er_int @ G @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_diff2
% 6.94/7.30 thf(fact_9058_prod_Ounion__diff2,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,G: nat > nat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( groups708209901874060359at_nat @ G @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( times_times_nat @ ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups708209901874060359at_nat @ G @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups708209901874060359at_nat @ G @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.union_diff2
% 6.94/7.30 thf(fact_9059_sum__Un__nat,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,F: int > nat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( groups4541462559716669496nt_nat @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ F @ B5 ) ) @ ( groups4541462559716669496nt_nat @ F @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un_nat
% 6.94/7.30 thf(fact_9060_sum__Un__nat,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,F: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( groups7237345082560585321er_nat @ F @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups7237345082560585321er_nat @ F @ A4 ) @ ( groups7237345082560585321er_nat @ F @ B5 ) ) @ ( groups7237345082560585321er_nat @ F @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un_nat
% 6.94/7.30 thf(fact_9061_sum__Un__nat,axiom,
% 6.94/7.30 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 6.94/7.30 ( ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.30 => ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.30 => ( ( groups977919841031483927at_nat @ F @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups977919841031483927at_nat @ F @ A4 ) @ ( groups977919841031483927at_nat @ F @ B5 ) ) @ ( groups977919841031483927at_nat @ F @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un_nat
% 6.94/7.30 thf(fact_9062_sum__Un__nat,axiom,
% 6.94/7.30 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,F: produc4166570645942440679at_nat > nat] :
% 6.94/7.30 ( ( finite1918287321285529104at_nat @ A4 )
% 6.94/7.30 => ( ( finite1918287321285529104at_nat @ B5 )
% 6.94/7.30 => ( ( groups7059897769266147197at_nat @ F @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups7059897769266147197at_nat @ F @ A4 ) @ ( groups7059897769266147197at_nat @ F @ B5 ) ) @ ( groups7059897769266147197at_nat @ F @ ( inf_in1697001100524423349at_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un_nat
% 6.94/7.30 thf(fact_9063_sum__Un__nat,axiom,
% 6.94/7.30 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > nat] :
% 6.94/7.30 ( ( finite4343798906461161616at_nat @ A4 )
% 6.94/7.30 => ( ( finite4343798906461161616at_nat @ B5 )
% 6.94/7.30 => ( ( groups3860910324918113789at_nat @ F @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups3860910324918113789at_nat @ F @ A4 ) @ ( groups3860910324918113789at_nat @ F @ B5 ) ) @ ( groups3860910324918113789at_nat @ F @ ( inf_in7913087082777306421at_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un_nat
% 6.94/7.30 thf(fact_9064_sum__Un__nat,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,F: nat > nat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( groups3542108847815614940at_nat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( groups3542108847815614940at_nat @ F @ B5 ) ) @ ( groups3542108847815614940at_nat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_Un_nat
% 6.94/7.30 thf(fact_9065_sum_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_Code_integer,A: code_integer,B: code_integer > rat,C2: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ S )
% 6.94/7.30 => ( ( ( member_Code_integer @ A @ S )
% 6.94/7.30 => ( ( groups6602215022474089585er_rat
% 6.94/7.30 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( plus_plus_rat @ ( B @ A ) @ ( groups6602215022474089585er_rat @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_Code_integer @ A @ S )
% 6.94/7.30 => ( ( groups6602215022474089585er_rat
% 6.94/7.30 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups6602215022474089585er_rat @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.delta_remove
% 6.94/7.30 thf(fact_9066_sum_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_Code_integer,A: code_integer,B: code_integer > nat,C2: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ S )
% 6.94/7.30 => ( ( ( member_Code_integer @ A @ S )
% 6.94/7.30 => ( ( groups7237345082560585321er_nat
% 6.94/7.30 @ ^ [K3: code_integer] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( plus_plus_nat @ ( B @ A ) @ ( groups7237345082560585321er_nat @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_Code_integer @ A @ S )
% 6.94/7.30 => ( ( groups7237345082560585321er_nat
% 6.94/7.30 @ ^ [K3: code_integer] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups7237345082560585321er_nat @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.delta_remove
% 6.94/7.30 thf(fact_9067_sum_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_Code_integer,A: code_integer,B: code_integer > int,C2: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ S )
% 6.94/7.30 => ( ( ( member_Code_integer @ A @ S )
% 6.94/7.30 => ( ( groups7234854612051535045er_int
% 6.94/7.30 @ ^ [K3: code_integer] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( plus_plus_int @ ( B @ A ) @ ( groups7234854612051535045er_int @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_Code_integer @ A @ S )
% 6.94/7.30 => ( ( groups7234854612051535045er_int
% 6.94/7.30 @ ^ [K3: code_integer] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups7234854612051535045er_int @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.delta_remove
% 6.94/7.30 thf(fact_9068_sum_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_o,A: $o,B: $o > rat,C2: $o > rat] :
% 6.94/7.30 ( ( finite_finite_o @ S )
% 6.94/7.30 => ( ( ( member_o @ A @ S )
% 6.94/7.30 => ( ( groups7872700643590313910_o_rat
% 6.94/7.30 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( plus_plus_rat @ ( B @ A ) @ ( groups7872700643590313910_o_rat @ C2 @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_o @ A @ S )
% 6.94/7.30 => ( ( groups7872700643590313910_o_rat
% 6.94/7.30 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups7872700643590313910_o_rat @ C2 @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.delta_remove
% 6.94/7.30 thf(fact_9069_sum_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_o,A: $o,B: $o > nat,C2: $o > nat] :
% 6.94/7.30 ( ( finite_finite_o @ S )
% 6.94/7.30 => ( ( ( member_o @ A @ S )
% 6.94/7.30 => ( ( groups8507830703676809646_o_nat
% 6.94/7.30 @ ^ [K3: $o] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( plus_plus_nat @ ( B @ A ) @ ( groups8507830703676809646_o_nat @ C2 @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_o @ A @ S )
% 6.94/7.30 => ( ( groups8507830703676809646_o_nat
% 6.94/7.30 @ ^ [K3: $o] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups8507830703676809646_o_nat @ C2 @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.delta_remove
% 6.94/7.30 thf(fact_9070_sum_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_o,A: $o,B: $o > int,C2: $o > int] :
% 6.94/7.30 ( ( finite_finite_o @ S )
% 6.94/7.30 => ( ( ( member_o @ A @ S )
% 6.94/7.30 => ( ( groups8505340233167759370_o_int
% 6.94/7.30 @ ^ [K3: $o] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( plus_plus_int @ ( B @ A ) @ ( groups8505340233167759370_o_int @ C2 @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_o @ A @ S )
% 6.94/7.30 => ( ( groups8505340233167759370_o_int
% 6.94/7.30 @ ^ [K3: $o] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups8505340233167759370_o_int @ C2 @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.delta_remove
% 6.94/7.30 thf(fact_9071_sum_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_nat,A: nat,B: nat > rat,C2: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ S )
% 6.94/7.30 => ( ( ( member_nat @ A @ S )
% 6.94/7.30 => ( ( groups2906978787729119204at_rat
% 6.94/7.30 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( plus_plus_rat @ ( B @ A ) @ ( groups2906978787729119204at_rat @ C2 @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_nat @ A @ S )
% 6.94/7.30 => ( ( groups2906978787729119204at_rat
% 6.94/7.30 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups2906978787729119204at_rat @ C2 @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.delta_remove
% 6.94/7.30 thf(fact_9072_sum_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_nat,A: nat,B: nat > int,C2: nat > int] :
% 6.94/7.30 ( ( finite_finite_nat @ S )
% 6.94/7.30 => ( ( ( member_nat @ A @ S )
% 6.94/7.30 => ( ( groups3539618377306564664at_int
% 6.94/7.30 @ ^ [K3: nat] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( plus_plus_int @ ( B @ A ) @ ( groups3539618377306564664at_int @ C2 @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_nat @ A @ S )
% 6.94/7.30 => ( ( groups3539618377306564664at_int
% 6.94/7.30 @ ^ [K3: nat] : ( if_int @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups3539618377306564664at_int @ C2 @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.delta_remove
% 6.94/7.30 thf(fact_9073_sum_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_int,A: int,B: int > rat,C2: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ S )
% 6.94/7.30 => ( ( ( member_int @ A @ S )
% 6.94/7.30 => ( ( groups3906332499630173760nt_rat
% 6.94/7.30 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( plus_plus_rat @ ( B @ A ) @ ( groups3906332499630173760nt_rat @ C2 @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_int @ A @ S )
% 6.94/7.30 => ( ( groups3906332499630173760nt_rat
% 6.94/7.30 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups3906332499630173760nt_rat @ C2 @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.delta_remove
% 6.94/7.30 thf(fact_9074_sum_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_int,A: int,B: int > nat,C2: int > nat] :
% 6.94/7.30 ( ( finite_finite_int @ S )
% 6.94/7.30 => ( ( ( member_int @ A @ S )
% 6.94/7.30 => ( ( groups4541462559716669496nt_nat
% 6.94/7.30 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( plus_plus_nat @ ( B @ A ) @ ( groups4541462559716669496nt_nat @ C2 @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_int @ A @ S )
% 6.94/7.30 => ( ( groups4541462559716669496nt_nat
% 6.94/7.30 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups4541462559716669496nt_nat @ C2 @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum.delta_remove
% 6.94/7.30 thf(fact_9075_sum__div__partition,axiom,
% 6.94/7.30 ! [A4: set_int,F: int > nat,B: nat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( divide_divide_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ B )
% 6.94/7.30 = ( plus_plus_nat
% 6.94/7.30 @ ( groups4541462559716669496nt_nat
% 6.94/7.30 @ ^ [A5: int] : ( divide_divide_nat @ ( F @ A5 ) @ B )
% 6.94/7.30 @ ( inf_inf_set_int @ A4
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [A5: int] : ( dvd_dvd_nat @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ ( divide_divide_nat
% 6.94/7.30 @ ( groups4541462559716669496nt_nat @ F
% 6.94/7.30 @ ( inf_inf_set_int @ A4
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [A5: int] :
% 6.94/7.30 ~ ( dvd_dvd_nat @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ B ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_div_partition
% 6.94/7.30 thf(fact_9076_sum__div__partition,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,F: code_integer > nat,B: nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( divide_divide_nat @ ( groups7237345082560585321er_nat @ F @ A4 ) @ B )
% 6.94/7.30 = ( plus_plus_nat
% 6.94/7.30 @ ( groups7237345082560585321er_nat
% 6.94/7.30 @ ^ [A5: code_integer] : ( divide_divide_nat @ ( F @ A5 ) @ B )
% 6.94/7.30 @ ( inf_in1364745209274528805nteger @ A4
% 6.94/7.30 @ ( collect_Code_integer
% 6.94/7.30 @ ^ [A5: code_integer] : ( dvd_dvd_nat @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ ( divide_divide_nat
% 6.94/7.30 @ ( groups7237345082560585321er_nat @ F
% 6.94/7.30 @ ( inf_in1364745209274528805nteger @ A4
% 6.94/7.30 @ ( collect_Code_integer
% 6.94/7.30 @ ^ [A5: code_integer] :
% 6.94/7.30 ~ ( dvd_dvd_nat @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ B ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_div_partition
% 6.94/7.30 thf(fact_9077_sum__div__partition,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,F: code_integer > int,B: int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( divide_divide_int @ ( groups7234854612051535045er_int @ F @ A4 ) @ B )
% 6.94/7.30 = ( plus_plus_int
% 6.94/7.30 @ ( groups7234854612051535045er_int
% 6.94/7.30 @ ^ [A5: code_integer] : ( divide_divide_int @ ( F @ A5 ) @ B )
% 6.94/7.30 @ ( inf_in1364745209274528805nteger @ A4
% 6.94/7.30 @ ( collect_Code_integer
% 6.94/7.30 @ ^ [A5: code_integer] : ( dvd_dvd_int @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ ( divide_divide_int
% 6.94/7.30 @ ( groups7234854612051535045er_int @ F
% 6.94/7.30 @ ( inf_in1364745209274528805nteger @ A4
% 6.94/7.30 @ ( collect_Code_integer
% 6.94/7.30 @ ^ [A5: code_integer] :
% 6.94/7.30 ~ ( dvd_dvd_int @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ B ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_div_partition
% 6.94/7.30 thf(fact_9078_sum__div__partition,axiom,
% 6.94/7.30 ! [A4: set_nat,F: nat > int,B: int] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( divide_divide_int @ ( groups3539618377306564664at_int @ F @ A4 ) @ B )
% 6.94/7.30 = ( plus_plus_int
% 6.94/7.30 @ ( groups3539618377306564664at_int
% 6.94/7.30 @ ^ [A5: nat] : ( divide_divide_int @ ( F @ A5 ) @ B )
% 6.94/7.30 @ ( inf_inf_set_nat @ A4
% 6.94/7.30 @ ( collect_nat
% 6.94/7.30 @ ^ [A5: nat] : ( dvd_dvd_int @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ ( divide_divide_int
% 6.94/7.30 @ ( groups3539618377306564664at_int @ F
% 6.94/7.30 @ ( inf_inf_set_nat @ A4
% 6.94/7.30 @ ( collect_nat
% 6.94/7.30 @ ^ [A5: nat] :
% 6.94/7.30 ~ ( dvd_dvd_int @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ B ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_div_partition
% 6.94/7.30 thf(fact_9079_sum__div__partition,axiom,
% 6.94/7.30 ! [A4: set_int,F: int > code_natural,B: code_natural] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( divide5121882707175180666atural @ ( groups6697149243333190288atural @ F @ A4 ) @ B )
% 6.94/7.30 = ( plus_p4538020629002901425atural
% 6.94/7.30 @ ( groups6697149243333190288atural
% 6.94/7.30 @ ^ [A5: int] : ( divide5121882707175180666atural @ ( F @ A5 ) @ B )
% 6.94/7.30 @ ( inf_inf_set_int @ A4
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [A5: int] : ( dvd_dvd_Code_natural @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ ( divide5121882707175180666atural
% 6.94/7.30 @ ( groups6697149243333190288atural @ F
% 6.94/7.30 @ ( inf_inf_set_int @ A4
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [A5: int] :
% 6.94/7.30 ~ ( dvd_dvd_Code_natural @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ B ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_div_partition
% 6.94/7.30 thf(fact_9080_sum__div__partition,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,F: code_integer > code_natural,B: code_natural] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( divide5121882707175180666atural @ ( groups8926444216418632897atural @ F @ A4 ) @ B )
% 6.94/7.30 = ( plus_p4538020629002901425atural
% 6.94/7.30 @ ( groups8926444216418632897atural
% 6.94/7.30 @ ^ [A5: code_integer] : ( divide5121882707175180666atural @ ( F @ A5 ) @ B )
% 6.94/7.30 @ ( inf_in1364745209274528805nteger @ A4
% 6.94/7.30 @ ( collect_Code_integer
% 6.94/7.30 @ ^ [A5: code_integer] : ( dvd_dvd_Code_natural @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ ( divide5121882707175180666atural
% 6.94/7.30 @ ( groups8926444216418632897atural @ F
% 6.94/7.30 @ ( inf_in1364745209274528805nteger @ A4
% 6.94/7.30 @ ( collect_Code_integer
% 6.94/7.30 @ ^ [A5: code_integer] :
% 6.94/7.30 ~ ( dvd_dvd_Code_natural @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ B ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_div_partition
% 6.94/7.30 thf(fact_9081_sum__div__partition,axiom,
% 6.94/7.30 ! [A4: set_nat,F: nat > code_natural,B: code_natural] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( divide5121882707175180666atural @ ( groups6325495683096345652atural @ F @ A4 ) @ B )
% 6.94/7.30 = ( plus_p4538020629002901425atural
% 6.94/7.30 @ ( groups6325495683096345652atural
% 6.94/7.30 @ ^ [A5: nat] : ( divide5121882707175180666atural @ ( F @ A5 ) @ B )
% 6.94/7.30 @ ( inf_inf_set_nat @ A4
% 6.94/7.30 @ ( collect_nat
% 6.94/7.30 @ ^ [A5: nat] : ( dvd_dvd_Code_natural @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ ( divide5121882707175180666atural
% 6.94/7.30 @ ( groups6325495683096345652atural @ F
% 6.94/7.30 @ ( inf_inf_set_nat @ A4
% 6.94/7.30 @ ( collect_nat
% 6.94/7.30 @ ^ [A5: nat] :
% 6.94/7.30 ~ ( dvd_dvd_Code_natural @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ B ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_div_partition
% 6.94/7.30 thf(fact_9082_sum__div__partition,axiom,
% 6.94/7.30 ! [A4: set_nat,F: nat > nat,B: nat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( divide_divide_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ B )
% 6.94/7.30 = ( plus_plus_nat
% 6.94/7.30 @ ( groups3542108847815614940at_nat
% 6.94/7.30 @ ^ [A5: nat] : ( divide_divide_nat @ ( F @ A5 ) @ B )
% 6.94/7.30 @ ( inf_inf_set_nat @ A4
% 6.94/7.30 @ ( collect_nat
% 6.94/7.30 @ ^ [A5: nat] : ( dvd_dvd_nat @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ ( divide_divide_nat
% 6.94/7.30 @ ( groups3542108847815614940at_nat @ F
% 6.94/7.30 @ ( inf_inf_set_nat @ A4
% 6.94/7.30 @ ( collect_nat
% 6.94/7.30 @ ^ [A5: nat] :
% 6.94/7.30 ~ ( dvd_dvd_nat @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ B ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_div_partition
% 6.94/7.30 thf(fact_9083_sum__div__partition,axiom,
% 6.94/7.30 ! [A4: set_int,F: int > int,B: int] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( divide_divide_int @ ( groups4538972089207619220nt_int @ F @ A4 ) @ B )
% 6.94/7.30 = ( plus_plus_int
% 6.94/7.30 @ ( groups4538972089207619220nt_int
% 6.94/7.30 @ ^ [A5: int] : ( divide_divide_int @ ( F @ A5 ) @ B )
% 6.94/7.30 @ ( inf_inf_set_int @ A4
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [A5: int] : ( dvd_dvd_int @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ ( divide_divide_int
% 6.94/7.30 @ ( groups4538972089207619220nt_int @ F
% 6.94/7.30 @ ( inf_inf_set_int @ A4
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [A5: int] :
% 6.94/7.30 ~ ( dvd_dvd_int @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ B ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_div_partition
% 6.94/7.30 thf(fact_9084_sum__div__partition,axiom,
% 6.94/7.30 ! [A4: set_list_nat,F: list_nat > nat,B: nat] :
% 6.94/7.30 ( ( finite8100373058378681591st_nat @ A4 )
% 6.94/7.30 => ( ( divide_divide_nat @ ( groups4396056296759096172at_nat @ F @ A4 ) @ B )
% 6.94/7.30 = ( plus_plus_nat
% 6.94/7.30 @ ( groups4396056296759096172at_nat
% 6.94/7.30 @ ^ [A5: list_nat] : ( divide_divide_nat @ ( F @ A5 ) @ B )
% 6.94/7.30 @ ( inf_inf_set_list_nat @ A4
% 6.94/7.30 @ ( collect_list_nat
% 6.94/7.30 @ ^ [A5: list_nat] : ( dvd_dvd_nat @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ ( divide_divide_nat
% 6.94/7.30 @ ( groups4396056296759096172at_nat @ F
% 6.94/7.30 @ ( inf_inf_set_list_nat @ A4
% 6.94/7.30 @ ( collect_list_nat
% 6.94/7.30 @ ^ [A5: list_nat] :
% 6.94/7.30 ~ ( dvd_dvd_nat @ B @ ( F @ A5 ) ) ) ) )
% 6.94/7.30 @ B ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_div_partition
% 6.94/7.30 thf(fact_9085_prod_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_Code_integer,A: code_integer,B: code_integer > assn,C2: code_integer > assn] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ S )
% 6.94/7.30 => ( ( ( member_Code_integer @ A @ S )
% 6.94/7.30 => ( ( groups1304777262505850412r_assn
% 6.94/7.30 @ ^ [K3: code_integer] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( times_times_assn @ ( B @ A ) @ ( groups1304777262505850412r_assn @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_Code_integer @ A @ S )
% 6.94/7.30 => ( ( groups1304777262505850412r_assn
% 6.94/7.30 @ ^ [K3: code_integer] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups1304777262505850412r_assn @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.delta_remove
% 6.94/7.30 thf(fact_9086_prod_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_o,A: $o,B: $o > assn,C2: $o > assn] :
% 6.94/7.30 ( ( finite_finite_o @ S )
% 6.94/7.30 => ( ( ( member_o @ A @ S )
% 6.94/7.30 => ( ( groups5301882518646026715o_assn
% 6.94/7.30 @ ^ [K3: $o] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( times_times_assn @ ( B @ A ) @ ( groups5301882518646026715o_assn @ C2 @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_o @ A @ S )
% 6.94/7.30 => ( ( groups5301882518646026715o_assn
% 6.94/7.30 @ ^ [K3: $o] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups5301882518646026715o_assn @ C2 @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.delta_remove
% 6.94/7.30 thf(fact_9087_prod_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_nat,A: nat,B: nat > assn,C2: nat > assn] :
% 6.94/7.30 ( ( finite_finite_nat @ S )
% 6.94/7.30 => ( ( ( member_nat @ A @ S )
% 6.94/7.30 => ( ( groups6906906614972039071t_assn
% 6.94/7.30 @ ^ [K3: nat] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( times_times_assn @ ( B @ A ) @ ( groups6906906614972039071t_assn @ C2 @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_nat @ A @ S )
% 6.94/7.30 => ( ( groups6906906614972039071t_assn
% 6.94/7.30 @ ^ [K3: nat] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups6906906614972039071t_assn @ C2 @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.delta_remove
% 6.94/7.30 thf(fact_9088_prod_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_int,A: int,B: int > assn,C2: int > assn] :
% 6.94/7.30 ( ( finite_finite_int @ S )
% 6.94/7.30 => ( ( ( member_int @ A @ S )
% 6.94/7.30 => ( ( groups7882442080178216443t_assn
% 6.94/7.30 @ ^ [K3: int] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( times_times_assn @ ( B @ A ) @ ( groups7882442080178216443t_assn @ C2 @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_int @ A @ S )
% 6.94/7.30 => ( ( groups7882442080178216443t_assn
% 6.94/7.30 @ ^ [K3: int] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups7882442080178216443t_assn @ C2 @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.delta_remove
% 6.94/7.30 thf(fact_9089_prod_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_Code_integer,A: code_integer,B: code_integer > rat,C2: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ S )
% 6.94/7.30 => ( ( ( member_Code_integer @ A @ S )
% 6.94/7.30 => ( ( groups2555765274223993564er_rat
% 6.94/7.30 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( times_times_rat @ ( B @ A ) @ ( groups2555765274223993564er_rat @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_Code_integer @ A @ S )
% 6.94/7.30 => ( ( groups2555765274223993564er_rat
% 6.94/7.30 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups2555765274223993564er_rat @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.delta_remove
% 6.94/7.30 thf(fact_9090_prod_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_o,A: $o,B: $o > rat,C2: $o > rat] :
% 6.94/7.30 ( ( finite_finite_o @ S )
% 6.94/7.30 => ( ( ( member_o @ A @ S )
% 6.94/7.30 => ( ( groups2869687844427037835_o_rat
% 6.94/7.30 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( times_times_rat @ ( B @ A ) @ ( groups2869687844427037835_o_rat @ C2 @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_o @ A @ S )
% 6.94/7.30 => ( ( groups2869687844427037835_o_rat
% 6.94/7.30 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups2869687844427037835_o_rat @ C2 @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.delta_remove
% 6.94/7.30 thf(fact_9091_prod_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_nat,A: nat,B: nat > rat,C2: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ S )
% 6.94/7.30 => ( ( ( member_nat @ A @ S )
% 6.94/7.30 => ( ( groups73079841787564623at_rat
% 6.94/7.30 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( times_times_rat @ ( B @ A ) @ ( groups73079841787564623at_rat @ C2 @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_nat @ A @ S )
% 6.94/7.30 => ( ( groups73079841787564623at_rat
% 6.94/7.30 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups73079841787564623at_rat @ C2 @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.delta_remove
% 6.94/7.30 thf(fact_9092_prod_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_int,A: int,B: int > rat,C2: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ S )
% 6.94/7.30 => ( ( ( member_int @ A @ S )
% 6.94/7.30 => ( ( groups1072433553688619179nt_rat
% 6.94/7.30 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( times_times_rat @ ( B @ A ) @ ( groups1072433553688619179nt_rat @ C2 @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_int @ A @ S )
% 6.94/7.30 => ( ( groups1072433553688619179nt_rat
% 6.94/7.30 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups1072433553688619179nt_rat @ C2 @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.delta_remove
% 6.94/7.30 thf(fact_9093_prod_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_Code_integer,A: code_integer,B: code_integer > nat,C2: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ S )
% 6.94/7.30 => ( ( ( member_Code_integer @ A @ S )
% 6.94/7.30 => ( ( groups3190895334310489300er_nat
% 6.94/7.30 @ ^ [K3: code_integer] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( times_times_nat @ ( B @ A ) @ ( groups3190895334310489300er_nat @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_Code_integer @ A @ S )
% 6.94/7.30 => ( ( groups3190895334310489300er_nat
% 6.94/7.30 @ ^ [K3: code_integer] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups3190895334310489300er_nat @ C2 @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.delta_remove
% 6.94/7.30 thf(fact_9094_prod_Odelta__remove,axiom,
% 6.94/7.30 ! [S: set_o,A: $o,B: $o > nat,C2: $o > nat] :
% 6.94/7.30 ( ( finite_finite_o @ S )
% 6.94/7.30 => ( ( ( member_o @ A @ S )
% 6.94/7.30 => ( ( groups3504817904513533571_o_nat
% 6.94/7.30 @ ^ [K3: $o] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( times_times_nat @ ( B @ A ) @ ( groups3504817904513533571_o_nat @ C2 @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 6.94/7.30 & ( ~ ( member_o @ A @ S )
% 6.94/7.30 => ( ( groups3504817904513533571_o_nat
% 6.94/7.30 @ ^ [K3: $o] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 6.94/7.30 @ S )
% 6.94/7.30 = ( groups3504817904513533571_o_nat @ C2 @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod.delta_remove
% 6.94/7.30 thf(fact_9095_effect__of__listI,axiom,
% 6.94/7.30 ! [A: array_nat,H5: heap_e7401611519738050253t_unit,Xs: list_nat,H: heap_e7401611519738050253t_unit] :
% 6.94/7.30 ( ( ( produc1210945592254923927t_unit @ A @ H5 )
% 6.94/7.30 = ( array_alloc_nat @ Xs @ H ) )
% 6.94/7.30 => ( heap_T1188250621483087889ay_nat @ ( array_of_list_nat @ Xs ) @ H @ H5 @ A @ ( plus_plus_nat @ one_one_nat @ ( size_size_list_nat @ Xs ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % effect_of_listI
% 6.94/7.30 thf(fact_9096_effect__of__listI,axiom,
% 6.94/7.30 ! [A: array_o,H5: heap_e7401611519738050253t_unit,Xs: list_o,H: heap_e7401611519738050253t_unit] :
% 6.94/7.30 ( ( ( produc3742984184817956739t_unit @ A @ H5 )
% 6.94/7.30 = ( array_alloc_o @ Xs @ H ) )
% 6.94/7.30 => ( heap_T1873992626244518189rray_o @ ( array_of_list_o @ Xs ) @ H @ H5 @ A @ ( plus_plus_nat @ one_one_nat @ ( size_size_list_o @ Xs ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % effect_of_listI
% 6.94/7.30 thf(fact_9097_effect__of__listI,axiom,
% 6.94/7.30 ! [A: array_int,H5: heap_e7401611519738050253t_unit,Xs: list_int,H: heap_e7401611519738050253t_unit] :
% 6.94/7.30 ( ( ( produc2888458824036673339t_unit @ A @ H5 )
% 6.94/7.30 = ( array_alloc_int @ Xs @ H ) )
% 6.94/7.30 => ( heap_T6233771638828666989ay_int @ ( array_of_list_int @ Xs ) @ H @ H5 @ A @ ( plus_plus_nat @ one_one_nat @ ( size_size_list_int @ Xs ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % effect_of_listI
% 6.94/7.30 thf(fact_9098_sum__strict__mono2,axiom,
% 6.94/7.30 ! [B5: set_o,A4: set_o,B: $o,F: $o > code_integer] :
% 6.94/7.30 ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.94/7.30 => ( ( member_o @ B @ ( minus_minus_set_o @ B5 @ A4 ) )
% 6.94/7.30 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ B ) )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ B5 )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ord_le6747313008572928689nteger @ ( groups4406642042086082107nteger @ F @ A4 ) @ ( groups4406642042086082107nteger @ F @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_strict_mono2
% 6.94/7.30 thf(fact_9099_sum__strict__mono2,axiom,
% 6.94/7.30 ! [B5: set_nat,A4: set_nat,B: nat,F: nat > code_integer] :
% 6.94/7.30 ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.94/7.30 => ( ( member_nat @ B @ ( minus_minus_set_nat @ B5 @ A4 ) )
% 6.94/7.30 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ B ) )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ B5 )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ord_le6747313008572928689nteger @ ( groups7501900531339628137nteger @ F @ A4 ) @ ( groups7501900531339628137nteger @ F @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_strict_mono2
% 6.94/7.30 thf(fact_9100_sum__strict__mono2,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,B: code_integer,F: code_integer > code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.94/7.30 => ( ( member_Code_integer @ B @ ( minus_2355218937544613996nteger @ B5 @ A4 ) )
% 6.94/7.30 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ B ) )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ B5 )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ord_le6747313008572928689nteger @ ( groups879477027807139574nteger @ F @ A4 ) @ ( groups879477027807139574nteger @ F @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_strict_mono2
% 6.94/7.30 thf(fact_9101_sum__strict__mono2,axiom,
% 6.94/7.30 ! [B5: set_o,A4: set_o,B: $o,F: $o > rat] :
% 6.94/7.30 ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.94/7.30 => ( ( member_o @ B @ ( minus_minus_set_o @ B5 @ A4 ) )
% 6.94/7.30 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ B5 )
% 6.94/7.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ord_less_rat @ ( groups7872700643590313910_o_rat @ F @ A4 ) @ ( groups7872700643590313910_o_rat @ F @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_strict_mono2
% 6.94/7.30 thf(fact_9102_sum__strict__mono2,axiom,
% 6.94/7.30 ! [B5: set_nat,A4: set_nat,B: nat,F: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.94/7.30 => ( ( member_nat @ B @ ( minus_minus_set_nat @ B5 @ A4 ) )
% 6.94/7.30 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ B5 )
% 6.94/7.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ ( groups2906978787729119204at_rat @ F @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_strict_mono2
% 6.94/7.30 thf(fact_9103_sum__strict__mono2,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,B: code_integer,F: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.94/7.30 => ( ( member_Code_integer @ B @ ( minus_2355218937544613996nteger @ B5 @ A4 ) )
% 6.94/7.30 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ B5 )
% 6.94/7.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ord_less_rat @ ( groups6602215022474089585er_rat @ F @ A4 ) @ ( groups6602215022474089585er_rat @ F @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_strict_mono2
% 6.94/7.30 thf(fact_9104_sum__strict__mono2,axiom,
% 6.94/7.30 ! [B5: set_o,A4: set_o,B: $o,F: $o > nat] :
% 6.94/7.30 ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.94/7.30 => ( ( member_o @ B @ ( minus_minus_set_o @ B5 @ A4 ) )
% 6.94/7.30 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ B5 )
% 6.94/7.30 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ord_less_nat @ ( groups8507830703676809646_o_nat @ F @ A4 ) @ ( groups8507830703676809646_o_nat @ F @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_strict_mono2
% 6.94/7.30 thf(fact_9105_sum__strict__mono2,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,B: code_integer,F: code_integer > nat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.94/7.30 => ( ( member_Code_integer @ B @ ( minus_2355218937544613996nteger @ B5 @ A4 ) )
% 6.94/7.30 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ B5 )
% 6.94/7.30 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ord_less_nat @ ( groups7237345082560585321er_nat @ F @ A4 ) @ ( groups7237345082560585321er_nat @ F @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_strict_mono2
% 6.94/7.30 thf(fact_9106_sum__strict__mono2,axiom,
% 6.94/7.30 ! [B5: set_o,A4: set_o,B: $o,F: $o > int] :
% 6.94/7.30 ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.94/7.30 => ( ( member_o @ B @ ( minus_minus_set_o @ B5 @ A4 ) )
% 6.94/7.30 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ B5 )
% 6.94/7.30 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ord_less_int @ ( groups8505340233167759370_o_int @ F @ A4 ) @ ( groups8505340233167759370_o_int @ F @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_strict_mono2
% 6.94/7.30 thf(fact_9107_sum__strict__mono2,axiom,
% 6.94/7.30 ! [B5: set_nat,A4: set_nat,B: nat,F: nat > int] :
% 6.94/7.30 ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.94/7.30 => ( ( member_nat @ B @ ( minus_minus_set_nat @ B5 @ A4 ) )
% 6.94/7.30 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ B5 )
% 6.94/7.30 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A4 ) @ ( groups3539618377306564664at_int @ F @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % sum_strict_mono2
% 6.94/7.30 thf(fact_9108_member__le__sum,axiom,
% 6.94/7.30 ! [I2: code_integer,A4: set_Code_integer,F: code_integer > code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ I2 @ A4 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ I2 @ bot_bo3990330152332043303nteger ) ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ ( groups879477027807139574nteger @ F @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % member_le_sum
% 6.94/7.30 thf(fact_9109_member__le__sum,axiom,
% 6.94/7.30 ! [I2: $o,A4: set_o,F: $o > code_integer] :
% 6.94/7.30 ( ( member_o @ I2 @ A4 )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ ( minus_minus_set_o @ A4 @ ( insert_o @ I2 @ bot_bot_set_o ) ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ ( groups4406642042086082107nteger @ F @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % member_le_sum
% 6.94/7.30 thf(fact_9110_member__le__sum,axiom,
% 6.94/7.30 ! [I2: nat,A4: set_nat,F: nat > code_integer] :
% 6.94/7.30 ( ( member_nat @ I2 @ A4 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ ( groups7501900531339628137nteger @ F @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % member_le_sum
% 6.94/7.30 thf(fact_9111_member__le__sum,axiom,
% 6.94/7.30 ! [I2: int,A4: set_int,F: int > code_integer] :
% 6.94/7.30 ( ( member_int @ I2 @ A4 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ ( minus_minus_set_int @ A4 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ ( groups7873554091576472773nteger @ F @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % member_le_sum
% 6.94/7.30 thf(fact_9112_member__le__sum,axiom,
% 6.94/7.30 ! [I2: code_integer,A4: set_Code_integer,F: code_integer > rat] :
% 6.94/7.30 ( ( member_Code_integer @ I2 @ A4 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ I2 @ bot_bo3990330152332043303nteger ) ) )
% 6.94/7.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups6602215022474089585er_rat @ F @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % member_le_sum
% 6.94/7.30 thf(fact_9113_member__le__sum,axiom,
% 6.94/7.30 ! [I2: $o,A4: set_o,F: $o > rat] :
% 6.94/7.30 ( ( member_o @ I2 @ A4 )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ ( minus_minus_set_o @ A4 @ ( insert_o @ I2 @ bot_bot_set_o ) ) )
% 6.94/7.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups7872700643590313910_o_rat @ F @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % member_le_sum
% 6.94/7.30 thf(fact_9114_member__le__sum,axiom,
% 6.94/7.30 ! [I2: nat,A4: set_nat,F: nat > rat] :
% 6.94/7.30 ( ( member_nat @ I2 @ A4 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 6.94/7.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups2906978787729119204at_rat @ F @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % member_le_sum
% 6.94/7.30 thf(fact_9115_member__le__sum,axiom,
% 6.94/7.30 ! [I2: int,A4: set_int,F: int > rat] :
% 6.94/7.30 ( ( member_int @ I2 @ A4 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ ( minus_minus_set_int @ A4 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 6.94/7.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups3906332499630173760nt_rat @ F @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % member_le_sum
% 6.94/7.30 thf(fact_9116_member__le__sum,axiom,
% 6.94/7.30 ! [I2: code_integer,A4: set_Code_integer,F: code_integer > nat] :
% 6.94/7.30 ( ( member_Code_integer @ I2 @ A4 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ I2 @ bot_bo3990330152332043303nteger ) ) )
% 6.94/7.30 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( groups7237345082560585321er_nat @ F @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % member_le_sum
% 6.94/7.30 thf(fact_9117_member__le__sum,axiom,
% 6.94/7.30 ! [I2: $o,A4: set_o,F: $o > nat] :
% 6.94/7.30 ( ( member_o @ I2 @ A4 )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ ( minus_minus_set_o @ A4 @ ( insert_o @ I2 @ bot_bot_set_o ) ) )
% 6.94/7.30 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 6.94/7.30 => ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( groups8507830703676809646_o_nat @ F @ A4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % member_le_sum
% 6.94/7.30 thf(fact_9118_prod__mono2,axiom,
% 6.94/7.30 ! [B5: set_o,A4: set_o,F: $o > code_integer] :
% 6.94/7.30 ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ A4 )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A3 ) ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ ( groups7694694392188491536nteger @ F @ A4 ) @ ( groups7694694392188491536nteger @ F @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono2
% 6.94/7.30 thf(fact_9119_prod__mono2,axiom,
% 6.94/7.30 ! [B5: set_nat,A4: set_nat,F: nat > code_integer] :
% 6.94/7.30 ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: nat] :
% 6.94/7.30 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ! [A3: nat] :
% 6.94/7.30 ( ( member_nat @ A3 @ A4 )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A3 ) ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F @ A4 ) @ ( groups3455450783089532116nteger @ F @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono2
% 6.94/7.30 thf(fact_9120_prod__mono2,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,F: code_integer > code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ! [A3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ A3 @ A4 )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A3 ) ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ ( groups3674199335183972705nteger @ F @ A4 ) @ ( groups3674199335183972705nteger @ F @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono2
% 6.94/7.30 thf(fact_9121_prod__mono2,axiom,
% 6.94/7.30 ! [B5: set_o,A4: set_o,F: $o > rat] :
% 6.94/7.30 ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ A4 )
% 6.94/7.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 6.94/7.30 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A4 ) @ ( groups2869687844427037835_o_rat @ F @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono2
% 6.94/7.30 thf(fact_9122_prod__mono2,axiom,
% 6.94/7.30 ! [B5: set_nat,A4: set_nat,F: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: nat] :
% 6.94/7.30 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ! [A3: nat] :
% 6.94/7.30 ( ( member_nat @ A3 @ A4 )
% 6.94/7.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 6.94/7.30 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A4 ) @ ( groups73079841787564623at_rat @ F @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono2
% 6.94/7.30 thf(fact_9123_prod__mono2,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,F: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ! [A3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ A3 @ A4 )
% 6.94/7.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 6.94/7.30 => ( ord_less_eq_rat @ ( groups2555765274223993564er_rat @ F @ A4 ) @ ( groups2555765274223993564er_rat @ F @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono2
% 6.94/7.30 thf(fact_9124_prod__mono2,axiom,
% 6.94/7.30 ! [B5: set_o,A4: set_o,F: $o > int] :
% 6.94/7.30 ( ( finite_finite_o @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_o @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: $o] :
% 6.94/7.30 ( ( member_o @ B3 @ ( minus_minus_set_o @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_less_eq_int @ one_one_int @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ! [A3: $o] :
% 6.94/7.30 ( ( member_o @ A3 @ A4 )
% 6.94/7.30 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 6.94/7.30 => ( ord_less_eq_int @ ( groups3502327434004483295_o_int @ F @ A4 ) @ ( groups3502327434004483295_o_int @ F @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono2
% 6.94/7.30 thf(fact_9125_prod__mono2,axiom,
% 6.94/7.30 ! [B5: set_Code_integer,A4: set_Code_integer,F: code_integer > int] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_less_eq_int @ one_one_int @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ! [A3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ A3 @ A4 )
% 6.94/7.30 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A3 ) ) )
% 6.94/7.30 => ( ord_less_eq_int @ ( groups3188404863801439024er_int @ F @ A4 ) @ ( groups3188404863801439024er_int @ F @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono2
% 6.94/7.30 thf(fact_9126_prod__mono2,axiom,
% 6.94/7.30 ! [B5: set_int,A4: set_int,F: int > code_integer] :
% 6.94/7.30 ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: int] :
% 6.94/7.30 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ! [A3: int] :
% 6.94/7.30 ( ( member_int @ A3 @ A4 )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A3 ) ) )
% 6.94/7.30 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F @ A4 ) @ ( groups3827104343326376752nteger @ F @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono2
% 6.94/7.30 thf(fact_9127_prod__mono2,axiom,
% 6.94/7.30 ! [B5: set_int,A4: set_int,F: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.94/7.30 => ( ! [B3: int] :
% 6.94/7.30 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 6.94/7.30 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B3 ) ) )
% 6.94/7.30 => ( ! [A3: int] :
% 6.94/7.30 ( ( member_int @ A3 @ A4 )
% 6.94/7.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A3 ) ) )
% 6.94/7.30 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A4 ) @ ( groups1072433553688619179nt_rat @ F @ B5 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_mono2
% 6.94/7.30 thf(fact_9128_prod__Un,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,F: int > rat] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 6.94/7.30 => ( ( F @ X3 )
% 6.94/7.30 != zero_zero_rat ) )
% 6.94/7.30 => ( ( groups1072433553688619179nt_rat @ F @ ( sup_sup_set_int @ A4 @ B5 ) )
% 6.94/7.30 = ( divide_divide_rat @ ( times_times_rat @ ( groups1072433553688619179nt_rat @ F @ A4 ) @ ( groups1072433553688619179nt_rat @ F @ B5 ) ) @ ( groups1072433553688619179nt_rat @ F @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_Un
% 6.94/7.30 thf(fact_9129_prod__Un,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_Code_integer,F: code_integer > rat] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) )
% 6.94/7.30 => ( ( F @ X3 )
% 6.94/7.30 != zero_zero_rat ) )
% 6.94/7.30 => ( ( groups2555765274223993564er_rat @ F @ ( sup_su848401254843788991nteger @ A4 @ B5 ) )
% 6.94/7.30 = ( divide_divide_rat @ ( times_times_rat @ ( groups2555765274223993564er_rat @ F @ A4 ) @ ( groups2555765274223993564er_rat @ F @ B5 ) ) @ ( groups2555765274223993564er_rat @ F @ ( inf_in1364745209274528805nteger @ A4 @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_Un
% 6.94/7.30 thf(fact_9130_prod__Un,axiom,
% 6.94/7.30 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > rat] :
% 6.94/7.30 ( ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.30 => ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.30 => ( ! [X3: product_prod_nat_nat] :
% 6.94/7.30 ( ( member8440522571783428010at_nat @ X3 @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) )
% 6.94/7.30 => ( ( F @ X3 )
% 6.94/7.30 != zero_zero_rat ) )
% 6.94/7.30 => ( ( groups3442636767675653108at_rat @ F @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( divide_divide_rat @ ( times_times_rat @ ( groups3442636767675653108at_rat @ F @ A4 ) @ ( groups3442636767675653108at_rat @ F @ B5 ) ) @ ( groups3442636767675653108at_rat @ F @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_Un
% 6.94/7.30 thf(fact_9131_prod__Un,axiom,
% 6.94/7.30 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat,F: produc4166570645942440679at_nat > rat] :
% 6.94/7.30 ( ( finite1918287321285529104at_nat @ A4 )
% 6.94/7.30 => ( ( finite1918287321285529104at_nat @ B5 )
% 6.94/7.30 => ( ! [X3: produc4166570645942440679at_nat] :
% 6.94/7.30 ( ( member6689249552917799696at_nat @ X3 @ ( inf_in1697001100524423349at_nat @ A4 @ B5 ) )
% 6.94/7.30 => ( ( F @ X3 )
% 6.94/7.30 != zero_zero_rat ) )
% 6.94/7.30 => ( ( groups5938585286922990810at_rat @ F @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( divide_divide_rat @ ( times_times_rat @ ( groups5938585286922990810at_rat @ F @ A4 ) @ ( groups5938585286922990810at_rat @ F @ B5 ) ) @ ( groups5938585286922990810at_rat @ F @ ( inf_in1697001100524423349at_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_Un
% 6.94/7.30 thf(fact_9132_prod__Un,axiom,
% 6.94/7.30 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > rat] :
% 6.94/7.30 ( ( finite4343798906461161616at_nat @ A4 )
% 6.94/7.30 => ( ( finite4343798906461161616at_nat @ B5 )
% 6.94/7.30 => ( ! [X3: produc3843707927480180839at_nat] :
% 6.94/7.30 ( ( member8757157785044589968at_nat @ X3 @ ( inf_in7913087082777306421at_nat @ A4 @ B5 ) )
% 6.94/7.30 => ( ( F @ X3 )
% 6.94/7.30 != zero_zero_rat ) )
% 6.94/7.30 => ( ( groups8874911130973611098at_rat @ F @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( divide_divide_rat @ ( times_times_rat @ ( groups8874911130973611098at_rat @ F @ A4 ) @ ( groups8874911130973611098at_rat @ F @ B5 ) ) @ ( groups8874911130973611098at_rat @ F @ ( inf_in7913087082777306421at_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_Un
% 6.94/7.30 thf(fact_9133_prod__Un,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,F: nat > rat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 6.94/7.30 => ( ( F @ X3 )
% 6.94/7.30 != zero_zero_rat ) )
% 6.94/7.30 => ( ( groups73079841787564623at_rat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 6.94/7.30 = ( divide_divide_rat @ ( times_times_rat @ ( groups73079841787564623at_rat @ F @ A4 ) @ ( groups73079841787564623at_rat @ F @ B5 ) ) @ ( groups73079841787564623at_rat @ F @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % prod_Un
% 6.94/7.30 thf(fact_9134_or__one__eq,axiom,
% 6.94/7.30 ! [A: code_natural] :
% 6.94/7.30 ( ( bit_se9127793120404214118atural @ A @ one_one_Code_natural )
% 6.94/7.30 = ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % or_one_eq
% 6.94/7.30 thf(fact_9135_or__one__eq,axiom,
% 6.94/7.30 ! [A: code_integer] :
% 6.94/7.30 ( ( bit_se1080825931792720795nteger @ A @ one_one_Code_integer )
% 6.94/7.30 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % or_one_eq
% 6.94/7.30 thf(fact_9136_or__one__eq,axiom,
% 6.94/7.30 ! [A: int] :
% 6.94/7.30 ( ( bit_se1409905431419307370or_int @ A @ one_one_int )
% 6.94/7.30 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % or_one_eq
% 6.94/7.30 thf(fact_9137_or__one__eq,axiom,
% 6.94/7.30 ! [A: nat] :
% 6.94/7.30 ( ( bit_se1412395901928357646or_nat @ A @ one_one_nat )
% 6.94/7.30 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % or_one_eq
% 6.94/7.30 thf(fact_9138_one__or__eq,axiom,
% 6.94/7.30 ! [A: code_natural] :
% 6.94/7.30 ( ( bit_se9127793120404214118atural @ one_one_Code_natural @ A )
% 6.94/7.30 = ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % one_or_eq
% 6.94/7.30 thf(fact_9139_one__or__eq,axiom,
% 6.94/7.30 ! [A: code_integer] :
% 6.94/7.30 ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ A )
% 6.94/7.30 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % one_or_eq
% 6.94/7.30 thf(fact_9140_one__or__eq,axiom,
% 6.94/7.30 ! [A: int] :
% 6.94/7.30 ( ( bit_se1409905431419307370or_int @ one_one_int @ A )
% 6.94/7.30 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % one_or_eq
% 6.94/7.30 thf(fact_9141_one__or__eq,axiom,
% 6.94/7.30 ! [A: nat] :
% 6.94/7.30 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ A )
% 6.94/7.30 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % one_or_eq
% 6.94/7.30 thf(fact_9142_OR__upper,axiom,
% 6.94/7.30 ! [X: int,N2: nat,Y: int] :
% 6.94/7.30 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.94/7.30 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 6.94/7.30 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 6.94/7.30 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % OR_upper
% 6.94/7.30 thf(fact_9143_or__not__numerals_I5_J,axiom,
% 6.94/7.30 ! [M: num,N2: num] :
% 6.94/7.30 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 6.94/7.30 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % or_not_numerals(5)
% 6.94/7.30 thf(fact_9144_take__bit__sum,axiom,
% 6.94/7.30 ( bit_se1745604003318907178nteger
% 6.94/7.30 = ( ^ [N: nat,A5: code_integer] :
% 6.94/7.30 ( groups7501900531339628137nteger
% 6.94/7.30 @ ^ [K3: nat] : ( bit_se7788150548672797655nteger @ K3 @ ( zero_n356916108424825756nteger @ ( bit_se9216721137139052372nteger @ A5 @ K3 ) ) )
% 6.94/7.30 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % take_bit_sum
% 6.94/7.30 thf(fact_9145_take__bit__sum,axiom,
% 6.94/7.30 ( bit_se2923211474154528505it_int
% 6.94/7.30 = ( ^ [N: nat,A5: int] :
% 6.94/7.30 ( groups3539618377306564664at_int
% 6.94/7.30 @ ^ [K3: nat] : ( bit_se545348938243370406it_int @ K3 @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ A5 @ K3 ) ) )
% 6.94/7.30 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % take_bit_sum
% 6.94/7.30 thf(fact_9146_take__bit__sum,axiom,
% 6.94/7.30 ( bit_se2925701944663578781it_nat
% 6.94/7.30 = ( ^ [N: nat,A5: nat] :
% 6.94/7.30 ( groups3542108847815614940at_nat
% 6.94/7.30 @ ^ [K3: nat] : ( bit_se547839408752420682it_nat @ K3 @ ( zero_n2687167440665602831ol_nat @ ( bit_se1148574629649215175it_nat @ A5 @ K3 ) ) )
% 6.94/7.30 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % take_bit_sum
% 6.94/7.30 thf(fact_9147_or__not__numerals_I8_J,axiom,
% 6.94/7.30 ! [M: num,N2: num] :
% 6.94/7.30 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 6.94/7.30 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % or_not_numerals(8)
% 6.94/7.30 thf(fact_9148_or__not__numerals_I9_J,axiom,
% 6.94/7.30 ! [M: num,N2: num] :
% 6.94/7.30 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 6.94/7.30 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % or_not_numerals(9)
% 6.94/7.30 thf(fact_9149_of__list__def,axiom,
% 6.94/7.30 ( array_of_list_nat
% 6.94/7.30 = ( ^ [Xs3: list_nat] :
% 6.94/7.30 ( heap_T4325564685996367510ay_nat
% 6.94/7.30 @ ^ [H6: heap_e7401611519738050253t_unit] :
% 6.94/7.30 ( produc8657510640128716596it_nat
% 6.94/7.30 @ ^ [R5: array_nat,H7: heap_e7401611519738050253t_unit] : ( produc4907525368653469954it_nat @ R5 @ ( produc584006145561248582it_nat @ H7 @ ( plus_plus_nat @ one_one_nat @ ( size_size_list_nat @ Xs3 ) ) ) )
% 6.94/7.30 @ ( array_alloc_nat @ Xs3 @ H6 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % of_list_def
% 6.94/7.30 thf(fact_9150_of__list__def,axiom,
% 6.94/7.30 ( array_of_list_o
% 6.94/7.30 = ( ^ [Xs3: list_o] :
% 6.94/7.30 ( heap_T8367841184088661864rray_o
% 6.94/7.30 @ ^ [H6: heap_e7401611519738050253t_unit] :
% 6.94/7.30 ( produc5512802776183222702it_nat
% 6.94/7.30 @ ^ [R5: array_o,H7: heap_e7401611519738050253t_unit] : ( produc2890842502232952598it_nat @ R5 @ ( produc584006145561248582it_nat @ H7 @ ( plus_plus_nat @ one_one_nat @ ( size_size_list_o @ Xs3 ) ) ) )
% 6.94/7.30 @ ( array_alloc_o @ Xs3 @ H6 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % of_list_def
% 6.94/7.30 thf(fact_9151_of__list__def,axiom,
% 6.94/7.30 ( array_of_list_int
% 6.94/7.30 = ( ^ [Xs3: list_int] :
% 6.94/7.30 ( heap_T147713666487170802ay_int
% 6.94/7.30 @ ^ [H6: heap_e7401611519738050253t_unit] :
% 6.94/7.30 ( produc3016605123915955252it_nat
% 6.94/7.30 @ ^ [R5: array_int,H7: heap_e7401611519738050253t_unit] : ( produc5351973125643376990it_nat @ R5 @ ( produc584006145561248582it_nat @ H7 @ ( plus_plus_nat @ one_one_nat @ ( size_size_list_int @ Xs3 ) ) ) )
% 6.94/7.30 @ ( array_alloc_int @ Xs3 @ H6 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % of_list_def
% 6.94/7.30 thf(fact_9152_finite__Collect__le__nat,axiom,
% 6.94/7.30 ! [K2: nat] :
% 6.94/7.30 ( finite_finite_nat
% 6.94/7.30 @ ( collect_nat
% 6.94/7.30 @ ^ [N: nat] : ( ord_less_eq_nat @ N @ K2 ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_le_nat
% 6.94/7.30 thf(fact_9153_finite__Collect__less__nat,axiom,
% 6.94/7.30 ! [K2: nat] :
% 6.94/7.30 ( finite_finite_nat
% 6.94/7.30 @ ( collect_nat
% 6.94/7.30 @ ^ [N: nat] : ( ord_less_nat @ N @ K2 ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_less_nat
% 6.94/7.30 thf(fact_9154_finite__Collect__subsets,axiom,
% 6.94/7.30 ! [A4: set_Pr958786334691620121nt_int] :
% 6.94/7.30 ( ( finite2998713641127702882nt_int @ A4 )
% 6.94/7.30 => ( finite8744585540193469122nt_int
% 6.94/7.30 @ ( collec5210948495886036740nt_int
% 6.94/7.30 @ ^ [B6: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ B6 @ A4 ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_subsets
% 6.94/7.30 thf(fact_9155_finite__Collect__subsets,axiom,
% 6.94/7.30 ! [A4: set_nat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( finite1152437895449049373et_nat
% 6.94/7.30 @ ( collect_set_nat
% 6.94/7.30 @ ^ [B6: set_nat] : ( ord_less_eq_set_nat @ B6 @ A4 ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_subsets
% 6.94/7.30 thf(fact_9156_finite__Collect__subsets,axiom,
% 6.94/7.30 ! [A4: set_Code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( finite6931041176100689706nteger
% 6.94/7.30 @ ( collec574505750873337192nteger
% 6.94/7.30 @ ^ [B6: set_Code_integer] : ( ord_le7084787975880047091nteger @ B6 @ A4 ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_subsets
% 6.94/7.30 thf(fact_9157_finite__Collect__subsets,axiom,
% 6.94/7.30 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.94/7.30 ( ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.30 => ( finite9047747110432174090at_nat
% 6.94/7.30 @ ( collec5514110066124741708at_nat
% 6.94/7.30 @ ^ [B6: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ B6 @ A4 ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_subsets
% 6.94/7.30 thf(fact_9158_finite__Collect__subsets,axiom,
% 6.94/7.30 ! [A4: set_int] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( finite6197958912794628473et_int
% 6.94/7.30 @ ( collect_set_int
% 6.94/7.30 @ ^ [B6: set_int] : ( ord_less_eq_set_int @ B6 @ A4 ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_subsets
% 6.94/7.30 thf(fact_9159_finite__induct__select,axiom,
% 6.94/7.30 ! [S: set_Pr4329608150637261639at_nat,P2: set_Pr4329608150637261639at_nat > $o] :
% 6.94/7.30 ( ( finite4343798906461161616at_nat @ S )
% 6.94/7.30 => ( ( P2 @ bot_bo228742789529271731at_nat )
% 6.94/7.30 => ( ! [T8: set_Pr4329608150637261639at_nat] :
% 6.94/7.30 ( ( ord_le2604355607129572851at_nat @ T8 @ S )
% 6.94/7.30 => ( ( P2 @ T8 )
% 6.94/7.30 => ? [X6: produc3843707927480180839at_nat] :
% 6.94/7.30 ( ( member8757157785044589968at_nat @ X6 @ ( minus_3314409938677909166at_nat @ S @ T8 ) )
% 6.94/7.30 & ( P2 @ ( insert9069300056098147895at_nat @ X6 @ T8 ) ) ) ) )
% 6.94/7.30 => ( P2 @ S ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_induct_select
% 6.94/7.30 thf(fact_9160_finite__induct__select,axiom,
% 6.94/7.30 ! [S: set_Code_integer,P2: set_Code_integer > $o] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ S )
% 6.94/7.30 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 6.94/7.30 => ( ! [T8: set_Code_integer] :
% 6.94/7.30 ( ( ord_le1307284697595431911nteger @ T8 @ S )
% 6.94/7.30 => ( ( P2 @ T8 )
% 6.94/7.30 => ? [X6: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X6 @ ( minus_2355218937544613996nteger @ S @ T8 ) )
% 6.94/7.30 & ( P2 @ ( insert_Code_integer @ X6 @ T8 ) ) ) ) )
% 6.94/7.30 => ( P2 @ S ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_induct_select
% 6.94/7.30 thf(fact_9161_finite__induct__select,axiom,
% 6.94/7.30 ! [S: set_o,P2: set_o > $o] :
% 6.94/7.30 ( ( finite_finite_o @ S )
% 6.94/7.30 => ( ( P2 @ bot_bot_set_o )
% 6.94/7.30 => ( ! [T8: set_o] :
% 6.94/7.30 ( ( ord_less_set_o @ T8 @ S )
% 6.94/7.30 => ( ( P2 @ T8 )
% 6.94/7.30 => ? [X6: $o] :
% 6.94/7.30 ( ( member_o @ X6 @ ( minus_minus_set_o @ S @ T8 ) )
% 6.94/7.30 & ( P2 @ ( insert_o @ X6 @ T8 ) ) ) ) )
% 6.94/7.30 => ( P2 @ S ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_induct_select
% 6.94/7.30 thf(fact_9162_finite__induct__select,axiom,
% 6.94/7.30 ! [S: set_nat,P2: set_nat > $o] :
% 6.94/7.30 ( ( finite_finite_nat @ S )
% 6.94/7.30 => ( ( P2 @ bot_bot_set_nat )
% 6.94/7.30 => ( ! [T8: set_nat] :
% 6.94/7.30 ( ( ord_less_set_nat @ T8 @ S )
% 6.94/7.30 => ( ( P2 @ T8 )
% 6.94/7.30 => ? [X6: nat] :
% 6.94/7.30 ( ( member_nat @ X6 @ ( minus_minus_set_nat @ S @ T8 ) )
% 6.94/7.30 & ( P2 @ ( insert_nat @ X6 @ T8 ) ) ) ) )
% 6.94/7.30 => ( P2 @ S ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_induct_select
% 6.94/7.30 thf(fact_9163_finite__induct__select,axiom,
% 6.94/7.30 ! [S: set_int,P2: set_int > $o] :
% 6.94/7.30 ( ( finite_finite_int @ S )
% 6.94/7.30 => ( ( P2 @ bot_bot_set_int )
% 6.94/7.30 => ( ! [T8: set_int] :
% 6.94/7.30 ( ( ord_less_set_int @ T8 @ S )
% 6.94/7.30 => ( ( P2 @ T8 )
% 6.94/7.30 => ? [X6: int] :
% 6.94/7.30 ( ( member_int @ X6 @ ( minus_minus_set_int @ S @ T8 ) )
% 6.94/7.30 & ( P2 @ ( insert_int @ X6 @ T8 ) ) ) ) )
% 6.94/7.30 => ( P2 @ S ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_induct_select
% 6.94/7.30 thf(fact_9164_finite__induct__select,axiom,
% 6.94/7.30 ! [S: set_Pr1261947904930325089at_nat,P2: set_Pr1261947904930325089at_nat > $o] :
% 6.94/7.30 ( ( finite6177210948735845034at_nat @ S )
% 6.94/7.30 => ( ( P2 @ bot_bo2099793752762293965at_nat )
% 6.94/7.30 => ( ! [T8: set_Pr1261947904930325089at_nat] :
% 6.94/7.30 ( ( ord_le7866589430770878221at_nat @ T8 @ S )
% 6.94/7.30 => ( ( P2 @ T8 )
% 6.94/7.30 => ? [X6: product_prod_nat_nat] :
% 6.94/7.30 ( ( member8440522571783428010at_nat @ X6 @ ( minus_1356011639430497352at_nat @ S @ T8 ) )
% 6.94/7.30 & ( P2 @ ( insert8211810215607154385at_nat @ X6 @ T8 ) ) ) ) )
% 6.94/7.30 => ( P2 @ S ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_induct_select
% 6.94/7.30 thf(fact_9165_finite__Un,axiom,
% 6.94/7.30 ! [F5: set_int,G4: set_int] :
% 6.94/7.30 ( ( finite_finite_int @ ( sup_sup_set_int @ F5 @ G4 ) )
% 6.94/7.30 = ( ( finite_finite_int @ F5 )
% 6.94/7.30 & ( finite_finite_int @ G4 ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Un
% 6.94/7.30 thf(fact_9166_finite__Un,axiom,
% 6.94/7.30 ! [F5: set_Code_integer,G4: set_Code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ ( sup_su848401254843788991nteger @ F5 @ G4 ) )
% 6.94/7.30 = ( ( finite6017078050557962740nteger @ F5 )
% 6.94/7.30 & ( finite6017078050557962740nteger @ G4 ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Un
% 6.94/7.30 thf(fact_9167_finite__Un,axiom,
% 6.94/7.30 ! [F5: set_Pr1261947904930325089at_nat,G4: set_Pr1261947904930325089at_nat] :
% 6.94/7.30 ( ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ F5 @ G4 ) )
% 6.94/7.30 = ( ( finite6177210948735845034at_nat @ F5 )
% 6.94/7.30 & ( finite6177210948735845034at_nat @ G4 ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Un
% 6.94/7.30 thf(fact_9168_finite__Un,axiom,
% 6.94/7.30 ! [F5: set_Pr8551490117392284871at_nat,G4: set_Pr8551490117392284871at_nat] :
% 6.94/7.30 ( ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ F5 @ G4 ) )
% 6.94/7.30 = ( ( finite1918287321285529104at_nat @ F5 )
% 6.94/7.30 & ( finite1918287321285529104at_nat @ G4 ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Un
% 6.94/7.30 thf(fact_9169_finite__Un,axiom,
% 6.94/7.30 ! [F5: set_Pr4329608150637261639at_nat,G4: set_Pr4329608150637261639at_nat] :
% 6.94/7.30 ( ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ F5 @ G4 ) )
% 6.94/7.30 = ( ( finite4343798906461161616at_nat @ F5 )
% 6.94/7.30 & ( finite4343798906461161616at_nat @ G4 ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Un
% 6.94/7.30 thf(fact_9170_finite__Un,axiom,
% 6.94/7.30 ! [F5: set_nat,G4: set_nat] :
% 6.94/7.30 ( ( finite_finite_nat @ ( sup_sup_set_nat @ F5 @ G4 ) )
% 6.94/7.30 = ( ( finite_finite_nat @ F5 )
% 6.94/7.30 & ( finite_finite_nat @ G4 ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Un
% 6.94/7.30 thf(fact_9171_finite__Collect__conjI,axiom,
% 6.94/7.30 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 6.94/7.30 ( ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P2 ) )
% 6.94/7.30 | ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q2 ) ) )
% 6.94/7.30 => ( finite8100373058378681591st_nat
% 6.94/7.30 @ ( collect_list_nat
% 6.94/7.30 @ ^ [X4: list_nat] :
% 6.94/7.30 ( ( P2 @ X4 )
% 6.94/7.30 & ( Q2 @ X4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_conjI
% 6.94/7.30 thf(fact_9172_finite__Collect__conjI,axiom,
% 6.94/7.30 ! [P2: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 6.94/7.30 ( ( ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ P2 ) )
% 6.94/7.30 | ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ Q2 ) ) )
% 6.94/7.30 => ( finite8744585540193469122nt_int
% 6.94/7.30 @ ( collec5210948495886036740nt_int
% 6.94/7.30 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.94/7.30 ( ( P2 @ X4 )
% 6.94/7.30 & ( Q2 @ X4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_conjI
% 6.94/7.30 thf(fact_9173_finite__Collect__conjI,axiom,
% 6.94/7.30 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 6.94/7.30 ( ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P2 ) )
% 6.94/7.30 | ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q2 ) ) )
% 6.94/7.30 => ( finite1152437895449049373et_nat
% 6.94/7.30 @ ( collect_set_nat
% 6.94/7.30 @ ^ [X4: set_nat] :
% 6.94/7.30 ( ( P2 @ X4 )
% 6.94/7.30 & ( Q2 @ X4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_conjI
% 6.94/7.30 thf(fact_9174_finite__Collect__conjI,axiom,
% 6.94/7.30 ! [P2: nat > $o,Q2: nat > $o] :
% 6.94/7.30 ( ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 6.94/7.30 | ( finite_finite_nat @ ( collect_nat @ Q2 ) ) )
% 6.94/7.30 => ( finite_finite_nat
% 6.94/7.30 @ ( collect_nat
% 6.94/7.30 @ ^ [X4: nat] :
% 6.94/7.30 ( ( P2 @ X4 )
% 6.94/7.30 & ( Q2 @ X4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_conjI
% 6.94/7.30 thf(fact_9175_finite__Collect__conjI,axiom,
% 6.94/7.30 ! [P2: int > $o,Q2: int > $o] :
% 6.94/7.30 ( ( ( finite_finite_int @ ( collect_int @ P2 ) )
% 6.94/7.30 | ( finite_finite_int @ ( collect_int @ Q2 ) ) )
% 6.94/7.30 => ( finite_finite_int
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [X4: int] :
% 6.94/7.30 ( ( P2 @ X4 )
% 6.94/7.30 & ( Q2 @ X4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_conjI
% 6.94/7.30 thf(fact_9176_finite__Collect__conjI,axiom,
% 6.94/7.30 ! [P2: code_integer > $o,Q2: code_integer > $o] :
% 6.94/7.30 ( ( ( finite6017078050557962740nteger @ ( collect_Code_integer @ P2 ) )
% 6.94/7.30 | ( finite6017078050557962740nteger @ ( collect_Code_integer @ Q2 ) ) )
% 6.94/7.30 => ( finite6017078050557962740nteger
% 6.94/7.30 @ ( collect_Code_integer
% 6.94/7.30 @ ^ [X4: code_integer] :
% 6.94/7.30 ( ( P2 @ X4 )
% 6.94/7.30 & ( Q2 @ X4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_conjI
% 6.94/7.30 thf(fact_9177_finite__Collect__conjI,axiom,
% 6.94/7.30 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 6.94/7.30 ( ( ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P2 ) )
% 6.94/7.30 | ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ Q2 ) ) )
% 6.94/7.30 => ( finite6177210948735845034at_nat
% 6.94/7.30 @ ( collec3392354462482085612at_nat
% 6.94/7.30 @ ^ [X4: product_prod_nat_nat] :
% 6.94/7.30 ( ( P2 @ X4 )
% 6.94/7.30 & ( Q2 @ X4 ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_conjI
% 6.94/7.30 thf(fact_9178_finite__Collect__disjI,axiom,
% 6.94/7.30 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 6.94/7.30 ( ( finite8100373058378681591st_nat
% 6.94/7.30 @ ( collect_list_nat
% 6.94/7.30 @ ^ [X4: list_nat] :
% 6.94/7.30 ( ( P2 @ X4 )
% 6.94/7.30 | ( Q2 @ X4 ) ) ) )
% 6.94/7.30 = ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P2 ) )
% 6.94/7.30 & ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q2 ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_disjI
% 6.94/7.30 thf(fact_9179_finite__Collect__disjI,axiom,
% 6.94/7.30 ! [P2: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 6.94/7.30 ( ( finite8744585540193469122nt_int
% 6.94/7.30 @ ( collec5210948495886036740nt_int
% 6.94/7.30 @ ^ [X4: set_Pr958786334691620121nt_int] :
% 6.94/7.30 ( ( P2 @ X4 )
% 6.94/7.30 | ( Q2 @ X4 ) ) ) )
% 6.94/7.30 = ( ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ P2 ) )
% 6.94/7.30 & ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_disjI
% 6.94/7.30 thf(fact_9180_finite__Collect__disjI,axiom,
% 6.94/7.30 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 6.94/7.30 ( ( finite1152437895449049373et_nat
% 6.94/7.30 @ ( collect_set_nat
% 6.94/7.30 @ ^ [X4: set_nat] :
% 6.94/7.30 ( ( P2 @ X4 )
% 6.94/7.30 | ( Q2 @ X4 ) ) ) )
% 6.94/7.30 = ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P2 ) )
% 6.94/7.30 & ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q2 ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_disjI
% 6.94/7.30 thf(fact_9181_finite__Collect__disjI,axiom,
% 6.94/7.30 ! [P2: nat > $o,Q2: nat > $o] :
% 6.94/7.30 ( ( finite_finite_nat
% 6.94/7.30 @ ( collect_nat
% 6.94/7.30 @ ^ [X4: nat] :
% 6.94/7.30 ( ( P2 @ X4 )
% 6.94/7.30 | ( Q2 @ X4 ) ) ) )
% 6.94/7.30 = ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 6.94/7.30 & ( finite_finite_nat @ ( collect_nat @ Q2 ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_disjI
% 6.94/7.30 thf(fact_9182_finite__Collect__disjI,axiom,
% 6.94/7.30 ! [P2: int > $o,Q2: int > $o] :
% 6.94/7.30 ( ( finite_finite_int
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [X4: int] :
% 6.94/7.30 ( ( P2 @ X4 )
% 6.94/7.30 | ( Q2 @ X4 ) ) ) )
% 6.94/7.30 = ( ( finite_finite_int @ ( collect_int @ P2 ) )
% 6.94/7.30 & ( finite_finite_int @ ( collect_int @ Q2 ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_disjI
% 6.94/7.30 thf(fact_9183_finite__Collect__disjI,axiom,
% 6.94/7.30 ! [P2: code_integer > $o,Q2: code_integer > $o] :
% 6.94/7.30 ( ( finite6017078050557962740nteger
% 6.94/7.30 @ ( collect_Code_integer
% 6.94/7.30 @ ^ [X4: code_integer] :
% 6.94/7.30 ( ( P2 @ X4 )
% 6.94/7.30 | ( Q2 @ X4 ) ) ) )
% 6.94/7.30 = ( ( finite6017078050557962740nteger @ ( collect_Code_integer @ P2 ) )
% 6.94/7.30 & ( finite6017078050557962740nteger @ ( collect_Code_integer @ Q2 ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_disjI
% 6.94/7.30 thf(fact_9184_finite__Collect__disjI,axiom,
% 6.94/7.30 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 6.94/7.30 ( ( finite6177210948735845034at_nat
% 6.94/7.30 @ ( collec3392354462482085612at_nat
% 6.94/7.30 @ ^ [X4: product_prod_nat_nat] :
% 6.94/7.30 ( ( P2 @ X4 )
% 6.94/7.30 | ( Q2 @ X4 ) ) ) )
% 6.94/7.30 = ( ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P2 ) )
% 6.94/7.30 & ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ Q2 ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_Collect_disjI
% 6.94/7.30 thf(fact_9185_finite__interval__int1,axiom,
% 6.94/7.30 ! [A: int,B: int] :
% 6.94/7.30 ( finite_finite_int
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [I: int] :
% 6.94/7.30 ( ( ord_less_eq_int @ A @ I )
% 6.94/7.30 & ( ord_less_eq_int @ I @ B ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_interval_int1
% 6.94/7.30 thf(fact_9186_finite__interval__int4,axiom,
% 6.94/7.30 ! [A: int,B: int] :
% 6.94/7.30 ( finite_finite_int
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [I: int] :
% 6.94/7.30 ( ( ord_less_int @ A @ I )
% 6.94/7.30 & ( ord_less_int @ I @ B ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_interval_int4
% 6.94/7.30 thf(fact_9187_finite__atLeastLessThan__integer,axiom,
% 6.94/7.30 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_atLeastLessThan_integer
% 6.94/7.30 thf(fact_9188_finite__atLeastAtMost__integer,axiom,
% 6.94/7.30 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or189985376899183464nteger @ L @ U ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_atLeastAtMost_integer
% 6.94/7.30 thf(fact_9189_finite__interval__int2,axiom,
% 6.94/7.30 ! [A: int,B: int] :
% 6.94/7.30 ( finite_finite_int
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [I: int] :
% 6.94/7.30 ( ( ord_less_eq_int @ A @ I )
% 6.94/7.30 & ( ord_less_int @ I @ B ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_interval_int2
% 6.94/7.30 thf(fact_9190_finite__interval__int3,axiom,
% 6.94/7.30 ! [A: int,B: int] :
% 6.94/7.30 ( finite_finite_int
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [I: int] :
% 6.94/7.30 ( ( ord_less_int @ A @ I )
% 6.94/7.30 & ( ord_less_eq_int @ I @ B ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_interval_int3
% 6.94/7.30 thf(fact_9191_finite__maxlen,axiom,
% 6.94/7.30 ! [M6: set_list_nat] :
% 6.94/7.30 ( ( finite8100373058378681591st_nat @ M6 )
% 6.94/7.30 => ? [N5: nat] :
% 6.94/7.30 ! [X6: list_nat] :
% 6.94/7.30 ( ( member_list_nat @ X6 @ M6 )
% 6.94/7.30 => ( ord_less_nat @ ( size_size_list_nat @ X6 ) @ N5 ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_maxlen
% 6.94/7.30 thf(fact_9192_finite__maxlen,axiom,
% 6.94/7.30 ! [M6: set_list_o] :
% 6.94/7.30 ( ( finite_finite_list_o @ M6 )
% 6.94/7.30 => ? [N5: nat] :
% 6.94/7.30 ! [X6: list_o] :
% 6.94/7.30 ( ( member_list_o @ X6 @ M6 )
% 6.94/7.30 => ( ord_less_nat @ ( size_size_list_o @ X6 ) @ N5 ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_maxlen
% 6.94/7.30 thf(fact_9193_finite__maxlen,axiom,
% 6.94/7.30 ! [M6: set_list_int] :
% 6.94/7.30 ( ( finite3922522038869484883st_int @ M6 )
% 6.94/7.30 => ? [N5: nat] :
% 6.94/7.30 ! [X6: list_int] :
% 6.94/7.30 ( ( member_list_int @ X6 @ M6 )
% 6.94/7.30 => ( ord_less_nat @ ( size_size_list_int @ X6 ) @ N5 ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_maxlen
% 6.94/7.30 thf(fact_9194_finite__divisors__int,axiom,
% 6.94/7.30 ! [I2: int] :
% 6.94/7.30 ( ( I2 != zero_zero_int )
% 6.94/7.30 => ( finite_finite_int
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [D5: int] : ( dvd_dvd_int @ D5 @ I2 ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_divisors_int
% 6.94/7.30 thf(fact_9195_finite__atLeastZeroLessThan__integer,axiom,
% 6.94/7.30 ! [U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_atLeastZeroLessThan_integer
% 6.94/7.30 thf(fact_9196_not__finite__existsD,axiom,
% 6.94/7.30 ! [P2: list_nat > $o] :
% 6.94/7.30 ( ~ ( finite8100373058378681591st_nat @ ( collect_list_nat @ P2 ) )
% 6.94/7.30 => ? [X_1: list_nat] : ( P2 @ X_1 ) ) ).
% 6.94/7.30
% 6.94/7.30 % not_finite_existsD
% 6.94/7.30 thf(fact_9197_not__finite__existsD,axiom,
% 6.94/7.30 ! [P2: set_Pr958786334691620121nt_int > $o] :
% 6.94/7.30 ( ~ ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ P2 ) )
% 6.94/7.30 => ? [X_1: set_Pr958786334691620121nt_int] : ( P2 @ X_1 ) ) ).
% 6.94/7.30
% 6.94/7.30 % not_finite_existsD
% 6.94/7.30 thf(fact_9198_not__finite__existsD,axiom,
% 6.94/7.30 ! [P2: set_nat > $o] :
% 6.94/7.30 ( ~ ( finite1152437895449049373et_nat @ ( collect_set_nat @ P2 ) )
% 6.94/7.30 => ? [X_1: set_nat] : ( P2 @ X_1 ) ) ).
% 6.94/7.30
% 6.94/7.30 % not_finite_existsD
% 6.94/7.30 thf(fact_9199_not__finite__existsD,axiom,
% 6.94/7.30 ! [P2: nat > $o] :
% 6.94/7.30 ( ~ ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 6.94/7.30 => ? [X_1: nat] : ( P2 @ X_1 ) ) ).
% 6.94/7.30
% 6.94/7.30 % not_finite_existsD
% 6.94/7.30 thf(fact_9200_not__finite__existsD,axiom,
% 6.94/7.30 ! [P2: int > $o] :
% 6.94/7.30 ( ~ ( finite_finite_int @ ( collect_int @ P2 ) )
% 6.94/7.30 => ? [X_1: int] : ( P2 @ X_1 ) ) ).
% 6.94/7.30
% 6.94/7.30 % not_finite_existsD
% 6.94/7.30 thf(fact_9201_not__finite__existsD,axiom,
% 6.94/7.30 ! [P2: code_integer > $o] :
% 6.94/7.30 ( ~ ( finite6017078050557962740nteger @ ( collect_Code_integer @ P2 ) )
% 6.94/7.30 => ? [X_1: code_integer] : ( P2 @ X_1 ) ) ).
% 6.94/7.30
% 6.94/7.30 % not_finite_existsD
% 6.94/7.30 thf(fact_9202_not__finite__existsD,axiom,
% 6.94/7.30 ! [P2: product_prod_nat_nat > $o] :
% 6.94/7.30 ( ~ ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P2 ) )
% 6.94/7.30 => ? [X_1: product_prod_nat_nat] : ( P2 @ X_1 ) ) ).
% 6.94/7.30
% 6.94/7.30 % not_finite_existsD
% 6.94/7.30 thf(fact_9203_pigeonhole__infinite__rel,axiom,
% 6.94/7.30 ! [A4: set_o,B5: set_nat,R3: $o > nat > $o] :
% 6.94/7.30 ( ~ ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ A4 )
% 6.94/7.30 => ? [Xa3: nat] :
% 6.94/7.30 ( ( member_nat @ Xa3 @ B5 )
% 6.94/7.30 & ( R3 @ X3 @ Xa3 ) ) )
% 6.94/7.30 => ? [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ B5 )
% 6.94/7.30 & ~ ( finite_finite_o
% 6.94/7.30 @ ( collect_o
% 6.94/7.30 @ ^ [A5: $o] :
% 6.94/7.30 ( ( member_o @ A5 @ A4 )
% 6.94/7.30 & ( R3 @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % pigeonhole_infinite_rel
% 6.94/7.30 thf(fact_9204_pigeonhole__infinite__rel,axiom,
% 6.94/7.30 ! [A4: set_o,B5: set_int,R3: $o > int > $o] :
% 6.94/7.30 ( ~ ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ A4 )
% 6.94/7.30 => ? [Xa3: int] :
% 6.94/7.30 ( ( member_int @ Xa3 @ B5 )
% 6.94/7.30 & ( R3 @ X3 @ Xa3 ) ) )
% 6.94/7.30 => ? [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ B5 )
% 6.94/7.30 & ~ ( finite_finite_o
% 6.94/7.30 @ ( collect_o
% 6.94/7.30 @ ^ [A5: $o] :
% 6.94/7.30 ( ( member_o @ A5 @ A4 )
% 6.94/7.30 & ( R3 @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % pigeonhole_infinite_rel
% 6.94/7.30 thf(fact_9205_pigeonhole__infinite__rel,axiom,
% 6.94/7.30 ! [A4: set_o,B5: set_Code_integer,R3: $o > code_integer > $o] :
% 6.94/7.30 ( ~ ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ! [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ A4 )
% 6.94/7.30 => ? [Xa3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ Xa3 @ B5 )
% 6.94/7.30 & ( R3 @ X3 @ Xa3 ) ) )
% 6.94/7.30 => ? [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ B5 )
% 6.94/7.30 & ~ ( finite_finite_o
% 6.94/7.30 @ ( collect_o
% 6.94/7.30 @ ^ [A5: $o] :
% 6.94/7.30 ( ( member_o @ A5 @ A4 )
% 6.94/7.30 & ( R3 @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % pigeonhole_infinite_rel
% 6.94/7.30 thf(fact_9206_pigeonhole__infinite__rel,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_nat,R3: nat > nat > $o] :
% 6.94/7.30 ( ~ ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ A4 )
% 6.94/7.30 => ? [Xa3: nat] :
% 6.94/7.30 ( ( member_nat @ Xa3 @ B5 )
% 6.94/7.30 & ( R3 @ X3 @ Xa3 ) ) )
% 6.94/7.30 => ? [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ B5 )
% 6.94/7.30 & ~ ( finite_finite_nat
% 6.94/7.30 @ ( collect_nat
% 6.94/7.30 @ ^ [A5: nat] :
% 6.94/7.30 ( ( member_nat @ A5 @ A4 )
% 6.94/7.30 & ( R3 @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % pigeonhole_infinite_rel
% 6.94/7.30 thf(fact_9207_pigeonhole__infinite__rel,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_int,R3: nat > int > $o] :
% 6.94/7.30 ( ~ ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ A4 )
% 6.94/7.30 => ? [Xa3: int] :
% 6.94/7.30 ( ( member_int @ Xa3 @ B5 )
% 6.94/7.30 & ( R3 @ X3 @ Xa3 ) ) )
% 6.94/7.30 => ? [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ B5 )
% 6.94/7.30 & ~ ( finite_finite_nat
% 6.94/7.30 @ ( collect_nat
% 6.94/7.30 @ ^ [A5: nat] :
% 6.94/7.30 ( ( member_nat @ A5 @ A4 )
% 6.94/7.30 & ( R3 @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % pigeonhole_infinite_rel
% 6.94/7.30 thf(fact_9208_pigeonhole__infinite__rel,axiom,
% 6.94/7.30 ! [A4: set_nat,B5: set_Code_integer,R3: nat > code_integer > $o] :
% 6.94/7.30 ( ~ ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ! [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ A4 )
% 6.94/7.30 => ? [Xa3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ Xa3 @ B5 )
% 6.94/7.30 & ( R3 @ X3 @ Xa3 ) ) )
% 6.94/7.30 => ? [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ B5 )
% 6.94/7.30 & ~ ( finite_finite_nat
% 6.94/7.30 @ ( collect_nat
% 6.94/7.30 @ ^ [A5: nat] :
% 6.94/7.30 ( ( member_nat @ A5 @ A4 )
% 6.94/7.30 & ( R3 @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % pigeonhole_infinite_rel
% 6.94/7.30 thf(fact_9209_pigeonhole__infinite__rel,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_nat,R3: int > nat > $o] :
% 6.94/7.30 ( ~ ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ A4 )
% 6.94/7.30 => ? [Xa3: nat] :
% 6.94/7.30 ( ( member_nat @ Xa3 @ B5 )
% 6.94/7.30 & ( R3 @ X3 @ Xa3 ) ) )
% 6.94/7.30 => ? [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ B5 )
% 6.94/7.30 & ~ ( finite_finite_int
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [A5: int] :
% 6.94/7.30 ( ( member_int @ A5 @ A4 )
% 6.94/7.30 & ( R3 @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % pigeonhole_infinite_rel
% 6.94/7.30 thf(fact_9210_pigeonhole__infinite__rel,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_int,R3: int > int > $o] :
% 6.94/7.30 ( ~ ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite_finite_int @ B5 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ A4 )
% 6.94/7.30 => ? [Xa3: int] :
% 6.94/7.30 ( ( member_int @ Xa3 @ B5 )
% 6.94/7.30 & ( R3 @ X3 @ Xa3 ) ) )
% 6.94/7.30 => ? [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ B5 )
% 6.94/7.30 & ~ ( finite_finite_int
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [A5: int] :
% 6.94/7.30 ( ( member_int @ A5 @ A4 )
% 6.94/7.30 & ( R3 @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % pigeonhole_infinite_rel
% 6.94/7.30 thf(fact_9211_pigeonhole__infinite__rel,axiom,
% 6.94/7.30 ! [A4: set_int,B5: set_Code_integer,R3: int > code_integer > $o] :
% 6.94/7.30 ( ~ ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.30 => ( ! [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ A4 )
% 6.94/7.30 => ? [Xa3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ Xa3 @ B5 )
% 6.94/7.30 & ( R3 @ X3 @ Xa3 ) ) )
% 6.94/7.30 => ? [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ B5 )
% 6.94/7.30 & ~ ( finite_finite_int
% 6.94/7.30 @ ( collect_int
% 6.94/7.30 @ ^ [A5: int] :
% 6.94/7.30 ( ( member_int @ A5 @ A4 )
% 6.94/7.30 & ( R3 @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % pigeonhole_infinite_rel
% 6.94/7.30 thf(fact_9212_pigeonhole__infinite__rel,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,B5: set_nat,R3: code_integer > nat > $o] :
% 6.94/7.30 ( ~ ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( finite_finite_nat @ B5 )
% 6.94/7.30 => ( ! [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ A4 )
% 6.94/7.30 => ? [Xa3: nat] :
% 6.94/7.30 ( ( member_nat @ Xa3 @ B5 )
% 6.94/7.30 & ( R3 @ X3 @ Xa3 ) ) )
% 6.94/7.30 => ? [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ B5 )
% 6.94/7.30 & ~ ( finite6017078050557962740nteger
% 6.94/7.30 @ ( collect_Code_integer
% 6.94/7.30 @ ^ [A5: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ A5 @ A4 )
% 6.94/7.30 & ( R3 @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % pigeonhole_infinite_rel
% 6.94/7.30 thf(fact_9213_finite__has__minimal2,axiom,
% 6.94/7.30 ! [A4: set_o,A: $o] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( member_o @ A @ A4 )
% 6.94/7.30 => ? [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ A4 )
% 6.94/7.30 & ( ord_less_eq_o @ X3 @ A )
% 6.94/7.30 & ! [Xa3: $o] :
% 6.94/7.30 ( ( member_o @ Xa3 @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_o @ Xa3 @ X3 )
% 6.94/7.30 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_has_minimal2
% 6.94/7.30 thf(fact_9214_finite__has__minimal2,axiom,
% 6.94/7.30 ! [A4: set_se6260736226359567993nt_int,A: set_Pr958786334691620121nt_int] :
% 6.94/7.30 ( ( finite8744585540193469122nt_int @ A4 )
% 6.94/7.30 => ( ( member2340774599025711042nt_int @ A @ A4 )
% 6.94/7.30 => ? [X3: set_Pr958786334691620121nt_int] :
% 6.94/7.30 ( ( member2340774599025711042nt_int @ X3 @ A4 )
% 6.94/7.30 & ( ord_le2843351958646193337nt_int @ X3 @ A )
% 6.94/7.30 & ! [Xa3: set_Pr958786334691620121nt_int] :
% 6.94/7.30 ( ( member2340774599025711042nt_int @ Xa3 @ A4 )
% 6.94/7.30 => ( ( ord_le2843351958646193337nt_int @ Xa3 @ X3 )
% 6.94/7.30 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_has_minimal2
% 6.94/7.30 thf(fact_9215_finite__has__minimal2,axiom,
% 6.94/7.30 ! [A4: set_set_nat,A: set_nat] :
% 6.94/7.30 ( ( finite1152437895449049373et_nat @ A4 )
% 6.94/7.30 => ( ( member_set_nat @ A @ A4 )
% 6.94/7.30 => ? [X3: set_nat] :
% 6.94/7.30 ( ( member_set_nat @ X3 @ A4 )
% 6.94/7.30 & ( ord_less_eq_set_nat @ X3 @ A )
% 6.94/7.30 & ! [Xa3: set_nat] :
% 6.94/7.30 ( ( member_set_nat @ Xa3 @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ Xa3 @ X3 )
% 6.94/7.30 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_has_minimal2
% 6.94/7.30 thf(fact_9216_finite__has__minimal2,axiom,
% 6.94/7.30 ! [A4: set_Code_integer,A: code_integer] :
% 6.94/7.30 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.30 => ( ( member_Code_integer @ A @ A4 )
% 6.94/7.30 => ? [X3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ X3 @ A4 )
% 6.94/7.30 & ( ord_le3102999989581377725nteger @ X3 @ A )
% 6.94/7.30 & ! [Xa3: code_integer] :
% 6.94/7.30 ( ( member_Code_integer @ Xa3 @ A4 )
% 6.94/7.30 => ( ( ord_le3102999989581377725nteger @ Xa3 @ X3 )
% 6.94/7.30 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_has_minimal2
% 6.94/7.30 thf(fact_9217_finite__has__minimal2,axiom,
% 6.94/7.30 ! [A4: set_set_int,A: set_int] :
% 6.94/7.30 ( ( finite6197958912794628473et_int @ A4 )
% 6.94/7.30 => ( ( member_set_int @ A @ A4 )
% 6.94/7.30 => ? [X3: set_int] :
% 6.94/7.30 ( ( member_set_int @ X3 @ A4 )
% 6.94/7.30 & ( ord_less_eq_set_int @ X3 @ A )
% 6.94/7.30 & ! [Xa3: set_int] :
% 6.94/7.30 ( ( member_set_int @ Xa3 @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_set_int @ Xa3 @ X3 )
% 6.94/7.30 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_has_minimal2
% 6.94/7.30 thf(fact_9218_finite__has__minimal2,axiom,
% 6.94/7.30 ! [A4: set_rat,A: rat] :
% 6.94/7.30 ( ( finite_finite_rat @ A4 )
% 6.94/7.30 => ( ( member_rat @ A @ A4 )
% 6.94/7.30 => ? [X3: rat] :
% 6.94/7.30 ( ( member_rat @ X3 @ A4 )
% 6.94/7.30 & ( ord_less_eq_rat @ X3 @ A )
% 6.94/7.30 & ! [Xa3: rat] :
% 6.94/7.30 ( ( member_rat @ Xa3 @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_rat @ Xa3 @ X3 )
% 6.94/7.30 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_has_minimal2
% 6.94/7.30 thf(fact_9219_finite__has__minimal2,axiom,
% 6.94/7.30 ! [A4: set_num,A: num] :
% 6.94/7.30 ( ( finite_finite_num @ A4 )
% 6.94/7.30 => ( ( member_num @ A @ A4 )
% 6.94/7.30 => ? [X3: num] :
% 6.94/7.30 ( ( member_num @ X3 @ A4 )
% 6.94/7.30 & ( ord_less_eq_num @ X3 @ A )
% 6.94/7.30 & ! [Xa3: num] :
% 6.94/7.30 ( ( member_num @ Xa3 @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_num @ Xa3 @ X3 )
% 6.94/7.30 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_has_minimal2
% 6.94/7.30 thf(fact_9220_finite__has__minimal2,axiom,
% 6.94/7.30 ! [A4: set_nat,A: nat] :
% 6.94/7.30 ( ( finite_finite_nat @ A4 )
% 6.94/7.30 => ( ( member_nat @ A @ A4 )
% 6.94/7.30 => ? [X3: nat] :
% 6.94/7.30 ( ( member_nat @ X3 @ A4 )
% 6.94/7.30 & ( ord_less_eq_nat @ X3 @ A )
% 6.94/7.30 & ! [Xa3: nat] :
% 6.94/7.30 ( ( member_nat @ Xa3 @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_nat @ Xa3 @ X3 )
% 6.94/7.30 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_has_minimal2
% 6.94/7.30 thf(fact_9221_finite__has__minimal2,axiom,
% 6.94/7.30 ! [A4: set_int,A: int] :
% 6.94/7.30 ( ( finite_finite_int @ A4 )
% 6.94/7.30 => ( ( member_int @ A @ A4 )
% 6.94/7.30 => ? [X3: int] :
% 6.94/7.30 ( ( member_int @ X3 @ A4 )
% 6.94/7.30 & ( ord_less_eq_int @ X3 @ A )
% 6.94/7.30 & ! [Xa3: int] :
% 6.94/7.30 ( ( member_int @ Xa3 @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_int @ Xa3 @ X3 )
% 6.94/7.30 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_has_minimal2
% 6.94/7.30 thf(fact_9222_finite__has__maximal2,axiom,
% 6.94/7.30 ! [A4: set_o,A: $o] :
% 6.94/7.30 ( ( finite_finite_o @ A4 )
% 6.94/7.30 => ( ( member_o @ A @ A4 )
% 6.94/7.30 => ? [X3: $o] :
% 6.94/7.30 ( ( member_o @ X3 @ A4 )
% 6.94/7.30 & ( ord_less_eq_o @ A @ X3 )
% 6.94/7.30 & ! [Xa3: $o] :
% 6.94/7.30 ( ( member_o @ Xa3 @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_o @ X3 @ Xa3 )
% 6.94/7.30 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_has_maximal2
% 6.94/7.30 thf(fact_9223_finite__has__maximal2,axiom,
% 6.94/7.30 ! [A4: set_se6260736226359567993nt_int,A: set_Pr958786334691620121nt_int] :
% 6.94/7.30 ( ( finite8744585540193469122nt_int @ A4 )
% 6.94/7.30 => ( ( member2340774599025711042nt_int @ A @ A4 )
% 6.94/7.30 => ? [X3: set_Pr958786334691620121nt_int] :
% 6.94/7.30 ( ( member2340774599025711042nt_int @ X3 @ A4 )
% 6.94/7.30 & ( ord_le2843351958646193337nt_int @ A @ X3 )
% 6.94/7.30 & ! [Xa3: set_Pr958786334691620121nt_int] :
% 6.94/7.30 ( ( member2340774599025711042nt_int @ Xa3 @ A4 )
% 6.94/7.30 => ( ( ord_le2843351958646193337nt_int @ X3 @ Xa3 )
% 6.94/7.30 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.30
% 6.94/7.30 % finite_has_maximal2
% 6.94/7.30 thf(fact_9224_finite__has__maximal2,axiom,
% 6.94/7.30 ! [A4: set_set_nat,A: set_nat] :
% 6.94/7.30 ( ( finite1152437895449049373et_nat @ A4 )
% 6.94/7.30 => ( ( member_set_nat @ A @ A4 )
% 6.94/7.30 => ? [X3: set_nat] :
% 6.94/7.30 ( ( member_set_nat @ X3 @ A4 )
% 6.94/7.30 & ( ord_less_eq_set_nat @ A @ X3 )
% 6.94/7.30 & ! [Xa3: set_nat] :
% 6.94/7.30 ( ( member_set_nat @ Xa3 @ A4 )
% 6.94/7.30 => ( ( ord_less_eq_set_nat @ X3 @ Xa3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_maximal2
% 6.94/7.31 thf(fact_9225_finite__has__maximal2,axiom,
% 6.94/7.31 ! [A4: set_Code_integer,A: code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ( member_Code_integer @ A @ A4 )
% 6.94/7.31 => ? [X3: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ X3 @ A4 )
% 6.94/7.31 & ( ord_le3102999989581377725nteger @ A @ X3 )
% 6.94/7.31 & ! [Xa3: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_le3102999989581377725nteger @ X3 @ Xa3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_maximal2
% 6.94/7.31 thf(fact_9226_finite__has__maximal2,axiom,
% 6.94/7.31 ! [A4: set_set_int,A: set_int] :
% 6.94/7.31 ( ( finite6197958912794628473et_int @ A4 )
% 6.94/7.31 => ( ( member_set_int @ A @ A4 )
% 6.94/7.31 => ? [X3: set_int] :
% 6.94/7.31 ( ( member_set_int @ X3 @ A4 )
% 6.94/7.31 & ( ord_less_eq_set_int @ A @ X3 )
% 6.94/7.31 & ! [Xa3: set_int] :
% 6.94/7.31 ( ( member_set_int @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_set_int @ X3 @ Xa3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_maximal2
% 6.94/7.31 thf(fact_9227_finite__has__maximal2,axiom,
% 6.94/7.31 ! [A4: set_rat,A: rat] :
% 6.94/7.31 ( ( finite_finite_rat @ A4 )
% 6.94/7.31 => ( ( member_rat @ A @ A4 )
% 6.94/7.31 => ? [X3: rat] :
% 6.94/7.31 ( ( member_rat @ X3 @ A4 )
% 6.94/7.31 & ( ord_less_eq_rat @ A @ X3 )
% 6.94/7.31 & ! [Xa3: rat] :
% 6.94/7.31 ( ( member_rat @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_rat @ X3 @ Xa3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_maximal2
% 6.94/7.31 thf(fact_9228_finite__has__maximal2,axiom,
% 6.94/7.31 ! [A4: set_num,A: num] :
% 6.94/7.31 ( ( finite_finite_num @ A4 )
% 6.94/7.31 => ( ( member_num @ A @ A4 )
% 6.94/7.31 => ? [X3: num] :
% 6.94/7.31 ( ( member_num @ X3 @ A4 )
% 6.94/7.31 & ( ord_less_eq_num @ A @ X3 )
% 6.94/7.31 & ! [Xa3: num] :
% 6.94/7.31 ( ( member_num @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_num @ X3 @ Xa3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_maximal2
% 6.94/7.31 thf(fact_9229_finite__has__maximal2,axiom,
% 6.94/7.31 ! [A4: set_nat,A: nat] :
% 6.94/7.31 ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ( member_nat @ A @ A4 )
% 6.94/7.31 => ? [X3: nat] :
% 6.94/7.31 ( ( member_nat @ X3 @ A4 )
% 6.94/7.31 & ( ord_less_eq_nat @ A @ X3 )
% 6.94/7.31 & ! [Xa3: nat] :
% 6.94/7.31 ( ( member_nat @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_nat @ X3 @ Xa3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_maximal2
% 6.94/7.31 thf(fact_9230_finite__has__maximal2,axiom,
% 6.94/7.31 ! [A4: set_int,A: int] :
% 6.94/7.31 ( ( finite_finite_int @ A4 )
% 6.94/7.31 => ( ( member_int @ A @ A4 )
% 6.94/7.31 => ? [X3: int] :
% 6.94/7.31 ( ( member_int @ X3 @ A4 )
% 6.94/7.31 & ( ord_less_eq_int @ A @ X3 )
% 6.94/7.31 & ! [Xa3: int] :
% 6.94/7.31 ( ( member_int @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_int @ X3 @ Xa3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_maximal2
% 6.94/7.31 thf(fact_9231_rev__finite__subset,axiom,
% 6.94/7.31 ! [B5: set_nat,A4: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.94/7.31 => ( finite_finite_nat @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % rev_finite_subset
% 6.94/7.31 thf(fact_9232_rev__finite__subset,axiom,
% 6.94/7.31 ! [B5: set_Code_integer,A4: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.31 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.94/7.31 => ( finite6017078050557962740nteger @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % rev_finite_subset
% 6.94/7.31 thf(fact_9233_rev__finite__subset,axiom,
% 6.94/7.31 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.31 => ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 6.94/7.31 => ( finite6177210948735845034at_nat @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % rev_finite_subset
% 6.94/7.31 thf(fact_9234_rev__finite__subset,axiom,
% 6.94/7.31 ! [B5: set_int,A4: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.94/7.31 => ( finite_finite_int @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % rev_finite_subset
% 6.94/7.31 thf(fact_9235_infinite__super,axiom,
% 6.94/7.31 ! [S: set_nat,T7: set_nat] :
% 6.94/7.31 ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.31 => ( ~ ( finite_finite_nat @ S )
% 6.94/7.31 => ~ ( finite_finite_nat @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_super
% 6.94/7.31 thf(fact_9236_infinite__super,axiom,
% 6.94/7.31 ! [S: set_Code_integer,T7: set_Code_integer] :
% 6.94/7.31 ( ( ord_le7084787975880047091nteger @ S @ T7 )
% 6.94/7.31 => ( ~ ( finite6017078050557962740nteger @ S )
% 6.94/7.31 => ~ ( finite6017078050557962740nteger @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_super
% 6.94/7.31 thf(fact_9237_infinite__super,axiom,
% 6.94/7.31 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( ord_le3146513528884898305at_nat @ S @ T7 )
% 6.94/7.31 => ( ~ ( finite6177210948735845034at_nat @ S )
% 6.94/7.31 => ~ ( finite6177210948735845034at_nat @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_super
% 6.94/7.31 thf(fact_9238_infinite__super,axiom,
% 6.94/7.31 ! [S: set_int,T7: set_int] :
% 6.94/7.31 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.31 => ( ~ ( finite_finite_int @ S )
% 6.94/7.31 => ~ ( finite_finite_int @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_super
% 6.94/7.31 thf(fact_9239_finite__subset,axiom,
% 6.94/7.31 ! [A4: set_nat,B5: set_nat] :
% 6.94/7.31 ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.94/7.31 => ( ( finite_finite_nat @ B5 )
% 6.94/7.31 => ( finite_finite_nat @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset
% 6.94/7.31 thf(fact_9240_finite__subset,axiom,
% 6.94/7.31 ! [A4: set_Code_integer,B5: set_Code_integer] :
% 6.94/7.31 ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.94/7.31 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.31 => ( finite6017078050557962740nteger @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset
% 6.94/7.31 thf(fact_9241_finite__subset,axiom,
% 6.94/7.31 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 6.94/7.31 => ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.31 => ( finite6177210948735845034at_nat @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset
% 6.94/7.31 thf(fact_9242_finite__subset,axiom,
% 6.94/7.31 ! [A4: set_int,B5: set_int] :
% 6.94/7.31 ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.94/7.31 => ( ( finite_finite_int @ B5 )
% 6.94/7.31 => ( finite_finite_int @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset
% 6.94/7.31 thf(fact_9243_finite__UnI,axiom,
% 6.94/7.31 ! [F5: set_int,G4: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ F5 )
% 6.94/7.31 => ( ( finite_finite_int @ G4 )
% 6.94/7.31 => ( finite_finite_int @ ( sup_sup_set_int @ F5 @ G4 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_UnI
% 6.94/7.31 thf(fact_9244_finite__UnI,axiom,
% 6.94/7.31 ! [F5: set_Code_integer,G4: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ F5 )
% 6.94/7.31 => ( ( finite6017078050557962740nteger @ G4 )
% 6.94/7.31 => ( finite6017078050557962740nteger @ ( sup_su848401254843788991nteger @ F5 @ G4 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_UnI
% 6.94/7.31 thf(fact_9245_finite__UnI,axiom,
% 6.94/7.31 ! [F5: set_Pr1261947904930325089at_nat,G4: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ F5 )
% 6.94/7.31 => ( ( finite6177210948735845034at_nat @ G4 )
% 6.94/7.31 => ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ F5 @ G4 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_UnI
% 6.94/7.31 thf(fact_9246_finite__UnI,axiom,
% 6.94/7.31 ! [F5: set_Pr8551490117392284871at_nat,G4: set_Pr8551490117392284871at_nat] :
% 6.94/7.31 ( ( finite1918287321285529104at_nat @ F5 )
% 6.94/7.31 => ( ( finite1918287321285529104at_nat @ G4 )
% 6.94/7.31 => ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ F5 @ G4 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_UnI
% 6.94/7.31 thf(fact_9247_finite__UnI,axiom,
% 6.94/7.31 ! [F5: set_Pr4329608150637261639at_nat,G4: set_Pr4329608150637261639at_nat] :
% 6.94/7.31 ( ( finite4343798906461161616at_nat @ F5 )
% 6.94/7.31 => ( ( finite4343798906461161616at_nat @ G4 )
% 6.94/7.31 => ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ F5 @ G4 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_UnI
% 6.94/7.31 thf(fact_9248_finite__UnI,axiom,
% 6.94/7.31 ! [F5: set_nat,G4: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ F5 )
% 6.94/7.31 => ( ( finite_finite_nat @ G4 )
% 6.94/7.31 => ( finite_finite_nat @ ( sup_sup_set_nat @ F5 @ G4 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_UnI
% 6.94/7.31 thf(fact_9249_Un__infinite,axiom,
% 6.94/7.31 ! [S: set_int,T7: set_int] :
% 6.94/7.31 ( ~ ( finite_finite_int @ S )
% 6.94/7.31 => ~ ( finite_finite_int @ ( sup_sup_set_int @ S @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % Un_infinite
% 6.94/7.31 thf(fact_9250_Un__infinite,axiom,
% 6.94/7.31 ! [S: set_Code_integer,T7: set_Code_integer] :
% 6.94/7.31 ( ~ ( finite6017078050557962740nteger @ S )
% 6.94/7.31 => ~ ( finite6017078050557962740nteger @ ( sup_su848401254843788991nteger @ S @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % Un_infinite
% 6.94/7.31 thf(fact_9251_Un__infinite,axiom,
% 6.94/7.31 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ~ ( finite6177210948735845034at_nat @ S )
% 6.94/7.31 => ~ ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ S @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % Un_infinite
% 6.94/7.31 thf(fact_9252_Un__infinite,axiom,
% 6.94/7.31 ! [S: set_Pr8551490117392284871at_nat,T7: set_Pr8551490117392284871at_nat] :
% 6.94/7.31 ( ~ ( finite1918287321285529104at_nat @ S )
% 6.94/7.31 => ~ ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ S @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % Un_infinite
% 6.94/7.31 thf(fact_9253_Un__infinite,axiom,
% 6.94/7.31 ! [S: set_Pr4329608150637261639at_nat,T7: set_Pr4329608150637261639at_nat] :
% 6.94/7.31 ( ~ ( finite4343798906461161616at_nat @ S )
% 6.94/7.31 => ~ ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ S @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % Un_infinite
% 6.94/7.31 thf(fact_9254_Un__infinite,axiom,
% 6.94/7.31 ! [S: set_nat,T7: set_nat] :
% 6.94/7.31 ( ~ ( finite_finite_nat @ S )
% 6.94/7.31 => ~ ( finite_finite_nat @ ( sup_sup_set_nat @ S @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % Un_infinite
% 6.94/7.31 thf(fact_9255_infinite__Un,axiom,
% 6.94/7.31 ! [S: set_int,T7: set_int] :
% 6.94/7.31 ( ( ~ ( finite_finite_int @ ( sup_sup_set_int @ S @ T7 ) ) )
% 6.94/7.31 = ( ~ ( finite_finite_int @ S )
% 6.94/7.31 | ~ ( finite_finite_int @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_Un
% 6.94/7.31 thf(fact_9256_infinite__Un,axiom,
% 6.94/7.31 ! [S: set_Code_integer,T7: set_Code_integer] :
% 6.94/7.31 ( ( ~ ( finite6017078050557962740nteger @ ( sup_su848401254843788991nteger @ S @ T7 ) ) )
% 6.94/7.31 = ( ~ ( finite6017078050557962740nteger @ S )
% 6.94/7.31 | ~ ( finite6017078050557962740nteger @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_Un
% 6.94/7.31 thf(fact_9257_infinite__Un,axiom,
% 6.94/7.31 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( ~ ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ S @ T7 ) ) )
% 6.94/7.31 = ( ~ ( finite6177210948735845034at_nat @ S )
% 6.94/7.31 | ~ ( finite6177210948735845034at_nat @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_Un
% 6.94/7.31 thf(fact_9258_infinite__Un,axiom,
% 6.94/7.31 ! [S: set_Pr8551490117392284871at_nat,T7: set_Pr8551490117392284871at_nat] :
% 6.94/7.31 ( ( ~ ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ S @ T7 ) ) )
% 6.94/7.31 = ( ~ ( finite1918287321285529104at_nat @ S )
% 6.94/7.31 | ~ ( finite1918287321285529104at_nat @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_Un
% 6.94/7.31 thf(fact_9259_infinite__Un,axiom,
% 6.94/7.31 ! [S: set_Pr4329608150637261639at_nat,T7: set_Pr4329608150637261639at_nat] :
% 6.94/7.31 ( ( ~ ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ S @ T7 ) ) )
% 6.94/7.31 = ( ~ ( finite4343798906461161616at_nat @ S )
% 6.94/7.31 | ~ ( finite4343798906461161616at_nat @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_Un
% 6.94/7.31 thf(fact_9260_infinite__Un,axiom,
% 6.94/7.31 ! [S: set_nat,T7: set_nat] :
% 6.94/7.31 ( ( ~ ( finite_finite_nat @ ( sup_sup_set_nat @ S @ T7 ) ) )
% 6.94/7.31 = ( ~ ( finite_finite_nat @ S )
% 6.94/7.31 | ~ ( finite_finite_nat @ T7 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_Un
% 6.94/7.31 thf(fact_9261_finite__psubset__induct,axiom,
% 6.94/7.31 ! [A4: set_nat,P2: set_nat > $o] :
% 6.94/7.31 ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ! [A9: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ A9 )
% 6.94/7.31 => ( ! [B10: set_nat] :
% 6.94/7.31 ( ( ord_less_set_nat @ B10 @ A9 )
% 6.94/7.31 => ( P2 @ B10 ) )
% 6.94/7.31 => ( P2 @ A9 ) ) )
% 6.94/7.31 => ( P2 @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_psubset_induct
% 6.94/7.31 thf(fact_9262_finite__psubset__induct,axiom,
% 6.94/7.31 ! [A4: set_int,P2: set_int > $o] :
% 6.94/7.31 ( ( finite_finite_int @ A4 )
% 6.94/7.31 => ( ! [A9: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ A9 )
% 6.94/7.31 => ( ! [B10: set_int] :
% 6.94/7.31 ( ( ord_less_set_int @ B10 @ A9 )
% 6.94/7.31 => ( P2 @ B10 ) )
% 6.94/7.31 => ( P2 @ A9 ) ) )
% 6.94/7.31 => ( P2 @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_psubset_induct
% 6.94/7.31 thf(fact_9263_finite__psubset__induct,axiom,
% 6.94/7.31 ! [A4: set_Code_integer,P2: set_Code_integer > $o] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ! [A9: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A9 )
% 6.94/7.31 => ( ! [B10: set_Code_integer] :
% 6.94/7.31 ( ( ord_le1307284697595431911nteger @ B10 @ A9 )
% 6.94/7.31 => ( P2 @ B10 ) )
% 6.94/7.31 => ( P2 @ A9 ) ) )
% 6.94/7.31 => ( P2 @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_psubset_induct
% 6.94/7.31 thf(fact_9264_finite__psubset__induct,axiom,
% 6.94/7.31 ! [A4: set_Pr1261947904930325089at_nat,P2: set_Pr1261947904930325089at_nat > $o] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.31 => ( ! [A9: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ A9 )
% 6.94/7.31 => ( ! [B10: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( ord_le7866589430770878221at_nat @ B10 @ A9 )
% 6.94/7.31 => ( P2 @ B10 ) )
% 6.94/7.31 => ( P2 @ A9 ) ) )
% 6.94/7.31 => ( P2 @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_psubset_induct
% 6.94/7.31 thf(fact_9265_Suc__0__or__eq,axiom,
% 6.94/7.31 ! [N2: nat] :
% 6.94/7.31 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 6.94/7.31 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % Suc_0_or_eq
% 6.94/7.31 thf(fact_9266_or__Suc__0__eq,axiom,
% 6.94/7.31 ! [N2: nat] :
% 6.94/7.31 ( ( bit_se1412395901928357646or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 6.94/7.31 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % or_Suc_0_eq
% 6.94/7.31 thf(fact_9267_or__nat__rec,axiom,
% 6.94/7.31 ( bit_se1412395901928357646or_nat
% 6.94/7.31 = ( ^ [M3: nat,N: nat] :
% 6.94/7.31 ( plus_plus_nat
% 6.94/7.31 @ ( zero_n2687167440665602831ol_nat
% 6.94/7.31 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 6.94/7.31 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 6.94/7.31 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % or_nat_rec
% 6.94/7.31 thf(fact_9268_finite__has__maximal,axiom,
% 6.94/7.31 ! [A4: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ( A4 != bot_bo3990330152332043303nteger )
% 6.94/7.31 => ? [X3: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ X3 @ A4 )
% 6.94/7.31 & ! [Xa3: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_le3102999989581377725nteger @ X3 @ Xa3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_maximal
% 6.94/7.31 thf(fact_9269_finite__has__maximal,axiom,
% 6.94/7.31 ! [A4: set_o] :
% 6.94/7.31 ( ( finite_finite_o @ A4 )
% 6.94/7.31 => ( ( A4 != bot_bot_set_o )
% 6.94/7.31 => ? [X3: $o] :
% 6.94/7.31 ( ( member_o @ X3 @ A4 )
% 6.94/7.31 & ! [Xa3: $o] :
% 6.94/7.31 ( ( member_o @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_o @ X3 @ Xa3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_maximal
% 6.94/7.31 thf(fact_9270_finite__has__maximal,axiom,
% 6.94/7.31 ! [A4: set_set_int] :
% 6.94/7.31 ( ( finite6197958912794628473et_int @ A4 )
% 6.94/7.31 => ( ( A4 != bot_bot_set_set_int )
% 6.94/7.31 => ? [X3: set_int] :
% 6.94/7.31 ( ( member_set_int @ X3 @ A4 )
% 6.94/7.31 & ! [Xa3: set_int] :
% 6.94/7.31 ( ( member_set_int @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_set_int @ X3 @ Xa3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_maximal
% 6.94/7.31 thf(fact_9271_finite__has__maximal,axiom,
% 6.94/7.31 ! [A4: set_rat] :
% 6.94/7.31 ( ( finite_finite_rat @ A4 )
% 6.94/7.31 => ( ( A4 != bot_bot_set_rat )
% 6.94/7.31 => ? [X3: rat] :
% 6.94/7.31 ( ( member_rat @ X3 @ A4 )
% 6.94/7.31 & ! [Xa3: rat] :
% 6.94/7.31 ( ( member_rat @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_rat @ X3 @ Xa3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_maximal
% 6.94/7.31 thf(fact_9272_finite__has__maximal,axiom,
% 6.94/7.31 ! [A4: set_num] :
% 6.94/7.31 ( ( finite_finite_num @ A4 )
% 6.94/7.31 => ( ( A4 != bot_bot_set_num )
% 6.94/7.31 => ? [X3: num] :
% 6.94/7.31 ( ( member_num @ X3 @ A4 )
% 6.94/7.31 & ! [Xa3: num] :
% 6.94/7.31 ( ( member_num @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_num @ X3 @ Xa3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_maximal
% 6.94/7.31 thf(fact_9273_finite__has__maximal,axiom,
% 6.94/7.31 ! [A4: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ( A4 != bot_bot_set_nat )
% 6.94/7.31 => ? [X3: nat] :
% 6.94/7.31 ( ( member_nat @ X3 @ A4 )
% 6.94/7.31 & ! [Xa3: nat] :
% 6.94/7.31 ( ( member_nat @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_nat @ X3 @ Xa3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_maximal
% 6.94/7.31 thf(fact_9274_finite__has__maximal,axiom,
% 6.94/7.31 ! [A4: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ A4 )
% 6.94/7.31 => ( ( A4 != bot_bot_set_int )
% 6.94/7.31 => ? [X3: int] :
% 6.94/7.31 ( ( member_int @ X3 @ A4 )
% 6.94/7.31 & ! [Xa3: int] :
% 6.94/7.31 ( ( member_int @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_int @ X3 @ Xa3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_maximal
% 6.94/7.31 thf(fact_9275_finite__has__minimal,axiom,
% 6.94/7.31 ! [A4: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ( A4 != bot_bo3990330152332043303nteger )
% 6.94/7.31 => ? [X3: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ X3 @ A4 )
% 6.94/7.31 & ! [Xa3: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_le3102999989581377725nteger @ Xa3 @ X3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_minimal
% 6.94/7.31 thf(fact_9276_finite__has__minimal,axiom,
% 6.94/7.31 ! [A4: set_o] :
% 6.94/7.31 ( ( finite_finite_o @ A4 )
% 6.94/7.31 => ( ( A4 != bot_bot_set_o )
% 6.94/7.31 => ? [X3: $o] :
% 6.94/7.31 ( ( member_o @ X3 @ A4 )
% 6.94/7.31 & ! [Xa3: $o] :
% 6.94/7.31 ( ( member_o @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_o @ Xa3 @ X3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_minimal
% 6.94/7.31 thf(fact_9277_finite__has__minimal,axiom,
% 6.94/7.31 ! [A4: set_set_int] :
% 6.94/7.31 ( ( finite6197958912794628473et_int @ A4 )
% 6.94/7.31 => ( ( A4 != bot_bot_set_set_int )
% 6.94/7.31 => ? [X3: set_int] :
% 6.94/7.31 ( ( member_set_int @ X3 @ A4 )
% 6.94/7.31 & ! [Xa3: set_int] :
% 6.94/7.31 ( ( member_set_int @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_set_int @ Xa3 @ X3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_minimal
% 6.94/7.31 thf(fact_9278_finite__has__minimal,axiom,
% 6.94/7.31 ! [A4: set_rat] :
% 6.94/7.31 ( ( finite_finite_rat @ A4 )
% 6.94/7.31 => ( ( A4 != bot_bot_set_rat )
% 6.94/7.31 => ? [X3: rat] :
% 6.94/7.31 ( ( member_rat @ X3 @ A4 )
% 6.94/7.31 & ! [Xa3: rat] :
% 6.94/7.31 ( ( member_rat @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_rat @ Xa3 @ X3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_minimal
% 6.94/7.31 thf(fact_9279_finite__has__minimal,axiom,
% 6.94/7.31 ! [A4: set_num] :
% 6.94/7.31 ( ( finite_finite_num @ A4 )
% 6.94/7.31 => ( ( A4 != bot_bot_set_num )
% 6.94/7.31 => ? [X3: num] :
% 6.94/7.31 ( ( member_num @ X3 @ A4 )
% 6.94/7.31 & ! [Xa3: num] :
% 6.94/7.31 ( ( member_num @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_num @ Xa3 @ X3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_minimal
% 6.94/7.31 thf(fact_9280_finite__has__minimal,axiom,
% 6.94/7.31 ! [A4: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ( A4 != bot_bot_set_nat )
% 6.94/7.31 => ? [X3: nat] :
% 6.94/7.31 ( ( member_nat @ X3 @ A4 )
% 6.94/7.31 & ! [Xa3: nat] :
% 6.94/7.31 ( ( member_nat @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_nat @ Xa3 @ X3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_minimal
% 6.94/7.31 thf(fact_9281_finite__has__minimal,axiom,
% 6.94/7.31 ! [A4: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ A4 )
% 6.94/7.31 => ( ( A4 != bot_bot_set_int )
% 6.94/7.31 => ? [X3: int] :
% 6.94/7.31 ( ( member_int @ X3 @ A4 )
% 6.94/7.31 & ! [Xa3: int] :
% 6.94/7.31 ( ( member_int @ Xa3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_int @ Xa3 @ X3 )
% 6.94/7.31 => ( X3 = Xa3 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_has_minimal
% 6.94/7.31 thf(fact_9282_finite__subset__induct_H,axiom,
% 6.94/7.31 ! [F5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat,P2: set_Pr4329608150637261639at_nat > $o] :
% 6.94/7.31 ( ( finite4343798906461161616at_nat @ F5 )
% 6.94/7.31 => ( ( ord_le1268244103169919719at_nat @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bo228742789529271731at_nat )
% 6.94/7.31 => ( ! [A3: produc3843707927480180839at_nat,F6: set_Pr4329608150637261639at_nat] :
% 6.94/7.31 ( ( finite4343798906461161616at_nat @ F6 )
% 6.94/7.31 => ( ( member8757157785044589968at_nat @ A3 @ A4 )
% 6.94/7.31 => ( ( ord_le1268244103169919719at_nat @ F6 @ A4 )
% 6.94/7.31 => ( ~ ( member8757157785044589968at_nat @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert9069300056098147895at_nat @ A3 @ F6 ) ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct'
% 6.94/7.31 thf(fact_9283_finite__subset__induct_H,axiom,
% 6.94/7.31 ! [F5: set_se6260736226359567993nt_int,A4: set_se6260736226359567993nt_int,P2: set_se6260736226359567993nt_int > $o] :
% 6.94/7.31 ( ( finite8744585540193469122nt_int @ F5 )
% 6.94/7.31 => ( ( ord_le483042692224249369nt_int @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bo1488462491386950373nt_int )
% 6.94/7.31 => ( ! [A3: set_Pr958786334691620121nt_int,F6: set_se6260736226359567993nt_int] :
% 6.94/7.31 ( ( finite8744585540193469122nt_int @ F6 )
% 6.94/7.31 => ( ( member2340774599025711042nt_int @ A3 @ A4 )
% 6.94/7.31 => ( ( ord_le483042692224249369nt_int @ F6 @ A4 )
% 6.94/7.31 => ( ~ ( member2340774599025711042nt_int @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert8897473484851387113nt_int @ A3 @ F6 ) ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct'
% 6.94/7.31 thf(fact_9284_finite__subset__induct_H,axiom,
% 6.94/7.31 ! [F5: set_set_nat,A4: set_set_nat,P2: set_set_nat > $o] :
% 6.94/7.31 ( ( finite1152437895449049373et_nat @ F5 )
% 6.94/7.31 => ( ( ord_le6893508408891458716et_nat @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bot_set_set_nat )
% 6.94/7.31 => ( ! [A3: set_nat,F6: set_set_nat] :
% 6.94/7.31 ( ( finite1152437895449049373et_nat @ F6 )
% 6.94/7.31 => ( ( member_set_nat @ A3 @ A4 )
% 6.94/7.31 => ( ( ord_le6893508408891458716et_nat @ F6 @ A4 )
% 6.94/7.31 => ( ~ ( member_set_nat @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert_set_nat @ A3 @ F6 ) ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct'
% 6.94/7.31 thf(fact_9285_finite__subset__induct_H,axiom,
% 6.94/7.31 ! [F5: set_Code_integer,A4: set_Code_integer,P2: set_Code_integer > $o] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ F5 )
% 6.94/7.31 => ( ( ord_le7084787975880047091nteger @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 6.94/7.31 => ( ! [A3: code_integer,F6: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ F6 )
% 6.94/7.31 => ( ( member_Code_integer @ A3 @ A4 )
% 6.94/7.31 => ( ( ord_le7084787975880047091nteger @ F6 @ A4 )
% 6.94/7.31 => ( ~ ( member_Code_integer @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert_Code_integer @ A3 @ F6 ) ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct'
% 6.94/7.31 thf(fact_9286_finite__subset__induct_H,axiom,
% 6.94/7.31 ! [F5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,P2: set_Pr1261947904930325089at_nat > $o] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ F5 )
% 6.94/7.31 => ( ( ord_le3146513528884898305at_nat @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bo2099793752762293965at_nat )
% 6.94/7.31 => ( ! [A3: product_prod_nat_nat,F6: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ F6 )
% 6.94/7.31 => ( ( member8440522571783428010at_nat @ A3 @ A4 )
% 6.94/7.31 => ( ( ord_le3146513528884898305at_nat @ F6 @ A4 )
% 6.94/7.31 => ( ~ ( member8440522571783428010at_nat @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert8211810215607154385at_nat @ A3 @ F6 ) ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct'
% 6.94/7.31 thf(fact_9287_finite__subset__induct_H,axiom,
% 6.94/7.31 ! [F5: set_o,A4: set_o,P2: set_o > $o] :
% 6.94/7.31 ( ( finite_finite_o @ F5 )
% 6.94/7.31 => ( ( ord_less_eq_set_o @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bot_set_o )
% 6.94/7.31 => ( ! [A3: $o,F6: set_o] :
% 6.94/7.31 ( ( finite_finite_o @ F6 )
% 6.94/7.31 => ( ( member_o @ A3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_set_o @ F6 @ A4 )
% 6.94/7.31 => ( ~ ( member_o @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert_o @ A3 @ F6 ) ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct'
% 6.94/7.31 thf(fact_9288_finite__subset__induct_H,axiom,
% 6.94/7.31 ! [F5: set_nat,A4: set_nat,P2: set_nat > $o] :
% 6.94/7.31 ( ( finite_finite_nat @ F5 )
% 6.94/7.31 => ( ( ord_less_eq_set_nat @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bot_set_nat )
% 6.94/7.31 => ( ! [A3: nat,F6: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ F6 )
% 6.94/7.31 => ( ( member_nat @ A3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_set_nat @ F6 @ A4 )
% 6.94/7.31 => ( ~ ( member_nat @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert_nat @ A3 @ F6 ) ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct'
% 6.94/7.31 thf(fact_9289_finite__subset__induct_H,axiom,
% 6.94/7.31 ! [F5: set_int,A4: set_int,P2: set_int > $o] :
% 6.94/7.31 ( ( finite_finite_int @ F5 )
% 6.94/7.31 => ( ( ord_less_eq_set_int @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bot_set_int )
% 6.94/7.31 => ( ! [A3: int,F6: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ F6 )
% 6.94/7.31 => ( ( member_int @ A3 @ A4 )
% 6.94/7.31 => ( ( ord_less_eq_set_int @ F6 @ A4 )
% 6.94/7.31 => ( ~ ( member_int @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert_int @ A3 @ F6 ) ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct'
% 6.94/7.31 thf(fact_9290_finite__subset__induct,axiom,
% 6.94/7.31 ! [F5: set_Pr4329608150637261639at_nat,A4: set_Pr4329608150637261639at_nat,P2: set_Pr4329608150637261639at_nat > $o] :
% 6.94/7.31 ( ( finite4343798906461161616at_nat @ F5 )
% 6.94/7.31 => ( ( ord_le1268244103169919719at_nat @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bo228742789529271731at_nat )
% 6.94/7.31 => ( ! [A3: produc3843707927480180839at_nat,F6: set_Pr4329608150637261639at_nat] :
% 6.94/7.31 ( ( finite4343798906461161616at_nat @ F6 )
% 6.94/7.31 => ( ( member8757157785044589968at_nat @ A3 @ A4 )
% 6.94/7.31 => ( ~ ( member8757157785044589968at_nat @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert9069300056098147895at_nat @ A3 @ F6 ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct
% 6.94/7.31 thf(fact_9291_finite__subset__induct,axiom,
% 6.94/7.31 ! [F5: set_se6260736226359567993nt_int,A4: set_se6260736226359567993nt_int,P2: set_se6260736226359567993nt_int > $o] :
% 6.94/7.31 ( ( finite8744585540193469122nt_int @ F5 )
% 6.94/7.31 => ( ( ord_le483042692224249369nt_int @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bo1488462491386950373nt_int )
% 6.94/7.31 => ( ! [A3: set_Pr958786334691620121nt_int,F6: set_se6260736226359567993nt_int] :
% 6.94/7.31 ( ( finite8744585540193469122nt_int @ F6 )
% 6.94/7.31 => ( ( member2340774599025711042nt_int @ A3 @ A4 )
% 6.94/7.31 => ( ~ ( member2340774599025711042nt_int @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert8897473484851387113nt_int @ A3 @ F6 ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct
% 6.94/7.31 thf(fact_9292_finite__subset__induct,axiom,
% 6.94/7.31 ! [F5: set_set_nat,A4: set_set_nat,P2: set_set_nat > $o] :
% 6.94/7.31 ( ( finite1152437895449049373et_nat @ F5 )
% 6.94/7.31 => ( ( ord_le6893508408891458716et_nat @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bot_set_set_nat )
% 6.94/7.31 => ( ! [A3: set_nat,F6: set_set_nat] :
% 6.94/7.31 ( ( finite1152437895449049373et_nat @ F6 )
% 6.94/7.31 => ( ( member_set_nat @ A3 @ A4 )
% 6.94/7.31 => ( ~ ( member_set_nat @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert_set_nat @ A3 @ F6 ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct
% 6.94/7.31 thf(fact_9293_finite__subset__induct,axiom,
% 6.94/7.31 ! [F5: set_Code_integer,A4: set_Code_integer,P2: set_Code_integer > $o] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ F5 )
% 6.94/7.31 => ( ( ord_le7084787975880047091nteger @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 6.94/7.31 => ( ! [A3: code_integer,F6: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ F6 )
% 6.94/7.31 => ( ( member_Code_integer @ A3 @ A4 )
% 6.94/7.31 => ( ~ ( member_Code_integer @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert_Code_integer @ A3 @ F6 ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct
% 6.94/7.31 thf(fact_9294_finite__subset__induct,axiom,
% 6.94/7.31 ! [F5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,P2: set_Pr1261947904930325089at_nat > $o] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ F5 )
% 6.94/7.31 => ( ( ord_le3146513528884898305at_nat @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bo2099793752762293965at_nat )
% 6.94/7.31 => ( ! [A3: product_prod_nat_nat,F6: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ F6 )
% 6.94/7.31 => ( ( member8440522571783428010at_nat @ A3 @ A4 )
% 6.94/7.31 => ( ~ ( member8440522571783428010at_nat @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert8211810215607154385at_nat @ A3 @ F6 ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct
% 6.94/7.31 thf(fact_9295_finite__subset__induct,axiom,
% 6.94/7.31 ! [F5: set_o,A4: set_o,P2: set_o > $o] :
% 6.94/7.31 ( ( finite_finite_o @ F5 )
% 6.94/7.31 => ( ( ord_less_eq_set_o @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bot_set_o )
% 6.94/7.31 => ( ! [A3: $o,F6: set_o] :
% 6.94/7.31 ( ( finite_finite_o @ F6 )
% 6.94/7.31 => ( ( member_o @ A3 @ A4 )
% 6.94/7.31 => ( ~ ( member_o @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert_o @ A3 @ F6 ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct
% 6.94/7.31 thf(fact_9296_finite__subset__induct,axiom,
% 6.94/7.31 ! [F5: set_nat,A4: set_nat,P2: set_nat > $o] :
% 6.94/7.31 ( ( finite_finite_nat @ F5 )
% 6.94/7.31 => ( ( ord_less_eq_set_nat @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bot_set_nat )
% 6.94/7.31 => ( ! [A3: nat,F6: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ F6 )
% 6.94/7.31 => ( ( member_nat @ A3 @ A4 )
% 6.94/7.31 => ( ~ ( member_nat @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert_nat @ A3 @ F6 ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct
% 6.94/7.31 thf(fact_9297_finite__subset__induct,axiom,
% 6.94/7.31 ! [F5: set_int,A4: set_int,P2: set_int > $o] :
% 6.94/7.31 ( ( finite_finite_int @ F5 )
% 6.94/7.31 => ( ( ord_less_eq_set_int @ F5 @ A4 )
% 6.94/7.31 => ( ( P2 @ bot_bot_set_int )
% 6.94/7.31 => ( ! [A3: int,F6: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ F6 )
% 6.94/7.31 => ( ( member_int @ A3 @ A4 )
% 6.94/7.31 => ( ~ ( member_int @ A3 @ F6 )
% 6.94/7.31 => ( ( P2 @ F6 )
% 6.94/7.31 => ( P2 @ ( insert_int @ A3 @ F6 ) ) ) ) ) )
% 6.94/7.31 => ( P2 @ F5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_subset_induct
% 6.94/7.31 thf(fact_9298_finite__remove__induct,axiom,
% 6.94/7.31 ! [B5: set_Pr4329608150637261639at_nat,P2: set_Pr4329608150637261639at_nat > $o] :
% 6.94/7.31 ( ( finite4343798906461161616at_nat @ B5 )
% 6.94/7.31 => ( ( P2 @ bot_bo228742789529271731at_nat )
% 6.94/7.31 => ( ! [A9: set_Pr4329608150637261639at_nat] :
% 6.94/7.31 ( ( finite4343798906461161616at_nat @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bo228742789529271731at_nat )
% 6.94/7.31 => ( ( ord_le1268244103169919719at_nat @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: produc3843707927480180839at_nat] :
% 6.94/7.31 ( ( member8757157785044589968at_nat @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_3314409938677909166at_nat @ A9 @ ( insert9069300056098147895at_nat @ X6 @ bot_bo228742789529271731at_nat ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_remove_induct
% 6.94/7.31 thf(fact_9299_finite__remove__induct,axiom,
% 6.94/7.31 ! [B5: set_se6260736226359567993nt_int,P2: set_se6260736226359567993nt_int > $o] :
% 6.94/7.31 ( ( finite8744585540193469122nt_int @ B5 )
% 6.94/7.31 => ( ( P2 @ bot_bo1488462491386950373nt_int )
% 6.94/7.31 => ( ! [A9: set_se6260736226359567993nt_int] :
% 6.94/7.31 ( ( finite8744585540193469122nt_int @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bo1488462491386950373nt_int )
% 6.94/7.31 => ( ( ord_le483042692224249369nt_int @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: set_Pr958786334691620121nt_int] :
% 6.94/7.31 ( ( member2340774599025711042nt_int @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_2612819937483484256nt_int @ A9 @ ( insert8897473484851387113nt_int @ X6 @ bot_bo1488462491386950373nt_int ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_remove_induct
% 6.94/7.31 thf(fact_9300_finite__remove__induct,axiom,
% 6.94/7.31 ! [B5: set_set_nat,P2: set_set_nat > $o] :
% 6.94/7.31 ( ( finite1152437895449049373et_nat @ B5 )
% 6.94/7.31 => ( ( P2 @ bot_bot_set_set_nat )
% 6.94/7.31 => ( ! [A9: set_set_nat] :
% 6.94/7.31 ( ( finite1152437895449049373et_nat @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bot_set_set_nat )
% 6.94/7.31 => ( ( ord_le6893508408891458716et_nat @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: set_nat] :
% 6.94/7.31 ( ( member_set_nat @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_2163939370556025621et_nat @ A9 @ ( insert_set_nat @ X6 @ bot_bot_set_set_nat ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_remove_induct
% 6.94/7.31 thf(fact_9301_finite__remove__induct,axiom,
% 6.94/7.31 ! [B5: set_Code_integer,P2: set_Code_integer > $o] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.31 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 6.94/7.31 => ( ! [A9: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bo3990330152332043303nteger )
% 6.94/7.31 => ( ( ord_le7084787975880047091nteger @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_2355218937544613996nteger @ A9 @ ( insert_Code_integer @ X6 @ bot_bo3990330152332043303nteger ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_remove_induct
% 6.94/7.31 thf(fact_9302_finite__remove__induct,axiom,
% 6.94/7.31 ! [B5: set_o,P2: set_o > $o] :
% 6.94/7.31 ( ( finite_finite_o @ B5 )
% 6.94/7.31 => ( ( P2 @ bot_bot_set_o )
% 6.94/7.31 => ( ! [A9: set_o] :
% 6.94/7.31 ( ( finite_finite_o @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bot_set_o )
% 6.94/7.31 => ( ( ord_less_eq_set_o @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: $o] :
% 6.94/7.31 ( ( member_o @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_minus_set_o @ A9 @ ( insert_o @ X6 @ bot_bot_set_o ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_remove_induct
% 6.94/7.31 thf(fact_9303_finite__remove__induct,axiom,
% 6.94/7.31 ! [B5: set_nat,P2: set_nat > $o] :
% 6.94/7.31 ( ( finite_finite_nat @ B5 )
% 6.94/7.31 => ( ( P2 @ bot_bot_set_nat )
% 6.94/7.31 => ( ! [A9: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bot_set_nat )
% 6.94/7.31 => ( ( ord_less_eq_set_nat @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: nat] :
% 6.94/7.31 ( ( member_nat @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_minus_set_nat @ A9 @ ( insert_nat @ X6 @ bot_bot_set_nat ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_remove_induct
% 6.94/7.31 thf(fact_9304_finite__remove__induct,axiom,
% 6.94/7.31 ! [B5: set_Pr1261947904930325089at_nat,P2: set_Pr1261947904930325089at_nat > $o] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.31 => ( ( P2 @ bot_bo2099793752762293965at_nat )
% 6.94/7.31 => ( ! [A9: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bo2099793752762293965at_nat )
% 6.94/7.31 => ( ( ord_le3146513528884898305at_nat @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: product_prod_nat_nat] :
% 6.94/7.31 ( ( member8440522571783428010at_nat @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_1356011639430497352at_nat @ A9 @ ( insert8211810215607154385at_nat @ X6 @ bot_bo2099793752762293965at_nat ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_remove_induct
% 6.94/7.31 thf(fact_9305_finite__remove__induct,axiom,
% 6.94/7.31 ! [B5: set_int,P2: set_int > $o] :
% 6.94/7.31 ( ( finite_finite_int @ B5 )
% 6.94/7.31 => ( ( P2 @ bot_bot_set_int )
% 6.94/7.31 => ( ! [A9: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bot_set_int )
% 6.94/7.31 => ( ( ord_less_eq_set_int @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: int] :
% 6.94/7.31 ( ( member_int @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_minus_set_int @ A9 @ ( insert_int @ X6 @ bot_bot_set_int ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_remove_induct
% 6.94/7.31 thf(fact_9306_remove__induct,axiom,
% 6.94/7.31 ! [P2: set_Pr4329608150637261639at_nat > $o,B5: set_Pr4329608150637261639at_nat] :
% 6.94/7.31 ( ( P2 @ bot_bo228742789529271731at_nat )
% 6.94/7.31 => ( ( ~ ( finite4343798906461161616at_nat @ B5 )
% 6.94/7.31 => ( P2 @ B5 ) )
% 6.94/7.31 => ( ! [A9: set_Pr4329608150637261639at_nat] :
% 6.94/7.31 ( ( finite4343798906461161616at_nat @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bo228742789529271731at_nat )
% 6.94/7.31 => ( ( ord_le1268244103169919719at_nat @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: produc3843707927480180839at_nat] :
% 6.94/7.31 ( ( member8757157785044589968at_nat @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_3314409938677909166at_nat @ A9 @ ( insert9069300056098147895at_nat @ X6 @ bot_bo228742789529271731at_nat ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % remove_induct
% 6.94/7.31 thf(fact_9307_remove__induct,axiom,
% 6.94/7.31 ! [P2: set_se6260736226359567993nt_int > $o,B5: set_se6260736226359567993nt_int] :
% 6.94/7.31 ( ( P2 @ bot_bo1488462491386950373nt_int )
% 6.94/7.31 => ( ( ~ ( finite8744585540193469122nt_int @ B5 )
% 6.94/7.31 => ( P2 @ B5 ) )
% 6.94/7.31 => ( ! [A9: set_se6260736226359567993nt_int] :
% 6.94/7.31 ( ( finite8744585540193469122nt_int @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bo1488462491386950373nt_int )
% 6.94/7.31 => ( ( ord_le483042692224249369nt_int @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: set_Pr958786334691620121nt_int] :
% 6.94/7.31 ( ( member2340774599025711042nt_int @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_2612819937483484256nt_int @ A9 @ ( insert8897473484851387113nt_int @ X6 @ bot_bo1488462491386950373nt_int ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % remove_induct
% 6.94/7.31 thf(fact_9308_remove__induct,axiom,
% 6.94/7.31 ! [P2: set_set_nat > $o,B5: set_set_nat] :
% 6.94/7.31 ( ( P2 @ bot_bot_set_set_nat )
% 6.94/7.31 => ( ( ~ ( finite1152437895449049373et_nat @ B5 )
% 6.94/7.31 => ( P2 @ B5 ) )
% 6.94/7.31 => ( ! [A9: set_set_nat] :
% 6.94/7.31 ( ( finite1152437895449049373et_nat @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bot_set_set_nat )
% 6.94/7.31 => ( ( ord_le6893508408891458716et_nat @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: set_nat] :
% 6.94/7.31 ( ( member_set_nat @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_2163939370556025621et_nat @ A9 @ ( insert_set_nat @ X6 @ bot_bot_set_set_nat ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % remove_induct
% 6.94/7.31 thf(fact_9309_remove__induct,axiom,
% 6.94/7.31 ! [P2: set_Code_integer > $o,B5: set_Code_integer] :
% 6.94/7.31 ( ( P2 @ bot_bo3990330152332043303nteger )
% 6.94/7.31 => ( ( ~ ( finite6017078050557962740nteger @ B5 )
% 6.94/7.31 => ( P2 @ B5 ) )
% 6.94/7.31 => ( ! [A9: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bo3990330152332043303nteger )
% 6.94/7.31 => ( ( ord_le7084787975880047091nteger @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_2355218937544613996nteger @ A9 @ ( insert_Code_integer @ X6 @ bot_bo3990330152332043303nteger ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % remove_induct
% 6.94/7.31 thf(fact_9310_remove__induct,axiom,
% 6.94/7.31 ! [P2: set_o > $o,B5: set_o] :
% 6.94/7.31 ( ( P2 @ bot_bot_set_o )
% 6.94/7.31 => ( ( ~ ( finite_finite_o @ B5 )
% 6.94/7.31 => ( P2 @ B5 ) )
% 6.94/7.31 => ( ! [A9: set_o] :
% 6.94/7.31 ( ( finite_finite_o @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bot_set_o )
% 6.94/7.31 => ( ( ord_less_eq_set_o @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: $o] :
% 6.94/7.31 ( ( member_o @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_minus_set_o @ A9 @ ( insert_o @ X6 @ bot_bot_set_o ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % remove_induct
% 6.94/7.31 thf(fact_9311_remove__induct,axiom,
% 6.94/7.31 ! [P2: set_nat > $o,B5: set_nat] :
% 6.94/7.31 ( ( P2 @ bot_bot_set_nat )
% 6.94/7.31 => ( ( ~ ( finite_finite_nat @ B5 )
% 6.94/7.31 => ( P2 @ B5 ) )
% 6.94/7.31 => ( ! [A9: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bot_set_nat )
% 6.94/7.31 => ( ( ord_less_eq_set_nat @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: nat] :
% 6.94/7.31 ( ( member_nat @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_minus_set_nat @ A9 @ ( insert_nat @ X6 @ bot_bot_set_nat ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % remove_induct
% 6.94/7.31 thf(fact_9312_remove__induct,axiom,
% 6.94/7.31 ! [P2: set_Pr1261947904930325089at_nat > $o,B5: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( P2 @ bot_bo2099793752762293965at_nat )
% 6.94/7.31 => ( ( ~ ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.31 => ( P2 @ B5 ) )
% 6.94/7.31 => ( ! [A9: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bo2099793752762293965at_nat )
% 6.94/7.31 => ( ( ord_le3146513528884898305at_nat @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: product_prod_nat_nat] :
% 6.94/7.31 ( ( member8440522571783428010at_nat @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_1356011639430497352at_nat @ A9 @ ( insert8211810215607154385at_nat @ X6 @ bot_bo2099793752762293965at_nat ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % remove_induct
% 6.94/7.31 thf(fact_9313_remove__induct,axiom,
% 6.94/7.31 ! [P2: set_int > $o,B5: set_int] :
% 6.94/7.31 ( ( P2 @ bot_bot_set_int )
% 6.94/7.31 => ( ( ~ ( finite_finite_int @ B5 )
% 6.94/7.31 => ( P2 @ B5 ) )
% 6.94/7.31 => ( ! [A9: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ A9 )
% 6.94/7.31 => ( ( A9 != bot_bot_set_int )
% 6.94/7.31 => ( ( ord_less_eq_set_int @ A9 @ B5 )
% 6.94/7.31 => ( ! [X6: int] :
% 6.94/7.31 ( ( member_int @ X6 @ A9 )
% 6.94/7.31 => ( P2 @ ( minus_minus_set_int @ A9 @ ( insert_int @ X6 @ bot_bot_set_int ) ) ) )
% 6.94/7.31 => ( P2 @ A9 ) ) ) ) )
% 6.94/7.31 => ( P2 @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % remove_induct
% 6.94/7.31 thf(fact_9314_set__encode__insert,axiom,
% 6.94/7.31 ! [A4: set_nat,N2: nat] :
% 6.94/7.31 ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ~ ( member_nat @ N2 @ A4 )
% 6.94/7.31 => ( ( nat_set_encode @ ( insert_nat @ N2 @ A4 ) )
% 6.94/7.31 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( nat_set_encode @ A4 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % set_encode_insert
% 6.94/7.31 thf(fact_9315_finite__nat__bounded,axiom,
% 6.94/7.31 ! [S: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ S )
% 6.94/7.31 => ? [K: nat] : ( ord_less_eq_set_nat @ S @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_nat_bounded
% 6.94/7.31 thf(fact_9316_finite__nat__iff__bounded,axiom,
% 6.94/7.31 ( finite_finite_nat
% 6.94/7.31 = ( ^ [S4: set_nat] :
% 6.94/7.31 ? [K3: nat] : ( ord_less_eq_set_nat @ S4 @ ( set_ord_lessThan_nat @ K3 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_nat_iff_bounded
% 6.94/7.31 thf(fact_9317_finite__nat__iff__bounded__le,axiom,
% 6.94/7.31 ( finite_finite_nat
% 6.94/7.31 = ( ^ [S4: set_nat] :
% 6.94/7.31 ? [K3: nat] : ( ord_less_eq_set_nat @ S4 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_nat_iff_bounded_le
% 6.94/7.31 thf(fact_9318_in__finite__psubset,axiom,
% 6.94/7.31 ! [A4: set_nat,B5: set_nat] :
% 6.94/7.31 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A4 @ B5 ) @ finite_psubset_nat )
% 6.94/7.31 = ( ( ord_less_set_nat @ A4 @ B5 )
% 6.94/7.31 & ( finite_finite_nat @ B5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % in_finite_psubset
% 6.94/7.31 thf(fact_9319_in__finite__psubset,axiom,
% 6.94/7.31 ! [A4: set_int,B5: set_int] :
% 6.94/7.31 ( ( member2572552093476627150et_int @ ( produc6363374080413544029et_int @ A4 @ B5 ) @ finite_psubset_int )
% 6.94/7.31 = ( ( ord_less_set_int @ A4 @ B5 )
% 6.94/7.31 & ( finite_finite_int @ B5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % in_finite_psubset
% 6.94/7.31 thf(fact_9320_in__finite__psubset,axiom,
% 6.94/7.31 ! [A4: set_Code_integer,B5: set_Code_integer] :
% 6.94/7.31 ( ( member4307123515891402160nteger @ ( produc7443773368509356479nteger @ A4 @ B5 ) @ finite2416775604798480986nteger )
% 6.94/7.31 = ( ( ord_le1307284697595431911nteger @ A4 @ B5 )
% 6.94/7.31 & ( finite6017078050557962740nteger @ B5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % in_finite_psubset
% 6.94/7.31 thf(fact_9321_in__finite__psubset,axiom,
% 6.94/7.31 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A4 @ B5 ) @ finite469560695537375940at_nat )
% 6.94/7.31 = ( ( ord_le7866589430770878221at_nat @ A4 @ B5 )
% 6.94/7.31 & ( finite6177210948735845034at_nat @ B5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % in_finite_psubset
% 6.94/7.31 thf(fact_9322_infinite__int__iff__unbounded__le,axiom,
% 6.94/7.31 ! [S: set_int] :
% 6.94/7.31 ( ( ~ ( finite_finite_int @ S ) )
% 6.94/7.31 = ( ! [M3: int] :
% 6.94/7.31 ? [N: int] :
% 6.94/7.31 ( ( ord_less_eq_int @ M3 @ ( abs_abs_int @ N ) )
% 6.94/7.31 & ( member_int @ N @ S ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_int_iff_unbounded_le
% 6.94/7.31 thf(fact_9323_infinite__int__iff__unbounded,axiom,
% 6.94/7.31 ! [S: set_int] :
% 6.94/7.31 ( ( ~ ( finite_finite_int @ S ) )
% 6.94/7.31 = ( ! [M3: int] :
% 6.94/7.31 ? [N: int] :
% 6.94/7.31 ( ( ord_less_int @ M3 @ ( abs_abs_int @ N ) )
% 6.94/7.31 & ( member_int @ N @ S ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_int_iff_unbounded
% 6.94/7.31 thf(fact_9324_finite__psubset__def,axiom,
% 6.94/7.31 ( finite_psubset_nat
% 6.94/7.31 = ( collec6662362479098859352et_nat
% 6.94/7.31 @ ( produc6247414631856714078_nat_o
% 6.94/7.31 @ ^ [A6: set_nat,B6: set_nat] :
% 6.94/7.31 ( ( ord_less_set_nat @ A6 @ B6 )
% 6.94/7.31 & ( finite_finite_nat @ B6 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_psubset_def
% 6.94/7.31 thf(fact_9325_finite__psubset__def,axiom,
% 6.94/7.31 ( finite_psubset_int
% 6.94/7.31 = ( collec957716948307931664et_int
% 6.94/7.31 @ ( produc4109468873575309990_int_o
% 6.94/7.31 @ ^ [A6: set_int,B6: set_int] :
% 6.94/7.31 ( ( ord_less_set_int @ A6 @ B6 )
% 6.94/7.31 & ( finite_finite_int @ B6 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_psubset_def
% 6.94/7.31 thf(fact_9326_finite__psubset__def,axiom,
% 6.94/7.31 ( finite2416775604798480986nteger
% 6.94/7.31 = ( collec2770208431294612722nteger
% 6.94/7.31 @ ( produc1658495936642081476eger_o
% 6.94/7.31 @ ^ [A6: set_Code_integer,B6: set_Code_integer] :
% 6.94/7.31 ( ( ord_le1307284697595431911nteger @ A6 @ B6 )
% 6.94/7.31 & ( finite6017078050557962740nteger @ B6 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_psubset_def
% 6.94/7.31 thf(fact_9327_finite__psubset__def,axiom,
% 6.94/7.31 ( finite469560695537375940at_nat
% 6.94/7.31 = ( collec6321179662152712658at_nat
% 6.94/7.31 @ ( produc410239310623530412_nat_o
% 6.94/7.31 @ ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( ord_le7866589430770878221at_nat @ A6 @ B6 )
% 6.94/7.31 & ( finite6177210948735845034at_nat @ B6 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_psubset_def
% 6.94/7.31 thf(fact_9328_unbounded__k__infinite,axiom,
% 6.94/7.31 ! [K2: nat,S: set_nat] :
% 6.94/7.31 ( ! [M5: nat] :
% 6.94/7.31 ( ( ord_less_nat @ K2 @ M5 )
% 6.94/7.31 => ? [N10: nat] :
% 6.94/7.31 ( ( ord_less_nat @ M5 @ N10 )
% 6.94/7.31 & ( member_nat @ N10 @ S ) ) )
% 6.94/7.31 => ~ ( finite_finite_nat @ S ) ) ).
% 6.94/7.31
% 6.94/7.31 % unbounded_k_infinite
% 6.94/7.31 thf(fact_9329_infinite__nat__iff__unbounded,axiom,
% 6.94/7.31 ! [S: set_nat] :
% 6.94/7.31 ( ( ~ ( finite_finite_nat @ S ) )
% 6.94/7.31 = ( ! [M3: nat] :
% 6.94/7.31 ? [N: nat] :
% 6.94/7.31 ( ( ord_less_nat @ M3 @ N )
% 6.94/7.31 & ( member_nat @ N @ S ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_nat_iff_unbounded
% 6.94/7.31 thf(fact_9330_infinite__nat__iff__unbounded__le,axiom,
% 6.94/7.31 ! [S: set_nat] :
% 6.94/7.31 ( ( ~ ( finite_finite_nat @ S ) )
% 6.94/7.31 = ( ! [M3: nat] :
% 6.94/7.31 ? [N: nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ M3 @ N )
% 6.94/7.31 & ( member_nat @ N @ S ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_nat_iff_unbounded_le
% 6.94/7.31 thf(fact_9331_or__int__unfold,axiom,
% 6.94/7.31 ( bit_se1409905431419307370or_int
% 6.94/7.31 = ( ^ [K3: int,L2: int] :
% 6.94/7.31 ( if_int
% 6.94/7.31 @ ( ( K3
% 6.94/7.31 = ( uminus_uminus_int @ one_one_int ) )
% 6.94/7.31 | ( L2
% 6.94/7.31 = ( uminus_uminus_int @ one_one_int ) ) )
% 6.94/7.31 @ ( uminus_uminus_int @ one_one_int )
% 6.94/7.31 @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % or_int_unfold
% 6.94/7.31 thf(fact_9332_or__nat__unfold,axiom,
% 6.94/7.31 ( bit_se1412395901928357646or_nat
% 6.94/7.31 = ( ^ [M3: nat,N: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N @ ( if_nat @ ( N = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % or_nat_unfold
% 6.94/7.31 thf(fact_9333_sum__diff1_H__aux,axiom,
% 6.94/7.31 ! [F5: set_Code_integer,I5: set_Code_integer,F: code_integer > code_integer,I2: code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ F5 )
% 6.94/7.31 => ( ( ord_le7084787975880047091nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [I: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ I @ I5 )
% 6.94/7.31 & ( ( F @ I )
% 6.94/7.31 != zero_z3403309356797280102nteger ) ) )
% 6.94/7.31 @ F5 )
% 6.94/7.31 => ( ( ( member_Code_integer @ I2 @ I5 )
% 6.94/7.31 => ( ( groups910942671188738463nteger @ F @ ( minus_2355218937544613996nteger @ I5 @ ( insert_Code_integer @ I2 @ bot_bo3990330152332043303nteger ) ) )
% 6.94/7.31 = ( minus_8373710615458151222nteger @ ( groups910942671188738463nteger @ F @ I5 ) @ ( F @ I2 ) ) ) )
% 6.94/7.31 & ( ~ ( member_Code_integer @ I2 @ I5 )
% 6.94/7.31 => ( ( groups910942671188738463nteger @ F @ ( minus_2355218937544613996nteger @ I5 @ ( insert_Code_integer @ I2 @ bot_bo3990330152332043303nteger ) ) )
% 6.94/7.31 = ( groups910942671188738463nteger @ F @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_diff1'_aux
% 6.94/7.31 thf(fact_9334_sum__diff1_H__aux,axiom,
% 6.94/7.31 ! [F5: set_o,I5: set_o,F: $o > code_integer,I2: $o] :
% 6.94/7.31 ( ( finite_finite_o @ F5 )
% 6.94/7.31 => ( ( ord_less_eq_set_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( ( member_o @ I @ I5 )
% 6.94/7.31 & ( ( F @ I )
% 6.94/7.31 != zero_z3403309356797280102nteger ) ) )
% 6.94/7.31 @ F5 )
% 6.94/7.31 => ( ( ( member_o @ I2 @ I5 )
% 6.94/7.31 => ( ( groups1402912129352969042nteger @ F @ ( minus_minus_set_o @ I5 @ ( insert_o @ I2 @ bot_bot_set_o ) ) )
% 6.94/7.31 = ( minus_8373710615458151222nteger @ ( groups1402912129352969042nteger @ F @ I5 ) @ ( F @ I2 ) ) ) )
% 6.94/7.31 & ( ~ ( member_o @ I2 @ I5 )
% 6.94/7.31 => ( ( groups1402912129352969042nteger @ F @ ( minus_minus_set_o @ I5 @ ( insert_o @ I2 @ bot_bot_set_o ) ) )
% 6.94/7.31 = ( groups1402912129352969042nteger @ F @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_diff1'_aux
% 6.94/7.31 thf(fact_9335_sum__diff1_H__aux,axiom,
% 6.94/7.31 ! [F5: set_nat,I5: set_nat,F: nat > code_integer,I2: nat] :
% 6.94/7.31 ( ( finite_finite_nat @ F5 )
% 6.94/7.31 => ( ( ord_less_eq_set_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [I: nat] :
% 6.94/7.31 ( ( member_nat @ I @ I5 )
% 6.94/7.31 & ( ( F @ I )
% 6.94/7.31 != zero_z3403309356797280102nteger ) ) )
% 6.94/7.31 @ F5 )
% 6.94/7.31 => ( ( ( member_nat @ I2 @ I5 )
% 6.94/7.31 => ( ( groups555127423416065298nteger @ F @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 6.94/7.31 = ( minus_8373710615458151222nteger @ ( groups555127423416065298nteger @ F @ I5 ) @ ( F @ I2 ) ) ) )
% 6.94/7.31 & ( ~ ( member_nat @ I2 @ I5 )
% 6.94/7.31 => ( ( groups555127423416065298nteger @ F @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 6.94/7.31 = ( groups555127423416065298nteger @ F @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_diff1'_aux
% 6.94/7.31 thf(fact_9336_sum__diff1_H__aux,axiom,
% 6.94/7.31 ! [F5: set_Code_integer,I5: set_Code_integer,F: code_integer > rat,I2: code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ F5 )
% 6.94/7.31 => ( ( ord_le7084787975880047091nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [I: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ I @ I5 )
% 6.94/7.31 & ( ( F @ I )
% 6.94/7.31 != zero_zero_rat ) ) )
% 6.94/7.31 @ F5 )
% 6.94/7.31 => ( ( ( member_Code_integer @ I2 @ I5 )
% 6.94/7.31 => ( ( groups8878813951405302554er_rat @ F @ ( minus_2355218937544613996nteger @ I5 @ ( insert_Code_integer @ I2 @ bot_bo3990330152332043303nteger ) ) )
% 6.94/7.31 = ( minus_minus_rat @ ( groups8878813951405302554er_rat @ F @ I5 ) @ ( F @ I2 ) ) ) )
% 6.94/7.31 & ( ~ ( member_Code_integer @ I2 @ I5 )
% 6.94/7.31 => ( ( groups8878813951405302554er_rat @ F @ ( minus_2355218937544613996nteger @ I5 @ ( insert_Code_integer @ I2 @ bot_bo3990330152332043303nteger ) ) )
% 6.94/7.31 = ( groups8878813951405302554er_rat @ F @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_diff1'_aux
% 6.94/7.31 thf(fact_9337_sum__diff1_H__aux,axiom,
% 6.94/7.31 ! [F5: set_o,I5: set_o,F: $o > rat,I2: $o] :
% 6.94/7.31 ( ( finite_finite_o @ F5 )
% 6.94/7.31 => ( ( ord_less_eq_set_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( ( member_o @ I @ I5 )
% 6.94/7.31 & ( ( F @ I )
% 6.94/7.31 != zero_zero_rat ) ) )
% 6.94/7.31 @ F5 )
% 6.94/7.31 => ( ( ( member_o @ I2 @ I5 )
% 6.94/7.31 => ( ( groups3921277224699582669_o_rat @ F @ ( minus_minus_set_o @ I5 @ ( insert_o @ I2 @ bot_bot_set_o ) ) )
% 6.94/7.31 = ( minus_minus_rat @ ( groups3921277224699582669_o_rat @ F @ I5 ) @ ( F @ I2 ) ) ) )
% 6.94/7.31 & ( ~ ( member_o @ I2 @ I5 )
% 6.94/7.31 => ( ( groups3921277224699582669_o_rat @ F @ ( minus_minus_set_o @ I5 @ ( insert_o @ I2 @ bot_bot_set_o ) ) )
% 6.94/7.31 = ( groups3921277224699582669_o_rat @ F @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_diff1'_aux
% 6.94/7.31 thf(fact_9338_sum__diff1_H__aux,axiom,
% 6.94/7.31 ! [F5: set_nat,I5: set_nat,F: nat > rat,I2: nat] :
% 6.94/7.31 ( ( finite_finite_nat @ F5 )
% 6.94/7.31 => ( ( ord_less_eq_set_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [I: nat] :
% 6.94/7.31 ( ( member_nat @ I @ I5 )
% 6.94/7.31 & ( ( F @ I )
% 6.94/7.31 != zero_zero_rat ) ) )
% 6.94/7.31 @ F5 )
% 6.94/7.31 => ( ( ( member_nat @ I2 @ I5 )
% 6.94/7.31 => ( ( groups1351286907653491341at_rat @ F @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 6.94/7.31 = ( minus_minus_rat @ ( groups1351286907653491341at_rat @ F @ I5 ) @ ( F @ I2 ) ) ) )
% 6.94/7.31 & ( ~ ( member_nat @ I2 @ I5 )
% 6.94/7.31 => ( ( groups1351286907653491341at_rat @ F @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 6.94/7.31 = ( groups1351286907653491341at_rat @ F @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_diff1'_aux
% 6.94/7.31 thf(fact_9339_sum__diff1_H__aux,axiom,
% 6.94/7.31 ! [F5: set_Code_integer,I5: set_Code_integer,F: code_integer > int,I2: code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ F5 )
% 6.94/7.31 => ( ( ord_le7084787975880047091nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [I: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ I @ I5 )
% 6.94/7.31 & ( ( F @ I )
% 6.94/7.31 != zero_zero_int ) ) )
% 6.94/7.31 @ F5 )
% 6.94/7.31 => ( ( ( member_Code_integer @ I2 @ I5 )
% 6.94/7.31 => ( ( groups288081504127972206er_int @ F @ ( minus_2355218937544613996nteger @ I5 @ ( insert_Code_integer @ I2 @ bot_bo3990330152332043303nteger ) ) )
% 6.94/7.31 = ( minus_minus_int @ ( groups288081504127972206er_int @ F @ I5 ) @ ( F @ I2 ) ) ) )
% 6.94/7.31 & ( ~ ( member_Code_integer @ I2 @ I5 )
% 6.94/7.31 => ( ( groups288081504127972206er_int @ F @ ( minus_2355218937544613996nteger @ I5 @ ( insert_Code_integer @ I2 @ bot_bo3990330152332043303nteger ) ) )
% 6.94/7.31 = ( groups288081504127972206er_int @ F @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_diff1'_aux
% 6.94/7.31 thf(fact_9340_sum__diff1_H__aux,axiom,
% 6.94/7.31 ! [F5: set_o,I5: set_o,F: $o > int,I2: $o] :
% 6.94/7.31 ( ( finite_finite_o @ F5 )
% 6.94/7.31 => ( ( ord_less_eq_set_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( ( member_o @ I @ I5 )
% 6.94/7.31 & ( ( F @ I )
% 6.94/7.31 != zero_zero_int ) ) )
% 6.94/7.31 @ F5 )
% 6.94/7.31 => ( ( ( member_o @ I2 @ I5 )
% 6.94/7.31 => ( ( groups4553916814277028129_o_int @ F @ ( minus_minus_set_o @ I5 @ ( insert_o @ I2 @ bot_bot_set_o ) ) )
% 6.94/7.31 = ( minus_minus_int @ ( groups4553916814277028129_o_int @ F @ I5 ) @ ( F @ I2 ) ) ) )
% 6.94/7.31 & ( ~ ( member_o @ I2 @ I5 )
% 6.94/7.31 => ( ( groups4553916814277028129_o_int @ F @ ( minus_minus_set_o @ I5 @ ( insert_o @ I2 @ bot_bot_set_o ) ) )
% 6.94/7.31 = ( groups4553916814277028129_o_int @ F @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_diff1'_aux
% 6.94/7.31 thf(fact_9341_sum__diff1_H__aux,axiom,
% 6.94/7.31 ! [F5: set_nat,I5: set_nat,F: nat > int,I2: nat] :
% 6.94/7.31 ( ( finite_finite_nat @ F5 )
% 6.94/7.31 => ( ( ord_less_eq_set_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [I: nat] :
% 6.94/7.31 ( ( member_nat @ I @ I5 )
% 6.94/7.31 & ( ( F @ I )
% 6.94/7.31 != zero_zero_int ) ) )
% 6.94/7.31 @ F5 )
% 6.94/7.31 => ( ( ( member_nat @ I2 @ I5 )
% 6.94/7.31 => ( ( groups1983926497230936801at_int @ F @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 6.94/7.31 = ( minus_minus_int @ ( groups1983926497230936801at_int @ F @ I5 ) @ ( F @ I2 ) ) ) )
% 6.94/7.31 & ( ~ ( member_nat @ I2 @ I5 )
% 6.94/7.31 => ( ( groups1983926497230936801at_int @ F @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 6.94/7.31 = ( groups1983926497230936801at_int @ F @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_diff1'_aux
% 6.94/7.31 thf(fact_9342_sum__diff1_H__aux,axiom,
% 6.94/7.31 ! [F5: set_int,I5: set_int,F: int > code_integer,I2: int] :
% 6.94/7.31 ( ( finite_finite_int @ F5 )
% 6.94/7.31 => ( ( ord_less_eq_set_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [I: int] :
% 6.94/7.31 ( ( member_int @ I @ I5 )
% 6.94/7.31 & ( ( F @ I )
% 6.94/7.31 != zero_z3403309356797280102nteger ) ) )
% 6.94/7.31 @ F5 )
% 6.94/7.31 => ( ( ( member_int @ I2 @ I5 )
% 6.94/7.31 => ( ( groups926780983652909934nteger @ F @ ( minus_minus_set_int @ I5 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 6.94/7.31 = ( minus_8373710615458151222nteger @ ( groups926780983652909934nteger @ F @ I5 ) @ ( F @ I2 ) ) ) )
% 6.94/7.31 & ( ~ ( member_int @ I2 @ I5 )
% 6.94/7.31 => ( ( groups926780983652909934nteger @ F @ ( minus_minus_set_int @ I5 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 6.94/7.31 = ( groups926780983652909934nteger @ F @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_diff1'_aux
% 6.94/7.31 thf(fact_9343_even__sum__iff,axiom,
% 6.94/7.31 ! [A4: set_o,F: $o > nat] :
% 6.94/7.31 ( ( finite_finite_o @ A4 )
% 6.94/7.31 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups8507830703676809646_o_nat @ F @ A4 ) )
% 6.94/7.31 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 6.94/7.31 @ ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [A5: $o] :
% 6.94/7.31 ( ( member_o @ A5 @ A4 )
% 6.94/7.31 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % even_sum_iff
% 6.94/7.31 thf(fact_9344_even__sum__iff,axiom,
% 6.94/7.31 ! [A4: set_int,F: int > nat] :
% 6.94/7.31 ( ( finite_finite_int @ A4 )
% 6.94/7.31 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups4541462559716669496nt_nat @ F @ A4 ) )
% 6.94/7.31 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 6.94/7.31 @ ( finite_card_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [A5: int] :
% 6.94/7.31 ( ( member_int @ A5 @ A4 )
% 6.94/7.31 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % even_sum_iff
% 6.94/7.31 thf(fact_9345_even__sum__iff,axiom,
% 6.94/7.31 ! [A4: set_Code_integer,F: code_integer > nat] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups7237345082560585321er_nat @ F @ A4 ) )
% 6.94/7.31 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 6.94/7.31 @ ( finite4902975817058060853nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [A5: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ A5 @ A4 )
% 6.94/7.31 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % even_sum_iff
% 6.94/7.31 thf(fact_9346_even__sum__iff,axiom,
% 6.94/7.31 ! [A4: set_o,F: $o > int] :
% 6.94/7.31 ( ( finite_finite_o @ A4 )
% 6.94/7.31 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups8505340233167759370_o_int @ F @ A4 ) )
% 6.94/7.31 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 6.94/7.31 @ ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [A5: $o] :
% 6.94/7.31 ( ( member_o @ A5 @ A4 )
% 6.94/7.31 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % even_sum_iff
% 6.94/7.31 thf(fact_9347_even__sum__iff,axiom,
% 6.94/7.31 ! [A4: set_nat,F: nat > int] :
% 6.94/7.31 ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ F @ A4 ) )
% 6.94/7.31 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 6.94/7.31 @ ( finite_card_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [A5: nat] :
% 6.94/7.31 ( ( member_nat @ A5 @ A4 )
% 6.94/7.31 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % even_sum_iff
% 6.94/7.31 thf(fact_9348_even__sum__iff,axiom,
% 6.94/7.31 ! [A4: set_Code_integer,F: code_integer > int] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups7234854612051535045er_int @ F @ A4 ) )
% 6.94/7.31 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 6.94/7.31 @ ( finite4902975817058060853nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [A5: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ A5 @ A4 )
% 6.94/7.31 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % even_sum_iff
% 6.94/7.31 thf(fact_9349_even__sum__iff,axiom,
% 6.94/7.31 ! [A4: set_o,F: $o > code_natural] :
% 6.94/7.31 ( ( finite_finite_o @ A4 )
% 6.94/7.31 => ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups3230237193842799622atural @ F @ A4 ) )
% 6.94/7.31 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 6.94/7.31 @ ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [A5: $o] :
% 6.94/7.31 ( ( member_o @ A5 @ A4 )
% 6.94/7.31 & ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % even_sum_iff
% 6.94/7.31 thf(fact_9350_even__sum__iff,axiom,
% 6.94/7.31 ! [A4: set_nat,F: nat > code_natural] :
% 6.94/7.31 ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6325495683096345652atural @ F @ A4 ) )
% 6.94/7.31 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 6.94/7.31 @ ( finite_card_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [A5: nat] :
% 6.94/7.31 ( ( member_nat @ A5 @ A4 )
% 6.94/7.31 & ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % even_sum_iff
% 6.94/7.31 thf(fact_9351_even__sum__iff,axiom,
% 6.94/7.31 ! [A4: set_int,F: int > code_natural] :
% 6.94/7.31 ( ( finite_finite_int @ A4 )
% 6.94/7.31 => ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6697149243333190288atural @ F @ A4 ) )
% 6.94/7.31 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 6.94/7.31 @ ( finite_card_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [A5: int] :
% 6.94/7.31 ( ( member_int @ A5 @ A4 )
% 6.94/7.31 & ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % even_sum_iff
% 6.94/7.31 thf(fact_9352_even__sum__iff,axiom,
% 6.94/7.31 ! [A4: set_Code_integer,F: code_integer > code_natural] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups8926444216418632897atural @ F @ A4 ) )
% 6.94/7.31 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 6.94/7.31 @ ( finite4902975817058060853nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [A5: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ A5 @ A4 )
% 6.94/7.31 & ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % even_sum_iff
% 6.94/7.31 thf(fact_9353_and__not__num_Oelims,axiom,
% 6.94/7.31 ! [X: num,Xa: num,Y: option_num] :
% 6.94/7.31 ( ( ( bit_and_not_num @ X @ Xa )
% 6.94/7.31 = Y )
% 6.94/7.31 => ( ( ( X = one )
% 6.94/7.31 => ( ( Xa = one )
% 6.94/7.31 => ( Y != none_num ) ) )
% 6.94/7.31 => ( ( ( X = one )
% 6.94/7.31 => ( ? [N5: num] :
% 6.94/7.31 ( Xa
% 6.94/7.31 = ( bit0 @ N5 ) )
% 6.94/7.31 => ( Y
% 6.94/7.31 != ( some_num @ one ) ) ) )
% 6.94/7.31 => ( ( ( X = one )
% 6.94/7.31 => ( ? [N5: num] :
% 6.94/7.31 ( Xa
% 6.94/7.31 = ( bit1 @ N5 ) )
% 6.94/7.31 => ( Y != none_num ) ) )
% 6.94/7.31 => ( ! [M5: num] :
% 6.94/7.31 ( ( X
% 6.94/7.31 = ( bit0 @ M5 ) )
% 6.94/7.31 => ( ( Xa = one )
% 6.94/7.31 => ( Y
% 6.94/7.31 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 6.94/7.31 => ( ! [M5: num] :
% 6.94/7.31 ( ( X
% 6.94/7.31 = ( bit0 @ M5 ) )
% 6.94/7.31 => ! [N5: num] :
% 6.94/7.31 ( ( Xa
% 6.94/7.31 = ( bit0 @ N5 ) )
% 6.94/7.31 => ( Y
% 6.94/7.31 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N5 ) ) ) ) )
% 6.94/7.31 => ( ! [M5: num] :
% 6.94/7.31 ( ( X
% 6.94/7.31 = ( bit0 @ M5 ) )
% 6.94/7.31 => ! [N5: num] :
% 6.94/7.31 ( ( Xa
% 6.94/7.31 = ( bit1 @ N5 ) )
% 6.94/7.31 => ( Y
% 6.94/7.31 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N5 ) ) ) ) )
% 6.94/7.31 => ( ! [M5: num] :
% 6.94/7.31 ( ( X
% 6.94/7.31 = ( bit1 @ M5 ) )
% 6.94/7.31 => ( ( Xa = one )
% 6.94/7.31 => ( Y
% 6.94/7.31 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 6.94/7.31 => ( ! [M5: num] :
% 6.94/7.31 ( ( X
% 6.94/7.31 = ( bit1 @ M5 ) )
% 6.94/7.31 => ! [N5: num] :
% 6.94/7.31 ( ( Xa
% 6.94/7.31 = ( bit0 @ N5 ) )
% 6.94/7.31 => ( Y
% 6.94/7.31 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 6.94/7.31 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 6.94/7.31 @ ( bit_and_not_num @ M5 @ N5 ) ) ) ) )
% 6.94/7.31 => ~ ! [M5: num] :
% 6.94/7.31 ( ( X
% 6.94/7.31 = ( bit1 @ M5 ) )
% 6.94/7.31 => ! [N5: num] :
% 6.94/7.31 ( ( Xa
% 6.94/7.31 = ( bit1 @ N5 ) )
% 6.94/7.31 => ( Y
% 6.94/7.31 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % and_not_num.elims
% 6.94/7.31 thf(fact_9354_card__Collect__less__nat,axiom,
% 6.94/7.31 ! [N2: nat] :
% 6.94/7.31 ( ( finite_card_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [I: nat] : ( ord_less_nat @ I @ N2 ) ) )
% 6.94/7.31 = N2 ) ).
% 6.94/7.31
% 6.94/7.31 % card_Collect_less_nat
% 6.94/7.31 thf(fact_9355_max_Obounded__iff,axiom,
% 6.94/7.31 ! [B: rat,C2: rat,A: rat] :
% 6.94/7.31 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A )
% 6.94/7.31 = ( ( ord_less_eq_rat @ B @ A )
% 6.94/7.31 & ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.bounded_iff
% 6.94/7.31 thf(fact_9356_max_Obounded__iff,axiom,
% 6.94/7.31 ! [B: num,C2: num,A: num] :
% 6.94/7.31 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A )
% 6.94/7.31 = ( ( ord_less_eq_num @ B @ A )
% 6.94/7.31 & ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.bounded_iff
% 6.94/7.31 thf(fact_9357_max_Obounded__iff,axiom,
% 6.94/7.31 ! [B: nat,C2: nat,A: nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A )
% 6.94/7.31 = ( ( ord_less_eq_nat @ B @ A )
% 6.94/7.31 & ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.bounded_iff
% 6.94/7.31 thf(fact_9358_max_Obounded__iff,axiom,
% 6.94/7.31 ! [B: int,C2: int,A: int] :
% 6.94/7.31 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A )
% 6.94/7.31 = ( ( ord_less_eq_int @ B @ A )
% 6.94/7.31 & ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.bounded_iff
% 6.94/7.31 thf(fact_9359_max_Oabsorb2,axiom,
% 6.94/7.31 ! [A: rat,B: rat] :
% 6.94/7.31 ( ( ord_less_eq_rat @ A @ B )
% 6.94/7.31 => ( ( ord_max_rat @ A @ B )
% 6.94/7.31 = B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb2
% 6.94/7.31 thf(fact_9360_max_Oabsorb2,axiom,
% 6.94/7.31 ! [A: num,B: num] :
% 6.94/7.31 ( ( ord_less_eq_num @ A @ B )
% 6.94/7.31 => ( ( ord_max_num @ A @ B )
% 6.94/7.31 = B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb2
% 6.94/7.31 thf(fact_9361_max_Oabsorb2,axiom,
% 6.94/7.31 ! [A: nat,B: nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ A @ B )
% 6.94/7.31 => ( ( ord_max_nat @ A @ B )
% 6.94/7.31 = B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb2
% 6.94/7.31 thf(fact_9362_max_Oabsorb2,axiom,
% 6.94/7.31 ! [A: int,B: int] :
% 6.94/7.31 ( ( ord_less_eq_int @ A @ B )
% 6.94/7.31 => ( ( ord_max_int @ A @ B )
% 6.94/7.31 = B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb2
% 6.94/7.31 thf(fact_9363_max_Oabsorb1,axiom,
% 6.94/7.31 ! [B: rat,A: rat] :
% 6.94/7.31 ( ( ord_less_eq_rat @ B @ A )
% 6.94/7.31 => ( ( ord_max_rat @ A @ B )
% 6.94/7.31 = A ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb1
% 6.94/7.31 thf(fact_9364_max_Oabsorb1,axiom,
% 6.94/7.31 ! [B: num,A: num] :
% 6.94/7.31 ( ( ord_less_eq_num @ B @ A )
% 6.94/7.31 => ( ( ord_max_num @ A @ B )
% 6.94/7.31 = A ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb1
% 6.94/7.31 thf(fact_9365_max_Oabsorb1,axiom,
% 6.94/7.31 ! [B: nat,A: nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ B @ A )
% 6.94/7.31 => ( ( ord_max_nat @ A @ B )
% 6.94/7.31 = A ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb1
% 6.94/7.31 thf(fact_9366_max_Oabsorb1,axiom,
% 6.94/7.31 ! [B: int,A: int] :
% 6.94/7.31 ( ( ord_less_eq_int @ B @ A )
% 6.94/7.31 => ( ( ord_max_int @ A @ B )
% 6.94/7.31 = A ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb1
% 6.94/7.31 thf(fact_9367_max__less__iff__conj,axiom,
% 6.94/7.31 ! [X: rat,Y: rat,Z3: rat] :
% 6.94/7.31 ( ( ord_less_rat @ ( ord_max_rat @ X @ Y ) @ Z3 )
% 6.94/7.31 = ( ( ord_less_rat @ X @ Z3 )
% 6.94/7.31 & ( ord_less_rat @ Y @ Z3 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_less_iff_conj
% 6.94/7.31 thf(fact_9368_max__less__iff__conj,axiom,
% 6.94/7.31 ! [X: num,Y: num,Z3: num] :
% 6.94/7.31 ( ( ord_less_num @ ( ord_max_num @ X @ Y ) @ Z3 )
% 6.94/7.31 = ( ( ord_less_num @ X @ Z3 )
% 6.94/7.31 & ( ord_less_num @ Y @ Z3 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_less_iff_conj
% 6.94/7.31 thf(fact_9369_max__less__iff__conj,axiom,
% 6.94/7.31 ! [X: nat,Y: nat,Z3: nat] :
% 6.94/7.31 ( ( ord_less_nat @ ( ord_max_nat @ X @ Y ) @ Z3 )
% 6.94/7.31 = ( ( ord_less_nat @ X @ Z3 )
% 6.94/7.31 & ( ord_less_nat @ Y @ Z3 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_less_iff_conj
% 6.94/7.31 thf(fact_9370_max__less__iff__conj,axiom,
% 6.94/7.31 ! [X: int,Y: int,Z3: int] :
% 6.94/7.31 ( ( ord_less_int @ ( ord_max_int @ X @ Y ) @ Z3 )
% 6.94/7.31 = ( ( ord_less_int @ X @ Z3 )
% 6.94/7.31 & ( ord_less_int @ Y @ Z3 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_less_iff_conj
% 6.94/7.31 thf(fact_9371_max_Oabsorb4,axiom,
% 6.94/7.31 ! [A: rat,B: rat] :
% 6.94/7.31 ( ( ord_less_rat @ A @ B )
% 6.94/7.31 => ( ( ord_max_rat @ A @ B )
% 6.94/7.31 = B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb4
% 6.94/7.31 thf(fact_9372_max_Oabsorb4,axiom,
% 6.94/7.31 ! [A: num,B: num] :
% 6.94/7.31 ( ( ord_less_num @ A @ B )
% 6.94/7.31 => ( ( ord_max_num @ A @ B )
% 6.94/7.31 = B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb4
% 6.94/7.31 thf(fact_9373_max_Oabsorb4,axiom,
% 6.94/7.31 ! [A: nat,B: nat] :
% 6.94/7.31 ( ( ord_less_nat @ A @ B )
% 6.94/7.31 => ( ( ord_max_nat @ A @ B )
% 6.94/7.31 = B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb4
% 6.94/7.31 thf(fact_9374_max_Oabsorb4,axiom,
% 6.94/7.31 ! [A: int,B: int] :
% 6.94/7.31 ( ( ord_less_int @ A @ B )
% 6.94/7.31 => ( ( ord_max_int @ A @ B )
% 6.94/7.31 = B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb4
% 6.94/7.31 thf(fact_9375_max_Oabsorb3,axiom,
% 6.94/7.31 ! [B: rat,A: rat] :
% 6.94/7.31 ( ( ord_less_rat @ B @ A )
% 6.94/7.31 => ( ( ord_max_rat @ A @ B )
% 6.94/7.31 = A ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb3
% 6.94/7.31 thf(fact_9376_max_Oabsorb3,axiom,
% 6.94/7.31 ! [B: num,A: num] :
% 6.94/7.31 ( ( ord_less_num @ B @ A )
% 6.94/7.31 => ( ( ord_max_num @ A @ B )
% 6.94/7.31 = A ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb3
% 6.94/7.31 thf(fact_9377_max_Oabsorb3,axiom,
% 6.94/7.31 ! [B: nat,A: nat] :
% 6.94/7.31 ( ( ord_less_nat @ B @ A )
% 6.94/7.31 => ( ( ord_max_nat @ A @ B )
% 6.94/7.31 = A ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb3
% 6.94/7.31 thf(fact_9378_max_Oabsorb3,axiom,
% 6.94/7.31 ! [B: int,A: int] :
% 6.94/7.31 ( ( ord_less_int @ B @ A )
% 6.94/7.31 => ( ( ord_max_int @ A @ B )
% 6.94/7.31 = A ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb3
% 6.94/7.31 thf(fact_9379_max__bot2,axiom,
% 6.94/7.31 ! [X: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( ord_ma7524802468073614006at_nat @ X @ bot_bo2099793752762293965at_nat )
% 6.94/7.31 = X ) ).
% 6.94/7.31
% 6.94/7.31 % max_bot2
% 6.94/7.31 thf(fact_9380_max__bot2,axiom,
% 6.94/7.31 ! [X: set_o] :
% 6.94/7.31 ( ( ord_max_set_o @ X @ bot_bot_set_o )
% 6.94/7.31 = X ) ).
% 6.94/7.31
% 6.94/7.31 % max_bot2
% 6.94/7.31 thf(fact_9381_max__bot2,axiom,
% 6.94/7.31 ! [X: set_nat] :
% 6.94/7.31 ( ( ord_max_set_nat @ X @ bot_bot_set_nat )
% 6.94/7.31 = X ) ).
% 6.94/7.31
% 6.94/7.31 % max_bot2
% 6.94/7.31 thf(fact_9382_max__bot2,axiom,
% 6.94/7.31 ! [X: set_int] :
% 6.94/7.31 ( ( ord_max_set_int @ X @ bot_bot_set_int )
% 6.94/7.31 = X ) ).
% 6.94/7.31
% 6.94/7.31 % max_bot2
% 6.94/7.31 thf(fact_9383_max__bot2,axiom,
% 6.94/7.31 ! [X: nat] :
% 6.94/7.31 ( ( ord_max_nat @ X @ bot_bot_nat )
% 6.94/7.31 = X ) ).
% 6.94/7.31
% 6.94/7.31 % max_bot2
% 6.94/7.31 thf(fact_9384_max__bot,axiom,
% 6.94/7.31 ! [X: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( ord_ma7524802468073614006at_nat @ bot_bo2099793752762293965at_nat @ X )
% 6.94/7.31 = X ) ).
% 6.94/7.31
% 6.94/7.31 % max_bot
% 6.94/7.31 thf(fact_9385_max__bot,axiom,
% 6.94/7.31 ! [X: set_o] :
% 6.94/7.31 ( ( ord_max_set_o @ bot_bot_set_o @ X )
% 6.94/7.31 = X ) ).
% 6.94/7.31
% 6.94/7.31 % max_bot
% 6.94/7.31 thf(fact_9386_max__bot,axiom,
% 6.94/7.31 ! [X: set_nat] :
% 6.94/7.31 ( ( ord_max_set_nat @ bot_bot_set_nat @ X )
% 6.94/7.31 = X ) ).
% 6.94/7.31
% 6.94/7.31 % max_bot
% 6.94/7.31 thf(fact_9387_max__bot,axiom,
% 6.94/7.31 ! [X: set_int] :
% 6.94/7.31 ( ( ord_max_set_int @ bot_bot_set_int @ X )
% 6.94/7.31 = X ) ).
% 6.94/7.31
% 6.94/7.31 % max_bot
% 6.94/7.31 thf(fact_9388_max__bot,axiom,
% 6.94/7.31 ! [X: nat] :
% 6.94/7.31 ( ( ord_max_nat @ bot_bot_nat @ X )
% 6.94/7.31 = X ) ).
% 6.94/7.31
% 6.94/7.31 % max_bot
% 6.94/7.31 thf(fact_9389_map__option__eq__Some,axiom,
% 6.94/7.31 ! [F: num > num,Xo: option_num,Y: num] :
% 6.94/7.31 ( ( ( map_option_num_num @ F @ Xo )
% 6.94/7.31 = ( some_num @ Y ) )
% 6.94/7.31 = ( ? [Z: num] :
% 6.94/7.31 ( ( Xo
% 6.94/7.31 = ( some_num @ Z ) )
% 6.94/7.31 & ( ( F @ Z )
% 6.94/7.31 = Y ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option_eq_Some
% 6.94/7.31 thf(fact_9390_map__option__eq__Some,axiom,
% 6.94/7.31 ! [F: num > produc7388388658123137530it_nat,Xo: option_num,Y: produc7388388658123137530it_nat] :
% 6.94/7.31 ( ( ( map_op2490657901765117089it_nat @ F @ Xo )
% 6.94/7.31 = ( some_P2818173045054083285it_nat @ Y ) )
% 6.94/7.31 = ( ? [Z: num] :
% 6.94/7.31 ( ( Xo
% 6.94/7.31 = ( some_num @ Z ) )
% 6.94/7.31 & ( ( F @ Z )
% 6.94/7.31 = Y ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option_eq_Some
% 6.94/7.31 thf(fact_9391_map__option__eq__Some,axiom,
% 6.94/7.31 ! [F: num > produc3260487557148687353it_nat,Xo: option_num,Y: produc3260487557148687353it_nat] :
% 6.94/7.31 ( ( ( map_op7586128837645442720it_nat @ F @ Xo )
% 6.94/7.31 = ( some_P7913643980934408916it_nat @ Y ) )
% 6.94/7.31 = ( ? [Z: num] :
% 6.94/7.31 ( ( Xo
% 6.94/7.31 = ( some_num @ Z ) )
% 6.94/7.31 & ( ( F @ Z )
% 6.94/7.31 = Y ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option_eq_Some
% 6.94/7.31 thf(fact_9392_map__option__eq__Some,axiom,
% 6.94/7.31 ! [F: num > produc8664842809031399944it_nat,Xo: option_num,Y: produc8664842809031399944it_nat] :
% 6.94/7.31 ( ( ( map_op8118133509425879471it_nat @ F @ Xo )
% 6.94/7.31 = ( some_P1914260805536162275it_nat @ Y ) )
% 6.94/7.31 = ( ? [Z: num] :
% 6.94/7.31 ( ( Xo
% 6.94/7.31 = ( some_num @ Z ) )
% 6.94/7.31 & ( ( F @ Z )
% 6.94/7.31 = Y ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option_eq_Some
% 6.94/7.31 thf(fact_9393_map__option__eq__Some,axiom,
% 6.94/7.31 ! [F: produc7388388658123137530it_nat > num,Xo: option4065278094766928714it_nat,Y: num] :
% 6.94/7.31 ( ( ( map_op6233829773304596897at_num @ F @ Xo )
% 6.94/7.31 = ( some_num @ Y ) )
% 6.94/7.31 = ( ? [Z: produc7388388658123137530it_nat] :
% 6.94/7.31 ( ( Xo
% 6.94/7.31 = ( some_P2818173045054083285it_nat @ Z ) )
% 6.94/7.31 & ( ( F @ Z )
% 6.94/7.31 = Y ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option_eq_Some
% 6.94/7.31 thf(fact_9394_map__option__eq__Some,axiom,
% 6.94/7.31 ! [F: produc3260487557148687353it_nat > num,Xo: option3562590408128118217it_nat,Y: num] :
% 6.94/7.31 ( ( ( map_op5165227558541518752at_num @ F @ Xo )
% 6.94/7.31 = ( some_num @ Y ) )
% 6.94/7.31 = ( ? [Z: produc3260487557148687353it_nat] :
% 6.94/7.31 ( ( Xo
% 6.94/7.31 = ( some_P7913643980934408916it_nat @ Z ) )
% 6.94/7.31 & ( ( F @ Z )
% 6.94/7.31 = Y ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option_eq_Some
% 6.94/7.31 thf(fact_9395_map__option__eq__Some,axiom,
% 6.94/7.31 ! [F: produc8664842809031399944it_nat > num,Xo: option8956607266484857688it_nat,Y: num] :
% 6.94/7.31 ( ( ( map_op2731889312448867759at_num @ F @ Xo )
% 6.94/7.31 = ( some_num @ Y ) )
% 6.94/7.31 = ( ? [Z: produc8664842809031399944it_nat] :
% 6.94/7.31 ( ( Xo
% 6.94/7.31 = ( some_P1914260805536162275it_nat @ Z ) )
% 6.94/7.31 & ( ( F @ Z )
% 6.94/7.31 = Y ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option_eq_Some
% 6.94/7.31 thf(fact_9396_map__option__eq__Some,axiom,
% 6.94/7.31 ! [F: produc7388388658123137530it_nat > produc7388388658123137530it_nat,Xo: option4065278094766928714it_nat,Y: produc7388388658123137530it_nat] :
% 6.94/7.31 ( ( ( map_op8581638957091552385it_nat @ F @ Xo )
% 6.94/7.31 = ( some_P2818173045054083285it_nat @ Y ) )
% 6.94/7.31 = ( ? [Z: produc7388388658123137530it_nat] :
% 6.94/7.31 ( ( Xo
% 6.94/7.31 = ( some_P2818173045054083285it_nat @ Z ) )
% 6.94/7.31 & ( ( F @ Z )
% 6.94/7.31 = Y ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option_eq_Some
% 6.94/7.31 thf(fact_9397_map__option__eq__Some,axiom,
% 6.94/7.31 ! [F: produc3260487557148687353it_nat > produc7388388658123137530it_nat,Xo: option3562590408128118217it_nat,Y: produc7388388658123137530it_nat] :
% 6.94/7.31 ( ( ( map_op7599720869725723008it_nat @ F @ Xo )
% 6.94/7.31 = ( some_P2818173045054083285it_nat @ Y ) )
% 6.94/7.31 = ( ? [Z: produc3260487557148687353it_nat] :
% 6.94/7.31 ( ( Xo
% 6.94/7.31 = ( some_P7913643980934408916it_nat @ Z ) )
% 6.94/7.31 & ( ( F @ Z )
% 6.94/7.31 = Y ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option_eq_Some
% 6.94/7.31 thf(fact_9398_map__option__eq__Some,axiom,
% 6.94/7.31 ! [F: produc8664842809031399944it_nat > produc7388388658123137530it_nat,Xo: option8956607266484857688it_nat,Y: produc7388388658123137530it_nat] :
% 6.94/7.31 ( ( ( map_op604423251913076367it_nat @ F @ Xo )
% 6.94/7.31 = ( some_P2818173045054083285it_nat @ Y ) )
% 6.94/7.31 = ( ? [Z: produc8664842809031399944it_nat] :
% 6.94/7.31 ( ( Xo
% 6.94/7.31 = ( some_P1914260805536162275it_nat @ Z ) )
% 6.94/7.31 & ( ( F @ Z )
% 6.94/7.31 = Y ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option_eq_Some
% 6.94/7.31 thf(fact_9399_None__eq__map__option__iff,axiom,
% 6.94/7.31 ! [F: num > num,X: option_num] :
% 6.94/7.31 ( ( none_num
% 6.94/7.31 = ( map_option_num_num @ F @ X ) )
% 6.94/7.31 = ( X = none_num ) ) ).
% 6.94/7.31
% 6.94/7.31 % None_eq_map_option_iff
% 6.94/7.31 thf(fact_9400_map__option__is__None,axiom,
% 6.94/7.31 ! [F: num > num,Opt: option_num] :
% 6.94/7.31 ( ( ( map_option_num_num @ F @ Opt )
% 6.94/7.31 = none_num )
% 6.94/7.31 = ( Opt = none_num ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option_is_None
% 6.94/7.31 thf(fact_9401_option_Omap__disc__iff,axiom,
% 6.94/7.31 ! [F: num > num,A: option_num] :
% 6.94/7.31 ( ( ( map_option_num_num @ F @ A )
% 6.94/7.31 = none_num )
% 6.94/7.31 = ( A = none_num ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.map_disc_iff
% 6.94/7.31 thf(fact_9402_max__0R,axiom,
% 6.94/7.31 ! [N2: nat] :
% 6.94/7.31 ( ( ord_max_nat @ N2 @ zero_zero_nat )
% 6.94/7.31 = N2 ) ).
% 6.94/7.31
% 6.94/7.31 % max_0R
% 6.94/7.31 thf(fact_9403_max__0L,axiom,
% 6.94/7.31 ! [N2: nat] :
% 6.94/7.31 ( ( ord_max_nat @ zero_zero_nat @ N2 )
% 6.94/7.31 = N2 ) ).
% 6.94/7.31
% 6.94/7.31 % max_0L
% 6.94/7.31 thf(fact_9404_max__nat_Oright__neutral,axiom,
% 6.94/7.31 ! [A: nat] :
% 6.94/7.31 ( ( ord_max_nat @ A @ zero_zero_nat )
% 6.94/7.31 = A ) ).
% 6.94/7.31
% 6.94/7.31 % max_nat.right_neutral
% 6.94/7.31 thf(fact_9405_max__nat_Oneutr__eq__iff,axiom,
% 6.94/7.31 ! [A: nat,B: nat] :
% 6.94/7.31 ( ( zero_zero_nat
% 6.94/7.31 = ( ord_max_nat @ A @ B ) )
% 6.94/7.31 = ( ( A = zero_zero_nat )
% 6.94/7.31 & ( B = zero_zero_nat ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_nat.neutr_eq_iff
% 6.94/7.31 thf(fact_9406_max__nat_Oleft__neutral,axiom,
% 6.94/7.31 ! [A: nat] :
% 6.94/7.31 ( ( ord_max_nat @ zero_zero_nat @ A )
% 6.94/7.31 = A ) ).
% 6.94/7.31
% 6.94/7.31 % max_nat.left_neutral
% 6.94/7.31 thf(fact_9407_max__nat_Oeq__neutr__iff,axiom,
% 6.94/7.31 ! [A: nat,B: nat] :
% 6.94/7.31 ( ( ( ord_max_nat @ A @ B )
% 6.94/7.31 = zero_zero_nat )
% 6.94/7.31 = ( ( A = zero_zero_nat )
% 6.94/7.31 & ( B = zero_zero_nat ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_nat.eq_neutr_iff
% 6.94/7.31 thf(fact_9408_max__Suc__Suc,axiom,
% 6.94/7.31 ! [M: nat,N2: nat] :
% 6.94/7.31 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 6.94/7.31 = ( suc @ ( ord_max_nat @ M @ N2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_Suc_Suc
% 6.94/7.31 thf(fact_9409_card__Collect__le__nat,axiom,
% 6.94/7.31 ! [N2: nat] :
% 6.94/7.31 ( ( finite_card_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [I: nat] : ( ord_less_eq_nat @ I @ N2 ) ) )
% 6.94/7.31 = ( suc @ N2 ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_Collect_le_nat
% 6.94/7.31 thf(fact_9410_max__number__of_I1_J,axiom,
% 6.94/7.31 ! [U: num,V: num] :
% 6.94/7.31 ( ( ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ U ) @ ( numera5444537566228673987atural @ V ) )
% 6.94/7.31 => ( ( ord_max_Code_natural @ ( numera5444537566228673987atural @ U ) @ ( numera5444537566228673987atural @ V ) )
% 6.94/7.31 = ( numera5444537566228673987atural @ V ) ) )
% 6.94/7.31 & ( ~ ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ U ) @ ( numera5444537566228673987atural @ V ) )
% 6.94/7.31 => ( ( ord_max_Code_natural @ ( numera5444537566228673987atural @ U ) @ ( numera5444537566228673987atural @ V ) )
% 6.94/7.31 = ( numera5444537566228673987atural @ U ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_number_of(1)
% 6.94/7.31 thf(fact_9411_max__number__of_I1_J,axiom,
% 6.94/7.31 ! [U: num,V: num] :
% 6.94/7.31 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 6.94/7.31 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 6.94/7.31 = ( numera6620942414471956472nteger @ V ) ) )
% 6.94/7.31 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 6.94/7.31 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 6.94/7.31 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_number_of(1)
% 6.94/7.31 thf(fact_9412_max__number__of_I1_J,axiom,
% 6.94/7.31 ! [U: num,V: num] :
% 6.94/7.31 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 6.94/7.31 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 6.94/7.31 = ( numeral_numeral_rat @ V ) ) )
% 6.94/7.31 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 6.94/7.31 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 6.94/7.31 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_number_of(1)
% 6.94/7.31 thf(fact_9413_max__number__of_I1_J,axiom,
% 6.94/7.31 ! [U: num,V: num] :
% 6.94/7.31 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 6.94/7.31 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 6.94/7.31 = ( numeral_numeral_nat @ V ) ) )
% 6.94/7.31 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 6.94/7.31 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 6.94/7.31 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_number_of(1)
% 6.94/7.31 thf(fact_9414_max__number__of_I1_J,axiom,
% 6.94/7.31 ! [U: num,V: num] :
% 6.94/7.31 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 6.94/7.31 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 6.94/7.31 = ( numeral_numeral_int @ V ) ) )
% 6.94/7.31 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 6.94/7.31 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 6.94/7.31 = ( numeral_numeral_int @ U ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_number_of(1)
% 6.94/7.31 thf(fact_9415_case__map__option,axiom,
% 6.94/7.31 ! [G: produc8923325533196201883nteger > produc8923325533196201883nteger,H: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer,X: option_Code_integer] :
% 6.94/7.31 ( ( case_o7134296353695833103nteger @ G @ H @ ( map_op3669829223712506439nteger @ F @ X ) )
% 6.94/7.31 = ( case_o7134296353695833103nteger @ G @ ( comp_C1593894019821074884nteger @ H @ F ) @ X ) ) ).
% 6.94/7.31
% 6.94/7.31 % case_map_option
% 6.94/7.31 thf(fact_9416_case__map__option,axiom,
% 6.94/7.31 ! [G: produc8923325533196201883nteger > produc8923325533196201883nteger,H: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,X: option_Code_integer] :
% 6.94/7.31 ( ( case_o1441893360019914891nteger @ G @ H @ ( map_op370346339404370627nteger @ F @ X ) )
% 6.94/7.31 = ( case_o7134296353695833103nteger @ G @ ( comp_C8797469213163452608nteger @ H @ F ) @ X ) ) ).
% 6.94/7.31
% 6.94/7.31 % case_map_option
% 6.94/7.31 thf(fact_9417_case__map__option,axiom,
% 6.94/7.31 ! [G: nat,H: int > nat,F: int > int,X: option_int] :
% 6.94/7.31 ( ( case_option_nat_int @ G @ H @ ( map_option_int_int @ F @ X ) )
% 6.94/7.31 = ( case_option_nat_int @ G @ ( comp_int_nat_int @ H @ F ) @ X ) ) ).
% 6.94/7.31
% 6.94/7.31 % case_map_option
% 6.94/7.31 thf(fact_9418_case__map__option,axiom,
% 6.94/7.31 ! [G: int,H: num > int,F: num > num,X: option_num] :
% 6.94/7.31 ( ( case_option_int_num @ G @ H @ ( map_option_num_num @ F @ X ) )
% 6.94/7.31 = ( case_option_int_num @ G @ ( comp_num_int_num @ H @ F ) @ X ) ) ).
% 6.94/7.31
% 6.94/7.31 % case_map_option
% 6.94/7.31 thf(fact_9419_case__map__option,axiom,
% 6.94/7.31 ! [G: option_num,H: num > option_num,F: num > num,X: option_num] :
% 6.94/7.31 ( ( case_o6005452278849405969um_num @ G @ H @ ( map_option_num_num @ F @ X ) )
% 6.94/7.31 = ( case_o6005452278849405969um_num @ G @ ( comp_n6731957995704128387um_num @ H @ F ) @ X ) ) ).
% 6.94/7.31
% 6.94/7.31 % case_map_option
% 6.94/7.31 thf(fact_9420_case__map__option,axiom,
% 6.94/7.31 ! [G: num,H: num > num,F: num > num,X: option_num] :
% 6.94/7.31 ( ( case_option_num_num @ G @ H @ ( map_option_num_num @ F @ X ) )
% 6.94/7.31 = ( case_option_num_num @ G @ ( comp_num_num_num @ H @ F ) @ X ) ) ).
% 6.94/7.31
% 6.94/7.31 % case_map_option
% 6.94/7.31 thf(fact_9421_prod__constant,axiom,
% 6.94/7.31 ! [Y: nat,A4: set_int] :
% 6.94/7.31 ( ( groups1707563613775114915nt_nat
% 6.94/7.31 @ ^ [X4: int] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( power_power_nat @ Y @ ( finite_card_int @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % prod_constant
% 6.94/7.31 thf(fact_9422_prod__constant,axiom,
% 6.94/7.31 ! [Y: nat,A4: set_list_nat] :
% 6.94/7.31 ( ( groups2907647131375434839at_nat
% 6.94/7.31 @ ^ [X4: list_nat] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( power_power_nat @ Y @ ( finite_card_list_nat @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % prod_constant
% 6.94/7.31 thf(fact_9423_prod__constant,axiom,
% 6.94/7.31 ! [Y: nat,A4: set_set_nat] :
% 6.94/7.31 ( ( groups4248547760180025341at_nat
% 6.94/7.31 @ ^ [X4: set_nat] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( power_power_nat @ Y @ ( finite_card_set_nat @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % prod_constant
% 6.94/7.31 thf(fact_9424_prod__constant,axiom,
% 6.94/7.31 ! [Y: int,A4: set_list_nat] :
% 6.94/7.31 ( ( groups2905156660866384563at_int
% 6.94/7.31 @ ^ [X4: list_nat] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( power_power_int @ Y @ ( finite_card_list_nat @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % prod_constant
% 6.94/7.31 thf(fact_9425_prod__constant,axiom,
% 6.94/7.31 ! [Y: int,A4: set_set_nat] :
% 6.94/7.31 ( ( groups4246057289670975065at_int
% 6.94/7.31 @ ^ [X4: set_nat] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( power_power_int @ Y @ ( finite_card_set_nat @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % prod_constant
% 6.94/7.31 thf(fact_9426_prod__constant,axiom,
% 6.94/7.31 ! [Y: nat,A4: set_nat] :
% 6.94/7.31 ( ( groups708209901874060359at_nat
% 6.94/7.31 @ ^ [X4: nat] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( power_power_nat @ Y @ ( finite_card_nat @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % prod_constant
% 6.94/7.31 thf(fact_9427_prod__constant,axiom,
% 6.94/7.31 ! [Y: int,A4: set_nat] :
% 6.94/7.31 ( ( groups705719431365010083at_int
% 6.94/7.31 @ ^ [X4: nat] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( power_power_int @ Y @ ( finite_card_nat @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % prod_constant
% 6.94/7.31 thf(fact_9428_prod__constant,axiom,
% 6.94/7.31 ! [Y: int,A4: set_int] :
% 6.94/7.31 ( ( groups1705073143266064639nt_int
% 6.94/7.31 @ ^ [X4: int] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( power_power_int @ Y @ ( finite_card_int @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % prod_constant
% 6.94/7.31 thf(fact_9429_max__number__of_I2_J,axiom,
% 6.94/7.31 ! [U: num,V: num] :
% 6.94/7.31 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 6.94/7.31 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 6.94/7.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 6.94/7.31 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 6.94/7.31 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 6.94/7.31 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_number_of(2)
% 6.94/7.31 thf(fact_9430_max__number__of_I2_J,axiom,
% 6.94/7.31 ! [U: num,V: num] :
% 6.94/7.31 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 6.94/7.31 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 6.94/7.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 6.94/7.31 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 6.94/7.31 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 6.94/7.31 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_number_of(2)
% 6.94/7.31 thf(fact_9431_max__number__of_I2_J,axiom,
% 6.94/7.31 ! [U: num,V: num] :
% 6.94/7.31 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 6.94/7.31 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 6.94/7.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 6.94/7.31 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 6.94/7.31 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 6.94/7.31 = ( numeral_numeral_int @ U ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_number_of(2)
% 6.94/7.31 thf(fact_9432_max__number__of_I3_J,axiom,
% 6.94/7.31 ! [U: num,V: num] :
% 6.94/7.31 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 6.94/7.31 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 6.94/7.31 = ( numera6620942414471956472nteger @ V ) ) )
% 6.94/7.31 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 6.94/7.31 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 6.94/7.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_number_of(3)
% 6.94/7.31 thf(fact_9433_max__number__of_I3_J,axiom,
% 6.94/7.31 ! [U: num,V: num] :
% 6.94/7.31 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 6.94/7.31 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 6.94/7.31 = ( numeral_numeral_rat @ V ) ) )
% 6.94/7.31 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 6.94/7.31 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 6.94/7.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_number_of(3)
% 6.94/7.31 thf(fact_9434_max__number__of_I3_J,axiom,
% 6.94/7.31 ! [U: num,V: num] :
% 6.94/7.31 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 6.94/7.31 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 6.94/7.31 = ( numeral_numeral_int @ V ) ) )
% 6.94/7.31 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 6.94/7.31 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 6.94/7.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_number_of(3)
% 6.94/7.31 thf(fact_9435_max__number__of_I4_J,axiom,
% 6.94/7.31 ! [U: num,V: num] :
% 6.94/7.31 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 6.94/7.31 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 6.94/7.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 6.94/7.31 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 6.94/7.31 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 6.94/7.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_number_of(4)
% 6.94/7.31 thf(fact_9436_max__number__of_I4_J,axiom,
% 6.94/7.31 ! [U: num,V: num] :
% 6.94/7.31 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 6.94/7.31 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 6.94/7.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 6.94/7.31 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 6.94/7.31 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 6.94/7.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_number_of(4)
% 6.94/7.31 thf(fact_9437_max__number__of_I4_J,axiom,
% 6.94/7.31 ! [U: num,V: num] :
% 6.94/7.31 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 6.94/7.31 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 6.94/7.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 6.94/7.31 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 6.94/7.31 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 6.94/7.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_number_of(4)
% 6.94/7.31 thf(fact_9438_sum__constant,axiom,
% 6.94/7.31 ! [Y: rat,A4: set_nat] :
% 6.94/7.31 ( ( groups2906978787729119204at_rat
% 6.94/7.31 @ ^ [X4: nat] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) @ Y ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_constant
% 6.94/7.31 thf(fact_9439_sum__constant,axiom,
% 6.94/7.31 ! [Y: rat,A4: set_int] :
% 6.94/7.31 ( ( groups3906332499630173760nt_rat
% 6.94/7.31 @ ^ [X4: int] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) @ Y ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_constant
% 6.94/7.31 thf(fact_9440_sum__constant,axiom,
% 6.94/7.31 ! [Y: int,A4: set_nat] :
% 6.94/7.31 ( ( groups3539618377306564664at_int
% 6.94/7.31 @ ^ [X4: nat] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ A4 ) ) @ Y ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_constant
% 6.94/7.31 thf(fact_9441_sum__constant,axiom,
% 6.94/7.31 ! [Y: nat,A4: set_int] :
% 6.94/7.31 ( ( groups4541462559716669496nt_nat
% 6.94/7.31 @ ^ [X4: int] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A4 ) ) @ Y ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_constant
% 6.94/7.31 thf(fact_9442_sum__constant,axiom,
% 6.94/7.31 ! [Y: code_integer,A4: set_nat] :
% 6.94/7.31 ( ( groups7501900531339628137nteger
% 6.94/7.31 @ ^ [X4: nat] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_nat @ A4 ) ) @ Y ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_constant
% 6.94/7.31 thf(fact_9443_sum__constant,axiom,
% 6.94/7.31 ! [Y: code_integer,A4: set_int] :
% 6.94/7.31 ( ( groups7873554091576472773nteger
% 6.94/7.31 @ ^ [X4: int] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_int @ A4 ) ) @ Y ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_constant
% 6.94/7.31 thf(fact_9444_sum__constant,axiom,
% 6.94/7.31 ! [Y: nat,A4: set_nat] :
% 6.94/7.31 ( ( groups3542108847815614940at_nat
% 6.94/7.31 @ ^ [X4: nat] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_nat @ A4 ) ) @ Y ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_constant
% 6.94/7.31 thf(fact_9445_sum__constant,axiom,
% 6.94/7.31 ! [Y: int,A4: set_int] :
% 6.94/7.31 ( ( groups4538972089207619220nt_int
% 6.94/7.31 @ ^ [X4: int] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_int @ A4 ) ) @ Y ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_constant
% 6.94/7.31 thf(fact_9446_sum__constant,axiom,
% 6.94/7.31 ! [Y: rat,A4: set_list_nat] :
% 6.94/7.31 ( ( groups3760926236672600436at_rat
% 6.94/7.31 @ ^ [X4: list_nat] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_list_nat @ A4 ) ) @ Y ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_constant
% 6.94/7.31 thf(fact_9447_sum__constant,axiom,
% 6.94/7.31 ! [Y: rat,A4: set_set_nat] :
% 6.94/7.31 ( ( groups7659867448343625626at_rat
% 6.94/7.31 @ ^ [X4: set_nat] : Y
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_set_nat @ A4 ) ) @ Y ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_constant
% 6.94/7.31 thf(fact_9448_card__atLeastAtMost__int,axiom,
% 6.94/7.31 ! [L: int,U: int] :
% 6.94/7.31 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 6.94/7.31 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_atLeastAtMost_int
% 6.94/7.31 thf(fact_9449_sum_Oinsert_H,axiom,
% 6.94/7.31 ! [I5: set_o,P3: $o > code_integer,I2: $o] :
% 6.94/7.31 ( ( finite_finite_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [X4: $o] :
% 6.94/7.31 ( ( member_o @ X4 @ I5 )
% 6.94/7.31 & ( ( P3 @ X4 )
% 6.94/7.31 != zero_z3403309356797280102nteger ) ) ) )
% 6.94/7.31 => ( ( ( member_o @ I2 @ I5 )
% 6.94/7.31 => ( ( groups1402912129352969042nteger @ P3 @ ( insert_o @ I2 @ I5 ) )
% 6.94/7.31 = ( groups1402912129352969042nteger @ P3 @ I5 ) ) )
% 6.94/7.31 & ( ~ ( member_o @ I2 @ I5 )
% 6.94/7.31 => ( ( groups1402912129352969042nteger @ P3 @ ( insert_o @ I2 @ I5 ) )
% 6.94/7.31 = ( plus_p5714425477246183910nteger @ ( P3 @ I2 ) @ ( groups1402912129352969042nteger @ P3 @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.insert'
% 6.94/7.31 thf(fact_9450_sum_Oinsert_H,axiom,
% 6.94/7.31 ! [I5: set_nat,P3: nat > code_integer,I2: nat] :
% 6.94/7.31 ( ( finite_finite_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [X4: nat] :
% 6.94/7.31 ( ( member_nat @ X4 @ I5 )
% 6.94/7.31 & ( ( P3 @ X4 )
% 6.94/7.31 != zero_z3403309356797280102nteger ) ) ) )
% 6.94/7.31 => ( ( ( member_nat @ I2 @ I5 )
% 6.94/7.31 => ( ( groups555127423416065298nteger @ P3 @ ( insert_nat @ I2 @ I5 ) )
% 6.94/7.31 = ( groups555127423416065298nteger @ P3 @ I5 ) ) )
% 6.94/7.31 & ( ~ ( member_nat @ I2 @ I5 )
% 6.94/7.31 => ( ( groups555127423416065298nteger @ P3 @ ( insert_nat @ I2 @ I5 ) )
% 6.94/7.31 = ( plus_p5714425477246183910nteger @ ( P3 @ I2 ) @ ( groups555127423416065298nteger @ P3 @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.insert'
% 6.94/7.31 thf(fact_9451_sum_Oinsert_H,axiom,
% 6.94/7.31 ! [I5: set_int,P3: int > code_integer,I2: int] :
% 6.94/7.31 ( ( finite_finite_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [X4: int] :
% 6.94/7.31 ( ( member_int @ X4 @ I5 )
% 6.94/7.31 & ( ( P3 @ X4 )
% 6.94/7.31 != zero_z3403309356797280102nteger ) ) ) )
% 6.94/7.31 => ( ( ( member_int @ I2 @ I5 )
% 6.94/7.31 => ( ( groups926780983652909934nteger @ P3 @ ( insert_int @ I2 @ I5 ) )
% 6.94/7.31 = ( groups926780983652909934nteger @ P3 @ I5 ) ) )
% 6.94/7.31 & ( ~ ( member_int @ I2 @ I5 )
% 6.94/7.31 => ( ( groups926780983652909934nteger @ P3 @ ( insert_int @ I2 @ I5 ) )
% 6.94/7.31 = ( plus_p5714425477246183910nteger @ ( P3 @ I2 ) @ ( groups926780983652909934nteger @ P3 @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.insert'
% 6.94/7.31 thf(fact_9452_sum_Oinsert_H,axiom,
% 6.94/7.31 ! [I5: set_Code_integer,P3: code_integer > code_integer,I2: code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [X4: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ X4 @ I5 )
% 6.94/7.31 & ( ( P3 @ X4 )
% 6.94/7.31 != zero_z3403309356797280102nteger ) ) ) )
% 6.94/7.31 => ( ( ( member_Code_integer @ I2 @ I5 )
% 6.94/7.31 => ( ( groups910942671188738463nteger @ P3 @ ( insert_Code_integer @ I2 @ I5 ) )
% 6.94/7.31 = ( groups910942671188738463nteger @ P3 @ I5 ) ) )
% 6.94/7.31 & ( ~ ( member_Code_integer @ I2 @ I5 )
% 6.94/7.31 => ( ( groups910942671188738463nteger @ P3 @ ( insert_Code_integer @ I2 @ I5 ) )
% 6.94/7.31 = ( plus_p5714425477246183910nteger @ ( P3 @ I2 ) @ ( groups910942671188738463nteger @ P3 @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.insert'
% 6.94/7.31 thf(fact_9453_sum_Oinsert_H,axiom,
% 6.94/7.31 ! [I5: set_o,P3: $o > rat,I2: $o] :
% 6.94/7.31 ( ( finite_finite_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [X4: $o] :
% 6.94/7.31 ( ( member_o @ X4 @ I5 )
% 6.94/7.31 & ( ( P3 @ X4 )
% 6.94/7.31 != zero_zero_rat ) ) ) )
% 6.94/7.31 => ( ( ( member_o @ I2 @ I5 )
% 6.94/7.31 => ( ( groups3921277224699582669_o_rat @ P3 @ ( insert_o @ I2 @ I5 ) )
% 6.94/7.31 = ( groups3921277224699582669_o_rat @ P3 @ I5 ) ) )
% 6.94/7.31 & ( ~ ( member_o @ I2 @ I5 )
% 6.94/7.31 => ( ( groups3921277224699582669_o_rat @ P3 @ ( insert_o @ I2 @ I5 ) )
% 6.94/7.31 = ( plus_plus_rat @ ( P3 @ I2 ) @ ( groups3921277224699582669_o_rat @ P3 @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.insert'
% 6.94/7.31 thf(fact_9454_sum_Oinsert_H,axiom,
% 6.94/7.31 ! [I5: set_nat,P3: nat > rat,I2: nat] :
% 6.94/7.31 ( ( finite_finite_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [X4: nat] :
% 6.94/7.31 ( ( member_nat @ X4 @ I5 )
% 6.94/7.31 & ( ( P3 @ X4 )
% 6.94/7.31 != zero_zero_rat ) ) ) )
% 6.94/7.31 => ( ( ( member_nat @ I2 @ I5 )
% 6.94/7.31 => ( ( groups1351286907653491341at_rat @ P3 @ ( insert_nat @ I2 @ I5 ) )
% 6.94/7.31 = ( groups1351286907653491341at_rat @ P3 @ I5 ) ) )
% 6.94/7.31 & ( ~ ( member_nat @ I2 @ I5 )
% 6.94/7.31 => ( ( groups1351286907653491341at_rat @ P3 @ ( insert_nat @ I2 @ I5 ) )
% 6.94/7.31 = ( plus_plus_rat @ ( P3 @ I2 ) @ ( groups1351286907653491341at_rat @ P3 @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.insert'
% 6.94/7.31 thf(fact_9455_sum_Oinsert_H,axiom,
% 6.94/7.31 ! [I5: set_int,P3: int > rat,I2: int] :
% 6.94/7.31 ( ( finite_finite_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [X4: int] :
% 6.94/7.31 ( ( member_int @ X4 @ I5 )
% 6.94/7.31 & ( ( P3 @ X4 )
% 6.94/7.31 != zero_zero_rat ) ) ) )
% 6.94/7.31 => ( ( ( member_int @ I2 @ I5 )
% 6.94/7.31 => ( ( groups2350640619554545897nt_rat @ P3 @ ( insert_int @ I2 @ I5 ) )
% 6.94/7.31 = ( groups2350640619554545897nt_rat @ P3 @ I5 ) ) )
% 6.94/7.31 & ( ~ ( member_int @ I2 @ I5 )
% 6.94/7.31 => ( ( groups2350640619554545897nt_rat @ P3 @ ( insert_int @ I2 @ I5 ) )
% 6.94/7.31 = ( plus_plus_rat @ ( P3 @ I2 ) @ ( groups2350640619554545897nt_rat @ P3 @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.insert'
% 6.94/7.31 thf(fact_9456_sum_Oinsert_H,axiom,
% 6.94/7.31 ! [I5: set_Code_integer,P3: code_integer > rat,I2: code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [X4: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ X4 @ I5 )
% 6.94/7.31 & ( ( P3 @ X4 )
% 6.94/7.31 != zero_zero_rat ) ) ) )
% 6.94/7.31 => ( ( ( member_Code_integer @ I2 @ I5 )
% 6.94/7.31 => ( ( groups8878813951405302554er_rat @ P3 @ ( insert_Code_integer @ I2 @ I5 ) )
% 6.94/7.31 = ( groups8878813951405302554er_rat @ P3 @ I5 ) ) )
% 6.94/7.31 & ( ~ ( member_Code_integer @ I2 @ I5 )
% 6.94/7.31 => ( ( groups8878813951405302554er_rat @ P3 @ ( insert_Code_integer @ I2 @ I5 ) )
% 6.94/7.31 = ( plus_plus_rat @ ( P3 @ I2 ) @ ( groups8878813951405302554er_rat @ P3 @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.insert'
% 6.94/7.31 thf(fact_9457_sum_Oinsert_H,axiom,
% 6.94/7.31 ! [I5: set_o,P3: $o > nat,I2: $o] :
% 6.94/7.31 ( ( finite_finite_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [X4: $o] :
% 6.94/7.31 ( ( member_o @ X4 @ I5 )
% 6.94/7.31 & ( ( P3 @ X4 )
% 6.94/7.31 != zero_zero_nat ) ) ) )
% 6.94/7.31 => ( ( ( member_o @ I2 @ I5 )
% 6.94/7.31 => ( ( groups4556407284786078405_o_nat @ P3 @ ( insert_o @ I2 @ I5 ) )
% 6.94/7.31 = ( groups4556407284786078405_o_nat @ P3 @ I5 ) ) )
% 6.94/7.31 & ( ~ ( member_o @ I2 @ I5 )
% 6.94/7.31 => ( ( groups4556407284786078405_o_nat @ P3 @ ( insert_o @ I2 @ I5 ) )
% 6.94/7.31 = ( plus_plus_nat @ ( P3 @ I2 ) @ ( groups4556407284786078405_o_nat @ P3 @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.insert'
% 6.94/7.31 thf(fact_9458_sum_Oinsert_H,axiom,
% 6.94/7.31 ! [I5: set_nat,P3: nat > nat,I2: nat] :
% 6.94/7.31 ( ( finite_finite_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [X4: nat] :
% 6.94/7.31 ( ( member_nat @ X4 @ I5 )
% 6.94/7.31 & ( ( P3 @ X4 )
% 6.94/7.31 != zero_zero_nat ) ) ) )
% 6.94/7.31 => ( ( ( member_nat @ I2 @ I5 )
% 6.94/7.31 => ( ( groups1986416967739987077at_nat @ P3 @ ( insert_nat @ I2 @ I5 ) )
% 6.94/7.31 = ( groups1986416967739987077at_nat @ P3 @ I5 ) ) )
% 6.94/7.31 & ( ~ ( member_nat @ I2 @ I5 )
% 6.94/7.31 => ( ( groups1986416967739987077at_nat @ P3 @ ( insert_nat @ I2 @ I5 ) )
% 6.94/7.31 = ( plus_plus_nat @ ( P3 @ I2 ) @ ( groups1986416967739987077at_nat @ P3 @ I5 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.insert'
% 6.94/7.31 thf(fact_9459_card__doubleton__eq__2__iff,axiom,
% 6.94/7.31 ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
% 6.94/7.31 ( ( ( finite3771342082235030671at_nat @ ( insert9069300056098147895at_nat @ A @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) )
% 6.94/7.31 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.94/7.31 = ( A != B ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_doubleton_eq_2_iff
% 6.94/7.31 thf(fact_9460_card__doubleton__eq__2__iff,axiom,
% 6.94/7.31 ! [A: list_nat,B: list_nat] :
% 6.94/7.31 ( ( ( finite_card_list_nat @ ( insert_list_nat @ A @ ( insert_list_nat @ B @ bot_bot_set_list_nat ) ) )
% 6.94/7.31 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.94/7.31 = ( A != B ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_doubleton_eq_2_iff
% 6.94/7.31 thf(fact_9461_card__doubleton__eq__2__iff,axiom,
% 6.94/7.31 ! [A: set_nat,B: set_nat] :
% 6.94/7.31 ( ( ( finite_card_set_nat @ ( insert_set_nat @ A @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 6.94/7.31 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.94/7.31 = ( A != B ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_doubleton_eq_2_iff
% 6.94/7.31 thf(fact_9462_card__doubleton__eq__2__iff,axiom,
% 6.94/7.31 ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 6.94/7.31 ( ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ A @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) )
% 6.94/7.31 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.94/7.31 = ( A != B ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_doubleton_eq_2_iff
% 6.94/7.31 thf(fact_9463_card__doubleton__eq__2__iff,axiom,
% 6.94/7.31 ! [A: $o,B: $o] :
% 6.94/7.31 ( ( ( finite_card_o @ ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 6.94/7.31 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.94/7.31 = ( A != B ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_doubleton_eq_2_iff
% 6.94/7.31 thf(fact_9464_card__doubleton__eq__2__iff,axiom,
% 6.94/7.31 ! [A: nat,B: nat] :
% 6.94/7.31 ( ( ( finite_card_nat @ ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 6.94/7.31 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.94/7.31 = ( A != B ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_doubleton_eq_2_iff
% 6.94/7.31 thf(fact_9465_card__doubleton__eq__2__iff,axiom,
% 6.94/7.31 ! [A: int,B: int] :
% 6.94/7.31 ( ( ( finite_card_int @ ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 6.94/7.31 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 6.94/7.31 = ( A != B ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_doubleton_eq_2_iff
% 6.94/7.31 thf(fact_9466_sum__of__bool__eq,axiom,
% 6.94/7.31 ! [A4: set_int,P2: int > $o] :
% 6.94/7.31 ( ( finite_finite_int @ A4 )
% 6.94/7.31 => ( ( finite_finite_int @ A4 )
% 6.94/7.31 => ( ( groups4541462559716669496nt_nat
% 6.94/7.31 @ ^ [X4: int] : ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) )
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( semiri1316708129612266289at_nat @ ( finite_card_int @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_of_bool_eq
% 6.94/7.31 thf(fact_9467_sum__of__bool__eq,axiom,
% 6.94/7.31 ! [A4: set_Code_integer,P2: code_integer > $o] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ( groups7237345082560585321er_nat
% 6.94/7.31 @ ^ [X4: code_integer] : ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) )
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( semiri1316708129612266289at_nat @ ( finite4902975817058060853nteger @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_of_bool_eq
% 6.94/7.31 thf(fact_9468_sum__of__bool__eq,axiom,
% 6.94/7.31 ! [A4: set_Code_integer,P2: code_integer > $o] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ( groups7234854612051535045er_int
% 6.94/7.31 @ ^ [X4: code_integer] : ( zero_n2684676970156552555ol_int @ ( P2 @ X4 ) )
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( semiri1314217659103216013at_int @ ( finite4902975817058060853nteger @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_of_bool_eq
% 6.94/7.31 thf(fact_9469_sum__of__bool__eq,axiom,
% 6.94/7.31 ! [A4: set_nat,P2: nat > $o] :
% 6.94/7.31 ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ( groups3539618377306564664at_int
% 6.94/7.31 @ ^ [X4: nat] : ( zero_n2684676970156552555ol_int @ ( P2 @ X4 ) )
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( semiri1314217659103216013at_int @ ( finite_card_nat @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_of_bool_eq
% 6.94/7.31 thf(fact_9470_sum__of__bool__eq,axiom,
% 6.94/7.31 ! [A4: set_int,P2: int > $o] :
% 6.94/7.31 ( ( finite_finite_int @ A4 )
% 6.94/7.31 => ( ( finite_finite_int @ A4 )
% 6.94/7.31 => ( ( groups7873554091576472773nteger
% 6.94/7.31 @ ^ [X4: int] : ( zero_n356916108424825756nteger @ ( P2 @ X4 ) )
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( semiri4939895301339042750nteger @ ( finite_card_int @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_of_bool_eq
% 6.94/7.31 thf(fact_9471_sum__of__bool__eq,axiom,
% 6.94/7.31 ! [A4: set_Code_integer,P2: code_integer > $o] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ( groups879477027807139574nteger
% 6.94/7.31 @ ^ [X4: code_integer] : ( zero_n356916108424825756nteger @ ( P2 @ X4 ) )
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( semiri4939895301339042750nteger @ ( finite4902975817058060853nteger @ ( inf_in1364745209274528805nteger @ A4 @ ( collect_Code_integer @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_of_bool_eq
% 6.94/7.31 thf(fact_9472_sum__of__bool__eq,axiom,
% 6.94/7.31 ! [A4: set_nat,P2: nat > $o] :
% 6.94/7.31 ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ( groups7501900531339628137nteger
% 6.94/7.31 @ ^ [X4: nat] : ( zero_n356916108424825756nteger @ ( P2 @ X4 ) )
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( semiri4939895301339042750nteger @ ( finite_card_nat @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_of_bool_eq
% 6.94/7.31 thf(fact_9473_sum__of__bool__eq,axiom,
% 6.94/7.31 ! [A4: set_nat,P2: nat > $o] :
% 6.94/7.31 ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ( groups3542108847815614940at_nat
% 6.94/7.31 @ ^ [X4: nat] : ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) )
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( semiri1316708129612266289at_nat @ ( finite_card_nat @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_of_bool_eq
% 6.94/7.31 thf(fact_9474_sum__of__bool__eq,axiom,
% 6.94/7.31 ! [A4: set_int,P2: int > $o] :
% 6.94/7.31 ( ( finite_finite_int @ A4 )
% 6.94/7.31 => ( ( finite_finite_int @ A4 )
% 6.94/7.31 => ( ( groups4538972089207619220nt_int
% 6.94/7.31 @ ^ [X4: int] : ( zero_n2684676970156552555ol_int @ ( P2 @ X4 ) )
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( semiri1314217659103216013at_int @ ( finite_card_int @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_of_bool_eq
% 6.94/7.31 thf(fact_9475_sum__of__bool__eq,axiom,
% 6.94/7.31 ! [A4: set_list_nat,P2: list_nat > $o] :
% 6.94/7.31 ( ( finite8100373058378681591st_nat @ A4 )
% 6.94/7.31 => ( ( finite8100373058378681591st_nat @ A4 )
% 6.94/7.31 => ( ( groups4396056296759096172at_nat
% 6.94/7.31 @ ^ [X4: list_nat] : ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) )
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( semiri1316708129612266289at_nat @ ( finite_card_list_nat @ ( inf_inf_set_list_nat @ A4 @ ( collect_list_nat @ P2 ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_of_bool_eq
% 6.94/7.31 thf(fact_9476_option_Osimps_I9_J,axiom,
% 6.94/7.31 ! [F: num > num,X2: num] :
% 6.94/7.31 ( ( map_option_num_num @ F @ ( some_num @ X2 ) )
% 6.94/7.31 = ( some_num @ ( F @ X2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.simps(9)
% 6.94/7.31 thf(fact_9477_option_Osimps_I9_J,axiom,
% 6.94/7.31 ! [F: produc7388388658123137530it_nat > num,X2: produc7388388658123137530it_nat] :
% 6.94/7.31 ( ( map_op6233829773304596897at_num @ F @ ( some_P2818173045054083285it_nat @ X2 ) )
% 6.94/7.31 = ( some_num @ ( F @ X2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.simps(9)
% 6.94/7.31 thf(fact_9478_option_Osimps_I9_J,axiom,
% 6.94/7.31 ! [F: produc3260487557148687353it_nat > num,X2: produc3260487557148687353it_nat] :
% 6.94/7.31 ( ( map_op5165227558541518752at_num @ F @ ( some_P7913643980934408916it_nat @ X2 ) )
% 6.94/7.31 = ( some_num @ ( F @ X2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.simps(9)
% 6.94/7.31 thf(fact_9479_option_Osimps_I9_J,axiom,
% 6.94/7.31 ! [F: produc8664842809031399944it_nat > num,X2: produc8664842809031399944it_nat] :
% 6.94/7.31 ( ( map_op2731889312448867759at_num @ F @ ( some_P1914260805536162275it_nat @ X2 ) )
% 6.94/7.31 = ( some_num @ ( F @ X2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.simps(9)
% 6.94/7.31 thf(fact_9480_option_Osimps_I9_J,axiom,
% 6.94/7.31 ! [F: num > produc7388388658123137530it_nat,X2: num] :
% 6.94/7.31 ( ( map_op2490657901765117089it_nat @ F @ ( some_num @ X2 ) )
% 6.94/7.31 = ( some_P2818173045054083285it_nat @ ( F @ X2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.simps(9)
% 6.94/7.31 thf(fact_9481_option_Osimps_I9_J,axiom,
% 6.94/7.31 ! [F: num > produc3260487557148687353it_nat,X2: num] :
% 6.94/7.31 ( ( map_op7586128837645442720it_nat @ F @ ( some_num @ X2 ) )
% 6.94/7.31 = ( some_P7913643980934408916it_nat @ ( F @ X2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.simps(9)
% 6.94/7.31 thf(fact_9482_option_Osimps_I9_J,axiom,
% 6.94/7.31 ! [F: num > produc8664842809031399944it_nat,X2: num] :
% 6.94/7.31 ( ( map_op8118133509425879471it_nat @ F @ ( some_num @ X2 ) )
% 6.94/7.31 = ( some_P1914260805536162275it_nat @ ( F @ X2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.simps(9)
% 6.94/7.31 thf(fact_9483_option_Osimps_I9_J,axiom,
% 6.94/7.31 ! [F: produc7388388658123137530it_nat > produc7388388658123137530it_nat,X2: produc7388388658123137530it_nat] :
% 6.94/7.31 ( ( map_op8581638957091552385it_nat @ F @ ( some_P2818173045054083285it_nat @ X2 ) )
% 6.94/7.31 = ( some_P2818173045054083285it_nat @ ( F @ X2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.simps(9)
% 6.94/7.31 thf(fact_9484_option_Osimps_I9_J,axiom,
% 6.94/7.31 ! [F: produc7388388658123137530it_nat > produc3260487557148687353it_nat,X2: produc7388388658123137530it_nat] :
% 6.94/7.31 ( ( map_op4453737856117102208it_nat @ F @ ( some_P2818173045054083285it_nat @ X2 ) )
% 6.94/7.31 = ( some_P7913643980934408916it_nat @ ( F @ X2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.simps(9)
% 6.94/7.31 thf(fact_9485_option_Osimps_I9_J,axiom,
% 6.94/7.31 ! [F: produc7388388658123137530it_nat > produc8664842809031399944it_nat,X2: produc7388388658123137530it_nat] :
% 6.94/7.31 ( ( map_op8924890681001947535it_nat @ F @ ( some_P2818173045054083285it_nat @ X2 ) )
% 6.94/7.31 = ( some_P1914260805536162275it_nat @ ( F @ X2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.simps(9)
% 6.94/7.31 thf(fact_9486_map__option__cong,axiom,
% 6.94/7.31 ! [X: option_num,Y: option_num,F: num > num,G: num > num] :
% 6.94/7.31 ( ( X = Y )
% 6.94/7.31 => ( ! [A3: num] :
% 6.94/7.31 ( ( Y
% 6.94/7.31 = ( some_num @ A3 ) )
% 6.94/7.31 => ( ( F @ A3 )
% 6.94/7.31 = ( G @ A3 ) ) )
% 6.94/7.31 => ( ( map_option_num_num @ F @ X )
% 6.94/7.31 = ( map_option_num_num @ G @ Y ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option_cong
% 6.94/7.31 thf(fact_9487_of__nat__max,axiom,
% 6.94/7.31 ! [X: nat,Y: nat] :
% 6.94/7.31 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y ) )
% 6.94/7.31 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % of_nat_max
% 6.94/7.31 thf(fact_9488_of__nat__max,axiom,
% 6.94/7.31 ! [X: nat,Y: nat] :
% 6.94/7.31 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y ) )
% 6.94/7.31 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % of_nat_max
% 6.94/7.31 thf(fact_9489_of__nat__max,axiom,
% 6.94/7.31 ! [X: nat,Y: nat] :
% 6.94/7.31 ( ( semiri4939895301339042750nteger @ ( ord_max_nat @ X @ Y ) )
% 6.94/7.31 = ( ord_max_Code_integer @ ( semiri4939895301339042750nteger @ X ) @ ( semiri4939895301339042750nteger @ Y ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % of_nat_max
% 6.94/7.31 thf(fact_9490_map__option_Ocomp,axiom,
% 6.94/7.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer] :
% 6.94/7.31 ( ( comp_o9011007105448239796nteger @ ( map_op9146685272036663823nteger @ F ) @ ( map_op3669829223712506439nteger @ G ) )
% 6.94/7.31 = ( map_op9146685272036663823nteger @ ( comp_C1593894019821074884nteger @ F @ G ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option.comp
% 6.94/7.31 thf(fact_9491_map__option_Ocomp,axiom,
% 6.94/7.31 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer] :
% 6.94/7.31 ( ( comp_o7188567781464924208nteger @ ( map_op3563471509957180299nteger @ F ) @ ( map_op370346339404370627nteger @ G ) )
% 6.94/7.31 = ( map_op9146685272036663823nteger @ ( comp_C8797469213163452608nteger @ F @ G ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option.comp
% 6.94/7.31 thf(fact_9492_map__option_Ocomp,axiom,
% 6.94/7.31 ! [F: int > nat,G: int > int] :
% 6.94/7.31 ( ( comp_o4824269118391204861on_int @ ( map_option_int_nat @ F ) @ ( map_option_int_int @ G ) )
% 6.94/7.31 = ( map_option_int_nat @ ( comp_int_nat_int @ F @ G ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option.comp
% 6.94/7.31 thf(fact_9493_map__option_Ocomp,axiom,
% 6.94/7.31 ! [F: num > num,G: num > num] :
% 6.94/7.31 ( ( comp_o8931257242830428707on_num @ ( map_option_num_num @ F ) @ ( map_option_num_num @ G ) )
% 6.94/7.31 = ( map_option_num_num @ ( comp_num_num_num @ F @ G ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option.comp
% 6.94/7.31 thf(fact_9494_option_Omap__comp,axiom,
% 6.94/7.31 ! [G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer,V: option_Code_integer] :
% 6.94/7.31 ( ( map_op9146685272036663823nteger @ G @ ( map_op3669829223712506439nteger @ F @ V ) )
% 6.94/7.31 = ( map_op9146685272036663823nteger @ ( comp_C1593894019821074884nteger @ G @ F ) @ V ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.map_comp
% 6.94/7.31 thf(fact_9495_option_Omap__comp,axiom,
% 6.94/7.31 ! [G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer,V: option_Code_integer] :
% 6.94/7.31 ( ( map_op3563471509957180299nteger @ G @ ( map_op370346339404370627nteger @ F @ V ) )
% 6.94/7.31 = ( map_op9146685272036663823nteger @ ( comp_C8797469213163452608nteger @ G @ F ) @ V ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.map_comp
% 6.94/7.31 thf(fact_9496_option_Omap__comp,axiom,
% 6.94/7.31 ! [G: int > nat,F: int > int,V: option_int] :
% 6.94/7.31 ( ( map_option_int_nat @ G @ ( map_option_int_int @ F @ V ) )
% 6.94/7.31 = ( map_option_int_nat @ ( comp_int_nat_int @ G @ F ) @ V ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.map_comp
% 6.94/7.31 thf(fact_9497_option_Omap__comp,axiom,
% 6.94/7.31 ! [G: num > num,F: num > num,V: option_num] :
% 6.94/7.31 ( ( map_option_num_num @ G @ ( map_option_num_num @ F @ V ) )
% 6.94/7.31 = ( map_option_num_num @ ( comp_num_num_num @ G @ F ) @ V ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.map_comp
% 6.94/7.31 thf(fact_9498_map__option_Ocompositionality,axiom,
% 6.94/7.31 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,Option: option_Code_integer] :
% 6.94/7.31 ( ( map_op9146685272036663823nteger @ F @ ( map_op3669829223712506439nteger @ G @ Option ) )
% 6.94/7.31 = ( map_op9146685272036663823nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ Option ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option.compositionality
% 6.94/7.31 thf(fact_9499_map__option_Ocompositionality,axiom,
% 6.94/7.31 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,Option: option_Code_integer] :
% 6.94/7.31 ( ( map_op3563471509957180299nteger @ F @ ( map_op370346339404370627nteger @ G @ Option ) )
% 6.94/7.31 = ( map_op9146685272036663823nteger @ ( comp_C8797469213163452608nteger @ F @ G ) @ Option ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option.compositionality
% 6.94/7.31 thf(fact_9500_map__option_Ocompositionality,axiom,
% 6.94/7.31 ! [F: int > nat,G: int > int,Option: option_int] :
% 6.94/7.31 ( ( map_option_int_nat @ F @ ( map_option_int_int @ G @ Option ) )
% 6.94/7.31 = ( map_option_int_nat @ ( comp_int_nat_int @ F @ G ) @ Option ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option.compositionality
% 6.94/7.31 thf(fact_9501_map__option_Ocompositionality,axiom,
% 6.94/7.31 ! [F: num > num,G: num > num,Option: option_num] :
% 6.94/7.31 ( ( map_option_num_num @ F @ ( map_option_num_num @ G @ Option ) )
% 6.94/7.31 = ( map_option_num_num @ ( comp_num_num_num @ F @ G ) @ Option ) ) ).
% 6.94/7.31
% 6.94/7.31 % map_option.compositionality
% 6.94/7.31 thf(fact_9502_nat__mult__max__left,axiom,
% 6.94/7.31 ! [M: nat,N2: nat,Q6: nat] :
% 6.94/7.31 ( ( times_times_nat @ ( ord_max_nat @ M @ N2 ) @ Q6 )
% 6.94/7.31 = ( ord_max_nat @ ( times_times_nat @ M @ Q6 ) @ ( times_times_nat @ N2 @ Q6 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % nat_mult_max_left
% 6.94/7.31 thf(fact_9503_nat__mult__max__right,axiom,
% 6.94/7.31 ! [M: nat,N2: nat,Q6: nat] :
% 6.94/7.31 ( ( times_times_nat @ M @ ( ord_max_nat @ N2 @ Q6 ) )
% 6.94/7.31 = ( ord_max_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q6 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % nat_mult_max_right
% 6.94/7.31 thf(fact_9504_max_Ostrict__coboundedI2,axiom,
% 6.94/7.31 ! [C2: rat,B: rat,A: rat] :
% 6.94/7.31 ( ( ord_less_rat @ C2 @ B )
% 6.94/7.31 => ( ord_less_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_coboundedI2
% 6.94/7.31 thf(fact_9505_max_Ostrict__coboundedI2,axiom,
% 6.94/7.31 ! [C2: num,B: num,A: num] :
% 6.94/7.31 ( ( ord_less_num @ C2 @ B )
% 6.94/7.31 => ( ord_less_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_coboundedI2
% 6.94/7.31 thf(fact_9506_max_Ostrict__coboundedI2,axiom,
% 6.94/7.31 ! [C2: nat,B: nat,A: nat] :
% 6.94/7.31 ( ( ord_less_nat @ C2 @ B )
% 6.94/7.31 => ( ord_less_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_coboundedI2
% 6.94/7.31 thf(fact_9507_max_Ostrict__coboundedI2,axiom,
% 6.94/7.31 ! [C2: int,B: int,A: int] :
% 6.94/7.31 ( ( ord_less_int @ C2 @ B )
% 6.94/7.31 => ( ord_less_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_coboundedI2
% 6.94/7.31 thf(fact_9508_max_Ostrict__coboundedI1,axiom,
% 6.94/7.31 ! [C2: rat,A: rat,B: rat] :
% 6.94/7.31 ( ( ord_less_rat @ C2 @ A )
% 6.94/7.31 => ( ord_less_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_coboundedI1
% 6.94/7.31 thf(fact_9509_max_Ostrict__coboundedI1,axiom,
% 6.94/7.31 ! [C2: num,A: num,B: num] :
% 6.94/7.31 ( ( ord_less_num @ C2 @ A )
% 6.94/7.31 => ( ord_less_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_coboundedI1
% 6.94/7.31 thf(fact_9510_max_Ostrict__coboundedI1,axiom,
% 6.94/7.31 ! [C2: nat,A: nat,B: nat] :
% 6.94/7.31 ( ( ord_less_nat @ C2 @ A )
% 6.94/7.31 => ( ord_less_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_coboundedI1
% 6.94/7.31 thf(fact_9511_max_Ostrict__coboundedI1,axiom,
% 6.94/7.31 ! [C2: int,A: int,B: int] :
% 6.94/7.31 ( ( ord_less_int @ C2 @ A )
% 6.94/7.31 => ( ord_less_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_coboundedI1
% 6.94/7.31 thf(fact_9512_max_Ostrict__order__iff,axiom,
% 6.94/7.31 ( ord_less_rat
% 6.94/7.31 = ( ^ [B4: rat,A5: rat] :
% 6.94/7.31 ( ( A5
% 6.94/7.31 = ( ord_max_rat @ A5 @ B4 ) )
% 6.94/7.31 & ( A5 != B4 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_order_iff
% 6.94/7.31 thf(fact_9513_max_Ostrict__order__iff,axiom,
% 6.94/7.31 ( ord_less_num
% 6.94/7.31 = ( ^ [B4: num,A5: num] :
% 6.94/7.31 ( ( A5
% 6.94/7.31 = ( ord_max_num @ A5 @ B4 ) )
% 6.94/7.31 & ( A5 != B4 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_order_iff
% 6.94/7.31 thf(fact_9514_max_Ostrict__order__iff,axiom,
% 6.94/7.31 ( ord_less_nat
% 6.94/7.31 = ( ^ [B4: nat,A5: nat] :
% 6.94/7.31 ( ( A5
% 6.94/7.31 = ( ord_max_nat @ A5 @ B4 ) )
% 6.94/7.31 & ( A5 != B4 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_order_iff
% 6.94/7.31 thf(fact_9515_max_Ostrict__order__iff,axiom,
% 6.94/7.31 ( ord_less_int
% 6.94/7.31 = ( ^ [B4: int,A5: int] :
% 6.94/7.31 ( ( A5
% 6.94/7.31 = ( ord_max_int @ A5 @ B4 ) )
% 6.94/7.31 & ( A5 != B4 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_order_iff
% 6.94/7.31 thf(fact_9516_max_Ostrict__boundedE,axiom,
% 6.94/7.31 ! [B: rat,C2: rat,A: rat] :
% 6.94/7.31 ( ( ord_less_rat @ ( ord_max_rat @ B @ C2 ) @ A )
% 6.94/7.31 => ~ ( ( ord_less_rat @ B @ A )
% 6.94/7.31 => ~ ( ord_less_rat @ C2 @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_boundedE
% 6.94/7.31 thf(fact_9517_max_Ostrict__boundedE,axiom,
% 6.94/7.31 ! [B: num,C2: num,A: num] :
% 6.94/7.31 ( ( ord_less_num @ ( ord_max_num @ B @ C2 ) @ A )
% 6.94/7.31 => ~ ( ( ord_less_num @ B @ A )
% 6.94/7.31 => ~ ( ord_less_num @ C2 @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_boundedE
% 6.94/7.31 thf(fact_9518_max_Ostrict__boundedE,axiom,
% 6.94/7.31 ! [B: nat,C2: nat,A: nat] :
% 6.94/7.31 ( ( ord_less_nat @ ( ord_max_nat @ B @ C2 ) @ A )
% 6.94/7.31 => ~ ( ( ord_less_nat @ B @ A )
% 6.94/7.31 => ~ ( ord_less_nat @ C2 @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_boundedE
% 6.94/7.31 thf(fact_9519_max_Ostrict__boundedE,axiom,
% 6.94/7.31 ! [B: int,C2: int,A: int] :
% 6.94/7.31 ( ( ord_less_int @ ( ord_max_int @ B @ C2 ) @ A )
% 6.94/7.31 => ~ ( ( ord_less_int @ B @ A )
% 6.94/7.31 => ~ ( ord_less_int @ C2 @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.strict_boundedE
% 6.94/7.31 thf(fact_9520_less__max__iff__disj,axiom,
% 6.94/7.31 ! [Z3: rat,X: rat,Y: rat] :
% 6.94/7.31 ( ( ord_less_rat @ Z3 @ ( ord_max_rat @ X @ Y ) )
% 6.94/7.31 = ( ( ord_less_rat @ Z3 @ X )
% 6.94/7.31 | ( ord_less_rat @ Z3 @ Y ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % less_max_iff_disj
% 6.94/7.31 thf(fact_9521_less__max__iff__disj,axiom,
% 6.94/7.31 ! [Z3: num,X: num,Y: num] :
% 6.94/7.31 ( ( ord_less_num @ Z3 @ ( ord_max_num @ X @ Y ) )
% 6.94/7.31 = ( ( ord_less_num @ Z3 @ X )
% 6.94/7.31 | ( ord_less_num @ Z3 @ Y ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % less_max_iff_disj
% 6.94/7.31 thf(fact_9522_less__max__iff__disj,axiom,
% 6.94/7.31 ! [Z3: nat,X: nat,Y: nat] :
% 6.94/7.31 ( ( ord_less_nat @ Z3 @ ( ord_max_nat @ X @ Y ) )
% 6.94/7.31 = ( ( ord_less_nat @ Z3 @ X )
% 6.94/7.31 | ( ord_less_nat @ Z3 @ Y ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % less_max_iff_disj
% 6.94/7.31 thf(fact_9523_less__max__iff__disj,axiom,
% 6.94/7.31 ! [Z3: int,X: int,Y: int] :
% 6.94/7.31 ( ( ord_less_int @ Z3 @ ( ord_max_int @ X @ Y ) )
% 6.94/7.31 = ( ( ord_less_int @ Z3 @ X )
% 6.94/7.31 | ( ord_less_int @ Z3 @ Y ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % less_max_iff_disj
% 6.94/7.31 thf(fact_9524_nat__add__max__left,axiom,
% 6.94/7.31 ! [M: nat,N2: nat,Q6: nat] :
% 6.94/7.31 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N2 ) @ Q6 )
% 6.94/7.31 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q6 ) @ ( plus_plus_nat @ N2 @ Q6 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % nat_add_max_left
% 6.94/7.31 thf(fact_9525_nat__add__max__right,axiom,
% 6.94/7.31 ! [M: nat,N2: nat,Q6: nat] :
% 6.94/7.31 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N2 @ Q6 ) )
% 6.94/7.31 = ( ord_max_nat @ ( plus_plus_nat @ M @ N2 ) @ ( plus_plus_nat @ M @ Q6 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % nat_add_max_right
% 6.94/7.31 thf(fact_9526_sup__max,axiom,
% 6.94/7.31 sup_sup_int = ord_max_int ).
% 6.94/7.31
% 6.94/7.31 % sup_max
% 6.94/7.31 thf(fact_9527_sup__max,axiom,
% 6.94/7.31 sup_sup_nat = ord_max_nat ).
% 6.94/7.31
% 6.94/7.31 % sup_max
% 6.94/7.31 thf(fact_9528_sup__int__def,axiom,
% 6.94/7.31 sup_sup_int = ord_max_int ).
% 6.94/7.31
% 6.94/7.31 % sup_int_def
% 6.94/7.31 thf(fact_9529_sup__nat__def,axiom,
% 6.94/7.31 sup_sup_nat = ord_max_nat ).
% 6.94/7.31
% 6.94/7.31 % sup_nat_def
% 6.94/7.31 thf(fact_9530_option_Omap__ident,axiom,
% 6.94/7.31 ! [T6: option_num] :
% 6.94/7.31 ( ( map_option_num_num
% 6.94/7.31 @ ^ [X4: num] : X4
% 6.94/7.31 @ T6 )
% 6.94/7.31 = T6 ) ).
% 6.94/7.31
% 6.94/7.31 % option.map_ident
% 6.94/7.31 thf(fact_9531_max_OcoboundedI2,axiom,
% 6.94/7.31 ! [C2: rat,B: rat,A: rat] :
% 6.94/7.31 ( ( ord_less_eq_rat @ C2 @ B )
% 6.94/7.31 => ( ord_less_eq_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.coboundedI2
% 6.94/7.31 thf(fact_9532_max_OcoboundedI2,axiom,
% 6.94/7.31 ! [C2: num,B: num,A: num] :
% 6.94/7.31 ( ( ord_less_eq_num @ C2 @ B )
% 6.94/7.31 => ( ord_less_eq_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.coboundedI2
% 6.94/7.31 thf(fact_9533_max_OcoboundedI2,axiom,
% 6.94/7.31 ! [C2: nat,B: nat,A: nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ C2 @ B )
% 6.94/7.31 => ( ord_less_eq_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.coboundedI2
% 6.94/7.31 thf(fact_9534_max_OcoboundedI2,axiom,
% 6.94/7.31 ! [C2: int,B: int,A: int] :
% 6.94/7.31 ( ( ord_less_eq_int @ C2 @ B )
% 6.94/7.31 => ( ord_less_eq_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.coboundedI2
% 6.94/7.31 thf(fact_9535_max_OcoboundedI1,axiom,
% 6.94/7.31 ! [C2: rat,A: rat,B: rat] :
% 6.94/7.31 ( ( ord_less_eq_rat @ C2 @ A )
% 6.94/7.31 => ( ord_less_eq_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.coboundedI1
% 6.94/7.31 thf(fact_9536_max_OcoboundedI1,axiom,
% 6.94/7.31 ! [C2: num,A: num,B: num] :
% 6.94/7.31 ( ( ord_less_eq_num @ C2 @ A )
% 6.94/7.31 => ( ord_less_eq_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.coboundedI1
% 6.94/7.31 thf(fact_9537_max_OcoboundedI1,axiom,
% 6.94/7.31 ! [C2: nat,A: nat,B: nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ C2 @ A )
% 6.94/7.31 => ( ord_less_eq_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.coboundedI1
% 6.94/7.31 thf(fact_9538_max_OcoboundedI1,axiom,
% 6.94/7.31 ! [C2: int,A: int,B: int] :
% 6.94/7.31 ( ( ord_less_eq_int @ C2 @ A )
% 6.94/7.31 => ( ord_less_eq_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.coboundedI1
% 6.94/7.31 thf(fact_9539_max_Oabsorb__iff2,axiom,
% 6.94/7.31 ( ord_less_eq_rat
% 6.94/7.31 = ( ^ [A5: rat,B4: rat] :
% 6.94/7.31 ( ( ord_max_rat @ A5 @ B4 )
% 6.94/7.31 = B4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb_iff2
% 6.94/7.31 thf(fact_9540_max_Oabsorb__iff2,axiom,
% 6.94/7.31 ( ord_less_eq_num
% 6.94/7.31 = ( ^ [A5: num,B4: num] :
% 6.94/7.31 ( ( ord_max_num @ A5 @ B4 )
% 6.94/7.31 = B4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb_iff2
% 6.94/7.31 thf(fact_9541_max_Oabsorb__iff2,axiom,
% 6.94/7.31 ( ord_less_eq_nat
% 6.94/7.31 = ( ^ [A5: nat,B4: nat] :
% 6.94/7.31 ( ( ord_max_nat @ A5 @ B4 )
% 6.94/7.31 = B4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb_iff2
% 6.94/7.31 thf(fact_9542_max_Oabsorb__iff2,axiom,
% 6.94/7.31 ( ord_less_eq_int
% 6.94/7.31 = ( ^ [A5: int,B4: int] :
% 6.94/7.31 ( ( ord_max_int @ A5 @ B4 )
% 6.94/7.31 = B4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb_iff2
% 6.94/7.31 thf(fact_9543_max_Oabsorb__iff1,axiom,
% 6.94/7.31 ( ord_less_eq_rat
% 6.94/7.31 = ( ^ [B4: rat,A5: rat] :
% 6.94/7.31 ( ( ord_max_rat @ A5 @ B4 )
% 6.94/7.31 = A5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb_iff1
% 6.94/7.31 thf(fact_9544_max_Oabsorb__iff1,axiom,
% 6.94/7.31 ( ord_less_eq_num
% 6.94/7.31 = ( ^ [B4: num,A5: num] :
% 6.94/7.31 ( ( ord_max_num @ A5 @ B4 )
% 6.94/7.31 = A5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb_iff1
% 6.94/7.31 thf(fact_9545_max_Oabsorb__iff1,axiom,
% 6.94/7.31 ( ord_less_eq_nat
% 6.94/7.31 = ( ^ [B4: nat,A5: nat] :
% 6.94/7.31 ( ( ord_max_nat @ A5 @ B4 )
% 6.94/7.31 = A5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb_iff1
% 6.94/7.31 thf(fact_9546_max_Oabsorb__iff1,axiom,
% 6.94/7.31 ( ord_less_eq_int
% 6.94/7.31 = ( ^ [B4: int,A5: int] :
% 6.94/7.31 ( ( ord_max_int @ A5 @ B4 )
% 6.94/7.31 = A5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.absorb_iff1
% 6.94/7.31 thf(fact_9547_le__max__iff__disj,axiom,
% 6.94/7.31 ! [Z3: rat,X: rat,Y: rat] :
% 6.94/7.31 ( ( ord_less_eq_rat @ Z3 @ ( ord_max_rat @ X @ Y ) )
% 6.94/7.31 = ( ( ord_less_eq_rat @ Z3 @ X )
% 6.94/7.31 | ( ord_less_eq_rat @ Z3 @ Y ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % le_max_iff_disj
% 6.94/7.31 thf(fact_9548_le__max__iff__disj,axiom,
% 6.94/7.31 ! [Z3: num,X: num,Y: num] :
% 6.94/7.31 ( ( ord_less_eq_num @ Z3 @ ( ord_max_num @ X @ Y ) )
% 6.94/7.31 = ( ( ord_less_eq_num @ Z3 @ X )
% 6.94/7.31 | ( ord_less_eq_num @ Z3 @ Y ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % le_max_iff_disj
% 6.94/7.31 thf(fact_9549_le__max__iff__disj,axiom,
% 6.94/7.31 ! [Z3: nat,X: nat,Y: nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ Z3 @ ( ord_max_nat @ X @ Y ) )
% 6.94/7.31 = ( ( ord_less_eq_nat @ Z3 @ X )
% 6.94/7.31 | ( ord_less_eq_nat @ Z3 @ Y ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % le_max_iff_disj
% 6.94/7.31 thf(fact_9550_le__max__iff__disj,axiom,
% 6.94/7.31 ! [Z3: int,X: int,Y: int] :
% 6.94/7.31 ( ( ord_less_eq_int @ Z3 @ ( ord_max_int @ X @ Y ) )
% 6.94/7.31 = ( ( ord_less_eq_int @ Z3 @ X )
% 6.94/7.31 | ( ord_less_eq_int @ Z3 @ Y ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % le_max_iff_disj
% 6.94/7.31 thf(fact_9551_max_Ocobounded2,axiom,
% 6.94/7.31 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.cobounded2
% 6.94/7.31 thf(fact_9552_max_Ocobounded2,axiom,
% 6.94/7.31 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.cobounded2
% 6.94/7.31 thf(fact_9553_max_Ocobounded2,axiom,
% 6.94/7.31 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.cobounded2
% 6.94/7.31 thf(fact_9554_max_Ocobounded2,axiom,
% 6.94/7.31 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.cobounded2
% 6.94/7.31 thf(fact_9555_max_Ocobounded1,axiom,
% 6.94/7.31 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.cobounded1
% 6.94/7.31 thf(fact_9556_max_Ocobounded1,axiom,
% 6.94/7.31 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.cobounded1
% 6.94/7.31 thf(fact_9557_max_Ocobounded1,axiom,
% 6.94/7.31 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.cobounded1
% 6.94/7.31 thf(fact_9558_max_Ocobounded1,axiom,
% 6.94/7.31 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.cobounded1
% 6.94/7.31 thf(fact_9559_max_Oorder__iff,axiom,
% 6.94/7.31 ( ord_less_eq_rat
% 6.94/7.31 = ( ^ [B4: rat,A5: rat] :
% 6.94/7.31 ( A5
% 6.94/7.31 = ( ord_max_rat @ A5 @ B4 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.order_iff
% 6.94/7.31 thf(fact_9560_max_Oorder__iff,axiom,
% 6.94/7.31 ( ord_less_eq_num
% 6.94/7.31 = ( ^ [B4: num,A5: num] :
% 6.94/7.31 ( A5
% 6.94/7.31 = ( ord_max_num @ A5 @ B4 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.order_iff
% 6.94/7.31 thf(fact_9561_max_Oorder__iff,axiom,
% 6.94/7.31 ( ord_less_eq_nat
% 6.94/7.31 = ( ^ [B4: nat,A5: nat] :
% 6.94/7.31 ( A5
% 6.94/7.31 = ( ord_max_nat @ A5 @ B4 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.order_iff
% 6.94/7.31 thf(fact_9562_max_Oorder__iff,axiom,
% 6.94/7.31 ( ord_less_eq_int
% 6.94/7.31 = ( ^ [B4: int,A5: int] :
% 6.94/7.31 ( A5
% 6.94/7.31 = ( ord_max_int @ A5 @ B4 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.order_iff
% 6.94/7.31 thf(fact_9563_max_OboundedI,axiom,
% 6.94/7.31 ! [B: rat,A: rat,C2: rat] :
% 6.94/7.31 ( ( ord_less_eq_rat @ B @ A )
% 6.94/7.31 => ( ( ord_less_eq_rat @ C2 @ A )
% 6.94/7.31 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.boundedI
% 6.94/7.31 thf(fact_9564_max_OboundedI,axiom,
% 6.94/7.31 ! [B: num,A: num,C2: num] :
% 6.94/7.31 ( ( ord_less_eq_num @ B @ A )
% 6.94/7.31 => ( ( ord_less_eq_num @ C2 @ A )
% 6.94/7.31 => ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.boundedI
% 6.94/7.31 thf(fact_9565_max_OboundedI,axiom,
% 6.94/7.31 ! [B: nat,A: nat,C2: nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ B @ A )
% 6.94/7.31 => ( ( ord_less_eq_nat @ C2 @ A )
% 6.94/7.31 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.boundedI
% 6.94/7.31 thf(fact_9566_max_OboundedI,axiom,
% 6.94/7.31 ! [B: int,A: int,C2: int] :
% 6.94/7.31 ( ( ord_less_eq_int @ B @ A )
% 6.94/7.31 => ( ( ord_less_eq_int @ C2 @ A )
% 6.94/7.31 => ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.boundedI
% 6.94/7.31 thf(fact_9567_max_OboundedE,axiom,
% 6.94/7.31 ! [B: rat,C2: rat,A: rat] :
% 6.94/7.31 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A )
% 6.94/7.31 => ~ ( ( ord_less_eq_rat @ B @ A )
% 6.94/7.31 => ~ ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.boundedE
% 6.94/7.31 thf(fact_9568_max_OboundedE,axiom,
% 6.94/7.31 ! [B: num,C2: num,A: num] :
% 6.94/7.31 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A )
% 6.94/7.31 => ~ ( ( ord_less_eq_num @ B @ A )
% 6.94/7.31 => ~ ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.boundedE
% 6.94/7.31 thf(fact_9569_max_OboundedE,axiom,
% 6.94/7.31 ! [B: nat,C2: nat,A: nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A )
% 6.94/7.31 => ~ ( ( ord_less_eq_nat @ B @ A )
% 6.94/7.31 => ~ ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.boundedE
% 6.94/7.31 thf(fact_9570_max_OboundedE,axiom,
% 6.94/7.31 ! [B: int,C2: int,A: int] :
% 6.94/7.31 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A )
% 6.94/7.31 => ~ ( ( ord_less_eq_int @ B @ A )
% 6.94/7.31 => ~ ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.boundedE
% 6.94/7.31 thf(fact_9571_max_OorderI,axiom,
% 6.94/7.31 ! [A: rat,B: rat] :
% 6.94/7.31 ( ( A
% 6.94/7.31 = ( ord_max_rat @ A @ B ) )
% 6.94/7.31 => ( ord_less_eq_rat @ B @ A ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.orderI
% 6.94/7.31 thf(fact_9572_max_OorderI,axiom,
% 6.94/7.31 ! [A: num,B: num] :
% 6.94/7.31 ( ( A
% 6.94/7.31 = ( ord_max_num @ A @ B ) )
% 6.94/7.31 => ( ord_less_eq_num @ B @ A ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.orderI
% 6.94/7.31 thf(fact_9573_max_OorderI,axiom,
% 6.94/7.31 ! [A: nat,B: nat] :
% 6.94/7.31 ( ( A
% 6.94/7.31 = ( ord_max_nat @ A @ B ) )
% 6.94/7.31 => ( ord_less_eq_nat @ B @ A ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.orderI
% 6.94/7.31 thf(fact_9574_max_OorderI,axiom,
% 6.94/7.31 ! [A: int,B: int] :
% 6.94/7.31 ( ( A
% 6.94/7.31 = ( ord_max_int @ A @ B ) )
% 6.94/7.31 => ( ord_less_eq_int @ B @ A ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.orderI
% 6.94/7.31 thf(fact_9575_max_OorderE,axiom,
% 6.94/7.31 ! [B: rat,A: rat] :
% 6.94/7.31 ( ( ord_less_eq_rat @ B @ A )
% 6.94/7.31 => ( A
% 6.94/7.31 = ( ord_max_rat @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.orderE
% 6.94/7.31 thf(fact_9576_max_OorderE,axiom,
% 6.94/7.31 ! [B: num,A: num] :
% 6.94/7.31 ( ( ord_less_eq_num @ B @ A )
% 6.94/7.31 => ( A
% 6.94/7.31 = ( ord_max_num @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.orderE
% 6.94/7.31 thf(fact_9577_max_OorderE,axiom,
% 6.94/7.31 ! [B: nat,A: nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ B @ A )
% 6.94/7.31 => ( A
% 6.94/7.31 = ( ord_max_nat @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.orderE
% 6.94/7.31 thf(fact_9578_max_OorderE,axiom,
% 6.94/7.31 ! [B: int,A: int] :
% 6.94/7.31 ( ( ord_less_eq_int @ B @ A )
% 6.94/7.31 => ( A
% 6.94/7.31 = ( ord_max_int @ A @ B ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.orderE
% 6.94/7.31 thf(fact_9579_max_Omono,axiom,
% 6.94/7.31 ! [C2: rat,A: rat,D2: rat,B: rat] :
% 6.94/7.31 ( ( ord_less_eq_rat @ C2 @ A )
% 6.94/7.31 => ( ( ord_less_eq_rat @ D2 @ B )
% 6.94/7.31 => ( ord_less_eq_rat @ ( ord_max_rat @ C2 @ D2 ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.mono
% 6.94/7.31 thf(fact_9580_max_Omono,axiom,
% 6.94/7.31 ! [C2: num,A: num,D2: num,B: num] :
% 6.94/7.31 ( ( ord_less_eq_num @ C2 @ A )
% 6.94/7.31 => ( ( ord_less_eq_num @ D2 @ B )
% 6.94/7.31 => ( ord_less_eq_num @ ( ord_max_num @ C2 @ D2 ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.mono
% 6.94/7.31 thf(fact_9581_max_Omono,axiom,
% 6.94/7.31 ! [C2: nat,A: nat,D2: nat,B: nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ C2 @ A )
% 6.94/7.31 => ( ( ord_less_eq_nat @ D2 @ B )
% 6.94/7.31 => ( ord_less_eq_nat @ ( ord_max_nat @ C2 @ D2 ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.mono
% 6.94/7.31 thf(fact_9582_max_Omono,axiom,
% 6.94/7.31 ! [C2: int,A: int,D2: int,B: int] :
% 6.94/7.31 ( ( ord_less_eq_int @ C2 @ A )
% 6.94/7.31 => ( ( ord_less_eq_int @ D2 @ B )
% 6.94/7.31 => ( ord_less_eq_int @ ( ord_max_int @ C2 @ D2 ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max.mono
% 6.94/7.31 thf(fact_9583_max__absorb2,axiom,
% 6.94/7.31 ! [X: set_int,Y: set_int] :
% 6.94/7.31 ( ( ord_less_eq_set_int @ X @ Y )
% 6.94/7.31 => ( ( ord_max_set_int @ X @ Y )
% 6.94/7.31 = Y ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_absorb2
% 6.94/7.31 thf(fact_9584_max__absorb2,axiom,
% 6.94/7.31 ! [X: rat,Y: rat] :
% 6.94/7.31 ( ( ord_less_eq_rat @ X @ Y )
% 6.94/7.31 => ( ( ord_max_rat @ X @ Y )
% 6.94/7.31 = Y ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_absorb2
% 6.94/7.31 thf(fact_9585_max__absorb2,axiom,
% 6.94/7.31 ! [X: num,Y: num] :
% 6.94/7.31 ( ( ord_less_eq_num @ X @ Y )
% 6.94/7.31 => ( ( ord_max_num @ X @ Y )
% 6.94/7.31 = Y ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_absorb2
% 6.94/7.31 thf(fact_9586_max__absorb2,axiom,
% 6.94/7.31 ! [X: nat,Y: nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ X @ Y )
% 6.94/7.31 => ( ( ord_max_nat @ X @ Y )
% 6.94/7.31 = Y ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_absorb2
% 6.94/7.31 thf(fact_9587_max__absorb2,axiom,
% 6.94/7.31 ! [X: int,Y: int] :
% 6.94/7.31 ( ( ord_less_eq_int @ X @ Y )
% 6.94/7.31 => ( ( ord_max_int @ X @ Y )
% 6.94/7.31 = Y ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_absorb2
% 6.94/7.31 thf(fact_9588_max__absorb1,axiom,
% 6.94/7.31 ! [Y: set_int,X: set_int] :
% 6.94/7.31 ( ( ord_less_eq_set_int @ Y @ X )
% 6.94/7.31 => ( ( ord_max_set_int @ X @ Y )
% 6.94/7.31 = X ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_absorb1
% 6.94/7.31 thf(fact_9589_max__absorb1,axiom,
% 6.94/7.31 ! [Y: rat,X: rat] :
% 6.94/7.31 ( ( ord_less_eq_rat @ Y @ X )
% 6.94/7.31 => ( ( ord_max_rat @ X @ Y )
% 6.94/7.31 = X ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_absorb1
% 6.94/7.31 thf(fact_9590_max__absorb1,axiom,
% 6.94/7.31 ! [Y: num,X: num] :
% 6.94/7.31 ( ( ord_less_eq_num @ Y @ X )
% 6.94/7.31 => ( ( ord_max_num @ X @ Y )
% 6.94/7.31 = X ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_absorb1
% 6.94/7.31 thf(fact_9591_max__absorb1,axiom,
% 6.94/7.31 ! [Y: nat,X: nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ Y @ X )
% 6.94/7.31 => ( ( ord_max_nat @ X @ Y )
% 6.94/7.31 = X ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_absorb1
% 6.94/7.31 thf(fact_9592_max__absorb1,axiom,
% 6.94/7.31 ! [Y: int,X: int] :
% 6.94/7.31 ( ( ord_less_eq_int @ Y @ X )
% 6.94/7.31 => ( ( ord_max_int @ X @ Y )
% 6.94/7.31 = X ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_absorb1
% 6.94/7.31 thf(fact_9593_max__def,axiom,
% 6.94/7.31 ( ord_max_set_int
% 6.94/7.31 = ( ^ [A5: set_int,B4: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_def
% 6.94/7.31 thf(fact_9594_max__def,axiom,
% 6.94/7.31 ( ord_max_rat
% 6.94/7.31 = ( ^ [A5: rat,B4: rat] : ( if_rat @ ( ord_less_eq_rat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_def
% 6.94/7.31 thf(fact_9595_max__def,axiom,
% 6.94/7.31 ( ord_max_num
% 6.94/7.31 = ( ^ [A5: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_def
% 6.94/7.31 thf(fact_9596_max__def,axiom,
% 6.94/7.31 ( ord_max_nat
% 6.94/7.31 = ( ^ [A5: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_def
% 6.94/7.31 thf(fact_9597_max__def,axiom,
% 6.94/7.31 ( ord_max_int
% 6.94/7.31 = ( ^ [A5: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_def
% 6.94/7.31 thf(fact_9598_max__add__distrib__right,axiom,
% 6.94/7.31 ! [X: rat,Y: rat,Z3: rat] :
% 6.94/7.31 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z3 ) )
% 6.94/7.31 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z3 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_add_distrib_right
% 6.94/7.31 thf(fact_9599_max__add__distrib__right,axiom,
% 6.94/7.31 ! [X: int,Y: int,Z3: int] :
% 6.94/7.31 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z3 ) )
% 6.94/7.31 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z3 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_add_distrib_right
% 6.94/7.31 thf(fact_9600_max__add__distrib__right,axiom,
% 6.94/7.31 ! [X: nat,Y: nat,Z3: nat] :
% 6.94/7.31 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z3 ) )
% 6.94/7.31 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z3 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_add_distrib_right
% 6.94/7.31 thf(fact_9601_max__add__distrib__left,axiom,
% 6.94/7.31 ! [X: rat,Y: rat,Z3: rat] :
% 6.94/7.31 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z3 )
% 6.94/7.31 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z3 ) @ ( plus_plus_rat @ Y @ Z3 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_add_distrib_left
% 6.94/7.31 thf(fact_9602_max__add__distrib__left,axiom,
% 6.94/7.31 ! [X: int,Y: int,Z3: int] :
% 6.94/7.31 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z3 )
% 6.94/7.31 = ( ord_max_int @ ( plus_plus_int @ X @ Z3 ) @ ( plus_plus_int @ Y @ Z3 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_add_distrib_left
% 6.94/7.31 thf(fact_9603_max__add__distrib__left,axiom,
% 6.94/7.31 ! [X: nat,Y: nat,Z3: nat] :
% 6.94/7.31 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z3 )
% 6.94/7.31 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z3 ) @ ( plus_plus_nat @ Y @ Z3 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_add_distrib_left
% 6.94/7.31 thf(fact_9604_option_Osimps_I8_J,axiom,
% 6.94/7.31 ! [F: num > num] :
% 6.94/7.31 ( ( map_option_num_num @ F @ none_num )
% 6.94/7.31 = none_num ) ).
% 6.94/7.31
% 6.94/7.31 % option.simps(8)
% 6.94/7.31 thf(fact_9605_max__def__raw,axiom,
% 6.94/7.31 ( ord_max_set_int
% 6.94/7.31 = ( ^ [A5: set_int,B4: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_def_raw
% 6.94/7.31 thf(fact_9606_max__def__raw,axiom,
% 6.94/7.31 ( ord_max_rat
% 6.94/7.31 = ( ^ [A5: rat,B4: rat] : ( if_rat @ ( ord_less_eq_rat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_def_raw
% 6.94/7.31 thf(fact_9607_max__def__raw,axiom,
% 6.94/7.31 ( ord_max_num
% 6.94/7.31 = ( ^ [A5: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_def_raw
% 6.94/7.31 thf(fact_9608_max__def__raw,axiom,
% 6.94/7.31 ( ord_max_nat
% 6.94/7.31 = ( ^ [A5: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_def_raw
% 6.94/7.31 thf(fact_9609_max__def__raw,axiom,
% 6.94/7.31 ( ord_max_int
% 6.94/7.31 = ( ^ [A5: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_def_raw
% 6.94/7.31 thf(fact_9610_n__subsets,axiom,
% 6.94/7.31 ! [A4: set_Pr958786334691620121nt_int,K2: nat] :
% 6.94/7.31 ( ( finite2998713641127702882nt_int @ A4 )
% 6.94/7.31 => ( ( finite4053189226111446337nt_int
% 6.94/7.31 @ ( collec5210948495886036740nt_int
% 6.94/7.31 @ ^ [B6: set_Pr958786334691620121nt_int] :
% 6.94/7.31 ( ( ord_le2843351958646193337nt_int @ B6 @ A4 )
% 6.94/7.31 & ( ( finite6756421564338198497nt_int @ B6 )
% 6.94/7.31 = K2 ) ) ) )
% 6.94/7.31 = ( binomial @ ( finite6756421564338198497nt_int @ A4 ) @ K2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % n_subsets
% 6.94/7.31 thf(fact_9611_n__subsets,axiom,
% 6.94/7.31 ! [A4: set_list_nat,K2: nat] :
% 6.94/7.31 ( ( finite8100373058378681591st_nat @ A4 )
% 6.94/7.31 => ( ( finite2364142230527598318st_nat
% 6.94/7.31 @ ( collect_set_list_nat
% 6.94/7.31 @ ^ [B6: set_list_nat] :
% 6.94/7.31 ( ( ord_le6045566169113846134st_nat @ B6 @ A4 )
% 6.94/7.31 & ( ( finite_card_list_nat @ B6 )
% 6.94/7.31 = K2 ) ) ) )
% 6.94/7.31 = ( binomial @ ( finite_card_list_nat @ A4 ) @ K2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % n_subsets
% 6.94/7.31 thf(fact_9612_n__subsets,axiom,
% 6.94/7.31 ! [A4: set_set_nat,K2: nat] :
% 6.94/7.31 ( ( finite1152437895449049373et_nat @ A4 )
% 6.94/7.31 => ( ( finite1149291290879098388et_nat
% 6.94/7.31 @ ( collect_set_set_nat
% 6.94/7.31 @ ^ [B6: set_set_nat] :
% 6.94/7.31 ( ( ord_le6893508408891458716et_nat @ B6 @ A4 )
% 6.94/7.31 & ( ( finite_card_set_nat @ B6 )
% 6.94/7.31 = K2 ) ) ) )
% 6.94/7.31 = ( binomial @ ( finite_card_set_nat @ A4 ) @ K2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % n_subsets
% 6.94/7.31 thf(fact_9613_n__subsets,axiom,
% 6.94/7.31 ! [A4: set_nat,K2: nat] :
% 6.94/7.31 ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ( finite_card_set_nat
% 6.94/7.31 @ ( collect_set_nat
% 6.94/7.31 @ ^ [B6: set_nat] :
% 6.94/7.31 ( ( ord_less_eq_set_nat @ B6 @ A4 )
% 6.94/7.31 & ( ( finite_card_nat @ B6 )
% 6.94/7.31 = K2 ) ) ) )
% 6.94/7.31 = ( binomial @ ( finite_card_nat @ A4 ) @ K2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % n_subsets
% 6.94/7.31 thf(fact_9614_n__subsets,axiom,
% 6.94/7.31 ! [A4: set_Code_integer,K2: nat] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ( finite1340570857867686763nteger
% 6.94/7.31 @ ( collec574505750873337192nteger
% 6.94/7.31 @ ^ [B6: set_Code_integer] :
% 6.94/7.31 ( ( ord_le7084787975880047091nteger @ B6 @ A4 )
% 6.94/7.31 & ( ( finite4902975817058060853nteger @ B6 )
% 6.94/7.31 = K2 ) ) ) )
% 6.94/7.31 = ( binomial @ ( finite4902975817058060853nteger @ A4 ) @ K2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % n_subsets
% 6.94/7.31 thf(fact_9615_n__subsets,axiom,
% 6.94/7.31 ! [A4: set_Pr1261947904930325089at_nat,K2: nat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.31 => ( ( finite4356350796350151305at_nat
% 6.94/7.31 @ ( collec5514110066124741708at_nat
% 6.94/7.31 @ ^ [B6: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( ord_le3146513528884898305at_nat @ B6 @ A4 )
% 6.94/7.31 & ( ( finite711546835091564841at_nat @ B6 )
% 6.94/7.31 = K2 ) ) ) )
% 6.94/7.31 = ( binomial @ ( finite711546835091564841at_nat @ A4 ) @ K2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % n_subsets
% 6.94/7.31 thf(fact_9616_n__subsets,axiom,
% 6.94/7.31 ! [A4: set_int,K2: nat] :
% 6.94/7.31 ( ( finite_finite_int @ A4 )
% 6.94/7.31 => ( ( finite_card_set_int
% 6.94/7.31 @ ( collect_set_int
% 6.94/7.31 @ ^ [B6: set_int] :
% 6.94/7.31 ( ( ord_less_eq_set_int @ B6 @ A4 )
% 6.94/7.31 & ( ( finite_card_int @ B6 )
% 6.94/7.31 = K2 ) ) ) )
% 6.94/7.31 = ( binomial @ ( finite_card_int @ A4 ) @ K2 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % n_subsets
% 6.94/7.31 thf(fact_9617_sum_Onon__neutral_H,axiom,
% 6.94/7.31 ! [G: $o > code_integer,I5: set_o] :
% 6.94/7.31 ( ( groups1402912129352969042nteger @ G
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [X4: $o] :
% 6.94/7.31 ( ( member_o @ X4 @ I5 )
% 6.94/7.31 & ( ( G @ X4 )
% 6.94/7.31 != zero_z3403309356797280102nteger ) ) ) )
% 6.94/7.31 = ( groups1402912129352969042nteger @ G @ I5 ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.non_neutral'
% 6.94/7.31 thf(fact_9618_sum_Onon__neutral_H,axiom,
% 6.94/7.31 ! [G: nat > code_integer,I5: set_nat] :
% 6.94/7.31 ( ( groups555127423416065298nteger @ G
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [X4: nat] :
% 6.94/7.31 ( ( member_nat @ X4 @ I5 )
% 6.94/7.31 & ( ( G @ X4 )
% 6.94/7.31 != zero_z3403309356797280102nteger ) ) ) )
% 6.94/7.31 = ( groups555127423416065298nteger @ G @ I5 ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.non_neutral'
% 6.94/7.31 thf(fact_9619_sum_Onon__neutral_H,axiom,
% 6.94/7.31 ! [G: int > code_integer,I5: set_int] :
% 6.94/7.31 ( ( groups926780983652909934nteger @ G
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [X4: int] :
% 6.94/7.31 ( ( member_int @ X4 @ I5 )
% 6.94/7.31 & ( ( G @ X4 )
% 6.94/7.31 != zero_z3403309356797280102nteger ) ) ) )
% 6.94/7.31 = ( groups926780983652909934nteger @ G @ I5 ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.non_neutral'
% 6.94/7.31 thf(fact_9620_sum_Onon__neutral_H,axiom,
% 6.94/7.31 ! [G: $o > rat,I5: set_o] :
% 6.94/7.31 ( ( groups3921277224699582669_o_rat @ G
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [X4: $o] :
% 6.94/7.31 ( ( member_o @ X4 @ I5 )
% 6.94/7.31 & ( ( G @ X4 )
% 6.94/7.31 != zero_zero_rat ) ) ) )
% 6.94/7.31 = ( groups3921277224699582669_o_rat @ G @ I5 ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.non_neutral'
% 6.94/7.31 thf(fact_9621_sum_Onon__neutral_H,axiom,
% 6.94/7.31 ! [G: nat > rat,I5: set_nat] :
% 6.94/7.31 ( ( groups1351286907653491341at_rat @ G
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [X4: nat] :
% 6.94/7.31 ( ( member_nat @ X4 @ I5 )
% 6.94/7.31 & ( ( G @ X4 )
% 6.94/7.31 != zero_zero_rat ) ) ) )
% 6.94/7.31 = ( groups1351286907653491341at_rat @ G @ I5 ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.non_neutral'
% 6.94/7.31 thf(fact_9622_sum_Onon__neutral_H,axiom,
% 6.94/7.31 ! [G: int > rat,I5: set_int] :
% 6.94/7.31 ( ( groups2350640619554545897nt_rat @ G
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [X4: int] :
% 6.94/7.31 ( ( member_int @ X4 @ I5 )
% 6.94/7.31 & ( ( G @ X4 )
% 6.94/7.31 != zero_zero_rat ) ) ) )
% 6.94/7.31 = ( groups2350640619554545897nt_rat @ G @ I5 ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.non_neutral'
% 6.94/7.31 thf(fact_9623_sum_Onon__neutral_H,axiom,
% 6.94/7.31 ! [G: $o > nat,I5: set_o] :
% 6.94/7.31 ( ( groups4556407284786078405_o_nat @ G
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [X4: $o] :
% 6.94/7.31 ( ( member_o @ X4 @ I5 )
% 6.94/7.31 & ( ( G @ X4 )
% 6.94/7.31 != zero_zero_nat ) ) ) )
% 6.94/7.31 = ( groups4556407284786078405_o_nat @ G @ I5 ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.non_neutral'
% 6.94/7.31 thf(fact_9624_sum_Onon__neutral_H,axiom,
% 6.94/7.31 ! [G: nat > nat,I5: set_nat] :
% 6.94/7.31 ( ( groups1986416967739987077at_nat @ G
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [X4: nat] :
% 6.94/7.31 ( ( member_nat @ X4 @ I5 )
% 6.94/7.31 & ( ( G @ X4 )
% 6.94/7.31 != zero_zero_nat ) ) ) )
% 6.94/7.31 = ( groups1986416967739987077at_nat @ G @ I5 ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.non_neutral'
% 6.94/7.31 thf(fact_9625_sum_Onon__neutral_H,axiom,
% 6.94/7.31 ! [G: int > nat,I5: set_int] :
% 6.94/7.31 ( ( groups2985770679641041633nt_nat @ G
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [X4: int] :
% 6.94/7.31 ( ( member_int @ X4 @ I5 )
% 6.94/7.31 & ( ( G @ X4 )
% 6.94/7.31 != zero_zero_nat ) ) ) )
% 6.94/7.31 = ( groups2985770679641041633nt_nat @ G @ I5 ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.non_neutral'
% 6.94/7.31 thf(fact_9626_sum_Onon__neutral_H,axiom,
% 6.94/7.31 ! [G: $o > int,I5: set_o] :
% 6.94/7.31 ( ( groups4553916814277028129_o_int @ G
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [X4: $o] :
% 6.94/7.31 ( ( member_o @ X4 @ I5 )
% 6.94/7.31 & ( ( G @ X4 )
% 6.94/7.31 != zero_zero_int ) ) ) )
% 6.94/7.31 = ( groups4553916814277028129_o_int @ G @ I5 ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.non_neutral'
% 6.94/7.31 thf(fact_9627_option_Osize__gen__o__map,axiom,
% 6.94/7.31 ! [F: int > nat,G: int > int] :
% 6.94/7.31 ( ( comp_o5073597352248849069on_int @ ( size_option_int @ F ) @ ( map_option_int_int @ G ) )
% 6.94/7.31 = ( size_option_int @ ( comp_int_nat_int @ F @ G ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.size_gen_o_map
% 6.94/7.31 thf(fact_9628_option_Osize__gen__o__map,axiom,
% 6.94/7.31 ! [F: num > nat,G: num > num] :
% 6.94/7.31 ( ( comp_o6878144249584144265on_num @ ( size_option_num @ F ) @ ( map_option_num_num @ G ) )
% 6.94/7.31 = ( size_option_num @ ( comp_num_nat_num @ F @ G ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % option.size_gen_o_map
% 6.94/7.31 thf(fact_9629_card__subset__eq,axiom,
% 6.94/7.31 ! [B5: set_list_nat,A4: set_list_nat] :
% 6.94/7.31 ( ( finite8100373058378681591st_nat @ B5 )
% 6.94/7.31 => ( ( ord_le6045566169113846134st_nat @ A4 @ B5 )
% 6.94/7.31 => ( ( ( finite_card_list_nat @ A4 )
% 6.94/7.31 = ( finite_card_list_nat @ B5 ) )
% 6.94/7.31 => ( A4 = B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_subset_eq
% 6.94/7.31 thf(fact_9630_card__subset__eq,axiom,
% 6.94/7.31 ! [B5: set_set_nat,A4: set_set_nat] :
% 6.94/7.31 ( ( finite1152437895449049373et_nat @ B5 )
% 6.94/7.31 => ( ( ord_le6893508408891458716et_nat @ A4 @ B5 )
% 6.94/7.31 => ( ( ( finite_card_set_nat @ A4 )
% 6.94/7.31 = ( finite_card_set_nat @ B5 ) )
% 6.94/7.31 => ( A4 = B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_subset_eq
% 6.94/7.31 thf(fact_9631_card__subset__eq,axiom,
% 6.94/7.31 ! [B5: set_nat,A4: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.94/7.31 => ( ( ( finite_card_nat @ A4 )
% 6.94/7.31 = ( finite_card_nat @ B5 ) )
% 6.94/7.31 => ( A4 = B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_subset_eq
% 6.94/7.31 thf(fact_9632_card__subset__eq,axiom,
% 6.94/7.31 ! [B5: set_Code_integer,A4: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.31 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.94/7.31 => ( ( ( finite4902975817058060853nteger @ A4 )
% 6.94/7.31 = ( finite4902975817058060853nteger @ B5 ) )
% 6.94/7.31 => ( A4 = B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_subset_eq
% 6.94/7.31 thf(fact_9633_card__subset__eq,axiom,
% 6.94/7.31 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.31 => ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 6.94/7.31 => ( ( ( finite711546835091564841at_nat @ A4 )
% 6.94/7.31 = ( finite711546835091564841at_nat @ B5 ) )
% 6.94/7.31 => ( A4 = B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_subset_eq
% 6.94/7.31 thf(fact_9634_card__subset__eq,axiom,
% 6.94/7.31 ! [B5: set_int,A4: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.94/7.31 => ( ( ( finite_card_int @ A4 )
% 6.94/7.31 = ( finite_card_int @ B5 ) )
% 6.94/7.31 => ( A4 = B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_subset_eq
% 6.94/7.31 thf(fact_9635_infinite__arbitrarily__large,axiom,
% 6.94/7.31 ! [A4: set_list_nat,N2: nat] :
% 6.94/7.31 ( ~ ( finite8100373058378681591st_nat @ A4 )
% 6.94/7.31 => ? [B9: set_list_nat] :
% 6.94/7.31 ( ( finite8100373058378681591st_nat @ B9 )
% 6.94/7.31 & ( ( finite_card_list_nat @ B9 )
% 6.94/7.31 = N2 )
% 6.94/7.31 & ( ord_le6045566169113846134st_nat @ B9 @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_arbitrarily_large
% 6.94/7.31 thf(fact_9636_infinite__arbitrarily__large,axiom,
% 6.94/7.31 ! [A4: set_set_nat,N2: nat] :
% 6.94/7.31 ( ~ ( finite1152437895449049373et_nat @ A4 )
% 6.94/7.31 => ? [B9: set_set_nat] :
% 6.94/7.31 ( ( finite1152437895449049373et_nat @ B9 )
% 6.94/7.31 & ( ( finite_card_set_nat @ B9 )
% 6.94/7.31 = N2 )
% 6.94/7.31 & ( ord_le6893508408891458716et_nat @ B9 @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_arbitrarily_large
% 6.94/7.31 thf(fact_9637_infinite__arbitrarily__large,axiom,
% 6.94/7.31 ! [A4: set_nat,N2: nat] :
% 6.94/7.31 ( ~ ( finite_finite_nat @ A4 )
% 6.94/7.31 => ? [B9: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ B9 )
% 6.94/7.31 & ( ( finite_card_nat @ B9 )
% 6.94/7.31 = N2 )
% 6.94/7.31 & ( ord_less_eq_set_nat @ B9 @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_arbitrarily_large
% 6.94/7.31 thf(fact_9638_infinite__arbitrarily__large,axiom,
% 6.94/7.31 ! [A4: set_Code_integer,N2: nat] :
% 6.94/7.31 ( ~ ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ? [B9: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ B9 )
% 6.94/7.31 & ( ( finite4902975817058060853nteger @ B9 )
% 6.94/7.31 = N2 )
% 6.94/7.31 & ( ord_le7084787975880047091nteger @ B9 @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_arbitrarily_large
% 6.94/7.31 thf(fact_9639_infinite__arbitrarily__large,axiom,
% 6.94/7.31 ! [A4: set_Pr1261947904930325089at_nat,N2: nat] :
% 6.94/7.31 ( ~ ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.31 => ? [B9: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ B9 )
% 6.94/7.31 & ( ( finite711546835091564841at_nat @ B9 )
% 6.94/7.31 = N2 )
% 6.94/7.31 & ( ord_le3146513528884898305at_nat @ B9 @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_arbitrarily_large
% 6.94/7.31 thf(fact_9640_infinite__arbitrarily__large,axiom,
% 6.94/7.31 ! [A4: set_int,N2: nat] :
% 6.94/7.31 ( ~ ( finite_finite_int @ A4 )
% 6.94/7.31 => ? [B9: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ B9 )
% 6.94/7.31 & ( ( finite_card_int @ B9 )
% 6.94/7.31 = N2 )
% 6.94/7.31 & ( ord_less_eq_set_int @ B9 @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % infinite_arbitrarily_large
% 6.94/7.31 thf(fact_9641_nat__minus__add__max,axiom,
% 6.94/7.31 ! [N2: nat,M: nat] :
% 6.94/7.31 ( ( plus_plus_nat @ ( minus_minus_nat @ N2 @ M ) @ M )
% 6.94/7.31 = ( ord_max_nat @ N2 @ M ) ) ).
% 6.94/7.31
% 6.94/7.31 % nat_minus_add_max
% 6.94/7.31 thf(fact_9642_card__le__if__inj__on__rel,axiom,
% 6.94/7.31 ! [B5: set_o,A4: set_o,R2: $o > $o > $o] :
% 6.94/7.31 ( ( finite_finite_o @ B5 )
% 6.94/7.31 => ( ! [A3: $o] :
% 6.94/7.31 ( ( member_o @ A3 @ A4 )
% 6.94/7.31 => ? [B11: $o] :
% 6.94/7.31 ( ( member_o @ B11 @ B5 )
% 6.94/7.31 & ( R2 @ A3 @ B11 ) ) )
% 6.94/7.31 => ( ! [A13: $o,A24: $o,B3: $o] :
% 6.94/7.31 ( ( member_o @ A13 @ A4 )
% 6.94/7.31 => ( ( member_o @ A24 @ A4 )
% 6.94/7.31 => ( ( member_o @ B3 @ B5 )
% 6.94/7.31 => ( ( R2 @ A13 @ B3 )
% 6.94/7.31 => ( ( R2 @ A24 @ B3 )
% 6.94/7.31 => ( A13 = A24 ) ) ) ) ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_o @ A4 ) @ ( finite_card_o @ B5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_if_inj_on_rel
% 6.94/7.31 thf(fact_9643_card__le__if__inj__on__rel,axiom,
% 6.94/7.31 ! [B5: set_o,A4: set_nat,R2: nat > $o > $o] :
% 6.94/7.31 ( ( finite_finite_o @ B5 )
% 6.94/7.31 => ( ! [A3: nat] :
% 6.94/7.31 ( ( member_nat @ A3 @ A4 )
% 6.94/7.31 => ? [B11: $o] :
% 6.94/7.31 ( ( member_o @ B11 @ B5 )
% 6.94/7.31 & ( R2 @ A3 @ B11 ) ) )
% 6.94/7.31 => ( ! [A13: nat,A24: nat,B3: $o] :
% 6.94/7.31 ( ( member_nat @ A13 @ A4 )
% 6.94/7.31 => ( ( member_nat @ A24 @ A4 )
% 6.94/7.31 => ( ( member_o @ B3 @ B5 )
% 6.94/7.31 => ( ( R2 @ A13 @ B3 )
% 6.94/7.31 => ( ( R2 @ A24 @ B3 )
% 6.94/7.31 => ( A13 = A24 ) ) ) ) ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_o @ B5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_if_inj_on_rel
% 6.94/7.31 thf(fact_9644_card__le__if__inj__on__rel,axiom,
% 6.94/7.31 ! [B5: set_o,A4: set_int,R2: int > $o > $o] :
% 6.94/7.31 ( ( finite_finite_o @ B5 )
% 6.94/7.31 => ( ! [A3: int] :
% 6.94/7.31 ( ( member_int @ A3 @ A4 )
% 6.94/7.31 => ? [B11: $o] :
% 6.94/7.31 ( ( member_o @ B11 @ B5 )
% 6.94/7.31 & ( R2 @ A3 @ B11 ) ) )
% 6.94/7.31 => ( ! [A13: int,A24: int,B3: $o] :
% 6.94/7.31 ( ( member_int @ A13 @ A4 )
% 6.94/7.31 => ( ( member_int @ A24 @ A4 )
% 6.94/7.31 => ( ( member_o @ B3 @ B5 )
% 6.94/7.31 => ( ( R2 @ A13 @ B3 )
% 6.94/7.31 => ( ( R2 @ A24 @ B3 )
% 6.94/7.31 => ( A13 = A24 ) ) ) ) ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_o @ B5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_if_inj_on_rel
% 6.94/7.31 thf(fact_9645_card__le__if__inj__on__rel,axiom,
% 6.94/7.31 ! [B5: set_nat,A4: set_o,R2: $o > nat > $o] :
% 6.94/7.31 ( ( finite_finite_nat @ B5 )
% 6.94/7.31 => ( ! [A3: $o] :
% 6.94/7.31 ( ( member_o @ A3 @ A4 )
% 6.94/7.31 => ? [B11: nat] :
% 6.94/7.31 ( ( member_nat @ B11 @ B5 )
% 6.94/7.31 & ( R2 @ A3 @ B11 ) ) )
% 6.94/7.31 => ( ! [A13: $o,A24: $o,B3: nat] :
% 6.94/7.31 ( ( member_o @ A13 @ A4 )
% 6.94/7.31 => ( ( member_o @ A24 @ A4 )
% 6.94/7.31 => ( ( member_nat @ B3 @ B5 )
% 6.94/7.31 => ( ( R2 @ A13 @ B3 )
% 6.94/7.31 => ( ( R2 @ A24 @ B3 )
% 6.94/7.31 => ( A13 = A24 ) ) ) ) ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_o @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_if_inj_on_rel
% 6.94/7.31 thf(fact_9646_card__le__if__inj__on__rel,axiom,
% 6.94/7.31 ! [B5: set_nat,A4: set_nat,R2: nat > nat > $o] :
% 6.94/7.31 ( ( finite_finite_nat @ B5 )
% 6.94/7.31 => ( ! [A3: nat] :
% 6.94/7.31 ( ( member_nat @ A3 @ A4 )
% 6.94/7.31 => ? [B11: nat] :
% 6.94/7.31 ( ( member_nat @ B11 @ B5 )
% 6.94/7.31 & ( R2 @ A3 @ B11 ) ) )
% 6.94/7.31 => ( ! [A13: nat,A24: nat,B3: nat] :
% 6.94/7.31 ( ( member_nat @ A13 @ A4 )
% 6.94/7.31 => ( ( member_nat @ A24 @ A4 )
% 6.94/7.31 => ( ( member_nat @ B3 @ B5 )
% 6.94/7.31 => ( ( R2 @ A13 @ B3 )
% 6.94/7.31 => ( ( R2 @ A24 @ B3 )
% 6.94/7.31 => ( A13 = A24 ) ) ) ) ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_if_inj_on_rel
% 6.94/7.31 thf(fact_9647_card__le__if__inj__on__rel,axiom,
% 6.94/7.31 ! [B5: set_nat,A4: set_int,R2: int > nat > $o] :
% 6.94/7.31 ( ( finite_finite_nat @ B5 )
% 6.94/7.31 => ( ! [A3: int] :
% 6.94/7.31 ( ( member_int @ A3 @ A4 )
% 6.94/7.31 => ? [B11: nat] :
% 6.94/7.31 ( ( member_nat @ B11 @ B5 )
% 6.94/7.31 & ( R2 @ A3 @ B11 ) ) )
% 6.94/7.31 => ( ! [A13: int,A24: int,B3: nat] :
% 6.94/7.31 ( ( member_int @ A13 @ A4 )
% 6.94/7.31 => ( ( member_int @ A24 @ A4 )
% 6.94/7.31 => ( ( member_nat @ B3 @ B5 )
% 6.94/7.31 => ( ( R2 @ A13 @ B3 )
% 6.94/7.31 => ( ( R2 @ A24 @ B3 )
% 6.94/7.31 => ( A13 = A24 ) ) ) ) ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_if_inj_on_rel
% 6.94/7.31 thf(fact_9648_card__le__if__inj__on__rel,axiom,
% 6.94/7.31 ! [B5: set_int,A4: set_o,R2: $o > int > $o] :
% 6.94/7.31 ( ( finite_finite_int @ B5 )
% 6.94/7.31 => ( ! [A3: $o] :
% 6.94/7.31 ( ( member_o @ A3 @ A4 )
% 6.94/7.31 => ? [B11: int] :
% 6.94/7.31 ( ( member_int @ B11 @ B5 )
% 6.94/7.31 & ( R2 @ A3 @ B11 ) ) )
% 6.94/7.31 => ( ! [A13: $o,A24: $o,B3: int] :
% 6.94/7.31 ( ( member_o @ A13 @ A4 )
% 6.94/7.31 => ( ( member_o @ A24 @ A4 )
% 6.94/7.31 => ( ( member_int @ B3 @ B5 )
% 6.94/7.31 => ( ( R2 @ A13 @ B3 )
% 6.94/7.31 => ( ( R2 @ A24 @ B3 )
% 6.94/7.31 => ( A13 = A24 ) ) ) ) ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_o @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_if_inj_on_rel
% 6.94/7.31 thf(fact_9649_card__le__if__inj__on__rel,axiom,
% 6.94/7.31 ! [B5: set_int,A4: set_nat,R2: nat > int > $o] :
% 6.94/7.31 ( ( finite_finite_int @ B5 )
% 6.94/7.31 => ( ! [A3: nat] :
% 6.94/7.31 ( ( member_nat @ A3 @ A4 )
% 6.94/7.31 => ? [B11: int] :
% 6.94/7.31 ( ( member_int @ B11 @ B5 )
% 6.94/7.31 & ( R2 @ A3 @ B11 ) ) )
% 6.94/7.31 => ( ! [A13: nat,A24: nat,B3: int] :
% 6.94/7.31 ( ( member_nat @ A13 @ A4 )
% 6.94/7.31 => ( ( member_nat @ A24 @ A4 )
% 6.94/7.31 => ( ( member_int @ B3 @ B5 )
% 6.94/7.31 => ( ( R2 @ A13 @ B3 )
% 6.94/7.31 => ( ( R2 @ A24 @ B3 )
% 6.94/7.31 => ( A13 = A24 ) ) ) ) ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_if_inj_on_rel
% 6.94/7.31 thf(fact_9650_card__le__if__inj__on__rel,axiom,
% 6.94/7.31 ! [B5: set_int,A4: set_int,R2: int > int > $o] :
% 6.94/7.31 ( ( finite_finite_int @ B5 )
% 6.94/7.31 => ( ! [A3: int] :
% 6.94/7.31 ( ( member_int @ A3 @ A4 )
% 6.94/7.31 => ? [B11: int] :
% 6.94/7.31 ( ( member_int @ B11 @ B5 )
% 6.94/7.31 & ( R2 @ A3 @ B11 ) ) )
% 6.94/7.31 => ( ! [A13: int,A24: int,B3: int] :
% 6.94/7.31 ( ( member_int @ A13 @ A4 )
% 6.94/7.31 => ( ( member_int @ A24 @ A4 )
% 6.94/7.31 => ( ( member_int @ B3 @ B5 )
% 6.94/7.31 => ( ( R2 @ A13 @ B3 )
% 6.94/7.31 => ( ( R2 @ A24 @ B3 )
% 6.94/7.31 => ( A13 = A24 ) ) ) ) ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_if_inj_on_rel
% 6.94/7.31 thf(fact_9651_card__le__if__inj__on__rel,axiom,
% 6.94/7.31 ! [B5: set_Code_integer,A4: set_o,R2: $o > code_integer > $o] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.31 => ( ! [A3: $o] :
% 6.94/7.31 ( ( member_o @ A3 @ A4 )
% 6.94/7.31 => ? [B11: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ B11 @ B5 )
% 6.94/7.31 & ( R2 @ A3 @ B11 ) ) )
% 6.94/7.31 => ( ! [A13: $o,A24: $o,B3: code_integer] :
% 6.94/7.31 ( ( member_o @ A13 @ A4 )
% 6.94/7.31 => ( ( member_o @ A24 @ A4 )
% 6.94/7.31 => ( ( member_Code_integer @ B3 @ B5 )
% 6.94/7.31 => ( ( R2 @ A13 @ B3 )
% 6.94/7.31 => ( ( R2 @ A24 @ B3 )
% 6.94/7.31 => ( A13 = A24 ) ) ) ) ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_o @ A4 ) @ ( finite4902975817058060853nteger @ B5 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_if_inj_on_rel
% 6.94/7.31 thf(fact_9652_card__insert__le,axiom,
% 6.94/7.31 ! [A4: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] : ( ord_less_eq_nat @ ( finite3771342082235030671at_nat @ A4 ) @ ( finite3771342082235030671at_nat @ ( insert9069300056098147895at_nat @ X @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_insert_le
% 6.94/7.31 thf(fact_9653_card__insert__le,axiom,
% 6.94/7.31 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] : ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_insert_le
% 6.94/7.31 thf(fact_9654_card__insert__le,axiom,
% 6.94/7.31 ! [A4: set_o,X: $o] : ( ord_less_eq_nat @ ( finite_card_o @ A4 ) @ ( finite_card_o @ ( insert_o @ X @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_insert_le
% 6.94/7.31 thf(fact_9655_card__insert__le,axiom,
% 6.94/7.31 ! [A4: set_nat,X: nat] : ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ ( insert_nat @ X @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_insert_le
% 6.94/7.31 thf(fact_9656_card__insert__le,axiom,
% 6.94/7.31 ! [A4: set_int,X: int] : ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ ( insert_int @ X @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_insert_le
% 6.94/7.31 thf(fact_9657_card__insert__le,axiom,
% 6.94/7.31 ! [A4: set_list_nat,X: list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_insert_le
% 6.94/7.31 thf(fact_9658_card__insert__le,axiom,
% 6.94/7.31 ! [A4: set_set_nat,X: set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_insert_le
% 6.94/7.31 thf(fact_9659_sum__multicount__gen,axiom,
% 6.94/7.31 ! [S2: set_o,T6: set_o,R3: $o > $o > $o,K2: $o > nat] :
% 6.94/7.31 ( ( finite_finite_o @ S2 )
% 6.94/7.31 => ( ( finite_finite_o @ T6 )
% 6.94/7.31 => ( ! [X3: $o] :
% 6.94/7.31 ( ( member_o @ X3 @ T6 )
% 6.94/7.31 => ( ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( ( member_o @ I @ S2 )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = ( K2 @ X3 ) ) )
% 6.94/7.31 => ( ( groups8507830703676809646_o_nat
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [J: $o] :
% 6.94/7.31 ( ( member_o @ J @ T6 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S2 )
% 6.94/7.31 = ( groups8507830703676809646_o_nat @ K2 @ T6 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount_gen
% 6.94/7.31 thf(fact_9660_sum__multicount__gen,axiom,
% 6.94/7.31 ! [S2: set_o,T6: set_int,R3: $o > int > $o,K2: int > nat] :
% 6.94/7.31 ( ( finite_finite_o @ S2 )
% 6.94/7.31 => ( ( finite_finite_int @ T6 )
% 6.94/7.31 => ( ! [X3: int] :
% 6.94/7.31 ( ( member_int @ X3 @ T6 )
% 6.94/7.31 => ( ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( ( member_o @ I @ S2 )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = ( K2 @ X3 ) ) )
% 6.94/7.31 => ( ( groups8507830703676809646_o_nat
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( finite_card_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [J: int] :
% 6.94/7.31 ( ( member_int @ J @ T6 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S2 )
% 6.94/7.31 = ( groups4541462559716669496nt_nat @ K2 @ T6 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount_gen
% 6.94/7.31 thf(fact_9661_sum__multicount__gen,axiom,
% 6.94/7.31 ! [S2: set_o,T6: set_Code_integer,R3: $o > code_integer > $o,K2: code_integer > nat] :
% 6.94/7.31 ( ( finite_finite_o @ S2 )
% 6.94/7.31 => ( ( finite6017078050557962740nteger @ T6 )
% 6.94/7.31 => ( ! [X3: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ X3 @ T6 )
% 6.94/7.31 => ( ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( ( member_o @ I @ S2 )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = ( K2 @ X3 ) ) )
% 6.94/7.31 => ( ( groups8507830703676809646_o_nat
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( finite4902975817058060853nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [J: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ J @ T6 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S2 )
% 6.94/7.31 = ( groups7237345082560585321er_nat @ K2 @ T6 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount_gen
% 6.94/7.31 thf(fact_9662_sum__multicount__gen,axiom,
% 6.94/7.31 ! [S2: set_int,T6: set_o,R3: int > $o > $o,K2: $o > nat] :
% 6.94/7.31 ( ( finite_finite_int @ S2 )
% 6.94/7.31 => ( ( finite_finite_o @ T6 )
% 6.94/7.31 => ( ! [X3: $o] :
% 6.94/7.31 ( ( member_o @ X3 @ T6 )
% 6.94/7.31 => ( ( finite_card_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [I: int] :
% 6.94/7.31 ( ( member_int @ I @ S2 )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = ( K2 @ X3 ) ) )
% 6.94/7.31 => ( ( groups4541462559716669496nt_nat
% 6.94/7.31 @ ^ [I: int] :
% 6.94/7.31 ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [J: $o] :
% 6.94/7.31 ( ( member_o @ J @ T6 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S2 )
% 6.94/7.31 = ( groups8507830703676809646_o_nat @ K2 @ T6 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount_gen
% 6.94/7.31 thf(fact_9663_sum__multicount__gen,axiom,
% 6.94/7.31 ! [S2: set_int,T6: set_int,R3: int > int > $o,K2: int > nat] :
% 6.94/7.31 ( ( finite_finite_int @ S2 )
% 6.94/7.31 => ( ( finite_finite_int @ T6 )
% 6.94/7.31 => ( ! [X3: int] :
% 6.94/7.31 ( ( member_int @ X3 @ T6 )
% 6.94/7.31 => ( ( finite_card_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [I: int] :
% 6.94/7.31 ( ( member_int @ I @ S2 )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = ( K2 @ X3 ) ) )
% 6.94/7.31 => ( ( groups4541462559716669496nt_nat
% 6.94/7.31 @ ^ [I: int] :
% 6.94/7.31 ( finite_card_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [J: int] :
% 6.94/7.31 ( ( member_int @ J @ T6 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S2 )
% 6.94/7.31 = ( groups4541462559716669496nt_nat @ K2 @ T6 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount_gen
% 6.94/7.31 thf(fact_9664_sum__multicount__gen,axiom,
% 6.94/7.31 ! [S2: set_int,T6: set_Code_integer,R3: int > code_integer > $o,K2: code_integer > nat] :
% 6.94/7.31 ( ( finite_finite_int @ S2 )
% 6.94/7.31 => ( ( finite6017078050557962740nteger @ T6 )
% 6.94/7.31 => ( ! [X3: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ X3 @ T6 )
% 6.94/7.31 => ( ( finite_card_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [I: int] :
% 6.94/7.31 ( ( member_int @ I @ S2 )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = ( K2 @ X3 ) ) )
% 6.94/7.31 => ( ( groups4541462559716669496nt_nat
% 6.94/7.31 @ ^ [I: int] :
% 6.94/7.31 ( finite4902975817058060853nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [J: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ J @ T6 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S2 )
% 6.94/7.31 = ( groups7237345082560585321er_nat @ K2 @ T6 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount_gen
% 6.94/7.31 thf(fact_9665_sum__multicount__gen,axiom,
% 6.94/7.31 ! [S2: set_Code_integer,T6: set_o,R3: code_integer > $o > $o,K2: $o > nat] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ S2 )
% 6.94/7.31 => ( ( finite_finite_o @ T6 )
% 6.94/7.31 => ( ! [X3: $o] :
% 6.94/7.31 ( ( member_o @ X3 @ T6 )
% 6.94/7.31 => ( ( finite4902975817058060853nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [I: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ I @ S2 )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = ( K2 @ X3 ) ) )
% 6.94/7.31 => ( ( groups7237345082560585321er_nat
% 6.94/7.31 @ ^ [I: code_integer] :
% 6.94/7.31 ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [J: $o] :
% 6.94/7.31 ( ( member_o @ J @ T6 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S2 )
% 6.94/7.31 = ( groups8507830703676809646_o_nat @ K2 @ T6 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount_gen
% 6.94/7.31 thf(fact_9666_sum__multicount__gen,axiom,
% 6.94/7.31 ! [S2: set_Code_integer,T6: set_int,R3: code_integer > int > $o,K2: int > nat] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ S2 )
% 6.94/7.31 => ( ( finite_finite_int @ T6 )
% 6.94/7.31 => ( ! [X3: int] :
% 6.94/7.31 ( ( member_int @ X3 @ T6 )
% 6.94/7.31 => ( ( finite4902975817058060853nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [I: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ I @ S2 )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = ( K2 @ X3 ) ) )
% 6.94/7.31 => ( ( groups7237345082560585321er_nat
% 6.94/7.31 @ ^ [I: code_integer] :
% 6.94/7.31 ( finite_card_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [J: int] :
% 6.94/7.31 ( ( member_int @ J @ T6 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S2 )
% 6.94/7.31 = ( groups4541462559716669496nt_nat @ K2 @ T6 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount_gen
% 6.94/7.31 thf(fact_9667_sum__multicount__gen,axiom,
% 6.94/7.31 ! [S2: set_Code_integer,T6: set_Code_integer,R3: code_integer > code_integer > $o,K2: code_integer > nat] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ S2 )
% 6.94/7.31 => ( ( finite6017078050557962740nteger @ T6 )
% 6.94/7.31 => ( ! [X3: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ X3 @ T6 )
% 6.94/7.31 => ( ( finite4902975817058060853nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [I: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ I @ S2 )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = ( K2 @ X3 ) ) )
% 6.94/7.31 => ( ( groups7237345082560585321er_nat
% 6.94/7.31 @ ^ [I: code_integer] :
% 6.94/7.31 ( finite4902975817058060853nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [J: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ J @ T6 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S2 )
% 6.94/7.31 = ( groups7237345082560585321er_nat @ K2 @ T6 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount_gen
% 6.94/7.31 thf(fact_9668_sum__multicount__gen,axiom,
% 6.94/7.31 ! [S2: set_o,T6: set_nat,R3: $o > nat > $o,K2: nat > nat] :
% 6.94/7.31 ( ( finite_finite_o @ S2 )
% 6.94/7.31 => ( ( finite_finite_nat @ T6 )
% 6.94/7.31 => ( ! [X3: nat] :
% 6.94/7.31 ( ( member_nat @ X3 @ T6 )
% 6.94/7.31 => ( ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( ( member_o @ I @ S2 )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = ( K2 @ X3 ) ) )
% 6.94/7.31 => ( ( groups8507830703676809646_o_nat
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( finite_card_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [J: nat] :
% 6.94/7.31 ( ( member_nat @ J @ T6 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S2 )
% 6.94/7.31 = ( groups3542108847815614940at_nat @ K2 @ T6 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount_gen
% 6.94/7.31 thf(fact_9669_card__eq__sum,axiom,
% 6.94/7.31 ( finite_card_int
% 6.94/7.31 = ( groups4541462559716669496nt_nat
% 6.94/7.31 @ ^ [X4: int] : one_one_nat ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_eq_sum
% 6.94/7.31 thf(fact_9670_card__eq__sum,axiom,
% 6.94/7.31 ( finite_card_list_nat
% 6.94/7.31 = ( groups4396056296759096172at_nat
% 6.94/7.31 @ ^ [X4: list_nat] : one_one_nat ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_eq_sum
% 6.94/7.31 thf(fact_9671_card__eq__sum,axiom,
% 6.94/7.31 ( finite_card_set_nat
% 6.94/7.31 = ( groups8294997508430121362at_nat
% 6.94/7.31 @ ^ [X4: set_nat] : one_one_nat ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_eq_sum
% 6.94/7.31 thf(fact_9672_card__eq__sum,axiom,
% 6.94/7.31 ( finite_card_nat
% 6.94/7.31 = ( groups3542108847815614940at_nat
% 6.94/7.31 @ ^ [X4: nat] : one_one_nat ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_eq_sum
% 6.94/7.31 thf(fact_9673_max__Suc2,axiom,
% 6.94/7.31 ! [M: nat,N2: nat] :
% 6.94/7.31 ( ( ord_max_nat @ M @ ( suc @ N2 ) )
% 6.94/7.31 = ( case_nat_nat @ ( suc @ N2 )
% 6.94/7.31 @ ^ [M7: nat] : ( suc @ ( ord_max_nat @ M7 @ N2 ) )
% 6.94/7.31 @ M ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_Suc2
% 6.94/7.31 thf(fact_9674_max__Suc1,axiom,
% 6.94/7.31 ! [N2: nat,M: nat] :
% 6.94/7.31 ( ( ord_max_nat @ ( suc @ N2 ) @ M )
% 6.94/7.31 = ( case_nat_nat @ ( suc @ N2 )
% 6.94/7.31 @ ^ [M7: nat] : ( suc @ ( ord_max_nat @ N2 @ M7 ) )
% 6.94/7.31 @ M ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_Suc1
% 6.94/7.31 thf(fact_9675_sum_Odistrib__triv_H,axiom,
% 6.94/7.31 ! [I5: set_nat,G: nat > rat,H: nat > rat] :
% 6.94/7.31 ( ( finite_finite_nat @ I5 )
% 6.94/7.31 => ( ( groups1351286907653491341at_rat
% 6.94/7.31 @ ^ [I: nat] : ( plus_plus_rat @ ( G @ I ) @ ( H @ I ) )
% 6.94/7.31 @ I5 )
% 6.94/7.31 = ( plus_plus_rat @ ( groups1351286907653491341at_rat @ G @ I5 ) @ ( groups1351286907653491341at_rat @ H @ I5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.distrib_triv'
% 6.94/7.31 thf(fact_9676_sum_Odistrib__triv_H,axiom,
% 6.94/7.31 ! [I5: set_int,G: int > rat,H: int > rat] :
% 6.94/7.31 ( ( finite_finite_int @ I5 )
% 6.94/7.31 => ( ( groups2350640619554545897nt_rat
% 6.94/7.31 @ ^ [I: int] : ( plus_plus_rat @ ( G @ I ) @ ( H @ I ) )
% 6.94/7.31 @ I5 )
% 6.94/7.31 = ( plus_plus_rat @ ( groups2350640619554545897nt_rat @ G @ I5 ) @ ( groups2350640619554545897nt_rat @ H @ I5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.distrib_triv'
% 6.94/7.31 thf(fact_9677_sum_Odistrib__triv_H,axiom,
% 6.94/7.31 ! [I5: set_Code_integer,G: code_integer > rat,H: code_integer > rat] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ I5 )
% 6.94/7.31 => ( ( groups8878813951405302554er_rat
% 6.94/7.31 @ ^ [I: code_integer] : ( plus_plus_rat @ ( G @ I ) @ ( H @ I ) )
% 6.94/7.31 @ I5 )
% 6.94/7.31 = ( plus_plus_rat @ ( groups8878813951405302554er_rat @ G @ I5 ) @ ( groups8878813951405302554er_rat @ H @ I5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.distrib_triv'
% 6.94/7.31 thf(fact_9678_sum_Odistrib__triv_H,axiom,
% 6.94/7.31 ! [I5: set_nat,G: nat > nat,H: nat > nat] :
% 6.94/7.31 ( ( finite_finite_nat @ I5 )
% 6.94/7.31 => ( ( groups1986416967739987077at_nat
% 6.94/7.31 @ ^ [I: nat] : ( plus_plus_nat @ ( G @ I ) @ ( H @ I ) )
% 6.94/7.31 @ I5 )
% 6.94/7.31 = ( plus_plus_nat @ ( groups1986416967739987077at_nat @ G @ I5 ) @ ( groups1986416967739987077at_nat @ H @ I5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.distrib_triv'
% 6.94/7.31 thf(fact_9679_sum_Odistrib__triv_H,axiom,
% 6.94/7.31 ! [I5: set_int,G: int > nat,H: int > nat] :
% 6.94/7.31 ( ( finite_finite_int @ I5 )
% 6.94/7.31 => ( ( groups2985770679641041633nt_nat
% 6.94/7.31 @ ^ [I: int] : ( plus_plus_nat @ ( G @ I ) @ ( H @ I ) )
% 6.94/7.31 @ I5 )
% 6.94/7.31 = ( plus_plus_nat @ ( groups2985770679641041633nt_nat @ G @ I5 ) @ ( groups2985770679641041633nt_nat @ H @ I5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.distrib_triv'
% 6.94/7.31 thf(fact_9680_sum_Odistrib__triv_H,axiom,
% 6.94/7.31 ! [I5: set_Code_integer,G: code_integer > nat,H: code_integer > nat] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ I5 )
% 6.94/7.31 => ( ( groups290571974637022482er_nat
% 6.94/7.31 @ ^ [I: code_integer] : ( plus_plus_nat @ ( G @ I ) @ ( H @ I ) )
% 6.94/7.31 @ I5 )
% 6.94/7.31 = ( plus_plus_nat @ ( groups290571974637022482er_nat @ G @ I5 ) @ ( groups290571974637022482er_nat @ H @ I5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.distrib_triv'
% 6.94/7.31 thf(fact_9681_sum_Odistrib__triv_H,axiom,
% 6.94/7.31 ! [I5: set_nat,G: nat > int,H: nat > int] :
% 6.94/7.31 ( ( finite_finite_nat @ I5 )
% 6.94/7.31 => ( ( groups1983926497230936801at_int
% 6.94/7.31 @ ^ [I: nat] : ( plus_plus_int @ ( G @ I ) @ ( H @ I ) )
% 6.94/7.31 @ I5 )
% 6.94/7.31 = ( plus_plus_int @ ( groups1983926497230936801at_int @ G @ I5 ) @ ( groups1983926497230936801at_int @ H @ I5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.distrib_triv'
% 6.94/7.31 thf(fact_9682_sum_Odistrib__triv_H,axiom,
% 6.94/7.31 ! [I5: set_int,G: int > int,H: int > int] :
% 6.94/7.31 ( ( finite_finite_int @ I5 )
% 6.94/7.31 => ( ( groups2983280209131991357nt_int
% 6.94/7.31 @ ^ [I: int] : ( plus_plus_int @ ( G @ I ) @ ( H @ I ) )
% 6.94/7.31 @ I5 )
% 6.94/7.31 = ( plus_plus_int @ ( groups2983280209131991357nt_int @ G @ I5 ) @ ( groups2983280209131991357nt_int @ H @ I5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.distrib_triv'
% 6.94/7.31 thf(fact_9683_sum_Odistrib__triv_H,axiom,
% 6.94/7.31 ! [I5: set_Code_integer,G: code_integer > int,H: code_integer > int] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ I5 )
% 6.94/7.31 => ( ( groups288081504127972206er_int
% 6.94/7.31 @ ^ [I: code_integer] : ( plus_plus_int @ ( G @ I ) @ ( H @ I ) )
% 6.94/7.31 @ I5 )
% 6.94/7.31 = ( plus_plus_int @ ( groups288081504127972206er_int @ G @ I5 ) @ ( groups288081504127972206er_int @ H @ I5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.distrib_triv'
% 6.94/7.31 thf(fact_9684_sum_Odistrib__triv_H,axiom,
% 6.94/7.31 ! [I5: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > rat,H: product_prod_nat_nat > rat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ I5 )
% 6.94/7.31 => ( ( groups3328076802468863542at_rat
% 6.94/7.31 @ ^ [I: product_prod_nat_nat] : ( plus_plus_rat @ ( G @ I ) @ ( H @ I ) )
% 6.94/7.31 @ I5 )
% 6.94/7.31 = ( plus_plus_rat @ ( groups3328076802468863542at_rat @ G @ I5 ) @ ( groups3328076802468863542at_rat @ H @ I5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum.distrib_triv'
% 6.94/7.31 thf(fact_9685_card__ge__0__finite,axiom,
% 6.94/7.31 ! [A4: set_list_nat] :
% 6.94/7.31 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A4 ) )
% 6.94/7.31 => ( finite8100373058378681591st_nat @ A4 ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_ge_0_finite
% 6.94/7.31 thf(fact_9686_card__ge__0__finite,axiom,
% 6.94/7.31 ! [A4: set_set_nat] :
% 6.94/7.31 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A4 ) )
% 6.94/7.31 => ( finite1152437895449049373et_nat @ A4 ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_ge_0_finite
% 6.94/7.31 thf(fact_9687_card__ge__0__finite,axiom,
% 6.94/7.31 ! [A4: set_nat] :
% 6.94/7.31 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 6.94/7.31 => ( finite_finite_nat @ A4 ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_ge_0_finite
% 6.94/7.31 thf(fact_9688_card__ge__0__finite,axiom,
% 6.94/7.31 ! [A4: set_int] :
% 6.94/7.31 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 6.94/7.31 => ( finite_finite_int @ A4 ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_ge_0_finite
% 6.94/7.31 thf(fact_9689_card__ge__0__finite,axiom,
% 6.94/7.31 ! [A4: set_Code_integer] :
% 6.94/7.31 ( ( ord_less_nat @ zero_zero_nat @ ( finite4902975817058060853nteger @ A4 ) )
% 6.94/7.31 => ( finite6017078050557962740nteger @ A4 ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_ge_0_finite
% 6.94/7.31 thf(fact_9690_card__ge__0__finite,axiom,
% 6.94/7.31 ! [A4: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( ord_less_nat @ zero_zero_nat @ ( finite711546835091564841at_nat @ A4 ) )
% 6.94/7.31 => ( finite6177210948735845034at_nat @ A4 ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_ge_0_finite
% 6.94/7.31 thf(fact_9691_finite__if__finite__subsets__card__bdd,axiom,
% 6.94/7.31 ! [F5: set_list_nat,C4: nat] :
% 6.94/7.31 ( ! [G5: set_list_nat] :
% 6.94/7.31 ( ( ord_le6045566169113846134st_nat @ G5 @ F5 )
% 6.94/7.31 => ( ( finite8100373058378681591st_nat @ G5 )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_list_nat @ G5 ) @ C4 ) ) )
% 6.94/7.31 => ( ( finite8100373058378681591st_nat @ F5 )
% 6.94/7.31 & ( ord_less_eq_nat @ ( finite_card_list_nat @ F5 ) @ C4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_if_finite_subsets_card_bdd
% 6.94/7.31 thf(fact_9692_finite__if__finite__subsets__card__bdd,axiom,
% 6.94/7.31 ! [F5: set_set_nat,C4: nat] :
% 6.94/7.31 ( ! [G5: set_set_nat] :
% 6.94/7.31 ( ( ord_le6893508408891458716et_nat @ G5 @ F5 )
% 6.94/7.31 => ( ( finite1152437895449049373et_nat @ G5 )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_set_nat @ G5 ) @ C4 ) ) )
% 6.94/7.31 => ( ( finite1152437895449049373et_nat @ F5 )
% 6.94/7.31 & ( ord_less_eq_nat @ ( finite_card_set_nat @ F5 ) @ C4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_if_finite_subsets_card_bdd
% 6.94/7.31 thf(fact_9693_finite__if__finite__subsets__card__bdd,axiom,
% 6.94/7.31 ! [F5: set_nat,C4: nat] :
% 6.94/7.31 ( ! [G5: set_nat] :
% 6.94/7.31 ( ( ord_less_eq_set_nat @ G5 @ F5 )
% 6.94/7.31 => ( ( finite_finite_nat @ G5 )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_nat @ G5 ) @ C4 ) ) )
% 6.94/7.31 => ( ( finite_finite_nat @ F5 )
% 6.94/7.31 & ( ord_less_eq_nat @ ( finite_card_nat @ F5 ) @ C4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_if_finite_subsets_card_bdd
% 6.94/7.31 thf(fact_9694_finite__if__finite__subsets__card__bdd,axiom,
% 6.94/7.31 ! [F5: set_Code_integer,C4: nat] :
% 6.94/7.31 ( ! [G5: set_Code_integer] :
% 6.94/7.31 ( ( ord_le7084787975880047091nteger @ G5 @ F5 )
% 6.94/7.31 => ( ( finite6017078050557962740nteger @ G5 )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ G5 ) @ C4 ) ) )
% 6.94/7.31 => ( ( finite6017078050557962740nteger @ F5 )
% 6.94/7.31 & ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ F5 ) @ C4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_if_finite_subsets_card_bdd
% 6.94/7.31 thf(fact_9695_finite__if__finite__subsets__card__bdd,axiom,
% 6.94/7.31 ! [F5: set_Pr1261947904930325089at_nat,C4: nat] :
% 6.94/7.31 ( ! [G5: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( ord_le3146513528884898305at_nat @ G5 @ F5 )
% 6.94/7.31 => ( ( finite6177210948735845034at_nat @ G5 )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ G5 ) @ C4 ) ) )
% 6.94/7.31 => ( ( finite6177210948735845034at_nat @ F5 )
% 6.94/7.31 & ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ F5 ) @ C4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_if_finite_subsets_card_bdd
% 6.94/7.31 thf(fact_9696_finite__if__finite__subsets__card__bdd,axiom,
% 6.94/7.31 ! [F5: set_int,C4: nat] :
% 6.94/7.31 ( ! [G5: set_int] :
% 6.94/7.31 ( ( ord_less_eq_set_int @ G5 @ F5 )
% 6.94/7.31 => ( ( finite_finite_int @ G5 )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_int @ G5 ) @ C4 ) ) )
% 6.94/7.31 => ( ( finite_finite_int @ F5 )
% 6.94/7.31 & ( ord_less_eq_nat @ ( finite_card_int @ F5 ) @ C4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % finite_if_finite_subsets_card_bdd
% 6.94/7.31 thf(fact_9697_card__seteq,axiom,
% 6.94/7.31 ! [B5: set_list_nat,A4: set_list_nat] :
% 6.94/7.31 ( ( finite8100373058378681591st_nat @ B5 )
% 6.94/7.31 => ( ( ord_le6045566169113846134st_nat @ A4 @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ B5 ) @ ( finite_card_list_nat @ A4 ) )
% 6.94/7.31 => ( A4 = B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_seteq
% 6.94/7.31 thf(fact_9698_card__seteq,axiom,
% 6.94/7.31 ! [B5: set_set_nat,A4: set_set_nat] :
% 6.94/7.31 ( ( finite1152437895449049373et_nat @ B5 )
% 6.94/7.31 => ( ( ord_le6893508408891458716et_nat @ A4 @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ B5 ) @ ( finite_card_set_nat @ A4 ) )
% 6.94/7.31 => ( A4 = B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_seteq
% 6.94/7.31 thf(fact_9699_card__seteq,axiom,
% 6.94/7.31 ! [B5: set_nat,A4: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B5 ) @ ( finite_card_nat @ A4 ) )
% 6.94/7.31 => ( A4 = B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_seteq
% 6.94/7.31 thf(fact_9700_card__seteq,axiom,
% 6.94/7.31 ! [B5: set_Code_integer,A4: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.31 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ B5 ) @ ( finite4902975817058060853nteger @ A4 ) )
% 6.94/7.31 => ( A4 = B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_seteq
% 6.94/7.31 thf(fact_9701_card__seteq,axiom,
% 6.94/7.31 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.31 => ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ B5 ) @ ( finite711546835091564841at_nat @ A4 ) )
% 6.94/7.31 => ( A4 = B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_seteq
% 6.94/7.31 thf(fact_9702_card__seteq,axiom,
% 6.94/7.31 ! [B5: set_int,A4: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_nat @ ( finite_card_int @ B5 ) @ ( finite_card_int @ A4 ) )
% 6.94/7.31 => ( A4 = B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_seteq
% 6.94/7.31 thf(fact_9703_card__mono,axiom,
% 6.94/7.31 ! [B5: set_list_nat,A4: set_list_nat] :
% 6.94/7.31 ( ( finite8100373058378681591st_nat @ B5 )
% 6.94/7.31 => ( ( ord_le6045566169113846134st_nat @ A4 @ B5 )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_mono
% 6.94/7.31 thf(fact_9704_card__mono,axiom,
% 6.94/7.31 ! [B5: set_set_nat,A4: set_set_nat] :
% 6.94/7.31 ( ( finite1152437895449049373et_nat @ B5 )
% 6.94/7.31 => ( ( ord_le6893508408891458716et_nat @ A4 @ B5 )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_mono
% 6.94/7.31 thf(fact_9705_card__mono,axiom,
% 6.94/7.31 ! [B5: set_nat,A4: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_mono
% 6.94/7.31 thf(fact_9706_card__mono,axiom,
% 6.94/7.31 ! [B5: set_Code_integer,A4: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.31 => ( ( ord_le7084787975880047091nteger @ A4 @ B5 )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_mono
% 6.94/7.31 thf(fact_9707_card__mono,axiom,
% 6.94/7.31 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.31 => ( ( ord_le3146513528884898305at_nat @ A4 @ B5 )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_mono
% 6.94/7.31 thf(fact_9708_card__mono,axiom,
% 6.94/7.31 ! [B5: set_int,A4: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_mono
% 6.94/7.31 thf(fact_9709_obtain__subset__with__card__n,axiom,
% 6.94/7.31 ! [N2: nat,S: set_list_nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ N2 @ ( finite_card_list_nat @ S ) )
% 6.94/7.31 => ~ ! [T8: set_list_nat] :
% 6.94/7.31 ( ( ord_le6045566169113846134st_nat @ T8 @ S )
% 6.94/7.31 => ( ( ( finite_card_list_nat @ T8 )
% 6.94/7.31 = N2 )
% 6.94/7.31 => ~ ( finite8100373058378681591st_nat @ T8 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % obtain_subset_with_card_n
% 6.94/7.31 thf(fact_9710_obtain__subset__with__card__n,axiom,
% 6.94/7.31 ! [N2: nat,S: set_set_nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ N2 @ ( finite_card_set_nat @ S ) )
% 6.94/7.31 => ~ ! [T8: set_set_nat] :
% 6.94/7.31 ( ( ord_le6893508408891458716et_nat @ T8 @ S )
% 6.94/7.31 => ( ( ( finite_card_set_nat @ T8 )
% 6.94/7.31 = N2 )
% 6.94/7.31 => ~ ( finite1152437895449049373et_nat @ T8 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % obtain_subset_with_card_n
% 6.94/7.31 thf(fact_9711_obtain__subset__with__card__n,axiom,
% 6.94/7.31 ! [N2: nat,S: set_nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ N2 @ ( finite_card_nat @ S ) )
% 6.94/7.31 => ~ ! [T8: set_nat] :
% 6.94/7.31 ( ( ord_less_eq_set_nat @ T8 @ S )
% 6.94/7.31 => ( ( ( finite_card_nat @ T8 )
% 6.94/7.31 = N2 )
% 6.94/7.31 => ~ ( finite_finite_nat @ T8 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % obtain_subset_with_card_n
% 6.94/7.31 thf(fact_9712_obtain__subset__with__card__n,axiom,
% 6.94/7.31 ! [N2: nat,S: set_Code_integer] :
% 6.94/7.31 ( ( ord_less_eq_nat @ N2 @ ( finite4902975817058060853nteger @ S ) )
% 6.94/7.31 => ~ ! [T8: set_Code_integer] :
% 6.94/7.31 ( ( ord_le7084787975880047091nteger @ T8 @ S )
% 6.94/7.31 => ( ( ( finite4902975817058060853nteger @ T8 )
% 6.94/7.31 = N2 )
% 6.94/7.31 => ~ ( finite6017078050557962740nteger @ T8 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % obtain_subset_with_card_n
% 6.94/7.31 thf(fact_9713_obtain__subset__with__card__n,axiom,
% 6.94/7.31 ! [N2: nat,S: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( ord_less_eq_nat @ N2 @ ( finite711546835091564841at_nat @ S ) )
% 6.94/7.31 => ~ ! [T8: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( ord_le3146513528884898305at_nat @ T8 @ S )
% 6.94/7.31 => ( ( ( finite711546835091564841at_nat @ T8 )
% 6.94/7.31 = N2 )
% 6.94/7.31 => ~ ( finite6177210948735845034at_nat @ T8 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % obtain_subset_with_card_n
% 6.94/7.31 thf(fact_9714_obtain__subset__with__card__n,axiom,
% 6.94/7.31 ! [N2: nat,S: set_int] :
% 6.94/7.31 ( ( ord_less_eq_nat @ N2 @ ( finite_card_int @ S ) )
% 6.94/7.31 => ~ ! [T8: set_int] :
% 6.94/7.31 ( ( ord_less_eq_set_int @ T8 @ S )
% 6.94/7.31 => ( ( ( finite_card_int @ T8 )
% 6.94/7.31 = N2 )
% 6.94/7.31 => ~ ( finite_finite_int @ T8 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % obtain_subset_with_card_n
% 6.94/7.31 thf(fact_9715_card__less__sym__Diff,axiom,
% 6.94/7.31 ! [A4: set_list_nat,B5: set_list_nat] :
% 6.94/7.31 ( ( finite8100373058378681591st_nat @ A4 )
% 6.94/7.31 => ( ( finite8100373058378681591st_nat @ B5 )
% 6.94/7.31 => ( ( ord_less_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) )
% 6.94/7.31 => ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B5 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_less_sym_Diff
% 6.94/7.31 thf(fact_9716_card__less__sym__Diff,axiom,
% 6.94/7.31 ! [A4: set_set_nat,B5: set_set_nat] :
% 6.94/7.31 ( ( finite1152437895449049373et_nat @ A4 )
% 6.94/7.31 => ( ( finite1152437895449049373et_nat @ B5 )
% 6.94/7.31 => ( ( ord_less_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) )
% 6.94/7.31 => ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B5 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_less_sym_Diff
% 6.94/7.31 thf(fact_9717_card__less__sym__Diff,axiom,
% 6.94/7.31 ! [A4: set_nat,B5: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ( finite_finite_nat @ B5 )
% 6.94/7.31 => ( ( ord_less_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) )
% 6.94/7.31 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_less_sym_Diff
% 6.94/7.31 thf(fact_9718_card__less__sym__Diff,axiom,
% 6.94/7.31 ! [A4: set_int,B5: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ A4 )
% 6.94/7.31 => ( ( finite_finite_int @ B5 )
% 6.94/7.31 => ( ( ord_less_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) )
% 6.94/7.31 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ B5 @ A4 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_less_sym_Diff
% 6.94/7.31 thf(fact_9719_card__less__sym__Diff,axiom,
% 6.94/7.31 ! [A4: set_Code_integer,B5: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.31 => ( ( ord_less_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B5 ) )
% 6.94/7.31 => ( ord_less_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ B5 @ A4 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_less_sym_Diff
% 6.94/7.31 thf(fact_9720_card__less__sym__Diff,axiom,
% 6.94/7.31 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.31 => ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.31 => ( ( ord_less_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) )
% 6.94/7.31 => ( ord_less_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_less_sym_Diff
% 6.94/7.31 thf(fact_9721_card__le__sym__Diff,axiom,
% 6.94/7.31 ! [A4: set_list_nat,B5: set_list_nat] :
% 6.94/7.31 ( ( finite8100373058378681591st_nat @ A4 )
% 6.94/7.31 => ( ( finite8100373058378681591st_nat @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B5 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_sym_Diff
% 6.94/7.31 thf(fact_9722_card__le__sym__Diff,axiom,
% 6.94/7.31 ! [A4: set_set_nat,B5: set_set_nat] :
% 6.94/7.31 ( ( finite1152437895449049373et_nat @ A4 )
% 6.94/7.31 => ( ( finite1152437895449049373et_nat @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B5 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_sym_Diff
% 6.94/7.31 thf(fact_9723_card__le__sym__Diff,axiom,
% 6.94/7.31 ! [A4: set_nat,B5: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ A4 )
% 6.94/7.31 => ( ( finite_finite_nat @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_sym_Diff
% 6.94/7.31 thf(fact_9724_card__le__sym__Diff,axiom,
% 6.94/7.31 ! [A4: set_int,B5: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ A4 )
% 6.94/7.31 => ( ( finite_finite_int @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ B5 @ A4 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_sym_Diff
% 6.94/7.31 thf(fact_9725_card__le__sym__Diff,axiom,
% 6.94/7.31 ! [A4: set_Code_integer,B5: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ A4 )
% 6.94/7.31 => ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B5 ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ B5 ) ) @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ B5 @ A4 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_sym_Diff
% 6.94/7.31 thf(fact_9726_card__le__sym__Diff,axiom,
% 6.94/7.31 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ A4 )
% 6.94/7.31 => ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.31 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) )
% 6.94/7.31 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_le_sym_Diff
% 6.94/7.31 thf(fact_9727_psubset__card__mono,axiom,
% 6.94/7.31 ! [B5: set_list_nat,A4: set_list_nat] :
% 6.94/7.31 ( ( finite8100373058378681591st_nat @ B5 )
% 6.94/7.31 => ( ( ord_le1190675801316882794st_nat @ A4 @ B5 )
% 6.94/7.31 => ( ord_less_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % psubset_card_mono
% 6.94/7.31 thf(fact_9728_psubset__card__mono,axiom,
% 6.94/7.31 ! [B5: set_set_nat,A4: set_set_nat] :
% 6.94/7.31 ( ( finite1152437895449049373et_nat @ B5 )
% 6.94/7.31 => ( ( ord_less_set_set_nat @ A4 @ B5 )
% 6.94/7.31 => ( ord_less_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % psubset_card_mono
% 6.94/7.31 thf(fact_9729_psubset__card__mono,axiom,
% 6.94/7.31 ! [B5: set_nat,A4: set_nat] :
% 6.94/7.31 ( ( finite_finite_nat @ B5 )
% 6.94/7.31 => ( ( ord_less_set_nat @ A4 @ B5 )
% 6.94/7.31 => ( ord_less_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % psubset_card_mono
% 6.94/7.31 thf(fact_9730_psubset__card__mono,axiom,
% 6.94/7.31 ! [B5: set_int,A4: set_int] :
% 6.94/7.31 ( ( finite_finite_int @ B5 )
% 6.94/7.31 => ( ( ord_less_set_int @ A4 @ B5 )
% 6.94/7.31 => ( ord_less_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % psubset_card_mono
% 6.94/7.31 thf(fact_9731_psubset__card__mono,axiom,
% 6.94/7.31 ! [B5: set_Code_integer,A4: set_Code_integer] :
% 6.94/7.31 ( ( finite6017078050557962740nteger @ B5 )
% 6.94/7.31 => ( ( ord_le1307284697595431911nteger @ A4 @ B5 )
% 6.94/7.31 => ( ord_less_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % psubset_card_mono
% 6.94/7.31 thf(fact_9732_psubset__card__mono,axiom,
% 6.94/7.31 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat] :
% 6.94/7.31 ( ( finite6177210948735845034at_nat @ B5 )
% 6.94/7.31 => ( ( ord_le7866589430770878221at_nat @ A4 @ B5 )
% 6.94/7.31 => ( ord_less_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % psubset_card_mono
% 6.94/7.31 thf(fact_9733_card__Un__le,axiom,
% 6.94/7.31 ! [A4: set_int,B5: set_int] : ( ord_less_eq_nat @ ( finite_card_int @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_Un_le
% 6.94/7.31 thf(fact_9734_card__Un__le,axiom,
% 6.94/7.31 ! [A4: set_list_nat,B5: set_list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( sup_sup_set_list_nat @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_Un_le
% 6.94/7.31 thf(fact_9735_card__Un__le,axiom,
% 6.94/7.31 ! [A4: set_set_nat,B5: set_set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( sup_sup_set_set_nat @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_Un_le
% 6.94/7.31 thf(fact_9736_card__Un__le,axiom,
% 6.94/7.31 ! [A4: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] : ( ord_less_eq_nat @ ( finite7007076676225009423at_nat @ ( sup_su3035147773818789531at_nat @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite7007076676225009423at_nat @ A4 ) @ ( finite7007076676225009423at_nat @ B5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_Un_le
% 6.94/7.31 thf(fact_9737_card__Un__le,axiom,
% 6.94/7.31 ! [A4: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] : ( ord_less_eq_nat @ ( finite3771342082235030671at_nat @ ( sup_su5525570899277871387at_nat @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite3771342082235030671at_nat @ A4 ) @ ( finite3771342082235030671at_nat @ B5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_Un_le
% 6.94/7.31 thf(fact_9738_card__Un__le,axiom,
% 6.94/7.31 ! [A4: set_nat,B5: set_nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_Un_le
% 6.94/7.31 thf(fact_9739_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 6.94/7.31 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 6.94/7.31 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 6.94/7.31 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 ) ) ).
% 6.94/7.31
% 6.94/7.31 % max_nat.semilattice_neutr_order_axioms
% 6.94/7.31 thf(fact_9740_card__less__Suc2,axiom,
% 6.94/7.31 ! [M6: set_nat,I2: nat] :
% 6.94/7.31 ( ~ ( member_nat @ zero_zero_nat @ M6 )
% 6.94/7.31 => ( ( finite_card_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [K3: nat] :
% 6.94/7.31 ( ( member_nat @ ( suc @ K3 ) @ M6 )
% 6.94/7.31 & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 6.94/7.31 = ( finite_card_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [K3: nat] :
% 6.94/7.31 ( ( member_nat @ K3 @ M6 )
% 6.94/7.31 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_less_Suc2
% 6.94/7.31 thf(fact_9741_card__less__Suc,axiom,
% 6.94/7.31 ! [M6: set_nat,I2: nat] :
% 6.94/7.31 ( ( member_nat @ zero_zero_nat @ M6 )
% 6.94/7.31 => ( ( suc
% 6.94/7.31 @ ( finite_card_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [K3: nat] :
% 6.94/7.31 ( ( member_nat @ ( suc @ K3 ) @ M6 )
% 6.94/7.31 & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 6.94/7.31 = ( finite_card_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [K3: nat] :
% 6.94/7.31 ( ( member_nat @ K3 @ M6 )
% 6.94/7.31 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_less_Suc
% 6.94/7.31 thf(fact_9742_card__less,axiom,
% 6.94/7.31 ! [M6: set_nat,I2: nat] :
% 6.94/7.31 ( ( member_nat @ zero_zero_nat @ M6 )
% 6.94/7.31 => ( ( finite_card_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [K3: nat] :
% 6.94/7.31 ( ( member_nat @ K3 @ M6 )
% 6.94/7.31 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 6.94/7.31 != zero_zero_nat ) ) ).
% 6.94/7.31
% 6.94/7.31 % card_less
% 6.94/7.31 thf(fact_9743_subset__card__intvl__is__intvl,axiom,
% 6.94/7.31 ! [A4: set_nat,K2: nat] :
% 6.94/7.31 ( ( ord_less_eq_set_nat @ A4 @ ( set_or4665077453230672383an_nat @ K2 @ ( plus_plus_nat @ K2 @ ( finite_card_nat @ A4 ) ) ) )
% 6.94/7.31 => ( A4
% 6.94/7.31 = ( set_or4665077453230672383an_nat @ K2 @ ( plus_plus_nat @ K2 @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % subset_card_intvl_is_intvl
% 6.94/7.31 thf(fact_9744_Max_Osemilattice__order__set__axioms,axiom,
% 6.94/7.31 ( lattic5374021519246970238et_rat @ ord_max_rat
% 6.94/7.31 @ ^ [X4: rat,Y4: rat] : ( ord_less_eq_rat @ Y4 @ X4 )
% 6.94/7.31 @ ^ [X4: rat,Y4: rat] : ( ord_less_rat @ Y4 @ X4 ) ) ).
% 6.94/7.31
% 6.94/7.31 % Max.semilattice_order_set_axioms
% 6.94/7.31 thf(fact_9745_Max_Osemilattice__order__set__axioms,axiom,
% 6.94/7.31 ( lattic2566483365489244608et_num @ ord_max_num
% 6.94/7.31 @ ^ [X4: num,Y4: num] : ( ord_less_eq_num @ Y4 @ X4 )
% 6.94/7.31 @ ^ [X4: num,Y4: num] : ( ord_less_num @ Y4 @ X4 ) ) ).
% 6.94/7.31
% 6.94/7.31 % Max.semilattice_order_set_axioms
% 6.94/7.31 thf(fact_9746_Max_Osemilattice__order__set__axioms,axiom,
% 6.94/7.31 ( lattic6009151579333465974et_nat @ ord_max_nat
% 6.94/7.31 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 6.94/7.31 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 ) ) ).
% 6.94/7.31
% 6.94/7.31 % Max.semilattice_order_set_axioms
% 6.94/7.31 thf(fact_9747_Max_Osemilattice__order__set__axioms,axiom,
% 6.94/7.31 ( lattic6006661108824415698et_int @ ord_max_int
% 6.94/7.31 @ ^ [X4: int,Y4: int] : ( ord_less_eq_int @ Y4 @ X4 )
% 6.94/7.31 @ ^ [X4: int,Y4: int] : ( ord_less_int @ Y4 @ X4 ) ) ).
% 6.94/7.31
% 6.94/7.31 % Max.semilattice_order_set_axioms
% 6.94/7.31 thf(fact_9748_sum__Suc,axiom,
% 6.94/7.31 ! [F: int > nat,A4: set_int] :
% 6.94/7.31 ( ( groups4541462559716669496nt_nat
% 6.94/7.31 @ ^ [X4: int] : ( suc @ ( F @ X4 ) )
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( finite_card_int @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_Suc
% 6.94/7.31 thf(fact_9749_sum__Suc,axiom,
% 6.94/7.31 ! [F: list_nat > nat,A4: set_list_nat] :
% 6.94/7.31 ( ( groups4396056296759096172at_nat
% 6.94/7.31 @ ^ [X4: list_nat] : ( suc @ ( F @ X4 ) )
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( plus_plus_nat @ ( groups4396056296759096172at_nat @ F @ A4 ) @ ( finite_card_list_nat @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_Suc
% 6.94/7.31 thf(fact_9750_sum__Suc,axiom,
% 6.94/7.31 ! [F: set_nat > nat,A4: set_set_nat] :
% 6.94/7.31 ( ( groups8294997508430121362at_nat
% 6.94/7.31 @ ^ [X4: set_nat] : ( suc @ ( F @ X4 ) )
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( plus_plus_nat @ ( groups8294997508430121362at_nat @ F @ A4 ) @ ( finite_card_set_nat @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_Suc
% 6.94/7.31 thf(fact_9751_sum__Suc,axiom,
% 6.94/7.31 ! [F: nat > nat,A4: set_nat] :
% 6.94/7.31 ( ( groups3542108847815614940at_nat
% 6.94/7.31 @ ^ [X4: nat] : ( suc @ ( F @ X4 ) )
% 6.94/7.31 @ A4 )
% 6.94/7.31 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( finite_card_nat @ A4 ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_Suc
% 6.94/7.31 thf(fact_9752_sum__multicount,axiom,
% 6.94/7.31 ! [S: set_o,T7: set_o,R3: $o > $o > $o,K2: nat] :
% 6.94/7.31 ( ( finite_finite_o @ S )
% 6.94/7.31 => ( ( finite_finite_o @ T7 )
% 6.94/7.31 => ( ! [X3: $o] :
% 6.94/7.31 ( ( member_o @ X3 @ T7 )
% 6.94/7.31 => ( ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( ( member_o @ I @ S )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = K2 ) )
% 6.94/7.31 => ( ( groups8507830703676809646_o_nat
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [J: $o] :
% 6.94/7.31 ( ( member_o @ J @ T7 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S )
% 6.94/7.31 = ( times_times_nat @ K2 @ ( finite_card_o @ T7 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount
% 6.94/7.31 thf(fact_9753_sum__multicount,axiom,
% 6.94/7.31 ! [S: set_o,T7: set_nat,R3: $o > nat > $o,K2: nat] :
% 6.94/7.31 ( ( finite_finite_o @ S )
% 6.94/7.31 => ( ( finite_finite_nat @ T7 )
% 6.94/7.31 => ( ! [X3: nat] :
% 6.94/7.31 ( ( member_nat @ X3 @ T7 )
% 6.94/7.31 => ( ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( ( member_o @ I @ S )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = K2 ) )
% 6.94/7.31 => ( ( groups8507830703676809646_o_nat
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( finite_card_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [J: nat] :
% 6.94/7.31 ( ( member_nat @ J @ T7 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S )
% 6.94/7.31 = ( times_times_nat @ K2 @ ( finite_card_nat @ T7 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount
% 6.94/7.31 thf(fact_9754_sum__multicount,axiom,
% 6.94/7.31 ! [S: set_o,T7: set_int,R3: $o > int > $o,K2: nat] :
% 6.94/7.31 ( ( finite_finite_o @ S )
% 6.94/7.31 => ( ( finite_finite_int @ T7 )
% 6.94/7.31 => ( ! [X3: int] :
% 6.94/7.31 ( ( member_int @ X3 @ T7 )
% 6.94/7.31 => ( ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( ( member_o @ I @ S )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = K2 ) )
% 6.94/7.31 => ( ( groups8507830703676809646_o_nat
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( finite_card_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [J: int] :
% 6.94/7.31 ( ( member_int @ J @ T7 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S )
% 6.94/7.31 = ( times_times_nat @ K2 @ ( finite_card_int @ T7 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount
% 6.94/7.31 thf(fact_9755_sum__multicount,axiom,
% 6.94/7.31 ! [S: set_o,T7: set_Code_integer,R3: $o > code_integer > $o,K2: nat] :
% 6.94/7.31 ( ( finite_finite_o @ S )
% 6.94/7.31 => ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.31 => ( ! [X3: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ X3 @ T7 )
% 6.94/7.31 => ( ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( ( member_o @ I @ S )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = K2 ) )
% 6.94/7.31 => ( ( groups8507830703676809646_o_nat
% 6.94/7.31 @ ^ [I: $o] :
% 6.94/7.31 ( finite4902975817058060853nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [J: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ J @ T7 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S )
% 6.94/7.31 = ( times_times_nat @ K2 @ ( finite4902975817058060853nteger @ T7 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount
% 6.94/7.31 thf(fact_9756_sum__multicount,axiom,
% 6.94/7.31 ! [S: set_int,T7: set_o,R3: int > $o > $o,K2: nat] :
% 6.94/7.31 ( ( finite_finite_int @ S )
% 6.94/7.31 => ( ( finite_finite_o @ T7 )
% 6.94/7.31 => ( ! [X3: $o] :
% 6.94/7.31 ( ( member_o @ X3 @ T7 )
% 6.94/7.31 => ( ( finite_card_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [I: int] :
% 6.94/7.31 ( ( member_int @ I @ S )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = K2 ) )
% 6.94/7.31 => ( ( groups4541462559716669496nt_nat
% 6.94/7.31 @ ^ [I: int] :
% 6.94/7.31 ( finite_card_o
% 6.94/7.31 @ ( collect_o
% 6.94/7.31 @ ^ [J: $o] :
% 6.94/7.31 ( ( member_o @ J @ T7 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S )
% 6.94/7.31 = ( times_times_nat @ K2 @ ( finite_card_o @ T7 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount
% 6.94/7.31 thf(fact_9757_sum__multicount,axiom,
% 6.94/7.31 ! [S: set_int,T7: set_nat,R3: int > nat > $o,K2: nat] :
% 6.94/7.31 ( ( finite_finite_int @ S )
% 6.94/7.31 => ( ( finite_finite_nat @ T7 )
% 6.94/7.31 => ( ! [X3: nat] :
% 6.94/7.31 ( ( member_nat @ X3 @ T7 )
% 6.94/7.31 => ( ( finite_card_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [I: int] :
% 6.94/7.31 ( ( member_int @ I @ S )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = K2 ) )
% 6.94/7.31 => ( ( groups4541462559716669496nt_nat
% 6.94/7.31 @ ^ [I: int] :
% 6.94/7.31 ( finite_card_nat
% 6.94/7.31 @ ( collect_nat
% 6.94/7.31 @ ^ [J: nat] :
% 6.94/7.31 ( ( member_nat @ J @ T7 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S )
% 6.94/7.31 = ( times_times_nat @ K2 @ ( finite_card_nat @ T7 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount
% 6.94/7.31 thf(fact_9758_sum__multicount,axiom,
% 6.94/7.31 ! [S: set_int,T7: set_int,R3: int > int > $o,K2: nat] :
% 6.94/7.31 ( ( finite_finite_int @ S )
% 6.94/7.31 => ( ( finite_finite_int @ T7 )
% 6.94/7.31 => ( ! [X3: int] :
% 6.94/7.31 ( ( member_int @ X3 @ T7 )
% 6.94/7.31 => ( ( finite_card_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [I: int] :
% 6.94/7.31 ( ( member_int @ I @ S )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = K2 ) )
% 6.94/7.31 => ( ( groups4541462559716669496nt_nat
% 6.94/7.31 @ ^ [I: int] :
% 6.94/7.31 ( finite_card_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [J: int] :
% 6.94/7.31 ( ( member_int @ J @ T7 )
% 6.94/7.31 & ( R3 @ I @ J ) ) ) )
% 6.94/7.31 @ S )
% 6.94/7.31 = ( times_times_nat @ K2 @ ( finite_card_int @ T7 ) ) ) ) ) ) ).
% 6.94/7.31
% 6.94/7.31 % sum_multicount
% 6.94/7.31 thf(fact_9759_sum__multicount,axiom,
% 6.94/7.31 ! [S: set_int,T7: set_Code_integer,R3: int > code_integer > $o,K2: nat] :
% 6.94/7.31 ( ( finite_finite_int @ S )
% 6.94/7.31 => ( ( finite6017078050557962740nteger @ T7 )
% 6.94/7.31 => ( ! [X3: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ X3 @ T7 )
% 6.94/7.31 => ( ( finite_card_int
% 6.94/7.31 @ ( collect_int
% 6.94/7.31 @ ^ [I: int] :
% 6.94/7.31 ( ( member_int @ I @ S )
% 6.94/7.31 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.31 = K2 ) )
% 6.94/7.31 => ( ( groups4541462559716669496nt_nat
% 6.94/7.31 @ ^ [I: int] :
% 6.94/7.31 ( finite4902975817058060853nteger
% 6.94/7.31 @ ( collect_Code_integer
% 6.94/7.31 @ ^ [J: code_integer] :
% 6.94/7.31 ( ( member_Code_integer @ J @ T7 )
% 6.94/7.32 & ( R3 @ I @ J ) ) ) )
% 6.94/7.32 @ S )
% 6.94/7.32 = ( times_times_nat @ K2 @ ( finite4902975817058060853nteger @ T7 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum_multicount
% 6.94/7.32 thf(fact_9760_sum__multicount,axiom,
% 6.94/7.32 ! [S: set_Code_integer,T7: set_o,R3: code_integer > $o > $o,K2: nat] :
% 6.94/7.32 ( ( finite6017078050557962740nteger @ S )
% 6.94/7.32 => ( ( finite_finite_o @ T7 )
% 6.94/7.32 => ( ! [X3: $o] :
% 6.94/7.32 ( ( member_o @ X3 @ T7 )
% 6.94/7.32 => ( ( finite4902975817058060853nteger
% 6.94/7.32 @ ( collect_Code_integer
% 6.94/7.32 @ ^ [I: code_integer] :
% 6.94/7.32 ( ( member_Code_integer @ I @ S )
% 6.94/7.32 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.32 = K2 ) )
% 6.94/7.32 => ( ( groups7237345082560585321er_nat
% 6.94/7.32 @ ^ [I: code_integer] :
% 6.94/7.32 ( finite_card_o
% 6.94/7.32 @ ( collect_o
% 6.94/7.32 @ ^ [J: $o] :
% 6.94/7.32 ( ( member_o @ J @ T7 )
% 6.94/7.32 & ( R3 @ I @ J ) ) ) )
% 6.94/7.32 @ S )
% 6.94/7.32 = ( times_times_nat @ K2 @ ( finite_card_o @ T7 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum_multicount
% 6.94/7.32 thf(fact_9761_sum__multicount,axiom,
% 6.94/7.32 ! [S: set_Code_integer,T7: set_nat,R3: code_integer > nat > $o,K2: nat] :
% 6.94/7.32 ( ( finite6017078050557962740nteger @ S )
% 6.94/7.32 => ( ( finite_finite_nat @ T7 )
% 6.94/7.32 => ( ! [X3: nat] :
% 6.94/7.32 ( ( member_nat @ X3 @ T7 )
% 6.94/7.32 => ( ( finite4902975817058060853nteger
% 6.94/7.32 @ ( collect_Code_integer
% 6.94/7.32 @ ^ [I: code_integer] :
% 6.94/7.32 ( ( member_Code_integer @ I @ S )
% 6.94/7.32 & ( R3 @ I @ X3 ) ) ) )
% 6.94/7.32 = K2 ) )
% 6.94/7.32 => ( ( groups7237345082560585321er_nat
% 6.94/7.32 @ ^ [I: code_integer] :
% 6.94/7.32 ( finite_card_nat
% 6.94/7.32 @ ( collect_nat
% 6.94/7.32 @ ^ [J: nat] :
% 6.94/7.32 ( ( member_nat @ J @ T7 )
% 6.94/7.32 & ( R3 @ I @ J ) ) ) )
% 6.94/7.32 @ S )
% 6.94/7.32 = ( times_times_nat @ K2 @ ( finite_card_nat @ T7 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum_multicount
% 6.94/7.32 thf(fact_9762_sum_Omono__neutral__left_H,axiom,
% 6.94/7.32 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > code_integer] :
% 6.94/7.32 ( ( ord_le3146513528884898305at_nat @ S @ T7 )
% 6.94/7.32 => ( ! [X3: product_prod_nat_nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ X3 @ ( minus_1356011639430497352at_nat @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_z3403309356797280102nteger ) )
% 6.94/7.32 => ( ( groups3803682039294397627nteger @ G @ S )
% 6.94/7.32 = ( groups3803682039294397627nteger @ G @ T7 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_left'
% 6.94/7.32 thf(fact_9763_sum_Omono__neutral__left_H,axiom,
% 6.94/7.32 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( ord_le3146513528884898305at_nat @ S @ T7 )
% 6.94/7.32 => ( ! [X3: product_prod_nat_nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ X3 @ ( minus_1356011639430497352at_nat @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_z1048942125864253310at_nat ) )
% 6.94/7.32 => ( ( groups8361914993108267113at_nat @ G @ S )
% 6.94/7.32 = ( groups8361914993108267113at_nat @ G @ T7 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_left'
% 6.94/7.32 thf(fact_9764_sum_Omono__neutral__left_H,axiom,
% 6.94/7.32 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > rat] :
% 6.94/7.32 ( ( ord_le3146513528884898305at_nat @ S @ T7 )
% 6.94/7.32 => ( ! [X3: product_prod_nat_nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ X3 @ ( minus_1356011639430497352at_nat @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_zero_rat ) )
% 6.94/7.32 => ( ( groups3328076802468863542at_rat @ G @ S )
% 6.94/7.32 = ( groups3328076802468863542at_rat @ G @ T7 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_left'
% 6.94/7.32 thf(fact_9765_sum_Omono__neutral__left_H,axiom,
% 6.94/7.32 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat] :
% 6.94/7.32 ( ( ord_le3146513528884898305at_nat @ S @ T7 )
% 6.94/7.32 => ( ! [X3: product_prod_nat_nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ X3 @ ( minus_1356011639430497352at_nat @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_zero_nat ) )
% 6.94/7.32 => ( ( groups3963206862555359278at_nat @ G @ S )
% 6.94/7.32 = ( groups3963206862555359278at_nat @ G @ T7 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_left'
% 6.94/7.32 thf(fact_9766_sum_Omono__neutral__left_H,axiom,
% 6.94/7.32 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > int] :
% 6.94/7.32 ( ( ord_le3146513528884898305at_nat @ S @ T7 )
% 6.94/7.32 => ( ! [X3: product_prod_nat_nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ X3 @ ( minus_1356011639430497352at_nat @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_zero_int ) )
% 6.94/7.32 => ( ( groups3960716392046309002at_int @ G @ S )
% 6.94/7.32 = ( groups3960716392046309002at_int @ G @ T7 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_left'
% 6.94/7.32 thf(fact_9767_sum_Omono__neutral__left_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,G: int > code_integer] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_z3403309356797280102nteger ) )
% 6.94/7.32 => ( ( groups926780983652909934nteger @ G @ S )
% 6.94/7.32 = ( groups926780983652909934nteger @ G @ T7 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_left'
% 6.94/7.32 thf(fact_9768_sum_Omono__neutral__left_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,G: int > multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_z1048942125864253310at_nat ) )
% 6.94/7.32 => ( ( groups6906599089918680438at_nat @ G @ S )
% 6.94/7.32 = ( groups6906599089918680438at_nat @ G @ T7 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_left'
% 6.94/7.32 thf(fact_9769_sum_Omono__neutral__left_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,G: int > rat] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_zero_rat ) )
% 6.94/7.32 => ( ( groups2350640619554545897nt_rat @ G @ S )
% 6.94/7.32 = ( groups2350640619554545897nt_rat @ G @ T7 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_left'
% 6.94/7.32 thf(fact_9770_sum_Omono__neutral__left_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,G: int > nat] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_zero_nat ) )
% 6.94/7.32 => ( ( groups2985770679641041633nt_nat @ G @ S )
% 6.94/7.32 = ( groups2985770679641041633nt_nat @ G @ T7 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_left'
% 6.94/7.32 thf(fact_9771_sum_Omono__neutral__left_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,G: int > int] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_zero_int ) )
% 6.94/7.32 => ( ( groups2983280209131991357nt_int @ G @ S )
% 6.94/7.32 = ( groups2983280209131991357nt_int @ G @ T7 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_left'
% 6.94/7.32 thf(fact_9772_sum_Omono__neutral__right_H,axiom,
% 6.94/7.32 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > code_integer] :
% 6.94/7.32 ( ( ord_le3146513528884898305at_nat @ S @ T7 )
% 6.94/7.32 => ( ! [X3: product_prod_nat_nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ X3 @ ( minus_1356011639430497352at_nat @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_z3403309356797280102nteger ) )
% 6.94/7.32 => ( ( groups3803682039294397627nteger @ G @ T7 )
% 6.94/7.32 = ( groups3803682039294397627nteger @ G @ S ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_right'
% 6.94/7.32 thf(fact_9773_sum_Omono__neutral__right_H,axiom,
% 6.94/7.32 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( ord_le3146513528884898305at_nat @ S @ T7 )
% 6.94/7.32 => ( ! [X3: product_prod_nat_nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ X3 @ ( minus_1356011639430497352at_nat @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_z1048942125864253310at_nat ) )
% 6.94/7.32 => ( ( groups8361914993108267113at_nat @ G @ T7 )
% 6.94/7.32 = ( groups8361914993108267113at_nat @ G @ S ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_right'
% 6.94/7.32 thf(fact_9774_sum_Omono__neutral__right_H,axiom,
% 6.94/7.32 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > rat] :
% 6.94/7.32 ( ( ord_le3146513528884898305at_nat @ S @ T7 )
% 6.94/7.32 => ( ! [X3: product_prod_nat_nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ X3 @ ( minus_1356011639430497352at_nat @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_zero_rat ) )
% 6.94/7.32 => ( ( groups3328076802468863542at_rat @ G @ T7 )
% 6.94/7.32 = ( groups3328076802468863542at_rat @ G @ S ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_right'
% 6.94/7.32 thf(fact_9775_sum_Omono__neutral__right_H,axiom,
% 6.94/7.32 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat] :
% 6.94/7.32 ( ( ord_le3146513528884898305at_nat @ S @ T7 )
% 6.94/7.32 => ( ! [X3: product_prod_nat_nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ X3 @ ( minus_1356011639430497352at_nat @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_zero_nat ) )
% 6.94/7.32 => ( ( groups3963206862555359278at_nat @ G @ T7 )
% 6.94/7.32 = ( groups3963206862555359278at_nat @ G @ S ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_right'
% 6.94/7.32 thf(fact_9776_sum_Omono__neutral__right_H,axiom,
% 6.94/7.32 ! [S: set_Pr1261947904930325089at_nat,T7: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > int] :
% 6.94/7.32 ( ( ord_le3146513528884898305at_nat @ S @ T7 )
% 6.94/7.32 => ( ! [X3: product_prod_nat_nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ X3 @ ( minus_1356011639430497352at_nat @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_zero_int ) )
% 6.94/7.32 => ( ( groups3960716392046309002at_int @ G @ T7 )
% 6.94/7.32 = ( groups3960716392046309002at_int @ G @ S ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_right'
% 6.94/7.32 thf(fact_9777_sum_Omono__neutral__right_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,G: int > code_integer] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_z3403309356797280102nteger ) )
% 6.94/7.32 => ( ( groups926780983652909934nteger @ G @ T7 )
% 6.94/7.32 = ( groups926780983652909934nteger @ G @ S ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_right'
% 6.94/7.32 thf(fact_9778_sum_Omono__neutral__right_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,G: int > multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_z1048942125864253310at_nat ) )
% 6.94/7.32 => ( ( groups6906599089918680438at_nat @ G @ T7 )
% 6.94/7.32 = ( groups6906599089918680438at_nat @ G @ S ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_right'
% 6.94/7.32 thf(fact_9779_sum_Omono__neutral__right_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,G: int > rat] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_zero_rat ) )
% 6.94/7.32 => ( ( groups2350640619554545897nt_rat @ G @ T7 )
% 6.94/7.32 = ( groups2350640619554545897nt_rat @ G @ S ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_right'
% 6.94/7.32 thf(fact_9780_sum_Omono__neutral__right_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,G: int > nat] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_zero_nat ) )
% 6.94/7.32 => ( ( groups2985770679641041633nt_nat @ G @ T7 )
% 6.94/7.32 = ( groups2985770679641041633nt_nat @ G @ S ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_right'
% 6.94/7.32 thf(fact_9781_sum_Omono__neutral__right_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,G: int > int] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_zero_int ) )
% 6.94/7.32 => ( ( groups2983280209131991357nt_int @ G @ T7 )
% 6.94/7.32 = ( groups2983280209131991357nt_int @ G @ S ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_right'
% 6.94/7.32 thf(fact_9782_sum_Omono__neutral__cong__left_H,axiom,
% 6.94/7.32 ! [S: set_o,T7: set_o,H: $o > code_integer,G: $o > code_integer] :
% 6.94/7.32 ( ( ord_less_eq_set_o @ S @ T7 )
% 6.94/7.32 => ( ! [I3: $o] :
% 6.94/7.32 ( ( member_o @ I3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.94/7.32 => ( ( H @ I3 )
% 6.94/7.32 = zero_z3403309356797280102nteger ) )
% 6.94/7.32 => ( ! [X3: $o] :
% 6.94/7.32 ( ( member_o @ X3 @ S )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = ( H @ X3 ) ) )
% 6.94/7.32 => ( ( groups1402912129352969042nteger @ G @ S )
% 6.94/7.32 = ( groups1402912129352969042nteger @ H @ T7 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_cong_left'
% 6.94/7.32 thf(fact_9783_sum_Omono__neutral__cong__left_H,axiom,
% 6.94/7.32 ! [S: set_nat,T7: set_nat,H: nat > code_integer,G: nat > code_integer] :
% 6.94/7.32 ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.32 => ( ! [I3: nat] :
% 6.94/7.32 ( ( member_nat @ I3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.32 => ( ( H @ I3 )
% 6.94/7.32 = zero_z3403309356797280102nteger ) )
% 6.94/7.32 => ( ! [X3: nat] :
% 6.94/7.32 ( ( member_nat @ X3 @ S )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = ( H @ X3 ) ) )
% 6.94/7.32 => ( ( groups555127423416065298nteger @ G @ S )
% 6.94/7.32 = ( groups555127423416065298nteger @ H @ T7 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_cong_left'
% 6.94/7.32 thf(fact_9784_sum_Omono__neutral__cong__left_H,axiom,
% 6.94/7.32 ! [S: set_o,T7: set_o,H: $o > rat,G: $o > rat] :
% 6.94/7.32 ( ( ord_less_eq_set_o @ S @ T7 )
% 6.94/7.32 => ( ! [I3: $o] :
% 6.94/7.32 ( ( member_o @ I3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.94/7.32 => ( ( H @ I3 )
% 6.94/7.32 = zero_zero_rat ) )
% 6.94/7.32 => ( ! [X3: $o] :
% 6.94/7.32 ( ( member_o @ X3 @ S )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = ( H @ X3 ) ) )
% 6.94/7.32 => ( ( groups3921277224699582669_o_rat @ G @ S )
% 6.94/7.32 = ( groups3921277224699582669_o_rat @ H @ T7 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_cong_left'
% 6.94/7.32 thf(fact_9785_sum_Omono__neutral__cong__left_H,axiom,
% 6.94/7.32 ! [S: set_nat,T7: set_nat,H: nat > rat,G: nat > rat] :
% 6.94/7.32 ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.32 => ( ! [I3: nat] :
% 6.94/7.32 ( ( member_nat @ I3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.32 => ( ( H @ I3 )
% 6.94/7.32 = zero_zero_rat ) )
% 6.94/7.32 => ( ! [X3: nat] :
% 6.94/7.32 ( ( member_nat @ X3 @ S )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = ( H @ X3 ) ) )
% 6.94/7.32 => ( ( groups1351286907653491341at_rat @ G @ S )
% 6.94/7.32 = ( groups1351286907653491341at_rat @ H @ T7 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_cong_left'
% 6.94/7.32 thf(fact_9786_sum_Omono__neutral__cong__left_H,axiom,
% 6.94/7.32 ! [S: set_o,T7: set_o,H: $o > nat,G: $o > nat] :
% 6.94/7.32 ( ( ord_less_eq_set_o @ S @ T7 )
% 6.94/7.32 => ( ! [I3: $o] :
% 6.94/7.32 ( ( member_o @ I3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.94/7.32 => ( ( H @ I3 )
% 6.94/7.32 = zero_zero_nat ) )
% 6.94/7.32 => ( ! [X3: $o] :
% 6.94/7.32 ( ( member_o @ X3 @ S )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = ( H @ X3 ) ) )
% 6.94/7.32 => ( ( groups4556407284786078405_o_nat @ G @ S )
% 6.94/7.32 = ( groups4556407284786078405_o_nat @ H @ T7 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_cong_left'
% 6.94/7.32 thf(fact_9787_sum_Omono__neutral__cong__left_H,axiom,
% 6.94/7.32 ! [S: set_nat,T7: set_nat,H: nat > nat,G: nat > nat] :
% 6.94/7.32 ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.32 => ( ! [I3: nat] :
% 6.94/7.32 ( ( member_nat @ I3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.32 => ( ( H @ I3 )
% 6.94/7.32 = zero_zero_nat ) )
% 6.94/7.32 => ( ! [X3: nat] :
% 6.94/7.32 ( ( member_nat @ X3 @ S )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = ( H @ X3 ) ) )
% 6.94/7.32 => ( ( groups1986416967739987077at_nat @ G @ S )
% 6.94/7.32 = ( groups1986416967739987077at_nat @ H @ T7 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_cong_left'
% 6.94/7.32 thf(fact_9788_sum_Omono__neutral__cong__left_H,axiom,
% 6.94/7.32 ! [S: set_o,T7: set_o,H: $o > int,G: $o > int] :
% 6.94/7.32 ( ( ord_less_eq_set_o @ S @ T7 )
% 6.94/7.32 => ( ! [I3: $o] :
% 6.94/7.32 ( ( member_o @ I3 @ ( minus_minus_set_o @ T7 @ S ) )
% 6.94/7.32 => ( ( H @ I3 )
% 6.94/7.32 = zero_zero_int ) )
% 6.94/7.32 => ( ! [X3: $o] :
% 6.94/7.32 ( ( member_o @ X3 @ S )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = ( H @ X3 ) ) )
% 6.94/7.32 => ( ( groups4553916814277028129_o_int @ G @ S )
% 6.94/7.32 = ( groups4553916814277028129_o_int @ H @ T7 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_cong_left'
% 6.94/7.32 thf(fact_9789_sum_Omono__neutral__cong__left_H,axiom,
% 6.94/7.32 ! [S: set_nat,T7: set_nat,H: nat > int,G: nat > int] :
% 6.94/7.32 ( ( ord_less_eq_set_nat @ S @ T7 )
% 6.94/7.32 => ( ! [I3: nat] :
% 6.94/7.32 ( ( member_nat @ I3 @ ( minus_minus_set_nat @ T7 @ S ) )
% 6.94/7.32 => ( ( H @ I3 )
% 6.94/7.32 = zero_zero_int ) )
% 6.94/7.32 => ( ! [X3: nat] :
% 6.94/7.32 ( ( member_nat @ X3 @ S )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = ( H @ X3 ) ) )
% 6.94/7.32 => ( ( groups1983926497230936801at_int @ G @ S )
% 6.94/7.32 = ( groups1983926497230936801at_int @ H @ T7 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_cong_left'
% 6.94/7.32 thf(fact_9790_sum_Omono__neutral__cong__left_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,H: int > code_integer,G: int > code_integer] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [I3: int] :
% 6.94/7.32 ( ( member_int @ I3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( H @ I3 )
% 6.94/7.32 = zero_z3403309356797280102nteger ) )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ S )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = ( H @ X3 ) ) )
% 6.94/7.32 => ( ( groups926780983652909934nteger @ G @ S )
% 6.94/7.32 = ( groups926780983652909934nteger @ H @ T7 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_cong_left'
% 6.94/7.32 thf(fact_9791_sum_Omono__neutral__cong__left_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,H: int > rat,G: int > rat] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [I3: int] :
% 6.94/7.32 ( ( member_int @ I3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( H @ I3 )
% 6.94/7.32 = zero_zero_rat ) )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ S )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = ( H @ X3 ) ) )
% 6.94/7.32 => ( ( groups2350640619554545897nt_rat @ G @ S )
% 6.94/7.32 = ( groups2350640619554545897nt_rat @ H @ T7 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_cong_left'
% 6.94/7.32 thf(fact_9792_sum_Omono__neutral__cong__right_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,G: int > code_integer,H: int > code_integer] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_z3403309356797280102nteger ) )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ S )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = ( H @ X3 ) ) )
% 6.94/7.32 => ( ( groups926780983652909934nteger @ G @ T7 )
% 6.94/7.32 = ( groups926780983652909934nteger @ H @ S ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_cong_right'
% 6.94/7.32 thf(fact_9793_sum_Omono__neutral__cong__right_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,G: int > multis2468970476368604999at_nat,H: int > multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_z1048942125864253310at_nat ) )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ S )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = ( H @ X3 ) ) )
% 6.94/7.32 => ( ( groups6906599089918680438at_nat @ G @ T7 )
% 6.94/7.32 = ( groups6906599089918680438at_nat @ H @ S ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_cong_right'
% 6.94/7.32 thf(fact_9794_sum_Omono__neutral__cong__right_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,G: int > rat,H: int > rat] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_zero_rat ) )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ S )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = ( H @ X3 ) ) )
% 6.94/7.32 => ( ( groups2350640619554545897nt_rat @ G @ T7 )
% 6.94/7.32 = ( groups2350640619554545897nt_rat @ H @ S ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_cong_right'
% 6.94/7.32 thf(fact_9795_sum_Omono__neutral__cong__right_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,G: int > nat,H: int > nat] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_zero_nat ) )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ S )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = ( H @ X3 ) ) )
% 6.94/7.32 => ( ( groups2985770679641041633nt_nat @ G @ T7 )
% 6.94/7.32 = ( groups2985770679641041633nt_nat @ H @ S ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_cong_right'
% 6.94/7.32 thf(fact_9796_sum_Omono__neutral__cong__right_H,axiom,
% 6.94/7.32 ! [S: set_int,T7: set_int,G: int > int,H: int > int] :
% 6.94/7.32 ( ( ord_less_eq_set_int @ S @ T7 )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ ( minus_minus_set_int @ T7 @ S ) )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = zero_zero_int ) )
% 6.94/7.32 => ( ! [X3: int] :
% 6.94/7.32 ( ( member_int @ X3 @ S )
% 6.94/7.32 => ( ( G @ X3 )
% 6.94/7.32 = ( H @ X3 ) ) )
% 6.94/7.32 => ( ( groups2983280209131991357nt_int @ G @ T7 )
% 6.94/7.32 = ( groups2983280209131991357nt_int @ H @ S ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum.mono_neutral_cong_right'
% 6.94/7.32 thf(fact_9797_subset__eq__atLeast0__lessThan__card,axiom,
% 6.94/7.32 ! [N7: set_nat,N2: nat] :
% 6.94/7.32 ( ( ord_less_eq_set_nat @ N7 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 6.94/7.32 => ( ord_less_eq_nat @ ( finite_card_nat @ N7 ) @ N2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % subset_eq_atLeast0_lessThan_card
% 6.94/7.32 thf(fact_9798_card__sum__le__nat__sum,axiom,
% 6.94/7.32 ! [S: set_nat] :
% 6.94/7.32 ( ord_less_eq_nat
% 6.94/7.32 @ ( groups3542108847815614940at_nat
% 6.94/7.32 @ ^ [X4: nat] : X4
% 6.94/7.32 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S ) ) )
% 6.94/7.32 @ ( groups3542108847815614940at_nat
% 6.94/7.32 @ ^ [X4: nat] : X4
% 6.94/7.32 @ S ) ) ).
% 6.94/7.32
% 6.94/7.32 % card_sum_le_nat_sum
% 6.94/7.32 thf(fact_9799_and__not__num_Opelims,axiom,
% 6.94/7.32 ! [X: num,Xa: num,Y: option_num] :
% 6.94/7.32 ( ( ( bit_and_not_num @ X @ Xa )
% 6.94/7.32 = Y )
% 6.94/7.32 => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 6.94/7.32 => ( ( ( X = one )
% 6.94/7.32 => ( ( Xa = one )
% 6.94/7.32 => ( ( Y = none_num )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 6.94/7.32 => ( ( ( X = one )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit0 @ N5 ) )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( some_num @ one ) )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N5 ) ) ) ) ) )
% 6.94/7.32 => ( ( ( X = one )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit1 @ N5 ) )
% 6.94/7.32 => ( ( Y = none_num )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N5 ) ) ) ) ) )
% 6.94/7.32 => ( ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit0 @ M5 ) )
% 6.94/7.32 => ( ( Xa = one )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( some_num @ ( bit0 @ M5 ) ) )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 6.94/7.32 => ( ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit0 @ M5 ) )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit0 @ N5 ) )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N5 ) ) )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N5 ) ) ) ) ) )
% 6.94/7.32 => ( ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit0 @ M5 ) )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit1 @ N5 ) )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N5 ) ) )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N5 ) ) ) ) ) )
% 6.94/7.32 => ( ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit1 @ M5 ) )
% 6.94/7.32 => ( ( Xa = one )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( some_num @ ( bit0 @ M5 ) ) )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 6.94/7.32 => ( ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit1 @ M5 ) )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit0 @ N5 ) )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 6.94/7.32 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 6.94/7.32 @ ( bit_and_not_num @ M5 @ N5 ) ) )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N5 ) ) ) ) ) )
% 6.94/7.32 => ~ ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit1 @ M5 ) )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit1 @ N5 ) )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N5 ) ) )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % and_not_num.pelims
% 6.94/7.32 thf(fact_9800_and__num_Oelims,axiom,
% 6.94/7.32 ! [X: num,Xa: num,Y: option_num] :
% 6.94/7.32 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 6.94/7.32 = Y )
% 6.94/7.32 => ( ( ( X = one )
% 6.94/7.32 => ( ( Xa = one )
% 6.94/7.32 => ( Y
% 6.94/7.32 != ( some_num @ one ) ) ) )
% 6.94/7.32 => ( ( ( X = one )
% 6.94/7.32 => ( ? [N5: num] :
% 6.94/7.32 ( Xa
% 6.94/7.32 = ( bit0 @ N5 ) )
% 6.94/7.32 => ( Y != none_num ) ) )
% 6.94/7.32 => ( ( ( X = one )
% 6.94/7.32 => ( ? [N5: num] :
% 6.94/7.32 ( Xa
% 6.94/7.32 = ( bit1 @ N5 ) )
% 6.94/7.32 => ( Y
% 6.94/7.32 != ( some_num @ one ) ) ) )
% 6.94/7.32 => ( ( ? [M5: num] :
% 6.94/7.32 ( X
% 6.94/7.32 = ( bit0 @ M5 ) )
% 6.94/7.32 => ( ( Xa = one )
% 6.94/7.32 => ( Y != none_num ) ) )
% 6.94/7.32 => ( ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit0 @ M5 ) )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit0 @ N5 ) )
% 6.94/7.32 => ( Y
% 6.94/7.32 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) ) ) )
% 6.94/7.32 => ( ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit0 @ M5 ) )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit1 @ N5 ) )
% 6.94/7.32 => ( Y
% 6.94/7.32 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) ) ) )
% 6.94/7.32 => ( ( ? [M5: num] :
% 6.94/7.32 ( X
% 6.94/7.32 = ( bit1 @ M5 ) )
% 6.94/7.32 => ( ( Xa = one )
% 6.94/7.32 => ( Y
% 6.94/7.32 != ( some_num @ one ) ) ) )
% 6.94/7.32 => ( ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit1 @ M5 ) )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit0 @ N5 ) )
% 6.94/7.32 => ( Y
% 6.94/7.32 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) ) ) )
% 6.94/7.32 => ~ ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit1 @ M5 ) )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit1 @ N5 ) )
% 6.94/7.32 => ( Y
% 6.94/7.32 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 6.94/7.32 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 6.94/7.32 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % and_num.elims
% 6.94/7.32 thf(fact_9801_Suc__funpow,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( compow_nat_nat @ N2 @ suc )
% 6.94/7.32 = ( plus_plus_nat @ N2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % Suc_funpow
% 6.94/7.32 thf(fact_9802_and__num_Osimps_I9_J,axiom,
% 6.94/7.32 ! [M: num,N2: num] :
% 6.94/7.32 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 6.94/7.32 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 6.94/7.32 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 6.94/7.32 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % and_num.simps(9)
% 6.94/7.32 thf(fact_9803_and__num_Opelims,axiom,
% 6.94/7.32 ! [X: num,Xa: num,Y: option_num] :
% 6.94/7.32 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 6.94/7.32 = Y )
% 6.94/7.32 => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 6.94/7.32 => ( ( ( X = one )
% 6.94/7.32 => ( ( Xa = one )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( some_num @ one ) )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 6.94/7.32 => ( ( ( X = one )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit0 @ N5 ) )
% 6.94/7.32 => ( ( Y = none_num )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N5 ) ) ) ) ) )
% 6.94/7.32 => ( ( ( X = one )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit1 @ N5 ) )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( some_num @ one ) )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N5 ) ) ) ) ) )
% 6.94/7.32 => ( ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit0 @ M5 ) )
% 6.94/7.32 => ( ( Xa = one )
% 6.94/7.32 => ( ( Y = none_num )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 6.94/7.32 => ( ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit0 @ M5 ) )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit0 @ N5 ) )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N5 ) ) ) ) ) )
% 6.94/7.32 => ( ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit0 @ M5 ) )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit1 @ N5 ) )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N5 ) ) ) ) ) )
% 6.94/7.32 => ( ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit1 @ M5 ) )
% 6.94/7.32 => ( ( Xa = one )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( some_num @ one ) )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 6.94/7.32 => ( ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit1 @ M5 ) )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit0 @ N5 ) )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N5 ) ) ) ) ) )
% 6.94/7.32 => ~ ! [M5: num] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( bit1 @ M5 ) )
% 6.94/7.32 => ! [N5: num] :
% 6.94/7.32 ( ( Xa
% 6.94/7.32 = ( bit1 @ N5 ) )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 6.94/7.32 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 6.94/7.32 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) )
% 6.94/7.32 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % and_num.pelims
% 6.94/7.32 thf(fact_9804_card__greaterThanLessThan__int,axiom,
% 6.94/7.32 ! [L: int,U: int] :
% 6.94/7.32 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 6.94/7.32 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % card_greaterThanLessThan_int
% 6.94/7.32 thf(fact_9805_finite__enumerate,axiom,
% 6.94/7.32 ! [S: set_nat] :
% 6.94/7.32 ( ( finite_finite_nat @ S )
% 6.94/7.32 => ? [R4: nat > nat] :
% 6.94/7.32 ( ( strict1292158309912662752at_nat @ R4 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S ) ) )
% 6.94/7.32 & ! [N10: nat] :
% 6.94/7.32 ( ( ord_less_nat @ N10 @ ( finite_card_nat @ S ) )
% 6.94/7.32 => ( member_nat @ ( R4 @ N10 ) @ S ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % finite_enumerate
% 6.94/7.32 thf(fact_9806_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 6.94/7.32 ! [L: int,U: int] :
% 6.94/7.32 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 6.94/7.32 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 6.94/7.32
% 6.94/7.32 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 6.94/7.32 thf(fact_9807_finite__greaterThanLessThan__integer,axiom,
% 6.94/7.32 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 6.94/7.32
% 6.94/7.32 % finite_greaterThanLessThan_integer
% 6.94/7.32 thf(fact_9808_sorted__list__of__set__greaterThanLessThan,axiom,
% 6.94/7.32 ! [I2: nat,J2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ ( suc @ I2 ) @ J2 )
% 6.94/7.32 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J2 ) )
% 6.94/7.32 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J2 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sorted_list_of_set_greaterThanLessThan
% 6.94/7.32 thf(fact_9809_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
% 6.94/7.32 ! [L: code_integer,U: code_integer] :
% 6.94/7.32 ( ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 6.94/7.32 = ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 6.94/7.32
% 6.94/7.32 % atLeastPlusOneLessThan_greaterThanLessThan_integer
% 6.94/7.32 thf(fact_9810_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 6.94/7.32 ! [N2: nat,J2: nat,I2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J2 @ ( suc @ I2 ) ) )
% 6.94/7.32 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J2 ) ) @ N2 )
% 6.94/7.32 = ( suc @ ( plus_plus_nat @ I2 @ N2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % nth_sorted_list_of_set_greaterThanLessThan
% 6.94/7.32 thf(fact_9811_split__seed__def,axiom,
% 6.94/7.32 ( split_seed
% 6.94/7.32 = ( ^ [S5: produc7822875418678951345atural] :
% 6.94/7.32 ( produc8282080750456430313atural
% 6.94/7.32 @ ^ [V2: code_natural,W3: code_natural] :
% 6.94/7.32 ( produc8282080750456430313atural
% 6.94/7.32 @ ^ [V4: 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 @ V4 @ ( 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 ) ) )
% 6.94/7.32 @ ( produc6591912806276919810atural @ ( next @ S5 ) ) )
% 6.94/7.32 @ S5 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % split_seed_def
% 6.94/7.32 thf(fact_9812_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 6.94/7.32 ! [N2: nat,J2: nat,I2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J2 @ I2 ) )
% 6.94/7.32 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J2 ) ) @ N2 )
% 6.94/7.32 = ( suc @ ( plus_plus_nat @ I2 @ N2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % nth_sorted_list_of_set_greaterThanAtMost
% 6.94/7.32 thf(fact_9813_times__int_Oabs__eq,axiom,
% 6.94/7.32 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 6.94/7.32 ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 6.94/7.32 = ( abs_Integ
% 6.94/7.32 @ ( produc27273713700761075at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y4 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V2 ) @ ( times_times_nat @ Y4 @ U3 ) ) ) )
% 6.94/7.32 @ Xa
% 6.94/7.32 @ X ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % times_int.abs_eq
% 6.94/7.32 thf(fact_9814_mod__pure,axiom,
% 6.94/7.32 ! [B: $o,H: produc3658429121746597890et_nat] :
% 6.94/7.32 ( ( rep_assn @ ( pure_assn @ B ) @ H )
% 6.94/7.32 = ( ( ( produc8586169260539613262et_nat @ H )
% 6.94/7.32 = bot_bot_set_nat )
% 6.94/7.32 & B ) ) ).
% 6.94/7.32
% 6.94/7.32 % mod_pure
% 6.94/7.32 thf(fact_9815_mod__emp,axiom,
% 6.94/7.32 ! [H: produc3658429121746597890et_nat] :
% 6.94/7.32 ( ( rep_assn @ one_one_assn @ H )
% 6.94/7.32 = ( ( produc8586169260539613262et_nat @ H )
% 6.94/7.32 = bot_bot_set_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % mod_emp
% 6.94/7.32 thf(fact_9816_uminus__int_Oabs__eq,axiom,
% 6.94/7.32 ! [X: product_prod_nat_nat] :
% 6.94/7.32 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 6.94/7.32 = ( abs_Integ
% 6.94/7.32 @ ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 )
% 6.94/7.32 @ X ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % uminus_int.abs_eq
% 6.94/7.32 thf(fact_9817_sorted__list__of__set__greaterThanAtMost,axiom,
% 6.94/7.32 ! [I2: nat,J2: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J2 )
% 6.94/7.32 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J2 ) )
% 6.94/7.32 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J2 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sorted_list_of_set_greaterThanAtMost
% 6.94/7.32 thf(fact_9818_less__int_Oabs__eq,axiom,
% 6.94/7.32 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 6.94/7.32 ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 6.94/7.32 = ( produc8739625826339149834_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U3 @ Y4 ) ) )
% 6.94/7.32 @ Xa
% 6.94/7.32 @ X ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_int.abs_eq
% 6.94/7.32 thf(fact_9819_less__eq__int_Oabs__eq,axiom,
% 6.94/7.32 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 6.94/7.32 ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 6.94/7.32 = ( produc8739625826339149834_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U3 @ Y4 ) ) )
% 6.94/7.32 @ Xa
% 6.94/7.32 @ X ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_eq_int.abs_eq
% 6.94/7.32 thf(fact_9820_plus__int_Oabs__eq,axiom,
% 6.94/7.32 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 6.94/7.32 ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 6.94/7.32 = ( abs_Integ
% 6.94/7.32 @ ( produc27273713700761075at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y4 @ V2 ) ) )
% 6.94/7.32 @ Xa
% 6.94/7.32 @ X ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % plus_int.abs_eq
% 6.94/7.32 thf(fact_9821_minus__int_Oabs__eq,axiom,
% 6.94/7.32 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 6.94/7.32 ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 6.94/7.32 = ( abs_Integ
% 6.94/7.32 @ ( produc27273713700761075at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ Y4 @ U3 ) ) )
% 6.94/7.32 @ Xa
% 6.94/7.32 @ X ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % minus_int.abs_eq
% 6.94/7.32 thf(fact_9822_rat__minus__code,axiom,
% 6.94/7.32 ! [P3: rat,Q6: rat] :
% 6.94/7.32 ( ( quotient_of @ ( minus_minus_rat @ P3 @ Q6 ) )
% 6.94/7.32 = ( produc4245557441103728435nt_int
% 6.94/7.32 @ ^ [A5: int,C3: int] :
% 6.94/7.32 ( produc4245557441103728435nt_int
% 6.94/7.32 @ ^ [B4: int,D5: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A5 @ D5 ) @ ( times_times_int @ B4 @ C3 ) ) @ ( times_times_int @ C3 @ D5 ) ) )
% 6.94/7.32 @ ( quotient_of @ Q6 ) )
% 6.94/7.32 @ ( quotient_of @ P3 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % rat_minus_code
% 6.94/7.32 thf(fact_9823_finite__greaterThanAtMost__integer,axiom,
% 6.94/7.32 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 6.94/7.32
% 6.94/7.32 % finite_greaterThanAtMost_integer
% 6.94/7.32 thf(fact_9824_drop__bit__nonnegative__int__iff,axiom,
% 6.94/7.32 ! [N2: nat,K2: int] :
% 6.94/7.32 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N2 @ K2 ) )
% 6.94/7.32 = ( ord_less_eq_int @ zero_zero_int @ K2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % drop_bit_nonnegative_int_iff
% 6.94/7.32 thf(fact_9825_drop__bit__negative__int__iff,axiom,
% 6.94/7.32 ! [N2: nat,K2: int] :
% 6.94/7.32 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N2 @ K2 ) @ zero_zero_int )
% 6.94/7.32 = ( ord_less_int @ K2 @ zero_zero_int ) ) ).
% 6.94/7.32
% 6.94/7.32 % drop_bit_negative_int_iff
% 6.94/7.32 thf(fact_9826_diff__rat__def,axiom,
% 6.94/7.32 ( minus_minus_rat
% 6.94/7.32 = ( ^ [Q8: rat,R5: rat] : ( plus_plus_rat @ Q8 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % diff_rat_def
% 6.94/7.32 thf(fact_9827_quotient__of__denom__pos_H,axiom,
% 6.94/7.32 ! [R2: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % quotient_of_denom_pos'
% 6.94/7.32 thf(fact_9828_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 6.94/7.32 ! [L: int,U: int] :
% 6.94/7.32 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 6.94/7.32 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 6.94/7.32
% 6.94/7.32 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 6.94/7.32 thf(fact_9829_quotient__of__denom__pos,axiom,
% 6.94/7.32 ! [R2: rat,P3: int,Q6: int] :
% 6.94/7.32 ( ( ( quotient_of @ R2 )
% 6.94/7.32 = ( product_Pair_int_int @ P3 @ Q6 ) )
% 6.94/7.32 => ( ord_less_int @ zero_zero_int @ Q6 ) ) ).
% 6.94/7.32
% 6.94/7.32 % quotient_of_denom_pos
% 6.94/7.32 thf(fact_9830_rat__floor__code,axiom,
% 6.94/7.32 ( archim3151403230148437115or_rat
% 6.94/7.32 = ( ^ [P7: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P7 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % rat_floor_code
% 6.94/7.32 thf(fact_9831_rat__uminus__code,axiom,
% 6.94/7.32 ! [P3: rat] :
% 6.94/7.32 ( ( quotient_of @ ( uminus_uminus_rat @ P3 ) )
% 6.94/7.32 = ( produc4245557441103728435nt_int
% 6.94/7.32 @ ^ [A5: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A5 ) )
% 6.94/7.32 @ ( quotient_of @ P3 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % rat_uminus_code
% 6.94/7.32 thf(fact_9832_rat__abs__code,axiom,
% 6.94/7.32 ! [P3: rat] :
% 6.94/7.32 ( ( quotient_of @ ( abs_abs_rat @ P3 ) )
% 6.94/7.32 = ( produc4245557441103728435nt_int
% 6.94/7.32 @ ^ [A5: int] : ( product_Pair_int_int @ ( abs_abs_int @ A5 ) )
% 6.94/7.32 @ ( quotient_of @ P3 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % rat_abs_code
% 6.94/7.32 thf(fact_9833_rat__less__eq__code,axiom,
% 6.94/7.32 ( ord_less_eq_rat
% 6.94/7.32 = ( ^ [P7: rat,Q8: rat] :
% 6.94/7.32 ( produc4947309494688390418_int_o
% 6.94/7.32 @ ^ [A5: int,C3: int] :
% 6.94/7.32 ( produc4947309494688390418_int_o
% 6.94/7.32 @ ^ [B4: int,D5: int] : ( ord_less_eq_int @ ( times_times_int @ A5 @ D5 ) @ ( times_times_int @ C3 @ B4 ) )
% 6.94/7.32 @ ( quotient_of @ Q8 ) )
% 6.94/7.32 @ ( quotient_of @ P7 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % rat_less_eq_code
% 6.94/7.32 thf(fact_9834_rat__less__code,axiom,
% 6.94/7.32 ( ord_less_rat
% 6.94/7.32 = ( ^ [P7: rat,Q8: rat] :
% 6.94/7.32 ( produc4947309494688390418_int_o
% 6.94/7.32 @ ^ [A5: int,C3: int] :
% 6.94/7.32 ( produc4947309494688390418_int_o
% 6.94/7.32 @ ^ [B4: int,D5: int] : ( ord_less_int @ ( times_times_int @ A5 @ D5 ) @ ( times_times_int @ C3 @ B4 ) )
% 6.94/7.32 @ ( quotient_of @ Q8 ) )
% 6.94/7.32 @ ( quotient_of @ P7 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % rat_less_code
% 6.94/7.32 thf(fact_9835_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
% 6.94/7.32 ! [L: code_integer,U: code_integer] :
% 6.94/7.32 ( ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 6.94/7.32 = ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 6.94/7.32
% 6.94/7.32 % atLeastPlusOneAtMost_greaterThanAtMost_integer
% 6.94/7.32 thf(fact_9836_rat__divide__code,axiom,
% 6.94/7.32 ! [P3: rat,Q6: rat] :
% 6.94/7.32 ( ( quotient_of @ ( divide_divide_rat @ P3 @ Q6 ) )
% 6.94/7.32 = ( produc4245557441103728435nt_int
% 6.94/7.32 @ ^ [A5: int,C3: int] :
% 6.94/7.32 ( produc4245557441103728435nt_int
% 6.94/7.32 @ ^ [B4: int,D5: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ D5 ) @ ( times_times_int @ C3 @ B4 ) ) )
% 6.94/7.32 @ ( quotient_of @ Q6 ) )
% 6.94/7.32 @ ( quotient_of @ P3 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % rat_divide_code
% 6.94/7.32 thf(fact_9837_rat__times__code,axiom,
% 6.94/7.32 ! [P3: rat,Q6: rat] :
% 6.94/7.32 ( ( quotient_of @ ( times_times_rat @ P3 @ Q6 ) )
% 6.94/7.32 = ( produc4245557441103728435nt_int
% 6.94/7.32 @ ^ [A5: int,C3: int] :
% 6.94/7.32 ( produc4245557441103728435nt_int
% 6.94/7.32 @ ^ [B4: int,D5: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ B4 ) @ ( times_times_int @ C3 @ D5 ) ) )
% 6.94/7.32 @ ( quotient_of @ Q6 ) )
% 6.94/7.32 @ ( quotient_of @ P3 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % rat_times_code
% 6.94/7.32 thf(fact_9838_rat__plus__code,axiom,
% 6.94/7.32 ! [P3: rat,Q6: rat] :
% 6.94/7.32 ( ( quotient_of @ ( plus_plus_rat @ P3 @ Q6 ) )
% 6.94/7.32 = ( produc4245557441103728435nt_int
% 6.94/7.32 @ ^ [A5: int,C3: int] :
% 6.94/7.32 ( produc4245557441103728435nt_int
% 6.94/7.32 @ ^ [B4: int,D5: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A5 @ D5 ) @ ( times_times_int @ B4 @ C3 ) ) @ ( times_times_int @ C3 @ D5 ) ) )
% 6.94/7.32 @ ( quotient_of @ Q6 ) )
% 6.94/7.32 @ ( quotient_of @ P3 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % rat_plus_code
% 6.94/7.32 thf(fact_9839_rat__inverse__code,axiom,
% 6.94/7.32 ! [P3: rat] :
% 6.94/7.32 ( ( quotient_of @ ( inverse_inverse_rat @ P3 ) )
% 6.94/7.32 = ( produc4245557441103728435nt_int
% 6.94/7.32 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( A5 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A5 ) @ B4 ) @ ( abs_abs_int @ A5 ) ) )
% 6.94/7.32 @ ( quotient_of @ P3 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % rat_inverse_code
% 6.94/7.32 thf(fact_9840_less__eq__int_Orep__eq,axiom,
% 6.94/7.32 ( ord_less_eq_int
% 6.94/7.32 = ( ^ [X4: int,Xa2: int] :
% 6.94/7.32 ( produc8739625826339149834_nat_o
% 6.94/7.32 @ ^ [Y4: nat,Z: nat] :
% 6.94/7.32 ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y4 @ V2 ) @ ( plus_plus_nat @ U3 @ Z ) ) )
% 6.94/7.32 @ ( rep_Integ @ X4 )
% 6.94/7.32 @ ( rep_Integ @ Xa2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_eq_int.rep_eq
% 6.94/7.32 thf(fact_9841_less__int_Orep__eq,axiom,
% 6.94/7.32 ( ord_less_int
% 6.94/7.32 = ( ^ [X4: int,Xa2: int] :
% 6.94/7.32 ( produc8739625826339149834_nat_o
% 6.94/7.32 @ ^ [Y4: nat,Z: nat] :
% 6.94/7.32 ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y4 @ V2 ) @ ( plus_plus_nat @ U3 @ Z ) ) )
% 6.94/7.32 @ ( rep_Integ @ X4 )
% 6.94/7.32 @ ( rep_Integ @ Xa2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_int.rep_eq
% 6.94/7.32 thf(fact_9842_abs__rat__def,axiom,
% 6.94/7.32 ( abs_abs_rat
% 6.94/7.32 = ( ^ [A5: rat] : ( if_rat @ ( ord_less_rat @ A5 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A5 ) @ A5 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % abs_rat_def
% 6.94/7.32 thf(fact_9843_less__eq__rat__def,axiom,
% 6.94/7.32 ( ord_less_eq_rat
% 6.94/7.32 = ( ^ [X4: rat,Y4: rat] :
% 6.94/7.32 ( ( ord_less_rat @ X4 @ Y4 )
% 6.94/7.32 | ( X4 = Y4 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_eq_rat_def
% 6.94/7.32 thf(fact_9844_sgn__rat__def,axiom,
% 6.94/7.32 ( sgn_sgn_rat
% 6.94/7.32 = ( ^ [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 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sgn_rat_def
% 6.94/7.32 thf(fact_9845_floor__rat__def,axiom,
% 6.94/7.32 ( archim3151403230148437115or_rat
% 6.94/7.32 = ( ^ [X4: rat] :
% 6.94/7.32 ( the_int
% 6.94/7.32 @ ^ [Z: int] :
% 6.94/7.32 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X4 )
% 6.94/7.32 & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z @ one_one_int ) ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % floor_rat_def
% 6.94/7.32 thf(fact_9846_uminus__int__def,axiom,
% 6.94/7.32 ( uminus_uminus_int
% 6.94/7.32 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 6.94/7.32 @ ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % uminus_int_def
% 6.94/7.32 thf(fact_9847_range,axiom,
% 6.94/7.32 ! [K2: code_natural,S2: produc7822875418678951345atural] :
% 6.94/7.32 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ K2 )
% 6.94/7.32 => ( ord_le5570908160329646204atural @ ( produc497848011034438852atural @ ( range @ K2 @ S2 ) ) @ K2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % range
% 6.94/7.32 thf(fact_9848_bezw__non__0,axiom,
% 6.94/7.32 ! [Y: nat,X: nat] :
% 6.94/7.32 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 6.94/7.32 => ( ( bezw @ X @ Y )
% 6.94/7.32 = ( 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 ) ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % bezw_non_0
% 6.94/7.32 thf(fact_9849_times__int__def,axiom,
% 6.94/7.32 ( times_times_int
% 6.94/7.32 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 6.94/7.32 @ ( produc27273713700761075at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y4 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V2 ) @ ( times_times_nat @ Y4 @ U3 ) ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % times_int_def
% 6.94/7.32 thf(fact_9850_plus__int__def,axiom,
% 6.94/7.32 ( plus_plus_int
% 6.94/7.32 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 6.94/7.32 @ ( produc27273713700761075at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y4 @ V2 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % plus_int_def
% 6.94/7.32 thf(fact_9851_minus__int__def,axiom,
% 6.94/7.32 ( minus_minus_int
% 6.94/7.32 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 6.94/7.32 @ ( produc27273713700761075at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ Y4 @ U3 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % minus_int_def
% 6.94/7.32 thf(fact_9852_normalize__def,axiom,
% 6.94/7.32 ( normalize
% 6.94/7.32 = ( ^ [P7: product_prod_int_int] :
% 6.94/7.32 ( 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 ) ) ) )
% 6.94/7.32 @ ( if_Pro3027730157355071871nt_int
% 6.94/7.32 @ ( ( product_snd_int_int @ P7 )
% 6.94/7.32 = zero_zero_int )
% 6.94/7.32 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 6.94/7.32 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % normalize_def
% 6.94/7.32 thf(fact_9853_gcd__pos__int,axiom,
% 6.94/7.32 ! [M: int,N2: int] :
% 6.94/7.32 ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N2 ) )
% 6.94/7.32 = ( ( M != zero_zero_int )
% 6.94/7.32 | ( N2 != zero_zero_int ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % gcd_pos_int
% 6.94/7.32 thf(fact_9854_gcd__ge__0__int,axiom,
% 6.94/7.32 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X @ Y ) ) ).
% 6.94/7.32
% 6.94/7.32 % gcd_ge_0_int
% 6.94/7.32 thf(fact_9855_bezout__int,axiom,
% 6.94/7.32 ! [X: int,Y: int] :
% 6.94/7.32 ? [U4: int,V5: int] :
% 6.94/7.32 ( ( plus_plus_int @ ( times_times_int @ U4 @ X ) @ ( times_times_int @ V5 @ Y ) )
% 6.94/7.32 = ( gcd_gcd_int @ X @ Y ) ) ).
% 6.94/7.32
% 6.94/7.32 % bezout_int
% 6.94/7.32 thf(fact_9856_gcd__le2__int,axiom,
% 6.94/7.32 ! [B: int,A: int] :
% 6.94/7.32 ( ( ord_less_int @ zero_zero_int @ B )
% 6.94/7.32 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 6.94/7.32
% 6.94/7.32 % gcd_le2_int
% 6.94/7.32 thf(fact_9857_gcd__le1__int,axiom,
% 6.94/7.32 ! [A: int,B: int] :
% 6.94/7.32 ( ( ord_less_int @ zero_zero_int @ A )
% 6.94/7.32 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 6.94/7.32
% 6.94/7.32 % gcd_le1_int
% 6.94/7.32 thf(fact_9858_gcd__cases__int,axiom,
% 6.94/7.32 ! [X: int,Y: int,P2: int > $o] :
% 6.94/7.32 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.94/7.32 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.94/7.32 => ( P2 @ ( gcd_gcd_int @ X @ Y ) ) ) )
% 6.94/7.32 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 6.94/7.32 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 6.94/7.32 => ( P2 @ ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y ) ) ) ) )
% 6.94/7.32 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 6.94/7.32 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 6.94/7.32 => ( P2 @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y ) ) ) )
% 6.94/7.32 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 6.94/7.32 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 6.94/7.32 => ( P2 @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 6.94/7.32 => ( P2 @ ( gcd_gcd_int @ X @ Y ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % gcd_cases_int
% 6.94/7.32 thf(fact_9859_gcd__unique__int,axiom,
% 6.94/7.32 ! [D2: int,A: int,B: int] :
% 6.94/7.32 ( ( ( ord_less_eq_int @ zero_zero_int @ D2 )
% 6.94/7.32 & ( dvd_dvd_int @ D2 @ A )
% 6.94/7.32 & ( dvd_dvd_int @ D2 @ B )
% 6.94/7.32 & ! [E3: int] :
% 6.94/7.32 ( ( ( dvd_dvd_int @ E3 @ A )
% 6.94/7.32 & ( dvd_dvd_int @ E3 @ B ) )
% 6.94/7.32 => ( dvd_dvd_int @ E3 @ D2 ) ) )
% 6.94/7.32 = ( D2
% 6.94/7.32 = ( gcd_gcd_int @ A @ B ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % gcd_unique_int
% 6.94/7.32 thf(fact_9860_gcd__non__0__int,axiom,
% 6.94/7.32 ! [Y: int,X: int] :
% 6.94/7.32 ( ( ord_less_int @ zero_zero_int @ Y )
% 6.94/7.32 => ( ( gcd_gcd_int @ X @ Y )
% 6.94/7.32 = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X @ Y ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % gcd_non_0_int
% 6.94/7.32 thf(fact_9861_gcd__pos__nat,axiom,
% 6.94/7.32 ! [M: nat,N2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N2 ) )
% 6.94/7.32 = ( ( M != zero_zero_nat )
% 6.94/7.32 | ( N2 != zero_zero_nat ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % gcd_pos_nat
% 6.94/7.32 thf(fact_9862_gcd__le2__nat,axiom,
% 6.94/7.32 ! [B: nat,A: nat] :
% 6.94/7.32 ( ( B != zero_zero_nat )
% 6.94/7.32 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 6.94/7.32
% 6.94/7.32 % gcd_le2_nat
% 6.94/7.32 thf(fact_9863_gcd__le1__nat,axiom,
% 6.94/7.32 ! [A: nat,B: nat] :
% 6.94/7.32 ( ( A != zero_zero_nat )
% 6.94/7.32 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 6.94/7.32
% 6.94/7.32 % gcd_le1_nat
% 6.94/7.32 thf(fact_9864_gcd__diff1__nat,axiom,
% 6.94/7.32 ! [N2: nat,M: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ N2 @ M )
% 6.94/7.32 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 )
% 6.94/7.32 = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % gcd_diff1_nat
% 6.94/7.32 thf(fact_9865_gcd__diff2__nat,axiom,
% 6.94/7.32 ! [M: nat,N2: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ M @ N2 )
% 6.94/7.32 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N2 @ M ) @ N2 )
% 6.94/7.32 = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % gcd_diff2_nat
% 6.94/7.32 thf(fact_9866_bezout__nat,axiom,
% 6.94/7.32 ! [A: nat,B: nat] :
% 6.94/7.32 ( ( A != zero_zero_nat )
% 6.94/7.32 => ? [X3: nat,Y3: nat] :
% 6.94/7.32 ( ( times_times_nat @ A @ X3 )
% 6.94/7.32 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % bezout_nat
% 6.94/7.32 thf(fact_9867_bezout__gcd__nat_H,axiom,
% 6.94/7.32 ! [B: nat,A: nat] :
% 6.94/7.32 ? [X3: nat,Y3: nat] :
% 6.94/7.32 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X3 ) )
% 6.94/7.32 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 6.94/7.32 = ( gcd_gcd_nat @ A @ B ) ) )
% 6.94/7.32 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X3 ) )
% 6.94/7.32 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 6.94/7.32 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % bezout_gcd_nat'
% 6.94/7.32 thf(fact_9868_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 6.94/7.32 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 6.94/7.32 @ ^ [M3: nat,N: nat] :
% 6.94/7.32 ( ( dvd_dvd_nat @ M3 @ N )
% 6.94/7.32 & ( M3 != N ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % gcd_nat.semilattice_neutr_order_axioms
% 6.94/7.32 thf(fact_9869_bezw__aux,axiom,
% 6.94/7.32 ! [X: nat,Y: nat] :
% 6.94/7.32 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y ) )
% 6.94/7.32 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % bezw_aux
% 6.94/7.32 thf(fact_9870_upto_Opsimps,axiom,
% 6.94/7.32 ! [I2: int,J2: int] :
% 6.94/7.32 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J2 ) )
% 6.94/7.32 => ( ( ( ord_less_eq_int @ I2 @ J2 )
% 6.94/7.32 => ( ( upto @ I2 @ J2 )
% 6.94/7.32 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) ) ) )
% 6.94/7.32 & ( ~ ( ord_less_eq_int @ I2 @ J2 )
% 6.94/7.32 => ( ( upto @ I2 @ J2 )
% 6.94/7.32 = nil_int ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto.psimps
% 6.94/7.32 thf(fact_9871_upto__Nil,axiom,
% 6.94/7.32 ! [I2: int,J2: int] :
% 6.94/7.32 ( ( ( upto @ I2 @ J2 )
% 6.94/7.32 = nil_int )
% 6.94/7.32 = ( ord_less_int @ J2 @ I2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto_Nil
% 6.94/7.32 thf(fact_9872_upto__Nil2,axiom,
% 6.94/7.32 ! [I2: int,J2: int] :
% 6.94/7.32 ( ( nil_int
% 6.94/7.32 = ( upto @ I2 @ J2 ) )
% 6.94/7.32 = ( ord_less_int @ J2 @ I2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto_Nil2
% 6.94/7.32 thf(fact_9873_upto__empty,axiom,
% 6.94/7.32 ! [J2: int,I2: int] :
% 6.94/7.32 ( ( ord_less_int @ J2 @ I2 )
% 6.94/7.32 => ( ( upto @ I2 @ J2 )
% 6.94/7.32 = nil_int ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto_empty
% 6.94/7.32 thf(fact_9874_nth__upto,axiom,
% 6.94/7.32 ! [I2: int,K2: nat,J2: int] :
% 6.94/7.32 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K2 ) ) @ J2 )
% 6.94/7.32 => ( ( nth_int @ ( upto @ I2 @ J2 ) @ K2 )
% 6.94/7.32 = ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % nth_upto
% 6.94/7.32 thf(fact_9875_length__upto,axiom,
% 6.94/7.32 ! [I2: int,J2: int] :
% 6.94/7.32 ( ( size_size_list_int @ ( upto @ I2 @ J2 ) )
% 6.94/7.32 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J2 @ I2 ) @ one_one_int ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % length_upto
% 6.94/7.32 thf(fact_9876_upto__rec__numeral_I1_J,axiom,
% 6.94/7.32 ! [M: num,N2: num] :
% 6.94/7.32 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 6.94/7.32 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 6.94/7.32 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 6.94/7.32 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 6.94/7.32 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 6.94/7.32 = nil_int ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto_rec_numeral(1)
% 6.94/7.32 thf(fact_9877_upto__rec__numeral_I4_J,axiom,
% 6.94/7.32 ! [M: num,N2: num] :
% 6.94/7.32 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.94/7.32 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.94/7.32 = ( 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 ) ) ) ) ) )
% 6.94/7.32 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.94/7.32 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.94/7.32 = nil_int ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto_rec_numeral(4)
% 6.94/7.32 thf(fact_9878_upto__rec__numeral_I3_J,axiom,
% 6.94/7.32 ! [M: num,N2: num] :
% 6.94/7.32 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 6.94/7.32 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 6.94/7.32 = ( 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 ) ) ) ) )
% 6.94/7.32 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 6.94/7.32 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 6.94/7.32 = nil_int ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto_rec_numeral(3)
% 6.94/7.32 thf(fact_9879_upto__rec__numeral_I2_J,axiom,
% 6.94/7.32 ! [M: num,N2: num] :
% 6.94/7.32 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.94/7.32 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.94/7.32 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 6.94/7.32 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.94/7.32 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 6.94/7.32 = nil_int ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto_rec_numeral(2)
% 6.94/7.32 thf(fact_9880_sorted__wrt__upto,axiom,
% 6.94/7.32 ! [I2: int,J2: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I2 @ J2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % sorted_wrt_upto
% 6.94/7.32 thf(fact_9881_sorted__upto,axiom,
% 6.94/7.32 ! [M: int,N2: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % sorted_upto
% 6.94/7.32 thf(fact_9882_greaterThanAtMost__upto,axiom,
% 6.94/7.32 ( set_or6656581121297822940st_int
% 6.94/7.32 = ( ^ [I: int,J: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % greaterThanAtMost_upto
% 6.94/7.32 thf(fact_9883_upto__rec1,axiom,
% 6.94/7.32 ! [I2: int,J2: int] :
% 6.94/7.32 ( ( ord_less_eq_int @ I2 @ J2 )
% 6.94/7.32 => ( ( upto @ I2 @ J2 )
% 6.94/7.32 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto_rec1
% 6.94/7.32 thf(fact_9884_upto_Oelims,axiom,
% 6.94/7.32 ! [X: int,Xa: int,Y: list_int] :
% 6.94/7.32 ( ( ( upto @ X @ Xa )
% 6.94/7.32 = Y )
% 6.94/7.32 => ( ( ( ord_less_eq_int @ X @ Xa )
% 6.94/7.32 => ( Y
% 6.94/7.32 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 6.94/7.32 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 6.94/7.32 => ( Y = nil_int ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto.elims
% 6.94/7.32 thf(fact_9885_upto_Osimps,axiom,
% 6.94/7.32 ( upto
% 6.94/7.32 = ( ^ [I: int,J: int] : ( if_list_int @ ( ord_less_eq_int @ I @ J ) @ ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) @ nil_int ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto.simps
% 6.94/7.32 thf(fact_9886_greaterThanLessThan__upto,axiom,
% 6.94/7.32 ( set_or5832277885323065728an_int
% 6.94/7.32 = ( ^ [I: int,J: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ ( minus_minus_int @ J @ one_one_int ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % greaterThanLessThan_upto
% 6.94/7.32 thf(fact_9887_upto_Opelims,axiom,
% 6.94/7.32 ! [X: int,Xa: int,Y: list_int] :
% 6.94/7.32 ( ( ( upto @ X @ Xa )
% 6.94/7.32 = Y )
% 6.94/7.32 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 6.94/7.32 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa )
% 6.94/7.32 => ( Y
% 6.94/7.32 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 6.94/7.32 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 6.94/7.32 => ( Y = nil_int ) ) )
% 6.94/7.32 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto.pelims
% 6.94/7.32 thf(fact_9888_num__of__nat_Osimps_I2_J,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.94/7.32 => ( ( num_of_nat @ ( suc @ N2 ) )
% 6.94/7.32 = ( inc @ ( num_of_nat @ N2 ) ) ) )
% 6.94/7.32 & ( ~ ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.94/7.32 => ( ( num_of_nat @ ( suc @ N2 ) )
% 6.94/7.32 = one ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % num_of_nat.simps(2)
% 6.94/7.32 thf(fact_9889_numeral__num__of__nat,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.94/7.32 => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 6.94/7.32 = N2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % numeral_num_of_nat
% 6.94/7.32 thf(fact_9890_num__of__nat__One,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ N2 @ one_one_nat )
% 6.94/7.32 => ( ( num_of_nat @ N2 )
% 6.94/7.32 = one ) ) ).
% 6.94/7.32
% 6.94/7.32 % num_of_nat_One
% 6.94/7.32 thf(fact_9891_num__of__nat__double,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.94/7.32 => ( ( num_of_nat @ ( plus_plus_nat @ N2 @ N2 ) )
% 6.94/7.32 = ( bit0 @ ( num_of_nat @ N2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % num_of_nat_double
% 6.94/7.32 thf(fact_9892_num__of__nat__plus__distrib,axiom,
% 6.94/7.32 ! [M: nat,N2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ zero_zero_nat @ M )
% 6.94/7.32 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.94/7.32 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N2 ) )
% 6.94/7.32 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N2 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % num_of_nat_plus_distrib
% 6.94/7.32 thf(fact_9893_pred__nat__def,axiom,
% 6.94/7.32 ( pred_nat
% 6.94/7.32 = ( collec3392354462482085612at_nat
% 6.94/7.32 @ ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [M3: nat,N: nat] :
% 6.94/7.32 ( N
% 6.94/7.32 = ( suc @ M3 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % pred_nat_def
% 6.94/7.32 thf(fact_9894_less__eq,axiom,
% 6.94/7.32 ! [M: nat,N2: nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N2 ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 6.94/7.32 = ( ord_less_nat @ M @ N2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_eq
% 6.94/7.32 thf(fact_9895_rat__floor__lemma,axiom,
% 6.94/7.32 ! [A: int,B: int] :
% 6.94/7.32 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 6.94/7.32 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % rat_floor_lemma
% 6.94/7.32 thf(fact_9896_upto__rec2,axiom,
% 6.94/7.32 ! [I2: int,J2: int] :
% 6.94/7.32 ( ( ord_less_eq_int @ I2 @ J2 )
% 6.94/7.32 => ( ( upto @ I2 @ J2 )
% 6.94/7.32 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J2 @ one_one_int ) ) @ ( cons_int @ J2 @ nil_int ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto_rec2
% 6.94/7.32 thf(fact_9897_less__rat,axiom,
% 6.94/7.32 ! [B: int,D2: int,A: int,C2: int] :
% 6.94/7.32 ( ( B != zero_zero_int )
% 6.94/7.32 => ( ( D2 != zero_zero_int )
% 6.94/7.32 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D2 ) )
% 6.94/7.32 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ D2 ) ) @ ( times_times_int @ ( times_times_int @ C2 @ B ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_rat
% 6.94/7.32 thf(fact_9898_le__rat,axiom,
% 6.94/7.32 ! [B: int,D2: int,A: int,C2: int] :
% 6.94/7.32 ( ( B != zero_zero_int )
% 6.94/7.32 => ( ( D2 != zero_zero_int )
% 6.94/7.32 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D2 ) )
% 6.94/7.32 = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ D2 ) ) @ ( times_times_int @ ( times_times_int @ C2 @ B ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % le_rat
% 6.94/7.32 thf(fact_9899_add__rat,axiom,
% 6.94/7.32 ! [B: int,D2: int,A: int,C2: int] :
% 6.94/7.32 ( ( B != zero_zero_int )
% 6.94/7.32 => ( ( D2 != zero_zero_int )
% 6.94/7.32 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D2 ) )
% 6.94/7.32 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ C2 @ B ) ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % add_rat
% 6.94/7.32 thf(fact_9900_Rat__induct__pos,axiom,
% 6.94/7.32 ! [P2: rat > $o,Q6: rat] :
% 6.94/7.32 ( ! [A3: int,B3: int] :
% 6.94/7.32 ( ( ord_less_int @ zero_zero_int @ B3 )
% 6.94/7.32 => ( P2 @ ( fract @ A3 @ B3 ) ) )
% 6.94/7.32 => ( P2 @ Q6 ) ) ).
% 6.94/7.32
% 6.94/7.32 % Rat_induct_pos
% 6.94/7.32 thf(fact_9901_upto__split2,axiom,
% 6.94/7.32 ! [I2: int,J2: int,K2: int] :
% 6.94/7.32 ( ( ord_less_eq_int @ I2 @ J2 )
% 6.94/7.32 => ( ( ord_less_eq_int @ J2 @ K2 )
% 6.94/7.32 => ( ( upto @ I2 @ K2 )
% 6.94/7.32 = ( append_int @ ( upto @ I2 @ J2 ) @ ( upto @ ( plus_plus_int @ J2 @ one_one_int ) @ K2 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto_split2
% 6.94/7.32 thf(fact_9902_upto__split1,axiom,
% 6.94/7.32 ! [I2: int,J2: int,K2: int] :
% 6.94/7.32 ( ( ord_less_eq_int @ I2 @ J2 )
% 6.94/7.32 => ( ( ord_less_eq_int @ J2 @ K2 )
% 6.94/7.32 => ( ( upto @ I2 @ K2 )
% 6.94/7.32 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J2 @ one_one_int ) ) @ ( upto @ J2 @ K2 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto_split1
% 6.94/7.32 thf(fact_9903_zero__less__Fract__iff,axiom,
% 6.94/7.32 ! [B: int,A: int] :
% 6.94/7.32 ( ( ord_less_int @ zero_zero_int @ B )
% 6.94/7.32 => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 6.94/7.32 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % zero_less_Fract_iff
% 6.94/7.32 thf(fact_9904_Fract__less__zero__iff,axiom,
% 6.94/7.32 ! [B: int,A: int] :
% 6.94/7.32 ( ( ord_less_int @ zero_zero_int @ B )
% 6.94/7.32 => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 6.94/7.32 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Fract_less_zero_iff
% 6.94/7.32 thf(fact_9905_Fract__less__one__iff,axiom,
% 6.94/7.32 ! [B: int,A: int] :
% 6.94/7.32 ( ( ord_less_int @ zero_zero_int @ B )
% 6.94/7.32 => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 6.94/7.32 = ( ord_less_int @ A @ B ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Fract_less_one_iff
% 6.94/7.32 thf(fact_9906_one__less__Fract__iff,axiom,
% 6.94/7.32 ! [B: int,A: int] :
% 6.94/7.32 ( ( ord_less_int @ zero_zero_int @ B )
% 6.94/7.32 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 6.94/7.32 = ( ord_less_int @ B @ A ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % one_less_Fract_iff
% 6.94/7.32 thf(fact_9907_Fract__add__one,axiom,
% 6.94/7.32 ! [N2: int,M: int] :
% 6.94/7.32 ( ( N2 != zero_zero_int )
% 6.94/7.32 => ( ( fract @ ( plus_plus_int @ M @ N2 ) @ N2 )
% 6.94/7.32 = ( plus_plus_rat @ ( fract @ M @ N2 ) @ one_one_rat ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Fract_add_one
% 6.94/7.32 thf(fact_9908_Fract__le__zero__iff,axiom,
% 6.94/7.32 ! [B: int,A: int] :
% 6.94/7.32 ( ( ord_less_int @ zero_zero_int @ B )
% 6.94/7.32 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 6.94/7.32 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Fract_le_zero_iff
% 6.94/7.32 thf(fact_9909_zero__le__Fract__iff,axiom,
% 6.94/7.32 ! [B: int,A: int] :
% 6.94/7.32 ( ( ord_less_int @ zero_zero_int @ B )
% 6.94/7.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 6.94/7.32 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % zero_le_Fract_iff
% 6.94/7.32 thf(fact_9910_one__le__Fract__iff,axiom,
% 6.94/7.32 ! [B: int,A: int] :
% 6.94/7.32 ( ( ord_less_int @ zero_zero_int @ B )
% 6.94/7.32 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 6.94/7.32 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % one_le_Fract_iff
% 6.94/7.32 thf(fact_9911_Fract__le__one__iff,axiom,
% 6.94/7.32 ! [B: int,A: int] :
% 6.94/7.32 ( ( ord_less_int @ zero_zero_int @ B )
% 6.94/7.32 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 6.94/7.32 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Fract_le_one_iff
% 6.94/7.32 thf(fact_9912_upto__split3,axiom,
% 6.94/7.32 ! [I2: int,J2: int,K2: int] :
% 6.94/7.32 ( ( ord_less_eq_int @ I2 @ J2 )
% 6.94/7.32 => ( ( ord_less_eq_int @ J2 @ K2 )
% 6.94/7.32 => ( ( upto @ I2 @ K2 )
% 6.94/7.32 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J2 @ one_one_int ) ) @ ( cons_int @ J2 @ ( upto @ ( plus_plus_int @ J2 @ one_one_int ) @ K2 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upto_split3
% 6.94/7.32 thf(fact_9913_sort__upto,axiom,
% 6.94/7.32 ! [I2: int,J2: int] :
% 6.94/7.32 ( ( linord1735203802627413978nt_int
% 6.94/7.32 @ ^ [X4: int] : X4
% 6.94/7.32 @ ( upto @ I2 @ J2 ) )
% 6.94/7.32 = ( upto @ I2 @ J2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % sort_upto
% 6.94/7.32 thf(fact_9914_sort__upt,axiom,
% 6.94/7.32 ! [M: nat,N2: nat] :
% 6.94/7.32 ( ( linord738340561235409698at_nat
% 6.94/7.32 @ ^ [X4: nat] : X4
% 6.94/7.32 @ ( upt @ M @ N2 ) )
% 6.94/7.32 = ( upt @ M @ N2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % sort_upt
% 6.94/7.32 thf(fact_9915_upt__0__eq__Nil__conv,axiom,
% 6.94/7.32 ! [J2: nat] :
% 6.94/7.32 ( ( ( upt @ zero_zero_nat @ J2 )
% 6.94/7.32 = nil_nat )
% 6.94/7.32 = ( J2 = zero_zero_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % upt_0_eq_Nil_conv
% 6.94/7.32 thf(fact_9916_upt__merge,axiom,
% 6.94/7.32 ! [I2: nat,J2: nat,K2: nat] :
% 6.94/7.32 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.94/7.32 & ( ord_less_eq_nat @ J2 @ K2 ) )
% 6.94/7.32 => ( ( append_nat @ ( upt @ I2 @ J2 ) @ ( upt @ J2 @ K2 ) )
% 6.94/7.32 = ( upt @ I2 @ K2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upt_merge
% 6.94/7.32 thf(fact_9917_upt__conv__Nil,axiom,
% 6.94/7.32 ! [J2: nat,I2: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ J2 @ I2 )
% 6.94/7.32 => ( ( upt @ I2 @ J2 )
% 6.94/7.32 = nil_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % upt_conv_Nil
% 6.94/7.32 thf(fact_9918_upt__eq__Nil__conv,axiom,
% 6.94/7.32 ! [I2: nat,J2: nat] :
% 6.94/7.32 ( ( ( upt @ I2 @ J2 )
% 6.94/7.32 = nil_nat )
% 6.94/7.32 = ( ( J2 = zero_zero_nat )
% 6.94/7.32 | ( ord_less_eq_nat @ J2 @ I2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upt_eq_Nil_conv
% 6.94/7.32 thf(fact_9919_nth__upt,axiom,
% 6.94/7.32 ! [I2: nat,K2: nat,J2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ J2 )
% 6.94/7.32 => ( ( nth_nat @ ( upt @ I2 @ J2 ) @ K2 )
% 6.94/7.32 = ( plus_plus_nat @ I2 @ K2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % nth_upt
% 6.94/7.32 thf(fact_9920_upt__rec__numeral,axiom,
% 6.94/7.32 ! [M: num,N2: num] :
% 6.94/7.32 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 6.94/7.32 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 6.94/7.32 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) )
% 6.94/7.32 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 6.94/7.32 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 6.94/7.32 = nil_nat ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upt_rec_numeral
% 6.94/7.32 thf(fact_9921_upt__eq__append__conv,axiom,
% 6.94/7.32 ! [I2: nat,J2: nat,Xs: list_nat,Ys3: list_nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.94/7.32 => ( ( ( upt @ I2 @ J2 )
% 6.94/7.32 = ( append_nat @ Xs @ Ys3 ) )
% 6.94/7.32 = ( ? [K3: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ I2 @ K3 )
% 6.94/7.32 & ( ord_less_eq_nat @ K3 @ J2 )
% 6.94/7.32 & ( ( upt @ I2 @ K3 )
% 6.94/7.32 = Xs )
% 6.94/7.32 & ( ( upt @ K3 @ J2 )
% 6.94/7.32 = Ys3 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upt_eq_append_conv
% 6.94/7.32 thf(fact_9922_map__add__upt_H,axiom,
% 6.94/7.32 ! [Ofs: nat,A: nat,B: nat] :
% 6.94/7.32 ( ( map_nat_nat
% 6.94/7.32 @ ^ [I: nat] : ( plus_plus_nat @ I @ Ofs )
% 6.94/7.32 @ ( upt @ A @ B ) )
% 6.94/7.32 = ( upt @ ( plus_plus_nat @ A @ Ofs ) @ ( plus_plus_nat @ B @ Ofs ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % map_add_upt'
% 6.94/7.32 thf(fact_9923_upt__append,axiom,
% 6.94/7.32 ! [I2: nat,J2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ I2 @ J2 )
% 6.94/7.32 => ( ( append_nat @ ( upt @ zero_zero_nat @ I2 ) @ ( upt @ I2 @ J2 ) )
% 6.94/7.32 = ( upt @ zero_zero_nat @ J2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upt_append
% 6.94/7.32 thf(fact_9924_upt__add__eq__append,axiom,
% 6.94/7.32 ! [I2: nat,J2: nat,K2: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.94/7.32 => ( ( upt @ I2 @ ( plus_plus_nat @ J2 @ K2 ) )
% 6.94/7.32 = ( append_nat @ ( upt @ I2 @ J2 ) @ ( upt @ J2 @ ( plus_plus_nat @ J2 @ K2 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upt_add_eq_append
% 6.94/7.32 thf(fact_9925_sorted__wrt__upt,axiom,
% 6.94/7.32 ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % sorted_wrt_upt
% 6.94/7.32 thf(fact_9926_map__add__upt,axiom,
% 6.94/7.32 ! [N2: nat,M: nat] :
% 6.94/7.32 ( ( map_nat_nat
% 6.94/7.32 @ ^ [I: nat] : ( plus_plus_nat @ I @ N2 )
% 6.94/7.32 @ ( upt @ zero_zero_nat @ M ) )
% 6.94/7.32 = ( upt @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % map_add_upt
% 6.94/7.32 thf(fact_9927_sorted__upt,axiom,
% 6.94/7.32 ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % sorted_upt
% 6.94/7.32 thf(fact_9928_upt__conv__Cons,axiom,
% 6.94/7.32 ! [I2: nat,J2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ I2 @ J2 )
% 6.94/7.32 => ( ( upt @ I2 @ J2 )
% 6.94/7.32 = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upt_conv_Cons
% 6.94/7.32 thf(fact_9929_upt__rec,axiom,
% 6.94/7.32 ( upt
% 6.94/7.32 = ( ^ [I: nat,J: nat] : ( if_list_nat @ ( ord_less_nat @ I @ J ) @ ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) @ nil_nat ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upt_rec
% 6.94/7.32 thf(fact_9930_upt__Suc,axiom,
% 6.94/7.32 ! [I2: nat,J2: nat] :
% 6.94/7.32 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.94/7.32 => ( ( upt @ I2 @ ( suc @ J2 ) )
% 6.94/7.32 = ( append_nat @ ( upt @ I2 @ J2 ) @ ( cons_nat @ J2 @ nil_nat ) ) ) )
% 6.94/7.32 & ( ~ ( ord_less_eq_nat @ I2 @ J2 )
% 6.94/7.32 => ( ( upt @ I2 @ ( suc @ J2 ) )
% 6.94/7.32 = nil_nat ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upt_Suc
% 6.94/7.32 thf(fact_9931_upt__Suc__append,axiom,
% 6.94/7.32 ! [I2: nat,J2: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ I2 @ J2 )
% 6.94/7.32 => ( ( upt @ I2 @ ( suc @ J2 ) )
% 6.94/7.32 = ( append_nat @ ( upt @ I2 @ J2 ) @ ( cons_nat @ J2 @ nil_nat ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upt_Suc_append
% 6.94/7.32 thf(fact_9932_upt__filter__extend,axiom,
% 6.94/7.32 ! [U: nat,U5: nat,P2: nat > $o] :
% 6.94/7.32 ( ( ord_less_eq_nat @ U @ U5 )
% 6.94/7.32 => ( ! [I3: nat] :
% 6.94/7.32 ( ( ( ord_less_eq_nat @ U @ I3 )
% 6.94/7.32 & ( ord_less_nat @ I3 @ U5 ) )
% 6.94/7.32 => ~ ( P2 @ I3 ) )
% 6.94/7.32 => ( ( filter_nat2 @ P2 @ ( upt @ zero_zero_nat @ U ) )
% 6.94/7.32 = ( filter_nat2 @ P2 @ ( upt @ zero_zero_nat @ U5 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upt_filter_extend
% 6.94/7.32 thf(fact_9933_map__decr__upt,axiom,
% 6.94/7.32 ! [M: nat,N2: nat] :
% 6.94/7.32 ( ( map_nat_nat
% 6.94/7.32 @ ^ [N: nat] : ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) )
% 6.94/7.32 @ ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 6.94/7.32 = ( upt @ M @ N2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % map_decr_upt
% 6.94/7.32 thf(fact_9934_upt__eq__lel__conv,axiom,
% 6.94/7.32 ! [L: nat,H: nat,Is1: list_nat,I2: nat,Is2: list_nat] :
% 6.94/7.32 ( ( ( upt @ L @ H )
% 6.94/7.32 = ( append_nat @ Is1 @ ( cons_nat @ I2 @ Is2 ) ) )
% 6.94/7.32 = ( ( Is1
% 6.94/7.32 = ( upt @ L @ I2 ) )
% 6.94/7.32 & ( Is2
% 6.94/7.32 = ( upt @ ( suc @ I2 ) @ H ) )
% 6.94/7.32 & ( ord_less_eq_nat @ L @ I2 )
% 6.94/7.32 & ( ord_less_nat @ I2 @ H ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upt_eq_lel_conv
% 6.94/7.32 thf(fact_9935_upt__eq__Cons__conv,axiom,
% 6.94/7.32 ! [I2: nat,J2: nat,X: nat,Xs: list_nat] :
% 6.94/7.32 ( ( ( upt @ I2 @ J2 )
% 6.94/7.32 = ( cons_nat @ X @ Xs ) )
% 6.94/7.32 = ( ( ord_less_nat @ I2 @ J2 )
% 6.94/7.32 & ( I2 = X )
% 6.94/7.32 & ( ( upt @ ( plus_plus_nat @ I2 @ one_one_nat ) @ J2 )
% 6.94/7.32 = Xs ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % upt_eq_Cons_conv
% 6.94/7.32 thf(fact_9936_sum__list__upt,axiom,
% 6.94/7.32 ! [M: nat,N2: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ M @ N2 )
% 6.94/7.32 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N2 ) )
% 6.94/7.32 = ( groups3542108847815614940at_nat
% 6.94/7.32 @ ^ [X4: nat] : X4
% 6.94/7.32 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sum_list_upt
% 6.94/7.32 thf(fact_9937_card__length__sum__list__rec,axiom,
% 6.94/7.32 ! [M: nat,N7: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 6.94/7.32 => ( ( finite_card_list_nat
% 6.94/7.32 @ ( collect_list_nat
% 6.94/7.32 @ ^ [L2: list_nat] :
% 6.94/7.32 ( ( ( size_size_list_nat @ L2 )
% 6.94/7.32 = M )
% 6.94/7.32 & ( ( groups4561878855575611511st_nat @ L2 )
% 6.94/7.32 = N7 ) ) ) )
% 6.94/7.32 = ( plus_plus_nat
% 6.94/7.32 @ ( finite_card_list_nat
% 6.94/7.32 @ ( collect_list_nat
% 6.94/7.32 @ ^ [L2: list_nat] :
% 6.94/7.32 ( ( ( size_size_list_nat @ L2 )
% 6.94/7.32 = ( minus_minus_nat @ M @ one_one_nat ) )
% 6.94/7.32 & ( ( groups4561878855575611511st_nat @ L2 )
% 6.94/7.32 = N7 ) ) ) )
% 6.94/7.32 @ ( finite_card_list_nat
% 6.94/7.32 @ ( collect_list_nat
% 6.94/7.32 @ ^ [L2: list_nat] :
% 6.94/7.32 ( ( ( size_size_list_nat @ L2 )
% 6.94/7.32 = M )
% 6.94/7.32 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 6.94/7.32 = N7 ) ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % card_length_sum_list_rec
% 6.94/7.32 thf(fact_9938_card__length__sum__list,axiom,
% 6.94/7.32 ! [M: nat,N7: nat] :
% 6.94/7.32 ( ( finite_card_list_nat
% 6.94/7.32 @ ( collect_list_nat
% 6.94/7.32 @ ^ [L2: list_nat] :
% 6.94/7.32 ( ( ( size_size_list_nat @ L2 )
% 6.94/7.32 = M )
% 6.94/7.32 & ( ( groups4561878855575611511st_nat @ L2 )
% 6.94/7.32 = N7 ) ) ) )
% 6.94/7.32 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N7 @ M ) @ one_one_nat ) @ N7 ) ) ).
% 6.94/7.32
% 6.94/7.32 % card_length_sum_list
% 6.94/7.32 thf(fact_9939_hd__upt,axiom,
% 6.94/7.32 ! [I2: nat,J2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ I2 @ J2 )
% 6.94/7.32 => ( ( hd_nat @ ( upt @ I2 @ J2 ) )
% 6.94/7.32 = I2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % hd_upt
% 6.94/7.32 thf(fact_9940_finite__int__iff__bounded__le,axiom,
% 6.94/7.32 ( finite_finite_int
% 6.94/7.32 = ( ^ [S4: set_int] :
% 6.94/7.32 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S4 ) @ ( set_ord_atMost_int @ K3 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % finite_int_iff_bounded_le
% 6.94/7.32 thf(fact_9941_finite__int__iff__bounded,axiom,
% 6.94/7.32 ( finite_finite_int
% 6.94/7.32 = ( ^ [S4: set_int] :
% 6.94/7.32 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S4 ) @ ( set_ord_lessThan_int @ K3 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % finite_int_iff_bounded
% 6.94/7.32 thf(fact_9942_image__add__int__atLeastLessThan,axiom,
% 6.94/7.32 ! [L: int,U: int] :
% 6.94/7.32 ( ( image_int_int
% 6.94/7.32 @ ^ [X4: int] : ( plus_plus_int @ X4 @ L )
% 6.94/7.32 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 6.94/7.32 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 6.94/7.32
% 6.94/7.32 % image_add_int_atLeastLessThan
% 6.94/7.32 thf(fact_9943_image__add__integer__atLeastLessThan,axiom,
% 6.94/7.32 ! [L: code_integer,U: code_integer] :
% 6.94/7.32 ( ( image_4470545334726330049nteger
% 6.94/7.32 @ ^ [X4: code_integer] : ( plus_p5714425477246183910nteger @ X4 @ L )
% 6.94/7.32 @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ U @ L ) ) )
% 6.94/7.32 = ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 6.94/7.32
% 6.94/7.32 % image_add_integer_atLeastLessThan
% 6.94/7.32 thf(fact_9944_image__atLeastZeroLessThan__integer,axiom,
% 6.94/7.32 ! [U: code_integer] :
% 6.94/7.32 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 6.94/7.32 => ( ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U )
% 6.94/7.32 = ( image_1215581382706833972nteger @ semiri4939895301339042750nteger @ ( set_ord_lessThan_nat @ ( code_nat_of_integer @ U ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % image_atLeastZeroLessThan_integer
% 6.94/7.32 thf(fact_9945_image__atLeastZeroLessThan__int,axiom,
% 6.94/7.32 ! [U: int] :
% 6.94/7.32 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 6.94/7.32 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 6.94/7.32 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % image_atLeastZeroLessThan_int
% 6.94/7.32 thf(fact_9946_image__minus__const__atLeastLessThan__nat,axiom,
% 6.94/7.32 ! [C2: nat,Y: nat,X: nat] :
% 6.94/7.32 ( ( ( ord_less_nat @ C2 @ Y )
% 6.94/7.32 => ( ( image_nat_nat
% 6.94/7.32 @ ^ [I: nat] : ( minus_minus_nat @ I @ C2 )
% 6.94/7.32 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 6.94/7.32 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C2 ) @ ( minus_minus_nat @ Y @ C2 ) ) ) )
% 6.94/7.32 & ( ~ ( ord_less_nat @ C2 @ Y )
% 6.94/7.32 => ( ( ( ord_less_nat @ X @ Y )
% 6.94/7.32 => ( ( image_nat_nat
% 6.94/7.32 @ ^ [I: nat] : ( minus_minus_nat @ I @ C2 )
% 6.94/7.32 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 6.94/7.32 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 6.94/7.32 & ( ~ ( ord_less_nat @ X @ Y )
% 6.94/7.32 => ( ( image_nat_nat
% 6.94/7.32 @ ^ [I: nat] : ( minus_minus_nat @ I @ C2 )
% 6.94/7.32 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 6.94/7.32 = bot_bot_set_nat ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % image_minus_const_atLeastLessThan_nat
% 6.94/7.32 thf(fact_9947_Sup__nat__empty,axiom,
% 6.94/7.32 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 6.94/7.32 = zero_zero_nat ) ).
% 6.94/7.32
% 6.94/7.32 % Sup_nat_empty
% 6.94/7.32 thf(fact_9948_Sup__unit__def,axiom,
% 6.94/7.32 ( comple4687483117567863418t_unit
% 6.94/7.32 = ( ^ [Uu3: set_Product_unit] : product_Unity ) ) ).
% 6.94/7.32
% 6.94/7.32 % Sup_unit_def
% 6.94/7.32 thf(fact_9949_UN__atMost__UNIV,axiom,
% 6.94/7.32 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 6.94/7.32 = top_top_set_nat ) ).
% 6.94/7.32
% 6.94/7.32 % UN_atMost_UNIV
% 6.94/7.32 thf(fact_9950_UN__lessThan__UNIV,axiom,
% 6.94/7.32 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 6.94/7.32 = top_top_set_nat ) ).
% 6.94/7.32
% 6.94/7.32 % UN_lessThan_UNIV
% 6.94/7.32 thf(fact_9951_Inf__unit__def,axiom,
% 6.94/7.32 ( comple2584293577114468500t_unit
% 6.94/7.32 = ( ^ [Uu3: set_Product_unit] : product_Unity ) ) ).
% 6.94/7.32
% 6.94/7.32 % Inf_unit_def
% 6.94/7.32 thf(fact_9952_Inf__nat__def1,axiom,
% 6.94/7.32 ! [K5: set_nat] :
% 6.94/7.32 ( ( K5 != bot_bot_set_nat )
% 6.94/7.32 => ( member_nat @ ( complete_Inf_Inf_nat @ K5 ) @ K5 ) ) ).
% 6.94/7.32
% 6.94/7.32 % Inf_nat_def1
% 6.94/7.32 thf(fact_9953_Inf__int__def,axiom,
% 6.94/7.32 ( complete_Inf_Inf_int
% 6.94/7.32 = ( ^ [X11: set_int] : ( uminus_uminus_int @ ( complete_Sup_Sup_int @ ( image_int_int @ uminus_uminus_int @ X11 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Inf_int_def
% 6.94/7.32 thf(fact_9954_range__mod,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.94/7.32 => ( ( image_nat_nat
% 6.94/7.32 @ ^ [M3: nat] : ( modulo_modulo_nat @ M3 @ N2 )
% 6.94/7.32 @ top_top_set_nat )
% 6.94/7.32 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % range_mod
% 6.94/7.32 thf(fact_9955_merge__true__star,axiom,
% 6.94/7.32 ( ( times_times_assn @ top_top_assn @ top_top_assn )
% 6.94/7.32 = top_top_assn ) ).
% 6.94/7.32
% 6.94/7.32 % merge_true_star
% 6.94/7.32 thf(fact_9956_assn__basic__inequalities_I1_J,axiom,
% 6.94/7.32 top_top_assn != one_one_assn ).
% 6.94/7.32
% 6.94/7.32 % assn_basic_inequalities(1)
% 6.94/7.32 thf(fact_9957_assn__basic__inequalities_I5_J,axiom,
% 6.94/7.32 top_top_assn != bot_bot_assn ).
% 6.94/7.32
% 6.94/7.32 % assn_basic_inequalities(5)
% 6.94/7.32 thf(fact_9958_mod__true,axiom,
% 6.94/7.32 ! [H: produc3658429121746597890et_nat] :
% 6.94/7.32 ( ( rep_assn @ top_top_assn @ H )
% 6.94/7.32 = ( in_range @ H ) ) ).
% 6.94/7.32
% 6.94/7.32 % mod_true
% 6.94/7.32 thf(fact_9959_UNIV__unit,axiom,
% 6.94/7.32 ( top_to1996260823553986621t_unit
% 6.94/7.32 = ( insert_Product_unit @ product_Unity @ bot_bo3957492148770167129t_unit ) ) ).
% 6.94/7.32
% 6.94/7.32 % UNIV_unit
% 6.94/7.32 thf(fact_9960_ent__true,axiom,
% 6.94/7.32 ! [P2: assn] : ( entails @ P2 @ top_top_assn ) ).
% 6.94/7.32
% 6.94/7.32 % ent_true
% 6.94/7.32 thf(fact_9961_top__unit__def,axiom,
% 6.94/7.32 top_top_Product_unit = product_Unity ).
% 6.94/7.32
% 6.94/7.32 % top_unit_def
% 6.94/7.32 thf(fact_9962_mod__star__trueI,axiom,
% 6.94/7.32 ! [P2: assn,H: produc3658429121746597890et_nat] :
% 6.94/7.32 ( ( rep_assn @ P2 @ H )
% 6.94/7.32 => ( rep_assn @ ( times_times_assn @ P2 @ top_top_assn ) @ H ) ) ).
% 6.94/7.32
% 6.94/7.32 % mod_star_trueI
% 6.94/7.32 thf(fact_9963_mod__star__trueE,axiom,
% 6.94/7.32 ! [P2: assn,H: produc3658429121746597890et_nat] :
% 6.94/7.32 ( ( rep_assn @ ( times_times_assn @ P2 @ top_top_assn ) @ H )
% 6.94/7.32 => ~ ! [H4: produc3658429121746597890et_nat] :
% 6.94/7.32 ~ ( rep_assn @ P2 @ H4 ) ) ).
% 6.94/7.32
% 6.94/7.32 % mod_star_trueE
% 6.94/7.32 thf(fact_9964_top__assn__def,axiom,
% 6.94/7.32 ( top_top_assn
% 6.94/7.32 = ( abs_assn @ in_range ) ) ).
% 6.94/7.32
% 6.94/7.32 % top_assn_def
% 6.94/7.32 thf(fact_9965_mod__h__bot__iff_I2_J,axiom,
% 6.94/7.32 ! [H: heap_e7401611519738050253t_unit] : ( rep_assn @ top_top_assn @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % mod_h_bot_iff(2)
% 6.94/7.32 thf(fact_9966_binomial__def,axiom,
% 6.94/7.32 ( binomial
% 6.94/7.32 = ( ^ [N: nat,K3: nat] :
% 6.94/7.32 ( finite_card_set_nat
% 6.94/7.32 @ ( collect_set_nat
% 6.94/7.32 @ ^ [K6: set_nat] :
% 6.94/7.32 ( ( member_set_nat @ K6 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 6.94/7.32 & ( ( finite_card_nat @ K6 )
% 6.94/7.32 = K3 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % binomial_def
% 6.94/7.32 thf(fact_9967_mod__star__trueE_H,axiom,
% 6.94/7.32 ! [P2: assn,H: produc3658429121746597890et_nat] :
% 6.94/7.32 ( ( rep_assn @ ( times_times_assn @ P2 @ top_top_assn ) @ H )
% 6.94/7.32 => ~ ! [H4: produc3658429121746597890et_nat] :
% 6.94/7.32 ( ( ( produc1824681642469235216et_nat @ H4 )
% 6.94/7.32 = ( produc1824681642469235216et_nat @ H ) )
% 6.94/7.32 => ( ( ord_less_eq_set_nat @ ( produc8586169260539613262et_nat @ H4 ) @ ( produc8586169260539613262et_nat @ H ) )
% 6.94/7.32 => ~ ( rep_assn @ P2 @ H4 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % mod_star_trueE'
% 6.94/7.32 thf(fact_9968_UNIV__bool,axiom,
% 6.94/7.32 ( top_top_set_o
% 6.94/7.32 = ( insert_o @ $false @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % UNIV_bool
% 6.94/7.32 thf(fact_9969_drop__upt,axiom,
% 6.94/7.32 ! [M: nat,I2: nat,J2: nat] :
% 6.94/7.32 ( ( drop_nat @ M @ ( upt @ I2 @ J2 ) )
% 6.94/7.32 = ( upt @ ( plus_plus_nat @ I2 @ M ) @ J2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % drop_upt
% 6.94/7.32 thf(fact_9970_take__upt,axiom,
% 6.94/7.32 ! [I2: nat,M: nat,N2: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M ) @ N2 )
% 6.94/7.32 => ( ( take_nat @ M @ ( upt @ I2 @ N2 ) )
% 6.94/7.32 = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % take_upt
% 6.94/7.32 thf(fact_9971_last__upt,axiom,
% 6.94/7.32 ! [I2: nat,J2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ I2 @ J2 )
% 6.94/7.32 => ( ( last_nat @ ( upt @ I2 @ J2 ) )
% 6.94/7.32 = ( minus_minus_nat @ J2 @ one_one_nat ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % last_upt
% 6.94/7.32 thf(fact_9972_less__natural_Orsp,axiom,
% 6.94/7.32 ( bNF_re578469030762574527_nat_o
% 6.94/7.32 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 6.94/7.32 @ ( bNF_re4705727531993890431at_o_o
% 6.94/7.32 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 6.94/7.32 @ ord_less_nat
% 6.94/7.32 @ ord_less_nat ) ).
% 6.94/7.32
% 6.94/7.32 % less_natural.rsp
% 6.94/7.32 thf(fact_9973_less__integer_Orsp,axiom,
% 6.94/7.32 ( bNF_re3403563459893282935_int_o
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ ( bNF_re5089333283451836215nt_o_o
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 6.94/7.32 @ ord_less_int
% 6.94/7.32 @ ord_less_int ) ).
% 6.94/7.32
% 6.94/7.32 % less_integer.rsp
% 6.94/7.32 thf(fact_9974_plus__integer_Orsp,axiom,
% 6.94/7.32 ( bNF_re711492959462206631nt_int
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ ( bNF_re4712519889275205905nt_int
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 6.94/7.32 @ plus_plus_int
% 6.94/7.32 @ plus_plus_int ) ).
% 6.94/7.32
% 6.94/7.32 % plus_integer.rsp
% 6.94/7.32 thf(fact_9975_plus__natural_Orsp,axiom,
% 6.94/7.32 ( bNF_re1345281282404953727at_nat
% 6.94/7.32 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 6.94/7.32 @ ( bNF_re5653821019739307937at_nat
% 6.94/7.32 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 6.94/7.32 @ plus_plus_nat
% 6.94/7.32 @ plus_plus_nat ) ).
% 6.94/7.32
% 6.94/7.32 % plus_natural.rsp
% 6.94/7.32 thf(fact_9976_sub_Orsp,axiom,
% 6.94/7.32 ( bNF_re8402795839162346335um_int
% 6.94/7.32 @ ^ [Y6: num,Z4: num] : ( Y6 = Z4 )
% 6.94/7.32 @ ( bNF_re1822329894187522285nt_int
% 6.94/7.32 @ ^ [Y6: num,Z4: num] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 6.94/7.32 @ ^ [M3: num,N: num] : ( minus_minus_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N ) )
% 6.94/7.32 @ ^ [M3: num,N: num] : ( minus_minus_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sub.rsp
% 6.94/7.32 thf(fact_9977_dup_Orsp,axiom,
% 6.94/7.32 ( bNF_re4712519889275205905nt_int
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 )
% 6.94/7.32 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 ) ) ).
% 6.94/7.32
% 6.94/7.32 % dup.rsp
% 6.94/7.32 thf(fact_9978_less__eq__natural_Orsp,axiom,
% 6.94/7.32 ( bNF_re578469030762574527_nat_o
% 6.94/7.32 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 6.94/7.32 @ ( bNF_re4705727531993890431at_o_o
% 6.94/7.32 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 6.94/7.32 @ ord_less_eq_nat
% 6.94/7.32 @ ord_less_eq_nat ) ).
% 6.94/7.32
% 6.94/7.32 % less_eq_natural.rsp
% 6.94/7.32 thf(fact_9979_less__eq__integer_Orsp,axiom,
% 6.94/7.32 ( bNF_re3403563459893282935_int_o
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ ( bNF_re5089333283451836215nt_o_o
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 6.94/7.32 @ ord_less_eq_int
% 6.94/7.32 @ ord_less_eq_int ) ).
% 6.94/7.32
% 6.94/7.32 % less_eq_integer.rsp
% 6.94/7.32 thf(fact_9980_butlast__upt,axiom,
% 6.94/7.32 ! [M: nat,N2: nat] :
% 6.94/7.32 ( ( butlast_nat @ ( upt @ M @ N2 ) )
% 6.94/7.32 = ( upt @ M @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % butlast_upt
% 6.94/7.32 thf(fact_9981_plus__rat_Otransfer,axiom,
% 6.94/7.32 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 6.94/7.32 @ ^ [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 ) ) )
% 6.94/7.32 @ plus_plus_rat ) ).
% 6.94/7.32
% 6.94/7.32 % plus_rat.transfer
% 6.94/7.32 thf(fact_9982_Fract_Otransfer,axiom,
% 6.94/7.32 ( bNF_re3461391660133120880nt_rat
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ ( bNF_re2214769303045360666nt_rat
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ pcr_rat )
% 6.94/7.32 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( B4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B4 ) )
% 6.94/7.32 @ fract ) ).
% 6.94/7.32
% 6.94/7.32 % Fract.transfer
% 6.94/7.32 thf(fact_9983_uminus__rat_Otransfer,axiom,
% 6.94/7.32 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 6.94/7.32 @ ^ [X4: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X4 ) ) @ ( product_snd_int_int @ X4 ) )
% 6.94/7.32 @ uminus_uminus_rat ) ).
% 6.94/7.32
% 6.94/7.32 % uminus_rat.transfer
% 6.94/7.32 thf(fact_9984_times__rat_Otransfer,axiom,
% 6.94/7.32 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 6.94/7.32 @ ^ [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 ) ) )
% 6.94/7.32 @ times_times_rat ) ).
% 6.94/7.32
% 6.94/7.32 % times_rat.transfer
% 6.94/7.32 thf(fact_9985_inverse__rat_Otransfer,axiom,
% 6.94/7.32 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 6.94/7.32 @ ^ [X4: product_prod_int_int] :
% 6.94/7.32 ( if_Pro3027730157355071871nt_int
% 6.94/7.32 @ ( ( product_fst_int_int @ X4 )
% 6.94/7.32 = zero_zero_int )
% 6.94/7.32 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 6.94/7.32 @ ( product_Pair_int_int @ ( product_snd_int_int @ X4 ) @ ( product_fst_int_int @ X4 ) ) )
% 6.94/7.32 @ inverse_inverse_rat ) ).
% 6.94/7.32
% 6.94/7.32 % inverse_rat.transfer
% 6.94/7.32 thf(fact_9986_positive_Otransfer,axiom,
% 6.94/7.32 ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 6.94/7.32 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) )
% 6.94/7.32 @ positive ) ).
% 6.94/7.32
% 6.94/7.32 % positive.transfer
% 6.94/7.32 thf(fact_9987_times__int_Otransfer,axiom,
% 6.94/7.32 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 6.94/7.32 @ ( produc27273713700761075at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y4 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V2 ) @ ( times_times_nat @ Y4 @ U3 ) ) ) ) )
% 6.94/7.32 @ times_times_int ) ).
% 6.94/7.32
% 6.94/7.32 % times_int.transfer
% 6.94/7.32 thf(fact_9988_positive__add,axiom,
% 6.94/7.32 ! [X: rat,Y: rat] :
% 6.94/7.32 ( ( positive @ X )
% 6.94/7.32 => ( ( positive @ Y )
% 6.94/7.32 => ( positive @ ( plus_plus_rat @ X @ Y ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % positive_add
% 6.94/7.32 thf(fact_9989_nat_Otransfer,axiom,
% 6.94/7.32 ( bNF_re4555766996558763186at_nat @ pcr_int
% 6.94/7.32 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 6.94/7.32 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 6.94/7.32 @ nat2 ) ).
% 6.94/7.32
% 6.94/7.32 % nat.transfer
% 6.94/7.32 thf(fact_9990_int__transfer,axiom,
% 6.94/7.32 ( bNF_re6830278522597306478at_int
% 6.94/7.32 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 6.94/7.32 @ pcr_int
% 6.94/7.32 @ ^ [N: nat] : ( product_Pair_nat_nat @ N @ zero_zero_nat )
% 6.94/7.32 @ semiri1314217659103216013at_int ) ).
% 6.94/7.32
% 6.94/7.32 % int_transfer
% 6.94/7.32 thf(fact_9991_less__rat__def,axiom,
% 6.94/7.32 ( ord_less_rat
% 6.94/7.32 = ( ^ [X4: rat,Y4: rat] : ( positive @ ( minus_minus_rat @ Y4 @ X4 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_rat_def
% 6.94/7.32 thf(fact_9992_uminus__int_Otransfer,axiom,
% 6.94/7.32 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 6.94/7.32 @ ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) )
% 6.94/7.32 @ uminus_uminus_int ) ).
% 6.94/7.32
% 6.94/7.32 % uminus_int.transfer
% 6.94/7.32 thf(fact_9993_positive__rat,axiom,
% 6.94/7.32 ! [A: int,B: int] :
% 6.94/7.32 ( ( positive @ ( fract @ A @ B ) )
% 6.94/7.32 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % positive_rat
% 6.94/7.32 thf(fact_9994_less__int_Otransfer,axiom,
% 6.94/7.32 ( bNF_re717283939379294677_int_o @ pcr_int
% 6.94/7.32 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 6.94/7.32 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 6.94/7.32 @ ( produc8739625826339149834_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U3 @ Y4 ) ) ) )
% 6.94/7.32 @ ord_less_int ) ).
% 6.94/7.32
% 6.94/7.32 % less_int.transfer
% 6.94/7.32 thf(fact_9995_less__eq__int_Otransfer,axiom,
% 6.94/7.32 ( bNF_re717283939379294677_int_o @ pcr_int
% 6.94/7.32 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 6.94/7.32 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 6.94/7.32 @ ( produc8739625826339149834_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U3 @ Y4 ) ) ) )
% 6.94/7.32 @ ord_less_eq_int ) ).
% 6.94/7.32
% 6.94/7.32 % less_eq_int.transfer
% 6.94/7.32 thf(fact_9996_plus__int_Otransfer,axiom,
% 6.94/7.32 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 6.94/7.32 @ ( produc27273713700761075at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y4 @ V2 ) ) ) )
% 6.94/7.32 @ plus_plus_int ) ).
% 6.94/7.32
% 6.94/7.32 % plus_int.transfer
% 6.94/7.32 thf(fact_9997_minus__int_Otransfer,axiom,
% 6.94/7.32 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 6.94/7.32 @ ( produc27273713700761075at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ Y4 @ U3 ) ) ) )
% 6.94/7.32 @ minus_minus_int ) ).
% 6.94/7.32
% 6.94/7.32 % minus_int.transfer
% 6.94/7.32 thf(fact_9998_positive_Orep__eq,axiom,
% 6.94/7.32 ( positive
% 6.94/7.32 = ( ^ [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 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % positive.rep_eq
% 6.94/7.32 thf(fact_9999_pred__nat__trancl__eq__le,axiom,
% 6.94/7.32 ! [M: nat,N2: nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N2 ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 6.94/7.32 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % pred_nat_trancl_eq_le
% 6.94/7.32 thf(fact_10000_prod__encode__def,axiom,
% 6.94/7.32 ( nat_prod_encode
% 6.94/7.32 = ( produc6842872674320459806at_nat
% 6.94/7.32 @ ^ [M3: nat,N: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M3 @ N ) ) @ M3 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % prod_encode_def
% 6.94/7.32 thf(fact_10001_min__0R,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( ord_min_nat @ N2 @ zero_zero_nat )
% 6.94/7.32 = zero_zero_nat ) ).
% 6.94/7.32
% 6.94/7.32 % min_0R
% 6.94/7.32 thf(fact_10002_min__0L,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( ord_min_nat @ zero_zero_nat @ N2 )
% 6.94/7.32 = zero_zero_nat ) ).
% 6.94/7.32
% 6.94/7.32 % min_0L
% 6.94/7.32 thf(fact_10003_min__Suc__Suc,axiom,
% 6.94/7.32 ! [M: nat,N2: nat] :
% 6.94/7.32 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 6.94/7.32 = ( suc @ ( ord_min_nat @ M @ N2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % min_Suc_Suc
% 6.94/7.32 thf(fact_10004_min__Suc__gt_I1_J,axiom,
% 6.94/7.32 ! [A: nat,B: nat] :
% 6.94/7.32 ( ( ord_less_nat @ A @ B )
% 6.94/7.32 => ( ( ord_min_nat @ ( suc @ A ) @ B )
% 6.94/7.32 = ( suc @ A ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % min_Suc_gt(1)
% 6.94/7.32 thf(fact_10005_min__Suc__gt_I2_J,axiom,
% 6.94/7.32 ! [A: nat,B: nat] :
% 6.94/7.32 ( ( ord_less_nat @ A @ B )
% 6.94/7.32 => ( ( ord_min_nat @ B @ ( suc @ A ) )
% 6.94/7.32 = ( suc @ A ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % min_Suc_gt(2)
% 6.94/7.32 thf(fact_10006_min__diff,axiom,
% 6.94/7.32 ! [M: nat,I2: nat,N2: nat] :
% 6.94/7.32 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I2 ) @ ( minus_minus_nat @ N2 @ I2 ) )
% 6.94/7.32 = ( minus_minus_nat @ ( ord_min_nat @ M @ N2 ) @ I2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % min_diff
% 6.94/7.32 thf(fact_10007_nat__mult__min__right,axiom,
% 6.94/7.32 ! [M: nat,N2: nat,Q6: nat] :
% 6.94/7.32 ( ( times_times_nat @ M @ ( ord_min_nat @ N2 @ Q6 ) )
% 6.94/7.32 = ( ord_min_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q6 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % nat_mult_min_right
% 6.94/7.32 thf(fact_10008_nat__mult__min__left,axiom,
% 6.94/7.32 ! [M: nat,N2: nat,Q6: nat] :
% 6.94/7.32 ( ( times_times_nat @ ( ord_min_nat @ M @ N2 ) @ Q6 )
% 6.94/7.32 = ( ord_min_nat @ ( times_times_nat @ M @ Q6 ) @ ( times_times_nat @ N2 @ Q6 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % nat_mult_min_left
% 6.94/7.32 thf(fact_10009_inf__nat__def,axiom,
% 6.94/7.32 inf_inf_nat = ord_min_nat ).
% 6.94/7.32
% 6.94/7.32 % inf_nat_def
% 6.94/7.32 thf(fact_10010_le__prod__encode__2,axiom,
% 6.94/7.32 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % le_prod_encode_2
% 6.94/7.32 thf(fact_10011_le__prod__encode__1,axiom,
% 6.94/7.32 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % le_prod_encode_1
% 6.94/7.32 thf(fact_10012_min__Suc1,axiom,
% 6.94/7.32 ! [N2: nat,M: nat] :
% 6.94/7.32 ( ( ord_min_nat @ ( suc @ N2 ) @ M )
% 6.94/7.32 = ( case_nat_nat @ zero_zero_nat
% 6.94/7.32 @ ^ [M7: nat] : ( suc @ ( ord_min_nat @ N2 @ M7 ) )
% 6.94/7.32 @ M ) ) ).
% 6.94/7.32
% 6.94/7.32 % min_Suc1
% 6.94/7.32 thf(fact_10013_min__Suc2,axiom,
% 6.94/7.32 ! [M: nat,N2: nat] :
% 6.94/7.32 ( ( ord_min_nat @ M @ ( suc @ N2 ) )
% 6.94/7.32 = ( case_nat_nat @ zero_zero_nat
% 6.94/7.32 @ ^ [M7: nat] : ( suc @ ( ord_min_nat @ M7 @ N2 ) )
% 6.94/7.32 @ M ) ) ).
% 6.94/7.32
% 6.94/7.32 % min_Suc2
% 6.94/7.32 thf(fact_10014_prod__encode__prod__decode__aux,axiom,
% 6.94/7.32 ! [K2: nat,M: nat] :
% 6.94/7.32 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K2 @ M ) )
% 6.94/7.32 = ( plus_plus_nat @ ( nat_triangle @ K2 ) @ M ) ) ).
% 6.94/7.32
% 6.94/7.32 % prod_encode_prod_decode_aux
% 6.94/7.32 thf(fact_10015_times__int_Orsp,axiom,
% 6.94/7.32 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 6.94/7.32 @ ( produc27273713700761075at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y4 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V2 ) @ ( times_times_nat @ Y4 @ U3 ) ) ) ) )
% 6.94/7.32 @ ( produc27273713700761075at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y4 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V2 ) @ ( times_times_nat @ Y4 @ U3 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % times_int.rsp
% 6.94/7.32 thf(fact_10016_intrel__iff,axiom,
% 6.94/7.32 ! [X: nat,Y: nat,U: nat,V: nat] :
% 6.94/7.32 ( ( intrel @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ U @ V ) )
% 6.94/7.32 = ( ( plus_plus_nat @ X @ V )
% 6.94/7.32 = ( plus_plus_nat @ U @ Y ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % intrel_iff
% 6.94/7.32 thf(fact_10017_uminus__int_Orsp,axiom,
% 6.94/7.32 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 6.94/7.32 @ ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) )
% 6.94/7.32 @ ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % uminus_int.rsp
% 6.94/7.32 thf(fact_10018_nat_Orsp,axiom,
% 6.94/7.32 ( bNF_re8246922863344978751at_nat @ intrel
% 6.94/7.32 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 6.94/7.32 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 6.94/7.32 @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % nat.rsp
% 6.94/7.32 thf(fact_10019_intrel__def,axiom,
% 6.94/7.32 ( intrel
% 6.94/7.32 = ( produc8739625826339149834_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [U3: nat,V2: nat] :
% 6.94/7.32 ( ( plus_plus_nat @ X4 @ V2 )
% 6.94/7.32 = ( plus_plus_nat @ U3 @ Y4 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % intrel_def
% 6.94/7.32 thf(fact_10020_less__int_Orsp,axiom,
% 6.94/7.32 ( bNF_re4202695980764964119_nat_o @ intrel
% 6.94/7.32 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 6.94/7.32 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 6.94/7.32 @ ( produc8739625826339149834_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U3 @ Y4 ) ) ) )
% 6.94/7.32 @ ( produc8739625826339149834_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U3 @ Y4 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_int.rsp
% 6.94/7.32 thf(fact_10021_less__eq__int_Orsp,axiom,
% 6.94/7.32 ( bNF_re4202695980764964119_nat_o @ intrel
% 6.94/7.32 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 6.94/7.32 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 6.94/7.32 @ ( produc8739625826339149834_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U3 @ Y4 ) ) ) )
% 6.94/7.32 @ ( produc8739625826339149834_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U3 @ Y4 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_eq_int.rsp
% 6.94/7.32 thf(fact_10022_plus__int_Orsp,axiom,
% 6.94/7.32 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 6.94/7.32 @ ( produc27273713700761075at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y4 @ V2 ) ) ) )
% 6.94/7.32 @ ( produc27273713700761075at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y4 @ V2 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % plus_int.rsp
% 6.94/7.32 thf(fact_10023_minus__int_Orsp,axiom,
% 6.94/7.32 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 6.94/7.32 @ ( produc27273713700761075at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ Y4 @ U3 ) ) ) )
% 6.94/7.32 @ ( produc27273713700761075at_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc2626176000494625587at_nat
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ Y4 @ U3 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % minus_int.rsp
% 6.94/7.32 thf(fact_10024_mono__Suc,axiom,
% 6.94/7.32 order_mono_nat_nat @ suc ).
% 6.94/7.32
% 6.94/7.32 % mono_Suc
% 6.94/7.32 thf(fact_10025_mono__times__nat,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.94/7.32 => ( order_mono_nat_nat @ ( times_times_nat @ N2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % mono_times_nat
% 6.94/7.32 thf(fact_10026_mono__ge2__power__minus__self,axiom,
% 6.94/7.32 ! [K2: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 6.94/7.32 => ( order_mono_nat_nat
% 6.94/7.32 @ ^ [M3: nat] : ( minus_minus_nat @ ( power_power_nat @ K2 @ M3 ) @ M3 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % mono_ge2_power_minus_self
% 6.94/7.32 thf(fact_10027_of__nat__eq__id,axiom,
% 6.94/7.32 semiri1316708129612266289at_nat = id_nat ).
% 6.94/7.32
% 6.94/7.32 % of_nat_eq_id
% 6.94/7.32 thf(fact_10028_less__int__def,axiom,
% 6.94/7.32 ( ord_less_int
% 6.94/7.32 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 6.94/7.32 @ ( produc8739625826339149834_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U3 @ Y4 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_int_def
% 6.94/7.32 thf(fact_10029_less__eq__int__def,axiom,
% 6.94/7.32 ( ord_less_eq_int
% 6.94/7.32 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 6.94/7.32 @ ( produc8739625826339149834_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [U3: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U3 @ Y4 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_eq_int_def
% 6.94/7.32 thf(fact_10030_nat__def,axiom,
% 6.94/7.32 ( nat2
% 6.94/7.32 = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % nat_def
% 6.94/7.32 thf(fact_10031_positive__def,axiom,
% 6.94/7.32 ( positive
% 6.94/7.32 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 6.94/7.32 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % positive_def
% 6.94/7.32 thf(fact_10032_less__integer__def,axiom,
% 6.94/7.32 ( ord_le6747313008572928689nteger
% 6.94/7.32 = ( map_fu2496120808607739376eger_o @ code_int_of_integer @ ( map_fu6957801986076833569nt_o_o @ code_int_of_integer @ id_o ) @ ord_less_int ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_integer_def
% 6.94/7.32 thf(fact_10033_less__eq__integer__def,axiom,
% 6.94/7.32 ( ord_le3102999989581377725nteger
% 6.94/7.32 = ( map_fu2496120808607739376eger_o @ code_int_of_integer @ ( map_fu6957801986076833569nt_o_o @ code_int_of_integer @ id_o ) @ ord_less_eq_int ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_eq_integer_def
% 6.94/7.32 thf(fact_10034_plus__integer__def,axiom,
% 6.94/7.32 ( plus_p5714425477246183910nteger
% 6.94/7.32 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ plus_plus_int ) ) ).
% 6.94/7.32
% 6.94/7.32 % plus_integer_def
% 6.94/7.32 thf(fact_10035_plus__rat__def,axiom,
% 6.94/7.32 ( plus_plus_rat
% 6.94/7.32 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 6.94/7.32 @ ^ [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 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % plus_rat_def
% 6.94/7.32 thf(fact_10036_inverse__rat__def,axiom,
% 6.94/7.32 ( inverse_inverse_rat
% 6.94/7.32 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 6.94/7.32 @ ^ [X4: product_prod_int_int] :
% 6.94/7.32 ( if_Pro3027730157355071871nt_int
% 6.94/7.32 @ ( ( product_fst_int_int @ X4 )
% 6.94/7.32 = zero_zero_int )
% 6.94/7.32 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 6.94/7.32 @ ( product_Pair_int_int @ ( product_snd_int_int @ X4 ) @ ( product_fst_int_int @ X4 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % inverse_rat_def
% 6.94/7.32 thf(fact_10037_times__rat__def,axiom,
% 6.94/7.32 ( times_times_rat
% 6.94/7.32 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 6.94/7.32 @ ^ [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 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % times_rat_def
% 6.94/7.32 thf(fact_10038_Fract__def,axiom,
% 6.94/7.32 ( fract
% 6.94/7.32 = ( map_fu7831380289885515383nt_rat @ id_int @ ( map_fu3424225382358772769nt_rat @ id_int @ abs_Rat )
% 6.94/7.32 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( B4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B4 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Fract_def
% 6.94/7.32 thf(fact_10039_uminus__rat__def,axiom,
% 6.94/7.32 ( uminus_uminus_rat
% 6.94/7.32 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 6.94/7.32 @ ^ [X4: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X4 ) ) @ ( product_snd_int_int @ X4 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % uminus_rat_def
% 6.94/7.32 thf(fact_10040_Code__Numeral_Odup__def,axiom,
% 6.94/7.32 ( code_dup
% 6.94/7.32 = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int
% 6.94/7.32 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Code_Numeral.dup_def
% 6.94/7.32 thf(fact_10041_plus__rat_Oabs__eq,axiom,
% 6.94/7.32 ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 6.94/7.32 ( ( ratrel @ Xa @ Xa )
% 6.94/7.32 => ( ( ratrel @ X @ X )
% 6.94/7.32 => ( ( plus_plus_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 6.94/7.32 = ( 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 ) ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % plus_rat.abs_eq
% 6.94/7.32 thf(fact_10042_positive_Oabs__eq,axiom,
% 6.94/7.32 ! [X: product_prod_int_int] :
% 6.94/7.32 ( ( ratrel @ X @ X )
% 6.94/7.32 => ( ( positive @ ( abs_Rat @ X ) )
% 6.94/7.32 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % positive.abs_eq
% 6.94/7.32 thf(fact_10043_Fract_Orsp,axiom,
% 6.94/7.32 ( bNF_re157797125943740599nt_int
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ ( bNF_re6250860962936578807nt_int
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ ratrel )
% 6.94/7.32 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( B4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B4 ) )
% 6.94/7.32 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( B4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B4 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Fract.rsp
% 6.94/7.32 thf(fact_10044_dup_Orep__eq,axiom,
% 6.94/7.32 ! [X: code_integer] :
% 6.94/7.32 ( ( code_int_of_integer @ ( code_dup @ X ) )
% 6.94/7.32 = ( plus_plus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ X ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % dup.rep_eq
% 6.94/7.32 thf(fact_10045_dup_Oabs__eq,axiom,
% 6.94/7.32 ! [X: int] :
% 6.94/7.32 ( ( code_dup @ ( code_integer_of_int @ X ) )
% 6.94/7.32 = ( code_integer_of_int @ ( plus_plus_int @ X @ X ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % dup.abs_eq
% 6.94/7.32 thf(fact_10046_ratrel__def,axiom,
% 6.94/7.32 ( ratrel
% 6.94/7.32 = ( ^ [X4: product_prod_int_int,Y4: product_prod_int_int] :
% 6.94/7.32 ( ( ( product_snd_int_int @ X4 )
% 6.94/7.32 != zero_zero_int )
% 6.94/7.32 & ( ( product_snd_int_int @ Y4 )
% 6.94/7.32 != zero_zero_int )
% 6.94/7.32 & ( ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) )
% 6.94/7.32 = ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % ratrel_def
% 6.94/7.32 thf(fact_10047_times__rat_Orsp,axiom,
% 6.94/7.32 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 6.94/7.32 @ ^ [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 ) ) )
% 6.94/7.32 @ ^ [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 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % times_rat.rsp
% 6.94/7.32 thf(fact_10048_uminus__rat_Orsp,axiom,
% 6.94/7.32 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 6.94/7.32 @ ^ [X4: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X4 ) ) @ ( product_snd_int_int @ X4 ) )
% 6.94/7.32 @ ^ [X4: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X4 ) ) @ ( product_snd_int_int @ X4 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % uminus_rat.rsp
% 6.94/7.32 thf(fact_10049_positive_Orsp,axiom,
% 6.94/7.32 ( bNF_re8699439704749558557nt_o_o @ ratrel
% 6.94/7.32 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) )
% 6.94/7.32 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % positive.rsp
% 6.94/7.32 thf(fact_10050_inverse__rat_Orsp,axiom,
% 6.94/7.32 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 6.94/7.32 @ ^ [X4: product_prod_int_int] :
% 6.94/7.32 ( if_Pro3027730157355071871nt_int
% 6.94/7.32 @ ( ( product_fst_int_int @ X4 )
% 6.94/7.32 = zero_zero_int )
% 6.94/7.32 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 6.94/7.32 @ ( product_Pair_int_int @ ( product_snd_int_int @ X4 ) @ ( product_fst_int_int @ X4 ) ) )
% 6.94/7.32 @ ^ [X4: product_prod_int_int] :
% 6.94/7.32 ( if_Pro3027730157355071871nt_int
% 6.94/7.32 @ ( ( product_fst_int_int @ X4 )
% 6.94/7.32 = zero_zero_int )
% 6.94/7.32 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 6.94/7.32 @ ( product_Pair_int_int @ ( product_snd_int_int @ X4 ) @ ( product_fst_int_int @ X4 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % inverse_rat.rsp
% 6.94/7.32 thf(fact_10051_plus__rat_Orsp,axiom,
% 6.94/7.32 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 6.94/7.32 @ ^ [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 ) ) )
% 6.94/7.32 @ ^ [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 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % plus_rat.rsp
% 6.94/7.32 thf(fact_10052_Code__Numeral_Osub__code_I8_J,axiom,
% 6.94/7.32 ! [M: num,N2: num] :
% 6.94/7.32 ( ( code_sub @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 6.94/7.32 = ( plus_p5714425477246183910nteger @ ( code_dup @ ( code_sub @ M @ N2 ) ) @ one_one_Code_integer ) ) ).
% 6.94/7.32
% 6.94/7.32 % Code_Numeral.sub_code(8)
% 6.94/7.32 thf(fact_10053_cr__rat__def,axiom,
% 6.94/7.32 ( cr_rat
% 6.94/7.32 = ( ^ [X4: product_prod_int_int,Y4: rat] :
% 6.94/7.32 ( ( ratrel @ X4 @ X4 )
% 6.94/7.32 & ( ( abs_Rat @ X4 )
% 6.94/7.32 = Y4 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % cr_rat_def
% 6.94/7.32 thf(fact_10054_Code__Numeral_Osub__def,axiom,
% 6.94/7.32 ( code_sub
% 6.94/7.32 = ( map_fu6891787308814931657nteger @ id_num @ ( map_fu8638147718074629079nteger @ id_num @ code_integer_of_int )
% 6.94/7.32 @ ^ [M3: num,N: num] : ( minus_minus_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Code_Numeral.sub_def
% 6.94/7.32 thf(fact_10055_less__natural_Oabs__eq,axiom,
% 6.94/7.32 ! [Xa: nat,X: nat] :
% 6.94/7.32 ( ( ord_le5570908160329646204atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 6.94/7.32 = ( ord_less_nat @ Xa @ X ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_natural.abs_eq
% 6.94/7.32 thf(fact_10056_plus__natural_Oabs__eq,axiom,
% 6.94/7.32 ! [Xa: nat,X: nat] :
% 6.94/7.32 ( ( plus_p4538020629002901425atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 6.94/7.32 = ( code_natural_of_nat @ ( plus_plus_nat @ Xa @ X ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % plus_natural.abs_eq
% 6.94/7.32 thf(fact_10057_less__eq__natural_Oabs__eq,axiom,
% 6.94/7.32 ! [Xa: nat,X: nat] :
% 6.94/7.32 ( ( ord_le1926595141338095240atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 6.94/7.32 = ( ord_less_eq_nat @ Xa @ X ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_eq_natural.abs_eq
% 6.94/7.32 thf(fact_10058_Max__divisors__self__nat,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( N2 != zero_zero_nat )
% 6.94/7.32 => ( ( lattic8265883725875713057ax_nat
% 6.94/7.32 @ ( collect_nat
% 6.94/7.32 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ N2 ) ) )
% 6.94/7.32 = N2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % Max_divisors_self_nat
% 6.94/7.32 thf(fact_10059_Max__divisors__self__int,axiom,
% 6.94/7.32 ! [N2: int] :
% 6.94/7.32 ( ( N2 != zero_zero_int )
% 6.94/7.32 => ( ( lattic8263393255366662781ax_int
% 6.94/7.32 @ ( collect_int
% 6.94/7.32 @ ^ [D5: int] : ( dvd_dvd_int @ D5 @ N2 ) ) )
% 6.94/7.32 = ( abs_abs_int @ N2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Max_divisors_self_int
% 6.94/7.32 thf(fact_10060_gcd__is__Max__divisors__int,axiom,
% 6.94/7.32 ! [N2: int,M: int] :
% 6.94/7.32 ( ( N2 != zero_zero_int )
% 6.94/7.32 => ( ( gcd_gcd_int @ M @ N2 )
% 6.94/7.32 = ( lattic8263393255366662781ax_int
% 6.94/7.32 @ ( collect_int
% 6.94/7.32 @ ^ [D5: int] :
% 6.94/7.32 ( ( dvd_dvd_int @ D5 @ M )
% 6.94/7.32 & ( dvd_dvd_int @ D5 @ N2 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % gcd_is_Max_divisors_int
% 6.94/7.32 thf(fact_10061_Sup__nat__def,axiom,
% 6.94/7.32 ( complete_Sup_Sup_nat
% 6.94/7.32 = ( ^ [X11: set_nat] : ( if_nat @ ( X11 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X11 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Sup_nat_def
% 6.94/7.32 thf(fact_10062_card__le__Suc__Max,axiom,
% 6.94/7.32 ! [S: set_nat] :
% 6.94/7.32 ( ( finite_finite_nat @ S )
% 6.94/7.32 => ( ord_less_eq_nat @ ( finite_card_nat @ S ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % card_le_Suc_Max
% 6.94/7.32 thf(fact_10063_divide__nat__def,axiom,
% 6.94/7.32 ( divide_divide_nat
% 6.94/7.32 = ( ^ [M3: nat,N: nat] :
% 6.94/7.32 ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat
% 6.94/7.32 @ ( lattic8265883725875713057ax_nat
% 6.94/7.32 @ ( collect_nat
% 6.94/7.32 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N ) @ M3 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % divide_nat_def
% 6.94/7.32 thf(fact_10064_gcd__is__Max__divisors__nat,axiom,
% 6.94/7.32 ! [N2: nat,M: nat] :
% 6.94/7.32 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.94/7.32 => ( ( gcd_gcd_nat @ M @ N2 )
% 6.94/7.32 = ( lattic8265883725875713057ax_nat
% 6.94/7.32 @ ( collect_nat
% 6.94/7.32 @ ^ [D5: nat] :
% 6.94/7.32 ( ( dvd_dvd_nat @ D5 @ M )
% 6.94/7.32 & ( dvd_dvd_nat @ D5 @ N2 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % gcd_is_Max_divisors_nat
% 6.94/7.32 thf(fact_10065_Gcd__eq__Max,axiom,
% 6.94/7.32 ! [M6: set_nat] :
% 6.94/7.32 ( ( finite_finite_nat @ M6 )
% 6.94/7.32 => ( ( M6 != bot_bot_set_nat )
% 6.94/7.32 => ( ~ ( member_nat @ zero_zero_nat @ M6 )
% 6.94/7.32 => ( ( gcd_Gcd_nat @ M6 )
% 6.94/7.32 = ( lattic8265883725875713057ax_nat
% 6.94/7.32 @ ( comple7806235888213564991et_nat
% 6.94/7.32 @ ( image_nat_set_nat
% 6.94/7.32 @ ^ [M3: nat] :
% 6.94/7.32 ( collect_nat
% 6.94/7.32 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M3 ) )
% 6.94/7.32 @ M6 ) ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Gcd_eq_Max
% 6.94/7.32 thf(fact_10066_INT__greaterThan__UNIV,axiom,
% 6.94/7.32 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 6.94/7.32 = bot_bot_set_nat ) ).
% 6.94/7.32
% 6.94/7.32 % INT_greaterThan_UNIV
% 6.94/7.32 thf(fact_10067_Gcd__abs__eq,axiom,
% 6.94/7.32 ! [K5: set_int] :
% 6.94/7.32 ( ( gcd_Gcd_int @ ( image_int_int @ abs_abs_int @ K5 ) )
% 6.94/7.32 = ( gcd_Gcd_int @ K5 ) ) ).
% 6.94/7.32
% 6.94/7.32 % Gcd_abs_eq
% 6.94/7.32 thf(fact_10068_Gcd__nat__abs__eq,axiom,
% 6.94/7.32 ! [K5: set_int] :
% 6.94/7.32 ( ( gcd_Gcd_nat
% 6.94/7.32 @ ( image_int_nat
% 6.94/7.32 @ ^ [K3: int] : ( nat2 @ ( abs_abs_int @ K3 ) )
% 6.94/7.32 @ K5 ) )
% 6.94/7.32 = ( nat2 @ ( gcd_Gcd_int @ K5 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Gcd_nat_abs_eq
% 6.94/7.32 thf(fact_10069_Gcd__int__eq,axiom,
% 6.94/7.32 ! [N7: set_nat] :
% 6.94/7.32 ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N7 ) )
% 6.94/7.32 = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N7 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Gcd_int_eq
% 6.94/7.32 thf(fact_10070_Gcd__int__greater__eq__0,axiom,
% 6.94/7.32 ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 6.94/7.32
% 6.94/7.32 % Gcd_int_greater_eq_0
% 6.94/7.32 thf(fact_10071_Gcd__int__def,axiom,
% 6.94/7.32 ( gcd_Gcd_int
% 6.94/7.32 = ( ^ [K6: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K6 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Gcd_int_def
% 6.94/7.32 thf(fact_10072_inj__on__diff__nat,axiom,
% 6.94/7.32 ! [N7: set_nat,K2: nat] :
% 6.94/7.32 ( ! [N5: nat] :
% 6.94/7.32 ( ( member_nat @ N5 @ N7 )
% 6.94/7.32 => ( ord_less_eq_nat @ K2 @ N5 ) )
% 6.94/7.32 => ( inj_on_nat_nat
% 6.94/7.32 @ ^ [N: nat] : ( minus_minus_nat @ N @ K2 )
% 6.94/7.32 @ N7 ) ) ).
% 6.94/7.32
% 6.94/7.32 % inj_on_diff_nat
% 6.94/7.32 thf(fact_10073_inj__Suc,axiom,
% 6.94/7.32 ! [N7: set_nat] : ( inj_on_nat_nat @ suc @ N7 ) ).
% 6.94/7.32
% 6.94/7.32 % inj_Suc
% 6.94/7.32 thf(fact_10074_UN__atLeast__UNIV,axiom,
% 6.94/7.32 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 6.94/7.32 = top_top_set_nat ) ).
% 6.94/7.32
% 6.94/7.32 % UN_atLeast_UNIV
% 6.94/7.32 thf(fact_10075_quotient__of__def,axiom,
% 6.94/7.32 ( quotient_of
% 6.94/7.32 = ( ^ [X4: rat] :
% 6.94/7.32 ( the_Pr4378521158711661632nt_int
% 6.94/7.32 @ ^ [Pair: product_prod_int_int] :
% 6.94/7.32 ( ( X4
% 6.94/7.32 = ( fract @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) )
% 6.94/7.32 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Pair ) )
% 6.94/7.32 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % quotient_of_def
% 6.94/7.32 thf(fact_10076_normalize__stable,axiom,
% 6.94/7.32 ! [Q6: int,P3: int] :
% 6.94/7.32 ( ( ord_less_int @ zero_zero_int @ Q6 )
% 6.94/7.32 => ( ( algebr932160517623751201me_int @ P3 @ Q6 )
% 6.94/7.32 => ( ( normalize @ ( product_Pair_int_int @ P3 @ Q6 ) )
% 6.94/7.32 = ( product_Pair_int_int @ P3 @ Q6 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % normalize_stable
% 6.94/7.32 thf(fact_10077_Rat__cases,axiom,
% 6.94/7.32 ! [Q6: rat] :
% 6.94/7.32 ~ ! [A3: int,B3: int] :
% 6.94/7.32 ( ( Q6
% 6.94/7.32 = ( fract @ A3 @ B3 ) )
% 6.94/7.32 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 6.94/7.32 => ~ ( algebr932160517623751201me_int @ A3 @ B3 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Rat_cases
% 6.94/7.32 thf(fact_10078_Rat__induct,axiom,
% 6.94/7.32 ! [P2: rat > $o,Q6: rat] :
% 6.94/7.32 ( ! [A3: int,B3: int] :
% 6.94/7.32 ( ( ord_less_int @ zero_zero_int @ B3 )
% 6.94/7.32 => ( ( algebr932160517623751201me_int @ A3 @ B3 )
% 6.94/7.32 => ( P2 @ ( fract @ A3 @ B3 ) ) ) )
% 6.94/7.32 => ( P2 @ Q6 ) ) ).
% 6.94/7.32
% 6.94/7.32 % Rat_induct
% 6.94/7.32 thf(fact_10079_Rat__cases__nonzero,axiom,
% 6.94/7.32 ! [Q6: rat] :
% 6.94/7.32 ( ! [A3: int,B3: int] :
% 6.94/7.32 ( ( Q6
% 6.94/7.32 = ( fract @ A3 @ B3 ) )
% 6.94/7.32 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 6.94/7.32 => ( ( A3 != zero_zero_int )
% 6.94/7.32 => ~ ( algebr932160517623751201me_int @ A3 @ B3 ) ) ) )
% 6.94/7.32 => ( Q6 = zero_zero_rat ) ) ).
% 6.94/7.32
% 6.94/7.32 % Rat_cases_nonzero
% 6.94/7.32 thf(fact_10080_quotient__of__unique,axiom,
% 6.94/7.32 ! [R2: rat] :
% 6.94/7.32 ? [X3: product_prod_int_int] :
% 6.94/7.32 ( ( R2
% 6.94/7.32 = ( fract @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) )
% 6.94/7.32 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ X3 ) )
% 6.94/7.32 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) )
% 6.94/7.32 & ! [Y5: product_prod_int_int] :
% 6.94/7.32 ( ( ( R2
% 6.94/7.32 = ( fract @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ Y5 ) ) )
% 6.94/7.32 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Y5 ) )
% 6.94/7.32 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ Y5 ) ) )
% 6.94/7.32 => ( Y5 = X3 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % quotient_of_unique
% 6.94/7.32 thf(fact_10081_coprime__diff__one__right__nat,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.94/7.32 => ( algebr934650988132801477me_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % coprime_diff_one_right_nat
% 6.94/7.32 thf(fact_10082_coprime__diff__one__left__nat,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 6.94/7.32 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ N2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % coprime_diff_one_left_nat
% 6.94/7.32 thf(fact_10083_Field__natLeq__on,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( field_nat
% 6.94/7.32 @ ( collec3392354462482085612at_nat
% 6.94/7.32 @ ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( ( ord_less_nat @ X4 @ N2 )
% 6.94/7.32 & ( ord_less_nat @ Y4 @ N2 )
% 6.94/7.32 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) )
% 6.94/7.32 = ( collect_nat
% 6.94/7.32 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Field_natLeq_on
% 6.94/7.32 thf(fact_10084_wf__less,axiom,
% 6.94/7.32 wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % wf_less
% 6.94/7.32 thf(fact_10085_less__than__iff,axiom,
% 6.94/7.32 ! [X: nat,Y: nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ less_than )
% 6.94/7.32 = ( ord_less_nat @ X @ Y ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_than_iff
% 6.94/7.32 thf(fact_10086_le__enumerate,axiom,
% 6.94/7.32 ! [S: set_nat,N2: nat] :
% 6.94/7.32 ( ~ ( finite_finite_nat @ S )
% 6.94/7.32 => ( ord_less_eq_nat @ N2 @ ( infini8530281810654367211te_nat @ S @ N2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % le_enumerate
% 6.94/7.32 thf(fact_10087_finite__le__enumerate,axiom,
% 6.94/7.32 ! [S: set_nat,N2: nat] :
% 6.94/7.32 ( ( finite_finite_nat @ S )
% 6.94/7.32 => ( ( ord_less_nat @ N2 @ ( finite_card_nat @ S ) )
% 6.94/7.32 => ( ord_less_eq_nat @ N2 @ ( infini8530281810654367211te_nat @ S @ N2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % finite_le_enumerate
% 6.94/7.32 thf(fact_10088_Least__eq__0,axiom,
% 6.94/7.32 ! [P2: nat > $o] :
% 6.94/7.32 ( ( P2 @ zero_zero_nat )
% 6.94/7.32 => ( ( ord_Least_nat @ P2 )
% 6.94/7.32 = zero_zero_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % Least_eq_0
% 6.94/7.32 thf(fact_10089_Inf__nat__def,axiom,
% 6.94/7.32 ( complete_Inf_Inf_nat
% 6.94/7.32 = ( ^ [X11: set_nat] :
% 6.94/7.32 ( ord_Least_nat
% 6.94/7.32 @ ^ [N: nat] : ( member_nat @ N @ X11 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Inf_nat_def
% 6.94/7.32 thf(fact_10090_Least__Suc2,axiom,
% 6.94/7.32 ! [P2: nat > $o,N2: nat,Q2: nat > $o,M: nat] :
% 6.94/7.32 ( ( P2 @ N2 )
% 6.94/7.32 => ( ( Q2 @ M )
% 6.94/7.32 => ( ~ ( P2 @ zero_zero_nat )
% 6.94/7.32 => ( ! [K: nat] :
% 6.94/7.32 ( ( P2 @ ( suc @ K ) )
% 6.94/7.32 = ( Q2 @ K ) )
% 6.94/7.32 => ( ( ord_Least_nat @ P2 )
% 6.94/7.32 = ( suc @ ( ord_Least_nat @ Q2 ) ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Least_Suc2
% 6.94/7.32 thf(fact_10091_Least__Suc,axiom,
% 6.94/7.32 ! [P2: nat > $o,N2: nat] :
% 6.94/7.32 ( ( P2 @ N2 )
% 6.94/7.32 => ( ~ ( P2 @ zero_zero_nat )
% 6.94/7.32 => ( ( ord_Least_nat @ P2 )
% 6.94/7.32 = ( suc
% 6.94/7.32 @ ( ord_Least_nat
% 6.94/7.32 @ ^ [M3: nat] : ( P2 @ ( suc @ M3 ) ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Least_Suc
% 6.94/7.32 thf(fact_10092_GreatestI__nat,axiom,
% 6.94/7.32 ! [P2: nat > $o,K2: nat,B: nat] :
% 6.94/7.32 ( ( P2 @ K2 )
% 6.94/7.32 => ( ! [Y3: nat] :
% 6.94/7.32 ( ( P2 @ Y3 )
% 6.94/7.32 => ( ord_less_eq_nat @ Y3 @ B ) )
% 6.94/7.32 => ( P2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % GreatestI_nat
% 6.94/7.32 thf(fact_10093_Greatest__le__nat,axiom,
% 6.94/7.32 ! [P2: nat > $o,K2: nat,B: nat] :
% 6.94/7.32 ( ( P2 @ K2 )
% 6.94/7.32 => ( ! [Y3: nat] :
% 6.94/7.32 ( ( P2 @ Y3 )
% 6.94/7.32 => ( ord_less_eq_nat @ Y3 @ B ) )
% 6.94/7.32 => ( ord_less_eq_nat @ K2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Greatest_le_nat
% 6.94/7.32 thf(fact_10094_GreatestI__ex__nat,axiom,
% 6.94/7.32 ! [P2: nat > $o,B: nat] :
% 6.94/7.32 ( ? [X_12: nat] : ( P2 @ X_12 )
% 6.94/7.32 => ( ! [Y3: nat] :
% 6.94/7.32 ( ( P2 @ Y3 )
% 6.94/7.32 => ( ord_less_eq_nat @ Y3 @ B ) )
% 6.94/7.32 => ( P2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % GreatestI_ex_nat
% 6.94/7.32 thf(fact_10095_Sup__int__def,axiom,
% 6.94/7.32 ( complete_Sup_Sup_int
% 6.94/7.32 = ( ^ [X11: set_int] :
% 6.94/7.32 ( the_int
% 6.94/7.32 @ ^ [X4: int] :
% 6.94/7.32 ( ( member_int @ X4 @ X11 )
% 6.94/7.32 & ! [Y4: int] :
% 6.94/7.32 ( ( member_int @ Y4 @ X11 )
% 6.94/7.32 => ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Sup_int_def
% 6.94/7.32 thf(fact_10096_filterlim__lessThan__at__top,axiom,
% 6.94/7.32 filter3212408913953519116et_nat @ set_ord_lessThan_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 6.94/7.32
% 6.94/7.32 % filterlim_lessThan_at_top
% 6.94/7.32 thf(fact_10097_filterlim__atMost__at__top,axiom,
% 6.94/7.32 filter3212408913953519116et_nat @ set_ord_atMost_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 6.94/7.32
% 6.94/7.32 % filterlim_atMost_at_top
% 6.94/7.32 thf(fact_10098_bij__betw__Suc,axiom,
% 6.94/7.32 ! [M6: set_nat,N7: set_nat] :
% 6.94/7.32 ( ( bij_betw_nat_nat @ suc @ M6 @ N7 )
% 6.94/7.32 = ( ( image_nat_nat @ suc @ M6 )
% 6.94/7.32 = N7 ) ) ).
% 6.94/7.32
% 6.94/7.32 % bij_betw_Suc
% 6.94/7.32 thf(fact_10099_sqr_Osimps_I3_J,axiom,
% 6.94/7.32 ! [N2: num] :
% 6.94/7.32 ( ( sqr @ ( bit1 @ N2 ) )
% 6.94/7.32 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N2 ) @ N2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % sqr.simps(3)
% 6.94/7.32 thf(fact_10100_Rep__unit,axiom,
% 6.94/7.32 ! [X: product_unit] : ( member_o @ ( product_Rep_unit @ X ) @ ( insert_o @ $true @ bot_bot_set_o ) ) ).
% 6.94/7.32
% 6.94/7.32 % Rep_unit
% 6.94/7.32 thf(fact_10101_Rep__unit__inject,axiom,
% 6.94/7.32 ! [X: product_unit,Y: product_unit] :
% 6.94/7.32 ( ( ( product_Rep_unit @ X )
% 6.94/7.32 = ( product_Rep_unit @ Y ) )
% 6.94/7.32 = ( X = Y ) ) ).
% 6.94/7.32
% 6.94/7.32 % Rep_unit_inject
% 6.94/7.32 thf(fact_10102_Rep__unit__induct,axiom,
% 6.94/7.32 ! [Y: $o,P2: $o > $o] :
% 6.94/7.32 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 6.94/7.32 => ( ! [X3: product_unit] : ( P2 @ ( product_Rep_unit @ X3 ) )
% 6.94/7.32 => ( P2 @ Y ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Rep_unit_induct
% 6.94/7.32 thf(fact_10103_Rep__unit__cases,axiom,
% 6.94/7.32 ! [Y: $o] :
% 6.94/7.32 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 6.94/7.32 => ~ ! [X3: product_unit] :
% 6.94/7.32 ( Y
% 6.94/7.32 = ( ~ ( product_Rep_unit @ X3 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Rep_unit_cases
% 6.94/7.32 thf(fact_10104_type__definition__unit,axiom,
% 6.94/7.32 type_d6188575255521822967unit_o @ product_Rep_unit @ product_Abs_unit @ ( insert_o @ $true @ bot_bot_set_o ) ).
% 6.94/7.32
% 6.94/7.32 % type_definition_unit
% 6.94/7.32 thf(fact_10105_Unity__def,axiom,
% 6.94/7.32 ( product_Unity
% 6.94/7.32 = ( product_Abs_unit @ $true ) ) ).
% 6.94/7.32
% 6.94/7.32 % Unity_def
% 6.94/7.32 thf(fact_10106_Rep__unit__inverse,axiom,
% 6.94/7.32 ! [X: product_unit] :
% 6.94/7.32 ( ( product_Abs_unit @ ( product_Rep_unit @ X ) )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 % Rep_unit_inverse
% 6.94/7.32 thf(fact_10107_Abs__unit__cases,axiom,
% 6.94/7.32 ! [X: product_unit] :
% 6.94/7.32 ~ ! [Y3: $o] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( product_Abs_unit @ Y3 ) )
% 6.94/7.32 => ~ ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Abs_unit_cases
% 6.94/7.32 thf(fact_10108_Abs__unit__induct,axiom,
% 6.94/7.32 ! [P2: product_unit > $o,X: product_unit] :
% 6.94/7.32 ( ! [Y3: $o] :
% 6.94/7.32 ( ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 6.94/7.32 => ( P2 @ ( product_Abs_unit @ Y3 ) ) )
% 6.94/7.32 => ( P2 @ X ) ) ).
% 6.94/7.32
% 6.94/7.32 % Abs_unit_induct
% 6.94/7.32 thf(fact_10109_Abs__unit__inject,axiom,
% 6.94/7.32 ! [X: $o,Y: $o] :
% 6.94/7.32 ( ( member_o @ X @ ( insert_o @ $true @ bot_bot_set_o ) )
% 6.94/7.32 => ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 6.94/7.32 => ( ( ( product_Abs_unit @ X )
% 6.94/7.32 = ( product_Abs_unit @ Y ) )
% 6.94/7.32 = ( X = Y ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Abs_unit_inject
% 6.94/7.32 thf(fact_10110_Abs__unit__inverse,axiom,
% 6.94/7.32 ! [Y: $o] :
% 6.94/7.32 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 6.94/7.32 => ( ( product_Rep_unit @ ( product_Abs_unit @ Y ) )
% 6.94/7.32 = Y ) ) ).
% 6.94/7.32
% 6.94/7.32 % Abs_unit_inverse
% 6.94/7.32 thf(fact_10111_plus__natural_Orep__eq,axiom,
% 6.94/7.32 ! [X: code_natural,Xa: code_natural] :
% 6.94/7.32 ( ( code_nat_of_natural @ ( plus_p4538020629002901425atural @ X @ Xa ) )
% 6.94/7.32 = ( plus_plus_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % plus_natural.rep_eq
% 6.94/7.32 thf(fact_10112_less__natural_Orep__eq,axiom,
% 6.94/7.32 ( ord_le5570908160329646204atural
% 6.94/7.32 = ( ^ [X4: code_natural,Xa2: code_natural] : ( ord_less_nat @ ( code_nat_of_natural @ X4 ) @ ( code_nat_of_natural @ Xa2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_natural.rep_eq
% 6.94/7.32 thf(fact_10113_less__eq__natural_Orep__eq,axiom,
% 6.94/7.32 ( ord_le1926595141338095240atural
% 6.94/7.32 = ( ^ [X4: code_natural,Xa2: code_natural] : ( ord_less_eq_nat @ ( code_nat_of_natural @ X4 ) @ ( code_nat_of_natural @ Xa2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_eq_natural.rep_eq
% 6.94/7.32 thf(fact_10114_plus__natural__def,axiom,
% 6.94/7.32 ( plus_p4538020629002901425atural
% 6.94/7.32 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ plus_plus_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % plus_natural_def
% 6.94/7.32 thf(fact_10115_less__natural__def,axiom,
% 6.94/7.32 ( ord_le5570908160329646204atural
% 6.94/7.32 = ( map_fu6256889081107267320ural_o @ code_nat_of_natural @ ( map_fu4892316939951275536at_o_o @ code_nat_of_natural @ id_o ) @ ord_less_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_natural_def
% 6.94/7.32 thf(fact_10116_less__eq__natural__def,axiom,
% 6.94/7.32 ( ord_le1926595141338095240atural
% 6.94/7.32 = ( map_fu6256889081107267320ural_o @ code_nat_of_natural @ ( map_fu4892316939951275536at_o_o @ code_nat_of_natural @ id_o ) @ ord_less_eq_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % less_eq_natural_def
% 6.94/7.32 thf(fact_10117_natural__decr,axiom,
% 6.94/7.32 ! [N2: code_natural] :
% 6.94/7.32 ( ( N2 != zero_z2226904508553997617atural )
% 6.94/7.32 => ( ord_less_nat @ ( minus_minus_nat @ ( code_nat_of_natural @ N2 ) @ ( suc @ zero_zero_nat ) ) @ ( code_nat_of_natural @ N2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % natural_decr
% 6.94/7.32 thf(fact_10118_eventually__sequentially__Suc,axiom,
% 6.94/7.32 ! [P2: nat > $o] :
% 6.94/7.32 ( ( eventually_nat
% 6.94/7.32 @ ^ [I: nat] : ( P2 @ ( suc @ I ) )
% 6.94/7.32 @ at_top_nat )
% 6.94/7.32 = ( eventually_nat @ P2 @ at_top_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % eventually_sequentially_Suc
% 6.94/7.32 thf(fact_10119_eventually__sequentially__seg,axiom,
% 6.94/7.32 ! [P2: nat > $o,K2: nat] :
% 6.94/7.32 ( ( eventually_nat
% 6.94/7.32 @ ^ [N: nat] : ( P2 @ ( plus_plus_nat @ N @ K2 ) )
% 6.94/7.32 @ at_top_nat )
% 6.94/7.32 = ( eventually_nat @ P2 @ at_top_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % eventually_sequentially_seg
% 6.94/7.32 thf(fact_10120_eventually__False__sequentially,axiom,
% 6.94/7.32 ~ ( eventually_nat
% 6.94/7.32 @ ^ [N: nat] : $false
% 6.94/7.32 @ at_top_nat ) ).
% 6.94/7.32
% 6.94/7.32 % eventually_False_sequentially
% 6.94/7.32 thf(fact_10121_eventually__sequentially,axiom,
% 6.94/7.32 ! [P2: nat > $o] :
% 6.94/7.32 ( ( eventually_nat @ P2 @ at_top_nat )
% 6.94/7.32 = ( ? [N8: nat] :
% 6.94/7.32 ! [N: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ N8 @ N )
% 6.94/7.32 => ( P2 @ N ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % eventually_sequentially
% 6.94/7.32 thf(fact_10122_eventually__sequentiallyI,axiom,
% 6.94/7.32 ! [C2: nat,P2: nat > $o] :
% 6.94/7.32 ( ! [X3: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ C2 @ X3 )
% 6.94/7.32 => ( P2 @ X3 ) )
% 6.94/7.32 => ( eventually_nat @ P2 @ at_top_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % eventually_sequentiallyI
% 6.94/7.32 thf(fact_10123_le__sequentially,axiom,
% 6.94/7.32 ! [F5: filter_nat] :
% 6.94/7.32 ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 6.94/7.32 = ( ! [N8: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N8 ) @ F5 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % le_sequentially
% 6.94/7.32 thf(fact_10124_natLeq__on__wo__rel,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( bNF_We3818239936649020644el_nat
% 6.94/7.32 @ ( collec3392354462482085612at_nat
% 6.94/7.32 @ ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( ( ord_less_nat @ X4 @ N2 )
% 6.94/7.32 & ( ord_less_nat @ Y4 @ N2 )
% 6.94/7.32 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % natLeq_on_wo_rel
% 6.94/7.32 thf(fact_10125_pair__lessI2,axiom,
% 6.94/7.32 ! [A: nat,B: nat,S2: nat,T6: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ A @ B )
% 6.94/7.32 => ( ( ord_less_nat @ S2 @ T6 )
% 6.94/7.32 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T6 ) ) @ fun_pair_less ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % pair_lessI2
% 6.94/7.32 thf(fact_10126_total__pair__less,axiom,
% 6.94/7.32 ! [A4: set_Pr1261947904930325089at_nat] : ( total_3592101749530773125at_nat @ A4 @ fun_pair_less ) ).
% 6.94/7.32
% 6.94/7.32 % total_pair_less
% 6.94/7.32 thf(fact_10127_trans__pair__less,axiom,
% 6.94/7.32 trans_4347625901269045472at_nat @ fun_pair_less ).
% 6.94/7.32
% 6.94/7.32 % trans_pair_less
% 6.94/7.32 thf(fact_10128_pair__less__iff1,axiom,
% 6.94/7.32 ! [X: nat,Y: nat,Z3: nat] :
% 6.94/7.32 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ X @ Z3 ) ) @ fun_pair_less )
% 6.94/7.32 = ( ord_less_nat @ Y @ Z3 ) ) ).
% 6.94/7.32
% 6.94/7.32 % pair_less_iff1
% 6.94/7.32 thf(fact_10129_wf__pair__less,axiom,
% 6.94/7.32 wf_Pro7803398752247294826at_nat @ fun_pair_less ).
% 6.94/7.32
% 6.94/7.32 % wf_pair_less
% 6.94/7.32 thf(fact_10130_pair__less__def,axiom,
% 6.94/7.32 ( fun_pair_less
% 6.94/7.32 = ( lex_prod_nat_nat @ less_than @ less_than ) ) ).
% 6.94/7.32
% 6.94/7.32 % pair_less_def
% 6.94/7.32 thf(fact_10131_pair__lessI1,axiom,
% 6.94/7.32 ! [A: nat,B: nat,S2: nat,T6: nat] :
% 6.94/7.32 ( ( ord_less_nat @ A @ B )
% 6.94/7.32 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T6 ) ) @ fun_pair_less ) ) ).
% 6.94/7.32
% 6.94/7.32 % pair_lessI1
% 6.94/7.32 thf(fact_10132_smin__insertI,axiom,
% 6.94/7.32 ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ X @ XS )
% 6.94/7.32 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 6.94/7.32 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_strict )
% 6.94/7.32 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_strict ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % smin_insertI
% 6.94/7.32 thf(fact_10133_pair__leqI2,axiom,
% 6.94/7.32 ! [A: nat,B: nat,S2: nat,T6: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ A @ B )
% 6.94/7.32 => ( ( ord_less_eq_nat @ S2 @ T6 )
% 6.94/7.32 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T6 ) ) @ fun_pair_leq ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % pair_leqI2
% 6.94/7.32 thf(fact_10134_pair__leq__def,axiom,
% 6.94/7.32 ( fun_pair_leq
% 6.94/7.32 = ( sup_su718114333110466843at_nat @ fun_pair_less @ id_Pro2258643101195443293at_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % pair_leq_def
% 6.94/7.32 thf(fact_10135_smin__emptyI,axiom,
% 6.94/7.32 ! [X7: set_Pr1261947904930325089at_nat] :
% 6.94/7.32 ( ( X7 != bot_bo2099793752762293965at_nat )
% 6.94/7.32 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X7 @ bot_bo2099793752762293965at_nat ) @ fun_min_strict ) ) ).
% 6.94/7.32
% 6.94/7.32 % smin_emptyI
% 6.94/7.32 thf(fact_10136_min__strict__def,axiom,
% 6.94/7.32 ( fun_min_strict
% 6.94/7.32 = ( min_ex6901939911449802026at_nat @ fun_pair_less ) ) ).
% 6.94/7.32
% 6.94/7.32 % min_strict_def
% 6.94/7.32 thf(fact_10137_pair__leqI1,axiom,
% 6.94/7.32 ! [A: nat,B: nat,S2: nat,T6: nat] :
% 6.94/7.32 ( ( ord_less_nat @ A @ B )
% 6.94/7.32 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T6 ) ) @ fun_pair_leq ) ) ).
% 6.94/7.32
% 6.94/7.32 % pair_leqI1
% 6.94/7.32 thf(fact_10138_wmax__insertI,axiom,
% 6.94/7.32 ! [Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ Y @ YS )
% 6.94/7.32 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 6.94/7.32 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_max_weak )
% 6.94/7.32 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ XS ) @ YS ) @ fun_max_weak ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % wmax_insertI
% 6.94/7.32 thf(fact_10139_wmin__insertI,axiom,
% 6.94/7.32 ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ X @ XS )
% 6.94/7.32 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 6.94/7.32 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_weak )
% 6.94/7.32 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_weak ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % wmin_insertI
% 6.94/7.32 thf(fact_10140_wmin__emptyI,axiom,
% 6.94/7.32 ! [X7: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X7 @ bot_bo2099793752762293965at_nat ) @ fun_min_weak ) ).
% 6.94/7.32
% 6.94/7.32 % wmin_emptyI
% 6.94/7.32 thf(fact_10141_wmax__emptyI,axiom,
% 6.94/7.32 ! [X7: set_Pr1261947904930325089at_nat] :
% 6.94/7.32 ( ( finite6177210948735845034at_nat @ X7 )
% 6.94/7.32 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ X7 ) @ fun_max_weak ) ) ).
% 6.94/7.32
% 6.94/7.32 % wmax_emptyI
% 6.94/7.32 thf(fact_10142_min__rpair__set,axiom,
% 6.94/7.32 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_min_strict @ fun_min_weak ) ).
% 6.94/7.32
% 6.94/7.32 % min_rpair_set
% 6.94/7.32 thf(fact_10143_min__weak__def,axiom,
% 6.94/7.32 ( fun_min_weak
% 6.94/7.32 = ( sup_su5525570899277871387at_nat @ ( min_ex6901939911449802026at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % min_weak_def
% 6.94/7.32 thf(fact_10144_max__weak__def,axiom,
% 6.94/7.32 ( fun_max_weak
% 6.94/7.32 = ( sup_su5525570899277871387at_nat @ ( max_ex8135407076693332796at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % max_weak_def
% 6.94/7.32 thf(fact_10145_smax__insertI,axiom,
% 6.94/7.32 ! [Y: product_prod_nat_nat,Y7: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,X7: set_Pr1261947904930325089at_nat] :
% 6.94/7.32 ( ( member8440522571783428010at_nat @ Y @ Y7 )
% 6.94/7.32 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 6.94/7.32 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X7 @ Y7 ) @ fun_max_strict )
% 6.94/7.32 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ X7 ) @ Y7 ) @ fun_max_strict ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % smax_insertI
% 6.94/7.32 thf(fact_10146_max__strict__def,axiom,
% 6.94/7.32 ( fun_max_strict
% 6.94/7.32 = ( max_ex8135407076693332796at_nat @ fun_pair_less ) ) ).
% 6.94/7.32
% 6.94/7.32 % max_strict_def
% 6.94/7.32 thf(fact_10147_max__rpair__set,axiom,
% 6.94/7.32 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_max_strict @ fun_max_weak ) ).
% 6.94/7.32
% 6.94/7.32 % max_rpair_set
% 6.94/7.32 thf(fact_10148_smax__emptyI,axiom,
% 6.94/7.32 ! [Y7: set_Pr1261947904930325089at_nat] :
% 6.94/7.32 ( ( finite6177210948735845034at_nat @ Y7 )
% 6.94/7.32 => ( ( Y7 != bot_bo2099793752762293965at_nat )
% 6.94/7.32 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ Y7 ) @ fun_max_strict ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % smax_emptyI
% 6.94/7.32 thf(fact_10149_division__segment__int__def,axiom,
% 6.94/7.32 ( euclid3395696857347342551nt_int
% 6.94/7.32 = ( ^ [K3: int] : ( if_int @ ( ord_less_eq_int @ zero_zero_int @ K3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % division_segment_int_def
% 6.94/7.32 thf(fact_10150_smsI,axiom,
% 6.94/7.32 ! [A4: multis2468970476368604999at_nat,B5: multis2468970476368604999at_nat,Z5: multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A4 ) @ ( set_ms8126754132646256062at_nat @ B5 ) ) @ fun_max_strict )
% 6.94/7.32 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z5 @ A4 ) @ ( plus_p7104986032573967614at_nat @ Z5 @ B5 ) ) @ ms_strict ) ) ).
% 6.94/7.32
% 6.94/7.32 % smsI
% 6.94/7.32 thf(fact_10151_wmsI,axiom,
% 6.94/7.32 ! [A4: multis2468970476368604999at_nat,B5: multis2468970476368604999at_nat,Z5: multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A4 ) @ ( set_ms8126754132646256062at_nat @ B5 ) ) @ fun_max_strict )
% 6.94/7.32 | ( ( A4 = zero_z1048942125864253310at_nat )
% 6.94/7.32 & ( B5 = zero_z1048942125864253310at_nat ) ) )
% 6.94/7.32 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z5 @ A4 ) @ ( plus_p7104986032573967614at_nat @ Z5 @ B5 ) ) @ ms_weak ) ) ).
% 6.94/7.32
% 6.94/7.32 % wmsI
% 6.94/7.32 thf(fact_10152_ms__weak__def,axiom,
% 6.94/7.32 ( ms_weak
% 6.94/7.32 = ( sup_su3035147773818789531at_nat @ ms_strict @ id_mul2649389997224486051at_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % ms_weak_def
% 6.94/7.32 thf(fact_10153_ms__weakI1,axiom,
% 6.94/7.32 ! [Z5: multis2468970476368604999at_nat,Z9: multis2468970476368604999at_nat,A4: multis2468970476368604999at_nat,B5: multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( pw_leq @ Z5 @ Z9 )
% 6.94/7.32 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A4 ) @ ( set_ms8126754132646256062at_nat @ B5 ) ) @ fun_max_strict )
% 6.94/7.32 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z5 @ A4 ) @ ( plus_p7104986032573967614at_nat @ Z9 @ B5 ) ) @ ms_weak ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % ms_weakI1
% 6.94/7.32 thf(fact_10154_ms__strictI,axiom,
% 6.94/7.32 ! [Z5: multis2468970476368604999at_nat,Z9: multis2468970476368604999at_nat,A4: multis2468970476368604999at_nat,B5: multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( pw_leq @ Z5 @ Z9 )
% 6.94/7.32 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A4 ) @ ( set_ms8126754132646256062at_nat @ B5 ) ) @ fun_max_strict )
% 6.94/7.32 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z5 @ A4 ) @ ( plus_p7104986032573967614at_nat @ Z9 @ B5 ) ) @ ms_strict ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % ms_strictI
% 6.94/7.32 thf(fact_10155_pw__leq_Ocases,axiom,
% 6.94/7.32 ! [A1: multis2468970476368604999at_nat,A23: multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( pw_leq @ A1 @ A23 )
% 6.94/7.32 => ( ( ( A1 = zero_z1048942125864253310at_nat )
% 6.94/7.32 => ( A23 != zero_z1048942125864253310at_nat ) )
% 6.94/7.32 => ~ ! [X3: product_prod_nat_nat,Y3: product_prod_nat_nat,X14: multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( A1
% 6.94/7.32 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X3 @ zero_z1048942125864253310at_nat ) @ X14 ) )
% 6.94/7.32 => ! [Y10: multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( A23
% 6.94/7.32 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y3 @ zero_z1048942125864253310at_nat ) @ Y10 ) )
% 6.94/7.32 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ fun_pair_leq )
% 6.94/7.32 => ~ ( pw_leq @ X14 @ Y10 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % pw_leq.cases
% 6.94/7.32 thf(fact_10156_pw__leq_Osimps,axiom,
% 6.94/7.32 ( pw_leq
% 6.94/7.32 = ( ^ [A12: multis2468970476368604999at_nat,A22: multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( ( A12 = zero_z1048942125864253310at_nat )
% 6.94/7.32 & ( A22 = zero_z1048942125864253310at_nat ) )
% 6.94/7.32 | ? [X4: product_prod_nat_nat,Y4: product_prod_nat_nat,X11: multis2468970476368604999at_nat,Y11: multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( A12
% 6.94/7.32 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X4 @ zero_z1048942125864253310at_nat ) @ X11 ) )
% 6.94/7.32 & ( A22
% 6.94/7.32 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y4 @ zero_z1048942125864253310at_nat ) @ Y11 ) )
% 6.94/7.32 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y4 ) @ fun_pair_leq )
% 6.94/7.32 & ( pw_leq @ X11 @ Y11 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % pw_leq.simps
% 6.94/7.32 thf(fact_10157_pw__leq__step,axiom,
% 6.94/7.32 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,X7: multis2468970476368604999at_nat,Y7: multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 6.94/7.32 => ( ( pw_leq @ X7 @ Y7 )
% 6.94/7.32 => ( pw_leq @ ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X @ zero_z1048942125864253310at_nat ) @ X7 ) @ ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y @ zero_z1048942125864253310at_nat ) @ Y7 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % pw_leq_step
% 6.94/7.32 thf(fact_10158_ms__weakI2,axiom,
% 6.94/7.32 ! [Z5: multis2468970476368604999at_nat,Z9: multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( pw_leq @ Z5 @ Z9 )
% 6.94/7.32 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z5 @ zero_z1048942125864253310at_nat ) @ ( plus_p7104986032573967614at_nat @ Z9 @ zero_z1048942125864253310at_nat ) ) @ ms_weak ) ) ).
% 6.94/7.32
% 6.94/7.32 % ms_weakI2
% 6.94/7.32 thf(fact_10159_pw__leq__split,axiom,
% 6.94/7.32 ! [X7: multis2468970476368604999at_nat,Y7: multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( pw_leq @ X7 @ Y7 )
% 6.94/7.32 => ? [A9: multis2468970476368604999at_nat,B9: multis2468970476368604999at_nat,Z10: multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( X7
% 6.94/7.32 = ( plus_p7104986032573967614at_nat @ A9 @ Z10 ) )
% 6.94/7.32 & ( Y7
% 6.94/7.32 = ( plus_p7104986032573967614at_nat @ B9 @ Z10 ) )
% 6.94/7.32 & ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A9 ) @ ( set_ms8126754132646256062at_nat @ B9 ) ) @ fun_max_strict )
% 6.94/7.32 | ( ( B9 = zero_z1048942125864253310at_nat )
% 6.94/7.32 & ( A9 = zero_z1048942125864253310at_nat ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % pw_leq_split
% 6.94/7.32 thf(fact_10160_bdd__above__nat,axiom,
% 6.94/7.32 condit2214826472909112428ve_nat = finite_finite_nat ).
% 6.94/7.32
% 6.94/7.32 % bdd_above_nat
% 6.94/7.32 thf(fact_10161_natLeq__on__well__order__on,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( order_2888998067076097458on_nat
% 6.94/7.32 @ ( collect_nat
% 6.94/7.32 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N2 ) )
% 6.94/7.32 @ ( collec3392354462482085612at_nat
% 6.94/7.32 @ ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( ( ord_less_nat @ X4 @ N2 )
% 6.94/7.32 & ( ord_less_nat @ Y4 @ N2 )
% 6.94/7.32 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % natLeq_on_well_order_on
% 6.94/7.32 thf(fact_10162_natLeq__on__Well__order,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( order_2888998067076097458on_nat
% 6.94/7.32 @ ( field_nat
% 6.94/7.32 @ ( collec3392354462482085612at_nat
% 6.94/7.32 @ ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( ( ord_less_nat @ X4 @ N2 )
% 6.94/7.32 & ( ord_less_nat @ Y4 @ N2 )
% 6.94/7.32 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) )
% 6.94/7.32 @ ( collec3392354462482085612at_nat
% 6.94/7.32 @ ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( ( ord_less_nat @ X4 @ N2 )
% 6.94/7.32 & ( ord_less_nat @ Y4 @ N2 )
% 6.94/7.32 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % natLeq_on_Well_order
% 6.94/7.32 thf(fact_10163_natLeq__Card__order,axiom,
% 6.94/7.32 bNF_Ca1281551314933786834on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 6.94/7.32
% 6.94/7.32 % natLeq_Card_order
% 6.94/7.32 thf(fact_10164_natLeq__antisym,axiom,
% 6.94/7.32 antisym_nat @ bNF_Ca8665028551170535155natLeq ).
% 6.94/7.32
% 6.94/7.32 % natLeq_antisym
% 6.94/7.32 thf(fact_10165_natLeq__natLess__Id,axiom,
% 6.94/7.32 ( bNF_Ca8459412986667044542atLess
% 6.94/7.32 = ( minus_1356011639430497352at_nat @ bNF_Ca8665028551170535155natLeq @ id_nat2 ) ) ).
% 6.94/7.32
% 6.94/7.32 % natLeq_natLess_Id
% 6.94/7.32 thf(fact_10166_natLeq__trans,axiom,
% 6.94/7.32 trans_nat @ bNF_Ca8665028551170535155natLeq ).
% 6.94/7.32
% 6.94/7.32 % natLeq_trans
% 6.94/7.32 thf(fact_10167_natLeq__underS__less,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 )
% 6.94/7.32 = ( collect_nat
% 6.94/7.32 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % natLeq_underS_less
% 6.94/7.32 thf(fact_10168_natLeq__Total,axiom,
% 6.94/7.32 total_on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 6.94/7.32
% 6.94/7.32 % natLeq_Total
% 6.94/7.32 thf(fact_10169_natLeq__Linear__order,axiom,
% 6.94/7.32 order_4473980167227706203on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 6.94/7.32
% 6.94/7.32 % natLeq_Linear_order
% 6.94/7.32 thf(fact_10170_natLeq__Preorder,axiom,
% 6.94/7.32 order_4861654808422542329on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 6.94/7.32
% 6.94/7.32 % natLeq_Preorder
% 6.94/7.32 thf(fact_10171_natLeq__Refl,axiom,
% 6.94/7.32 refl_on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 6.94/7.32
% 6.94/7.32 % natLeq_Refl
% 6.94/7.32 thf(fact_10172_Field__natLeq,axiom,
% 6.94/7.32 ( ( field_nat @ bNF_Ca8665028551170535155natLeq )
% 6.94/7.32 = top_top_set_nat ) ).
% 6.94/7.32
% 6.94/7.32 % Field_natLeq
% 6.94/7.32 thf(fact_10173_natLeq__def,axiom,
% 6.94/7.32 ( bNF_Ca8665028551170535155natLeq
% 6.94/7.32 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % natLeq_def
% 6.94/7.32 thf(fact_10174_natLeq__Well__order,axiom,
% 6.94/7.32 order_2888998067076097458on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 6.94/7.32
% 6.94/7.32 % natLeq_Well_order
% 6.94/7.32 thf(fact_10175_Restr__natLeq2,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 6.94/7.32 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 )
% 6.94/7.32 @ ^ [Uu2: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 ) ) )
% 6.94/7.32 = ( collec3392354462482085612at_nat
% 6.94/7.32 @ ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( ( ord_less_nat @ X4 @ N2 )
% 6.94/7.32 & ( ord_less_nat @ Y4 @ N2 )
% 6.94/7.32 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Restr_natLeq2
% 6.94/7.32 thf(fact_10176_Restr__natLeq,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 6.94/7.32 @ ( produc457027306803732586at_nat
% 6.94/7.32 @ ( collect_nat
% 6.94/7.32 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N2 ) )
% 6.94/7.32 @ ^ [Uu2: nat] :
% 6.94/7.32 ( collect_nat
% 6.94/7.32 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N2 ) ) ) )
% 6.94/7.32 = ( collec3392354462482085612at_nat
% 6.94/7.32 @ ( produc6081775807080527818_nat_o
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] :
% 6.94/7.32 ( ( ord_less_nat @ X4 @ N2 )
% 6.94/7.32 & ( ord_less_nat @ Y4 @ N2 )
% 6.94/7.32 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Restr_natLeq
% 6.94/7.32 thf(fact_10177_card__of__nat,axiom,
% 6.94/7.32 member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ top_top_set_nat ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 6.94/7.32
% 6.94/7.32 % card_of_nat
% 6.94/7.32 thf(fact_10178_card__of__Field__natLeq,axiom,
% 6.94/7.32 member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 6.94/7.32
% 6.94/7.32 % card_of_Field_natLeq
% 6.94/7.32 thf(fact_10179_eventually__prod__sequentially,axiom,
% 6.94/7.32 ! [P2: product_prod_nat_nat > $o] :
% 6.94/7.32 ( ( eventu1038000079068216329at_nat @ P2 @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 6.94/7.32 = ( ? [N8: nat] :
% 6.94/7.32 ! [M3: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ N8 @ M3 )
% 6.94/7.32 => ! [N: nat] :
% 6.94/7.32 ( ( ord_less_eq_nat @ N8 @ N )
% 6.94/7.32 => ( P2 @ ( product_Pair_nat_nat @ N @ M3 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % eventually_prod_sequentially
% 6.94/7.32 thf(fact_10180_prod__decode__triangle__add,axiom,
% 6.94/7.32 ! [K2: nat,M: nat] :
% 6.94/7.32 ( ( nat_prod_decode @ ( plus_plus_nat @ ( nat_triangle @ K2 ) @ M ) )
% 6.94/7.32 = ( nat_prod_decode_aux @ K2 @ M ) ) ).
% 6.94/7.32
% 6.94/7.32 % prod_decode_triangle_add
% 6.94/7.32 thf(fact_10181_list__decode_Oelims,axiom,
% 6.94/7.32 ! [X: nat,Y: list_nat] :
% 6.94/7.32 ( ( ( nat_list_decode @ X )
% 6.94/7.32 = Y )
% 6.94/7.32 => ( ( ( X = zero_zero_nat )
% 6.94/7.32 => ( Y != nil_nat ) )
% 6.94/7.32 => ~ ! [N5: nat] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( suc @ N5 ) )
% 6.94/7.32 => ( Y
% 6.94/7.32 != ( produc2761476792215241774st_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 6.94/7.32 @ ( nat_prod_decode @ N5 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % list_decode.elims
% 6.94/7.32 thf(fact_10182_list__decode_Osimps_I2_J,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( nat_list_decode @ ( suc @ N2 ) )
% 6.94/7.32 = ( produc2761476792215241774st_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 6.94/7.32 @ ( nat_prod_decode @ N2 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % list_decode.simps(2)
% 6.94/7.32 thf(fact_10183_list__decode_Opelims,axiom,
% 6.94/7.32 ! [X: nat,Y: list_nat] :
% 6.94/7.32 ( ( ( nat_list_decode @ X )
% 6.94/7.32 = Y )
% 6.94/7.32 => ( ( accp_nat @ nat_list_decode_rel @ X )
% 6.94/7.32 => ( ( ( X = zero_zero_nat )
% 6.94/7.32 => ( ( Y = nil_nat )
% 6.94/7.32 => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 6.94/7.32 => ~ ! [N5: nat] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( suc @ N5 ) )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( produc2761476792215241774st_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 6.94/7.32 @ ( nat_prod_decode @ N5 ) ) )
% 6.94/7.32 => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N5 ) ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % list_decode.pelims
% 6.94/7.32 thf(fact_10184_list__decode_Opsimps_I2_J,axiom,
% 6.94/7.32 ! [N2: nat] :
% 6.94/7.32 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N2 ) )
% 6.94/7.32 => ( ( nat_list_decode @ ( suc @ N2 ) )
% 6.94/7.32 = ( produc2761476792215241774st_nat
% 6.94/7.32 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 6.94/7.32 @ ( nat_prod_decode @ N2 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % list_decode.psimps(2)
% 6.94/7.32 thf(fact_10185_rat_Odomain,axiom,
% 6.94/7.32 ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 6.94/7.32 = ( ^ [X4: product_prod_int_int] :
% 6.94/7.32 ? [Y4: product_prod_int_int] :
% 6.94/7.32 ( ( basic_4387203522000727145nt_int
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ X4
% 6.94/7.32 @ Y4 )
% 6.94/7.32 & ( ratrel @ Y4 @ Y4 ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % rat.domain
% 6.94/7.32 thf(fact_10186_int_Oid__abs__transfer,axiom,
% 6.94/7.32 ( bNF_re7934895593101944656at_int
% 6.94/7.32 @ ( basic_5328504652464829177at_nat
% 6.94/7.32 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 6.94/7.32 @ pcr_int
% 6.94/7.32 @ ^ [X4: product_prod_nat_nat] : X4
% 6.94/7.32 @ abs_Integ ) ).
% 6.94/7.32
% 6.94/7.32 % int.id_abs_transfer
% 6.94/7.32 thf(fact_10187_rat_Odomain__par__left__total,axiom,
% 6.94/7.32 ! [P6: product_prod_int_int > $o] :
% 6.94/7.32 ( ( left_t3131394472396969446nt_int
% 6.94/7.32 @ ( basic_4387203522000727145nt_int
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) ) )
% 6.94/7.32 => ( ( bNF_re8699439704749558557nt_o_o
% 6.94/7.32 @ ( basic_4387203522000727145nt_int
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 6.94/7.32 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 )
% 6.94/7.32 @ P6
% 6.94/7.32 @ ^ [X4: product_prod_int_int] : ( ratrel @ X4 @ X4 ) )
% 6.94/7.32 => ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 6.94/7.32 = P6 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % rat.domain_par_left_total
% 6.94/7.32 thf(fact_10188_rat_Odomain__par,axiom,
% 6.94/7.32 ! [DR1: int > $o,DR2: int > $o,P22: product_prod_int_int > $o] :
% 6.94/7.32 ( ( ( domainp_int_int
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 6.94/7.32 = DR1 )
% 6.94/7.32 => ( ( ( domainp_int_int
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 6.94/7.32 = DR2 )
% 6.94/7.32 => ( ( bNF_re8699439704749558557nt_o_o
% 6.94/7.32 @ ( basic_4387203522000727145nt_int
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 6.94/7.32 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 6.94/7.32 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 )
% 6.94/7.32 @ P22
% 6.94/7.32 @ ^ [X4: product_prod_int_int] : ( ratrel @ X4 @ X4 ) )
% 6.94/7.32 => ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 6.94/7.32 = ( inf_in3604695632404883862_int_o @ ( basic_1567116559311922317nt_int @ DR1 @ DR2 ) @ P22 ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % rat.domain_par
% 6.94/7.32 thf(fact_10189_Abs__rat__cases,axiom,
% 6.94/7.32 ! [X: rat] :
% 6.94/7.32 ~ ! [Y3: set_Pr958786334691620121nt_int] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( abs_rat @ Y3 ) )
% 6.94/7.32 => ~ ( member2340774599025711042nt_int @ Y3
% 6.94/7.32 @ ( collec5210948495886036740nt_int
% 6.94/7.32 @ ^ [C3: set_Pr958786334691620121nt_int] :
% 6.94/7.32 ? [X4: product_prod_int_int] :
% 6.94/7.32 ( ( ratrel @ X4 @ X4 )
% 6.94/7.32 & ( C3
% 6.94/7.32 = ( collec213857154873943460nt_int @ ( ratrel @ X4 ) ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Abs_rat_cases
% 6.94/7.32 thf(fact_10190_Abs__rat__induct,axiom,
% 6.94/7.32 ! [P2: rat > $o,X: rat] :
% 6.94/7.32 ( ! [Y3: set_Pr958786334691620121nt_int] :
% 6.94/7.32 ( ( member2340774599025711042nt_int @ Y3
% 6.94/7.32 @ ( collec5210948495886036740nt_int
% 6.94/7.32 @ ^ [C3: set_Pr958786334691620121nt_int] :
% 6.94/7.32 ? [X4: product_prod_int_int] :
% 6.94/7.32 ( ( ratrel @ X4 @ X4 )
% 6.94/7.32 & ( C3
% 6.94/7.32 = ( collec213857154873943460nt_int @ ( ratrel @ X4 ) ) ) ) ) )
% 6.94/7.32 => ( P2 @ ( abs_rat @ Y3 ) ) )
% 6.94/7.32 => ( P2 @ X ) ) ).
% 6.94/7.32
% 6.94/7.32 % Abs_rat_induct
% 6.94/7.32 thf(fact_10191_Abs__rat__inject,axiom,
% 6.94/7.32 ! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
% 6.94/7.32 ( ( member2340774599025711042nt_int @ X
% 6.94/7.32 @ ( collec5210948495886036740nt_int
% 6.94/7.32 @ ^ [C3: set_Pr958786334691620121nt_int] :
% 6.94/7.32 ? [X4: product_prod_int_int] :
% 6.94/7.32 ( ( ratrel @ X4 @ X4 )
% 6.94/7.32 & ( C3
% 6.94/7.32 = ( collec213857154873943460nt_int @ ( ratrel @ X4 ) ) ) ) ) )
% 6.94/7.32 => ( ( member2340774599025711042nt_int @ Y
% 6.94/7.32 @ ( collec5210948495886036740nt_int
% 6.94/7.32 @ ^ [C3: set_Pr958786334691620121nt_int] :
% 6.94/7.32 ? [X4: product_prod_int_int] :
% 6.94/7.32 ( ( ratrel @ X4 @ X4 )
% 6.94/7.32 & ( C3
% 6.94/7.32 = ( collec213857154873943460nt_int @ ( ratrel @ X4 ) ) ) ) ) )
% 6.94/7.32 => ( ( ( abs_rat @ X )
% 6.94/7.32 = ( abs_rat @ Y ) )
% 6.94/7.32 = ( X = Y ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Abs_rat_inject
% 6.94/7.32 thf(fact_10192_Abs__rat__inverse,axiom,
% 6.94/7.32 ! [Y: set_Pr958786334691620121nt_int] :
% 6.94/7.32 ( ( member2340774599025711042nt_int @ Y
% 6.94/7.32 @ ( collec5210948495886036740nt_int
% 6.94/7.32 @ ^ [C3: set_Pr958786334691620121nt_int] :
% 6.94/7.32 ? [X4: product_prod_int_int] :
% 6.94/7.32 ( ( ratrel @ X4 @ X4 )
% 6.94/7.32 & ( C3
% 6.94/7.32 = ( collec213857154873943460nt_int @ ( ratrel @ X4 ) ) ) ) ) )
% 6.94/7.32 => ( ( rep_rat @ ( abs_rat @ Y ) )
% 6.94/7.32 = Y ) ) ).
% 6.94/7.32
% 6.94/7.32 % Abs_rat_inverse
% 6.94/7.32 thf(fact_10193_type__definition__rat,axiom,
% 6.94/7.32 ( type_d8554052265237484179nt_int @ rep_rat @ abs_rat
% 6.94/7.32 @ ( collec5210948495886036740nt_int
% 6.94/7.32 @ ^ [C3: set_Pr958786334691620121nt_int] :
% 6.94/7.32 ? [X4: product_prod_int_int] :
% 6.94/7.32 ( ( ratrel @ X4 @ X4 )
% 6.94/7.32 & ( C3
% 6.94/7.32 = ( collec213857154873943460nt_int @ ( ratrel @ X4 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % type_definition_rat
% 6.94/7.32 thf(fact_10194_Rep__rat,axiom,
% 6.94/7.32 ! [X: rat] :
% 6.94/7.32 ( member2340774599025711042nt_int @ ( rep_rat @ X )
% 6.94/7.32 @ ( collec5210948495886036740nt_int
% 6.94/7.32 @ ^ [C3: set_Pr958786334691620121nt_int] :
% 6.94/7.32 ? [X4: product_prod_int_int] :
% 6.94/7.32 ( ( ratrel @ X4 @ X4 )
% 6.94/7.32 & ( C3
% 6.94/7.32 = ( collec213857154873943460nt_int @ ( ratrel @ X4 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Rep_rat
% 6.94/7.32 thf(fact_10195_Rep__rat__cases,axiom,
% 6.94/7.32 ! [Y: set_Pr958786334691620121nt_int] :
% 6.94/7.32 ( ( member2340774599025711042nt_int @ Y
% 6.94/7.32 @ ( collec5210948495886036740nt_int
% 6.94/7.32 @ ^ [C3: set_Pr958786334691620121nt_int] :
% 6.94/7.32 ? [X4: product_prod_int_int] :
% 6.94/7.32 ( ( ratrel @ X4 @ X4 )
% 6.94/7.32 & ( C3
% 6.94/7.32 = ( collec213857154873943460nt_int @ ( ratrel @ X4 ) ) ) ) ) )
% 6.94/7.32 => ~ ! [X3: rat] :
% 6.94/7.32 ( Y
% 6.94/7.32 != ( rep_rat @ X3 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Rep_rat_cases
% 6.94/7.32 thf(fact_10196_Rep__rat__induct,axiom,
% 6.94/7.32 ! [Y: set_Pr958786334691620121nt_int,P2: set_Pr958786334691620121nt_int > $o] :
% 6.94/7.32 ( ( member2340774599025711042nt_int @ Y
% 6.94/7.32 @ ( collec5210948495886036740nt_int
% 6.94/7.32 @ ^ [C3: set_Pr958786334691620121nt_int] :
% 6.94/7.32 ? [X4: product_prod_int_int] :
% 6.94/7.32 ( ( ratrel @ X4 @ X4 )
% 6.94/7.32 & ( C3
% 6.94/7.32 = ( collec213857154873943460nt_int @ ( ratrel @ X4 ) ) ) ) ) )
% 6.94/7.32 => ( ! [X3: rat] : ( P2 @ ( rep_rat @ X3 ) )
% 6.94/7.32 => ( P2 @ Y ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % Rep_rat_induct
% 6.94/7.32 thf(fact_10197_one__assn__def,axiom,
% 6.94/7.32 ( one_one_assn
% 6.94/7.32 = ( abs_assn @ one_assn_raw ) ) ).
% 6.94/7.32
% 6.94/7.32 % one_assn_def
% 6.94/7.32 thf(fact_10198_natLeq__Partial__order,axiom,
% 6.94/7.32 order_5251275573222108571on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 6.94/7.32
% 6.94/7.32 % natLeq_Partial_order
% 6.94/7.32 thf(fact_10199_one__assn__raw_Osimps,axiom,
% 6.94/7.32 ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.94/7.32 ( ( one_assn_raw @ ( produc7507926704131184380et_nat @ H @ As ) )
% 6.94/7.32 = ( As = bot_bot_set_nat ) ) ).
% 6.94/7.32
% 6.94/7.32 % one_assn_raw.simps
% 6.94/7.32 thf(fact_10200_one__assn__raw_Oelims_I1_J,axiom,
% 6.94/7.32 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 6.94/7.32 ( ( ( one_assn_raw @ X )
% 6.94/7.32 = Y )
% 6.94/7.32 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.94/7.32 => ( Y
% 6.94/7.32 = ( As2 != bot_bot_set_nat ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % one_assn_raw.elims(1)
% 6.94/7.32 thf(fact_10201_one__assn__raw_Oelims_I2_J,axiom,
% 6.94/7.32 ! [X: produc3658429121746597890et_nat] :
% 6.94/7.32 ( ( one_assn_raw @ X )
% 6.94/7.32 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.94/7.32 => ( As2 != bot_bot_set_nat ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % one_assn_raw.elims(2)
% 6.94/7.32 thf(fact_10202_one__assn__raw_Oelims_I3_J,axiom,
% 6.94/7.32 ! [X: produc3658429121746597890et_nat] :
% 6.94/7.32 ( ~ ( one_assn_raw @ X )
% 6.94/7.32 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.94/7.32 => ( As2 = bot_bot_set_nat ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % one_assn_raw.elims(3)
% 6.94/7.32 thf(fact_10203_one__assn__raw_Opelims_I3_J,axiom,
% 6.94/7.32 ! [X: produc3658429121746597890et_nat] :
% 6.94/7.32 ( ~ ( one_assn_raw @ X )
% 6.94/7.32 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 6.94/7.32 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.94/7.32 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.94/7.32 => ( As2 = bot_bot_set_nat ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % one_assn_raw.pelims(3)
% 6.94/7.32 thf(fact_10204_one__assn__raw_Opelims_I2_J,axiom,
% 6.94/7.32 ! [X: produc3658429121746597890et_nat] :
% 6.94/7.32 ( ( one_assn_raw @ X )
% 6.94/7.32 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 6.94/7.32 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.94/7.32 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.94/7.32 => ( As2 != bot_bot_set_nat ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % one_assn_raw.pelims(2)
% 6.94/7.32 thf(fact_10205_one__assn__raw_Opelims_I1_J,axiom,
% 6.94/7.32 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 6.94/7.32 ( ( ( one_assn_raw @ X )
% 6.94/7.32 = Y )
% 6.94/7.32 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 6.94/7.32 => ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.94/7.32 ( ( X
% 6.94/7.32 = ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 6.94/7.32 => ( ( Y
% 6.94/7.32 = ( As2 = bot_bot_set_nat ) )
% 6.94/7.32 => ~ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % one_assn_raw.pelims(1)
% 6.94/7.32 thf(fact_10206_integer__of__char__code,axiom,
% 6.94/7.32 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 6.94/7.32 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 6.94/7.32 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ B72 ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B62 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B52 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B42 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B32 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B22 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B1 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B0 ) ) ) ).
% 6.94/7.32
% 6.94/7.32 % integer_of_char_code
% 6.94/7.32
% 6.94/7.32 % Helper facts (59)
% 6.94/7.32 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 6.94/7.32 ! [X: int,Y: int] :
% 6.94/7.32 ( ( if_int @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 6.94/7.32 ! [X: int,Y: int] :
% 6.94/7.32 ( ( if_int @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 6.94/7.32 ! [X: nat,Y: nat] :
% 6.94/7.32 ( ( if_nat @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 6.94/7.32 ! [X: nat,Y: nat] :
% 6.94/7.32 ( ( if_nat @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 6.94/7.32 ! [X: num,Y: num] :
% 6.94/7.32 ( ( if_num @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 6.94/7.32 ! [X: num,Y: num] :
% 6.94/7.32 ( ( if_num @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 6.94/7.32 ! [X: rat,Y: rat] :
% 6.94/7.32 ( ( if_rat @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 6.94/7.32 ! [X: rat,Y: rat] :
% 6.94/7.32 ( ( if_rat @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Assertions__Oassn_T,axiom,
% 6.94/7.32 ! [X: assn,Y: assn] :
% 6.94/7.32 ( ( if_assn @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Assertions__Oassn_T,axiom,
% 6.94/7.32 ! [X: assn,Y: assn] :
% 6.94/7.32 ( ( if_assn @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 6.94/7.32 ! [X: code_integer,Y: code_integer] :
% 6.94/7.32 ( ( if_Code_integer @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 6.94/7.32 ! [X: code_integer,Y: code_integer] :
% 6.94/7.32 ( ( if_Code_integer @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 6.94/7.32 ! [X: code_natural,Y: code_natural] :
% 6.94/7.32 ( ( if_Code_natural @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 6.94/7.32 ! [X: code_natural,Y: code_natural] :
% 6.94/7.32 ( ( if_Code_natural @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 6.94/7.32 ! [X: set_int,Y: set_int] :
% 6.94/7.32 ( ( if_set_int @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 6.94/7.32 ! [X: set_int,Y: set_int] :
% 6.94/7.32 ( ( if_set_int @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 6.94/7.32 ! [X: list_int,Y: list_int] :
% 6.94/7.32 ( ( if_list_int @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 6.94/7.32 ! [X: list_int,Y: list_int] :
% 6.94/7.32 ( ( if_list_int @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 6.94/7.32 ! [X: list_nat,Y: list_nat] :
% 6.94/7.32 ( ( if_list_nat @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 6.94/7.32 ! [X: list_nat,Y: list_nat] :
% 6.94/7.32 ( ( if_list_nat @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 6.94/7.32 ! [X: int > int,Y: int > int] :
% 6.94/7.32 ( ( if_int_int @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 6.94/7.32 ! [X: int > int,Y: int > int] :
% 6.94/7.32 ( ( if_int_int @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_I_Eo_J_J_T,axiom,
% 6.94/7.32 ! [X: option_set_o,Y: option_set_o] :
% 6.94/7.32 ( ( if_option_set_o @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_I_Eo_J_J_T,axiom,
% 6.94/7.32 ! [X: option_set_o,Y: option_set_o] :
% 6.94/7.32 ( ( if_option_set_o @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J_T,axiom,
% 6.94/7.32 ! [X: option_set_int,Y: option_set_int] :
% 6.94/7.32 ( ( if_option_set_int @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J_T,axiom,
% 6.94/7.32 ! [X: option_set_int,Y: option_set_int] :
% 6.94/7.32 ( ( if_option_set_int @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_T,axiom,
% 6.94/7.32 ! [X: option_set_nat,Y: option_set_nat] :
% 6.94/7.32 ( ( if_option_set_nat @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_T,axiom,
% 6.94/7.32 ! [X: option_set_nat,Y: option_set_nat] :
% 6.94/7.32 ( ( if_option_set_nat @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 6.94/7.32 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 6.94/7.32 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 6.94/7.32 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 6.94/7.32 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 6.94/7.32 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 6.94/7.32 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 6.94/7.32 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 6.94/7.32 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 6.94/7.32 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 6.94/7.32 ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 6.94/7.32 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 6.94/7.32 ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 6.94/7.32 ! [X: int > product_prod_int_int,Y: int > product_prod_int_int] :
% 6.94/7.32 ( ( if_int2409958687428134794nt_int @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 6.94/7.32 ! [X: int > product_prod_int_int,Y: int > product_prod_int_int] :
% 6.94/7.32 ( ( if_int2409958687428134794nt_int @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 6.94/7.32 ! [X: multis2468970476368604999at_nat,Y: multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( if_mul8430962117462786573at_nat @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 6.94/7.32 ! [X: multis2468970476368604999at_nat,Y: multis2468970476368604999at_nat] :
% 6.94/7.32 ( ( if_mul8430962117462786573at_nat @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.94/7.32 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.94/7.32 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.94/7.32 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.94/7.32 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 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,
% 6.94/7.32 ! [X: option8963830502488799655at_nat,Y: option8963830502488799655at_nat] :
% 6.94/7.32 ( ( if_opt7704869406773131885at_nat @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 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,
% 6.94/7.32 ! [X: option8963830502488799655at_nat,Y: option8963830502488799655at_nat] :
% 6.94/7.32 ( ( if_opt7704869406773131885at_nat @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 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,
% 6.94/7.32 ! [X: option3562590408128118217it_nat,Y: option3562590408128118217it_nat] :
% 6.94/7.32 ( ( if_opt6883606601682554499it_nat @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 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,
% 6.94/7.32 ! [X: option3562590408128118217it_nat,Y: option3562590408128118217it_nat] :
% 6.94/7.32 ( ( if_opt6883606601682554499it_nat @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_T,axiom,
% 6.94/7.32 ! [X: option4065278094766928714it_nat,Y: option4065278094766928714it_nat] :
% 6.94/7.32 ( ( if_opt7386294288321364996it_nat @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_T,axiom,
% 6.94/7.32 ! [X: option4065278094766928714it_nat,Y: option4065278094766928714it_nat] :
% 6.94/7.32 ( ( if_opt7386294288321364996it_nat @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 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,
% 6.94/7.32 ! [X: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
% 6.94/7.32 ( ( if_opt1729522071442692626it_nat @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 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,
% 6.94/7.32 ! [X: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
% 6.94/7.32 ( ( if_opt1729522071442692626it_nat @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001_062_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_T,axiom,
% 6.94/7.32 ! [X: produc7822875418678951345atural > produc5835291356934675326atural,Y: produc7822875418678951345atural > produc5835291356934675326atural] :
% 6.94/7.32 ( ( if_Pro2760142802149639654atural @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001_062_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_T,axiom,
% 6.94/7.32 ! [X: produc7822875418678951345atural > produc5835291356934675326atural,Y: produc7822875418678951345atural > produc5835291356934675326atural] :
% 6.94/7.32 ( ( if_Pro2760142802149639654atural @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__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,
% 6.94/7.32 ! [X: produc6653097349344004940it_nat > produc3260487557148687353it_nat,Y: produc6653097349344004940it_nat > produc3260487557148687353it_nat] :
% 6.94/7.32 ( ( if_Pro3578090444564244254it_nat @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__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,
% 6.94/7.32 ! [X: produc6653097349344004940it_nat > produc3260487557148687353it_nat,Y: produc6653097349344004940it_nat > produc3260487557148687353it_nat] :
% 6.94/7.32 ( ( if_Pro3578090444564244254it_nat @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_T,axiom,
% 6.94/7.32 ! [X: produc6653097349344004940it_nat > produc7388388658123137530it_nat,Y: produc6653097349344004940it_nat > produc7388388658123137530it_nat] :
% 6.94/7.32 ( ( if_Pro4080778131203054751it_nat @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_T,axiom,
% 6.94/7.32 ! [X: produc6653097349344004940it_nat > produc7388388658123137530it_nat,Y: produc6653097349344004940it_nat > produc7388388658123137530it_nat] :
% 6.94/7.32 ( ( if_Pro4080778131203054751it_nat @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_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_T,axiom,
% 6.94/7.32 ! [X: produc3658429121746597890et_nat > produc3925858234332021118et_nat,Y: produc3658429121746597890et_nat > produc3925858234332021118et_nat] :
% 6.94/7.32 ( ( if_Pro6440128116348121305et_nat @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_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_T,axiom,
% 6.94/7.32 ! [X: produc3658429121746597890et_nat > produc3925858234332021118et_nat,Y: produc3658429121746597890et_nat > produc3925858234332021118et_nat] :
% 6.94/7.32 ( ( if_Pro6440128116348121305et_nat @ $true @ X @ Y )
% 6.94/7.32 = X ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_3_1_If_001_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_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_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_T,axiom,
% 6.94/7.32 ! [P2: $o] :
% 6.94/7.32 ( ( P2 = $true )
% 6.94/7.32 | ( P2 = $false ) ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_2_1_If_001_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_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_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_T,axiom,
% 6.94/7.32 ! [X: produc3925858234332021118et_nat > produc2732055786443039994et_nat,Y: produc3925858234332021118et_nat > produc2732055786443039994et_nat] :
% 6.94/7.32 ( ( if_Pro5796790085669187537et_nat @ $false @ X @ Y )
% 6.94/7.32 = Y ) ).
% 6.94/7.32
% 6.94/7.32 thf(help_If_1_1_If_001_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_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_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_T,axiom,
% 8.20/8.59 ! [X: produc3925858234332021118et_nat > produc2732055786443039994et_nat,Y: produc3925858234332021118et_nat > produc2732055786443039994et_nat] :
% 8.20/8.59 ( ( if_Pro5796790085669187537et_nat @ $true @ X @ Y )
% 8.20/8.59 = X ) ).
% 8.20/8.59
% 8.20/8.59 % Conjectures (1)
% 8.20/8.59 thf(conj_0,conjecture,
% 8.20/8.59 rep_assn @ ( q @ rg ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h3 @ as @ h ) ) ).
% 8.20/8.59
% 8.20/8.59 %------------------------------------------------------------------------------
% 8.20/8.59 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.YMKiKWlJw8/cvc5---1.0.5_798.p...
% 8.20/8.59 (declare-sort $$unsorted 0)
% 8.20/8.59 (declare-sort tptp.produc7766336532480398636_nat_o 0)
% 8.20/8.59 (declare-sort tptp.produc6999243976208994655_nat_o 0)
% 8.20/8.59 (declare-sort tptp.set_Pr3444600963470892981et_nat 0)
% 8.20/8.59 (declare-sort tptp.produc5657529347773406293et_nat 0)
% 8.20/8.59 (declare-sort tptp.produc50402934264563236_nat_o 0)
% 8.20/8.59 (declare-sort tptp.produc8628075524815789655_nat_o 0)
% 8.20/8.59 (declare-sort tptp.set_Pr7928877670098842301et_nat 0)
% 8.20/8.59 (declare-sort tptp.produc6830853553727218525et_nat 0)
% 8.20/8.59 (declare-sort tptp.option2860828798490689354et_nat 0)
% 8.20/8.59 (declare-sort tptp.list_P362550909693114634et_nat 0)
% 8.20/8.59 (declare-sort tptp.set_Pr8536935166611901872et_nat 0)
% 8.20/8.59 (declare-sort tptp.produc2732055786443039994et_nat 0)
% 8.20/8.59 (declare-sort tptp.produc1319942482725812455at_nat 0)
% 8.20/8.59 (declare-sort tptp.produc1399344845416535567atural 0)
% 8.20/8.59 (declare-sort tptp.produc7538756082594784606_nat_b 0)
% 8.20/8.59 (declare-sort tptp.produc7140141985219958623_nat_a 0)
% 8.20/8.59 (declare-sort tptp.produc7250841696378415494atural 0)
% 8.20/8.59 (declare-sort tptp.set_Pr5508209795250834101it_nat 0)
% 8.20/8.59 (declare-sort tptp.set_Pr2819221443900773171it_nat 0)
% 8.20/8.59 (declare-sort tptp.set_Pr2161125870931222855_nat_o 0)
% 8.20/8.59 (declare-sort tptp.produc1273031398460193109it_nat 0)
% 8.20/8.59 (declare-sort tptp.produc9011797661310329043it_nat 0)
% 8.20/8.59 (declare-sort tptp.option5190343406534369742et_nat 0)
% 8.20/8.59 (declare-sort tptp.produc8449588929630179473_nat_b 0)
% 8.20/8.59 (declare-sort tptp.produc2763251018811306770_nat_a 0)
% 8.20/8.59 (declare-sort tptp.list_P2321686559999237006et_nat 0)
% 8.20/8.59 (declare-sort tptp.set_Pr3286484037609594932et_nat 0)
% 8.20/8.59 (declare-sort tptp.produc4928098042776334183_nat_o 0)
% 8.20/8.59 (declare-sort tptp.set_Pr719794911490849221et_nat 0)
% 8.20/8.59 (declare-sort tptp.produc3925858234332021118et_nat 0)
% 8.20/8.59 (declare-sort tptp.produc8111630337999740517et_nat 0)
% 8.20/8.59 (declare-sort tptp.set_Pr4389693562480114009it_nat 0)
% 8.20/8.59 (declare-sort tptp.produc5966032636589952099nteger 0)
% 8.20/8.59 (declare-sort tptp.produc8961450480463052793it_nat 0)
% 8.20/8.59 (declare-sort tptp.option2498585697089621389at_nat 0)
% 8.20/8.59 (declare-sort tptp.produc3911288613690379145it_nat 0)
% 8.20/8.59 (declare-sort tptp.option1583680563626158861at_nat 0)
% 8.20/8.59 (declare-sort tptp.set_Pr8551490117392284871at_nat 0)
% 8.20/8.59 (declare-sort tptp.option7428179582072448501nteger 0)
% 8.20/8.59 (declare-sort tptp.produc6756470014200349799atural 0)
% 8.20/8.59 (declare-sort tptp.produc2207270350733924475it_nat 0)
% 8.20/8.59 (declare-sort tptp.produc4453839368661128058it_nat 0)
% 8.20/8.59 (declare-sort tptp.produc3500511559948749619nt_int 0)
% 8.20/8.59 (declare-sort tptp.produc4166570645942440679at_nat 0)
% 8.20/8.59 (declare-sort tptp.set_Pr4329608150637261639at_nat 0)
% 8.20/8.59 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 8.20/8.59 (declare-sort tptp.option4277301481530639448it_nat 0)
% 8.20/8.59 (declare-sort tptp.option2555668343544256180it_nat 0)
% 8.20/8.59 (declare-sort tptp.option8956607266484857688it_nat 0)
% 8.20/8.59 (declare-sort tptp.option1013472963438093988it_nat 0)
% 8.20/8.59 (declare-sort tptp.list_P626663023886443800it_nat 0)
% 8.20/8.59 (declare-sort tptp.produc3843707927480180839at_nat 0)
% 8.20/8.59 (declare-sort tptp.produc6751673265320737416it_nat 0)
% 8.20/8.59 (declare-sort tptp.produc7196121022310644452it_nat 0)
% 8.20/8.59 (declare-sort tptp.option4065278094766928714it_nat 0)
% 8.20/8.59 (declare-sort tptp.option3562590408128118217it_nat 0)
% 8.20/8.59 (declare-sort tptp.set_Pr8693737435421807431at_nat 0)
% 8.20/8.59 (declare-sort tptp.set_Pr2560585780119916871nt_int 0)
% 8.20/8.59 (declare-sort tptp.produc8664842809031399944it_nat 0)
% 8.20/8.59 (declare-sort tptp.list_P7438302566501821706it_nat 0)
% 8.20/8.59 (declare-sort tptp.list_P6935614879863011209it_nat 0)
% 8.20/8.59 (declare-sort tptp.produc8032495849646651230it_nat 0)
% 8.20/8.59 (declare-sort tptp.set_Pr7600907837789447088it_nat 0)
% 8.20/8.59 (declare-sort tptp.set_Pr7098220151150636591it_nat 0)
% 8.20/8.59 (declare-sort tptp.produc6197004810343482825et_nat 0)
% 8.20/8.59 (declare-sort tptp.list_P7985473006766602707_nat_o 0)
% 8.20/8.59 (declare-sort tptp.produc5835291356934675326atural 0)
% 8.20/8.59 (declare-sort tptp.produc5728234346263159722nt_int 0)
% 8.20/8.59 (declare-sort tptp.produc859450856879609959at_nat 0)
% 8.20/8.59 (declare-sort tptp.produc1219242969750017639nt_int 0)
% 8.20/8.59 (declare-sort tptp.option936205604648967762et_nat 0)
% 8.20/8.59 (declare-sort tptp.produc7388388658123137530it_nat 0)
% 8.20/8.59 (declare-sort tptp.produc3260487557148687353it_nat 0)
% 8.20/8.59 (declare-sort tptp.set_Pr7577011563204128103nteger 0)
% 8.20/8.59 (declare-sort tptp.list_P9062070895058802706et_nat 0)
% 8.20/8.59 (declare-sort tptp.option233860712434008220it_nat 0)
% 8.20/8.59 (declare-sort tptp.produc6491284506569428743nteger 0)
% 8.20/8.59 (declare-sort tptp.produc1730305018825802663t_unit 0)
% 8.20/8.59 (declare-sort tptp.produc3407818250607552075t_unit 0)
% 8.20/8.59 (declare-sort tptp.list_P131111800688179804it_nat 0)
% 8.20/8.59 (declare-sort tptp.produc3658429121746597890et_nat 0)
% 8.20/8.59 (declare-sort tptp.produc5011041761010125393t_unit 0)
% 8.20/8.59 (declare-sort tptp.set_Pr5488025237498180813et_nat 0)
% 8.20/8.59 (declare-sort tptp.set_Pr2522554150109002629et_int 0)
% 8.20/8.59 (declare-sort tptp.produc6653097349344004940it_nat 0)
% 8.20/8.59 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 8.20/8.59 (declare-sort tptp.option8963830502488799655at_nat 0)
% 8.20/8.59 (declare-sort tptp.option1893999432384633940_int_o 0)
% 8.20/8.59 (declare-sort tptp.option8057788054806935849nteger 0)
% 8.20/8.59 (declare-sort tptp.set_se7855581050983116737at_nat 0)
% 8.20/8.59 (declare-sort tptp.set_se6260736226359567993nt_int 0)
% 8.20/8.59 (declare-sort tptp.produc7819656566062154093et_nat 0)
% 8.20/8.59 (declare-sort tptp.produc2115011035271226405et_int 0)
% 8.20/8.59 (declare-sort tptp.produc7822875418678951345atural 0)
% 8.20/8.59 (declare-sort tptp.produc8923325533196201883nteger 0)
% 8.20/8.59 (declare-sort tptp.multis2468970476368604999at_nat 0)
% 8.20/8.59 (declare-sort tptp.option4624381673175914239nt_int 0)
% 8.20/8.59 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 8.20/8.59 (declare-sort tptp.set_He475150555083384525t_unit 0)
% 8.20/8.59 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 8.20/8.59 (declare-sort tptp.list_P3521021558325789923at_int 0)
% 8.20/8.59 (declare-sort tptp.list_P8198026277950538467nt_nat 0)
% 8.20/8.59 (declare-sort tptp.list_P5707943133018811711nt_int 0)
% 8.20/8.59 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 8.20/8.59 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 8.20/8.59 (declare-sort tptp.heap_T3836121109492952855ay_nat 0)
% 8.20/8.59 (declare-sort tptp.heap_T1346037964561226099ay_int 0)
% 8.20/8.59 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 8.20/8.59 (declare-sort tptp.list_P5087981734274514673_int_o 0)
% 8.20/8.59 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 8.20/8.59 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 8.20/8.59 (declare-sort tptp.set_set_list_nat 0)
% 8.20/8.59 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 8.20/8.59 (declare-sort tptp.set_set_set_nat 0)
% 8.20/8.59 (declare-sort tptp.set_set_Code_integer 0)
% 8.20/8.59 (declare-sort tptp.heap_T5738788834812785303t_unit 0)
% 8.20/8.59 (declare-sort tptp.set_Product_prod_b_b 0)
% 8.20/8.59 (declare-sort tptp.set_Product_prod_a_a 0)
% 8.20/8.59 (declare-sort tptp.heap_T5660665574680485309rray_o 0)
% 8.20/8.59 (declare-sort tptp.heap_e7401611519738050253t_unit 0)
% 8.20/8.59 (declare-sort tptp.product_prod_num_num 0)
% 8.20/8.59 (declare-sort tptp.product_prod_nat_num 0)
% 8.20/8.59 (declare-sort tptp.product_prod_nat_nat 0)
% 8.20/8.59 (declare-sort tptp.product_prod_nat_int 0)
% 8.20/8.59 (declare-sort tptp.product_prod_int_nat 0)
% 8.20/8.59 (declare-sort tptp.product_prod_int_int 0)
% 8.20/8.59 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 8.20/8.59 (declare-sort tptp.set_Product_prod_o_o 0)
% 8.20/8.59 (declare-sort tptp.list_option_num 0)
% 8.20/8.59 (declare-sort tptp.option_set_nat 0)
% 8.20/8.59 (declare-sort tptp.option_set_int 0)
% 8.20/8.59 (declare-sort tptp.option_Code_integer 0)
% 8.20/8.59 (declare-sort tptp.filter_set_nat 0)
% 8.20/8.59 (declare-sort tptp.heap_Time_Heap_nat 0)
% 8.20/8.59 (declare-sort tptp.heap_Time_Heap_int 0)
% 8.20/8.59 (declare-sort tptp.set_list_nat 0)
% 8.20/8.59 (declare-sort tptp.set_list_int 0)
% 8.20/8.59 (declare-sort tptp.product_prod_nat_o 0)
% 8.20/8.59 (declare-sort tptp.product_prod_int_o 0)
% 8.20/8.59 (declare-sort tptp.product_prod_o_nat 0)
% 8.20/8.59 (declare-sort tptp.product_prod_o_int 0)
% 8.20/8.59 (declare-sort tptp.set_set_nat 0)
% 8.20/8.59 (declare-sort tptp.set_set_int 0)
% 8.20/8.59 (declare-sort tptp.set_Code_integer 0)
% 8.20/8.59 (declare-sort tptp.array_Product_unit 0)
% 8.20/8.59 (declare-sort tptp.list_Product_unit 0)
% 8.20/8.59 (declare-sort tptp.option_assn 0)
% 8.20/8.59 (declare-sort tptp.ref_Product_unit 0)
% 8.20/8.59 (declare-sort tptp.set_Product_unit 0)
% 8.20/8.59 (declare-sort tptp.product_prod_b_b 0)
% 8.20/8.59 (declare-sort tptp.product_prod_a_a 0)
% 8.20/8.59 (declare-sort tptp.option_set_o 0)
% 8.20/8.59 (declare-sort tptp.heap_Time_Heap_b 0)
% 8.20/8.59 (declare-sort tptp.heap_Time_Heap_a 0)
% 8.20/8.59 (declare-sort tptp.heap_Time_Heap_o 0)
% 8.20/8.59 (declare-sort tptp.set_list_o 0)
% 8.20/8.59 (declare-sort tptp.product_prod_o_o 0)
% 8.20/8.59 (declare-sort tptp.set_assn 0)
% 8.20/8.59 (declare-sort tptp.option_rat 0)
% 8.20/8.59 (declare-sort tptp.option_num 0)
% 8.20/8.59 (declare-sort tptp.option_nat 0)
% 8.20/8.59 (declare-sort tptp.option_int 0)
% 8.20/8.59 (declare-sort tptp.list_char 0)
% 8.20/8.59 (declare-sort tptp.filter_nat 0)
% 8.20/8.59 (declare-sort tptp.array_nat 0)
% 8.20/8.59 (declare-sort tptp.array_int 0)
% 8.20/8.59 (declare-sort tptp.list_rat 0)
% 8.20/8.59 (declare-sort tptp.list_num 0)
% 8.20/8.59 (declare-sort tptp.list_nat 0)
% 8.20/8.59 (declare-sort tptp.list_int 0)
% 8.20/8.59 (declare-sort tptp.set_rat 0)
% 8.20/8.59 (declare-sort tptp.set_num 0)
% 8.20/8.59 (declare-sort tptp.set_nat 0)
% 8.20/8.59 (declare-sort tptp.set_int 0)
% 8.20/8.59 (declare-sort tptp.code_natural 0)
% 8.20/8.59 (declare-sort tptp.code_integer 0)
% 8.20/8.59 (declare-sort tptp.product_unit 0)
% 8.20/8.59 (declare-sort tptp.option_o 0)
% 8.20/8.59 (declare-sort tptp.list_b 0)
% 8.20/8.59 (declare-sort tptp.list_a 0)
% 8.20/8.59 (declare-sort tptp.array_o 0)
% 8.20/8.59 (declare-sort tptp.list_o 0)
% 8.20/8.59 (declare-sort tptp.assn 0)
% 8.20/8.59 (declare-sort tptp.set_o 0)
% 8.20/8.59 (declare-sort tptp.char 0)
% 8.20/8.59 (declare-sort tptp.rat 0)
% 8.20/8.59 (declare-sort tptp.num 0)
% 8.20/8.59 (declare-sort tptp.nat 0)
% 8.20/8.59 (declare-sort tptp.int 0)
% 8.20/8.59 (declare-sort tptp.b 0)
% 8.20/8.59 (declare-sort tptp.a 0)
% 8.20/8.59 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 8.20/8.59 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 8.20/8.59 (declare-fun tptp.archimedean_frac_rat (tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 8.20/8.59 (declare-fun tptp.array_alloc_o (tptp.list_o tptp.heap_e7401611519738050253t_unit) tptp.produc5011041761010125393t_unit)
% 8.20/8.59 (declare-fun tptp.array_alloc_int (tptp.list_int tptp.heap_e7401611519738050253t_unit) tptp.produc3407818250607552075t_unit)
% 8.20/8.59 (declare-fun tptp.array_alloc_nat (tptp.list_nat tptp.heap_e7401611519738050253t_unit) tptp.produc1730305018825802663t_unit)
% 8.20/8.59 (declare-fun tptp.array_len_o (tptp.array_o) tptp.heap_Time_Heap_nat)
% 8.20/8.59 (declare-fun tptp.array_len_int (tptp.array_int) tptp.heap_Time_Heap_nat)
% 8.20/8.59 (declare-fun tptp.array_len_nat (tptp.array_nat) tptp.heap_Time_Heap_nat)
% 8.20/8.59 (declare-fun tptp.array_make_o (tptp.nat (-> tptp.nat Bool)) tptp.heap_T5660665574680485309rray_o)
% 8.20/8.59 (declare-fun tptp.array_make_int (tptp.nat (-> tptp.nat tptp.int)) tptp.heap_T1346037964561226099ay_int)
% 8.20/8.59 (declare-fun tptp.array_make_nat (tptp.nat (-> tptp.nat tptp.nat)) tptp.heap_T3836121109492952855ay_nat)
% 8.20/8.59 (declare-fun tptp.array_nth_o (tptp.array_o tptp.nat) tptp.heap_Time_Heap_o)
% 8.20/8.59 (declare-fun tptp.array_nth_int (tptp.array_int tptp.nat) tptp.heap_Time_Heap_int)
% 8.20/8.59 (declare-fun tptp.array_nth_nat (tptp.array_nat tptp.nat) tptp.heap_Time_Heap_nat)
% 8.20/8.59 (declare-fun tptp.array_7872002506669749220t_unit (tptp.array_Product_unit tptp.nat) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (declare-fun tptp.array_of_list_o (tptp.list_o) tptp.heap_T5660665574680485309rray_o)
% 8.20/8.59 (declare-fun tptp.array_of_list_int (tptp.list_int) tptp.heap_T1346037964561226099ay_int)
% 8.20/8.59 (declare-fun tptp.array_of_list_nat (tptp.list_nat) tptp.heap_T3836121109492952855ay_nat)
% 8.20/8.59 (declare-fun tptp.abs_assn ((-> tptp.produc3658429121746597890et_nat Bool)) tptp.assn)
% 8.20/8.59 (declare-fun tptp.rep_assn (tptp.assn tptp.produc3658429121746597890et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.entails (tptp.assn tptp.assn) Bool)
% 8.20/8.59 (declare-fun tptp.in_range (tptp.produc3658429121746597890et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.in_range_rel (tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.one_assn_raw (tptp.produc3658429121746597890et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.one_assn_raw_rel (tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.pure_assn (Bool) tptp.assn)
% 8.20/8.59 (declare-fun tptp.pure_a825153325127701367it_nat (Bool tptp.produc3658429121746597890et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.pure_a6022498039421069578it_nat (tptp.produc6197004810343482825et_nat tptp.produc6197004810343482825et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.relH (tptp.set_nat tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit) Bool)
% 8.20/8.59 (declare-fun tptp.snga_assn_o (tptp.array_o tptp.list_o) tptp.assn)
% 8.20/8.59 (declare-fun tptp.snga_assn_int (tptp.array_int tptp.list_int) tptp.assn)
% 8.20/8.59 (declare-fun tptp.snga_assn_nat (tptp.array_nat tptp.list_nat) tptp.assn)
% 8.20/8.59 (declare-fun tptp.snga_a4522542871529764173t_unit (tptp.array_Product_unit tptp.list_Product_unit) tptp.assn)
% 8.20/8.59 (declare-fun tptp.sngr_a5825115052027484668t_unit (tptp.ref_Product_unit tptp.product_unit) tptp.assn)
% 8.20/8.59 (declare-fun tptp.times_assn_raw ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.times_assn_raw_rel (tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.wand_assn (tptp.assn tptp.assn) tptp.assn)
% 8.20/8.59 (declare-fun tptp.wand_raw ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.wand_raw_rel (tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.bNF_Ca3793111618940312692of_nat (tptp.set_nat) tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.bNF_Ca1281551314933786834on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.bNF_Ca8665028551170535155natLeq () tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.bNF_Ca8459412986667044542atLess () tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.bNF_Ca1965613569405424510nt_int (tptp.set_Pr958786334691620121nt_int (-> tptp.int tptp.int)) Bool)
% 8.20/8.59 (declare-fun tptp.bNF_Ca1968104039914474786nt_nat (tptp.set_Pr958786334691620121nt_int (-> tptp.int tptp.nat)) Bool)
% 8.20/8.59 (declare-fun tptp.bNF_Ca7748807862925029228nt_num (tptp.set_Pr958786334691620121nt_int (-> tptp.int tptp.num)) Bool)
% 8.20/8.59 (declare-fun tptp.bNF_Ca1332973979827979050nt_rat (tptp.set_Pr958786334691620121nt_int (-> tptp.int tptp.rat)) Bool)
% 8.20/8.59 (declare-fun tptp.bNF_Ca583493526879471924et_int (tptp.set_Pr958786334691620121nt_int (-> tptp.int tptp.set_int)) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.bNF_re711492959462206631nt_int ((-> tptp.int tptp.int Bool) (-> (-> tptp.int tptp.int) (-> tptp.int tptp.int) Bool) (-> tptp.int tptp.int tptp.int) (-> tptp.int tptp.int tptp.int)) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.bNF_re5089333283451836215nt_o_o ((-> tptp.int tptp.int Bool) (-> Bool Bool Bool) (-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.bNF_re1345281282404953727at_nat ((-> tptp.nat tptp.nat Bool) (-> (-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) Bool) (-> tptp.nat tptp.nat tptp.nat) (-> tptp.nat tptp.nat tptp.nat)) Bool)
% 8.20/8.59 (declare-fun tptp.bNF_re4705727531993890431at_o_o ((-> tptp.nat tptp.nat Bool) (-> Bool Bool Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.bNF_re5653821019739307937at_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat)) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.bNF_re7934895593101944656at_int ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.int)) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.bNF_We5258908940166488438at_nat () tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.59 (declare-fun tptp.bNF_We3818239936649020644el_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.basic_1567116559311922317nt_int ((-> tptp.int Bool) (-> tptp.int Bool) tptp.product_prod_int_int) Bool)
% 8.20/8.59 (declare-fun tptp.basic_4387203522000727145nt_int ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool) tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 8.20/8.59 (declare-fun tptp.basic_5328504652464829177at_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 8.20/8.59 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.gbinom8545251970709558553nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.gbinom7368847122466276068atural (tptp.code_natural tptp.nat) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 8.20/8.59 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.bit_and_not_num_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 8.20/8.59 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.bit_ri7632146776885996613nteger (tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.bit_se2773287842338716102atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.bit_se168947363167071951atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.bit_se943457434206027407atural (tptp.nat) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.bit_se1080825931792720795nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.bit_se9127793120404214118atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.bit_se7788150548672797655nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.bit_se1617098188084679374atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.bit_se569199155075624693atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.bit_se7083795435491715335atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.bit_se3222712562003087583nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.bit_se2046307713759805098atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.bit_se9216721137139052372nteger (tptp.code_integer tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.bit_se8040316288895769887atural (tptp.code_natural tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.bit_un4731106466462545111um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 8.20/8.59 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 8.20/8.59 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 8.20/8.59 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 8.20/8.59 (declare-fun tptp.code_dup (tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 8.20/8.59 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 8.20/8.59 (declare-fun tptp.code_nat_of_natural (tptp.code_natural) tptp.nat)
% 8.20/8.59 (declare-fun tptp.code_natural_of_nat (tptp.nat) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 8.20/8.59 (declare-fun tptp.code_sub (tptp.num tptp.num) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.complete_Inf_Inf_int (tptp.set_int) tptp.int)
% 8.20/8.59 (declare-fun tptp.complete_Inf_Inf_nat (tptp.set_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.comple2584293577114468500t_unit (tptp.set_Product_unit) tptp.product_unit)
% 8.20/8.59 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 8.20/8.59 (declare-fun tptp.complete_Sup_Sup_nat (tptp.set_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.comple4687483117567863418t_unit (tptp.set_Product_unit) tptp.product_unit)
% 8.20/8.59 (declare-fun tptp.comple7399068483239264473et_nat (tptp.set_set_nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.condit2214826472909112428ve_nat (tptp.set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 8.20/8.59 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 8.20/8.59 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 8.20/8.59 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 8.20/8.59 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 8.20/8.59 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 8.20/8.59 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 8.20/8.59 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 8.20/8.59 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 8.20/8.59 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 8.20/8.59 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 8.20/8.59 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 8.20/8.59 (declare-fun tptp.euclid3395696857347342551nt_int (tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.semiri2447717529341329178atural (tptp.nat) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 8.20/8.59 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 8.20/8.59 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.filter3212408913953519116et_nat ((-> tptp.nat tptp.set_nat) tptp.filter_set_nat tptp.filter_nat) Bool)
% 8.20/8.59 (declare-fun tptp.finite3254316476582989077op_nat (tptp.set_nat) tptp.filter_set_nat)
% 8.20/8.59 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 8.20/8.59 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite4902975817058060853nteger (tptp.set_Code_integer) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite6756421564338198497nt_int (tptp.set_Pr958786334691620121nt_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite7007076676225009423at_nat (tptp.set_Pr8551490117392284871at_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite711546835091564841at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite3771342082235030671at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite1340570857867686763nteger (tptp.set_set_Code_integer) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite_card_set_int (tptp.set_set_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite2364142230527598318st_nat (tptp.set_set_list_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite_card_set_nat (tptp.set_set_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite4053189226111446337nt_int (tptp.set_se6260736226359567993nt_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite4356350796350151305at_nat (tptp.set_se7855581050983116737at_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite1149291290879098388et_nat (tptp.set_set_set_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 8.20/8.59 (declare-fun tptp.finite_finite_assn (tptp.set_assn) Bool)
% 8.20/8.59 (declare-fun tptp.finite6017078050557962740nteger (tptp.set_Code_integer) Bool)
% 8.20/8.59 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 8.20/8.59 (declare-fun tptp.finite_finite_list_o (tptp.set_list_o) Bool)
% 8.20/8.59 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 8.20/8.59 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 8.20/8.59 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 8.20/8.59 (declare-fun tptp.finite2998713641127702882nt_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 8.20/8.59 (declare-fun tptp.finite1918287321285529104at_nat (tptp.set_Pr8551490117392284871at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.finite6177210948735845034at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.finite4343798906461161616at_nat (tptp.set_Pr4329608150637261639at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 8.20/8.59 (declare-fun tptp.finite6931041176100689706nteger (tptp.set_set_Code_integer) Bool)
% 8.20/8.59 (declare-fun tptp.finite6197958912794628473et_int (tptp.set_set_int) Bool)
% 8.20/8.59 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.finite8744585540193469122nt_int (tptp.set_se6260736226359567993nt_int) Bool)
% 8.20/8.59 (declare-fun tptp.finite9047747110432174090at_nat (tptp.set_se7855581050983116737at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.comp_C3983183376822107068nteger ((-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> (-> tptp.code_integer tptp.code_integer) tptp.code_integer tptp.code_integer) (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.comp_C95226695241045696nteger ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> (-> tptp.code_integer tptp.code_integer) tptp.code_integer) (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.comp_C7449957260575251196nteger ((-> tptp.code_integer tptp.code_integer) (-> tptp.code_integer tptp.code_integer) tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.comp_C4049556595663050210at_nat ((-> tptp.code_integer tptp.nat) (-> tptp.nat tptp.code_integer) tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.comp_i1585864551200866970er_int ((-> tptp.int tptp.code_integer) (-> tptp.int tptp.int) tptp.int) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.comp_int_nat_int ((-> tptp.int tptp.nat) (-> tptp.int tptp.int) tptp.int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.comp_int_nat_nat ((-> tptp.int tptp.nat) (-> tptp.nat tptp.int) tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.comp_int_rat_int ((-> tptp.int tptp.rat) (-> tptp.int tptp.int) tptp.int) tptp.rat)
% 8.20/8.59 (declare-fun tptp.comp_n3898172953802868194er_nat ((-> tptp.nat tptp.code_integer) (-> tptp.nat tptp.nat) tptp.nat) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.comp_nat_int_nat ((-> tptp.nat tptp.int) (-> tptp.nat tptp.nat) tptp.nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.comp_n8698576032424989604at_nat ((-> tptp.nat tptp.multis2468970476368604999at_nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.multis2468970476368604999at_nat)
% 8.20/8.59 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.comp_nat_rat_nat ((-> tptp.nat tptp.rat) (-> tptp.nat tptp.nat) tptp.nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.comp_num_int_num ((-> tptp.num tptp.int) (-> tptp.num tptp.num) tptp.num) tptp.int)
% 8.20/8.59 (declare-fun tptp.comp_num_nat_num ((-> tptp.num tptp.nat) (-> tptp.num tptp.num) tptp.num) tptp.nat)
% 8.20/8.59 (declare-fun tptp.comp_num_num_num ((-> tptp.num tptp.num) (-> tptp.num tptp.num) tptp.num) tptp.num)
% 8.20/8.59 (declare-fun tptp.comp_n6731957995704128387um_num ((-> tptp.num tptp.option_num) (-> tptp.num tptp.num) tptp.num) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.comp_o7188567781464924208nteger ((-> tptp.option8057788054806935849nteger tptp.option7428179582072448501nteger) (-> tptp.option_Code_integer tptp.option8057788054806935849nteger) tptp.option_Code_integer) tptp.option7428179582072448501nteger)
% 8.20/8.59 (declare-fun tptp.comp_o9011007105448239796nteger ((-> tptp.option_Code_integer tptp.option7428179582072448501nteger) (-> tptp.option_Code_integer tptp.option_Code_integer) tptp.option_Code_integer) tptp.option7428179582072448501nteger)
% 8.20/8.59 (declare-fun tptp.comp_o5073597352248849069on_int ((-> tptp.option_int tptp.nat) (-> tptp.option_int tptp.option_int) tptp.option_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.comp_o4824269118391204861on_int ((-> tptp.option_int tptp.option_nat) (-> tptp.option_int tptp.option_int) tptp.option_int) tptp.option_nat)
% 8.20/8.59 (declare-fun tptp.comp_o6878144249584144265on_num ((-> tptp.option_num tptp.nat) (-> tptp.option_num tptp.option_num) tptp.option_num) tptp.nat)
% 8.20/8.59 (declare-fun tptp.comp_o8931257242830428707on_num ((-> tptp.option_num tptp.option_num) (-> tptp.option_num tptp.option_num) tptp.option_num) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.comp_P3118722334806803912t_unit ((-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat) (-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat) tptp.heap_e7401611519738050253t_unit) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.comp_P8552900652980440422t_unit ((-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat) (-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat) tptp.heap_e7401611519738050253t_unit) tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.comp_P6401406225962756324t_unit ((-> tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat) (-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat) tptp.heap_e7401611519738050253t_unit) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.comp_rat_nat_nat ((-> tptp.rat tptp.nat) (-> tptp.nat tptp.rat) tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.id_o (Bool) Bool)
% 8.20/8.59 (declare-fun tptp.id_int (tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.id_num (tptp.num) tptp.num)
% 8.20/8.59 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.map_fu8272188784021352819nteger ((-> tptp.code_integer tptp.int) (-> (-> tptp.int tptp.int) tptp.code_integer tptp.code_integer) (-> tptp.int tptp.int tptp.int) tptp.code_integer tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.map_fu6957801986076833569nt_o_o ((-> tptp.code_integer tptp.int) (-> Bool Bool) (-> tptp.int Bool) tptp.code_integer) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.map_fu6549440983881763648atural ((-> tptp.code_natural tptp.nat) (-> (-> tptp.nat tptp.nat) tptp.code_natural tptp.code_natural) (-> tptp.nat tptp.nat tptp.nat) tptp.code_natural tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.map_fu4892316939951275536at_o_o ((-> tptp.code_natural tptp.nat) (-> Bool Bool) (-> tptp.nat Bool) tptp.code_natural) Bool)
% 8.20/8.59 (declare-fun tptp.map_fu1239815594074539274atural ((-> tptp.code_natural tptp.nat) (-> tptp.nat tptp.code_natural) (-> tptp.nat tptp.nat) tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.map_fu6891787308814931657nteger ((-> tptp.num tptp.num) (-> (-> tptp.num tptp.int) tptp.num tptp.code_integer) (-> tptp.num tptp.num tptp.int) tptp.num tptp.num) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.map_fu8638147718074629079nteger ((-> tptp.num tptp.num) (-> tptp.int tptp.code_integer) (-> tptp.num tptp.int) tptp.num) tptp.code_integer)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.fun_max_strict () tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.59 (declare-fun tptp.fun_max_weak () tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.59 (declare-fun tptp.fun_min_strict () tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.59 (declare-fun tptp.fun_min_weak () tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.59 (declare-fun tptp.fun_pair_leq () tptp.set_Pr8693737435421807431at_nat)
% 8.20/8.59 (declare-fun tptp.fun_pair_less () tptp.set_Pr8693737435421807431at_nat)
% 8.20/8.59 (declare-fun tptp.fun_re2478310338295953701at_nat (tptp.produc1319942482725812455at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 8.20/8.59 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 8.20/8.59 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.minus_minus_o_o ((-> Bool Bool) (-> Bool Bool) Bool) Bool)
% 8.20/8.59 (declare-fun tptp.minus_minus_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.minus_1139252259498527702_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 8.20/8.59 (declare-fun tptp.minus_minus_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.minus_6910147592129066416_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.minus_357216186751819389_int_o ((-> tptp.set_Pr958786334691620121nt_int Bool) (-> tptp.set_Pr958786334691620121nt_int Bool) tptp.set_Pr958786334691620121nt_int) Bool)
% 8.20/8.59 (declare-fun tptp.minus_minus_assn (tptp.assn tptp.assn) tptp.assn)
% 8.20/8.59 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.minus_7197305767214868737atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.minus_4286766774447292334at_nat (tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) tptp.multis2468970476368604999at_nat)
% 8.20/8.59 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.minus_minus_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 8.20/8.59 (declare-fun tptp.minus_2355218937544613996nteger (tptp.set_Code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 8.20/8.59 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.minus_7954133019191499631st_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 8.20/8.59 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.minus_minus_set_num (tptp.set_num tptp.set_num) tptp.set_num)
% 8.20/8.59 (declare-fun tptp.minus_1052850069191792384nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 8.20/8.59 (declare-fun tptp.minus_5060654252129873198at_nat (tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat) tptp.set_Pr8551490117392284871at_nat)
% 8.20/8.59 (declare-fun tptp.minus_1356011639430497352at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.minus_3314409938677909166at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.59 (declare-fun tptp.minus_minus_set_rat (tptp.set_rat tptp.set_rat) tptp.set_rat)
% 8.20/8.59 (declare-fun tptp.minus_2163939370556025621et_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 8.20/8.59 (declare-fun tptp.minus_2612819937483484256nt_int (tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int) tptp.set_se6260736226359567993nt_int)
% 8.20/8.59 (declare-fun tptp.one_one_assn () tptp.assn)
% 8.20/8.59 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.one_one_Code_natural () tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.one_one_int () tptp.int)
% 8.20/8.59 (declare-fun tptp.one_one_nat () tptp.nat)
% 8.20/8.59 (declare-fun tptp.one_one_rat () tptp.rat)
% 8.20/8.59 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.plus_p4538020629002901425atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.plus_p7104986032573967614at_nat (tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) tptp.multis2468970476368604999at_nat)
% 8.20/8.59 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 8.20/8.59 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.times_times_assn (tptp.assn tptp.assn) tptp.assn)
% 8.20/8.59 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.times_2397367101498566445atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 8.20/8.59 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.uminus_uminus_o_o ((-> Bool Bool) Bool) Bool)
% 8.20/8.59 (declare-fun tptp.uminus_uminus_int_o ((-> tptp.int Bool) tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.uminus5770388063884162150_nat_o ((-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 8.20/8.59 (declare-fun tptp.uminus_uminus_nat_o ((-> tptp.nat Bool) tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.uminus7117520113953359693_int_o ((-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 8.20/8.59 (declare-fun tptp.uminus6401447641752708672_nat_o ((-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.uminus8147837162492574189_int_o ((-> tptp.set_Pr958786334691620121nt_int Bool) tptp.set_Pr958786334691620121nt_int) Bool)
% 8.20/8.59 (declare-fun tptp.uminus_uminus_assn (tptp.assn) tptp.assn)
% 8.20/8.59 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.uminus2952777764628376836t_unit (tptp.product_unit) tptp.product_unit)
% 8.20/8.59 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.uminus_uminus_set_o (tptp.set_o) tptp.set_o)
% 8.20/8.59 (declare-fun tptp.uminus804700908173204444nteger (tptp.set_Code_integer) tptp.set_Code_integer)
% 8.20/8.59 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.uminus3195874150345416415st_nat (tptp.set_list_nat) tptp.set_list_nat)
% 8.20/8.59 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.uminus2330091110623919550at_nat (tptp.set_Pr8551490117392284871at_nat) tptp.set_Pr8551490117392284871at_nat)
% 8.20/8.59 (declare-fun tptp.uminus6524753893492686040at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.uminus935396558254630718at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.59 (declare-fun tptp.uminus613421341184616069et_nat (tptp.set_set_nat) tptp.set_set_nat)
% 8.20/8.59 (declare-fun tptp.uminus6423885277529793776nt_int (tptp.set_se6260736226359567993nt_int) tptp.set_se6260736226359567993nt_int)
% 8.20/8.59 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.zero_z2226904508553997617atural () tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.zero_zero_int () tptp.int)
% 8.20/8.59 (declare-fun tptp.zero_z1048942125864253310at_nat () tptp.multis2468970476368604999at_nat)
% 8.20/8.59 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 8.20/8.59 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups4406642042086082107nteger ((-> Bool tptp.code_integer) tptp.set_o) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.groups3230237193842799622atural ((-> Bool tptp.code_natural) tptp.set_o) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.groups8505340233167759370_o_int ((-> Bool tptp.int) tptp.set_o) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups8507830703676809646_o_nat ((-> Bool tptp.nat) tptp.set_o) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups7872700643590313910_o_rat ((-> Bool tptp.rat) tptp.set_o) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups879477027807139574nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.groups8926444216418632897atural ((-> tptp.code_integer tptp.code_natural) tptp.set_Code_integer) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.groups7234854612051535045er_int ((-> tptp.code_integer tptp.int) tptp.set_Code_integer) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups7237345082560585321er_nat ((-> tptp.code_integer tptp.nat) tptp.set_Code_integer) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups6602215022474089585er_rat ((-> tptp.code_integer tptp.rat) tptp.set_Code_integer) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.groups6697149243333190288atural ((-> tptp.int tptp.code_natural) tptp.set_int) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups4396056296759096172at_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups3760926236672600436at_rat ((-> tptp.list_nat tptp.rat) tptp.set_list_nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.groups6325495683096345652atural ((-> tptp.nat tptp.code_natural) tptp.set_nat) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups6857163185585827899at_nat ((-> tptp.nat tptp.multis2468970476368604999at_nat) tptp.set_nat) tptp.multis2468970476368604999at_nat)
% 8.20/8.59 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups7059897769266147197at_nat ((-> tptp.produc4166570645942440679at_nat tptp.nat) tptp.set_Pr8551490117392284871at_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups6424767709179651461at_rat ((-> tptp.produc4166570645942440679at_nat tptp.rat) tptp.set_Pr8551490117392284871at_nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups975429370522433651at_int ((-> tptp.product_prod_nat_nat tptp.int) tptp.set_Pr1261947904930325089at_nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups342789780944988191at_rat ((-> tptp.product_prod_nat_nat tptp.rat) tptp.set_Pr1261947904930325089at_nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups3860910324918113789at_nat ((-> tptp.produc3843707927480180839at_nat tptp.nat) tptp.set_Pr4329608150637261639at_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups3225780264831618053at_rat ((-> tptp.produc3843707927480180839at_nat tptp.rat) tptp.set_Pr4329608150637261639at_nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups9190459664516455967nteger ((-> tptp.set_nat tptp.code_integer) tptp.set_set_nat) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.groups8294997508430121362at_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups7659867448343625626at_rat ((-> tptp.set_nat tptp.rat) tptp.set_set_nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups185207323561075247nt_nat ((-> tptp.set_Pr958786334691620121nt_int tptp.nat) tptp.set_se6260736226359567993nt_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups1402912129352969042nteger ((-> Bool tptp.code_integer) tptp.set_o) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.groups4553916814277028129_o_int ((-> Bool tptp.int) tptp.set_o) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups4556407284786078405_o_nat ((-> Bool tptp.nat) tptp.set_o) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups3921277224699582669_o_rat ((-> Bool tptp.rat) tptp.set_o) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups910942671188738463nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.groups288081504127972206er_int ((-> tptp.code_integer tptp.int) tptp.set_Code_integer) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups290571974637022482er_nat ((-> tptp.code_integer tptp.nat) tptp.set_Code_integer) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups8878813951405302554er_rat ((-> tptp.code_integer tptp.rat) tptp.set_Code_integer) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups926780983652909934nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.groups2983280209131991357nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups6906599089918680438at_nat ((-> tptp.int tptp.multis2468970476368604999at_nat) tptp.set_int) tptp.multis2468970476368604999at_nat)
% 8.20/8.59 (declare-fun tptp.groups2985770679641041633nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups2350640619554545897nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups555127423416065298nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.groups1983926497230936801at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups1986416967739987077at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups1351286907653491341at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups3803682039294397627nteger ((-> tptp.product_prod_nat_nat tptp.code_integer) tptp.set_Pr1261947904930325089at_nat) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.groups3960716392046309002at_int ((-> tptp.product_prod_nat_nat tptp.int) tptp.set_Pr1261947904930325089at_nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups8361914993108267113at_nat ((-> tptp.product_prod_nat_nat tptp.multis2468970476368604999at_nat) tptp.set_Pr1261947904930325089at_nat) tptp.multis2468970476368604999at_nat)
% 8.20/8.59 (declare-fun tptp.groups3963206862555359278at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups3328076802468863542at_rat ((-> tptp.product_prod_nat_nat tptp.rat) tptp.set_Pr1261947904930325089at_nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups5301882518646026715o_assn ((-> Bool tptp.assn) tptp.set_o) tptp.assn)
% 8.20/8.59 (declare-fun tptp.groups7694694392188491536nteger ((-> Bool tptp.code_integer) tptp.set_o) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.groups3502327434004483295_o_int ((-> Bool tptp.int) tptp.set_o) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups3504817904513533571_o_nat ((-> Bool tptp.nat) tptp.set_o) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups2869687844427037835_o_rat ((-> Bool tptp.rat) tptp.set_o) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups1304777262505850412r_assn ((-> tptp.code_integer tptp.assn) tptp.set_Code_integer) tptp.assn)
% 8.20/8.59 (declare-fun tptp.groups3674199335183972705nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.groups3188404863801439024er_int ((-> tptp.code_integer tptp.int) tptp.set_Code_integer) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups3190895334310489300er_nat ((-> tptp.code_integer tptp.nat) tptp.set_Code_integer) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups2555765274223993564er_rat ((-> tptp.code_integer tptp.rat) tptp.set_Code_integer) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups7882442080178216443t_assn ((-> tptp.int tptp.assn) tptp.set_int) tptp.assn)
% 8.20/8.59 (declare-fun tptp.groups3827104343326376752nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups2905156660866384563at_int ((-> tptp.list_nat tptp.int) tptp.set_list_nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups2907647131375434839at_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups6906906614972039071t_assn ((-> tptp.nat tptp.assn) tptp.set_nat) tptp.assn)
% 8.20/8.59 (declare-fun tptp.groups3455450783089532116nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.groups2279045934846249631atural ((-> tptp.nat tptp.code_natural) tptp.set_nat) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups5938585286922990810at_rat ((-> tptp.produc4166570645942440679at_nat tptp.rat) tptp.set_Pr8551490117392284871at_nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups4075276357253098568at_int ((-> tptp.product_prod_nat_nat tptp.int) tptp.set_Pr1261947904930325089at_nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups4077766827762148844at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups3442636767675653108at_rat ((-> tptp.product_prod_nat_nat tptp.rat) tptp.set_Pr1261947904930325089at_nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups8874911130973611098at_rat ((-> tptp.produc3843707927480180839at_nat tptp.rat) tptp.set_Pr4329608150637261639at_nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups4246057289670975065at_int ((-> tptp.set_nat tptp.int) tptp.set_set_nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups4248547760180025341at_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups3417619833198082522nteger ((-> Bool tptp.code_integer) tptp.code_integer tptp.list_o) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.groups2241214984954800037atural ((-> Bool tptp.code_natural) tptp.code_natural tptp.list_o) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups9119017779487936845_o_nat ((-> Bool tptp.nat) tptp.nat tptp.list_o) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups8483887719401441109_o_rat ((-> Bool tptp.rat) tptp.rat tptp.list_o) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups8485231416243008693nt_int ((-> tptp.int tptp.int) tptp.int tptp.list_int) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups8487721886752058969nt_nat ((-> tptp.int tptp.nat) tptp.nat tptp.list_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups7852591826665563233nt_rat ((-> tptp.int tptp.rat) tptp.rat tptp.list_int) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups7485877704341954137at_int ((-> tptp.nat tptp.int) tptp.int tptp.list_nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.groups7488368174851004413at_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.list_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.groups6853238114764508677at_rat ((-> tptp.nat tptp.rat) tptp.rat tptp.list_nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.nO_MAT4469370267861770177al_int (tptp.code_natural tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.nO_MAT4471860738370820453al_nat (tptp.code_natural tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.nO_MAT3836730678284324717al_rat (tptp.code_natural tptp.rat) Bool)
% 8.20/8.59 (declare-fun tptp.nO_MATCH_int_int (tptp.int tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.nO_MATCH_int_nat (tptp.int tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.nO_MATCH_int_rat (tptp.int tptp.rat) Bool)
% 8.20/8.59 (declare-fun tptp.nO_MATCH_nat_int (tptp.nat tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.nO_MATCH_nat_nat (tptp.nat tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.nO_MATCH_nat_rat (tptp.nat tptp.rat) Bool)
% 8.20/8.59 (declare-fun tptp.nO_MATCH_rat_rat (tptp.rat tptp.rat) Bool)
% 8.20/8.59 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 8.20/8.59 (declare-fun tptp.the_Pr4378521158711661632nt_int ((-> tptp.product_prod_int_int Bool)) tptp.product_prod_int_int)
% 8.20/8.59 (declare-fun tptp.defaul566961228789861419t_unit () tptp.product_unit)
% 8.20/8.59 (declare-fun tptp.lim_Product_unit (tptp.heap_e7401611519738050253t_unit) tptp.nat)
% 8.20/8.59 (declare-fun tptp.heap_T6183433275982383450t_unit ((-> tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (declare-fun tptp.heap_Time_Heap_a2 ((-> tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)) tptp.heap_Time_Heap_a)
% 8.20/8.59 (declare-fun tptp.heap_Time_Heap_b2 ((-> tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)) tptp.heap_Time_Heap_b)
% 8.20/8.59 (declare-fun tptp.heap_T4142866422068808505t_unit ((-> tptp.product_unit tptp.nat) tptp.heap_T5738788834812785303t_unit) tptp.nat)
% 8.20/8.59 (declare-fun tptp.heap_T4436805183663264329t_unit (tptp.set_He475150555083384525t_unit) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (declare-fun tptp.heap_T4208721593536448476t_unit ((-> tptp.product_unit Bool) tptp.product_unit) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (declare-fun tptp.heap_Time_assert_a ((-> tptp.a Bool) tptp.a) tptp.heap_Time_Heap_a)
% 8.20/8.59 (declare-fun tptp.heap_Time_assert_b ((-> tptp.b Bool) tptp.b) tptp.heap_Time_Heap_b)
% 8.20/8.59 (declare-fun tptp.heap_T2633723481742716231t_unit (tptp.heap_T5738788834812785303t_unit (-> tptp.product_unit tptp.heap_T5738788834812785303t_unit)) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (declare-fun tptp.heap_T757603679106148408unit_a (tptp.heap_T5738788834812785303t_unit (-> tptp.product_unit tptp.heap_Time_Heap_a)) tptp.heap_Time_Heap_a)
% 8.20/8.59 (declare-fun tptp.heap_T757603679106148409unit_b (tptp.heap_T5738788834812785303t_unit (-> tptp.product_unit tptp.heap_Time_Heap_b)) tptp.heap_Time_Heap_b)
% 8.20/8.59 (declare-fun tptp.heap_T8685611227969916822t_unit (tptp.heap_Time_Heap_a (-> tptp.a tptp.heap_T5738788834812785303t_unit)) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.heap_Time_bind_a_b (tptp.heap_Time_Heap_a (-> tptp.a tptp.heap_Time_Heap_b)) tptp.heap_Time_Heap_b)
% 8.20/8.59 (declare-fun tptp.heap_T3413130826733729493t_unit (tptp.heap_Time_Heap_b (-> tptp.b tptp.heap_T5738788834812785303t_unit)) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (declare-fun tptp.heap_Time_bind_b_a (tptp.heap_Time_Heap_b (-> tptp.b tptp.heap_Time_Heap_a)) tptp.heap_Time_Heap_a)
% 8.20/8.59 (declare-fun tptp.heap_Time_bind_b_b (tptp.heap_Time_Heap_b (-> tptp.b tptp.heap_Time_Heap_b)) tptp.heap_Time_Heap_b)
% 8.20/8.59 (declare-fun tptp.heap_T1873992626244518189rray_o (tptp.heap_T5660665574680485309rray_o tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.array_o tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.heap_T6233771638828666989ay_int (tptp.heap_T1346037964561226099ay_int tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.array_int tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.heap_T1188250621483087889ay_nat (tptp.heap_T3836121109492952855ay_nat tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.array_nat tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.heap_T6553295506729943825t_unit (tptp.heap_T5738788834812785303t_unit tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.product_unit tptp.nat) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.heap_Time_effect_b (tptp.heap_Time_Heap_b tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.b tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.heap_T8140152426084121245rray_o (tptp.heap_T5660665574680485309rray_o tptp.heap_e7401611519738050253t_unit) tptp.option1013472963438093988it_nat)
% 8.20/8.59 (declare-fun tptp.heap_T7249310324989956861ay_int (tptp.heap_T1346037964561226099ay_int tptp.heap_e7401611519738050253t_unit) tptp.option2555668343544256180it_nat)
% 8.20/8.59 (declare-fun tptp.heap_T2203789307644377761ay_nat (tptp.heap_T3836121109492952855ay_nat tptp.heap_e7401611519738050253t_unit) tptp.option4277301481530639448it_nat)
% 8.20/8.59 (declare-fun tptp.heap_T875086893843062177t_unit (tptp.heap_T5738788834812785303t_unit tptp.heap_e7401611519738050253t_unit) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.heap_Time_execute_a (tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit) tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.heap_Time_execute_b (tptp.heap_Time_Heap_b tptp.heap_e7401611519738050253t_unit) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.heap_T8440541562793052209t_unit ((-> tptp.heap_e7401611519738050253t_unit Bool) (-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat)) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (declare-fun tptp.heap_Time_guard_a ((-> tptp.heap_e7401611519738050253t_unit Bool) (-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat)) tptp.heap_Time_Heap_a)
% 8.20/8.59 (declare-fun tptp.heap_Time_guard_b ((-> tptp.heap_e7401611519738050253t_unit Bool) (-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat)) tptp.heap_Time_Heap_b)
% 8.20/8.59 (declare-fun tptp.heap_T8367841184088661864rray_o ((-> tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat)) tptp.heap_T5660665574680485309rray_o)
% 8.20/8.59 (declare-fun tptp.heap_T147713666487170802ay_int ((-> tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat)) tptp.heap_T1346037964561226099ay_int)
% 8.20/8.59 (declare-fun tptp.heap_T4325564685996367510ay_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat)) tptp.heap_T3836121109492952855ay_nat)
% 8.20/8.59 (declare-fun tptp.heap_T6927113302350381334t_unit ((-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat)) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (declare-fun tptp.heap_Time_heap_a ((-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat)) tptp.heap_Time_Heap_a)
% 8.20/8.59 (declare-fun tptp.heap_Time_heap_b ((-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat)) tptp.heap_Time_Heap_b)
% 8.20/8.59 (declare-fun tptp.heap_T2927564422264180874t_unit (tptp.list_char) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (declare-fun tptp.heap_Time_raise_a (tptp.list_char) tptp.heap_Time_Heap_a)
% 8.20/8.59 (declare-fun tptp.heap_Time_raise_b (tptp.list_char) tptp.heap_Time_Heap_b)
% 8.20/8.59 (declare-fun tptp.heap_T7507251653302230130t_unit (tptp.product_unit) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (declare-fun tptp.heap_Time_return_a (tptp.a) tptp.heap_Time_Heap_a)
% 8.20/8.59 (declare-fun tptp.heap_Time_return_b (tptp.b) tptp.heap_Time_Heap_b)
% 8.20/8.59 (declare-fun tptp.heap_T584514906347983379t_unit (tptp.heap_T5738788834812785303t_unit tptp.heap_e7401611519738050253t_unit) Bool)
% 8.20/8.59 (declare-fun tptp.heap_Time_success_a (tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit) Bool)
% 8.20/8.59 (declare-fun tptp.heap_Time_success_b (tptp.heap_Time_Heap_b tptp.heap_e7401611519738050253t_unit) Bool)
% 8.20/8.59 (declare-fun tptp.heap_T560649228465745139t_unit ((-> tptp.heap_e7401611519738050253t_unit tptp.product_unit)) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (declare-fun tptp.heap_Time_tap_a ((-> tptp.heap_e7401611519738050253t_unit tptp.a)) tptp.heap_Time_Heap_a)
% 8.20/8.59 (declare-fun tptp.heap_Time_tap_b ((-> tptp.heap_e7401611519738050253t_unit tptp.b)) tptp.heap_Time_Heap_b)
% 8.20/8.59 (declare-fun tptp.heap_T3616969660504097270t_unit (tptp.nat tptp.option8956607266484857688it_nat) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.heap_T7616092557645711335rame_a (tptp.nat tptp.option3562590408128118217it_nat) tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.heap_T7616092557645711336rame_b (tptp.nat tptp.option4065278094766928714it_nat) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.heap_T996182799752388649t_unit (tptp.produc3911288613690379145it_nat tptp.produc3911288613690379145it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.heap_T8132184524487034138_rel_a (tptp.produc4453839368661128058it_nat tptp.produc4453839368661128058it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.heap_T8132184524487034139_rel_b (tptp.produc2207270350733924475it_nat tptp.produc2207270350733924475it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.heap_T4284346855313245393t_unit (tptp.product_unit) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (declare-fun tptp.heap_Time_ureturn_a (tptp.a) tptp.heap_Time_Heap_a)
% 8.20/8.59 (declare-fun tptp.heap_Time_ureturn_b (tptp.b) tptp.heap_Time_Heap_b)
% 8.20/8.59 (declare-fun tptp.heap_Time_wait (tptp.nat) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (declare-fun tptp.hoare_hoare_triple_o (tptp.assn tptp.heap_Time_Heap_o (-> Bool tptp.assn)) Bool)
% 8.20/8.59 (declare-fun tptp.hoare_3065115510600077593le_int (tptp.assn tptp.heap_Time_Heap_int (-> tptp.int tptp.assn)) Bool)
% 8.20/8.59 (declare-fun tptp.hoare_3067605981109127869le_nat (tptp.assn tptp.heap_Time_Heap_nat (-> tptp.nat tptp.assn)) Bool)
% 8.20/8.59 (declare-fun tptp.hoare_8945653483474564448t_unit (tptp.assn tptp.heap_T5738788834812785303t_unit (-> tptp.product_unit tptp.assn)) Bool)
% 8.20/8.59 (declare-fun tptp.hoare_hoare_triple_a (tptp.assn tptp.heap_Time_Heap_a (-> tptp.a tptp.assn)) Bool)
% 8.20/8.59 (declare-fun tptp.hoare_hoare_triple_b (tptp.assn tptp.heap_Time_Heap_b (-> tptp.b tptp.assn)) Bool)
% 8.20/8.59 (declare-fun tptp.hoare_new_addrs (tptp.heap_e7401611519738050253t_unit tptp.set_nat tptp.heap_e7401611519738050253t_unit) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.if_int2409958687428134794nt_int (Bool (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.product_prod_int_int) tptp.int) tptp.product_prod_int_int)
% 8.20/8.59 (declare-fun tptp.if_Pro5796790085669187537et_nat (Bool (-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat) (-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat) tptp.produc3925858234332021118et_nat) tptp.produc2732055786443039994et_nat)
% 8.20/8.59 (declare-fun tptp.if_Pro2760142802149639654atural (Bool (-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) (-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 8.20/8.59 (declare-fun tptp.if_Pro3578090444564244254it_nat (Bool (-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat) (-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat) tptp.produc6653097349344004940it_nat) tptp.produc3260487557148687353it_nat)
% 8.20/8.59 (declare-fun tptp.if_Pro4080778131203054751it_nat (Bool (-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat) (-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat) tptp.produc6653097349344004940it_nat) tptp.produc7388388658123137530it_nat)
% 8.20/8.59 (declare-fun tptp.if_Pro6440128116348121305et_nat (Bool (-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat) (-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat) tptp.produc3658429121746597890et_nat) tptp.produc3925858234332021118et_nat)
% 8.20/8.59 (declare-fun tptp.if_assn (Bool tptp.assn tptp.assn) tptp.assn)
% 8.20/8.59 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.if_Code_natural (Bool tptp.code_natural tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 8.20/8.59 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.if_mul8430962117462786573at_nat (Bool tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) tptp.multis2468970476368604999at_nat)
% 8.20/8.59 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 8.20/8.59 (declare-fun tptp.if_opt1729522071442692626it_nat (Bool tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.if_opt6883606601682554499it_nat (Bool tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat) tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.if_opt7386294288321364996it_nat (Bool tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.if_option_set_o (Bool tptp.option_set_o tptp.option_set_o) tptp.option_set_o)
% 8.20/8.59 (declare-fun tptp.if_option_set_int (Bool tptp.option_set_int tptp.option_set_int) tptp.option_set_int)
% 8.20/8.59 (declare-fun tptp.if_option_set_nat (Bool tptp.option_set_nat tptp.option_set_nat) tptp.option_set_nat)
% 8.20/8.59 (declare-fun tptp.if_opt7704869406773131885at_nat (Bool tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat) tptp.option8963830502488799655at_nat)
% 8.20/8.59 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 8.20/8.59 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 8.20/8.59 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 8.20/8.59 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 8.20/8.59 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.infini8530281810654367211te_nat (tptp.set_nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 8.20/8.59 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 8.20/8.59 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 8.20/8.59 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 8.20/8.59 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.ring_11222124179247155820nteger () tptp.set_Code_integer)
% 8.20/8.59 (declare-fun tptp.ring_1_Ints_int () tptp.set_int)
% 8.20/8.59 (declare-fun tptp.ring_1_Ints_rat () tptp.set_rat)
% 8.20/8.59 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.inf_inf_o_o ((-> Bool Bool) (-> Bool Bool) Bool) Bool)
% 8.20/8.59 (declare-fun tptp.inf_inf_int_int_o ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool) tptp.int tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.inf_inf_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.inf_inf_list_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 8.20/8.59 (declare-fun tptp.inf_inf_nat_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.inf_inf_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.inf_inf_set_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.inf_in5102985939729578038_int_o ((-> tptp.set_Pr958786334691620121nt_int Bool) (-> tptp.set_Pr958786334691620121nt_int Bool) tptp.set_Pr958786334691620121nt_int) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.inf_in844129575377303227_nat_o ((-> tptp.b tptp.produc6653097349344004940it_nat Bool) (-> tptp.b tptp.produc6653097349344004940it_nat Bool) tptp.b tptp.produc6653097349344004940it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.inf_inf_assn (tptp.assn tptp.assn) tptp.assn)
% 8.20/8.59 (declare-fun tptp.inf_inf_int (tptp.int tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.inf_in7104746047340619750_int_o (tptp.option1893999432384633940_int_o tptp.option1893999432384633940_int_o) tptp.option1893999432384633940_int_o)
% 8.20/8.59 (declare-fun tptp.inf_inf_option_assn (tptp.option_assn tptp.option_assn) tptp.option_assn)
% 8.20/8.59 (declare-fun tptp.inf_inf_option_nat (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 8.20/8.59 (declare-fun tptp.inf_in7812914138253463912et_nat (tptp.option_set_nat tptp.option_set_nat) tptp.option_set_nat)
% 8.20/8.59 (declare-fun tptp.inf_in777885744494410645at_nat (tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat) tptp.option8963830502488799655at_nat)
% 8.20/8.59 (declare-fun tptp.inf_inf_Product_unit (tptp.product_unit tptp.product_unit) tptp.product_unit)
% 8.20/8.59 (declare-fun tptp.inf_inf_rat (tptp.rat tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.inf_inf_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 8.20/8.59 (declare-fun tptp.inf_inf_set_assn (tptp.set_assn tptp.set_assn) tptp.set_assn)
% 8.20/8.59 (declare-fun tptp.inf_in1364745209274528805nteger (tptp.set_Code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 8.20/8.59 (declare-fun tptp.inf_inf_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.inf_inf_set_list_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 8.20/8.59 (declare-fun tptp.inf_inf_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.inf_inf_set_num (tptp.set_num tptp.set_num) tptp.set_num)
% 8.20/8.59 (declare-fun tptp.inf_in3088352823822785602et_nat (tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat) tptp.set_Pr8536935166611901872et_nat)
% 8.20/8.59 (declare-fun tptp.inf_in1768905781608824518et_nat (tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat) tptp.set_Pr3286484037609594932et_nat)
% 8.20/8.59 (declare-fun tptp.inf_in2269163501485487111nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 8.20/8.59 (declare-fun tptp.inf_in1697001100524423349at_nat (tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat) tptp.set_Pr8551490117392284871at_nat)
% 8.20/8.59 (declare-fun tptp.inf_in2572325071724192079at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.inf_in7913087082777306421at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.59 (declare-fun tptp.inf_in3493107508024165057it_nat (tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat) tptp.set_Pr7098220151150636591it_nat)
% 8.20/8.59 (declare-fun tptp.inf_in3995795194662975554it_nat (tptp.set_Pr7600907837789447088it_nat tptp.set_Pr7600907837789447088it_nat) tptp.set_Pr7600907837789447088it_nat)
% 8.20/8.59 (declare-fun tptp.inf_inf_set_rat (tptp.set_rat tptp.set_rat) tptp.set_rat)
% 8.20/8.59 (declare-fun tptp.inf_inf_set_set_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 8.20/8.59 (declare-fun tptp.inf_in8396524679539076455nt_int (tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int) tptp.set_se6260736226359567993nt_int)
% 8.20/8.59 (declare-fun tptp.semila8603258263270017530r_assn ((-> tptp.assn tptp.assn tptp.assn) tptp.assn (-> tptp.assn tptp.assn Bool) (-> tptp.assn tptp.assn Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.sup_sup_o_o ((-> Bool Bool) (-> Bool Bool) Bool) Bool)
% 8.20/8.59 (declare-fun tptp.sup_sup_int_int_o ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool) tptp.int tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.sup_sup_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.sup_sup_list_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.sup_sup_nat_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.sup_sup_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.sup_su6256023009775730178_nat_o ((-> tptp.produc4166570645942440679at_nat Bool) (-> tptp.produc4166570645942440679at_nat Bool) tptp.produc4166570645942440679at_nat) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.sup_su2080679670758317954_nat_o ((-> tptp.produc3843707927480180839at_nat Bool) (-> tptp.produc3843707927480180839at_nat Bool) tptp.produc3843707927480180839at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.sup_sup_set_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.sup_su1852724690005176016_int_o ((-> tptp.set_Pr958786334691620121nt_int Bool) (-> tptp.set_Pr958786334691620121nt_int Bool) tptp.set_Pr958786334691620121nt_int) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.sup_su4207681470386032469_nat_o ((-> tptp.b tptp.produc6653097349344004940it_nat Bool) (-> tptp.b tptp.produc6653097349344004940it_nat Bool) tptp.b tptp.produc6653097349344004940it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.sup_sup_assn (tptp.assn tptp.assn) tptp.assn)
% 8.20/8.59 (declare-fun tptp.sup_sup_int (tptp.int tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.sup_sup_option_int (tptp.option_int tptp.option_int) tptp.option_int)
% 8.20/8.59 (declare-fun tptp.sup_sup_option_nat (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 8.20/8.59 (declare-fun tptp.sup_su3598758113090618626et_nat (tptp.option_set_nat tptp.option_set_nat) tptp.option_set_nat)
% 8.20/8.59 (declare-fun tptp.sup_su5873096292857799009at_nat (tptp.option2498585697089621389at_nat tptp.option2498585697089621389at_nat) tptp.option2498585697089621389at_nat)
% 8.20/8.59 (declare-fun tptp.sup_su2273273666271716065at_nat (tptp.option1583680563626158861at_nat tptp.option1583680563626158861at_nat) tptp.option1583680563626158861at_nat)
% 8.20/8.59 (declare-fun tptp.sup_sup_Product_unit (tptp.product_unit tptp.product_unit) tptp.product_unit)
% 8.20/8.59 (declare-fun tptp.sup_sup_rat (tptp.rat tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.sup_sup_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 8.20/8.59 (declare-fun tptp.sup_su848401254843788991nteger (tptp.set_Code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 8.20/8.59 (declare-fun tptp.sup_sup_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.sup_sup_set_list_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 8.20/8.59 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.sup_sup_set_num (tptp.set_num tptp.set_num) tptp.set_num)
% 8.20/8.59 (declare-fun tptp.sup_su8975264963432250076et_nat (tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat) tptp.set_Pr8536935166611901872et_nat)
% 8.20/8.59 (declare-fun tptp.sup_su7128418612487073120et_nat (tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat) tptp.set_Pr3286484037609594932et_nat)
% 8.20/8.59 (declare-fun tptp.sup_su6024340866399070445nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 8.20/8.59 (declare-fun tptp.sup_su3035147773818789531at_nat (tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat) tptp.set_Pr8551490117392284871at_nat)
% 8.20/8.59 (declare-fun tptp.sup_su6327502436637775413at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.sup_su718114333110466843at_nat (tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr8693737435421807431at_nat)
% 8.20/8.59 (declare-fun tptp.sup_su5525570899277871387at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.59 (declare-fun tptp.sup_su3211442154794319707it_nat (tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat) tptp.set_Pr7098220151150636591it_nat)
% 8.20/8.59 (declare-fun tptp.sup_su3714129841433130204it_nat (tptp.set_Pr7600907837789447088it_nat tptp.set_Pr7600907837789447088it_nat) tptp.set_Pr7600907837789447088it_nat)
% 8.20/8.59 (declare-fun tptp.sup_sup_set_rat (tptp.set_rat tptp.set_rat) tptp.set_rat)
% 8.20/8.59 (declare-fun tptp.sup_sup_set_set_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 8.20/8.59 (declare-fun tptp.sup_su2047564715030645325nt_int (tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int) tptp.set_se6260736226359567993nt_int)
% 8.20/8.59 (declare-fun tptp.lattic8263393255366662781ax_int (tptp.set_int) tptp.int)
% 8.20/8.59 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.lattic8660852769118194346_int_o ((-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int Bool) (-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) Bool) (-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.lattic5623431474481994958t_assn ((-> tptp.assn tptp.assn tptp.assn) (-> tptp.assn tptp.assn Bool) (-> tptp.assn tptp.assn Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.lattic6006661108824415698et_int ((-> tptp.int tptp.int tptp.int) (-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.lattic6009151579333465974et_nat ((-> tptp.nat tptp.nat tptp.nat) (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.lattic2566483365489244608et_num ((-> tptp.num tptp.num tptp.num) (-> tptp.num tptp.num Bool) (-> tptp.num tptp.num Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.lattic5374021519246970238et_rat ((-> tptp.rat tptp.rat tptp.rat) (-> tptp.rat tptp.rat Bool) (-> tptp.rat tptp.rat Bool)) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 8.20/8.59 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.butlast_nat (tptp.list_nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.drop_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.enumerate_o (tptp.nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 8.20/8.59 (declare-fun tptp.enumerate_int (tptp.nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 8.20/8.59 (declare-fun tptp.enumerate_nat (tptp.nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 8.20/8.59 (declare-fun tptp.filter_nat2 ((-> tptp.nat Bool) tptp.list_nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.find_o ((-> Bool Bool) tptp.list_o) tptp.option_o)
% 8.20/8.59 (declare-fun tptp.find_int ((-> tptp.int Bool) tptp.list_int) tptp.option_int)
% 8.20/8.59 (declare-fun tptp.find_nat ((-> tptp.nat Bool) tptp.list_nat) tptp.option_nat)
% 8.20/8.59 (declare-fun tptp.find_num ((-> tptp.num Bool) tptp.list_num) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.find_P5317947125398478060it_nat ((-> tptp.produc8664842809031399944it_nat Bool) tptp.list_P626663023886443800it_nat) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.find_P4815471733760996061it_nat ((-> tptp.produc3260487557148687353it_nat Bool) tptp.list_P6935614879863011209it_nat) tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.find_P8943372834735446238it_nat ((-> tptp.produc7388388658123137530it_nat Bool) tptp.list_P7438302566501821706it_nat) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.last_nat (tptp.list_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.linord1735203802627413978nt_int ((-> tptp.int tptp.int) tptp.list_int) tptp.list_int)
% 8.20/8.59 (declare-fun tptp.linord738340561235409698at_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.cons_P6219271836124797827_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.list_P7985473006766602707_nat_o) tptp.list_P7985473006766602707_nat_o)
% 8.20/8.59 (declare-fun tptp.cons_o (Bool tptp.list_o) tptp.list_o)
% 8.20/8.59 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 8.20/8.59 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.cons_num (tptp.num tptp.list_num) tptp.list_num)
% 8.20/8.59 (declare-fun tptp.cons_option_num (tptp.option_num tptp.list_option_num) tptp.list_option_num)
% 8.20/8.59 (declare-fun tptp.cons_P6329468272379687876et_nat (tptp.produc2732055786443039994et_nat tptp.list_P362550909693114634et_nat) tptp.list_P362550909693114634et_nat)
% 8.20/8.59 (declare-fun tptp.cons_P3419706843779801160et_nat (tptp.produc3925858234332021118et_nat tptp.list_P2321686559999237006et_nat) tptp.list_P2321686559999237006et_nat)
% 8.20/8.59 (declare-fun tptp.cons_P7873165156130251286it_nat (tptp.produc6653097349344004940it_nat tptp.list_P131111800688179804it_nat) tptp.list_P131111800688179804it_nat)
% 8.20/8.59 (declare-fun tptp.cons_P2869003950965171916et_nat (tptp.produc3658429121746597890et_nat tptp.list_P9062070895058802706et_nat) tptp.list_P9062070895058802706et_nat)
% 8.20/8.59 (declare-fun tptp.cons_P3334398858971670639nt_int (tptp.product_prod_int_int tptp.list_P5707943133018811711nt_int) tptp.list_P5707943133018811711nt_int)
% 8.20/8.59 (declare-fun tptp.cons_P7512249878480867347nt_nat (tptp.product_prod_int_nat tptp.list_P8198026277950538467nt_nat) tptp.list_P8198026277950538467nt_nat)
% 8.20/8.59 (declare-fun tptp.cons_P2335045147070616083at_int (tptp.product_prod_nat_int tptp.list_P3521021558325789923at_int) tptp.list_P3521021558325789923at_int)
% 8.20/8.59 (declare-fun tptp.cons_P6512896166579812791at_nat (tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat) tptp.list_P6011104703257516679at_nat)
% 8.20/8.59 (declare-fun tptp.cons_P4136552807766418642it_nat (tptp.produc8664842809031399944it_nat tptp.list_P626663023886443800it_nat) tptp.list_P626663023886443800it_nat)
% 8.20/8.59 (declare-fun tptp.cons_P2339423585217329347it_nat (tptp.produc3260487557148687353it_nat tptp.list_P6935614879863011209it_nat) tptp.list_P6935614879863011209it_nat)
% 8.20/8.59 (declare-fun tptp.cons_P6467324686191779524it_nat (tptp.produc7388388658123137530it_nat tptp.list_P7438302566501821706it_nat) tptp.list_P7438302566501821706it_nat)
% 8.20/8.59 (declare-fun tptp.cons_rat (tptp.rat tptp.list_rat) tptp.list_rat)
% 8.20/8.59 (declare-fun tptp.cons_a (tptp.a tptp.list_a) tptp.list_a)
% 8.20/8.59 (declare-fun tptp.cons_b (tptp.b tptp.list_b) tptp.list_b)
% 8.20/8.59 (declare-fun tptp.nil_int () tptp.list_int)
% 8.20/8.59 (declare-fun tptp.nil_nat () tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 8.20/8.59 (declare-fun tptp.nth_option_num (tptp.list_option_num tptp.nat) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 8.20/8.59 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 8.20/8.59 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 8.20/8.59 (declare-fun tptp.nth_Pr4561283279332054789it_nat (tptp.list_P131111800688179804it_nat tptp.nat) tptp.produc6653097349344004940it_nat)
% 8.20/8.59 (declare-fun tptp.nth_Pr7514405829937366042_int_o (tptp.list_P5087981734274514673_int_o tptp.nat) tptp.product_prod_int_o)
% 8.20/8.59 (declare-fun tptp.nth_Pr4439495888332055232nt_int (tptp.list_P5707943133018811711nt_int tptp.nat) tptp.product_prod_int_int)
% 8.20/8.59 (declare-fun tptp.nth_Pr8617346907841251940nt_nat (tptp.list_P8198026277950538467nt_nat tptp.nat) tptp.product_prod_int_nat)
% 8.20/8.59 (declare-fun tptp.nth_Pr112076138515278198_nat_o (tptp.list_P7333126701944960589_nat_o tptp.nat) tptp.product_prod_nat_o)
% 8.20/8.59 (declare-fun tptp.nth_Pr3440142176431000676at_int (tptp.list_P3521021558325789923at_int tptp.nat) tptp.product_prod_nat_int)
% 8.20/8.59 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 8.20/8.59 (declare-fun tptp.nth_Pr2956344619228612545it_nat (tptp.list_P626663023886443800it_nat tptp.nat) tptp.produc8664842809031399944it_nat)
% 8.20/8.59 (declare-fun tptp.nth_Pr8687047199098054322it_nat (tptp.list_P6935614879863011209it_nat tptp.nat) tptp.produc3260487557148687353it_nat)
% 8.20/8.59 (declare-fun tptp.nth_Pr3591576263217728691it_nat (tptp.list_P7438302566501821706it_nat tptp.nat) tptp.produc7388388658123137530it_nat)
% 8.20/8.59 (declare-fun tptp.nth_Product_unit (tptp.list_Product_unit tptp.nat) tptp.product_unit)
% 8.20/8.59 (declare-fun tptp.nth_rat (tptp.list_rat tptp.nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.nth_b (tptp.list_b tptp.nat) tptp.b)
% 8.20/8.59 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 8.20/8.59 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 8.20/8.59 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 8.20/8.59 (declare-fun tptp.product_int_o (tptp.list_int tptp.list_o) tptp.list_P5087981734274514673_int_o)
% 8.20/8.59 (declare-fun tptp.product_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 8.20/8.59 (declare-fun tptp.product_int_nat (tptp.list_int tptp.list_nat) tptp.list_P8198026277950538467nt_nat)
% 8.20/8.59 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 8.20/8.59 (declare-fun tptp.product_nat_int (tptp.list_nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 8.20/8.59 (declare-fun tptp.product_nat_nat (tptp.list_nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 8.20/8.59 (declare-fun tptp.produc1870533552098665926it_nat (tptp.list_b tptp.list_P131111800688179804it_nat) tptp.list_P7438302566501821706it_nat)
% 8.20/8.59 (declare-fun tptp.rotate1_o (tptp.list_o) tptp.list_o)
% 8.20/8.59 (declare-fun tptp.rotate1_int (tptp.list_int) tptp.list_int)
% 8.20/8.59 (declare-fun tptp.rotate1_nat (tptp.list_nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.rotate_o (tptp.nat tptp.list_o) tptp.list_o)
% 8.20/8.59 (declare-fun tptp.rotate_int (tptp.nat tptp.list_int) tptp.list_int)
% 8.20/8.59 (declare-fun tptp.rotate_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.sorted_wrt_o ((-> Bool Bool Bool) tptp.list_o) Bool)
% 8.20/8.59 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 8.20/8.59 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 8.20/8.59 (declare-fun tptp.sorted_wrt_num ((-> tptp.num tptp.num Bool) tptp.list_num) Bool)
% 8.20/8.59 (declare-fun tptp.sorted_wrt_rat ((-> tptp.rat tptp.rat Bool) tptp.list_rat) Bool)
% 8.20/8.59 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 8.20/8.59 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 8.20/8.59 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 8.20/8.59 (declare-fun tptp.zip_Pr8136144321567152340et_nat (tptp.list_P7985473006766602707_nat_o tptp.list_P2321686559999237006et_nat) tptp.list_P362550909693114634et_nat)
% 8.20/8.59 (declare-fun tptp.zip_Pr7134870689397686104et_nat (tptp.list_P7985473006766602707_nat_o tptp.list_P9062070895058802706et_nat) tptp.list_P2321686559999237006et_nat)
% 8.20/8.59 (declare-fun tptp.zip_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 8.20/8.59 (declare-fun tptp.zip_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 8.20/8.59 (declare-fun tptp.zip_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 8.20/8.59 (declare-fun tptp.zip_int_o (tptp.list_int tptp.list_o) tptp.list_P5087981734274514673_int_o)
% 8.20/8.59 (declare-fun tptp.zip_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 8.20/8.59 (declare-fun tptp.zip_int_nat (tptp.list_int tptp.list_nat) tptp.list_P8198026277950538467nt_nat)
% 8.20/8.59 (declare-fun tptp.zip_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 8.20/8.59 (declare-fun tptp.zip_nat_int (tptp.list_nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 8.20/8.59 (declare-fun tptp.zip_nat_nat (tptp.list_nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 8.20/8.59 (declare-fun tptp.zip_a_1859587264247984595it_nat (tptp.list_a tptp.list_P131111800688179804it_nat) tptp.list_P6935614879863011209it_nat)
% 8.20/8.59 (declare-fun tptp.zip_b_5987488365222434772it_nat (tptp.list_b tptp.list_P131111800688179804it_nat) tptp.list_P7438302566501821706it_nat)
% 8.20/8.59 (declare-fun tptp.eps_Opt_int ((-> tptp.int Bool)) tptp.option_int)
% 8.20/8.59 (declare-fun tptp.eps_Opt_num ((-> tptp.num Bool)) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.eps_Op6423059015816587746et_nat ((-> tptp.produc3925858234332021118et_nat Bool)) tptp.option5190343406534369742et_nat)
% 8.20/8.59 (declare-fun tptp.eps_Op8301357815426737072it_nat ((-> tptp.produc6653097349344004940it_nat Bool)) tptp.option233860712434008220it_nat)
% 8.20/8.59 (declare-fun tptp.eps_Op2013419657081471078et_nat ((-> tptp.produc3658429121746597890et_nat Bool)) tptp.option936205604648967762et_nat)
% 8.20/8.59 (declare-fun tptp.eps_Op3393321821070424684it_nat ((-> tptp.produc8664842809031399944it_nat Bool)) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.eps_Op1741419982095519837it_nat ((-> tptp.produc3260487557148687353it_nat Bool)) tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.eps_Op5869321083069970014it_nat ((-> tptp.produc7388388658123137530it_nat Bool)) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.biject1468766312547416318et_nat (tptp.set_Pr8536935166611901872et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.biject2615096655818420098et_nat (tptp.set_Pr3286484037609594932et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.bijective_int_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 8.20/8.59 (declare-fun tptp.biject5714339216877808333at_nat (tptp.set_Pr8551490117392284871at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.bijective_nat_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.biject3503750217840948301at_nat (tptp.set_Pr8693737435421807431at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.biject8592306251674886141it_nat (tptp.set_Pr7098220151150636591it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.biject3496835315794560510it_nat (tptp.set_Pr7600907837789447088it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.dflt_None_set_o (tptp.set_o) tptp.option_set_o)
% 8.20/8.59 (declare-fun tptp.dflt_None_set_int (tptp.set_int) tptp.option_set_int)
% 8.20/8.59 (declare-fun tptp.dflt_None_set_nat (tptp.set_nat) tptp.option_set_nat)
% 8.20/8.59 (declare-fun tptp.dflt_N6592383573632408824at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.option8963830502488799655at_nat)
% 8.20/8.59 (declare-fun tptp.map_to_set_int_int ((-> tptp.int tptp.option_int)) tptp.set_Pr958786334691620121nt_int)
% 8.20/8.59 (declare-fun tptp.map_to_set_nat_nat ((-> tptp.nat tptp.option_nat)) tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.rel_of7774016450764239315et_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.option5190343406534369742et_nat) (-> tptp.produc2732055786443039994et_nat Bool)) tptp.set_Pr8536935166611901872et_nat)
% 8.20/8.59 (declare-fun tptp.rel_of4838799251197538391et_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.option936205604648967762et_nat) (-> tptp.produc3925858234332021118et_nat Bool)) tptp.set_Pr3286484037609594932et_nat)
% 8.20/8.59 (declare-fun tptp.rel_of_int_int ((-> tptp.int tptp.option_int) (-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 8.20/8.59 (declare-fun tptp.rel_of_nat_nat ((-> tptp.nat tptp.option_nat) (-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.rel_of2761222537318653906it_nat ((-> tptp.a tptp.option233860712434008220it_nat) (-> tptp.produc3260487557148687353it_nat Bool)) tptp.set_Pr7098220151150636591it_nat)
% 8.20/8.59 (declare-fun tptp.rel_of6889123638293104083it_nat ((-> tptp.b tptp.option233860712434008220it_nat) (-> tptp.produc7388388658123137530it_nat Bool)) tptp.set_Pr7600907837789447088it_nat)
% 8.20/8.59 (declare-fun tptp.set_to2047380710992656148et_nat (tptp.set_Pr8536935166611901872et_nat (-> tptp.produc3658429121746597890et_nat Bool)) tptp.option5190343406534369742et_nat)
% 8.20/8.59 (declare-fun tptp.set_to6040779677306527128et_nat (tptp.set_Pr3286484037609594932et_nat (-> tptp.produc3658429121746597890et_nat Bool)) tptp.option936205604648967762et_nat)
% 8.20/8.59 (declare-fun tptp.set_to_map_int_int (tptp.set_Pr958786334691620121nt_int tptp.int) tptp.option_int)
% 8.20/8.59 (declare-fun tptp.set_to_map_nat_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.option_nat)
% 8.20/8.59 (declare-fun tptp.set_to2008915276733485075it_nat (tptp.set_Pr7098220151150636591it_nat tptp.a) tptp.option233860712434008220it_nat)
% 8.20/8.59 (declare-fun tptp.set_to6136816377707935252it_nat (tptp.set_Pr7600907837789447088it_nat tptp.b) tptp.option233860712434008220it_nat)
% 8.20/8.59 (declare-fun tptp.slice_o (tptp.nat tptp.nat tptp.list_o) tptp.list_o)
% 8.20/8.59 (declare-fun tptp.slice_int (tptp.nat tptp.nat tptp.list_int) tptp.list_int)
% 8.20/8.59 (declare-fun tptp.slice_nat (tptp.nat tptp.nat tptp.list_nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.the_default_num (tptp.num tptp.option_num) tptp.num)
% 8.20/8.59 (declare-fun tptp.the_de2487931475039285041it_nat (tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat) tptp.produc8664842809031399944it_nat)
% 8.20/8.59 (declare-fun tptp.the_de542837501814275618it_nat (tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat) tptp.produc3260487557148687353it_nat)
% 8.20/8.59 (declare-fun tptp.the_de4670738602788725795it_nat (tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat) tptp.produc7388388658123137530it_nat)
% 8.20/8.59 (declare-fun tptp.the_default_set_o (tptp.set_o tptp.option_set_o) tptp.set_o)
% 8.20/8.59 (declare-fun tptp.the_default_set_int (tptp.set_int tptp.option_set_int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.the_default_set_nat (tptp.set_nat tptp.option_set_nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.the_de3668382347305825784at_nat (tptp.set_Pr1261947904930325089at_nat tptp.option8963830502488799655at_nat) tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.uncurry_int_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 8.20/8.59 (declare-fun tptp.uncurry_int_int_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 8.20/8.59 (declare-fun tptp.uncurr7650761721940715016nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.add_ms2612439473150266591at_nat (tptp.product_prod_nat_nat tptp.multis2468970476368604999at_nat) tptp.multis2468970476368604999at_nat)
% 8.20/8.59 (declare-fun tptp.ms_strict () tptp.set_Pr8551490117392284871at_nat)
% 8.20/8.59 (declare-fun tptp.ms_weak () tptp.set_Pr8551490117392284871at_nat)
% 8.20/8.59 (declare-fun tptp.pw_leq (tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.set_ms8126754132646256062at_nat (tptp.multis2468970476368604999at_nat) tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.case_nat_int (tptp.int (-> tptp.nat tptp.int) tptp.nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.semiri3763490453095760265atural (tptp.nat) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.semiri4055485073559036834nteger ((-> tptp.code_integer tptp.code_integer) tptp.nat tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.semiri7787848453975740701ux_rat ((-> tptp.rat tptp.rat) tptp.nat tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.size_s1564113455978345259t_unit (tptp.heap_T5738788834812785303t_unit) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s5443766701097040955_o_nat (tptp.list_P6285523579766656935_o_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s341701280123345136it_nat (tptp.list_P131111800688179804it_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s4246224855604898693_int_o (tptp.list_P5087981734274514673_int_o) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s5157815400016825771nt_int (tptp.list_P5707943133018811711nt_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s7647898544948552527nt_nat (tptp.list_P8198026277950538467nt_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s6491369823275344609_nat_o (tptp.list_P7333126701944960589_nat_o) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s2970893825323803983at_int (tptp.list_P3521021558325789923at_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s4881146867534228396it_nat (tptp.list_P626663023886443800it_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s4069378446737875485it_nat (tptp.list_P6935614879863011209it_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s4572066133376685982it_nat (tptp.list_P7438302566501821706it_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s245203480648594047t_unit (tptp.list_Product_unit) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_size_list_rat (tptp.list_rat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_size_list_b (tptp.list_b) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s8510653225128441779at_nat (tptp.multis2468970476368604999at_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s8766407808098229740it_nat (tptp.option8956607266484857688it_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s2363601347547812957it_nat (tptp.option3562590408128118217it_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_s2866289034186623454it_nat (tptp.option4065278094766928714it_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.nat_list_decode (tptp.nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.nat_list_decode_rel (tptp.nat tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.nat_prod_decode (tptp.nat) tptp.product_prod_nat_nat)
% 8.20/8.59 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 8.20/8.59 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 8.20/8.59 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 8.20/8.59 (declare-fun tptp.inc (tptp.num) tptp.num)
% 8.20/8.59 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 8.20/8.59 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 8.20/8.59 (declare-fun tptp.one () tptp.num)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 8.20/8.59 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 8.20/8.59 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.numera5444537566228673987atural (tptp.num) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 8.20/8.59 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 8.20/8.59 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 8.20/8.59 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 8.20/8.59 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 8.20/8.59 (declare-fun tptp.combine_options_num ((-> tptp.num tptp.num tptp.num) tptp.option_num tptp.option_num) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.combin4318129983670048329it_nat ((-> tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat) tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.combin5819755802923621690it_nat ((-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat) tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat) tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.combin724284867043296059it_nat ((-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat) tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.none_P2320557853698873699_int_o () tptp.option1893999432384633940_int_o)
% 8.20/8.59 (declare-fun tptp.none_assn () tptp.option_assn)
% 8.20/8.59 (declare-fun tptp.none_nat () tptp.option_nat)
% 8.20/8.59 (declare-fun tptp.none_num () tptp.option_num)
% 8.20/8.59 (declare-fun tptp.none_P199884684680593241et_nat () tptp.option2860828798490689354et_nat)
% 8.20/8.59 (declare-fun tptp.none_P4972525538344268765et_nat () tptp.option5190343406534369742et_nat)
% 8.20/8.59 (declare-fun tptp.none_P2377608414092835994nt_int () tptp.option4624381673175914239nt_int)
% 8.20/8.59 (declare-fun tptp.none_P9117596204409417319it_nat () tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.none_P2651198173097904984it_nat () tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.none_P6779099274072355161it_nat () tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.none_set_o () tptp.option_set_o)
% 8.20/8.59 (declare-fun tptp.none_set_int () tptp.option_set_int)
% 8.20/8.59 (declare-fun tptp.none_set_nat () tptp.option_set_nat)
% 8.20/8.59 (declare-fun tptp.none_s625347054029921090at_nat () tptp.option8963830502488799655at_nat)
% 8.20/8.59 (declare-fun tptp.some_P180497116919641311_int_o ((-> tptp.product_prod_int_int Bool)) tptp.option1893999432384633940_int_o)
% 8.20/8.59 (declare-fun tptp.some_o (Bool) tptp.option_o)
% 8.20/8.59 (declare-fun tptp.some_assn (tptp.assn) tptp.option_assn)
% 8.20/8.59 (declare-fun tptp.some_int (tptp.int) tptp.option_int)
% 8.20/8.59 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 8.20/8.59 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.some_P1630309045189364437et_nat (tptp.produc2732055786443039994et_nat) tptp.option2860828798490689354et_nat)
% 8.20/8.59 (declare-fun tptp.some_P750831030444334937et_nat (tptp.produc3925858234332021118et_nat) tptp.option5190343406534369742et_nat)
% 8.20/8.59 (declare-fun tptp.some_P3509045262911171395it_nat (tptp.produc8032495849646651230it_nat) tptp.option1013472963438093988it_nat)
% 8.20/8.59 (declare-fun tptp.some_P8650484732927216191it_nat (tptp.produc7196121022310644452it_nat) tptp.option2555668343544256180it_nat)
% 8.20/8.59 (declare-fun tptp.some_P8206036975937309155it_nat (tptp.produc6751673265320737416it_nat) tptp.option4277301481530639448it_nat)
% 8.20/8.59 (declare-fun tptp.some_P1054239925786823975it_nat (tptp.produc6653097349344004940it_nat) tptp.option233860712434008220it_nat)
% 8.20/8.59 (declare-fun tptp.some_P624177172695371229et_nat (tptp.produc3658429121746597890et_nat) tptp.option936205604648967762et_nat)
% 8.20/8.59 (declare-fun tptp.some_P4184893108420464158nt_int (tptp.product_prod_int_int) tptp.option4624381673175914239nt_int)
% 8.20/8.59 (declare-fun tptp.some_P1914260805536162275it_nat (tptp.produc8664842809031399944it_nat) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.some_P7913643980934408916it_nat (tptp.produc3260487557148687353it_nat) tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.some_P2818173045054083285it_nat (tptp.produc7388388658123137530it_nat) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.some_rat (tptp.rat) tptp.option_rat)
% 8.20/8.59 (declare-fun tptp.some_set_o (tptp.set_o) tptp.option_set_o)
% 8.20/8.59 (declare-fun tptp.some_set_int (tptp.set_int) tptp.option_set_int)
% 8.20/8.59 (declare-fun tptp.some_set_nat (tptp.set_nat) tptp.option_set_nat)
% 8.20/8.59 (declare-fun tptp.some_s287724117700012716at_nat (tptp.set_Pr8551490117392284871at_nat) tptp.option2498585697089621389at_nat)
% 8.20/8.59 (declare-fun tptp.some_s147305329494351046at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.option8963830502488799655at_nat)
% 8.20/8.59 (declare-fun tptp.some_s5890477192898017836at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.option1583680563626158861at_nat)
% 8.20/8.59 (declare-fun tptp.case_o1441893360019914891nteger ((-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.option8057788054806935849nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 8.20/8.59 (declare-fun tptp.case_o7134296353695833103nteger ((-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.option_Code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 8.20/8.59 (declare-fun tptp.case_option_o_assn (Bool (-> tptp.assn Bool) tptp.option_assn) Bool)
% 8.20/8.59 (declare-fun tptp.case_option_o_int (Bool (-> tptp.int Bool) tptp.option_int) Bool)
% 8.20/8.59 (declare-fun tptp.case_option_o_nat (Bool (-> tptp.nat Bool) tptp.option_nat) Bool)
% 8.20/8.59 (declare-fun tptp.case_option_o_num (Bool (-> tptp.num Bool) tptp.option_num) Bool)
% 8.20/8.59 (declare-fun tptp.case_o2686588417244861013it_nat (Bool (-> tptp.produc8664842809031399944it_nat Bool) tptp.option8956607266484857688it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.case_o3267218206291580230it_nat (Bool (-> tptp.produc3260487557148687353it_nat Bool) tptp.option3562590408128118217it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.case_o7395119307266030407it_nat (Bool (-> tptp.produc7388388658123137530it_nat Bool) tptp.option4065278094766928714it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.case_option_o_rat (Bool (-> tptp.rat Bool) tptp.option_rat) Bool)
% 8.20/8.59 (declare-fun tptp.case_o223999843215110191et_int (Bool (-> tptp.set_int Bool) tptp.option_set_int) Bool)
% 8.20/8.59 (declare-fun tptp.case_o356765784539232260er_num (tptp.code_integer (-> tptp.num tptp.code_integer) tptp.option_num) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.case_o5621594795226839503al_num (tptp.code_natural (-> tptp.num tptp.code_natural) tptp.option_num) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 8.20/8.59 (declare-fun tptp.case_option_nat_int (tptp.nat (-> tptp.int tptp.nat) tptp.option_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.case_option_nat_num (tptp.nat (-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 8.20/8.59 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 8.20/8.59 (declare-fun tptp.case_o670596351732880613_int_o (tptp.option1893999432384633940_int_o (-> (-> tptp.product_prod_int_int Bool) tptp.option1893999432384633940_int_o) tptp.option1893999432384633940_int_o) tptp.option1893999432384633940_int_o)
% 8.20/8.59 (declare-fun tptp.case_o4484465799723439917n_assn (tptp.option_assn (-> tptp.assn tptp.option_assn) tptp.option_assn) tptp.option_assn)
% 8.20/8.59 (declare-fun tptp.case_o390784466056649525nt_int (tptp.option_int (-> tptp.int tptp.option_int) tptp.option_int) tptp.option_int)
% 8.20/8.59 (declare-fun tptp.case_o7429725398727453821at_nat (tptp.option_nat (-> tptp.nat tptp.option_nat) tptp.option_nat) tptp.option_nat)
% 8.20/8.59 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.case_o2963978774867076333it_nat (tptp.option8956607266484857688it_nat (-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat) tptp.option8956607266484857688it_nat) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.case_o7727800614283616222it_nat (tptp.option8956607266484857688it_nat (-> tptp.produc3260487557148687353it_nat tptp.option8956607266484857688it_nat) tptp.option3562590408128118217it_nat) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.case_o2632329678403290591it_nat (tptp.option8956607266484857688it_nat (-> tptp.produc7388388658123137530it_nat tptp.option8956607266484857688it_nat) tptp.option4065278094766928714it_nat) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.case_o6061097939050036047it_nat (tptp.option3562590408128118217it_nat (-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat) tptp.option3562590408128118217it_nat) tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.case_o965627003169710416it_nat (tptp.option3562590408128118217it_nat (-> tptp.produc7388388658123137530it_nat tptp.option3562590408128118217it_nat) tptp.option4065278094766928714it_nat) tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.case_o1773283271472524752it_nat (tptp.option4065278094766928714it_nat (-> tptp.produc3260487557148687353it_nat tptp.option4065278094766928714it_nat) tptp.option3562590408128118217it_nat) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.case_o5901184372446974929it_nat (tptp.option4065278094766928714it_nat (-> tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat) tptp.option4065278094766928714it_nat) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.case_o8757249484648823045at_nat (tptp.option2498585697089621389at_nat (-> tptp.set_Pr8551490117392284871at_nat tptp.option2498585697089621389at_nat) tptp.option2498585697089621389at_nat) tptp.option2498585697089621389at_nat)
% 8.20/8.59 (declare-fun tptp.case_o311359030874850053at_nat (tptp.option8963830502488799655at_nat (-> tptp.set_Pr1261947904930325089at_nat tptp.option8963830502488799655at_nat) tptp.option8963830502488799655at_nat) tptp.option8963830502488799655at_nat)
% 8.20/8.59 (declare-fun tptp.case_o9080059180780454917at_nat (tptp.option1583680563626158861at_nat (-> tptp.set_Pr4329608150637261639at_nat tptp.option1583680563626158861at_nat) tptp.option1583680563626158861at_nat) tptp.option1583680563626158861at_nat)
% 8.20/8.59 (declare-fun tptp.map_op3563471509957180299nteger ((-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.option8057788054806935849nteger) tptp.option7428179582072448501nteger)
% 8.20/8.59 (declare-fun tptp.map_op370346339404370627nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.option_Code_integer) tptp.option8057788054806935849nteger)
% 8.20/8.59 (declare-fun tptp.map_op9146685272036663823nteger ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.option_Code_integer) tptp.option7428179582072448501nteger)
% 8.20/8.59 (declare-fun tptp.map_op3669829223712506439nteger ((-> tptp.code_integer tptp.code_integer) tptp.option_Code_integer) tptp.option_Code_integer)
% 8.20/8.59 (declare-fun tptp.map_option_int_int ((-> tptp.int tptp.int) tptp.option_int) tptp.option_int)
% 8.20/8.59 (declare-fun tptp.map_option_int_nat ((-> tptp.int tptp.nat) tptp.option_int) tptp.option_nat)
% 8.20/8.59 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.map_op8118133509425879471it_nat ((-> tptp.num tptp.produc8664842809031399944it_nat) tptp.option_num) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.map_op7586128837645442720it_nat ((-> tptp.num tptp.produc3260487557148687353it_nat) tptp.option_num) tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.map_op2490657901765117089it_nat ((-> tptp.num tptp.produc7388388658123137530it_nat) tptp.option_num) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.map_op2731889312448867759at_num ((-> tptp.produc8664842809031399944it_nat tptp.num) tptp.option8956607266484857688it_nat) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.map_op604423251913076367it_nat ((-> tptp.produc8664842809031399944it_nat tptp.produc7388388658123137530it_nat) tptp.option8956607266484857688it_nat) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.map_op5165227558541518752at_num ((-> tptp.produc3260487557148687353it_nat tptp.num) tptp.option3562590408128118217it_nat) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.map_op7599720869725723008it_nat ((-> tptp.produc3260487557148687353it_nat tptp.produc7388388658123137530it_nat) tptp.option3562590408128118217it_nat) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.map_op6233829773304596897at_num ((-> tptp.produc7388388658123137530it_nat tptp.num) tptp.option4065278094766928714it_nat) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.map_op8924890681001947535it_nat ((-> tptp.produc7388388658123137530it_nat tptp.produc8664842809031399944it_nat) tptp.option4065278094766928714it_nat) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.map_op4453737856117102208it_nat ((-> tptp.produc7388388658123137530it_nat tptp.produc3260487557148687353it_nat) tptp.option4065278094766928714it_nat) tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.map_op8581638957091552385it_nat ((-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat) tptp.option4065278094766928714it_nat) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.size_option_int ((-> tptp.int tptp.nat) tptp.option_int) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_o29782932136985253it_nat ((-> tptp.produc8664842809031399944it_nat tptp.nat) tptp.option8956607266484857688it_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_o1731029420616209814it_nat ((-> tptp.produc3260487557148687353it_nat tptp.nat) tptp.option3562590408128118217it_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.size_o5858930521590659991it_nat ((-> tptp.produc7388388658123137530it_nat tptp.nat) tptp.option4065278094766928714it_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.order_4473980167227706203on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.order_5251275573222108571on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.order_4861654808422542329on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.order_underS_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.order_2888998067076097458on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.bot_bo3790638025767943357_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.bot_bo5580076615179976505_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.bot_bot_o_o (Bool) Bool)
% 8.20/8.59 (declare-fun tptp.bot_bot_int_int_o (tptp.int tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.bot_bot_int_o (tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.bot_bot_list_nat_o (tptp.list_nat) Bool)
% 8.20/8.59 (declare-fun tptp.bot_bot_nat_nat_o (tptp.nat tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.bot_bo8147686125503663512_int_o (tptp.product_prod_int_int) Bool)
% 8.20/8.59 (declare-fun tptp.bot_bo482883023278783056_nat_o (tptp.product_prod_nat_nat) Bool)
% 8.20/8.59 (declare-fun tptp.bot_bot_set_nat_o (tptp.set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.bot_bo2686080419298087992_int_o (tptp.set_Pr958786334691620121nt_int) Bool)
% 8.20/8.59 (declare-fun tptp.bot_bo3200480807726169982_nat_o (tptp.a tptp.produc6653097349344004940it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.bot_bo5216386038637673661_nat_o (tptp.b tptp.produc6653097349344004940it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.bot_bot_assn () tptp.assn)
% 8.20/8.59 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 8.20/8.59 (declare-fun tptp.bot_bot_option_num () tptp.option_num)
% 8.20/8.59 (declare-fun tptp.bot_bot_Product_unit () tptp.product_unit)
% 8.20/8.59 (declare-fun tptp.bot_bot_set_o () tptp.set_o)
% 8.20/8.59 (declare-fun tptp.bot_bot_set_assn () tptp.set_assn)
% 8.20/8.59 (declare-fun tptp.bot_bo3990330152332043303nteger () tptp.set_Code_integer)
% 8.20/8.59 (declare-fun tptp.bot_bo8105976889876132193t_unit () tptp.set_He475150555083384525t_unit)
% 8.20/8.59 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 8.20/8.59 (declare-fun tptp.bot_bot_set_list_nat () tptp.set_list_nat)
% 8.20/8.59 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 8.20/8.59 (declare-fun tptp.bot_bo5635537948650799172et_nat () tptp.set_Pr8536935166611901872et_nat)
% 8.20/8.59 (declare-fun tptp.bot_bo1481135142794719944et_nat () tptp.set_Pr3286484037609594932et_nat)
% 8.20/8.59 (declare-fun tptp.bot_bo1796632182523588997nt_int () tptp.set_Pr958786334691620121nt_int)
% 8.20/8.59 (declare-fun tptp.bot_bo8422036546324065075at_nat () tptp.set_Pr8551490117392284871at_nat)
% 8.20/8.59 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.bot_bo228742789529271731at_nat () tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.59 (declare-fun tptp.bot_bo8480459777671986371it_nat () tptp.set_Pr7098220151150636591it_nat)
% 8.20/8.59 (declare-fun tptp.bot_bo8983147464310796868it_nat () tptp.set_Pr7600907837789447088it_nat)
% 8.20/8.59 (declare-fun tptp.bot_bo3957492148770167129t_unit () tptp.set_Product_unit)
% 8.20/8.59 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 8.20/8.59 (declare-fun tptp.bot_bot_set_set_int () tptp.set_set_int)
% 8.20/8.59 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 8.20/8.59 (declare-fun tptp.bot_bo1488462491386950373nt_int () tptp.set_se6260736226359567993nt_int)
% 8.20/8.59 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat)
% 8.20/8.59 (declare-fun tptp.ord_less_o_o ((-> Bool Bool) (-> Bool Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le8213806771718485336_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_set_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le2688692977766382584_int_o ((-> tptp.set_Pr958786334691620121nt_int Bool) (-> tptp.set_Pr958786334691620121nt_int Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_o (Bool Bool) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_assn (tptp.assn tptp.assn) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le5570908160329646204atural (tptp.code_natural tptp.code_natural) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_option_assn (tptp.option_assn tptp.option_assn) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_option_int (tptp.option_int tptp.option_int) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_option_nat (tptp.option_nat tptp.option_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_option_num (tptp.option_num tptp.option_num) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_option_rat (tptp.option_rat tptp.option_rat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le361264281704409273t_unit (tptp.product_unit tptp.product_unit) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_set_o (tptp.set_o tptp.set_o) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_set_assn (tptp.set_assn tptp.set_assn) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le1190675801316882794st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le7563427860532173253nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le7642048601412989811at_nat (tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le7866589430770878221at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le2604355607129572851at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_set_set_int (tptp.set_set_int tptp.set_set_int) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le1924305788584680229nt_int (tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le6753239538765779593_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool) (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le8000401564054156549_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool) (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_eq_o_o ((-> Bool Bool) (-> Bool Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le6741204236512500942_int_o ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_eq_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le2646555220125990790_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le7226304311989208114_nat_o ((-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool) (-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le1658592502415435381_nat_o ((-> tptp.produc2732055786443039994et_nat Bool) (-> tptp.produc2732055786443039994et_nat Bool)) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.ord_le8369615600986905444_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.ord_le704812498762024988_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.ord_le2239182809043710856_num_o ((-> tptp.product_prod_num_num Bool) (-> tptp.product_prod_num_num Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le3964352015994296041_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le8334417538754933252_int_o ((-> tptp.set_Pr958786334691620121nt_int Bool) (-> tptp.set_Pr958786334691620121nt_int Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le7992815620007647562_nat_o ((-> tptp.a tptp.produc6653097349344004940it_nat Bool) (-> tptp.a tptp.produc6653097349344004940it_nat Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le785348814064375433_nat_o ((-> tptp.b tptp.produc6653097349344004940it_nat Bool) (-> tptp.b tptp.produc6653097349344004940it_nat Bool)) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_eq_o (Bool Bool) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_eq_assn (tptp.assn tptp.assn) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le1926595141338095240atural (tptp.code_natural tptp.code_natural) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le1736525451366464988on_int (tptp.option_int tptp.option_int) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le5914376470875661696on_nat (tptp.option_nat tptp.option_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le6622620407824499402on_num (tptp.option_num tptp.option_num) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le2406147912482264968on_rat (tptp.option_rat tptp.option_rat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le353528952715127954et_int (tptp.option_set_int tptp.option_set_int) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le3221252021190050221t_unit (tptp.product_unit tptp.product_unit) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_eq_set_assn (tptp.set_assn tptp.set_assn) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le6045566169113846134st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le4763372923235995152et_nat (tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le5966269811547037844et_nat (tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le2843351958646193337nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le8081472938463900775at_nat (tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le1268244103169919719at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le4478181985103859343it_nat (tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le4980869671742669840it_nat (tptp.set_Pr7600907837789447088it_nat tptp.set_Pr7600907837789447088it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le4403425263959731960et_int (tptp.set_set_int tptp.set_set_int) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.ord_le483042692224249369nt_int (tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int) Bool)
% 8.20/8.59 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.ord_max_Code_natural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 8.20/8.59 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.ord_max_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 8.20/8.59 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.ord_ma7524802468073614006at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 8.20/8.59 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 8.20/8.59 (declare-fun tptp.ordering_top_assn ((-> tptp.assn tptp.assn Bool) (-> tptp.assn tptp.assn Bool) tptp.assn) Bool)
% 8.20/8.59 (declare-fun tptp.ordering_top_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.top_top_assn () tptp.assn)
% 8.20/8.59 (declare-fun tptp.top_top_Product_unit () tptp.product_unit)
% 8.20/8.59 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 8.20/8.59 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 8.20/8.59 (declare-fun tptp.power_power_assn (tptp.assn tptp.nat) tptp.assn)
% 8.20/8.59 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.power_7079662738309270450atural (tptp.code_natural tptp.nat) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.produc5247183594425207759_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat) (-> tptp.produc3658429121746597890et_nat Bool)) tptp.produc6999243976208994655_nat_o)
% 8.20/8.59 (declare-fun tptp.produc417064122970982599_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat) (-> tptp.produc3658429121746597890et_nat Bool)) tptp.produc8628075524815789655_nat_o)
% 8.20/8.59 (declare-fun tptp.produc2044891599319335296atural ((-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.code_natural) tptp.produc7250841696378415494atural)
% 8.20/8.59 (declare-fun tptp.produc8811497915304161060nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.int) tptp.produc5728234346263159722nt_int)
% 8.20/8.59 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 8.20/8.59 (declare-fun tptp.produc7368190662567826135_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool)) tptp.produc4928098042776334183_nat_o)
% 8.20/8.59 (declare-fun tptp.produc2245416461498447860et_nat ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) tptp.produc2732055786443039994et_nat)
% 8.20/8.59 (declare-fun tptp.produc5001842942810119800et_nat ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) tptp.produc3925858234332021118et_nat)
% 8.20/8.59 (declare-fun tptp.produc8795196974146716930_nat_a ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat) tptp.a) tptp.produc2763251018811306770_nat_a)
% 8.20/8.59 (declare-fun tptp.produc5258162843807585025_nat_b ((-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat) tptp.b) tptp.produc8449588929630179473_nat_b)
% 8.20/8.59 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 8.20/8.59 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 8.20/8.59 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 8.20/8.59 (declare-fun tptp.produc3762353314782720579et_nat (Bool tptp.produc3658429121746597890et_nat) tptp.produc6197004810343482825et_nat)
% 8.20/8.59 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 8.20/8.59 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 8.20/8.59 (declare-fun tptp.produc3574140220909816553atural (tptp.code_natural tptp.code_natural) tptp.produc7822875418678951345atural)
% 8.20/8.59 (declare-fun tptp.produc722914403947760862_nat_o (tptp.code_natural tptp.produc6999243976208994655_nat_o) tptp.produc7766336532480398636_nat_o)
% 8.20/8.59 (declare-fun tptp.produc1685672994636548566_nat_o (tptp.code_natural tptp.produc8628075524815789655_nat_o) tptp.produc50402934264563236_nat_o)
% 8.20/8.59 (declare-fun tptp.produc7296465590736685127atural (tptp.code_natural tptp.produc7250841696378415494atural) tptp.produc1399344845416535567atural)
% 8.20/8.59 (declare-fun tptp.produc6480503542405096427nt_int (tptp.code_natural tptp.produc5728234346263159722nt_int) tptp.produc3500511559948749619nt_int)
% 8.20/8.59 (declare-fun tptp.produc1823638919063574929_nat_a (tptp.code_natural tptp.produc2763251018811306770_nat_a) tptp.produc7140141985219958623_nat_a)
% 8.20/8.59 (declare-fun tptp.produc7509976829882447632_nat_b (tptp.code_natural tptp.produc8449588929630179473_nat_b) tptp.produc7538756082594784606_nat_b)
% 8.20/8.59 (declare-fun tptp.produc6639722614265839536atural (tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 8.20/8.59 (declare-fun tptp.produc3742984184817956739t_unit (tptp.array_o tptp.heap_e7401611519738050253t_unit) tptp.produc5011041761010125393t_unit)
% 8.20/8.59 (declare-fun tptp.produc2890842502232952598it_nat (tptp.array_o tptp.produc6653097349344004940it_nat) tptp.produc8032495849646651230it_nat)
% 8.20/8.59 (declare-fun tptp.produc2888458824036673339t_unit (tptp.array_int tptp.heap_e7401611519738050253t_unit) tptp.produc3407818250607552075t_unit)
% 8.20/8.59 (declare-fun tptp.produc5351973125643376990it_nat (tptp.array_int tptp.produc6653097349344004940it_nat) tptp.produc7196121022310644452it_nat)
% 8.20/8.59 (declare-fun tptp.produc1210945592254923927t_unit (tptp.array_nat tptp.heap_e7401611519738050253t_unit) tptp.produc1730305018825802663t_unit)
% 8.20/8.59 (declare-fun tptp.produc4907525368653469954it_nat (tptp.array_nat tptp.produc6653097349344004940it_nat) tptp.produc6751673265320737416it_nat)
% 8.20/8.59 (declare-fun tptp.produc584006145561248582it_nat (tptp.heap_e7401611519738050253t_unit tptp.nat) tptp.produc6653097349344004940it_nat)
% 8.20/8.59 (declare-fun tptp.produc7507926704131184380et_nat (tptp.heap_e7401611519738050253t_unit tptp.set_nat) tptp.produc3658429121746597890et_nat)
% 8.20/8.59 (declare-fun tptp.product_Pair_int_o (tptp.int Bool) tptp.product_prod_int_o)
% 8.20/8.59 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 8.20/8.59 (declare-fun tptp.product_Pair_int_nat (tptp.int tptp.nat) tptp.product_prod_int_nat)
% 8.20/8.59 (declare-fun tptp.produc4348348721325984599at_nat (tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) tptp.produc4166570645942440679at_nat)
% 8.20/8.59 (declare-fun tptp.product_Pair_nat_o (tptp.nat Bool) tptp.product_prod_nat_o)
% 8.20/8.59 (declare-fun tptp.product_Pair_nat_int (tptp.nat tptp.int) tptp.product_prod_nat_int)
% 8.20/8.59 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 8.20/8.59 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 8.20/8.59 (declare-fun tptp.produc638857205735767105it_nat (tptp.nat tptp.option8956607266484857688it_nat) tptp.produc3911288613690379145it_nat)
% 8.20/8.59 (declare-fun tptp.produc4111269673004989362it_nat (tptp.nat tptp.option3562590408128118217it_nat) tptp.produc4453839368661128058it_nat)
% 8.20/8.59 (declare-fun tptp.produc4613957359643799859it_nat (tptp.nat tptp.option4065278094766928714it_nat) tptp.produc2207270350733924475it_nat)
% 8.20/8.59 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 8.20/8.59 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 8.20/8.59 (declare-fun tptp.produc1940133919992309389et_nat (tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat) tptp.produc5657529347773406293et_nat)
% 8.20/8.59 (declare-fun tptp.produc8599840265553166229et_nat (tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat) tptp.produc6830853553727218525et_nat)
% 8.20/8.59 (declare-fun tptp.produc4480994950612372183atural (tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural) tptp.produc6756470014200349799atural)
% 8.20/8.59 (declare-fun tptp.produc3130510018828335921it_nat (tptp.produc6653097349344004940it_nat tptp.produc6653097349344004940it_nat) tptp.produc8961450480463052793it_nat)
% 8.20/8.59 (declare-fun tptp.produc8199053930788261021et_nat (tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat) tptp.produc8111630337999740517et_nat)
% 8.20/8.59 (declare-fun tptp.produc3646306378393792727nt_int (tptp.product_prod_int_int tptp.product_prod_int_int) tptp.produc1219242969750017639nt_int)
% 8.20/8.59 (declare-fun tptp.produc6161850002892822231at_nat (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc859450856879609959at_nat)
% 8.20/8.59 (declare-fun tptp.produc1743342482959036555it_nat (tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat) tptp.produc9011797661310329043it_nat)
% 8.20/8.59 (declare-fun tptp.produc6853161671299316109it_nat (tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat) tptp.produc1273031398460193109it_nat)
% 8.20/8.59 (declare-fun tptp.produc7133225469290080770it_nat (tptp.product_unit tptp.produc6653097349344004940it_nat) tptp.produc8664842809031399944it_nat)
% 8.20/8.59 (declare-fun tptp.produc7443773368509356479nteger (tptp.set_Code_integer tptp.set_Code_integer) tptp.produc6491284506569428743nteger)
% 8.20/8.59 (declare-fun tptp.produc6363374080413544029et_int (tptp.set_int tptp.set_int) tptp.produc2115011035271226405et_int)
% 8.20/8.59 (declare-fun tptp.produc4532415448927165861et_nat (tptp.set_nat tptp.set_nat) tptp.produc7819656566062154093et_nat)
% 8.20/8.59 (declare-fun tptp.produc2922128104949294807at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.produc3843707927480180839at_nat)
% 8.20/8.59 (declare-fun tptp.produc9060074326276436823at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.produc1319942482725812455at_nat)
% 8.20/8.59 (declare-fun tptp.produc9178034014595674355it_nat (tptp.a tptp.produc6653097349344004940it_nat) tptp.produc3260487557148687353it_nat)
% 8.20/8.59 (declare-fun tptp.product_Pair_a_a (tptp.a tptp.a) tptp.product_prod_a_a)
% 8.20/8.59 (declare-fun tptp.produc4082563078715348724it_nat (tptp.b tptp.produc6653097349344004940it_nat) tptp.produc7388388658123137530it_nat)
% 8.20/8.59 (declare-fun tptp.product_Pair_b_b (tptp.b tptp.b) tptp.product_prod_b_b)
% 8.20/8.59 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.product_Unity () tptp.product_unit)
% 8.20/8.59 (declare-fun tptp.produc9020447175693601247nteger ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc5966032636589952099nteger)
% 8.20/8.59 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 8.20/8.59 (declare-fun tptp.produc4463282112584876420nt_int ((-> tptp.int tptp.int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 8.20/8.59 (declare-fun tptp.produc969530845752564945_nat_o ((-> tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat) tptp.produc2732055786443039994et_nat) tptp.produc2732055786443039994et_nat)
% 8.20/8.59 (declare-fun tptp.produc1515462096303866701_nat_o ((-> tptp.produc3925858234332021118et_nat tptp.produc3658429121746597890et_nat) tptp.produc2732055786443039994et_nat) tptp.produc3925858234332021118et_nat)
% 8.20/8.59 (declare-fun tptp.produc701890989253350758_nat_a ((-> tptp.produc6653097349344004940it_nat tptp.produc6653097349344004940it_nat) tptp.produc3260487557148687353it_nat) tptp.produc3260487557148687353it_nat)
% 8.20/8.59 (declare-fun tptp.produc701890989253350759_nat_b ((-> tptp.produc6653097349344004940it_nat tptp.produc6653097349344004940it_nat) tptp.produc7388388658123137530it_nat) tptp.produc7388388658123137530it_nat)
% 8.20/8.59 (declare-fun tptp.produc7714581247149323085_nat_o ((-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat) tptp.produc3925858234332021118et_nat) tptp.produc2732055786443039994et_nat)
% 8.20/8.59 (declare-fun tptp.produc8750854537940449737_nat_o ((-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat) tptp.produc3925858234332021118et_nat) tptp.produc3925858234332021118et_nat)
% 8.20/8.59 (declare-fun tptp.produc5101573711933517782_nat_o ((-> tptp.produc2732055786443039994et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.produc6216949301066131538_nat_o ((-> tptp.produc3925858234332021118et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.produc175634133007206835_int_o ((-> tptp.product_prod_int_int Bool) tptp.int tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.produc1016772743285680337nt_int ((-> tptp.product_prod_int_int tptp.int) tptp.int tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.produc8249235968001453780nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int) tptp.int tptp.int) tptp.product_prod_int_int)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.produc3709033845735585303_nat_o ((-> tptp.produc3260487557148687353it_nat Bool) tptp.a tptp.produc6653097349344004940it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.produc8043051624866120150_nat_o ((-> tptp.produc7388388658123137530it_nat Bool) tptp.b tptp.produc6653097349344004940it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.produc8005341501107743676_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 8.20/8.59 (declare-fun tptp.produc7926200574084438792nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 8.20/8.59 (declare-fun tptp.produc297006045350968285nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.produc838355143741117751_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool) tptp.produc2732055786443039994et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.produc2377985495875741467et_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat) tptp.produc2732055786443039994et_nat) tptp.produc2732055786443039994et_nat)
% 8.20/8.59 (declare-fun tptp.produc1437786849005270451_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.produc4058941399401191971et_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat) tptp.produc3925858234332021118et_nat) tptp.produc3925858234332021118et_nat)
% 8.20/8.59 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 8.20/8.59 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 8.20/8.59 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 8.20/8.59 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 8.20/8.59 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 8.20/8.59 (declare-fun tptp.produc8282080750456430313atural ((-> tptp.code_natural tptp.code_natural tptp.produc6756470014200349799atural) tptp.produc7822875418678951345atural) tptp.produc6756470014200349799atural)
% 8.20/8.59 (declare-fun tptp.produc8638916746724166107atural ((-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.produc5835291356934675326atural) tptp.produc5835291356934675326atural)
% 8.20/8.59 (declare-fun tptp.produc5512802776183222702it_nat ((-> tptp.array_o tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat) tptp.produc5011041761010125393t_unit) tptp.produc8032495849646651230it_nat)
% 8.20/8.59 (declare-fun tptp.produc3016605123915955252it_nat ((-> tptp.array_int tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat) tptp.produc3407818250607552075t_unit) tptp.produc7196121022310644452it_nat)
% 8.20/8.59 (declare-fun tptp.produc8657510640128716596it_nat ((-> tptp.array_nat tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat) tptp.produc1730305018825802663t_unit) tptp.produc6751673265320737416it_nat)
% 8.20/8.59 (declare-fun tptp.produc7488178964372371019it_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option8956607266484857688it_nat) tptp.produc6653097349344004940it_nat) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.produc5645566021302314940it_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option3562590408128118217it_nat) tptp.produc6653097349344004940it_nat) tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.produc6148253707941125437it_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option4065278094766928714it_nat) tptp.produc6653097349344004940it_nat) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.produc1459180154077124618_int_o ((-> tptp.int tptp.int tptp.product_prod_int_int Bool) tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 8.20/8.59 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 8.20/8.59 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 8.20/8.59 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 8.20/8.59 (declare-fun tptp.produc4257766111578684402_set_o ((-> tptp.int tptp.int tptp.set_o) tptp.product_prod_int_int) tptp.set_o)
% 8.20/8.59 (declare-fun tptp.produc73460835934605544et_int ((-> tptp.int tptp.int tptp.set_int) tptp.product_prod_int_int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.produc4251311855443802252et_nat ((-> tptp.int tptp.int tptp.set_nat) tptp.product_prod_int_int) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.produc5233655623923918146et_nat ((-> tptp.int tptp.int tptp.set_set_nat) tptp.product_prod_int_int) tptp.set_set_nat)
% 8.20/8.59 (declare-fun tptp.produc7771776839612048883nt_int ((-> tptp.int tptp.int tptp.set_se6260736226359567993nt_int) tptp.product_prod_int_int) tptp.set_se6260736226359567993nt_int)
% 8.20/8.59 (declare-fun tptp.produc5410597840814988588_nat_o ((-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool) tptp.produc4166570645942440679at_nat) Bool)
% 8.20/8.59 (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)
% 8.20/8.59 (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)
% 8.20/8.59 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 8.20/8.59 (declare-fun tptp.produc6840382203811409530at_int ((-> tptp.nat tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.int)
% 8.20/8.59 (declare-fun tptp.produc2761476792215241774st_nat ((-> tptp.nat tptp.nat tptp.list_nat) tptp.product_prod_nat_nat) tptp.list_nat)
% 8.20/8.59 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 8.20/8.59 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 8.20/8.59 (declare-fun tptp.produc1676490119946744748_int_o ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.produc1219242969750017639nt_int) Bool)
% 8.20/8.59 (declare-fun tptp.produc6590410687421337004_nat_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.produc859450856879609959at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.produc1658495936642081476eger_o ((-> tptp.set_Code_integer tptp.set_Code_integer Bool) tptp.produc6491284506569428743nteger) Bool)
% 8.20/8.59 (declare-fun tptp.produc4109468873575309990_int_o ((-> tptp.set_int tptp.set_int Bool) tptp.produc2115011035271226405et_int) Bool)
% 8.20/8.59 (declare-fun tptp.produc6247414631856714078_nat_o ((-> tptp.set_nat tptp.set_nat Bool) tptp.produc7819656566062154093et_nat) Bool)
% 8.20/8.59 (declare-fun tptp.produc410239310623530412_nat_o ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool) tptp.produc3843707927480180839at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.produc8860486935419594360_nat_o ((-> tptp.a tptp.produc6653097349344004940it_nat Bool) tptp.produc3260487557148687353it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.produc5648861294512138360it_nat ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat) tptp.produc3260487557148687353it_nat) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.produc7850007024774191849it_nat ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat) tptp.produc3260487557148687353it_nat) tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.produc8352694711413002346it_nat ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat) tptp.produc3260487557148687353it_nat) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.produc2183267410226956569it_nat ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat) tptp.produc3260487557148687353it_nat) tptp.produc3260487557148687353it_nat)
% 8.20/8.59 (declare-fun tptp.produc5350075035600711000_set_o ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_o) tptp.produc3260487557148687353it_nat) tptp.set_o)
% 8.20/8.59 (declare-fun tptp.produc7315013382793309350et_nat ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_nat) tptp.produc3260487557148687353it_nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.produc3971132677695353399_nat_o ((-> tptp.b tptp.produc6653097349344004940it_nat Bool) tptp.produc7388388658123137530it_nat) Bool)
% 8.20/8.59 (declare-fun tptp.produc450363836004716793it_nat ((-> tptp.b tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat) tptp.produc7388388658123137530it_nat) tptp.option8956607266484857688it_nat)
% 8.20/8.59 (declare-fun tptp.produc3428986626803312746it_nat ((-> tptp.b tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat) tptp.produc7388388658123137530it_nat) tptp.option3562590408128118217it_nat)
% 8.20/8.59 (declare-fun tptp.produc3931674313442123243it_nat ((-> tptp.b tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat) tptp.produc7388388658123137530it_nat) tptp.option4065278094766928714it_nat)
% 8.20/8.59 (declare-fun tptp.produc7293086598567236123it_nat ((-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat) tptp.produc7388388658123137530it_nat) tptp.produc7388388658123137530it_nat)
% 8.20/8.59 (declare-fun tptp.produc8188766211626073367_set_o ((-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_o) tptp.produc7388388658123137530it_nat) tptp.set_o)
% 8.20/8.59 (declare-fun tptp.produc3880912149997675267et_int ((-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_int) tptp.produc7388388658123137530it_nat) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.produc8058763169506871975et_nat ((-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_nat) tptp.produc7388388658123137530it_nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.produc497848011034438852atural (tptp.produc5835291356934675326atural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.produc1824681642469235216et_nat (tptp.produc3658429121746597890et_nat) tptp.heap_e7401611519738050253t_unit)
% 8.20/8.59 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 8.20/8.59 (declare-fun tptp.produc6591912806276919810atural (tptp.produc5835291356934675326atural) tptp.produc7822875418678951345atural)
% 8.20/8.59 (declare-fun tptp.produc8586169260539613262et_nat (tptp.produc3658429121746597890et_nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 8.20/8.59 (declare-fun tptp.produc6963641260316735276nt_int ((-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.int tptp.product_prod_int_int) tptp.int) tptp.product_prod_int_int)
% 8.20/8.59 (declare-fun tptp.produc7537777246833756098et_nat ((-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat) (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat) tptp.produc3925858234332021118et_nat) tptp.produc2732055786443039994et_nat)
% 8.20/8.59 (declare-fun tptp.produc5538323210962509403atural ((-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 8.20/8.59 (declare-fun tptp.produc3714732129343117170it_nat ((-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat) (-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat) tptp.produc6653097349344004940it_nat) tptp.produc3260487557148687353it_nat)
% 8.20/8.59 (declare-fun tptp.produc8824551317683396724it_nat ((-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat) (-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat) tptp.produc6653097349344004940it_nat) tptp.produc7388388658123137530it_nat)
% 8.20/8.59 (declare-fun tptp.produc2318911012118706502et_nat ((-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat) (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat) tptp.produc3658429121746597890et_nat) tptp.produc3925858234332021118et_nat)
% 8.20/8.59 (declare-fun tptp.product_Abs_unit (Bool) tptp.product_unit)
% 8.20/8.59 (declare-fun tptp.product_Rep_unit (tptp.product_unit) Bool)
% 8.20/8.59 (declare-fun tptp.inc_shift (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.iterat2702368289246022656et_nat (tptp.code_natural (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) tptp.produc2732055786443039994et_nat)
% 8.20/8.59 (declare-fun tptp.iterat1233435593421607556et_nat (tptp.code_natural (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) tptp.produc3925858234332021118et_nat)
% 8.20/8.59 (declare-fun tptp.iterat8892046348760725948atural (tptp.code_natural (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 8.20/8.59 (declare-fun tptp.iterate_int_int (tptp.code_natural (-> tptp.int tptp.int tptp.product_prod_int_int) tptp.int tptp.int) tptp.product_prod_int_int)
% 8.20/8.59 (declare-fun tptp.iterat4993027441371875583it_nat (tptp.code_natural (-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat) tptp.a tptp.produc6653097349344004940it_nat) tptp.produc3260487557148687353it_nat)
% 8.20/8.59 (declare-fun tptp.iterat9120928542346325760it_nat (tptp.code_natural (-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat) tptp.b tptp.produc6653097349344004940it_nat) tptp.produc7388388658123137530it_nat)
% 8.20/8.59 (declare-fun tptp.iterat7486693702726674333et_nat (tptp.produc7766336532480398636_nat_o tptp.produc7766336532480398636_nat_o) Bool)
% 8.20/8.59 (declare-fun tptp.iterat2000369294365210145et_nat (tptp.produc50402934264563236_nat_o tptp.produc50402934264563236_nat_o) Bool)
% 8.20/8.59 (declare-fun tptp.iterat8136814461032266713atural (tptp.produc1399344845416535567atural tptp.produc1399344845416535567atural) Bool)
% 8.20/8.59 (declare-fun tptp.iterate_rel_int_int (tptp.produc3500511559948749619nt_int tptp.produc3500511559948749619nt_int) Bool)
% 8.20/8.59 (declare-fun tptp.iterat3051942729801024412it_nat (tptp.produc7140141985219958623_nat_a tptp.produc7140141985219958623_nat_a) Bool)
% 8.20/8.59 (declare-fun tptp.iterat7179843830775474589it_nat (tptp.produc7538756082594784606_nat_b tptp.produc7538756082594784606_nat_b) Bool)
% 8.20/8.59 (declare-fun tptp.log (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.log_rel (tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural) Bool)
% 8.20/8.59 (declare-fun tptp.minus_shift (tptp.code_natural tptp.code_natural tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.next (tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 8.20/8.59 (declare-fun tptp.range (tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 8.20/8.59 (declare-fun tptp.split_seed (tptp.produc7822875418678951345atural) tptp.produc6756470014200349799atural)
% 8.20/8.59 (declare-fun tptp.abs_Rat (tptp.product_prod_int_int) tptp.rat)
% 8.20/8.59 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 8.20/8.59 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 8.20/8.59 (declare-fun tptp.cr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 8.20/8.59 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 8.20/8.59 (declare-fun tptp.pcr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 8.20/8.59 (declare-fun tptp.positive (tptp.rat) Bool)
% 8.20/8.59 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 8.20/8.59 (declare-fun tptp.abs_rat (tptp.set_Pr958786334691620121nt_int) tptp.rat)
% 8.20/8.59 (declare-fun tptp.rep_rat (tptp.rat) tptp.set_Pr958786334691620121nt_int)
% 8.20/8.59 (declare-fun tptp.ratrel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 8.20/8.59 (declare-fun tptp.ref_ch7259622376331601608t_unit ((-> tptp.product_unit tptp.product_unit) tptp.ref_Product_unit) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (declare-fun tptp.ref_get_Product_unit (tptp.heap_e7401611519738050253t_unit tptp.ref_Product_unit) tptp.product_unit)
% 8.20/8.59 (declare-fun tptp.ref_lo7930775386976318366t_unit (tptp.ref_Product_unit) tptp.heap_T5738788834812785303t_unit)
% 8.20/8.59 (declare-fun tptp.ref_set_Product_unit (tptp.ref_Product_unit tptp.product_unit tptp.heap_e7401611519738050253t_unit) tptp.heap_e7401611519738050253t_unit)
% 8.20/8.59 (declare-fun tptp.domainp_int_int ((-> tptp.int tptp.int Bool) tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.domain9213661015745956397nt_rat ((-> tptp.product_prod_int_int tptp.rat Bool) tptp.product_prod_int_int) Bool)
% 8.20/8.59 (declare-fun tptp.field_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.id_int2 () tptp.set_Pr958786334691620121nt_int)
% 8.20/8.59 (declare-fun tptp.id_mul2649389997224486051at_nat () tptp.set_Pr8551490117392284871at_nat)
% 8.20/8.59 (declare-fun tptp.id_nat2 () tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.id_Pro2258643101195443293at_nat () tptp.set_Pr8693737435421807431at_nat)
% 8.20/8.59 (declare-fun tptp.id_set1796276052702428605at_nat () tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.59 (declare-fun tptp.antisym_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.refl_on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.total_on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.total_3592101749530773125at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.trans_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.trans_4347625901269045472at_nat (tptp.set_Pr8693737435421807431at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.algebr932160517623751201me_int (tptp.int tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.algebr934650988132801477me_nat (tptp.nat tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.divide5121882707175180666atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 8.20/8.59 (declare-fun tptp.dvd_dvd_Code_natural (tptp.code_natural tptp.code_natural) Bool)
% 8.20/8.59 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 8.20/8.59 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 8.20/8.59 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 8.20/8.59 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.modulo8411746178871703098atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.zero_n8403883297036319079atural (Bool) tptp.code_natural)
% 8.20/8.59 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 8.20/8.59 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 8.20/8.59 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 8.20/8.59 (declare-fun tptp.collect_o ((-> Bool Bool)) tptp.set_o)
% 8.20/8.59 (declare-fun tptp.collect_assn ((-> tptp.assn Bool)) tptp.set_assn)
% 8.20/8.59 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 8.20/8.59 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 8.20/8.59 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 8.20/8.59 (declare-fun tptp.collec5543584681430388431et_nat ((-> tptp.produc2732055786443039994et_nat Bool)) tptp.set_Pr8536935166611901872et_nat)
% 8.20/8.59 (declare-fun tptp.collec1402215087704437587et_nat ((-> tptp.produc3925858234332021118et_nat Bool)) tptp.set_Pr3286484037609594932et_nat)
% 8.20/8.59 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 8.20/8.59 (declare-fun tptp.collec5204685387357076818at_nat ((-> tptp.produc4166570645942440679at_nat Bool)) tptp.set_Pr8551490117392284871at_nat)
% 8.20/8.59 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.collec7447955092554649554nt_int ((-> tptp.produc1219242969750017639nt_int Bool)) tptp.set_Pr2560585780119916871nt_int)
% 8.20/8.59 (declare-fun tptp.collec7088162979684241874at_nat ((-> tptp.produc859450856879609959at_nat Bool)) tptp.set_Pr8693737435421807431at_nat)
% 8.20/8.59 (declare-fun tptp.collec2770208431294612722nteger ((-> tptp.produc6491284506569428743nteger Bool)) tptp.set_Pr7577011563204128103nteger)
% 8.20/8.59 (declare-fun tptp.collec957716948307931664et_int ((-> tptp.produc2115011035271226405et_int Bool)) tptp.set_Pr2522554150109002629et_int)
% 8.20/8.59 (declare-fun tptp.collec6662362479098859352et_nat ((-> tptp.produc7819656566062154093et_nat Bool)) tptp.set_Pr5488025237498180813et_nat)
% 8.20/8.59 (declare-fun tptp.collec6321179662152712658at_nat ((-> tptp.produc3843707927480180839at_nat Bool)) tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.59 (declare-fun tptp.collec4148678073425210574it_nat ((-> tptp.produc3260487557148687353it_nat Bool)) tptp.set_Pr7098220151150636591it_nat)
% 8.20/8.59 (declare-fun tptp.collec8276579174399660751it_nat ((-> tptp.produc7388388658123137530it_nat Bool)) tptp.set_Pr7600907837789447088it_nat)
% 8.20/8.59 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 8.20/8.59 (declare-fun tptp.collec574505750873337192nteger ((-> tptp.set_Code_integer Bool)) tptp.set_set_Code_integer)
% 8.20/8.59 (declare-fun tptp.collect_set_int ((-> tptp.set_int Bool)) tptp.set_set_int)
% 8.20/8.59 (declare-fun tptp.collect_set_list_nat ((-> tptp.set_list_nat Bool)) tptp.set_set_list_nat)
% 8.20/8.59 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 8.20/8.59 (declare-fun tptp.collec5210948495886036740nt_int ((-> tptp.set_Pr958786334691620121nt_int Bool)) tptp.set_se6260736226359567993nt_int)
% 8.20/8.59 (declare-fun tptp.collec5514110066124741708at_nat ((-> tptp.set_Pr1261947904930325089at_nat Bool)) tptp.set_se7855581050983116737at_nat)
% 8.20/8.59 (declare-fun tptp.collect_set_set_nat ((-> tptp.set_set_nat Bool)) tptp.set_set_set_nat)
% 8.20/8.59 (declare-fun tptp.pow_nat (tptp.set_nat) tptp.set_set_nat)
% 8.20/8.59 (declare-fun tptp.image_4470545334726330049nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) tptp.set_Code_integer)
% 8.20/8.59 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.image_int_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.image_1215581382706833972nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.set_Code_integer)
% 8.20/8.59 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 8.20/8.59 (declare-fun tptp.insert_o (Bool tptp.set_o) tptp.set_o)
% 8.20/8.59 (declare-fun tptp.insert_assn (tptp.assn tptp.set_assn) tptp.set_assn)
% 8.20/8.59 (declare-fun tptp.insert_Code_integer (tptp.code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 8.20/8.59 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.insert_list_nat (tptp.list_nat tptp.set_list_nat) tptp.set_list_nat)
% 8.20/8.59 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.insert_num (tptp.num tptp.set_num) tptp.set_num)
% 8.20/8.59 (declare-fun tptp.insert5033312907999012233nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 8.20/8.59 (declare-fun tptp.insert6337962749363155127at_nat (tptp.produc4166570645942440679at_nat tptp.set_Pr8551490117392284871at_nat) tptp.set_Pr8551490117392284871at_nat)
% 8.20/8.59 (declare-fun tptp.insert8211810215607154385at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.59 (declare-fun tptp.insert9069300056098147895at_nat (tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.59 (declare-fun tptp.insert_Product_unit (tptp.product_unit tptp.set_Product_unit) tptp.set_Product_unit)
% 8.20/8.59 (declare-fun tptp.insert_rat (tptp.rat tptp.set_rat) tptp.set_rat)
% 8.20/8.59 (declare-fun tptp.insert_set_nat (tptp.set_nat tptp.set_set_nat) tptp.set_set_nat)
% 8.20/8.59 (declare-fun tptp.insert8897473484851387113nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int) tptp.set_se6260736226359567993nt_int)
% 8.20/8.59 (declare-fun tptp.is_empty_o (tptp.set_o) Bool)
% 8.20/8.59 (declare-fun tptp.is_empty_int (tptp.set_int) Bool)
% 8.20/8.59 (declare-fun tptp.is_empty_nat (tptp.set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.is_emp1662574758705540307at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.is_singleton_o (tptp.set_o) Bool)
% 8.20/8.59 (declare-fun tptp.is_singleton_int (tptp.set_int) Bool)
% 8.20/8.59 (declare-fun tptp.is_singleton_nat (tptp.set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.is_sin2850979758926227957at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.is_sin2937591304547752795at_nat (tptp.set_Pr4329608150637261639at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.is_singleton_set_nat (tptp.set_set_nat) Bool)
% 8.20/8.59 (declare-fun tptp.is_sin6299389887212142093nt_int (tptp.set_se6260736226359567993nt_int) Bool)
% 8.20/8.59 (declare-fun tptp.the_elem_o (tptp.set_o) Bool)
% 8.20/8.59 (declare-fun tptp.the_elem_int (tptp.set_int) tptp.int)
% 8.20/8.59 (declare-fun tptp.the_elem_nat (tptp.set_nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.the_el2281957884133575798at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.product_prod_nat_nat)
% 8.20/8.59 (declare-fun tptp.the_el221668144340439132at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.produc3843707927480180839at_nat)
% 8.20/8.59 (declare-fun tptp.set_fo1959793692361082170t_assn ((-> tptp.nat tptp.assn tptp.assn) tptp.nat tptp.nat tptp.assn) tptp.assn)
% 8.20/8.59 (declare-fun tptp.set_fo1084959871951514735nteger ((-> tptp.nat tptp.code_integer tptp.code_integer) tptp.nat tptp.nat tptp.code_integer) tptp.code_integer)
% 8.20/8.59 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 8.20/8.59 (declare-fun tptp.set_fo4497565046347964853at_nat ((-> tptp.nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) tptp.nat tptp.nat tptp.multis2468970476368604999at_nat) tptp.multis2468970476368604999at_nat)
% 8.20/8.59 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 8.20/8.59 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 8.20/8.59 (declare-fun tptp.set_fo3699595496184130361el_nat (tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat) Bool)
% 8.20/8.59 (declare-fun tptp.set_or8904488021354931149Most_o (Bool Bool) tptp.set_o)
% 8.20/8.59 (declare-fun tptp.set_or7959216805967363635t_assn (tptp.assn tptp.assn) tptp.set_assn)
% 8.20/8.59 (declare-fun tptp.set_or189985376899183464nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 8.20/8.59 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 8.20/8.59 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 8.20/8.59 (declare-fun tptp.set_or370866239135849197et_int (tptp.set_int tptp.set_int) tptp.set_set_int)
% 8.20/8.59 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 8.20/8.59 (declare-fun tptp.set_or2481441762145802318nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_se6260736226359567993nt_int)
% 8.20/8.59 (declare-fun tptp.set_or7139685690850216873Than_o (Bool Bool) tptp.set_o)
% 8.20/8.59 (declare-fun tptp.set_or5523502641901747543n_assn (tptp.assn tptp.assn) tptp.set_assn)
% 8.20/8.59 (declare-fun tptp.set_or8404916559141939852nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 8.20/8.59 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.set_or1222409239386451017an_num (tptp.num tptp.num) tptp.set_num)
% 8.20/8.59 (declare-fun tptp.set_or4029947393144176647an_rat (tptp.rat tptp.rat) tptp.set_rat)
% 8.20/8.59 (declare-fun tptp.set_or8585797421378605585et_int (tptp.set_int tptp.set_int) tptp.set_set_int)
% 8.20/8.59 (declare-fun tptp.set_or3540276404033026485et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 8.20/8.59 (declare-fun tptp.set_or2826562449856406570nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_se6260736226359567993nt_int)
% 8.20/8.59 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.set_ord_atMost_o (Bool) tptp.set_o)
% 8.20/8.59 (declare-fun tptp.set_or9101266186257409494nteger (tptp.code_integer) tptp.set_Code_integer)
% 8.20/8.59 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.set_ord_atMost_num (tptp.num) tptp.set_num)
% 8.20/8.59 (declare-fun tptp.set_ord_atMost_rat (tptp.rat) tptp.set_rat)
% 8.20/8.59 (declare-fun tptp.set_or58775011639299419et_int (tptp.set_int) tptp.set_set_int)
% 8.20/8.59 (declare-fun tptp.set_or4236626031148496127et_nat (tptp.set_nat) tptp.set_set_nat)
% 8.20/8.59 (declare-fun tptp.set_or2459421552957432928nt_int (tptp.set_Pr958786334691620121nt_int) tptp.set_se6260736226359567993nt_int)
% 8.20/8.59 (declare-fun tptp.set_or2715278749043346189nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 8.20/8.59 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.set_or4266950643985792945nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 8.20/8.59 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 8.20/8.59 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 8.20/8.59 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 8.20/8.60 (declare-fun tptp.set_ord_lessThan_o (Bool) tptp.set_o)
% 8.20/8.60 (declare-fun tptp.set_or7637083652282234053n_assn (tptp.assn) tptp.set_assn)
% 8.20/8.60 (declare-fun tptp.set_or5754767410780653050nteger (tptp.code_integer) tptp.set_Code_integer)
% 8.20/8.60 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 8.20/8.60 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 8.20/8.60 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 8.20/8.60 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 8.20/8.60 (declare-fun tptp.set_or890127255671739683et_nat (tptp.set_nat) tptp.set_set_nat)
% 8.20/8.60 (declare-fun tptp.set_or4940836740269066044nt_int (tptp.set_Pr958786334691620121nt_int) tptp.set_se6260736226359567993nt_int)
% 8.20/8.60 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 8.20/8.60 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 8.20/8.60 (declare-fun tptp.left_t3131394472396969446nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)) Bool)
% 8.20/8.60 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.60 (declare-fun tptp.transitive_trancl_o (tptp.set_Product_prod_o_o) tptp.set_Product_prod_o_o)
% 8.20/8.60 (declare-fun tptp.transi6261509568448316235cl_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 8.20/8.60 (declare-fun tptp.transi5749863603491437800at_nat (tptp.set_Pr8551490117392284871at_nat) tptp.set_Pr8551490117392284871at_nat)
% 8.20/8.60 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.60 (declare-fun tptp.transi5221092739591632921et_nat (tptp.set_Pr3444600963470892981et_nat) tptp.set_Pr3444600963470892981et_nat)
% 8.20/8.60 (declare-fun tptp.transi3145040225084697757et_nat (tptp.set_Pr7928877670098842301et_nat) tptp.set_Pr7928877670098842301et_nat)
% 8.20/8.60 (declare-fun tptp.transi6288783178788033498nt_int (tptp.set_Pr2560585780119916871nt_int) tptp.set_Pr2560585780119916871nt_int)
% 8.20/8.60 (declare-fun tptp.transi7613985180851635224it_nat (tptp.set_Pr2819221443900773171it_nat) tptp.set_Pr2819221443900773171it_nat)
% 8.20/8.60 (declare-fun tptp.transi2518514244971309593it_nat (tptp.set_Pr5508209795250834101it_nat) tptp.set_Pr5508209795250834101it_nat)
% 8.20/8.60 (declare-fun tptp.transi2703068831062848130at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.60 (declare-fun tptp.type_d6188575255521822967unit_o ((-> tptp.product_unit Bool) (-> Bool tptp.product_unit) tptp.set_o) Bool)
% 8.20/8.60 (declare-fun tptp.type_d8554052265237484179nt_int ((-> tptp.rat tptp.set_Pr958786334691620121nt_int) (-> tptp.set_Pr958786334691620121nt_int tptp.rat) tptp.set_se6260736226359567993nt_int) Bool)
% 8.20/8.60 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P6019419558468335806at_nat ((-> tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat Bool) tptp.produc4471711990508489141at_nat) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P1862375125659990705et_nat ((-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool) tptp.produc2732055786443039994et_nat) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P8458817951426537472et_nat ((-> tptp.produc6197004810343482825et_nat tptp.produc6197004810343482825et_nat Bool) tptp.produc6197004810343482825et_nat) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P8126237942716283194atural ((-> tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural Bool) tptp.produc7822875418678951345atural) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P5472185023545635811_nat_o ((-> tptp.produc7766336532480398636_nat_o tptp.produc7766336532480398636_nat_o Bool) tptp.produc7766336532480398636_nat_o) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P2863604582003348699_nat_o ((-> tptp.produc50402934264563236_nat_o tptp.produc50402934264563236_nat_o Bool) tptp.produc50402934264563236_nat_o) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P9117636446167716760atural ((-> tptp.produc1399344845416535567atural tptp.produc1399344845416535567atural Bool) tptp.produc1399344845416535567atural) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P5309764456724190780nt_int ((-> tptp.produc3500511559948749619nt_int tptp.produc3500511559948749619nt_int Bool) tptp.produc3500511559948749619nt_int) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P7857408453303007510_nat_a ((-> tptp.produc7140141985219958623_nat_a tptp.produc7140141985219958623_nat_a Bool) tptp.produc7140141985219958623_nat_a) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P8256022550677833493_nat_b ((-> tptp.produc7538756082594784606_nat_b tptp.produc7538756082594784606_nat_b Bool) tptp.produc7538756082594784606_nat_b) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P5801069581201407417et_nat ((-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P414730952086964626it_nat ((-> tptp.produc3911288613690379145it_nat tptp.produc3911288613690379145it_nat Bool) tptp.produc3911288613690379145it_nat) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P6263092265436569219it_nat ((-> tptp.produc4453839368661128058it_nat tptp.produc4453839368661128058it_nat Bool) tptp.produc4453839368661128058it_nat) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P4016523247509365636it_nat ((-> tptp.produc2207270350733924475it_nat tptp.produc2207270350733924475it_nat Bool) tptp.produc2207270350733924475it_nat) Bool)
% 8.20/8.60 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 8.20/8.60 (declare-fun tptp.finite2416775604798480986nteger () tptp.set_Pr7577011563204128103nteger)
% 8.20/8.60 (declare-fun tptp.finite_psubset_int () tptp.set_Pr2522554150109002629et_int)
% 8.20/8.60 (declare-fun tptp.finite_psubset_nat () tptp.set_Pr5488025237498180813et_nat)
% 8.20/8.60 (declare-fun tptp.finite469560695537375940at_nat () tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.60 (declare-fun tptp.less_than () tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.60 (declare-fun tptp.lex_pr4722427456421979612et_nat (tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr7928877670098842301et_nat) tptp.set_Pr3444600963470892981et_nat)
% 8.20/8.60 (declare-fun tptp.lex_pr5340572901959109728et_nat (tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr719794911490849221et_nat) tptp.set_Pr7928877670098842301et_nat)
% 8.20/8.60 (declare-fun tptp.lex_prod_int_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr2560585780119916871nt_int)
% 8.20/8.60 (declare-fun tptp.lex_prod_nat_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr8693737435421807431at_nat)
% 8.20/8.60 (declare-fun tptp.lex_pr7699060183197734619it_nat (tptp.set_Product_prod_a_a tptp.set_Pr4389693562480114009it_nat) tptp.set_Pr2819221443900773171it_nat)
% 8.20/8.60 (declare-fun tptp.lex_pr2603589247317408988it_nat (tptp.set_Product_prod_b_b tptp.set_Pr4389693562480114009it_nat) tptp.set_Pr5508209795250834101it_nat)
% 8.20/8.60 (declare-fun tptp.max_ex8135407076693332796at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.60 (declare-fun tptp.measure_int ((-> tptp.int tptp.nat)) tptp.set_Pr958786334691620121nt_int)
% 8.20/8.60 (declare-fun tptp.min_ex6901939911449802026at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr4329608150637261639at_nat)
% 8.20/8.60 (declare-fun tptp.mlex_prod_int ((-> tptp.int tptp.nat) tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 8.20/8.60 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 8.20/8.60 (declare-fun tptp.wf_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.60 (declare-fun tptp.wf_Pro7803398752247294826at_nat (tptp.set_Pr8693737435421807431at_nat) Bool)
% 8.20/8.60 (declare-fun tptp.same_f1912051055550046943et_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) Bool) (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr7928877670098842301et_nat)) tptp.set_Pr3444600963470892981et_nat)
% 8.20/8.60 (declare-fun tptp.same_f7251492184213700963et_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) Bool) (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr719794911490849221et_nat)) tptp.set_Pr7928877670098842301et_nat)
% 8.20/8.60 (declare-fun tptp.same_fst_int_int ((-> tptp.int Bool) (-> tptp.int tptp.set_Pr958786334691620121nt_int)) tptp.set_Pr2560585780119916871nt_int)
% 8.20/8.60 (declare-fun tptp.same_fst_nat_nat ((-> tptp.nat Bool) (-> tptp.nat tptp.set_Pr1261947904930325089at_nat)) tptp.set_Pr8693737435421807431at_nat)
% 8.20/8.60 (declare-fun tptp.same_f8818375097021863134it_nat ((-> tptp.a Bool) (-> tptp.a tptp.set_Pr4389693562480114009it_nat)) tptp.set_Pr2819221443900773171it_nat)
% 8.20/8.60 (declare-fun tptp.same_f3722904161141537503it_nat ((-> tptp.b Bool) (-> tptp.b tptp.set_Pr4389693562480114009it_nat)) tptp.set_Pr5508209795250834101it_nat)
% 8.20/8.60 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 8.20/8.60 (declare-fun tptp.member_assn (tptp.assn tptp.set_assn) Bool)
% 8.20/8.60 (declare-fun tptp.member_Code_integer (tptp.code_integer tptp.set_Code_integer) Bool)
% 8.20/8.60 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 8.20/8.60 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 8.20/8.60 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 8.20/8.60 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 8.20/8.60 (declare-fun tptp.member8781333585448626064_nat_o (tptp.produc4928098042776334183_nat_o tptp.set_Pr2161125870931222855_nat_o) Bool)
% 8.20/8.60 (declare-fun tptp.member6124377750444531601et_nat (tptp.produc2732055786443039994et_nat tptp.set_Pr8536935166611901872et_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member1996754912294343701et_nat (tptp.produc3925858234332021118et_nat tptp.set_Pr3286484037609594932et_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member7466972457876170832od_o_o (tptp.product_prod_o_o tptp.set_Product_prod_o_o) Bool)
% 8.20/8.60 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 8.20/8.60 (declare-fun tptp.member6689249552917799696at_nat (tptp.produc4166570645942440679at_nat tptp.set_Pr8551490117392284871at_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member6341495586645257982et_nat (tptp.produc5657529347773406293et_nat tptp.set_Pr3444600963470892981et_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member4763271486408492550et_nat (tptp.produc6830853553727218525et_nat tptp.set_Pr7928877670098842301et_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member5617269971687963298it_nat (tptp.produc8961450480463052793it_nat tptp.set_Pr4389693562480114009it_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member6099555550032318734et_nat (tptp.produc8111630337999740517et_nat tptp.set_Pr719794911490849221et_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member8566619992076573584nt_int (tptp.produc1219242969750017639nt_int tptp.set_Pr2560585780119916871nt_int) Bool)
% 8.20/8.60 (declare-fun tptp.member8206827879206165904at_nat (tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member5335690527091456380it_nat (tptp.produc9011797661310329043it_nat tptp.set_Pr2819221443900773171it_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member6820296301096096254it_nat (tptp.produc1273031398460193109it_nat tptp.set_Pr5508209795250834101it_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member4307123515891402160nteger (tptp.produc6491284506569428743nteger tptp.set_Pr7577011563204128103nteger) Bool)
% 8.20/8.60 (declare-fun tptp.member2572552093476627150et_int (tptp.produc2115011035271226405et_int tptp.set_Pr2522554150109002629et_int) Bool)
% 8.20/8.60 (declare-fun tptp.member8277197624267554838et_nat (tptp.produc7819656566062154093et_nat tptp.set_Pr5488025237498180813et_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member8757157785044589968at_nat (tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member4554412811331277712it_nat (tptp.produc3260487557148687353it_nat tptp.set_Pr7098220151150636591it_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member1426531477525435216od_a_a (tptp.product_prod_a_a tptp.set_Product_prod_a_a) Bool)
% 8.20/8.60 (declare-fun tptp.member8682313912305727889it_nat (tptp.produc7388388658123137530it_nat tptp.set_Pr7600907837789447088it_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member7862447936710763792od_b_b (tptp.product_prod_b_b tptp.set_Product_prod_b_b) Bool)
% 8.20/8.60 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 8.20/8.60 (declare-fun tptp.member_set_int (tptp.set_int tptp.set_set_int) Bool)
% 8.20/8.60 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 8.20/8.60 (declare-fun tptp.member2340774599025711042nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int) Bool)
% 8.20/8.60 (declare-fun tptp.p () tptp.assn)
% 8.20/8.60 (declare-fun tptp.q (tptp.b) tptp.assn)
% 8.20/8.60 (declare-fun tptp.r (tptp.a) tptp.assn)
% 8.20/8.60 (declare-fun tptp.as () tptp.set_nat)
% 8.20/8.60 (declare-fun tptp.f () tptp.heap_Time_Heap_a)
% 8.20/8.60 (declare-fun tptp.g (tptp.a) tptp.heap_Time_Heap_b)
% 8.20/8.60 (declare-fun tptp.h () tptp.heap_e7401611519738050253t_unit)
% 8.20/8.60 (declare-fun tptp.h2 () tptp.heap_e7401611519738050253t_unit)
% 8.20/8.60 (declare-fun tptp.h3 () tptp.heap_e7401611519738050253t_unit)
% 8.20/8.60 (declare-fun tptp.rf () tptp.a)
% 8.20/8.60 (declare-fun tptp.rg () tptp.b)
% 8.20/8.60 (declare-fun tptp.t () tptp.nat)
% 8.20/8.60 (declare-fun tptp.t2 () tptp.nat)
% 8.20/8.60 (assert (let ((_let_1 (@ (@ tptp.hoare_new_addrs tptp.h3) tptp.as))) (= (@ (@ (@ tptp.hoare_new_addrs tptp.h2) (@ _let_1 tptp.h2)) tptp.h) (@ _let_1 tptp.h))))
% 8.20/8.60 (assert (@ (@ tptp.rep_assn tptp.p) (@ (@ tptp.produc7507926704131184380et_nat tptp.h3) tptp.as)))
% 8.20/8.60 (assert (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (@ (@ (@ tptp.hoare_new_addrs H) As) H) As)))
% 8.20/8.60 (assert (@ (@ tptp.rep_assn (@ tptp.q tptp.rg)) (@ (@ tptp.produc7507926704131184380et_nat tptp.h) (@ (@ (@ tptp.hoare_new_addrs tptp.h2) (@ (@ (@ tptp.hoare_new_addrs tptp.h3) tptp.as) tptp.h2)) tptp.h))))
% 8.20/8.60 (assert (@ (@ tptp.rep_assn (@ tptp.r tptp.rf)) (@ (@ tptp.produc7507926704131184380et_nat tptp.h2) (@ (@ (@ tptp.hoare_new_addrs tptp.h3) tptp.as) tptp.h2))))
% 8.20/8.60 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ tptp.rep_assn X) (@ tptp.rep_assn Y)) (= X Y))))
% 8.20/8.60 (assert (forall ((X1 tptp.int) (X2 tptp.int) (Y1 tptp.int) (Y2 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X2) (@ (@ tptp.product_Pair_int_int Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((X1 tptp.b) (X2 tptp.produc6653097349344004940it_nat) (Y1 tptp.b) (Y2 tptp.produc6653097349344004940it_nat)) (= (= (@ (@ tptp.produc4082563078715348724it_nat X1) X2) (@ (@ tptp.produc4082563078715348724it_nat Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (A2 tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A2) B2)) (and (= A A2) (= B B2)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((A tptp.b) (B tptp.produc6653097349344004940it_nat) (A2 tptp.b) (B2 tptp.produc6653097349344004940it_nat)) (= (= (@ (@ tptp.produc4082563078715348724it_nat A) B) (@ (@ tptp.produc4082563078715348724it_nat A2) B2)) (and (= A A2) (= B B2)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (not (= X (@ (@ tptp.produc7507926704131184380et_nat H2) As2)))))))
% 8.20/8.60 (assert (forall ((X tptp.produc2732055786443039994et_nat)) (not (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (not (= X (@ (@ tptp.produc2245416461498447860et_nat P) (@ (@ tptp.produc5001842942810119800et_nat Q) (@ (@ tptp.produc7507926704131184380et_nat H2) As2)))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc2732055786443039994et_nat Bool)) (X tptp.produc2732055786443039994et_nat)) (=> (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 (-> tptp.produc3658429121746597890et_nat Bool)) (C tptp.heap_e7401611519738050253t_unit) (D tptp.set_nat)) (@ P2 (@ (@ tptp.produc2245416461498447860et_nat A3) (@ (@ tptp.produc5001842942810119800et_nat B3) (@ (@ tptp.produc7507926704131184380et_nat C) D))))) (@ P2 X))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc3925858234332021118et_nat Bool)) (X tptp.produc3925858234332021118et_nat)) (=> (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.heap_e7401611519738050253t_unit) (C tptp.set_nat)) (@ P2 (@ (@ tptp.produc5001842942810119800et_nat A3) (@ (@ tptp.produc7507926704131184380et_nat B3) C)))) (@ P2 X))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc2732055786443039994et_nat Bool)) (X tptp.produc2732055786443039994et_nat)) (=> (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 (-> tptp.produc3658429121746597890et_nat Bool)) (C tptp.produc3658429121746597890et_nat)) (@ P2 (@ (@ tptp.produc2245416461498447860et_nat A3) (@ (@ tptp.produc5001842942810119800et_nat B3) C)))) (@ P2 X))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc7388388658123137530it_nat Bool)) (X tptp.produc7388388658123137530it_nat)) (=> (forall ((A3 tptp.b) (B3 tptp.heap_e7401611519738050253t_unit) (C tptp.nat)) (@ P2 (@ (@ tptp.produc4082563078715348724it_nat A3) (@ (@ tptp.produc584006145561248582it_nat B3) C)))) (@ P2 X))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc3260487557148687353it_nat Bool)) (X tptp.produc3260487557148687353it_nat)) (=> (forall ((A3 tptp.a) (B3 tptp.heap_e7401611519738050253t_unit) (C tptp.nat)) (@ P2 (@ (@ tptp.produc9178034014595674355it_nat A3) (@ (@ tptp.produc584006145561248582it_nat B3) C)))) (@ P2 X))))
% 8.20/8.60 (assert (forall ((Y tptp.produc2732055786443039994et_nat)) (not (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 (-> tptp.produc3658429121746597890et_nat Bool)) (C tptp.heap_e7401611519738050253t_unit) (D tptp.set_nat)) (not (= Y (@ (@ tptp.produc2245416461498447860et_nat A3) (@ (@ tptp.produc5001842942810119800et_nat B3) (@ (@ tptp.produc7507926704131184380et_nat C) D)))))))))
% 8.20/8.60 (assert (forall ((Y tptp.produc3925858234332021118et_nat)) (not (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.heap_e7401611519738050253t_unit) (C tptp.set_nat)) (not (= Y (@ (@ tptp.produc5001842942810119800et_nat A3) (@ (@ tptp.produc7507926704131184380et_nat B3) C))))))))
% 8.20/8.60 (assert (forall ((Y tptp.produc2732055786443039994et_nat)) (not (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 (-> tptp.produc3658429121746597890et_nat Bool)) (C tptp.produc3658429121746597890et_nat)) (not (= Y (@ (@ tptp.produc2245416461498447860et_nat A3) (@ (@ tptp.produc5001842942810119800et_nat B3) C))))))))
% 8.20/8.60 (assert (forall ((Y tptp.produc7388388658123137530it_nat)) (not (forall ((A3 tptp.b) (B3 tptp.heap_e7401611519738050253t_unit) (C tptp.nat)) (not (= Y (@ (@ tptp.produc4082563078715348724it_nat A3) (@ (@ tptp.produc584006145561248582it_nat B3) C))))))))
% 8.20/8.60 (assert (forall ((Y tptp.produc3260487557148687353it_nat)) (not (forall ((A3 tptp.a) (B3 tptp.heap_e7401611519738050253t_unit) (C tptp.nat)) (not (= Y (@ (@ tptp.produc9178034014595674355it_nat A3) (@ (@ tptp.produc584006145561248582it_nat B3) C))))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (assert (forall ((A tptp.b) (B tptp.produc6653097349344004940it_nat) (A2 tptp.b) (B2 tptp.produc6653097349344004940it_nat)) (=> (= (@ (@ tptp.produc4082563078715348724it_nat A) B) (@ (@ tptp.produc4082563078715348724it_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.product_prod_int_int Bool)) (P3 tptp.product_prod_int_int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (@ P2 (@ (@ tptp.product_Pair_int_int A3) B3))) (@ P2 P3))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc3925858234332021118et_nat Bool)) (P3 tptp.produc3925858234332021118et_nat)) (=> (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3658429121746597890et_nat)) (@ P2 (@ (@ tptp.produc5001842942810119800et_nat A3) B3))) (@ P2 P3))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc2732055786443039994et_nat Bool)) (P3 tptp.produc2732055786443039994et_nat)) (=> (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3925858234332021118et_nat)) (@ P2 (@ (@ tptp.produc2245416461498447860et_nat A3) B3))) (@ P2 P3))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc7388388658123137530it_nat Bool)) (P3 tptp.produc7388388658123137530it_nat)) (=> (forall ((A3 tptp.b) (B3 tptp.produc6653097349344004940it_nat)) (@ P2 (@ (@ tptp.produc4082563078715348724it_nat A3) B3))) (@ P2 P3))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc3260487557148687353it_nat Bool)) (P3 tptp.produc3260487557148687353it_nat)) (=> (forall ((A3 tptp.a) (B3 tptp.produc6653097349344004940it_nat)) (@ P2 (@ (@ tptp.produc9178034014595674355it_nat A3) B3))) (@ P2 P3))))
% 8.20/8.60 (assert (forall ((P3 tptp.product_prod_int_int)) (exists ((X3 tptp.int) (Y3 tptp.int)) (= P3 (@ (@ tptp.product_Pair_int_int X3) Y3)))))
% 8.20/8.60 (assert (forall ((P3 tptp.produc3925858234332021118et_nat)) (exists ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 tptp.produc3658429121746597890et_nat)) (= P3 (@ (@ tptp.produc5001842942810119800et_nat X3) Y3)))))
% 8.20/8.60 (assert (forall ((P3 tptp.produc2732055786443039994et_nat)) (exists ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 tptp.produc3925858234332021118et_nat)) (= P3 (@ (@ tptp.produc2245416461498447860et_nat X3) Y3)))))
% 8.20/8.60 (assert (forall ((P3 tptp.produc7388388658123137530it_nat)) (exists ((X3 tptp.b) (Y3 tptp.produc6653097349344004940it_nat)) (= P3 (@ (@ tptp.produc4082563078715348724it_nat X3) Y3)))))
% 8.20/8.60 (assert (forall ((P3 tptp.produc3260487557148687353it_nat)) (exists ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (= P3 (@ (@ tptp.produc9178034014595674355it_nat X3) Y3)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (S tptp.set_Pr958786334691620121nt_int) (P2 (-> tptp.int tptp.int Bool))) (let ((_let_1 (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P2 A) B)) (exists ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A3) B3)) S) (@ (@ P2 A3) B3))))))))
% 8.20/8.60 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (S tptp.set_Pr3286484037609594932et_nat) (P2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P2 A) B)) (exists ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A3) B3)) S) (@ (@ P2 A3) B3))))))))
% 8.20/8.60 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (S tptp.set_Pr8536935166611901872et_nat) (P2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool))) (let ((_let_1 (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P2 A) B)) (exists ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3925858234332021118et_nat)) (and (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A3) B3)) S) (@ (@ P2 A3) B3))))))))
% 8.20/8.60 (assert (forall ((A tptp.b) (B tptp.produc6653097349344004940it_nat) (S tptp.set_Pr7600907837789447088it_nat) (P2 (-> tptp.b tptp.produc6653097349344004940it_nat Bool))) (let ((_let_1 (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat A) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P2 A) B)) (exists ((A3 tptp.b) (B3 tptp.produc6653097349344004940it_nat)) (and (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat A3) B3)) S) (@ (@ P2 A3) B3))))))))
% 8.20/8.60 (assert (forall ((A tptp.a) (B tptp.produc6653097349344004940it_nat) (S tptp.set_Pr7098220151150636591it_nat) (P2 (-> tptp.a tptp.produc6653097349344004940it_nat Bool))) (let ((_let_1 (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat A) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P2 A) B)) (exists ((A3 tptp.a) (B3 tptp.produc6653097349344004940it_nat)) (and (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat A3) B3)) S) (@ (@ P2 A3) B3))))))))
% 8.20/8.60 (assert (forall ((Y tptp.product_prod_int_int)) (not (forall ((A3 tptp.int) (B3 tptp.int)) (not (= Y (@ (@ tptp.product_Pair_int_int A3) B3)))))))
% 8.20/8.60 (assert (forall ((Y tptp.produc3925858234332021118et_nat)) (not (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3658429121746597890et_nat)) (not (= Y (@ (@ tptp.produc5001842942810119800et_nat A3) B3)))))))
% 8.20/8.60 (assert (forall ((Y tptp.produc2732055786443039994et_nat)) (not (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3925858234332021118et_nat)) (not (= Y (@ (@ tptp.produc2245416461498447860et_nat A3) B3)))))))
% 8.20/8.60 (assert (forall ((Y tptp.produc7388388658123137530it_nat)) (not (forall ((A3 tptp.b) (B3 tptp.produc6653097349344004940it_nat)) (not (= Y (@ (@ tptp.produc4082563078715348724it_nat A3) B3)))))))
% 8.20/8.60 (assert (forall ((Y tptp.produc3260487557148687353it_nat)) (not (forall ((A3 tptp.a) (B3 tptp.produc6653097349344004940it_nat)) (not (= Y (@ (@ tptp.produc9178034014595674355it_nat A3) B3)))))))
% 8.20/8.60 (assert (@ (@ (@ tptp.hoare_hoare_triple_a tptp.p) tptp.f) tptp.r))
% 8.20/8.60 (assert (forall ((X tptp.a)) (@ (@ (@ tptp.hoare_hoare_triple_b (@ tptp.r X)) (@ tptp.g X)) tptp.q)))
% 8.20/8.60 (assert (= (@ (@ tptp.heap_Time_execute_b (@ tptp.g tptp.rf)) tptp.h2) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat tptp.rg) (@ (@ tptp.produc584006145561248582it_nat tptp.h) tptp.t)))))
% 8.20/8.60 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit tptp.h2)) (@ tptp.lim_Product_unit tptp.h)))
% 8.20/8.60 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit tptp.h3)) (@ tptp.lim_Product_unit tptp.h2)))
% 8.20/8.60 (assert (= (@ (@ tptp.heap_Time_execute_a tptp.f) tptp.h3) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat tptp.rf) (@ (@ tptp.produc584006145561248582it_nat tptp.h2) tptp.t2)))))
% 8.20/8.60 (assert (forall ((A Bool) (P2 (-> Bool Bool))) (= (@ (@ tptp.member_o A) (@ tptp.collect_o P2)) (@ P2 A))))
% 8.20/8.60 (assert (forall ((A tptp.list_nat) (P2 (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P2)) (@ P2 A))))
% 8.20/8.60 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (P2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (= (@ (@ tptp.member2340774599025711042nt_int A) (@ tptp.collec5210948495886036740nt_int P2)) (@ P2 A))))
% 8.20/8.60 (assert (forall ((A tptp.set_nat) (P2 (-> tptp.set_nat Bool))) (= (@ (@ tptp.member_set_nat A) (@ tptp.collect_set_nat P2)) (@ P2 A))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (P2 (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P2)) (@ P2 A))))
% 8.20/8.60 (assert (forall ((A tptp.int) (P2 (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P2)) (@ P2 A))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_o)) (= (@ tptp.collect_o (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) A4))) A4)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) A4))) A4)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int)) (= (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) A4))) A4)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_set_nat)) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A4))) A4)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A4))) A4)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A4))) A4)))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.list_nat Bool)) (Q2 (-> tptp.list_nat Bool))) (=> (forall ((X3 tptp.list_nat)) (= (@ P2 X3) (@ Q2 X3))) (= (@ tptp.collect_list_nat P2) (@ tptp.collect_list_nat Q2)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.set_Pr958786334691620121nt_int Bool)) (Q2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (=> (forall ((X3 tptp.set_Pr958786334691620121nt_int)) (= (@ P2 X3) (@ Q2 X3))) (= (@ tptp.collec5210948495886036740nt_int P2) (@ tptp.collec5210948495886036740nt_int Q2)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.set_nat Bool)) (Q2 (-> tptp.set_nat Bool))) (=> (forall ((X3 tptp.set_nat)) (= (@ P2 X3) (@ Q2 X3))) (= (@ tptp.collect_set_nat P2) (@ tptp.collect_set_nat Q2)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P2 X3) (@ Q2 X3))) (= (@ tptp.collect_nat P2) (@ tptp.collect_nat Q2)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (= (@ P2 X3) (@ Q2 X3))) (= (@ tptp.collect_int P2) (@ tptp.collect_int Q2)))))
% 8.20/8.60 (assert (= tptp.bijective_int_int (lambda ((R tptp.set_Pr958786334691620121nt_int)) (and (forall ((X4 tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int X4))) (=> (and (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Y4)) R) (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Z)) R)) (= Y4 Z)))) (forall ((X4 tptp.int) (Y4 tptp.int) (Z tptp.int)) (=> (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Z)) R) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y4) Z)) R)) (= X4 Y4)))))))
% 8.20/8.60 (assert (= tptp.biject2615096655818420098et_nat (lambda ((R tptp.set_Pr3286484037609594932et_nat)) (and (forall ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat) (Z tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat X4))) (=> (and (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Y4)) R) (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Z)) R)) (= Y4 Z)))) (forall ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 (-> tptp.produc3658429121746597890et_nat Bool)) (Z tptp.produc3658429121746597890et_nat)) (=> (and (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Z)) R) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat Y4) Z)) R)) (= X4 Y4)))))))
% 8.20/8.60 (assert (= tptp.biject1468766312547416318et_nat (lambda ((R tptp.set_Pr8536935166611901872et_nat)) (and (forall ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat) (Z tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat X4))) (=> (and (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Y4)) R) (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Z)) R)) (= Y4 Z)))) (forall ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 (-> tptp.produc3658429121746597890et_nat Bool)) (Z tptp.produc3925858234332021118et_nat)) (=> (and (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Z)) R) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat Y4) Z)) R)) (= X4 Y4)))))))
% 8.20/8.60 (assert (= tptp.biject3496835315794560510it_nat (lambda ((R tptp.set_Pr7600907837789447088it_nat)) (and (forall ((X4 tptp.b) (Y4 tptp.produc6653097349344004940it_nat) (Z tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.produc4082563078715348724it_nat X4))) (=> (and (@ (@ tptp.member8682313912305727889it_nat (@ _let_1 Y4)) R) (@ (@ tptp.member8682313912305727889it_nat (@ _let_1 Z)) R)) (= Y4 Z)))) (forall ((X4 tptp.b) (Y4 tptp.b) (Z tptp.produc6653097349344004940it_nat)) (=> (and (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat X4) Z)) R) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat Y4) Z)) R)) (= X4 Y4)))))))
% 8.20/8.60 (assert (= tptp.biject8592306251674886141it_nat (lambda ((R tptp.set_Pr7098220151150636591it_nat)) (and (forall ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat) (Z tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.produc9178034014595674355it_nat X4))) (=> (and (@ (@ tptp.member4554412811331277712it_nat (@ _let_1 Y4)) R) (@ (@ tptp.member4554412811331277712it_nat (@ _let_1 Z)) R)) (= Y4 Z)))) (forall ((X4 tptp.a) (Y4 tptp.a) (Z tptp.produc6653097349344004940it_nat)) (=> (and (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Z)) R) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat Y4) Z)) R)) (= X4 Y4)))))))
% 8.20/8.60 (assert (forall ((R2 tptp.int) (S2 tptp.int) (R3 tptp.set_Pr958786334691620121nt_int) (S3 tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int R2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 S2)) R3) (=> (= S3 S2) (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 S3)) R3))))))
% 8.20/8.60 (assert (forall ((R2 (-> tptp.produc3658429121746597890et_nat Bool)) (S2 tptp.produc3658429121746597890et_nat) (R3 tptp.set_Pr3286484037609594932et_nat) (S3 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat R2))) (=> (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 S2)) R3) (=> (= S3 S2) (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 S3)) R3))))))
% 8.20/8.60 (assert (forall ((R2 (-> tptp.produc3658429121746597890et_nat Bool)) (S2 tptp.produc3925858234332021118et_nat) (R3 tptp.set_Pr8536935166611901872et_nat) (S3 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat R2))) (=> (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 S2)) R3) (=> (= S3 S2) (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 S3)) R3))))))
% 8.20/8.60 (assert (forall ((R2 tptp.b) (S2 tptp.produc6653097349344004940it_nat) (R3 tptp.set_Pr7600907837789447088it_nat) (S3 tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.produc4082563078715348724it_nat R2))) (=> (@ (@ tptp.member8682313912305727889it_nat (@ _let_1 S2)) R3) (=> (= S3 S2) (@ (@ tptp.member8682313912305727889it_nat (@ _let_1 S3)) R3))))))
% 8.20/8.60 (assert (forall ((R2 tptp.a) (S2 tptp.produc6653097349344004940it_nat) (R3 tptp.set_Pr7098220151150636591it_nat) (S3 tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.produc9178034014595674355it_nat R2))) (=> (@ (@ tptp.member4554412811331277712it_nat (@ _let_1 S2)) R3) (=> (= S3 S2) (@ (@ tptp.member4554412811331277712it_nat (@ _let_1 S3)) R3))))))
% 8.20/8.60 (assert (forall ((F (-> tptp.product_prod_int_int Bool)) (A tptp.int) (B tptp.int)) (=> (@ F (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ (@ tptp.produc175634133007206835_int_o F) A) B))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((F (-> tptp.produc7388388658123137530it_nat Bool)) (A tptp.b) (B tptp.produc6653097349344004940it_nat)) (=> (@ F (@ (@ tptp.produc4082563078715348724it_nat A) B)) (@ (@ (@ tptp.produc8043051624866120150_nat_o F) A) B))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))))))
% 8.20/8.60 (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))))))))
% 8.20/8.60 (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))))))))
% 8.20/8.60 (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))))))))
% 8.20/8.60 (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))))))))
% 8.20/8.60 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C2 tptp.set_int) (D2 tptp.set_int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_int B) C2) (=> (= C2 D2) (@ (@ tptp.ord_less_eq_set_int A) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (= C2 D2) (@ (@ tptp.ord_less_eq_rat A) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num) (D2 tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (= C2 D2) (@ (@ tptp.ord_less_eq_num A) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (= C2 D2) (@ (@ tptp.ord_less_eq_nat A) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (= C2 D2) (@ (@ tptp.ord_less_eq_int A) D2))))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_Time_Heap_a) (Q2 (-> tptp.a tptp.assn))) (=> (forall ((H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H2) (@ (@ (@ tptp.hoare_hoare_triple_a P2) C2) Q2))) (@ (@ (@ tptp.hoare_hoare_triple_a P2) C2) Q2))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_Time_Heap_b) (Q2 (-> tptp.b tptp.assn))) (=> (forall ((H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H2) (@ (@ (@ tptp.hoare_hoare_triple_b P2) C2) Q2))) (@ (@ (@ tptp.hoare_hoare_triple_b P2) C2) Q2))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_T5738788834812785303t_unit) (Q2 (-> tptp.product_unit tptp.assn))) (=> (forall ((H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H2) (@ (@ (@ tptp.hoare_8945653483474564448t_unit P2) C2) Q2))) (@ (@ (@ tptp.hoare_8945653483474564448t_unit P2) C2) Q2))))
% 8.20/8.60 (assert (forall ((F (-> tptp.product_prod_int_int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ (@ tptp.produc175634133007206835_int_o F) A) B) (@ F (@ (@ tptp.product_Pair_int_int A) B)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((F (-> tptp.produc7388388658123137530it_nat Bool)) (A tptp.b) (B tptp.produc6653097349344004940it_nat)) (=> (@ (@ (@ tptp.produc8043051624866120150_nat_o F) A) B) (@ F (@ (@ tptp.produc4082563078715348724it_nat A) B)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((F (-> tptp.product_prod_int_int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ (@ tptp.produc175634133007206835_int_o F) A) B) (@ F (@ (@ tptp.product_Pair_int_int A) B)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((F (-> tptp.produc7388388658123137530it_nat Bool)) (A tptp.b) (B tptp.produc6653097349344004940it_nat)) (=> (@ (@ (@ tptp.produc8043051624866120150_nat_o F) A) B) (@ F (@ (@ tptp.produc4082563078715348724it_nat A) B)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((X2 tptp.produc7388388658123137530it_nat) (Y2 tptp.produc7388388658123137530it_nat)) (= (= (@ tptp.some_P2818173045054083285it_nat X2) (@ tptp.some_P2818173045054083285it_nat Y2)) (= X2 Y2))))
% 8.20/8.60 (assert (forall ((X2 tptp.produc3260487557148687353it_nat) (Y2 tptp.produc3260487557148687353it_nat)) (= (= (@ tptp.some_P7913643980934408916it_nat X2) (@ tptp.some_P7913643980934408916it_nat Y2)) (= X2 Y2))))
% 8.20/8.60 (assert (forall ((X2 tptp.produc8664842809031399944it_nat) (Y2 tptp.produc8664842809031399944it_nat)) (= (= (@ tptp.some_P1914260805536162275it_nat X2) (@ tptp.some_P1914260805536162275it_nat Y2)) (= X2 Y2))))
% 8.20/8.60 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.some_num X2) (@ tptp.some_num Y2)) (= X2 Y2))))
% 8.20/8.60 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 8.20/8.60 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 8.20/8.60 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 8.20/8.60 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 8.20/8.60 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 8.20/8.60 (assert (forall ((X tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X) X)))
% 8.20/8.60 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) X)))
% 8.20/8.60 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) X)))
% 8.20/8.60 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 8.20/8.60 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) X)))
% 8.20/8.60 (assert (not (forall ((Rg tptp.b) (H3 tptp.heap_e7401611519738050253t_unit)) (=> (exists ((T tptp.nat)) (= (@ (@ tptp.heap_Time_execute_b (@ tptp.g tptp.rf)) tptp.h2) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat Rg) (@ (@ tptp.produc584006145561248582it_nat H3) T))))) (=> (@ (@ tptp.rep_assn (@ tptp.q Rg)) (@ (@ tptp.produc7507926704131184380et_nat H3) (@ (@ (@ tptp.hoare_new_addrs tptp.h2) (@ (@ (@ tptp.hoare_new_addrs tptp.h3) tptp.as) tptp.h2)) H3))) (=> (@ (@ (@ 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.hoare_new_addrs tptp.h3) tptp.as) tptp.h2))))))) tptp.h2) H3) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit tptp.h2)) (@ tptp.lim_Product_unit H3)))))))))
% 8.20/8.60 (assert (not (forall ((Rf tptp.a) (H4 tptp.heap_e7401611519738050253t_unit)) (=> (exists ((T2 tptp.nat)) (= (@ (@ tptp.heap_Time_execute_a tptp.f) tptp.h3) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat Rf) (@ (@ tptp.produc584006145561248582it_nat H4) T2))))) (=> (@ (@ tptp.rep_assn (@ tptp.r Rf)) (@ (@ tptp.produc7507926704131184380et_nat H4) (@ (@ (@ tptp.hoare_new_addrs tptp.h3) tptp.as) H4))) (=> (@ (@ (@ tptp.relH (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit tptp.h3)) (not (@ (@ tptp.member_nat A5) tptp.as)))))) tptp.h3) H4) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit tptp.h3)) (@ tptp.lim_Product_unit H4)))))))))
% 8.20/8.60 (assert (forall ((Uu tptp.produc7388388658123137530it_nat) (X tptp.produc7388388658123137530it_nat)) (= (@ (@ tptp.the_de4670738602788725795it_nat Uu) (@ tptp.some_P2818173045054083285it_nat X)) X)))
% 8.20/8.60 (assert (forall ((Uu tptp.produc3260487557148687353it_nat) (X tptp.produc3260487557148687353it_nat)) (= (@ (@ tptp.the_de542837501814275618it_nat Uu) (@ tptp.some_P7913643980934408916it_nat X)) X)))
% 8.20/8.60 (assert (forall ((Uu tptp.produc8664842809031399944it_nat) (X tptp.produc8664842809031399944it_nat)) (= (@ (@ tptp.the_de2487931475039285041it_nat Uu) (@ tptp.some_P1914260805536162275it_nat X)) X)))
% 8.20/8.60 (assert (forall ((Uu tptp.num) (X tptp.num)) (= (@ (@ tptp.the_default_num Uu) (@ tptp.some_num X)) X)))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_Time_Heap_a) (Q2 (-> tptp.a tptp.assn)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.hoare_hoare_triple_a P2) C2) Q2) (=> (@ (@ tptp.rep_assn P2) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (exists ((H4 tptp.heap_e7401611519738050253t_unit) (R4 tptp.a) (T3 tptp.nat)) (and (@ (@ (@ (@ (@ tptp.heap_Time_effect_a C2) H) H4) R4) T3) (@ (@ tptp.rep_assn (@ Q2 R4)) (@ (@ tptp.produc7507926704131184380et_nat H4) (@ (@ (@ tptp.hoare_new_addrs H) As) H4)))))))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_Time_Heap_b) (Q2 (-> tptp.b tptp.assn)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.hoare_hoare_triple_b P2) C2) Q2) (=> (@ (@ tptp.rep_assn P2) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (exists ((H4 tptp.heap_e7401611519738050253t_unit) (R4 tptp.b) (T3 tptp.nat)) (and (@ (@ (@ (@ (@ tptp.heap_Time_effect_b C2) H) H4) R4) T3) (@ (@ tptp.rep_assn (@ Q2 R4)) (@ (@ tptp.produc7507926704131184380et_nat H4) (@ (@ (@ tptp.hoare_new_addrs H) As) H4)))))))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_T5738788834812785303t_unit) (Q2 (-> tptp.product_unit tptp.assn)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.hoare_8945653483474564448t_unit P2) C2) Q2) (=> (@ (@ tptp.rep_assn P2) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (exists ((H4 tptp.heap_e7401611519738050253t_unit) (R4 tptp.product_unit) (T3 tptp.nat)) (and (@ (@ (@ (@ (@ tptp.heap_T6553295506729943825t_unit C2) H) H4) R4) T3) (@ (@ tptp.rep_assn (@ Q2 R4)) (@ (@ tptp.produc7507926704131184380et_nat H4) (@ (@ (@ tptp.hoare_new_addrs H) As) H4)))))))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_Time_Heap_a) (Q2 (-> tptp.a tptp.assn)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.hoare_hoare_triple_a P2) C2) Q2) (=> (@ (@ tptp.rep_assn P2) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (@ (@ tptp.heap_Time_success_a C2) H)))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_Time_Heap_b) (Q2 (-> tptp.b tptp.assn)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.hoare_hoare_triple_b P2) C2) Q2) (=> (@ (@ tptp.rep_assn P2) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (@ (@ tptp.heap_Time_success_b C2) H)))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_T5738788834812785303t_unit) (Q2 (-> tptp.product_unit tptp.assn)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.hoare_8945653483474564448t_unit P2) C2) Q2) (=> (@ (@ tptp.rep_assn P2) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (@ (@ tptp.heap_T584514906347983379t_unit C2) H)))))
% 8.20/8.60 (assert (= tptp.bNF_Ca583493526879471924et_int (lambda ((R5 tptp.set_Pr958786334691620121nt_int) (As3 (-> tptp.int tptp.set_int))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R5) (@ (@ tptp.ord_less_eq_set_int (@ As3 I)) (@ As3 J)))))))
% 8.20/8.60 (assert (= tptp.bNF_Ca1332973979827979050nt_rat (lambda ((R5 tptp.set_Pr958786334691620121nt_int) (As3 (-> tptp.int tptp.rat))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R5) (@ (@ tptp.ord_less_eq_rat (@ As3 I)) (@ As3 J)))))))
% 8.20/8.60 (assert (= tptp.bNF_Ca7748807862925029228nt_num (lambda ((R5 tptp.set_Pr958786334691620121nt_int) (As3 (-> tptp.int tptp.num))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R5) (@ (@ tptp.ord_less_eq_num (@ As3 I)) (@ As3 J)))))))
% 8.20/8.60 (assert (= tptp.bNF_Ca1968104039914474786nt_nat (lambda ((R5 tptp.set_Pr958786334691620121nt_int) (As3 (-> tptp.int tptp.nat))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R5) (@ (@ tptp.ord_less_eq_nat (@ As3 I)) (@ As3 J)))))))
% 8.20/8.60 (assert (= tptp.bNF_Ca1965613569405424510nt_int (lambda ((R5 tptp.set_Pr958786334691620121nt_int) (As3 (-> tptp.int tptp.int))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R5) (@ (@ tptp.ord_less_eq_int (@ As3 I)) (@ As3 J)))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_b) (G tptp.heap_Time_Heap_b)) (=> (forall ((H2 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.heap_Time_execute_b F) H2) (@ (@ tptp.heap_Time_execute_b G) H2))) (= F G))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_a) (G tptp.heap_Time_Heap_a)) (=> (forall ((H2 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.heap_Time_execute_a F) H2) (@ (@ tptp.heap_Time_execute_a G) H2))) (= F G))))
% 8.20/8.60 (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.hoare_new_addrs tptp.h3) tptp.as) tptp.h2))))))) tptp.h2) tptp.h))
% 8.20/8.60 (assert (@ (@ (@ tptp.relH (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit tptp.h3)) (not (@ (@ tptp.member_nat A5) tptp.as)))))) tptp.h3) tptp.h2))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((Bs tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.relH Bs) H) H5) (=> (@ (@ tptp.ord_less_eq_set_nat As) Bs) (@ (@ (@ tptp.relH As) H) H5)))))
% 8.20/8.60 (assert (forall ((X tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X))))
% 8.20/8.60 (assert (forall ((X tptp.int)) (exists ((Y3 tptp.int)) (@ (@ tptp.ord_less_int Y3) X))))
% 8.20/8.60 (assert (forall ((X tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X) X_1))))
% 8.20/8.60 (assert (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))))
% 8.20/8.60 (assert (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X) X_1))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (not (@ (@ tptp.ord_less_assn B) A)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (=> (= A B) (=> (@ (@ tptp.ord_less_assn B) C2) (@ (@ tptp.ord_less_assn A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_rat B) C2) (@ (@ tptp.ord_less_rat A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_num B) C2) (@ (@ tptp.ord_less_num A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C2) (@ (@ tptp.ord_less_nat A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_int B) C2) (@ (@ tptp.ord_less_int A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y5) X3) (@ P2 Y5))) (@ P2 X3))) (@ P2 A))))
% 8.20/8.60 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y) X)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 8.20/8.60 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X)) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 8.20/8.60 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 8.20/8.60 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X)) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 8.20/8.60 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A) (not (@ (@ tptp.ord_less_assn A) B)))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))))
% 8.20/8.60 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 8.20/8.60 (assert (forall ((A tptp.assn)) (not (@ (@ tptp.ord_less_assn A) A))))
% 8.20/8.60 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 8.20/8.60 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 8.20/8.60 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 8.20/8.60 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 8.20/8.60 (assert (= (lambda ((P4 (-> tptp.nat Bool))) (exists ((X5 tptp.nat)) (@ P4 X5))) (lambda ((P5 (-> tptp.nat Bool))) (exists ((N tptp.nat)) (and (@ P5 N) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N) (not (@ P5 M3)))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.rat)) (@ (@ P2 A3) A3)) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_num A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.num)) (@ (@ P2 A3) A3)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.nat)) (@ (@ P2 A3) A3)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.int)) (@ (@ P2 A3) A3)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_assn B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_rat B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_num B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (or (@ (@ tptp.ord_less_rat Y) X) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (or (@ (@ tptp.ord_less_num Y) X) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (or (@ (@ tptp.ord_less_int Y) X) (= X Y)))))
% 8.20/8.60 (assert (forall ((B tptp.assn) (A tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C2))) (=> (@ (@ tptp.ord_less_assn B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C2))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (assert (forall ((B tptp.num) (A tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C2))) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (not (= A B)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 8.20/8.60 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A) (not (= A B)))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (= A B)))))
% 8.20/8.60 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (@ (@ tptp.ord_less_assn Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_rat Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_num Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_int Y) X)))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (not (@ (@ tptp.ord_less_assn B) A)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 8.20/8.60 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z3 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_assn Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_rat Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num) (Z3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_num Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (F (-> tptp.assn tptp.assn)) (B tptp.assn) (C2 tptp.assn)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.assn tptp.rat)) (B tptp.assn) (C2 tptp.assn)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (F (-> tptp.assn tptp.num)) (B tptp.assn) (C2 tptp.assn)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (F (-> tptp.assn tptp.nat)) (B tptp.assn) (C2 tptp.assn)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (F (-> tptp.assn tptp.int)) (B tptp.assn) (C2 tptp.assn)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (F (-> tptp.rat tptp.assn)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.assn)) (C2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.assn)) (C2 tptp.assn)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((X tptp.assn)) (not (@ (@ tptp.ord_less_assn X) X))))
% 8.20/8.60 (assert (forall ((X tptp.rat)) (not (@ (@ tptp.ord_less_rat X) X))))
% 8.20/8.60 (assert (forall ((X tptp.num)) (not (@ (@ tptp.ord_less_num X) X))))
% 8.20/8.60 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 8.20/8.60 (assert (forall ((X tptp.int)) (not (@ (@ tptp.ord_less_int X) X))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (F (-> tptp.assn tptp.assn)) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C2) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (F (-> tptp.rat tptp.assn)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (F (-> tptp.num tptp.assn)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (F (-> tptp.nat tptp.assn)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (F (-> tptp.int tptp.assn)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.assn tptp.rat)) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C2) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.assn)) (C2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (@ (@ tptp.ord_less_assn (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.assn)) (C2 tptp.assn)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_assn (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (@ (@ tptp.ord_less_assn Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.assn) (Y tptp.assn) (P2 Bool)) (=> (@ (@ tptp.ord_less_assn X) Y) (=> (@ (@ tptp.ord_less_assn Y) X) P2))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat) (P2 Bool)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) X) P2))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num) (P2 Bool)) (=> (@ (@ tptp.ord_less_num X) Y) (=> (@ (@ tptp.ord_less_num Y) X) P2))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (P2 Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P2))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int) (P2 Bool)) (=> (@ (@ tptp.ord_less_int X) Y) (=> (@ (@ tptp.ord_less_int Y) X) P2))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y) (@ (@ tptp.ord_less_rat Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X) Y) (= X Y) (@ (@ tptp.ord_less_num Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (= Y X)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= Y X)))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= Y X)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= Y X)))))
% 8.20/8.60 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (@ (@ tptp.ord_less_assn Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 8.20/8.60 (assert (forall ((As tptp.set_nat) (H1 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 H1))) (=> (@ _let_2 H22) (=> (@ (@ _let_1 H22) H32) (@ _let_2 H32)))))))
% 8.20/8.60 (assert (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.relH As))) (=> (@ (@ _let_1 H) H5) (@ (@ _let_1 H5) H)))))
% 8.20/8.60 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (not (@ (@ tptp.ord_less_assn X) Y)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (not (@ (@ tptp.ord_less_rat X) Y)))))
% 8.20/8.60 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (not (@ (@ tptp.ord_less_num X) Y)))))
% 8.20/8.60 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))))
% 8.20/8.60 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (not (@ (@ tptp.ord_less_int X) Y)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (not (@ (@ tptp.ord_less_assn X) Y)) (= (@ (@ tptp.ord_less_eq_assn X) Y) (= X Y)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (= (not (@ (@ tptp.ord_less_assn X) Y)) (= X Y)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 8.20/8.60 (assert (forall ((Z3 tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X3) (@ (@ tptp.ord_less_eq_rat Y) X3))) (@ (@ tptp.ord_less_eq_rat Y) Z3))))
% 8.20/8.60 (assert (forall ((Y tptp.rat) (Z3 tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (@ (@ tptp.ord_less_eq_rat X3) Z3))) (@ (@ tptp.ord_less_eq_rat Y) Z3))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y) X)) (@ (@ tptp.ord_less_rat X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X)) (@ (@ tptp.ord_less_num X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X)) (@ (@ tptp.ord_less_int X) Y))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_assn (lambda ((A5 tptp.assn) (B4 tptp.assn)) (or (@ (@ tptp.ord_less_assn A5) B4) (= A5 B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B4 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A5) B4) (= A5 B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (or (@ (@ tptp.ord_less_rat A5) B4) (= A5 B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_num (lambda ((A5 tptp.num) (B4 tptp.num)) (or (@ (@ tptp.ord_less_num A5) B4) (= A5 B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (or (@ (@ tptp.ord_less_nat A5) B4) (= A5 B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (or (@ (@ tptp.ord_less_int A5) B4) (= A5 B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_assn (lambda ((A5 tptp.assn) (B4 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A5) B4) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B4) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B4) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_num (lambda ((A5 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B4) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B4) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B4) (not (= A5 B4))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) B) (=> (@ (@ tptp.ord_less_assn B) C2) (@ (@ tptp.ord_less_assn A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_set_int B) C2) (@ (@ tptp.ord_less_set_int A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) C2) (@ (@ tptp.ord_less_rat A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num B) C2) (@ (@ tptp.ord_less_num A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C2) (@ (@ tptp.ord_less_nat A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int B) C2) (@ (@ tptp.ord_less_int A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_assn B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (= tptp.ord_less_assn (lambda ((A5 tptp.assn) (B4 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A5) B4) (not (@ (@ tptp.ord_less_eq_assn B4) A5))))))
% 8.20/8.60 (assert (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B4) (not (@ (@ tptp.ord_less_eq_set_int B4) A5))))))
% 8.20/8.60 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B4) (not (@ (@ tptp.ord_less_eq_rat B4) A5))))))
% 8.20/8.60 (assert (= tptp.ord_less_num (lambda ((A5 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B4) (not (@ (@ tptp.ord_less_eq_num B4) A5))))))
% 8.20/8.60 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B4) (not (@ (@ tptp.ord_less_eq_nat B4) A5))))))
% 8.20/8.60 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B4) (not (@ (@ tptp.ord_less_eq_int B4) A5))))))
% 8.20/8.60 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X) (=> (forall ((W tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) W) (=> (@ (@ tptp.ord_less_rat W) X) (@ (@ tptp.ord_less_eq_rat Y) W)))) (@ (@ tptp.ord_less_eq_rat Y) Z3)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (forall ((W tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) W) (=> (@ (@ tptp.ord_less_rat W) Y) (@ (@ tptp.ord_less_eq_rat W) Z3)))) (@ (@ tptp.ord_less_eq_rat Y) Z3)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_assn (lambda ((B4 tptp.assn) (A5 tptp.assn)) (or (@ (@ tptp.ord_less_assn B4) A5) (= A5 B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_set_int (lambda ((B4 tptp.set_int) (A5 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int B4) A5) (= A5 B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (or (@ (@ tptp.ord_less_rat B4) A5) (= A5 B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A5 tptp.num)) (or (@ (@ tptp.ord_less_num B4) A5) (= A5 B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (or (@ (@ tptp.ord_less_nat B4) A5) (= A5 B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (or (@ (@ tptp.ord_less_int B4) A5) (= A5 B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_assn (lambda ((B4 tptp.assn) (A5 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn B4) A5) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_set_int (lambda ((B4 tptp.set_int) (A5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B4) A5) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A5) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A5) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A5) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A5) (not (= A5 B4))))))
% 8.20/8.60 (assert (forall ((B tptp.assn) (A tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C2))) (=> (@ (@ tptp.ord_less_eq_assn B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int C2))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (assert (forall ((B tptp.num) (A tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C2))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (assert (forall ((B tptp.assn) (A tptp.assn) (C2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A) (=> (@ (@ tptp.ord_less_eq_assn C2) B) (@ (@ tptp.ord_less_assn C2) A)))))
% 8.20/8.60 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C2 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int C2) B) (@ (@ tptp.ord_less_set_int C2) A)))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C2) B) (@ (@ tptp.ord_less_rat C2) A)))))
% 8.20/8.60 (assert (forall ((B tptp.num) (A tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ (@ tptp.ord_less_eq_num C2) B) (@ (@ tptp.ord_less_num C2) A)))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C2) B) (@ (@ tptp.ord_less_nat C2) A)))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) B) (@ (@ tptp.ord_less_int C2) A)))))
% 8.20/8.60 (assert (= tptp.ord_less_assn (lambda ((B4 tptp.assn) (A5 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn B4) A5) (not (@ (@ tptp.ord_less_eq_assn A5) B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_set_int (lambda ((B4 tptp.set_int) (A5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B4) A5) (not (@ (@ tptp.ord_less_eq_set_int A5) B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A5) (not (@ (@ tptp.ord_less_eq_rat A5) B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A5) (not (@ (@ tptp.ord_less_eq_num A5) B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A5) (not (@ (@ tptp.ord_less_eq_nat A5) B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A5) (not (@ (@ tptp.ord_less_eq_int A5) B4))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (@ (@ tptp.ord_less_eq_assn A) B))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 8.20/8.60 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A) (@ (@ tptp.ord_less_eq_assn B) A))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))))
% 8.20/8.60 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_assn (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (or (@ (@ tptp.ord_less_assn X4) Y4) (= X4 Y4)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_rat X4) Y4) (= X4 Y4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_num (lambda ((X4 tptp.num) (Y4 tptp.num)) (or (@ (@ tptp.ord_less_num X4) Y4) (= X4 Y4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (or (@ (@ tptp.ord_less_nat X4) Y4) (= X4 Y4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (or (@ (@ tptp.ord_less_int X4) Y4) (= X4 Y4)))))
% 8.20/8.60 (assert (= tptp.ord_less_assn (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn X4) Y4) (not (= X4 Y4))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (assert (= tptp.ord_less_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X4) Y4) (not (= X4 Y4))))))
% 8.20/8.60 (assert (= tptp.ord_less_num (lambda ((X4 tptp.num) (Y4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X4) Y4) (not (= X4 Y4))))))
% 8.20/8.60 (assert (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y4) (not (= X4 Y4))))))
% 8.20/8.60 (assert (= tptp.ord_less_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X4) Y4) (not (= X4 Y4))))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_num Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_int Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (@ (@ tptp.ord_less_eq_assn X) Y))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_assn A) B)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_assn A) B) (@ (@ tptp.ord_less_assn A) B)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat A) B)))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 8.20/8.60 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z3 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (=> (@ (@ tptp.ord_less_assn Y) Z3) (@ (@ tptp.ord_less_assn X) Z3)))))
% 8.20/8.60 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (=> (@ (@ tptp.ord_less_set_int Y) Z3) (@ (@ tptp.ord_less_set_int X) Z3)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) Z3) (@ (@ tptp.ord_less_rat X) Z3)))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num) (Z3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_num Y) Z3) (@ (@ tptp.ord_less_num X) Z3)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z3) (@ (@ tptp.ord_less_nat X) Z3)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_int Y) Z3) (@ (@ tptp.ord_less_int X) Z3)))))
% 8.20/8.60 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z3 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_assn Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num) (Z3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (F (-> tptp.assn tptp.assn)) (B tptp.assn) (C2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (F (-> tptp.rat tptp.assn)) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_assn A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (F (-> tptp.num tptp.assn)) (B tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_assn A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (F (-> tptp.nat tptp.assn)) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_assn A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (F (-> tptp.int tptp.assn)) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_assn A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.assn tptp.rat)) (B tptp.assn) (C2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C2) (=> (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 C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.assn)) (C2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_assn (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.assn)) (C2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_assn (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (F (-> tptp.rat tptp.assn)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_assn (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (F (-> tptp.num tptp.assn)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_assn (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.assn)) (C2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (@ (@ tptp.ord_less_eq_assn (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.assn)) (C2 tptp.assn)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_assn (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.assn)) (C2 tptp.assn)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_assn (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.assn)) (C2 tptp.assn)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_assn (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.assn)) (C2 tptp.assn)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_assn (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_rat Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_num Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_int Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (or (@ (@ tptp.ord_less_assn X) Y) (= X Y)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (or (@ (@ tptp.ord_less_num X) Y) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))))
% 8.20/8.60 (assert (forall ((N2 tptp.nat) (P2 (-> tptp.nat Bool))) (=> (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) N2) (not (@ P2 N3)))) (@ P2 N2)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat N4) N2) (@ P2 N4))))))
% 8.20/8.60 (assert (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit) (P2 tptp.assn)) (let ((_let_1 (@ tptp.rep_assn P2))) (=> (@ (@ (@ tptp.relH As) H) H5) (= (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As)) (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H5) As)))))))
% 8.20/8.60 (assert (= tptp.hoare_hoare_triple_a (lambda ((P5 tptp.assn) (C3 tptp.heap_Time_Heap_a) (Q3 (-> tptp.a tptp.assn))) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P5) (@ (@ tptp.produc7507926704131184380et_nat H6) As4)) (exists ((R5 tptp.a) (H7 tptp.heap_e7401611519738050253t_unit)) (and (exists ((T4 tptp.nat)) (= (@ (@ tptp.heap_Time_execute_a C3) H6) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) T4))))) (@ (@ tptp.rep_assn (@ Q3 R5)) (@ (@ tptp.produc7507926704131184380et_nat H7) (@ (@ (@ tptp.hoare_new_addrs H6) As4) 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) As4)))))) H6) H7) (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H6)) (@ tptp.lim_Product_unit H7)))))))))
% 8.20/8.60 (assert (= tptp.hoare_hoare_triple_b (lambda ((P5 tptp.assn) (C3 tptp.heap_Time_Heap_b) (Q3 (-> tptp.b tptp.assn))) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P5) (@ (@ tptp.produc7507926704131184380et_nat H6) As4)) (exists ((R5 tptp.b) (H7 tptp.heap_e7401611519738050253t_unit)) (and (exists ((T4 tptp.nat)) (= (@ (@ tptp.heap_Time_execute_b C3) H6) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) T4))))) (@ (@ tptp.rep_assn (@ Q3 R5)) (@ (@ tptp.produc7507926704131184380et_nat H7) (@ (@ (@ tptp.hoare_new_addrs H6) As4) 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) As4)))))) H6) H7) (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H6)) (@ tptp.lim_Product_unit H7)))))))))
% 8.20/8.60 (assert (= tptp.hoare_8945653483474564448t_unit (lambda ((P5 tptp.assn) (C3 tptp.heap_T5738788834812785303t_unit) (Q3 (-> tptp.product_unit tptp.assn))) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P5) (@ (@ tptp.produc7507926704131184380et_nat H6) As4)) (exists ((R5 tptp.product_unit) (H7 tptp.heap_e7401611519738050253t_unit)) (and (exists ((T4 tptp.nat)) (= (@ (@ tptp.heap_T875086893843062177t_unit C3) H6) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) T4))))) (@ (@ tptp.rep_assn (@ Q3 R5)) (@ (@ tptp.produc7507926704131184380et_nat H7) (@ (@ (@ tptp.hoare_new_addrs H6) As4) 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) As4)))))) H6) H7) (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H6)) (@ tptp.lim_Product_unit H7)))))))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_Time_Heap_a) (Q2 (-> tptp.a tptp.assn))) (=> (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P2) (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (exists ((R6 tptp.a) (H8 tptp.heap_e7401611519738050253t_unit) (T5 tptp.nat)) (and (= (@ (@ tptp.heap_Time_execute_a C2) H2) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R6) (@ (@ tptp.produc584006145561248582it_nat H8) T5)))) (@ (@ tptp.rep_assn (@ Q2 R6)) (@ (@ tptp.produc7507926704131184380et_nat H8) (@ (@ (@ tptp.hoare_new_addrs H2) As2) H8))) (@ (@ (@ tptp.relH (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit H2)) (not (@ (@ tptp.member_nat A5) As2)))))) H2) H8) (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H2)) (@ tptp.lim_Product_unit H8)))))) (@ (@ (@ tptp.hoare_hoare_triple_a P2) C2) Q2))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_Time_Heap_b) (Q2 (-> tptp.b tptp.assn))) (=> (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P2) (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (exists ((R6 tptp.b) (H8 tptp.heap_e7401611519738050253t_unit) (T5 tptp.nat)) (and (= (@ (@ tptp.heap_Time_execute_b C2) H2) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat R6) (@ (@ tptp.produc584006145561248582it_nat H8) T5)))) (@ (@ tptp.rep_assn (@ Q2 R6)) (@ (@ tptp.produc7507926704131184380et_nat H8) (@ (@ (@ tptp.hoare_new_addrs H2) As2) H8))) (@ (@ (@ tptp.relH (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit H2)) (not (@ (@ tptp.member_nat A5) As2)))))) H2) H8) (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H2)) (@ tptp.lim_Product_unit H8)))))) (@ (@ (@ tptp.hoare_hoare_triple_b P2) C2) Q2))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_T5738788834812785303t_unit) (Q2 (-> tptp.product_unit tptp.assn))) (=> (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P2) (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (exists ((R6 tptp.product_unit) (H8 tptp.heap_e7401611519738050253t_unit) (T5 tptp.nat)) (and (= (@ (@ tptp.heap_T875086893843062177t_unit C2) H2) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R6) (@ (@ tptp.produc584006145561248582it_nat H8) T5)))) (@ (@ tptp.rep_assn (@ Q2 R6)) (@ (@ tptp.produc7507926704131184380et_nat H8) (@ (@ (@ tptp.hoare_new_addrs H2) As2) H8))) (@ (@ (@ tptp.relH (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit H2)) (not (@ (@ tptp.member_nat A5) As2)))))) H2) H8) (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H2)) (@ tptp.lim_Product_unit H8)))))) (@ (@ (@ tptp.hoare_8945653483474564448t_unit P2) C2) Q2))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_Time_Heap_a) (Q2 (-> tptp.a tptp.assn)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.hoare_hoare_triple_a P2) C2) Q2) (=> (@ (@ tptp.rep_assn P2) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (not (forall ((R4 tptp.a) (H4 tptp.heap_e7401611519738050253t_unit)) (=> (exists ((T3 tptp.nat)) (= (@ (@ tptp.heap_Time_execute_a C2) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R4) (@ (@ tptp.produc584006145561248582it_nat H4) T3))))) (=> (@ (@ tptp.rep_assn (@ Q2 R4)) (@ (@ tptp.produc7507926704131184380et_nat H4) (@ (@ (@ tptp.hoare_new_addrs H) As) H4))) (=> (@ (@ (@ 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) H4) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H)) (@ tptp.lim_Product_unit H4))))))))))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_Time_Heap_b) (Q2 (-> tptp.b tptp.assn)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.hoare_hoare_triple_b P2) C2) Q2) (=> (@ (@ tptp.rep_assn P2) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (not (forall ((R4 tptp.b) (H4 tptp.heap_e7401611519738050253t_unit)) (=> (exists ((T3 tptp.nat)) (= (@ (@ tptp.heap_Time_execute_b C2) H) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat R4) (@ (@ tptp.produc584006145561248582it_nat H4) T3))))) (=> (@ (@ tptp.rep_assn (@ Q2 R4)) (@ (@ tptp.produc7507926704131184380et_nat H4) (@ (@ (@ tptp.hoare_new_addrs H) As) H4))) (=> (@ (@ (@ 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) H4) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H)) (@ tptp.lim_Product_unit H4))))))))))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_T5738788834812785303t_unit) (Q2 (-> tptp.product_unit tptp.assn)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.hoare_8945653483474564448t_unit P2) C2) Q2) (=> (@ (@ tptp.rep_assn P2) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (not (forall ((R4 tptp.product_unit) (H4 tptp.heap_e7401611519738050253t_unit)) (=> (exists ((T3 tptp.nat)) (= (@ (@ tptp.heap_T875086893843062177t_unit C2) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R4) (@ (@ tptp.produc584006145561248582it_nat H4) T3))))) (=> (@ (@ tptp.rep_assn (@ Q2 R4)) (@ (@ tptp.produc7507926704131184380et_nat H4) (@ (@ (@ tptp.hoare_new_addrs H) As) H4))) (=> (@ (@ (@ 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) H4) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H)) (@ tptp.lim_Product_unit H4))))))))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ tptp.heap_T584514906347983379t_unit F) H) (not (forall ((R4 tptp.product_unit) (H4 tptp.produc6653097349344004940it_nat)) (not (= (@ (@ tptp.heap_T875086893843062177t_unit F) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R4) H4)))))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_b) (H tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ tptp.heap_Time_success_b F) H) (not (forall ((R4 tptp.b) (H4 tptp.produc6653097349344004940it_nat)) (not (= (@ (@ tptp.heap_Time_execute_b F) H) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat R4) H4)))))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ tptp.heap_Time_success_a F) H) (not (forall ((R4 tptp.a) (H4 tptp.produc6653097349344004940it_nat)) (not (= (@ (@ tptp.heap_Time_execute_a F) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R4) H4)))))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num) (Z3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_num Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_num Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.set_int) (Z4 tptp.set_int)) (= Y6 Z4)) (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)))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.rat) (Z4 tptp.rat)) (= Y6 Z4)) (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_rat Y4) X4)))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4)) (lambda ((X4 tptp.num) (Y4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_num Y4) X4)))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat Y4) X4)))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (lambda ((X4 tptp.int) (Y4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_int Y4) X4)))))
% 8.20/8.60 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C2 tptp.set_int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_int B) C2) (@ (@ tptp.ord_less_eq_set_int A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (@ (@ tptp.ord_less_eq_rat A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_num B) C2) (@ (@ tptp.ord_less_eq_num A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ (@ tptp.ord_less_eq_nat A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ (@ tptp.ord_less_eq_int A) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= X Y)))))
% 8.20/8.60 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ _let_1 C2))))))
% 8.20/8.60 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num) (Z3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z3) (@ _let_1 Z3))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.rat) (B3 tptp.rat)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A3) B3) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ P2 B3) A3) (@ (@ P2 A3) B3))) (@ (@ P2 A) B)))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.set_int) (Z4 tptp.set_int)) (= Y6 Z4)) (lambda ((A5 tptp.set_int) (B4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B4) A5) (@ (@ tptp.ord_less_eq_set_int A5) B4)))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.rat) (Z4 tptp.rat)) (= Y6 Z4)) (lambda ((A5 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A5) (@ (@ tptp.ord_less_eq_rat A5) B4)))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4)) (lambda ((A5 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A5) (@ (@ tptp.ord_less_eq_num A5) B4)))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (lambda ((A5 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A5) (@ (@ tptp.ord_less_eq_nat A5) B4)))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (lambda ((A5 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A5) (@ (@ tptp.ord_less_eq_int A5) B4)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A B)))))
% 8.20/8.60 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 8.20/8.60 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C2))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (assert (forall ((B tptp.num) (A tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A B)))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.set_int) (Z4 tptp.set_int)) (= Y6 Z4)) (lambda ((A5 tptp.set_int) (B4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B4) (@ (@ tptp.ord_less_eq_set_int B4) A5)))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.rat) (Z4 tptp.rat)) (= Y6 Z4)) (lambda ((A5 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B4) (@ (@ tptp.ord_less_eq_rat B4) A5)))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4)) (lambda ((A5 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B4) (@ (@ tptp.ord_less_eq_num B4) A5)))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (lambda ((A5 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B4) (@ (@ tptp.ord_less_eq_nat B4) A5)))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (lambda ((A5 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B4) (@ (@ tptp.ord_less_eq_int B4) A5)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (F (-> tptp.int tptp.num)) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C2))))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (= X Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_eq_num Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C2 tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C2 tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C2 tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C2 tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C2 tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C2) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C2 tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C2 tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C2)))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C2) (=> (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)) C2))))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))))
% 8.20/8.60 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 8.20/8.60 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 8.20/8.60 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 8.20/8.60 (assert (= tptp.heap_T6553295506729943825t_unit (lambda ((C3 tptp.heap_T5738788834812785303t_unit) (H6 tptp.heap_e7401611519738050253t_unit) (H7 tptp.heap_e7401611519738050253t_unit) (R5 tptp.product_unit) (N tptp.nat)) (= (@ (@ tptp.heap_T875086893843062177t_unit C3) H6) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) N)))))))
% 8.20/8.60 (assert (= tptp.heap_Time_effect_b (lambda ((C3 tptp.heap_Time_Heap_b) (H6 tptp.heap_e7401611519738050253t_unit) (H7 tptp.heap_e7401611519738050253t_unit) (R5 tptp.b) (N tptp.nat)) (= (@ (@ tptp.heap_Time_execute_b C3) H6) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) N)))))))
% 8.20/8.60 (assert (= tptp.heap_Time_effect_a (lambda ((C3 tptp.heap_Time_Heap_a) (H6 tptp.heap_e7401611519738050253t_unit) (H7 tptp.heap_e7401611519738050253t_unit) (R5 tptp.a) (N tptp.nat)) (= (@ (@ tptp.heap_Time_execute_a C3) H6) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) N)))))))
% 8.20/8.60 (assert (forall ((C2 tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit) (R2 tptp.product_unit) (H5 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat)) (=> (= (@ (@ tptp.heap_T875086893843062177t_unit C2) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R2) (@ (@ tptp.produc584006145561248582it_nat H5) N2)))) (@ (@ (@ (@ (@ tptp.heap_T6553295506729943825t_unit C2) H) H5) R2) N2))))
% 8.20/8.60 (assert (forall ((C2 tptp.heap_Time_Heap_b) (H tptp.heap_e7401611519738050253t_unit) (R2 tptp.b) (H5 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat)) (=> (= (@ (@ tptp.heap_Time_execute_b C2) H) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat R2) (@ (@ tptp.produc584006145561248582it_nat H5) N2)))) (@ (@ (@ (@ (@ tptp.heap_Time_effect_b C2) H) H5) R2) N2))))
% 8.20/8.60 (assert (forall ((C2 tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (R2 tptp.a) (H5 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat)) (=> (= (@ (@ tptp.heap_Time_execute_a C2) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R2) (@ (@ tptp.produc584006145561248582it_nat H5) N2)))) (@ (@ (@ (@ (@ tptp.heap_Time_effect_a C2) H) H5) R2) N2))))
% 8.20/8.60 (assert (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N) (not (= M3 N))))))
% 8.20/8.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_nat M3) N) (= M3 N)))))
% 8.20/8.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N2) (= M N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 8.20/8.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (not (= M N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 8.20/8.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat) (J2 tptp.nat)) (=> (forall ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J3) (@ (@ tptp.ord_less_nat (@ F I3)) (@ F J3)))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ F J2))))))
% 8.20/8.60 (assert (forall ((N2 tptp.nat) (P2 (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (@ P2 K))) (=> (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) I4) (@ P2 I4))) (@ P2 K)))) (@ P2 M)))))
% 8.20/8.60 (assert (forall ((T6 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z2) (not (@ (@ tptp.ord_less_eq_rat T6) X6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z2) (not (@ (@ tptp.ord_less_eq_num T6) X6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z2) (not (@ (@ tptp.ord_less_eq_nat T6) X6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z2) (not (@ (@ tptp.ord_less_eq_int T6) X6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z2) (@ (@ tptp.ord_less_eq_rat X6) T6))))))
% 8.20/8.60 (assert (forall ((T6 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z2) (@ (@ tptp.ord_less_eq_num X6) T6))))))
% 8.20/8.60 (assert (forall ((T6 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z2) (@ (@ tptp.ord_less_eq_nat X6) T6))))))
% 8.20/8.60 (assert (forall ((T6 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z2) (@ (@ tptp.ord_less_eq_int X6) T6))))))
% 8.20/8.60 (assert (forall ((T6 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X6) (@ (@ tptp.ord_less_eq_rat T6) X6))))))
% 8.20/8.60 (assert (forall ((T6 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X6) (@ (@ tptp.ord_less_eq_num T6) X6))))))
% 8.20/8.60 (assert (forall ((T6 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X6) (@ (@ tptp.ord_less_eq_nat T6) X6))))))
% 8.20/8.60 (assert (forall ((T6 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X6) (@ (@ tptp.ord_less_eq_int T6) X6))))))
% 8.20/8.60 (assert (forall ((S tptp.set_list_nat) (P2 (-> tptp.list_nat Bool))) (= (@ (@ tptp.ord_le6045566169113846134st_nat S) (@ tptp.collect_list_nat P2)) (forall ((X4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X4) S) (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((S tptp.set_se6260736226359567993nt_int) (P2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (= (@ (@ tptp.ord_le483042692224249369nt_int S) (@ tptp.collec5210948495886036740nt_int P2)) (forall ((X4 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X4) S) (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((S tptp.set_set_nat) (P2 (-> tptp.set_nat Bool))) (= (@ (@ tptp.ord_le6893508408891458716et_nat S) (@ tptp.collect_set_nat P2)) (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) S) (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((S tptp.set_nat) (P2 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat S) (@ tptp.collect_nat P2)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S) (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((S tptp.set_int) (P2 (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int S) (@ tptp.collect_int P2)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S) (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((X7 tptp.set_o) (P2 (-> Bool Bool))) (@ (@ tptp.ord_less_eq_set_o (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) X7) (@ P2 X4))))) X7)))
% 8.20/8.60 (assert (forall ((X7 tptp.set_list_nat) (P2 (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) X7) (@ P2 X4))))) X7)))
% 8.20/8.60 (assert (forall ((X7 tptp.set_se6260736226359567993nt_int) (P2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (@ (@ tptp.ord_le483042692224249369nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (and (@ (@ tptp.member2340774599025711042nt_int X4) X7) (@ P2 X4))))) X7)))
% 8.20/8.60 (assert (forall ((X7 tptp.set_set_nat) (P2 (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) X7) (@ P2 X4))))) X7)))
% 8.20/8.60 (assert (forall ((X7 tptp.set_nat) (P2 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) X7) (@ P2 X4))))) X7)))
% 8.20/8.60 (assert (forall ((X7 tptp.set_int) (P2 (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) X7) (@ P2 X4))))) X7)))
% 8.20/8.60 (assert (forall ((X Bool) (Z5 tptp.set_o) (X7 tptp.set_o) (P2 (-> Bool Bool))) (=> (@ (@ tptp.member_o X) Z5) (=> (@ (@ tptp.ord_less_eq_set_o Z5) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) X7) (@ P2 X4))))) (@ P2 X)))))
% 8.20/8.60 (assert (forall ((X tptp.list_nat) (Z5 tptp.set_list_nat) (X7 tptp.set_list_nat) (P2 (-> tptp.list_nat Bool))) (=> (@ (@ tptp.member_list_nat X) Z5) (=> (@ (@ tptp.ord_le6045566169113846134st_nat Z5) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) X7) (@ P2 X4))))) (@ P2 X)))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr958786334691620121nt_int) (Z5 tptp.set_se6260736226359567993nt_int) (X7 tptp.set_se6260736226359567993nt_int) (P2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (=> (@ (@ tptp.member2340774599025711042nt_int X) Z5) (=> (@ (@ tptp.ord_le483042692224249369nt_int Z5) (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (and (@ (@ tptp.member2340774599025711042nt_int X4) X7) (@ P2 X4))))) (@ P2 X)))))
% 8.20/8.60 (assert (forall ((X tptp.set_nat) (Z5 tptp.set_set_nat) (X7 tptp.set_set_nat) (P2 (-> tptp.set_nat Bool))) (=> (@ (@ tptp.member_set_nat X) Z5) (=> (@ (@ tptp.ord_le6893508408891458716et_nat Z5) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) X7) (@ P2 X4))))) (@ P2 X)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Z5 tptp.set_nat) (X7 tptp.set_nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X) Z5) (=> (@ (@ tptp.ord_less_eq_set_nat Z5) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) X7) (@ P2 X4))))) (@ P2 X)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Z5 tptp.set_int) (X7 tptp.set_int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.member_int X) Z5) (=> (@ (@ tptp.ord_less_eq_set_int Z5) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) X7) (@ P2 X4))))) (@ P2 X)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool)) (Q4 (-> tptp.rat Bool))) (=> (exists ((Z6 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z6) X3) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z6) X3) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X6) (= (and (@ P2 X6) (@ Q2 X6)) (and (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q2 (-> tptp.num Bool)) (Q4 (-> tptp.num Bool))) (=> (exists ((Z6 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z6) X3) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z6) X3) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X6) (= (and (@ P2 X6) (@ Q2 X6)) (and (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z6 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z6) X3) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z6) X3) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X6) (= (and (@ P2 X6) (@ Q2 X6)) (and (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z6) X3) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z6) X3) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X6) (= (and (@ P2 X6) (@ Q2 X6)) (and (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool)) (Q4 (-> tptp.rat Bool))) (=> (exists ((Z6 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z6) X3) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z6) X3) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X6) (= (or (@ P2 X6) (@ Q2 X6)) (or (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q2 (-> tptp.num Bool)) (Q4 (-> tptp.num Bool))) (=> (exists ((Z6 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z6) X3) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z6) X3) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X6) (= (or (@ P2 X6) (@ Q2 X6)) (or (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z6 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z6) X3) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z6) X3) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X6) (= (or (@ P2 X6) (@ Q2 X6)) (or (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z6) X3) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z6) X3) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X6) (= (or (@ P2 X6) (@ Q2 X6)) (or (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((T6 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X6) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X6) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X6) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X6) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X6) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X6) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X6) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X6) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X6) (not (@ (@ tptp.ord_less_rat X6) T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X6) (not (@ (@ tptp.ord_less_num X6) T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X6) (not (@ (@ tptp.ord_less_nat X6) T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X6) (not (@ (@ tptp.ord_less_int X6) T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X6) (@ (@ tptp.ord_less_rat T6) X6))))))
% 8.20/8.60 (assert (forall ((T6 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X6) (@ (@ tptp.ord_less_num T6) X6))))))
% 8.20/8.60 (assert (forall ((T6 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X6) (@ (@ tptp.ord_less_nat T6) X6))))))
% 8.20/8.60 (assert (forall ((T6 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X6) (@ (@ tptp.ord_less_int T6) X6))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool)) (Q4 (-> tptp.rat Bool))) (=> (exists ((Z6 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z6) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z6) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z2) (= (and (@ P2 X6) (@ Q2 X6)) (and (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q2 (-> tptp.num Bool)) (Q4 (-> tptp.num Bool))) (=> (exists ((Z6 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z6) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z6) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z2) (= (and (@ P2 X6) (@ Q2 X6)) (and (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z6 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z6) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z6) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z2) (= (and (@ P2 X6) (@ Q2 X6)) (and (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z6) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z6) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z2) (= (and (@ P2 X6) (@ Q2 X6)) (and (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q2 (-> tptp.rat Bool)) (Q4 (-> tptp.rat Bool))) (=> (exists ((Z6 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z6) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z6) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z2) (= (or (@ P2 X6) (@ Q2 X6)) (or (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q2 (-> tptp.num Bool)) (Q4 (-> tptp.num Bool))) (=> (exists ((Z6 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z6) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z6) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z2) (= (or (@ P2 X6) (@ Q2 X6)) (or (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z6 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z6) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z6) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z2) (= (or (@ P2 X6) (@ Q2 X6)) (or (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z6) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z6) (= (@ Q2 X3) (@ Q4 X3))))) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z2) (= (or (@ P2 X6) (@ Q2 X6)) (or (@ P6 X6) (@ Q4 X6))))))))))
% 8.20/8.60 (assert (forall ((T6 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z2) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z2) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z2) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z2) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z2) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z2) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z2) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z2) (not (= X6 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X6))) (=> (@ _let_1 Z2) (@ _let_1 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X6))) (=> (@ _let_1 Z2) (@ _let_1 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X6))) (=> (@ _let_1 Z2) (@ _let_1 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X6))) (=> (@ _let_1 Z2) (@ _let_1 T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z2) (not (@ (@ tptp.ord_less_rat T6) X6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z2) (not (@ (@ tptp.ord_less_num T6) X6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z2) (not (@ (@ tptp.ord_less_nat T6) X6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z2) (not (@ (@ tptp.ord_less_int T6) X6)))))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (not (@ P2 N5)) (exists ((M4 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N5) (not (@ P2 M4)))))) (@ P2 N2))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N5) (@ P2 M4))) (@ P2 N5))) (@ P2 N2))))
% 8.20/8.60 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 8.20/8.60 (assert (forall ((S2 tptp.nat) (T6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat S2) T6) (not (= S2 T6)))))
% 8.20/8.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) M) (not (= M N2)))))
% 8.20/8.60 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 8.20/8.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (= M N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat N2) M)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat Bool)) (K2 tptp.nat) (B tptp.nat)) (=> (@ P2 K2) (=> (forall ((Y3 tptp.nat)) (=> (@ P2 Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X3 tptp.nat)) (and (@ P2 X3) (forall ((Y5 tptp.nat)) (=> (@ P2 Y5) (@ (@ tptp.ord_less_eq_nat Y5) X3)))))))))
% 8.20/8.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat N2) M))))
% 8.20/8.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= M N2)))))
% 8.20/8.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J2) (=> (@ (@ tptp.ord_less_eq_nat J2) K2) (@ _let_1 K2))))))
% 8.20/8.60 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) N2)))
% 8.20/8.60 (assert (forall ((T6 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X6) (not (@ (@ tptp.ord_less_eq_rat X6) T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X6) (not (@ (@ tptp.ord_less_eq_num X6) T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X6) (not (@ (@ tptp.ord_less_eq_nat X6) T6)))))))
% 8.20/8.60 (assert (forall ((T6 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X6) (not (@ (@ tptp.ord_less_eq_int X6) T6)))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit) (X tptp.product_unit) (H5 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G (-> tptp.product_unit tptp.heap_Time_Heap_b))) (=> (= (@ (@ tptp.heap_T875086893843062177t_unit F) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat X) (@ (@ tptp.produc584006145561248582it_nat H5) N2)))) (= (@ (@ tptp.heap_Time_execute_b (@ (@ tptp.heap_T757603679106148409unit_b F) G)) H) (@ (@ tptp.heap_T7616092557645711336rame_b N2) (@ (@ tptp.heap_Time_execute_b (@ G X)) H5))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit) (X tptp.product_unit) (H5 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 H5) 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)) H5))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_b) (H tptp.heap_e7401611519738050253t_unit) (X tptp.b) (H5 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G (-> tptp.b tptp.heap_Time_Heap_b))) (=> (= (@ (@ tptp.heap_Time_execute_b F) H) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat X) (@ (@ tptp.produc584006145561248582it_nat H5) N2)))) (= (@ (@ tptp.heap_Time_execute_b (@ (@ tptp.heap_Time_bind_b_b F) G)) H) (@ (@ tptp.heap_T7616092557645711336rame_b N2) (@ (@ tptp.heap_Time_execute_b (@ G X)) H5))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_b) (H tptp.heap_e7401611519738050253t_unit) (X tptp.b) (H5 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G (-> tptp.b tptp.heap_Time_Heap_a))) (=> (= (@ (@ tptp.heap_Time_execute_b F) H) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat X) (@ (@ tptp.produc584006145561248582it_nat H5) N2)))) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_bind_b_a F) G)) H) (@ (@ tptp.heap_T7616092557645711335rame_a N2) (@ (@ tptp.heap_Time_execute_a (@ G X)) H5))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (X tptp.a) (H5 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G (-> tptp.a tptp.heap_Time_Heap_b))) (=> (= (@ (@ tptp.heap_Time_execute_a F) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat X) (@ (@ tptp.produc584006145561248582it_nat H5) N2)))) (= (@ (@ tptp.heap_Time_execute_b (@ (@ tptp.heap_Time_bind_a_b F) G)) H) (@ (@ tptp.heap_T7616092557645711336rame_b N2) (@ (@ tptp.heap_Time_execute_b (@ G X)) H5))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (X tptp.a) (H5 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 H5) 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)) H5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (= A4 B5)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (not (= A4 B5)) (@ (@ tptp.ord_less_set_int A4) B5)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o)) (=> (forall ((X3 Bool)) (let ((_let_1 (@ tptp.member_o X3))) (=> (@ _let_1 A4) (@ _let_1 B5)))) (@ (@ tptp.ord_less_eq_set_o A4) B5))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (=> (forall ((X3 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int X3))) (=> (@ _let_1 A4) (@ _let_1 B5)))) (@ (@ tptp.ord_le483042692224249369nt_int A4) B5))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (=> (@ _let_1 A4) (@ _let_1 B5)))) (@ (@ tptp.ord_le6893508408891458716et_nat A4) B5))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A4) (@ _let_1 B5)))) (@ (@ tptp.ord_less_eq_set_nat A4) B5))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A4) (@ _let_1 B5)))) (@ (@ tptp.ord_less_eq_set_int A4) B5))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ P2 A) (=> (not (@ P2 B)) (exists ((C tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A) C) (@ (@ tptp.ord_less_eq_nat C) B) (forall ((X6 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X6) (@ (@ tptp.ord_less_nat X6) C)) (@ P2 X6))) (forall ((D3 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X3) (@ (@ tptp.ord_less_nat X3) D3)) (@ P2 X3))) (@ (@ tptp.ord_less_eq_nat D3) C))))))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ P2 A) (=> (not (@ P2 B)) (exists ((C tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) C) (@ (@ tptp.ord_less_eq_int C) B) (forall ((X6 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X6) (@ (@ tptp.ord_less_int X6) C)) (@ P2 X6))) (forall ((D3 tptp.int)) (=> (forall ((X3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X3) (@ (@ tptp.ord_less_int X3) D3)) (@ P2 X3))) (@ (@ tptp.ord_less_eq_int D3) C))))))))))
% 8.20/8.60 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B2) A2)) (@ (@ tptp.ord_less_rat A2) B2))))
% 8.20/8.60 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B2) A2)) (@ (@ tptp.ord_less_num A2) B2))))
% 8.20/8.60 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B2) A2)) (@ (@ tptp.ord_less_nat A2) B2))))
% 8.20/8.60 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B2) A2)) (@ (@ tptp.ord_less_int A2) B2))))
% 8.20/8.60 (assert (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit) (X tptp.product_unit) (H5 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 H5) N2)))) (=> (= (@ (@ tptp.heap_T875086893843062177t_unit (@ G X)) H5) (@ 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)))))))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit) (X tptp.product_unit) (H5 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G (-> tptp.product_unit tptp.heap_Time_Heap_b)) (Y tptp.b) (H9 tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H9))) (let ((_let_2 (@ tptp.produc4082563078715348724it_nat Y))) (=> (= (@ (@ tptp.heap_T875086893843062177t_unit F) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat X) (@ (@ tptp.produc584006145561248582it_nat H5) N2)))) (=> (= (@ (@ tptp.heap_Time_execute_b (@ G X)) H5) (@ tptp.some_P2818173045054083285it_nat (@ _let_2 (@ _let_1 N6)))) (= (@ (@ tptp.heap_Time_execute_b (@ (@ tptp.heap_T757603679106148409unit_b F) G)) H) (@ tptp.some_P2818173045054083285it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat N2) N6)))))))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit) (X tptp.product_unit) (H5 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 H5) N2)))) (=> (= (@ (@ tptp.heap_Time_execute_a (@ G X)) H5) (@ 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)))))))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_b) (H tptp.heap_e7401611519738050253t_unit) (X tptp.b) (H5 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G (-> tptp.b 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_b F) H) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat X) (@ (@ tptp.produc584006145561248582it_nat H5) N2)))) (=> (= (@ (@ tptp.heap_T875086893843062177t_unit (@ G X)) H5) (@ tptp.some_P1914260805536162275it_nat (@ _let_2 (@ _let_1 N6)))) (= (@ (@ tptp.heap_T875086893843062177t_unit (@ (@ tptp.heap_T3413130826733729493t_unit F) G)) H) (@ tptp.some_P1914260805536162275it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat N2) N6)))))))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_b) (H tptp.heap_e7401611519738050253t_unit) (X tptp.b) (H5 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G (-> tptp.b tptp.heap_Time_Heap_b)) (Y tptp.b) (H9 tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H9))) (let ((_let_2 (@ tptp.produc4082563078715348724it_nat Y))) (=> (= (@ (@ tptp.heap_Time_execute_b F) H) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat X) (@ (@ tptp.produc584006145561248582it_nat H5) N2)))) (=> (= (@ (@ tptp.heap_Time_execute_b (@ G X)) H5) (@ tptp.some_P2818173045054083285it_nat (@ _let_2 (@ _let_1 N6)))) (= (@ (@ tptp.heap_Time_execute_b (@ (@ tptp.heap_Time_bind_b_b F) G)) H) (@ tptp.some_P2818173045054083285it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat N2) N6)))))))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_b) (H tptp.heap_e7401611519738050253t_unit) (X tptp.b) (H5 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G (-> tptp.b 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_b F) H) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat X) (@ (@ tptp.produc584006145561248582it_nat H5) N2)))) (=> (= (@ (@ tptp.heap_Time_execute_a (@ G X)) H5) (@ tptp.some_P7913643980934408916it_nat (@ _let_2 (@ _let_1 N6)))) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_bind_b_a F) G)) H) (@ tptp.some_P7913643980934408916it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat N2) N6)))))))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (X tptp.a) (H5 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 H5) N2)))) (=> (= (@ (@ tptp.heap_T875086893843062177t_unit (@ G X)) H5) (@ 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)))))))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (X tptp.a) (H5 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G (-> tptp.a tptp.heap_Time_Heap_b)) (Y tptp.b) (H9 tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H9))) (let ((_let_2 (@ tptp.produc4082563078715348724it_nat Y))) (=> (= (@ (@ tptp.heap_Time_execute_a F) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat X) (@ (@ tptp.produc584006145561248582it_nat H5) N2)))) (=> (= (@ (@ tptp.heap_Time_execute_b (@ G X)) H5) (@ tptp.some_P2818173045054083285it_nat (@ _let_2 (@ _let_1 N6)))) (= (@ (@ tptp.heap_Time_execute_b (@ (@ tptp.heap_Time_bind_a_b F) G)) H) (@ tptp.some_P2818173045054083285it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat N2) N6)))))))))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (X tptp.a) (H5 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 H5) N2)))) (=> (= (@ (@ tptp.heap_Time_execute_a (@ G X)) H5) (@ 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)))))))))))
% 8.20/8.60 (assert (= tptp.hoare_new_addrs (lambda ((H6 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat) (H7 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.sup_sup_set_nat As4) (@ 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)))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (P2 (-> Bool Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_o B5))) (=> (@ _let_1 A4) (= (@ _let_1 (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A4) (@ P2 X4))))) (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) B5) (@ P2 X4))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_list_nat) (A4 tptp.set_list_nat) (P2 (-> tptp.list_nat Bool))) (let ((_let_1 (@ tptp.ord_le6045566169113846134st_nat B5))) (=> (@ _let_1 A4) (= (@ _let_1 (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) A4) (@ P2 X4))))) (forall ((X4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X4) B5) (@ P2 X4))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_se6260736226359567993nt_int) (A4 tptp.set_se6260736226359567993nt_int) (P2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (let ((_let_1 (@ tptp.ord_le483042692224249369nt_int B5))) (=> (@ _let_1 A4) (= (@ _let_1 (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (and (@ (@ tptp.member2340774599025711042nt_int X4) A4) (@ P2 X4))))) (forall ((X4 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X4) B5) (@ P2 X4))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_set_nat) (A4 tptp.set_set_nat) (P2 (-> tptp.set_nat Bool))) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat B5))) (=> (@ _let_1 A4) (= (@ _let_1 (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A4) (@ P2 X4))))) (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) B5) (@ P2 X4))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (P2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_nat B5))) (=> (@ _let_1 A4) (= (@ _let_1 (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ P2 X4))))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) B5) (@ P2 X4))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (P2 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_int B5))) (=> (@ _let_1 A4) (= (@ _let_1 (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ P2 X4))))) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) B5) (@ P2 X4))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (Q2 (-> Bool Bool)) (P2 (-> Bool Bool))) (=> (@ (@ tptp.ord_less_eq_set_o B5) A4) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) B5) (=> (@ Q2 X3) (@ P2 X3)))) (@ (@ tptp.ord_less_eq_set_o (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) B5) (@ Q2 X4))))) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A4) (@ P2 X4)))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_list_nat) (A4 tptp.set_list_nat) (Q2 (-> tptp.list_nat Bool)) (P2 (-> tptp.list_nat Bool))) (=> (@ (@ tptp.ord_le6045566169113846134st_nat B5) A4) (=> (forall ((X3 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X3) B5) (=> (@ Q2 X3) (@ P2 X3)))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) B5) (@ Q2 X4))))) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) A4) (@ P2 X4)))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_se6260736226359567993nt_int) (A4 tptp.set_se6260736226359567993nt_int) (Q2 (-> tptp.set_Pr958786334691620121nt_int Bool)) (P2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (=> (@ (@ tptp.ord_le483042692224249369nt_int B5) A4) (=> (forall ((X3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X3) B5) (=> (@ Q2 X3) (@ P2 X3)))) (@ (@ tptp.ord_le483042692224249369nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (and (@ (@ tptp.member2340774599025711042nt_int X4) B5) (@ Q2 X4))))) (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (and (@ (@ tptp.member2340774599025711042nt_int X4) A4) (@ P2 X4)))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_set_nat) (A4 tptp.set_set_nat) (Q2 (-> tptp.set_nat Bool)) (P2 (-> tptp.set_nat Bool))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat B5) A4) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) B5) (=> (@ Q2 X3) (@ P2 X3)))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) B5) (@ Q2 X4))))) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A4) (@ P2 X4)))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (Q2 (-> tptp.nat Bool)) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) B5) (=> (@ Q2 X3) (@ P2 X3)))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) B5) (@ Q2 X4))))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ P2 X4)))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (Q2 (-> tptp.int Bool)) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B5) (=> (@ Q2 X3) (@ P2 X3)))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) B5) (@ Q2 X4))))) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ P2 X4)))))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_list_nat) (P2 (-> tptp.list_nat Bool)) (Q2 (-> tptp.list_nat Bool))) (let ((_let_1 (@ tptp.ord_le6045566169113846134st_nat A4))) (= (@ _let_1 (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ P2 X4) (@ Q2 X4))))) (and (@ _let_1 (@ tptp.collect_list_nat P2)) (@ _let_1 (@ tptp.collect_list_nat Q2)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (P2 (-> tptp.set_Pr958786334691620121nt_int Bool)) (Q2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (let ((_let_1 (@ tptp.ord_le483042692224249369nt_int A4))) (= (@ _let_1 (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (and (@ P2 X4) (@ Q2 X4))))) (and (@ _let_1 (@ tptp.collec5210948495886036740nt_int P2)) (@ _let_1 (@ tptp.collec5210948495886036740nt_int Q2)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_set_nat) (P2 (-> tptp.set_nat Bool)) (Q2 (-> tptp.set_nat Bool))) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat A4))) (= (@ _let_1 (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ P2 X4) (@ Q2 X4))))) (and (@ _let_1 (@ tptp.collect_set_nat P2)) (@ _let_1 (@ tptp.collect_set_nat Q2)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A4))) (= (@ _let_1 (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ P2 X4) (@ Q2 X4))))) (and (@ _let_1 (@ tptp.collect_nat P2)) (@ _let_1 (@ tptp.collect_nat Q2)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_int A4))) (= (@ _let_1 (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ P2 X4) (@ Q2 X4))))) (and (@ _let_1 (@ tptp.collect_int P2)) (@ _let_1 (@ tptp.collect_int Q2)))))))
% 8.20/8.60 (assert (forall ((C2 Bool) (B5 tptp.set_o) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (=> (=> (not (@ _let_1 B5)) (@ _let_1 A4)) (@ _let_1 (@ (@ tptp.sup_sup_set_o A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (B5 tptp.set_se6260736226359567993nt_int) (A4 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (=> (not (@ _let_1 B5)) (@ _let_1 A4)) (@ _let_1 (@ (@ tptp.sup_su2047564715030645325nt_int A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_nat) (B5 tptp.set_set_nat) (A4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (=> (not (@ _let_1 B5)) (@ _let_1 A4)) (@ _let_1 (@ (@ tptp.sup_sup_set_set_nat A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.int) (B5 tptp.set_int) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (=> (not (@ _let_1 B5)) (@ _let_1 A4)) (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.produc4166570645942440679at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (A4 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.member6689249552917799696at_nat C2))) (=> (=> (not (@ _let_1 B5)) (@ _let_1 A4)) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C2))) (=> (=> (not (@ _let_1 B5)) (@ _let_1 A4)) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.nat) (B5 tptp.set_nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (=> (not (@ _let_1 B5)) (@ _let_1 A4)) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A4) B5)) (or (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (= (@ _let_1 (@ (@ tptp.sup_su2047564715030645325nt_int A4) B5)) (or (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_set_nat A4) B5)) (or (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (or (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.produc4166570645942440679at_nat) (A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.member6689249552917799696at_nat C2))) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5)) (or (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C2))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5)) (or (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (or (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K2))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5)) C4) (and (@ (@ tptp.ord_le8081472938463900775at_nat A4) C4) (@ (@ tptp.ord_le8081472938463900775at_nat B5) C4)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5)) C4) (and (@ (@ tptp.ord_le1268244103169919719at_nat A4) C4) (@ (@ tptp.ord_le1268244103169919719at_nat B5) C4)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A4) B5)) C4) (and (@ (@ tptp.ord_less_eq_set_nat A4) C4) (@ (@ tptp.ord_less_eq_set_nat B5) C4)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (C4 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int A4) B5)) C4) (and (@ (@ tptp.ord_less_eq_set_int A4) C4) (@ (@ tptp.ord_less_eq_set_int B5) C4)))))
% 8.20/8.60 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K2))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.sup_sup_option_int (@ tptp.some_int X)) (@ tptp.some_int Y)) (@ tptp.some_int (@ (@ tptp.sup_sup_int X) Y)))))
% 8.20/8.60 (assert (forall ((As tptp.set_nat) (As5 tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ (@ tptp.relH (@ (@ tptp.sup_sup_set_nat As) As5)) H) H5) (and (@ (@ (@ tptp.relH As) H) H5) (@ (@ (@ tptp.relH As5) H) H5)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o) (C2 Bool)) (let ((_let_1 (@ tptp.member_o C2))) (=> (@ (@ tptp.ord_less_set_o A4) B5) (=> (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int) (C2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (@ (@ tptp.ord_le1924305788584680229nt_int A4) B5) (=> (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (@ (@ tptp.ord_less_set_set_nat A4) B5) (=> (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ (@ tptp.ord_less_set_nat A4) B5) (=> (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (C2 tptp.int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ (@ tptp.ord_less_set_int A4) B5) (=> (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (assert (= tptp.ord_le1924305788584680229nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (@ (@ tptp.ord_le2688692977766382584_int_o (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) A6))) (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) B6))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (assert (forall ((C2 Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_o A4) B5)) (=> (not (@ _let_1 A4)) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (@ _let_1 (@ (@ tptp.sup_su2047564715030645325nt_int A4) B5)) (=> (not (@ _let_1 A4)) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_set_nat A4) B5)) (=> (not (@ _let_1 A4)) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (=> (not (@ _let_1 A4)) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.produc4166570645942440679at_nat) (A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.member6689249552917799696at_nat C2))) (=> (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5)) (=> (not (@ _let_1 A4)) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C2))) (=> (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5)) (=> (not (@ _let_1 A4)) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (=> (not (@ _let_1 A4)) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((C2 Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (=> (@ _let_1 A4) (@ _let_1 (@ (@ tptp.sup_sup_set_o A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (@ _let_1 A4) (@ _let_1 (@ (@ tptp.sup_su2047564715030645325nt_int A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (@ _let_1 A4) (@ _let_1 (@ (@ tptp.sup_sup_set_set_nat A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 A4) (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.produc4166570645942440679at_nat) (A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.member6689249552917799696at_nat C2))) (=> (@ _let_1 A4) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C2))) (=> (@ _let_1 A4) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 A4) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 Bool) (B5 tptp.set_o) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.sup_sup_set_o A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (B5 tptp.set_se6260736226359567993nt_int) (A4 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.sup_su2047564715030645325nt_int A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_nat) (B5 tptp.set_set_nat) (A4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.sup_sup_set_set_nat A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.int) (B5 tptp.set_int) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.produc4166570645942440679at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (A4 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.member6689249552917799696at_nat C2))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C2))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5))))))
% 8.20/8.60 (assert (forall ((C2 tptp.nat) (B5 tptp.set_nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (P2 (-> tptp.produc4166570645942440679at_nat Bool))) (= (exists ((X4 tptp.produc4166570645942440679at_nat)) (and (@ (@ tptp.member6689249552917799696at_nat X4) (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5)) (@ P2 X4))) (or (exists ((X4 tptp.produc4166570645942440679at_nat)) (and (@ (@ tptp.member6689249552917799696at_nat X4) A4) (@ P2 X4))) (exists ((X4 tptp.produc4166570645942440679at_nat)) (and (@ (@ tptp.member6689249552917799696at_nat X4) B5) (@ P2 X4)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (P2 (-> tptp.produc3843707927480180839at_nat Bool))) (= (exists ((X4 tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X4) (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5)) (@ P2 X4))) (or (exists ((X4 tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X4) A4) (@ P2 X4))) (exists ((X4 tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X4) B5) (@ P2 X4)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (P2 (-> tptp.nat Bool))) (= (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ P2 X4))) (or (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ P2 X4))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) B5) (@ P2 X4)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (P2 (-> tptp.produc4166570645942440679at_nat Bool))) (= (forall ((X4 tptp.produc4166570645942440679at_nat)) (=> (@ (@ tptp.member6689249552917799696at_nat X4) (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5)) (@ P2 X4))) (and (forall ((X4 tptp.produc4166570645942440679at_nat)) (=> (@ (@ tptp.member6689249552917799696at_nat X4) A4) (@ P2 X4))) (forall ((X4 tptp.produc4166570645942440679at_nat)) (=> (@ (@ tptp.member6689249552917799696at_nat X4) B5) (@ P2 X4)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (P2 (-> tptp.produc3843707927480180839at_nat Bool))) (= (forall ((X4 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X4) (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5)) (@ P2 X4))) (and (forall ((X4 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X4) A4) (@ P2 X4))) (forall ((X4 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X4) B5) (@ P2 X4)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (P2 (-> tptp.nat Bool))) (= (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ P2 X4))) (and (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ P2 X4))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) B5) (@ P2 X4)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat A4))) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat B5) C4))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A4))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B5) C4))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A4))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B5) C4))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A4) A4) A4)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A4) A4) A4)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A4) A4) A4)))
% 8.20/8.60 (assert (= tptp.sup_su3035147773818789531at_nat (lambda ((A6 tptp.set_Pr8551490117392284871at_nat) (B6 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.sup_su3035147773818789531at_nat B6) A6))))
% 8.20/8.60 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((A6 tptp.set_Pr4329608150637261639at_nat) (B6 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat B6) A6))))
% 8.20/8.60 (assert (= tptp.sup_sup_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat B6) A6))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat A4))) (let ((_let_2 (@ _let_1 B5))) (= (@ _let_1 _let_2) _let_2)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A4))) (let ((_let_2 (@ _let_1 B5))) (= (@ _let_1 _let_2) _let_2)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A4))) (let ((_let_2 (@ _let_1 B5))) (= (@ _let_1 _let_2) _let_2)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat A4))) (let ((_let_2 (@ tptp.sup_su3035147773818789531at_nat B5))) (= (@ _let_1 (@ _let_2 C4)) (@ _let_2 (@ _let_1 C4)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A4))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat B5))) (= (@ _let_1 (@ _let_2 C4)) (@ _let_2 (@ _let_1 C4)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A4))) (let ((_let_2 (@ tptp.sup_sup_set_nat B5))) (= (@ _let_1 (@ _let_2 C4)) (@ _let_2 (@ _let_1 C4)))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.list_nat Bool)) (Q2 (-> tptp.list_nat Bool))) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (or (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.sup_sup_set_list_nat (@ tptp.collect_list_nat P2)) (@ tptp.collect_list_nat Q2)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.set_Pr958786334691620121nt_int Bool)) (Q2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (= (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (or (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.sup_su2047564715030645325nt_int (@ tptp.collec5210948495886036740nt_int P2)) (@ tptp.collec5210948495886036740nt_int Q2)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.set_nat Bool)) (Q2 (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (or (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.sup_sup_set_set_nat (@ tptp.collect_set_nat P2)) (@ tptp.collect_set_nat Q2)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (or (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.sup_sup_set_int (@ tptp.collect_int P2)) (@ tptp.collect_int Q2)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc4166570645942440679at_nat Bool)) (Q2 (-> tptp.produc4166570645942440679at_nat Bool))) (= (@ tptp.collec5204685387357076818at_nat (lambda ((X4 tptp.produc4166570645942440679at_nat)) (or (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.sup_su3035147773818789531at_nat (@ tptp.collec5204685387357076818at_nat P2)) (@ tptp.collec5204685387357076818at_nat Q2)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc3843707927480180839at_nat Bool)) (Q2 (-> tptp.produc3843707927480180839at_nat Bool))) (= (@ tptp.collec6321179662152712658at_nat (lambda ((X4 tptp.produc3843707927480180839at_nat)) (or (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.collec6321179662152712658at_nat P2)) (@ tptp.collec6321179662152712658at_nat Q2)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (or (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.sup_sup_set_nat (@ tptp.collect_nat P2)) (@ tptp.collect_nat Q2)))))
% 8.20/8.60 (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))))))))
% 8.20/8.60 (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))))))))
% 8.20/8.60 (assert (= tptp.sup_su2047564715030645325nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int X4))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 8.20/8.60 (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))))))))
% 8.20/8.60 (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))))))))
% 8.20/8.60 (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))))))))
% 8.20/8.60 (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))))))))
% 8.20/8.60 (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))))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (D4 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat A4) C4) (=> (@ (@ tptp.ord_le8081472938463900775at_nat B5) D4) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5)) (@ (@ tptp.sup_su3035147773818789531at_nat C4) D4))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (D4 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A4) C4) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B5) D4) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5)) (@ (@ tptp.sup_su5525570899277871387at_nat C4) D4))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (C4 tptp.set_nat) (B5 tptp.set_nat) (D4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A4) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) D4) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.sup_sup_set_nat C4) D4))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (C4 tptp.set_int) (B5 tptp.set_int) (D4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int B5) D4) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.sup_sup_set_int C4) D4))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat A4) C4) (=> (@ (@ tptp.ord_le8081472938463900775at_nat B5) C4) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5)) C4)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A4) C4) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B5) C4) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5)) C4)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (C4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A4) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) C4) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A4) B5)) C4)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (C4 tptp.set_int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int A4) B5)) C4)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat A4) (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat A4) (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A4) (@ (@ tptp.sup_sup_set_nat A4) B5))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A4) (@ (@ tptp.sup_sup_set_int A4) B5))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_Pr8551490117392284871at_nat) (A4 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat B5) (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_Pr4329608150637261639at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat B5) (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B5) (@ (@ tptp.sup_sup_set_nat A4) B5))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B5) (@ (@ tptp.sup_sup_set_int A4) B5))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat A4) B5) (= (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5) B5))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A4) B5) (= (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5) B5))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (= (@ (@ tptp.sup_sup_set_nat A4) B5) B5))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (= (@ (@ tptp.sup_sup_set_int A4) B5) B5))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_Pr8551490117392284871at_nat) (A4 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat B5) A4) (= (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5) A4))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_Pr4329608150637261639at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B5) A4) (= (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5) A4))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (= (@ (@ tptp.sup_sup_set_nat A4) B5) A4))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (= (@ (@ tptp.sup_sup_set_int A4) B5) A4))))
% 8.20/8.60 (assert (forall ((C4 tptp.set_Pr8551490117392284871at_nat) (A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat C4) (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5)) (not (forall ((A7 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat A7) A4) (forall ((B7 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat B7) B5) (not (= C4 (@ (@ tptp.sup_su3035147773818789531at_nat A7) B7)))))))))))
% 8.20/8.60 (assert (forall ((C4 tptp.set_Pr4329608150637261639at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C4) (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5)) (not (forall ((A7 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A7) A4) (forall ((B7 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B7) B5) (not (= C4 (@ (@ tptp.sup_su5525570899277871387at_nat A7) B7)))))))))))
% 8.20/8.60 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C4) (@ (@ tptp.sup_sup_set_nat A4) B5)) (not (forall ((A7 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A7) A4) (forall ((B7 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B7) B5) (not (= C4 (@ (@ tptp.sup_sup_set_nat A7) B7)))))))))))
% 8.20/8.60 (assert (forall ((C4 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int C4) (@ (@ tptp.sup_sup_set_int A4) B5)) (not (forall ((A7 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A7) A4) (forall ((B7 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B7) B5) (not (= C4 (@ (@ tptp.sup_sup_set_int A7) B7)))))))))))
% 8.20/8.60 (assert (= tptp.ord_le8081472938463900775at_nat (lambda ((A6 tptp.set_Pr8551490117392284871at_nat) (B6 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A6) B6) B6))))
% 8.20/8.60 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((A6 tptp.set_Pr4329608150637261639at_nat) (B6 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A6) B6) B6))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A6) B6) B6))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A6) B6) B6))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J2)) K2) (@ (@ tptp.ord_less_nat I2) K2))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat K2) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L))))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J2)) I2))))
% 8.20/8.60 (assert (forall ((J2 tptp.nat) (I2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J2) I2)) I2))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) K2)))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) M))))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J2))))))
% 8.20/8.60 (assert (forall ((K2 tptp.nat) (L tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K2) N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 8.20/8.60 (assert (forall ((M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K2)) N2) (not (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (@ (@ tptp.ord_less_eq_nat K2) N2)))))))
% 8.20/8.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat N2) M))))
% 8.20/8.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat M) N2))))
% 8.20/8.60 (assert (forall ((M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K2)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 8.20/8.60 (assert (forall ((M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K2)) N2) (@ (@ tptp.ord_less_eq_nat K2) N2))))
% 8.20/8.60 (assert (forall ((K2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) L) (exists ((N5 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K2) N5))))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_eq_nat K2) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L))))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) K2)))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) M))))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J2) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J2))))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (exists ((K3 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M3) K3))))))
% 8.20/8.60 (assert (forall ((N2 tptp.nat) (R2 tptp.b) (H tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H))) (let ((_let_2 (@ tptp.produc4082563078715348724it_nat R2))) (= (@ (@ tptp.heap_T7616092557645711336rame_b N2) (@ tptp.some_P2818173045054083285it_nat (@ _let_2 (@ _let_1 N6)))) (@ tptp.some_P2818173045054083285it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat N2) N6)))))))))
% 8.20/8.60 (assert (forall ((N2 tptp.nat) (R2 tptp.a) (H tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H))) (let ((_let_2 (@ tptp.produc9178034014595674355it_nat R2))) (= (@ (@ 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)))))))))
% 8.20/8.60 (assert (forall ((N2 tptp.nat) (R2 tptp.product_unit) (H tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H))) (let ((_let_2 (@ tptp.produc7133225469290080770it_nat R2))) (= (@ (@ 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)))))))))
% 8.20/8.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K2 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)) K2)) (@ F (@ (@ tptp.plus_plus_nat M) K2))))))
% 8.20/8.60 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 8.20/8.60 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 8.20/8.60 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 8.20/8.60 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 8.20/8.60 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((A tptp.assn)) (not (@ (@ tptp.ord_less_assn A) A))))
% 8.20/8.60 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 8.20/8.60 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 8.20/8.60 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 8.20/8.60 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o) (X Bool)) (let ((_let_1 (@ tptp.member_o X))) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int) (X tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int X))) (=> (@ (@ tptp.ord_le483042692224249369nt_int A4) B5) (=> (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A4) B5) (=> (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o) (C2 Bool)) (let ((_let_1 (@ tptp.member_o C2))) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int) (C2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (@ (@ tptp.ord_le483042692224249369nt_int A4) B5) (=> (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A4) B5) (=> (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (C2 tptp.int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A4) B5) (not (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (@ (@ tptp.ord_less_eq_set_int B5) A4))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (= A4 B5) (not (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (not (@ (@ tptp.ord_less_eq_set_int B5) A4)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (assert (= tptp.ord_le483042692224249369nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (forall ((X4 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int X4))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (= A4 B5) (@ (@ tptp.ord_less_eq_set_int A4) B5))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (= A4 B5) (@ (@ tptp.ord_less_eq_set_int B5) A4))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (forall ((T4 Bool)) (let ((_let_1 (@ tptp.member_o T4))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 8.20/8.60 (assert (= tptp.ord_le483042692224249369nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (forall ((T4 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int T4))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 8.20/8.60 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (forall ((T4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat T4))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((T4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T4))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((T4 tptp.int)) (let ((_let_1 (@ tptp.member_int T4))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A4) A4)))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.list_nat Bool)) (Q2 (-> tptp.list_nat Bool))) (=> (forall ((X3 tptp.list_nat)) (=> (@ P2 X3) (@ Q2 X3))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat P2)) (@ tptp.collect_list_nat Q2)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.set_Pr958786334691620121nt_int Bool)) (Q2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (=> (forall ((X3 tptp.set_Pr958786334691620121nt_int)) (=> (@ P2 X3) (@ Q2 X3))) (@ (@ tptp.ord_le483042692224249369nt_int (@ tptp.collec5210948495886036740nt_int P2)) (@ tptp.collec5210948495886036740nt_int Q2)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.set_nat Bool)) (Q2 (-> tptp.set_nat Bool))) (=> (forall ((X3 tptp.set_nat)) (=> (@ P2 X3) (@ Q2 X3))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P2)) (@ tptp.collect_set_nat Q2)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ P2 X3) (@ Q2 X3))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P2)) (@ tptp.collect_nat Q2)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (@ P2 X3) (@ Q2 X3))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P2)) (@ tptp.collect_int Q2)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A4))) (=> (@ _let_1 B5) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (@ _let_1 C4))))))
% 8.20/8.60 (assert (= (lambda ((Y6 tptp.set_int) (Z4 tptp.set_int)) (= Y6 Z4)) (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (@ (@ tptp.ord_less_eq_set_int B6) A6)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.list_nat Bool)) (Q2 (-> tptp.list_nat Bool))) (= (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat P2)) (@ tptp.collect_list_nat Q2)) (forall ((X4 tptp.list_nat)) (=> (@ P2 X4) (@ Q2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.set_Pr958786334691620121nt_int Bool)) (Q2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (= (@ (@ tptp.ord_le483042692224249369nt_int (@ tptp.collec5210948495886036740nt_int P2)) (@ tptp.collec5210948495886036740nt_int Q2)) (forall ((X4 tptp.set_Pr958786334691620121nt_int)) (=> (@ P2 X4) (@ Q2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.set_nat Bool)) (Q2 (-> tptp.set_nat Bool))) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P2)) (@ tptp.collect_set_nat Q2)) (forall ((X4 tptp.set_nat)) (=> (@ P2 X4) (@ Q2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P2)) (@ tptp.collect_nat Q2)) (forall ((X4 tptp.nat)) (=> (@ P2 X4) (@ Q2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P2)) (@ tptp.collect_int Q2)) (forall ((X4 tptp.int)) (=> (@ P2 X4) (@ Q2 X4))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A4) B5) (@ (@ tptp.ord_less_eq_set_int A4) B5))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A4))) (=> (@ _let_1 B5) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (@ _let_1 C4))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (C4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (@ (@ tptp.ord_less_set_int B5) C4) (@ (@ tptp.ord_less_set_int A4) C4)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_o) (P2 (-> Bool Bool))) (@ (@ tptp.ord_less_eq_set_o (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A4) (@ P2 X4))))) A4)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_list_nat) (P2 (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) A4) (@ P2 X4))))) A4)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (P2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (@ (@ tptp.ord_le483042692224249369nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (and (@ (@ tptp.member2340774599025711042nt_int X4) A4) (@ P2 X4))))) A4)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_set_nat) (P2 (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A4) (@ P2 X4))))) A4)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ P2 X4))))) A4)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ P2 X4))))) A4)))
% 8.20/8.60 (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))))))
% 8.20/8.60 (assert (= tptp.ord_le483042692224249369nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (@ (@ tptp.ord_le8334417538754933252_int_o (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) A6))) (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) B6))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat X) Y)) Z3) (and (@ (@ tptp.ord_le8081472938463900775at_nat X) Z3) (@ (@ tptp.ord_le8081472938463900775at_nat Y) Z3)))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat X) Y)) Z3) (and (@ (@ tptp.ord_le1268244103169919719at_nat X) Z3) (@ (@ tptp.ord_le1268244103169919719at_nat Y) Z3)))))
% 8.20/8.60 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat X) Y)) Z3) (and (@ (@ tptp.ord_less_eq_set_nat X) Z3) (@ (@ tptp.ord_less_eq_set_nat Y) Z3)))))
% 8.20/8.60 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int X) Y)) Z3) (and (@ (@ tptp.ord_less_eq_set_int X) Z3) (@ (@ tptp.ord_less_eq_set_int Y) Z3)))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat X) Y)) Z3) (and (@ (@ tptp.ord_less_eq_rat X) Z3) (@ (@ tptp.ord_less_eq_rat Y) Z3)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat X) Y)) Z3) (and (@ (@ tptp.ord_less_eq_nat X) Z3) (@ (@ tptp.ord_less_eq_nat Y) Z3)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int X) Y)) Z3) (and (@ (@ tptp.ord_less_eq_int X) Z3) (@ (@ tptp.ord_less_eq_int Y) Z3)))))
% 8.20/8.60 (assert (forall ((B tptp.set_Pr8551490117392284871at_nat) (C2 tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat B) C2)) A) (and (@ (@ tptp.ord_le8081472938463900775at_nat B) A) (@ (@ tptp.ord_le8081472938463900775at_nat C2) A)))))
% 8.20/8.60 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B) C2)) A) (and (@ (@ tptp.ord_le1268244103169919719at_nat B) A) (@ (@ tptp.ord_le1268244103169919719at_nat C2) A)))))
% 8.20/8.60 (assert (forall ((B tptp.set_nat) (C2 tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B) C2)) A) (and (@ (@ tptp.ord_less_eq_set_nat B) A) (@ (@ tptp.ord_less_eq_set_nat C2) A)))))
% 8.20/8.60 (assert (forall ((B tptp.set_int) (C2 tptp.set_int) (A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int B) C2)) A) (and (@ (@ tptp.ord_less_eq_set_int B) A) (@ (@ tptp.ord_less_eq_set_int C2) A)))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B) C2)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C2) A)))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C2)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C2) A)))))
% 8.20/8.60 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B) C2)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C2) A)))))
% 8.20/8.60 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 8.20/8.60 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 8.20/8.60 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.ord_less_rat A) B))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_nat A) B))))
% 8.20/8.60 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.ord_less_int A) B))))
% 8.20/8.60 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 8.20/8.60 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 8.20/8.60 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 8.20/8.60 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.ord_less_eq_int A) B))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C2) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C2) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C2) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) D2))))))
% 8.20/8.60 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J2) (@ (@ tptp.ord_less_eq_rat K2) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_eq_nat K2) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J2) (@ (@ tptp.ord_less_eq_int K2) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J2) (@ (@ tptp.ord_less_rat K2) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_nat K2) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J2) (@ (@ tptp.ord_less_int K2) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 8.20/8.60 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A) A) A)))
% 8.20/8.60 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) A) A)))
% 8.20/8.60 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) A) A)))
% 8.20/8.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.sup_sup_nat A) A) A)))
% 8.20/8.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.sup_sup_int A) A) A)))
% 8.20/8.60 (assert (forall ((B tptp.multis2468970476368604999at_nat) (A tptp.multis2468970476368604999at_nat) (C2 tptp.multis2468970476368604999at_nat)) (= (= (@ (@ tptp.plus_p7104986032573967614at_nat B) A) (@ (@ tptp.plus_p7104986032573967614at_nat C2) A)) (= B C2))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C2) A)) (= B C2))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C2) A)) (= B C2))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C2) A)) (= B C2))))
% 8.20/8.60 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat) (C2 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.sup_sup_int A) B))) (= (@ (@ tptp.sup_sup_int _let_1) B) _let_1))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat X) X) X)))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) X) X)))
% 8.20/8.60 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) X) X)))
% 8.20/8.60 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.sup_sup_nat X) X) X)))
% 8.20/8.60 (assert (forall ((X tptp.int)) (= (@ (@ tptp.sup_sup_int X) X) X)))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (H tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.sup_sup_assn P2) Q2)) H) (or (@ (@ tptp.rep_assn P2) H) (@ (@ tptp.rep_assn Q2) H)))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (assert (= tptp.sup_su2047564715030645325nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (@ tptp.collec5210948495886036740nt_int (@ (@ tptp.sup_su1852724690005176016_int_o (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) A6))) (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) B6)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (assert (forall ((B tptp.multis2468970476368604999at_nat) (A tptp.multis2468970476368604999at_nat) (C2 tptp.multis2468970476368604999at_nat)) (=> (= (@ (@ tptp.plus_p7104986032573967614at_nat B) A) (@ (@ tptp.plus_p7104986032573967614at_nat C2) A)) (= B C2))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C2) A)) (= B C2))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C2) A)) (= B C2))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C2) A)) (= B C2))))
% 8.20/8.60 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat) (C2 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (=> (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (=> (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 8.20/8.60 (assert (forall ((B tptp.multis2468970476368604999at_nat) (A tptp.multis2468970476368604999at_nat) (C2 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat B))) (let ((_let_2 (@ tptp.plus_p7104986032573967614at_nat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B))) (let ((_let_2 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B))) (let ((_let_2 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 8.20/8.60 (assert (= tptp.plus_p7104986032573967614at_nat (lambda ((A5 tptp.multis2468970476368604999at_nat) (B4 tptp.multis2468970476368604999at_nat)) (@ (@ tptp.plus_p7104986032573967614at_nat B4) A5))))
% 8.20/8.60 (assert (= tptp.plus_plus_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat B4) A5))))
% 8.20/8.60 (assert (= tptp.plus_plus_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.plus_plus_nat B4) A5))))
% 8.20/8.60 (assert (= tptp.plus_plus_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int B4) A5))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C2) A)) (= B C2))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C2) A)) (= B C2))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 8.20/8.60 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat) (C2 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A))) (= (@ (@ tptp.plus_p7104986032573967614at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_p7104986032573967614at_nat B) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_int B) C2))))))
% 8.20/8.60 (assert (forall ((B5 tptp.multis2468970476368604999at_nat) (K2 tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat) (A tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A))) (let ((_let_2 (@ tptp.plus_p7104986032573967614at_nat K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.rat) (K2 tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (let ((_let_2 (@ tptp.plus_plus_rat K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.nat) (K2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.int) (K2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 8.20/8.60 (assert (forall ((A4 tptp.multis2468970476368604999at_nat) (K2 tptp.multis2468970476368604999at_nat) (A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_p7104986032573967614at_nat A4) B) (@ _let_1 (@ (@ tptp.plus_p7104986032573967614at_nat A) B)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.rat) (K2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_rat A4) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.nat) (K2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A4) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.int) (K2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A4) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 8.20/8.60 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (= I2 J2) (= K2 L)) (= (@ (@ tptp.plus_plus_rat I2) K2) (@ (@ tptp.plus_plus_rat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (= I2 J2) (= K2 L)) (= (@ (@ tptp.plus_plus_nat I2) K2) (@ (@ tptp.plus_plus_nat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (= I2 J2) (= K2 L)) (= (@ (@ tptp.plus_plus_int I2) K2) (@ (@ tptp.plus_plus_int J2) L)))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (let ((_let_2 (@ tptp.sup_su3035147773818789531at_nat Y))) (= (@ _let_1 (@ _let_2 Z3)) (@ _let_2 (@ _let_1 Z3)))))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat Y))) (= (@ _let_1 (@ _let_2 Z3)) (@ _let_2 (@ _let_1 Z3)))))))
% 8.20/8.60 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 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 Z3)) (@ _let_2 (@ _let_1 Z3)))))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (let ((_let_2 (@ tptp.sup_sup_nat Y))) (= (@ _let_1 (@ _let_2 Z3)) (@ _let_2 (@ _let_1 Z3)))))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X))) (let ((_let_2 (@ tptp.sup_sup_int Y))) (= (@ _let_1 (@ _let_2 Z3)) (@ _let_2 (@ _let_1 Z3)))))))
% 8.20/8.60 (assert (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (C2 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat B))) (let ((_let_2 (@ tptp.sup_su3035147773818789531at_nat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 8.20/8.60 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat B))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 8.20/8.60 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C2 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 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat B))) (let ((_let_2 (@ tptp.sup_sup_nat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int B))) (let ((_let_2 (@ tptp.sup_sup_int A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 8.20/8.60 (assert (= tptp.sup_su3035147773818789531at_nat (lambda ((X4 tptp.set_Pr8551490117392284871at_nat) (Y4 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.sup_su3035147773818789531at_nat Y4) X4))))
% 8.20/8.60 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((X4 tptp.set_Pr4329608150637261639at_nat) (Y4 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat Y4) X4))))
% 8.20/8.60 (assert (= tptp.sup_sup_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat Y4) X4))))
% 8.20/8.60 (assert (= tptp.sup_sup_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.sup_sup_nat Y4) X4))))
% 8.20/8.60 (assert (= tptp.sup_sup_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.sup_sup_int Y4) X4))))
% 8.20/8.60 (assert (= tptp.sup_su3035147773818789531at_nat (lambda ((A5 tptp.set_Pr8551490117392284871at_nat) (B4 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.sup_su3035147773818789531at_nat B4) A5))))
% 8.20/8.60 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat) (B4 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat B4) A5))))
% 8.20/8.60 (assert (= tptp.sup_sup_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat B4) A5))))
% 8.20/8.60 (assert (= tptp.sup_sup_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.sup_sup_nat B4) A5))))
% 8.20/8.60 (assert (= tptp.sup_sup_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.sup_sup_int B4) A5))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 Y)) Z3) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) Z3) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) Z3) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (= (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) Z3) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X))) (= (@ (@ tptp.sup_sup_int (@ _let_1 Y)) Z3) (@ _let_1 (@ (@ tptp.sup_sup_int Y) Z3))))))
% 8.20/8.60 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (C2 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat A))) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat B) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat A))) (= (@ (@ tptp.sup_sup_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_sup_nat B) C2))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int A))) (= (@ (@ tptp.sup_sup_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.sup_sup_int B) C2))))))
% 8.20/8.60 (assert (= tptp.sup_su3035147773818789531at_nat (lambda ((X4 tptp.set_Pr8551490117392284871at_nat) (Y4 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.sup_su3035147773818789531at_nat Y4) X4))))
% 8.20/8.60 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((X4 tptp.set_Pr4329608150637261639at_nat) (Y4 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat Y4) X4))))
% 8.20/8.60 (assert (= tptp.sup_sup_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat Y4) X4))))
% 8.20/8.60 (assert (= tptp.sup_sup_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.sup_sup_nat Y4) X4))))
% 8.20/8.60 (assert (= tptp.sup_sup_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.sup_sup_int Y4) X4))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 Y)) Z3) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) Z3) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) Z3) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (= (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) Z3) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X))) (= (@ (@ tptp.sup_sup_int (@ _let_1 Y)) Z3) (@ _let_1 (@ (@ tptp.sup_sup_int Y) Z3))))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (let ((_let_2 (@ tptp.sup_su3035147773818789531at_nat Y))) (= (@ _let_1 (@ _let_2 Z3)) (@ _let_2 (@ _let_1 Z3)))))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat Y))) (= (@ _let_1 (@ _let_2 Z3)) (@ _let_2 (@ _let_1 Z3)))))))
% 8.20/8.60 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 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 Z3)) (@ _let_2 (@ _let_1 Z3)))))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (let ((_let_2 (@ tptp.sup_sup_nat Y))) (= (@ _let_1 (@ _let_2 Z3)) (@ _let_2 (@ _let_1 Z3)))))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X))) (let ((_let_2 (@ tptp.sup_sup_int Y))) (= (@ _let_1 (@ _let_2 Z3)) (@ _let_2 (@ _let_1 Z3)))))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 8.20/8.60 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.ord_less_eq_int A) B))))
% 8.20/8.60 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 8.20/8.60 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 8.20/8.60 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (exists ((C3 tptp.nat)) (= B4 (@ (@ tptp.plus_plus_nat A5) C3))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C))))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C2) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C2) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) D2))))))
% 8.20/8.60 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J2) (@ (@ tptp.ord_less_eq_rat K2) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat K2) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J2) (@ (@ tptp.ord_less_eq_int K2) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_rat K2) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_nat K2) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_eq_int K2) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J2) (= K2 L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (= K2 L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J2) (= K2 L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.ord_less_rat A) B))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_nat A) B))))
% 8.20/8.60 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.ord_less_int A) B))))
% 8.20/8.60 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 8.20/8.60 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 8.20/8.60 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C2) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) D2))))))
% 8.20/8.60 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J2) (= K2 L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J2) (= K2 L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J2) (= K2 L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_rat K2) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_nat K2) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (= I2 J2) (@ (@ tptp.ord_less_int K2) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (K2 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J2) (@ (@ tptp.ord_less_rat K2) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K2)) (@ (@ tptp.plus_plus_rat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat K2) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ (@ tptp.plus_plus_nat J2) L)))))
% 8.20/8.60 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J2) (@ (@ tptp.ord_less_int K2) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K2)) (@ (@ tptp.plus_plus_int J2) L)))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.ord_le8081472938463900775at_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_int) (B tptp.set_int) (A tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.ord_le8081472938463900775at_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 8.20/8.60 (assert (= tptp.ord_le8081472938463900775at_nat (lambda ((A5 tptp.set_Pr8551490117392284871at_nat) (B4 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A5) B4) B4))))
% 8.20/8.60 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat) (B4 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A5) B4) B4))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A5) B4) B4))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B4 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A5) B4) B4))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.sup_sup_rat A5) B4) B4))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A5) B4) B4))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.sup_sup_int A5) B4) B4))))
% 8.20/8.60 (assert (= tptp.ord_le8081472938463900775at_nat (lambda ((B4 tptp.set_Pr8551490117392284871at_nat) (A5 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A5) B4) A5))))
% 8.20/8.60 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((B4 tptp.set_Pr4329608150637261639at_nat) (A5 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A5) B4) A5))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A5) B4) A5))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_set_int (lambda ((B4 tptp.set_int) (A5 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A5) B4) A5))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (= (@ (@ tptp.sup_sup_rat A5) B4) A5))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A5) B4) A5))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (= (@ (@ tptp.sup_sup_int A5) B4) A5))))
% 8.20/8.60 (assert (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat B) (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))
% 8.20/8.60 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat B) (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))
% 8.20/8.60 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B) (@ (@ tptp.sup_sup_set_nat A) B))))
% 8.20/8.60 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B) (@ (@ tptp.sup_sup_set_int A) B))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.sup_sup_rat A) B))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.sup_sup_nat A) B))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.sup_sup_int A) B))))
% 8.20/8.60 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat A) (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))
% 8.20/8.60 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat A) (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))
% 8.20/8.60 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.sup_sup_set_nat A) B))))
% 8.20/8.60 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) (@ (@ tptp.sup_sup_set_int A) B))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.sup_sup_rat A) B))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.sup_sup_nat A) B))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.sup_sup_int A) B))))
% 8.20/8.60 (assert (= tptp.ord_le8081472938463900775at_nat (lambda ((B4 tptp.set_Pr8551490117392284871at_nat) (A5 tptp.set_Pr8551490117392284871at_nat)) (= A5 (@ (@ tptp.sup_su3035147773818789531at_nat A5) B4)))))
% 8.20/8.60 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((B4 tptp.set_Pr4329608150637261639at_nat) (A5 tptp.set_Pr4329608150637261639at_nat)) (= A5 (@ (@ tptp.sup_su5525570899277871387at_nat A5) B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (= A5 (@ (@ tptp.sup_sup_set_nat A5) B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_set_int (lambda ((B4 tptp.set_int) (A5 tptp.set_int)) (= A5 (@ (@ tptp.sup_sup_set_int A5) B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (= A5 (@ (@ tptp.sup_sup_rat A5) B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (= A5 (@ (@ tptp.sup_sup_nat A5) B4)))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (= A5 (@ (@ tptp.sup_sup_int A5) B4)))))
% 8.20/8.60 (assert (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (C2 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat B) A) (=> (@ (@ tptp.ord_le8081472938463900775at_nat C2) A) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat B) C2)) A)))))
% 8.20/8.60 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B) A) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C2) A) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B) C2)) A)))))
% 8.20/8.60 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat C2) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B) C2)) A)))))
% 8.20/8.60 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int C2) A) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int B) C2)) A)))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C2) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B) C2)) A)))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C2) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C2)) A)))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B) C2)) A)))))
% 8.20/8.60 (assert (forall ((B tptp.set_Pr8551490117392284871at_nat) (C2 tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat B) C2)) A) (not (=> (@ (@ tptp.ord_le8081472938463900775at_nat B) A) (not (@ (@ tptp.ord_le8081472938463900775at_nat C2) A)))))))
% 8.20/8.60 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B) C2)) A) (not (=> (@ (@ tptp.ord_le1268244103169919719at_nat B) A) (not (@ (@ tptp.ord_le1268244103169919719at_nat C2) A)))))))
% 8.20/8.60 (assert (forall ((B tptp.set_nat) (C2 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (not (@ (@ tptp.ord_less_eq_set_nat C2) A)))))))
% 8.20/8.60 (assert (forall ((B tptp.set_int) (C2 tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_set_int B) A) (not (@ (@ tptp.ord_less_eq_set_int C2) A)))))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C2) A)))))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C2) A)))))))
% 8.20/8.60 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C2) A)))))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.sup_sup_rat X) Y) Y))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.sup_sup_nat X) Y) Y))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.sup_sup_int X) Y) Y))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.sup_sup_rat X) Y) X))))
% 8.20/8.60 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.sup_sup_nat X) Y) X))))
% 8.20/8.60 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.sup_sup_int X) Y) X))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.sup_sup_rat A) B) B))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.sup_sup_nat A) B) B))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.sup_sup_int A) B) B))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.sup_sup_rat A) B) A))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.sup_sup_nat A) B) A))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.sup_sup_int A) B) A))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.sup_sup_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.sup_sup_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.sup_sup_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.sup_sup_rat A) B)))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.sup_sup_nat A) B)))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.sup_sup_int A) B)))))
% 8.20/8.60 (assert (= tptp.ord_le8081472938463900775at_nat (lambda ((X4 tptp.set_Pr8551490117392284871at_nat) (Y4 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat X4) Y4) Y4))))
% 8.20/8.60 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((X4 tptp.set_Pr4329608150637261639at_nat) (Y4 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X4) Y4) Y4))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X4) Y4) Y4))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_set_int (lambda ((X4 tptp.set_int) (Y4 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X4) Y4) Y4))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.sup_sup_rat X4) Y4) Y4))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.sup_sup_nat X4) Y4) Y4))))
% 8.20/8.60 (assert (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.sup_sup_int X4) Y4) Y4))))
% 8.20/8.60 (assert (forall ((Y tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat Y) X) (=> (@ (@ tptp.ord_le8081472938463900775at_nat Z3) X) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z3)) X)))))
% 8.20/8.60 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Y) X) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Z3) X) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z3)) X)))))
% 8.20/8.60 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat) (Z3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (=> (@ (@ tptp.ord_less_eq_set_nat Z3) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat Y) Z3)) X)))))
% 8.20/8.60 (assert (forall ((Y tptp.set_int) (X tptp.set_int) (Z3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (=> (@ (@ tptp.ord_less_eq_set_int Z3) X) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int Y) Z3)) X)))))
% 8.20/8.60 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (=> (@ (@ tptp.ord_less_eq_rat Z3) X) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat Y) Z3)) X)))))
% 8.20/8.60 (assert (forall ((Y tptp.nat) (X tptp.nat) (Z3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (=> (@ (@ tptp.ord_less_eq_nat Z3) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat Y) Z3)) X)))))
% 8.20/8.60 (assert (forall ((Y tptp.int) (X tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (=> (@ (@ tptp.ord_less_eq_int Z3) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int Y) Z3)) X)))))
% 8.20/8.60 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat) (C2 tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (D2 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat A) C2) (=> (@ (@ tptp.ord_le8081472938463900775at_nat B) D2) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A) B)) (@ (@ tptp.sup_su3035147773818789531at_nat C2) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (D2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) C2) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B) D2) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (@ (@ tptp.sup_su5525570899277871387at_nat C2) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat) (D2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C2) (=> (@ (@ 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 C2) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.set_int) (C2 tptp.set_int) (B tptp.set_int) (D2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) C2) (=> (@ (@ 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 C2) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) C2) (=> (@ (@ tptp.ord_less_eq_rat B) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat A) B)) (@ (@ tptp.sup_sup_rat C2) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C2) (=> (@ (@ tptp.ord_less_eq_nat B) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) (@ (@ tptp.sup_sup_nat C2) D2))))))
% 8.20/8.60 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) C2) (=> (@ (@ tptp.ord_less_eq_int B) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A) B)) (@ (@ tptp.sup_sup_int C2) D2))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (D2 tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat C2) A) (=> (@ (@ tptp.ord_le8081472938463900775at_nat D2) B) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat C2) D2)) (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (D2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C2) A) (=> (@ (@ tptp.ord_le1268244103169919719at_nat D2) B) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat C2) D2)) (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_nat) (A tptp.set_nat) (D2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C2) A) (=> (@ (@ tptp.ord_less_eq_set_nat D2) B) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat C2) D2)) (@ (@ tptp.sup_sup_set_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_int) (A tptp.set_int) (D2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int C2) A) (=> (@ (@ tptp.ord_less_eq_set_int D2) B) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int C2) D2)) (@ (@ tptp.sup_sup_set_int A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.rat) (A tptp.rat) (D2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) A) (=> (@ (@ tptp.ord_less_eq_rat D2) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat C2) D2)) (@ (@ tptp.sup_sup_rat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.nat) (A tptp.nat) (D2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) A) (=> (@ (@ tptp.ord_less_eq_nat D2) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat C2) D2)) (@ (@ tptp.sup_sup_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.int) (A tptp.int) (D2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) A) (=> (@ (@ tptp.ord_less_eq_int D2) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int C2) D2)) (@ (@ tptp.sup_sup_int A) B))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (assert (forall ((Y tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat Y) (@ (@ tptp.sup_su3035147773818789531at_nat X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int Y) (@ (@ tptp.sup_sup_set_int X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.rat) (X tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y) (@ (@ tptp.sup_sup_rat X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_int Y) (@ (@ tptp.sup_sup_int X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat X) (@ (@ tptp.sup_su3035147773818789531at_nat X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X) (@ (@ tptp.sup_sup_set_int X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.sup_sup_rat X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.sup_sup_int X) Y))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat X) (@ (@ tptp.sup_su3035147773818789531at_nat X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X) (@ (@ tptp.sup_sup_set_int X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.sup_sup_rat X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.sup_sup_int X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat Y) (@ (@ tptp.sup_su3035147773818789531at_nat X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int Y) (@ (@ tptp.sup_sup_set_int X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.rat) (X tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y) (@ (@ tptp.sup_sup_rat X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))))
% 8.20/8.60 (assert (forall ((Y tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_int Y) (@ (@ tptp.sup_sup_int X) Y))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.ord_le7642048601412989811at_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.assn) (B tptp.assn) (A tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_assn A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.ord_le7642048601412989811at_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_assn A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 8.20/8.60 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 8.20/8.60 (assert (= tptp.ord_le7642048601412989811at_nat (lambda ((B4 tptp.set_Pr8551490117392284871at_nat) (A5 tptp.set_Pr8551490117392284871at_nat)) (and (= A5 (@ (@ tptp.sup_su3035147773818789531at_nat A5) B4)) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_le2604355607129572851at_nat (lambda ((B4 tptp.set_Pr4329608150637261639at_nat) (A5 tptp.set_Pr4329608150637261639at_nat)) (and (= A5 (@ (@ tptp.sup_su5525570899277871387at_nat A5) B4)) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (and (= A5 (@ (@ tptp.sup_sup_set_nat A5) B4)) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_assn (lambda ((B4 tptp.assn) (A5 tptp.assn)) (and (= A5 (@ (@ tptp.sup_sup_assn A5) B4)) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (and (= A5 (@ (@ tptp.sup_sup_rat A5) B4)) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (and (= A5 (@ (@ tptp.sup_sup_nat A5) B4)) (not (= A5 B4))))))
% 8.20/8.60 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A5 tptp.int)) (and (= A5 (@ (@ tptp.sup_sup_int A5) B4)) (not (= A5 B4))))))
% 8.20/8.60 (assert (forall ((B tptp.set_Pr8551490117392284871at_nat) (C2 tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le7642048601412989811at_nat (@ (@ tptp.sup_su3035147773818789531at_nat B) C2)) A) (not (=> (@ (@ tptp.ord_le7642048601412989811at_nat B) A) (not (@ (@ tptp.ord_le7642048601412989811at_nat C2) A)))))))
% 8.20/8.60 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (C2 tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le2604355607129572851at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B) C2)) A) (not (=> (@ (@ tptp.ord_le2604355607129572851at_nat B) A) (not (@ (@ tptp.ord_le2604355607129572851at_nat C2) A)))))))
% 8.20/8.60 (assert (forall ((B tptp.set_nat) (C2 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat (@ (@ tptp.sup_sup_set_nat B) C2)) A) (not (=> (@ (@ tptp.ord_less_set_nat B) A) (not (@ (@ tptp.ord_less_set_nat C2) A)))))))
% 8.20/8.60 (assert (forall ((B tptp.assn) (C2 tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn (@ (@ tptp.sup_sup_assn B) C2)) A) (not (=> (@ (@ tptp.ord_less_assn B) A) (not (@ (@ tptp.ord_less_assn C2) A)))))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.sup_sup_rat B) C2)) A) (not (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat C2) A)))))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.sup_sup_nat B) C2)) A) (not (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat C2) A)))))))
% 8.20/8.60 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.sup_sup_int B) C2)) A) (not (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int C2) A)))))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (= (@ (@ tptp.sup_sup_assn A) B) B))))
% 8.20/8.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.sup_sup_rat A) B) B))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.sup_sup_nat A) B) B))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.sup_sup_int A) B) B))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A) (= (@ (@ tptp.sup_sup_assn A) B) A))))
% 8.20/8.60 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.sup_sup_rat A) B) A))))
% 8.20/8.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.sup_sup_nat A) B) A))))
% 8.20/8.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.sup_sup_int A) B) A))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (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))))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_o) (S tptp.set_o)) (= (@ (@ tptp.ord_less_eq_o_o (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) R3))) (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) S))) (@ (@ tptp.ord_less_eq_set_o R3) S))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_se6260736226359567993nt_int) (S tptp.set_se6260736226359567993nt_int)) (= (@ (@ tptp.ord_le8334417538754933252_int_o (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) R3))) (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) S))) (@ (@ tptp.ord_le483042692224249369nt_int R3) S))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_set_nat) (S tptp.set_set_nat)) (= (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) R3))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) S))) (@ (@ tptp.ord_le6893508408891458716et_nat R3) S))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) R3))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) S))) (@ (@ tptp.ord_less_eq_set_nat R3) S))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_int) (S tptp.set_int)) (= (@ (@ tptp.ord_less_eq_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) R3))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) S))) (@ (@ tptp.ord_less_eq_set_int R3) S))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Xa tptp.option4065278094766928714it_nat) (Y tptp.option4065278094766928714it_nat)) (=> (= (@ (@ tptp.heap_T7616092557645711336rame_b X) Xa) Y) (=> (forall ((R4 tptp.b) (H2 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H2))) (let ((_let_2 (@ tptp.produc4082563078715348724it_nat R4))) (=> (= Xa (@ tptp.some_P2818173045054083285it_nat (@ _let_2 (@ _let_1 N4)))) (not (= Y (@ tptp.some_P2818173045054083285it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat X) N4)))))))))) (not (=> (= Xa tptp.none_P6779099274072355161it_nat) (not (= Y tptp.none_P6779099274072355161it_nat))))))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Xa tptp.option3562590408128118217it_nat) (Y tptp.option3562590408128118217it_nat)) (=> (= (@ (@ tptp.heap_T7616092557645711335rame_a X) Xa) Y) (=> (forall ((R4 tptp.a) (H2 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H2))) (let ((_let_2 (@ tptp.produc9178034014595674355it_nat R4))) (=> (= 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))))))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Xa tptp.option8956607266484857688it_nat) (Y tptp.option8956607266484857688it_nat)) (=> (= (@ (@ tptp.heap_T3616969660504097270t_unit X) Xa) Y) (=> (forall ((R4 tptp.product_unit) (H2 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H2))) (let ((_let_2 (@ tptp.produc7133225469290080770it_nat R4))) (=> (= 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))))))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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 ((Z tptp.set_Pr8551490117392284871at_nat)) (@ tptp.some_s287724117700012716at_nat (@ (@ tptp.sup_su3035147773818789531at_nat X8) Z)))) Y4))) X4))))
% 8.20/8.60 (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 ((Z tptp.set_Pr4329608150637261639at_nat)) (@ tptp.some_s5890477192898017836at_nat (@ (@ tptp.sup_su5525570899277871387at_nat X8) Z)))) Y4))) X4))))
% 8.20/8.60 (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 ((Z tptp.set_nat)) (@ tptp.some_set_nat (@ (@ tptp.sup_sup_set_nat X8) Z)))) Y4))) X4))))
% 8.20/8.60 (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 ((Z tptp.nat)) (@ tptp.some_nat (@ (@ tptp.sup_sup_nat X8) Z)))) Y4))) X4))))
% 8.20/8.60 (assert (= tptp.sup_sup_option_int (lambda ((X4 tptp.option_int) (Y4 tptp.option_int)) (@ (@ (@ tptp.case_o390784466056649525nt_int Y4) (lambda ((X8 tptp.int)) (@ (@ (@ tptp.case_o390784466056649525nt_int X4) (lambda ((Z tptp.int)) (@ tptp.some_int (@ (@ tptp.sup_sup_int X8) Z)))) Y4))) X4))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_o) (S tptp.set_o)) (= (@ (@ tptp.sup_sup_o_o (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) R3))) (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) S))) (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) (@ (@ tptp.sup_sup_set_o R3) S))))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_se6260736226359567993nt_int) (S tptp.set_se6260736226359567993nt_int)) (= (@ (@ tptp.sup_su1852724690005176016_int_o (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) R3))) (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) S))) (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) (@ (@ tptp.sup_su2047564715030645325nt_int R3) S))))))
% 8.20/8.60 (assert (forall ((R3 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) R3))) (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 R3) S))))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_int) (S tptp.set_int)) (= (@ (@ tptp.sup_sup_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) R3))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) S))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) (@ (@ tptp.sup_sup_set_int R3) S))))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_Pr8551490117392284871at_nat) (S tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su6256023009775730178_nat_o (lambda ((X4 tptp.produc4166570645942440679at_nat)) (@ (@ tptp.member6689249552917799696at_nat X4) R3))) (lambda ((X4 tptp.produc4166570645942440679at_nat)) (@ (@ tptp.member6689249552917799696at_nat X4) S))) (lambda ((X4 tptp.produc4166570645942440679at_nat)) (@ (@ tptp.member6689249552917799696at_nat X4) (@ (@ tptp.sup_su3035147773818789531at_nat R3) S))))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su2080679670758317954_nat_o (lambda ((X4 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X4) R3))) (lambda ((X4 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X4) S))) (lambda ((X4 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X4) (@ (@ tptp.sup_su5525570899277871387at_nat R3) S))))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.sup_sup_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) R3))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) S))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) (@ (@ tptp.sup_sup_set_nat R3) S))))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (S tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.sup_sup_int_int_o (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y4)) R3))) (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y4)) S))) (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y4)) (@ (@ tptp.sup_su6024340866399070445nt_int R3) S))))))
% 8.20/8.60 (assert (forall ((R3 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)) R3))) (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 R3) S))))))
% 8.20/8.60 (assert (forall ((R3 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)) R3))) (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 R3) S))))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_Pr7600907837789447088it_nat) (S tptp.set_Pr7600907837789447088it_nat)) (= (@ (@ tptp.sup_su4207681470386032469_nat_o (lambda ((X4 tptp.b) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat X4) Y4)) R3))) (lambda ((X4 tptp.b) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat X4) Y4)) S))) (lambda ((X4 tptp.b) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat X4) Y4)) (@ (@ tptp.sup_su3714129841433130204it_nat R3) S))))))
% 8.20/8.60 (assert (forall ((R3 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)) R3))) (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 R3) S))))))
% 8.20/8.60 (assert (forall ((R3 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)) R3))) (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 R3) S))))))
% 8.20/8.60 (assert (forall ((R3 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)) R3))) (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 R3) S))))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (S tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.ord_le6741204236512500942_int_o (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y4)) R3))) (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y4)) S))) (@ (@ tptp.ord_le2843351958646193337nt_int R3) S))))
% 8.20/8.60 (assert (forall ((R3 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)) R3))) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Y4)) S))) (@ (@ tptp.ord_le5966269811547037844et_nat R3) S))))
% 8.20/8.60 (assert (forall ((R3 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)) R3))) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Y4)) S))) (@ (@ tptp.ord_le4763372923235995152et_nat R3) S))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_Pr7600907837789447088it_nat) (S tptp.set_Pr7600907837789447088it_nat)) (= (@ (@ tptp.ord_le785348814064375433_nat_o (lambda ((X4 tptp.b) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat X4) Y4)) R3))) (lambda ((X4 tptp.b) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat X4) Y4)) S))) (@ (@ tptp.ord_le4980869671742669840it_nat R3) S))))
% 8.20/8.60 (assert (forall ((R3 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)) R3))) (lambda ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Y4)) S))) (@ (@ tptp.ord_le4478181985103859343it_nat R3) S))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (S tptp.set_Pr958786334691620121nt_int)) (= (= (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y4)) R3)) (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y4)) S))) (= R3 S))))
% 8.20/8.60 (assert (forall ((R3 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)) R3)) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Y4)) S))) (= R3 S))))
% 8.20/8.60 (assert (forall ((R3 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)) R3)) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Y4)) S))) (= R3 S))))
% 8.20/8.60 (assert (forall ((R3 tptp.set_Pr7600907837789447088it_nat) (S tptp.set_Pr7600907837789447088it_nat)) (= (= (lambda ((X4 tptp.b) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat X4) Y4)) R3)) (lambda ((X4 tptp.b) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat X4) Y4)) S))) (= R3 S))))
% 8.20/8.60 (assert (forall ((R3 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)) R3)) (lambda ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Y4)) S))) (= R3 S))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.heap_e7401611519738050253t_unit Bool)) (H tptp.heap_e7401611519738050253t_unit) (F (-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat))) (=> (@ P2 H) (= (@ (@ tptp.heap_T875086893843062177t_unit (@ (@ tptp.heap_T8440541562793052209t_unit P2) F)) H) (@ tptp.some_P1914260805536162275it_nat (@ F H))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.heap_e7401611519738050253t_unit Bool)) (H tptp.heap_e7401611519738050253t_unit) (F (-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat))) (=> (@ P2 H) (= (@ (@ tptp.heap_Time_execute_b (@ (@ tptp.heap_Time_guard_b P2) F)) H) (@ tptp.some_P2818173045054083285it_nat (@ F H))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.heap_e7401611519738050253t_unit Bool)) (H tptp.heap_e7401611519738050253t_unit) (F (-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat))) (=> (@ P2 H) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_guard_a P2) F)) H) (@ tptp.some_P7913643980934408916it_nat (@ F H))))))
% 8.20/8.60 (assert (forall ((X tptp.produc7388388658123137530it_nat)) (= (@ tptp.eps_Op5869321083069970014it_nat (lambda ((Y4 tptp.produc7388388658123137530it_nat)) (= Y4 X))) (@ tptp.some_P2818173045054083285it_nat X))))
% 8.20/8.60 (assert (forall ((X tptp.produc3260487557148687353it_nat)) (= (@ tptp.eps_Op1741419982095519837it_nat (lambda ((Y4 tptp.produc3260487557148687353it_nat)) (= Y4 X))) (@ tptp.some_P7913643980934408916it_nat X))))
% 8.20/8.60 (assert (forall ((X tptp.produc8664842809031399944it_nat)) (= (@ tptp.eps_Op3393321821070424684it_nat (lambda ((Y4 tptp.produc8664842809031399944it_nat)) (= Y4 X))) (@ tptp.some_P1914260805536162275it_nat X))))
% 8.20/8.60 (assert (forall ((X tptp.num)) (= (@ tptp.eps_Opt_num (lambda ((Y4 tptp.num)) (= Y4 X))) (@ tptp.some_num X))))
% 8.20/8.60 (assert (forall ((X tptp.option4065278094766928714it_nat)) (= (not (= X tptp.none_P6779099274072355161it_nat)) (exists ((Y4 tptp.produc7388388658123137530it_nat)) (= X (@ tptp.some_P2818173045054083285it_nat Y4))))))
% 8.20/8.60 (assert (forall ((X tptp.option3562590408128118217it_nat)) (= (not (= X tptp.none_P2651198173097904984it_nat)) (exists ((Y4 tptp.produc3260487557148687353it_nat)) (= X (@ tptp.some_P7913643980934408916it_nat Y4))))))
% 8.20/8.60 (assert (forall ((X tptp.option8956607266484857688it_nat)) (= (not (= X tptp.none_P9117596204409417319it_nat)) (exists ((Y4 tptp.produc8664842809031399944it_nat)) (= X (@ tptp.some_P1914260805536162275it_nat Y4))))))
% 8.20/8.60 (assert (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y4 tptp.num)) (= X (@ tptp.some_num Y4))))))
% 8.20/8.60 (assert (forall ((X tptp.option4065278094766928714it_nat)) (= (forall ((Y4 tptp.produc7388388658123137530it_nat)) (not (= X (@ tptp.some_P2818173045054083285it_nat Y4)))) (= X tptp.none_P6779099274072355161it_nat))))
% 8.20/8.60 (assert (forall ((X tptp.option3562590408128118217it_nat)) (= (forall ((Y4 tptp.produc3260487557148687353it_nat)) (not (= X (@ tptp.some_P7913643980934408916it_nat Y4)))) (= X tptp.none_P2651198173097904984it_nat))))
% 8.20/8.60 (assert (forall ((X tptp.option8956607266484857688it_nat)) (= (forall ((Y4 tptp.produc8664842809031399944it_nat)) (not (= X (@ tptp.some_P1914260805536162275it_nat Y4)))) (= X tptp.none_P9117596204409417319it_nat))))
% 8.20/8.60 (assert (forall ((X tptp.option_num)) (= (forall ((Y4 tptp.num)) (not (= X (@ tptp.some_num Y4)))) (= X tptp.none_num))))
% 8.20/8.60 (assert (forall ((X tptp.produc7388388658123137530it_nat)) (= (@ tptp.eps_Op5869321083069970014it_nat (@ (lambda ((Y6 tptp.produc7388388658123137530it_nat) (Z4 tptp.produc7388388658123137530it_nat)) (= Y6 Z4)) X)) (@ tptp.some_P2818173045054083285it_nat X))))
% 8.20/8.60 (assert (forall ((X tptp.produc3260487557148687353it_nat)) (= (@ tptp.eps_Op1741419982095519837it_nat (@ (lambda ((Y6 tptp.produc3260487557148687353it_nat) (Z4 tptp.produc3260487557148687353it_nat)) (= Y6 Z4)) X)) (@ tptp.some_P7913643980934408916it_nat X))))
% 8.20/8.60 (assert (forall ((X tptp.produc8664842809031399944it_nat)) (= (@ tptp.eps_Op3393321821070424684it_nat (@ (lambda ((Y6 tptp.produc8664842809031399944it_nat) (Z4 tptp.produc8664842809031399944it_nat)) (= Y6 Z4)) X)) (@ tptp.some_P1914260805536162275it_nat X))))
% 8.20/8.60 (assert (forall ((X tptp.num)) (= (@ tptp.eps_Opt_num (@ (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4)) X)) (@ tptp.some_num X))))
% 8.20/8.60 (assert (forall ((X tptp.option_num)) (@ (@ tptp.ord_le6622620407824499402on_num tptp.none_num) X)))
% 8.20/8.60 (assert (forall ((X tptp.option_num)) (not (@ (@ tptp.ord_less_option_num X) tptp.none_num))))
% 8.20/8.60 (assert (= (@ tptp.eps_Opt_num (lambda ((Uu2 tptp.num)) false)) tptp.none_num))
% 8.20/8.60 (assert (forall ((V tptp.option4624381673175914239nt_int)) (= (forall ((X4 tptp.int) (Y4 tptp.int)) (not (= V (@ tptp.some_P4184893108420464158nt_int (@ (@ tptp.product_Pair_int_int X4) Y4))))) (= V tptp.none_P2377608414092835994nt_int))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((V tptp.option4065278094766928714it_nat)) (= (forall ((X4 tptp.b) (Y4 tptp.produc6653097349344004940it_nat)) (not (= V (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat X4) Y4))))) (= V tptp.none_P6779099274072355161it_nat))))
% 8.20/8.60 (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))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((X tptp.num)) (not (@ (@ tptp.ord_le6622620407824499402on_num (@ tptp.some_num X)) tptp.none_num))))
% 8.20/8.60 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_option_num tptp.none_num) (@ tptp.some_num X))))
% 8.20/8.60 (assert (forall ((F1 tptp.int) (F2 (-> tptp.num tptp.int))) (= (@ (@ (@ tptp.case_option_int_num F1) F2) tptp.none_num) F1)))
% 8.20/8.60 (assert (forall ((F1 tptp.option_num) (F2 (-> tptp.num tptp.option_num))) (= (@ (@ (@ tptp.case_o6005452278849405969um_num F1) F2) tptp.none_num) F1)))
% 8.20/8.60 (assert (forall ((F1 tptp.num) (F2 (-> tptp.num tptp.num))) (= (@ (@ (@ tptp.case_option_num_num F1) F2) tptp.none_num) F1)))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.heap_e7401611519738050253t_unit Bool)) (H tptp.heap_e7401611519738050253t_unit) (F (-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat))) (=> (not (@ P2 H)) (= (@ (@ tptp.heap_Time_execute_b (@ (@ tptp.heap_Time_guard_b P2) F)) H) tptp.none_P6779099274072355161it_nat))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.heap_e7401611519738050253t_unit Bool)) (H tptp.heap_e7401611519738050253t_unit) (F (-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat))) (=> (not (@ P2 H)) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_guard_a P2) F)) H) tptp.none_P2651198173097904984it_nat))))
% 8.20/8.60 (assert (forall ((S2 tptp.list_char)) (= (@ tptp.heap_Time_execute_b (@ tptp.heap_Time_raise_b S2)) (lambda ((Uu2 tptp.heap_e7401611519738050253t_unit)) tptp.none_P6779099274072355161it_nat))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((H (-> tptp.int tptp.int)) (F1 tptp.int) (F2 (-> tptp.num tptp.int)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_option_int_num F1) F2) Option)) (@ (@ (@ tptp.case_option_int_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F2 X4)))) Option))))
% 8.20/8.60 (assert (forall ((H (-> tptp.int tptp.option_num)) (F1 tptp.int) (F2 (-> tptp.num tptp.int)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_option_int_num F1) F2) Option)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F2 X4)))) Option))))
% 8.20/8.60 (assert (forall ((H (-> tptp.int tptp.num)) (F1 tptp.int) (F2 (-> tptp.num tptp.int)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_option_int_num F1) F2) Option)) (@ (@ (@ tptp.case_option_num_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F2 X4)))) Option))))
% 8.20/8.60 (assert (forall ((H (-> tptp.option_num tptp.int)) (F1 tptp.option_num) (F2 (-> tptp.num tptp.option_num)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_o6005452278849405969um_num F1) F2) Option)) (@ (@ (@ tptp.case_option_int_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F2 X4)))) Option))))
% 8.20/8.60 (assert (forall ((H (-> tptp.option_num tptp.option_num)) (F1 tptp.option_num) (F2 (-> tptp.num tptp.option_num)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_o6005452278849405969um_num F1) F2) Option)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F2 X4)))) Option))))
% 8.20/8.60 (assert (forall ((H (-> tptp.option_num tptp.num)) (F1 tptp.option_num) (F2 (-> tptp.num tptp.option_num)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_o6005452278849405969um_num F1) F2) Option)) (@ (@ (@ tptp.case_option_num_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F2 X4)))) Option))))
% 8.20/8.60 (assert (forall ((H (-> tptp.num tptp.int)) (F1 tptp.num) (F2 (-> tptp.num tptp.num)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_option_num_num F1) F2) Option)) (@ (@ (@ tptp.case_option_int_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F2 X4)))) Option))))
% 8.20/8.60 (assert (forall ((H (-> tptp.num tptp.option_num)) (F1 tptp.num) (F2 (-> tptp.num tptp.num)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_option_num_num F1) F2) Option)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F2 X4)))) Option))))
% 8.20/8.60 (assert (forall ((H (-> tptp.num tptp.num)) (F1 tptp.num) (F2 (-> tptp.num tptp.num)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_option_num_num F1) F2) Option)) (@ (@ (@ tptp.case_option_num_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F2 X4)))) Option))))
% 8.20/8.60 (assert (forall ((X2 tptp.produc7388388658123137530it_nat)) (not (= tptp.none_P6779099274072355161it_nat (@ tptp.some_P2818173045054083285it_nat X2)))))
% 8.20/8.60 (assert (forall ((X2 tptp.produc3260487557148687353it_nat)) (not (= tptp.none_P2651198173097904984it_nat (@ tptp.some_P7913643980934408916it_nat X2)))))
% 8.20/8.60 (assert (forall ((X2 tptp.produc8664842809031399944it_nat)) (not (= tptp.none_P9117596204409417319it_nat (@ tptp.some_P1914260805536162275it_nat X2)))))
% 8.20/8.60 (assert (forall ((X2 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X2)))))
% 8.20/8.60 (assert (forall ((Option tptp.option4065278094766928714it_nat) (X2 tptp.produc7388388658123137530it_nat)) (=> (= Option (@ tptp.some_P2818173045054083285it_nat X2)) (not (= Option tptp.none_P6779099274072355161it_nat)))))
% 8.20/8.60 (assert (forall ((Option tptp.option3562590408128118217it_nat) (X2 tptp.produc3260487557148687353it_nat)) (=> (= Option (@ tptp.some_P7913643980934408916it_nat X2)) (not (= Option tptp.none_P2651198173097904984it_nat)))))
% 8.20/8.60 (assert (forall ((Option tptp.option8956607266484857688it_nat) (X2 tptp.produc8664842809031399944it_nat)) (=> (= Option (@ tptp.some_P1914260805536162275it_nat X2)) (not (= Option tptp.none_P9117596204409417319it_nat)))))
% 8.20/8.60 (assert (forall ((Option tptp.option_num) (X2 tptp.num)) (=> (= Option (@ tptp.some_num X2)) (not (= Option tptp.none_num)))))
% 8.20/8.60 (assert (forall ((Y tptp.option4065278094766928714it_nat)) (=> (not (= Y tptp.none_P6779099274072355161it_nat)) (not (forall ((X22 tptp.produc7388388658123137530it_nat)) (not (= Y (@ tptp.some_P2818173045054083285it_nat X22))))))))
% 8.20/8.60 (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))))))))
% 8.20/8.60 (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))))))))
% 8.20/8.60 (assert (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X22 tptp.num)) (not (= Y (@ tptp.some_num X22))))))))
% 8.20/8.60 (assert (= (lambda ((P4 (-> tptp.option4065278094766928714it_nat Bool))) (exists ((X5 tptp.option4065278094766928714it_nat)) (@ P4 X5))) (lambda ((P5 (-> tptp.option4065278094766928714it_nat Bool))) (or (@ P5 tptp.none_P6779099274072355161it_nat) (exists ((X4 tptp.produc7388388658123137530it_nat)) (@ P5 (@ tptp.some_P2818173045054083285it_nat X4)))))))
% 8.20/8.60 (assert (= (lambda ((P4 (-> tptp.option3562590408128118217it_nat Bool))) (exists ((X5 tptp.option3562590408128118217it_nat)) (@ P4 X5))) (lambda ((P5 (-> tptp.option3562590408128118217it_nat Bool))) (or (@ P5 tptp.none_P2651198173097904984it_nat) (exists ((X4 tptp.produc3260487557148687353it_nat)) (@ P5 (@ tptp.some_P7913643980934408916it_nat X4)))))))
% 8.20/8.60 (assert (= (lambda ((P4 (-> tptp.option8956607266484857688it_nat Bool))) (exists ((X5 tptp.option8956607266484857688it_nat)) (@ P4 X5))) (lambda ((P5 (-> tptp.option8956607266484857688it_nat Bool))) (or (@ P5 tptp.none_P9117596204409417319it_nat) (exists ((X4 tptp.produc8664842809031399944it_nat)) (@ P5 (@ tptp.some_P1914260805536162275it_nat X4)))))))
% 8.20/8.60 (assert (= (lambda ((P4 (-> tptp.option_num Bool))) (exists ((X5 tptp.option_num)) (@ P4 X5))) (lambda ((P5 (-> tptp.option_num Bool))) (or (@ P5 tptp.none_num) (exists ((X4 tptp.num)) (@ P5 (@ tptp.some_num X4)))))))
% 8.20/8.60 (assert (= (lambda ((P4 (-> tptp.option4065278094766928714it_nat Bool))) (forall ((X5 tptp.option4065278094766928714it_nat)) (@ P4 X5))) (lambda ((P5 (-> tptp.option4065278094766928714it_nat Bool))) (and (@ P5 tptp.none_P6779099274072355161it_nat) (forall ((X4 tptp.produc7388388658123137530it_nat)) (@ P5 (@ tptp.some_P2818173045054083285it_nat X4)))))))
% 8.20/8.60 (assert (= (lambda ((P4 (-> tptp.option3562590408128118217it_nat Bool))) (forall ((X5 tptp.option3562590408128118217it_nat)) (@ P4 X5))) (lambda ((P5 (-> tptp.option3562590408128118217it_nat Bool))) (and (@ P5 tptp.none_P2651198173097904984it_nat) (forall ((X4 tptp.produc3260487557148687353it_nat)) (@ P5 (@ tptp.some_P7913643980934408916it_nat X4)))))))
% 8.20/8.60 (assert (= (lambda ((P4 (-> tptp.option8956607266484857688it_nat Bool))) (forall ((X5 tptp.option8956607266484857688it_nat)) (@ P4 X5))) (lambda ((P5 (-> tptp.option8956607266484857688it_nat Bool))) (and (@ P5 tptp.none_P9117596204409417319it_nat) (forall ((X4 tptp.produc8664842809031399944it_nat)) (@ P5 (@ tptp.some_P1914260805536162275it_nat X4)))))))
% 8.20/8.60 (assert (= (lambda ((P4 (-> tptp.option_num Bool))) (forall ((X5 tptp.option_num)) (@ P4 X5))) (lambda ((P5 (-> tptp.option_num Bool))) (and (@ P5 tptp.none_num) (forall ((X4 tptp.num)) (@ P5 (@ tptp.some_num X4)))))))
% 8.20/8.60 (assert (forall ((X tptp.option_num) (P2 (-> tptp.option_num tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.num)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 8.20/8.60 (assert (forall ((X tptp.option4065278094766928714it_nat) (P2 (-> tptp.option4065278094766928714it_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_P6779099274072355161it_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.produc7388388658123137530it_nat) (B3 tptp.num)) (=> (= X (@ tptp.some_P2818173045054083285it_nat A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 8.20/8.60 (assert (forall ((X tptp.option3562590408128118217it_nat) (P2 (-> tptp.option3562590408128118217it_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_P2651198173097904984it_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.produc3260487557148687353it_nat) (B3 tptp.num)) (=> (= X (@ tptp.some_P7913643980934408916it_nat A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 8.20/8.60 (assert (forall ((X tptp.option8956607266484857688it_nat) (P2 (-> tptp.option8956607266484857688it_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_P9117596204409417319it_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.produc8664842809031399944it_nat) (B3 tptp.num)) (=> (= X (@ tptp.some_P1914260805536162275it_nat A3)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 8.20/8.60 (assert (forall ((X tptp.option_num) (P2 (-> tptp.option_num tptp.option4065278094766928714it_nat Bool)) (Y tptp.option4065278094766928714it_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P6779099274072355161it_nat) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.produc7388388658123137530it_nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_P2818173045054083285it_nat B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 8.20/8.60 (assert (forall ((X tptp.option_num) (P2 (-> tptp.option_num tptp.option3562590408128118217it_nat Bool)) (Y tptp.option3562590408128118217it_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P2651198173097904984it_nat) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.produc3260487557148687353it_nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_P7913643980934408916it_nat B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 8.20/8.60 (assert (forall ((X tptp.option_num) (P2 (-> tptp.option_num tptp.option8956607266484857688it_nat Bool)) (Y tptp.option8956607266484857688it_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P9117596204409417319it_nat) _let_1) (=> (forall ((A3 tptp.num) (B3 tptp.produc8664842809031399944it_nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_P1914260805536162275it_nat B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 8.20/8.60 (assert (forall ((X tptp.option4065278094766928714it_nat) (P2 (-> tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat Bool)) (Y tptp.option4065278094766928714it_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_P6779099274072355161it_nat) _let_1) (=> (=> (= Y tptp.none_P6779099274072355161it_nat) _let_1) (=> (forall ((A3 tptp.produc7388388658123137530it_nat) (B3 tptp.produc7388388658123137530it_nat)) (=> (= X (@ tptp.some_P2818173045054083285it_nat A3)) (=> (= Y (@ tptp.some_P2818173045054083285it_nat B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 8.20/8.60 (assert (forall ((X tptp.option4065278094766928714it_nat) (P2 (-> tptp.option4065278094766928714it_nat tptp.option3562590408128118217it_nat Bool)) (Y tptp.option3562590408128118217it_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_P6779099274072355161it_nat) _let_1) (=> (=> (= Y tptp.none_P2651198173097904984it_nat) _let_1) (=> (forall ((A3 tptp.produc7388388658123137530it_nat) (B3 tptp.produc3260487557148687353it_nat)) (=> (= X (@ tptp.some_P2818173045054083285it_nat A3)) (=> (= Y (@ tptp.some_P7913643980934408916it_nat B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 8.20/8.60 (assert (forall ((X tptp.option4065278094766928714it_nat) (P2 (-> tptp.option4065278094766928714it_nat tptp.option8956607266484857688it_nat Bool)) (Y tptp.option8956607266484857688it_nat)) (let ((_let_1 (@ (@ P2 X) Y))) (=> (=> (= X tptp.none_P6779099274072355161it_nat) _let_1) (=> (=> (= Y tptp.none_P9117596204409417319it_nat) _let_1) (=> (forall ((A3 tptp.produc7388388658123137530it_nat) (B3 tptp.produc8664842809031399944it_nat)) (=> (= X (@ tptp.some_P2818173045054083285it_nat A3)) (=> (= Y (@ tptp.some_P1914260805536162275it_nat B3)) (@ (@ P2 X) Y)))) _let_1))))))
% 8.20/8.60 (assert (forall ((X tptp.option_num)) (=> (@ (@ tptp.ord_le6622620407824499402on_num X) tptp.none_num) (= X tptp.none_num))))
% 8.20/8.60 (assert (forall ((X tptp.option_num)) (@ (@ tptp.ord_le6622620407824499402on_num tptp.none_num) X)))
% 8.20/8.60 (assert (forall ((F1 tptp.int) (F2 (-> tptp.num tptp.int)) (X2 tptp.num)) (= (@ (@ (@ tptp.case_option_int_num F1) F2) (@ tptp.some_num X2)) (@ F2 X2))))
% 8.20/8.60 (assert (forall ((F1 tptp.option_num) (F2 (-> tptp.num tptp.option_num)) (X2 tptp.num)) (= (@ (@ (@ tptp.case_o6005452278849405969um_num F1) F2) (@ tptp.some_num X2)) (@ F2 X2))))
% 8.20/8.60 (assert (forall ((F1 tptp.num) (F2 (-> tptp.num tptp.num)) (X2 tptp.num)) (= (@ (@ (@ tptp.case_option_num_num F1) F2) (@ tptp.some_num X2)) (@ F2 X2))))
% 8.20/8.60 (assert (forall ((X tptp.num)) (= (@ (@ tptp.the_default_num X) tptp.none_num) X)))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc7388388658123137530it_nat Bool)) (X tptp.produc7388388658123137530it_nat)) (=> (= (@ tptp.eps_Op5869321083069970014it_nat P2) (@ tptp.some_P2818173045054083285it_nat X)) (@ P2 X))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc3260487557148687353it_nat Bool)) (X tptp.produc3260487557148687353it_nat)) (=> (= (@ tptp.eps_Op1741419982095519837it_nat P2) (@ tptp.some_P7913643980934408916it_nat X)) (@ P2 X))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc8664842809031399944it_nat Bool)) (X tptp.produc8664842809031399944it_nat)) (=> (= (@ tptp.eps_Op3393321821070424684it_nat P2) (@ tptp.some_P1914260805536162275it_nat X)) (@ P2 X))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.num Bool)) (X tptp.num)) (=> (= (@ tptp.eps_Opt_num P2) (@ tptp.some_num X)) (@ P2 X))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc7388388658123137530it_nat Bool)) (X tptp.produc7388388658123137530it_nat)) (=> (forall ((X9 tptp.produc7388388658123137530it_nat)) (=> (@ P2 X) (=> (@ P2 X9) (= X9 X)))) (= (= (@ tptp.eps_Op5869321083069970014it_nat P2) (@ tptp.some_P2818173045054083285it_nat X)) (@ P2 X)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc3260487557148687353it_nat Bool)) (X tptp.produc3260487557148687353it_nat)) (=> (forall ((X9 tptp.produc3260487557148687353it_nat)) (=> (@ P2 X) (=> (@ P2 X9) (= X9 X)))) (= (= (@ tptp.eps_Op1741419982095519837it_nat P2) (@ tptp.some_P7913643980934408916it_nat X)) (@ P2 X)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.produc8664842809031399944it_nat Bool)) (X tptp.produc8664842809031399944it_nat)) (=> (forall ((X9 tptp.produc8664842809031399944it_nat)) (=> (@ P2 X) (=> (@ P2 X9) (= X9 X)))) (= (= (@ tptp.eps_Op3393321821070424684it_nat P2) (@ tptp.some_P1914260805536162275it_nat X)) (@ P2 X)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.num Bool)) (X tptp.num)) (=> (forall ((X9 tptp.num)) (=> (@ P2 X) (=> (@ P2 X9) (= X9 X)))) (= (= (@ tptp.eps_Opt_num P2) (@ tptp.some_num X)) (@ P2 X)))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_b) (H tptp.heap_e7401611519738050253t_unit) (G (-> tptp.b tptp.heap_Time_Heap_b))) (=> (= (@ (@ tptp.heap_Time_execute_b F) H) tptp.none_P6779099274072355161it_nat) (= (@ (@ tptp.heap_Time_execute_b (@ (@ tptp.heap_Time_bind_b_b F) G)) H) tptp.none_P6779099274072355161it_nat))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_b) (H tptp.heap_e7401611519738050253t_unit) (G (-> tptp.b tptp.heap_Time_Heap_a))) (=> (= (@ (@ tptp.heap_Time_execute_b F) H) tptp.none_P6779099274072355161it_nat) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_bind_b_a F) G)) H) tptp.none_P2651198173097904984it_nat))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (G (-> tptp.a tptp.heap_Time_Heap_b))) (=> (= (@ (@ tptp.heap_Time_execute_a F) H) tptp.none_P2651198173097904984it_nat) (= (@ (@ tptp.heap_Time_execute_b (@ (@ tptp.heap_Time_bind_a_b F) G)) H) tptp.none_P6779099274072355161it_nat))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (= tptp.heap_Time_success_b (lambda ((F3 tptp.heap_Time_Heap_b) (H6 tptp.heap_e7401611519738050253t_unit)) (not (= (@ (@ tptp.heap_Time_execute_b F3) H6) tptp.none_P6779099274072355161it_nat)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_b) (H tptp.heap_e7401611519738050253t_unit)) (=> (not (= (@ (@ tptp.heap_Time_execute_b F) H) tptp.none_P6779099274072355161it_nat)) (@ (@ tptp.heap_Time_success_b F) H))))
% 8.20/8.60 (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))))
% 8.20/8.60 (assert (forall ((X tptp.option_num)) (=> (@ (@ tptp.ord_less_option_num tptp.none_num) X) (exists ((Z2 tptp.num)) (= X (@ tptp.some_num Z2))))))
% 8.20/8.60 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_option_num tptp.none_num) (@ tptp.some_num X))))
% 8.20/8.60 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le2843351958646193337nt_int R2) S2))))
% 8.20/8.60 (assert (forall ((R2 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 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le5966269811547037844et_nat R2) S2))))
% 8.20/8.60 (assert (forall ((R2 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 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le4763372923235995152et_nat R2) S2))))
% 8.20/8.60 (assert (forall ((R2 tptp.set_Pr7600907837789447088it_nat) (S2 tptp.set_Pr7600907837789447088it_nat)) (=> (forall ((X3 tptp.b) (Y3 tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat X3) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le4980869671742669840it_nat R2) S2))))
% 8.20/8.60 (assert (forall ((R2 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 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le4478181985103859343it_nat R2) S2))))
% 8.20/8.60 (assert (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit)) (=> (forall ((X3 tptp.product_unit) (H4 tptp.produc6653097349344004940it_nat)) (not (= (@ (@ tptp.heap_T875086893843062177t_unit F) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat X3) H4))))) (= (@ (@ tptp.heap_T875086893843062177t_unit F) H) tptp.none_P9117596204409417319it_nat))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_b) (H tptp.heap_e7401611519738050253t_unit)) (=> (forall ((X3 tptp.b) (H4 tptp.produc6653097349344004940it_nat)) (not (= (@ (@ tptp.heap_Time_execute_b F) H) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat X3) H4))))) (= (@ (@ tptp.heap_Time_execute_b F) H) tptp.none_P6779099274072355161it_nat))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit)) (=> (forall ((X3 tptp.a) (H4 tptp.produc6653097349344004940it_nat)) (not (= (@ (@ tptp.heap_Time_execute_a F) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat X3) H4))))) (= (@ (@ tptp.heap_Time_execute_a F) H) tptp.none_P2651198173097904984it_nat))))
% 8.20/8.60 (assert (forall ((X tptp.produc2207270350733924475it_nat)) (=> (forall ((N5 tptp.nat) (R4 tptp.b) (H2 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (not (= X (@ (@ tptp.produc4613957359643799859it_nat N5) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat R4) (@ (@ tptp.produc584006145561248582it_nat H2) N4))))))) (not (forall ((N5 tptp.nat)) (not (= X (@ (@ tptp.produc4613957359643799859it_nat N5) tptp.none_P6779099274072355161it_nat))))))))
% 8.20/8.60 (assert (forall ((X tptp.produc4453839368661128058it_nat)) (=> (forall ((N5 tptp.nat) (R4 tptp.a) (H2 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (not (= X (@ (@ tptp.produc4111269673004989362it_nat N5) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R4) (@ (@ tptp.produc584006145561248582it_nat H2) N4))))))) (not (forall ((N5 tptp.nat)) (not (= X (@ (@ tptp.produc4111269673004989362it_nat N5) tptp.none_P2651198173097904984it_nat))))))))
% 8.20/8.60 (assert (forall ((X tptp.produc3911288613690379145it_nat)) (=> (forall ((N5 tptp.nat) (R4 tptp.product_unit) (H2 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (not (= X (@ (@ tptp.produc638857205735767105it_nat N5) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R4) (@ (@ tptp.produc584006145561248582it_nat H2) N4))))))) (not (forall ((N5 tptp.nat)) (not (= X (@ (@ tptp.produc638857205735767105it_nat N5) tptp.none_P9117596204409417319it_nat))))))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (Xa tptp.option4065278094766928714it_nat) (Y tptp.option4065278094766928714it_nat)) (let ((_let_1 (@ tptp.produc4613957359643799859it_nat X))) (let ((_let_2 (@ tptp.accp_P4016523247509365636it_nat tptp.heap_T8132184524487034139_rel_b))) (=> (= (@ (@ tptp.heap_T7616092557645711336rame_b X) Xa) Y) (=> (@ _let_2 (@ _let_1 Xa)) (=> (forall ((R4 tptp.b) (H2 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H2))) (let ((_let_2 (@ tptp.produc4082563078715348724it_nat R4))) (let ((_let_3 (@ tptp.some_P2818173045054083285it_nat (@ _let_2 (@ _let_1 N4))))) (=> (= Xa _let_3) (=> (= Y (@ tptp.some_P2818173045054083285it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat X) N4))))) (not (@ (@ tptp.accp_P4016523247509365636it_nat tptp.heap_T8132184524487034139_rel_b) (@ (@ tptp.produc4613957359643799859it_nat X) _let_3))))))))) (not (=> (= Xa tptp.none_P6779099274072355161it_nat) (=> (= Y tptp.none_P6779099274072355161it_nat) (not (@ _let_2 (@ _let_1 tptp.none_P6779099274072355161it_nat)))))))))))))
% 8.20/8.60 (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 ((R4 tptp.a) (H2 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H2))) (let ((_let_2 (@ tptp.produc9178034014595674355it_nat R4))) (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)))))))))))))
% 8.20/8.60 (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 ((R4 tptp.product_unit) (H2 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H2))) (let ((_let_2 (@ tptp.produc7133225469290080770it_nat R4))) (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)))))))))))))
% 8.20/8.60 (assert (forall ((P2 Bool) (Q2 (-> tptp.num Bool)) (X tptp.option_num) (R3 (-> tptp.int Bool)) (F tptp.int) (G (-> tptp.num tptp.int))) (=> (@ (@ (@ tptp.case_option_o_num P2) Q2) X) (=> (=> P2 (@ R3 F)) (=> (forall ((Q5 tptp.num)) (=> (@ Q2 Q5) (@ R3 (@ G Q5)))) (@ R3 (@ (@ (@ tptp.case_option_int_num F) G) X)))))))
% 8.20/8.60 (assert (forall ((P2 Bool) (Q2 (-> tptp.num Bool)) (X tptp.option_num) (R3 (-> tptp.option_num Bool)) (F tptp.option_num) (G (-> tptp.num tptp.option_num))) (=> (@ (@ (@ tptp.case_option_o_num P2) Q2) X) (=> (=> P2 (@ R3 F)) (=> (forall ((Q5 tptp.num)) (=> (@ Q2 Q5) (@ R3 (@ G Q5)))) (@ R3 (@ (@ (@ tptp.case_o6005452278849405969um_num F) G) X)))))))
% 8.20/8.60 (assert (forall ((P2 Bool) (Q2 (-> tptp.num Bool)) (X tptp.option_num) (R3 (-> tptp.num Bool)) (F tptp.num) (G (-> tptp.num tptp.num))) (=> (@ (@ (@ tptp.case_option_o_num P2) Q2) X) (=> (=> P2 (@ R3 F)) (=> (forall ((Q5 tptp.num)) (=> (@ Q2 Q5) (@ R3 (@ G Q5)))) (@ R3 (@ (@ (@ tptp.case_option_num_num F) G) X)))))))
% 8.20/8.60 (assert (= tptp.set_to_map_int_int (lambda ((S4 tptp.set_Pr958786334691620121nt_int) (K3 tptp.int)) (@ tptp.eps_Opt_int (lambda ((V2 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int K3) V2)) S4))))))
% 8.20/8.60 (assert (= tptp.set_to6040779677306527128et_nat (lambda ((S4 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)) S4))))))
% 8.20/8.60 (assert (= tptp.set_to2047380710992656148et_nat (lambda ((S4 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)) S4))))))
% 8.20/8.60 (assert (= tptp.set_to6136816377707935252it_nat (lambda ((S4 tptp.set_Pr7600907837789447088it_nat) (K3 tptp.b)) (@ tptp.eps_Op8301357815426737072it_nat (lambda ((V2 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat K3) V2)) S4))))))
% 8.20/8.60 (assert (= tptp.set_to2008915276733485075it_nat (lambda ((S4 tptp.set_Pr7098220151150636591it_nat) (K3 tptp.a)) (@ tptp.eps_Op8301357815426737072it_nat (lambda ((V2 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat K3) V2)) S4))))))
% 8.20/8.60 (assert (= tptp.heap_Time_guard_b (lambda ((P5 (-> tptp.heap_e7401611519738050253t_unit Bool)) (F3 (-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat))) (@ tptp.heap_Time_Heap_b2 (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ (@ tptp.if_opt7386294288321364996it_nat (@ P5 H6)) (@ tptp.some_P2818173045054083285it_nat (@ F3 H6))) tptp.none_P6779099274072355161it_nat))))))
% 8.20/8.60 (assert (= tptp.heap_Time_guard_a (lambda ((P5 (-> 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 (@ P5 H6)) (@ tptp.some_P7913643980934408916it_nat (@ F3 H6))) tptp.none_P2651198173097904984it_nat))))))
% 8.20/8.60 (assert (= tptp.heap_T8440541562793052209t_unit (lambda ((P5 (-> 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 (@ P5 H6)) (@ tptp.some_P1914260805536162275it_nat (@ F3 H6))) tptp.none_P9117596204409417319it_nat))))))
% 8.20/8.60 (assert (forall ((X (-> tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)) (Ya (-> tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat))) (= (= (@ tptp.heap_T6183433275982383450t_unit X) (@ tptp.heap_T6183433275982383450t_unit Ya)) (= X Ya))))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_b)) (= (@ tptp.heap_Time_Heap_b2 (@ tptp.heap_Time_execute_b F)) F)))
% 8.20/8.60 (assert (forall ((F tptp.heap_Time_Heap_a)) (= (@ tptp.heap_Time_Heap_a2 (@ tptp.heap_Time_execute_a F)) F)))
% 8.20/8.60 (assert (forall ((F tptp.heap_T5738788834812785303t_unit)) (= (@ tptp.heap_T6183433275982383450t_unit (@ tptp.heap_T875086893843062177t_unit F)) F)))
% 8.20/8.60 (assert (forall ((Y tptp.heap_T5738788834812785303t_unit)) (not (forall ((X3 (-> tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat))) (not (= Y (@ tptp.heap_T6183433275982383450t_unit X3)))))))
% 8.20/8.60 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat))) (= (@ tptp.heap_Time_execute_b (@ tptp.heap_Time_Heap_b2 F)) F)))
% 8.20/8.60 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat))) (= (@ tptp.heap_Time_execute_a (@ tptp.heap_Time_Heap_a2 F)) F)))
% 8.20/8.60 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat))) (= (@ tptp.heap_T875086893843062177t_unit (@ tptp.heap_T6183433275982383450t_unit F)) F)))
% 8.20/8.60 (assert (forall ((Option tptp.option_num)) (= (not (= Option tptp.none_num)) (@ (@ (@ tptp.case_option_o_num false) (lambda ((Uu2 tptp.num)) true)) Option))))
% 8.20/8.60 (assert (forall ((Option tptp.option_num)) (= (= Option tptp.none_num) (@ (@ (@ tptp.case_option_o_num true) (lambda ((Uu2 tptp.num)) false)) Option))))
% 8.20/8.60 (assert (forall ((P2 Bool) (Q2 (-> tptp.produc7388388658123137530it_nat Bool)) (X tptp.option4065278094766928714it_nat)) (=> (@ (@ (@ tptp.case_o7395119307266030407it_nat P2) Q2) X) (=> (=> (= X tptp.none_P6779099274072355161it_nat) (not P2)) (not (forall ((Y3 tptp.produc7388388658123137530it_nat)) (=> (= X (@ tptp.some_P2818173045054083285it_nat Y3)) (not (@ Q2 Y3)))))))))
% 8.20/8.60 (assert (forall ((P2 Bool) (Q2 (-> tptp.produc3260487557148687353it_nat Bool)) (X tptp.option3562590408128118217it_nat)) (=> (@ (@ (@ tptp.case_o3267218206291580230it_nat P2) Q2) X) (=> (=> (= X tptp.none_P2651198173097904984it_nat) (not P2)) (not (forall ((Y3 tptp.produc3260487557148687353it_nat)) (=> (= X (@ tptp.some_P7913643980934408916it_nat Y3)) (not (@ Q2 Y3)))))))))
% 8.20/8.60 (assert (forall ((P2 Bool) (Q2 (-> tptp.produc8664842809031399944it_nat Bool)) (X tptp.option8956607266484857688it_nat)) (=> (@ (@ (@ tptp.case_o2686588417244861013it_nat P2) Q2) X) (=> (=> (= X tptp.none_P9117596204409417319it_nat) (not P2)) (not (forall ((Y3 tptp.produc8664842809031399944it_nat)) (=> (= X (@ tptp.some_P1914260805536162275it_nat Y3)) (not (@ Q2 Y3)))))))))
% 8.20/8.60 (assert (forall ((P2 Bool) (Q2 (-> tptp.num Bool)) (X tptp.option_num)) (=> (@ (@ (@ tptp.case_option_o_num P2) Q2) X) (=> (=> (= X tptp.none_num) (not P2)) (not (forall ((Y3 tptp.num)) (=> (= X (@ tptp.some_num Y3)) (not (@ Q2 Y3)))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_Pr8551490117392284871at_nat) (K2 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 K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_Pr4329608150637261639at_nat) (K2 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 K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.set_nat) (K2 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 K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.nat) (K2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat A))) (let ((_let_2 (@ tptp.sup_sup_nat K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 8.20/8.60 (assert (forall ((B5 tptp.int) (K2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int A))) (let ((_let_2 (@ tptp.sup_sup_int K2))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (K2 tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A4) B) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A) B)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (K2 tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A4) B) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (K2 tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.sup_sup_set_nat A4) B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.nat) (K2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.sup_sup_nat A4) B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B)))))))
% 8.20/8.60 (assert (forall ((A4 tptp.int) (K2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.sup_sup_int A4) B) (@ _let_1 (@ (@ tptp.sup_sup_int A) B)))))))
% 8.20/8.60 (assert (= tptp.ord_le353528952715127954et_int (lambda ((X4 tptp.option_set_int) (Y4 tptp.option_set_int)) (@ (@ (@ tptp.case_o223999843215110191et_int true) (lambda ((Z tptp.set_int)) (@ (@ (@ tptp.case_o223999843215110191et_int false) (@ tptp.ord_less_eq_set_int Z)) Y4))) X4))))
% 8.20/8.60 (assert (= tptp.ord_le2406147912482264968on_rat (lambda ((X4 tptp.option_rat) (Y4 tptp.option_rat)) (@ (@ (@ tptp.case_option_o_rat true) (lambda ((Z tptp.rat)) (@ (@ (@ tptp.case_option_o_rat false) (@ tptp.ord_less_eq_rat Z)) Y4))) X4))))
% 8.20/8.60 (assert (= tptp.ord_le6622620407824499402on_num (lambda ((X4 tptp.option_num) (Y4 tptp.option_num)) (@ (@ (@ tptp.case_option_o_num true) (lambda ((Z tptp.num)) (@ (@ (@ tptp.case_option_o_num false) (@ tptp.ord_less_eq_num Z)) Y4))) X4))))
% 8.20/8.60 (assert (= tptp.ord_le5914376470875661696on_nat (lambda ((X4 tptp.option_nat) (Y4 tptp.option_nat)) (@ (@ (@ tptp.case_option_o_nat true) (lambda ((Z tptp.nat)) (@ (@ (@ tptp.case_option_o_nat false) (@ tptp.ord_less_eq_nat Z)) Y4))) X4))))
% 8.20/8.60 (assert (= tptp.ord_le1736525451366464988on_int (lambda ((X4 tptp.option_int) (Y4 tptp.option_int)) (@ (@ (@ tptp.case_option_o_int true) (lambda ((Z tptp.int)) (@ (@ (@ tptp.case_option_o_int false) (@ tptp.ord_less_eq_int Z)) Y4))) X4))))
% 8.20/8.60 (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 ((Z tptp.assn)) (@ (@ tptp.ord_less_assn Z) Y4))) X4))) __flatten_var_0))))
% 8.20/8.60 (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 ((Z tptp.rat)) (@ (@ tptp.ord_less_rat Z) Y4))) X4))) __flatten_var_0))))
% 8.20/8.60 (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 ((Z tptp.num)) (@ (@ tptp.ord_less_num Z) Y4))) X4))) __flatten_var_0))))
% 8.20/8.60 (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 ((Z tptp.nat)) (@ (@ tptp.ord_less_nat Z) Y4))) X4))) __flatten_var_0))))
% 8.20/8.60 (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 ((Z tptp.int)) (@ (@ tptp.ord_less_int Z) Y4))) X4))) __flatten_var_0))))
% 8.20/8.60 (assert (= tptp.heap_T2927564422264180874t_unit (lambda ((S5 tptp.list_char)) (@ tptp.heap_T6183433275982383450t_unit (lambda ((Uu2 tptp.heap_e7401611519738050253t_unit)) tptp.none_P9117596204409417319it_nat)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((R1 (-> tptp.nat tptp.nat Bool)) (R22 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_le2646555220125990790_nat_o R1) R22) (@ (@ tptp.ord_less_eq_nat_o (@ tptp.accp_nat R22)) (@ tptp.accp_nat R1)))))
% 8.20/8.60 (assert (forall ((D4 (-> tptp.product_prod_num_num Bool)) (R3 (-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)) (X tptp.product_prod_num_num) (P2 (-> tptp.product_prod_num_num Bool))) (=> (@ (@ tptp.ord_le2239182809043710856_num_o D4) (@ tptp.accp_P3113834385874906142um_num R3)) (=> (forall ((X3 tptp.product_prod_num_num) (Z2 tptp.product_prod_num_num)) (=> (@ D4 X3) (=> (@ (@ R3 Z2) X3) (@ D4 Z2)))) (=> (@ D4 X) (=> (forall ((X3 tptp.product_prod_num_num)) (=> (@ D4 X3) (=> (forall ((Z6 tptp.product_prod_num_num)) (=> (@ (@ R3 Z6) X3) (@ P2 Z6))) (@ P2 X3)))) (@ P2 X)))))))
% 8.20/8.60 (assert (forall ((D4 (-> tptp.product_prod_nat_nat Bool)) (R3 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat) (P2 (-> tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le704812498762024988_nat_o D4) (@ tptp.accp_P4275260045618599050at_nat R3)) (=> (forall ((X3 tptp.product_prod_nat_nat) (Z2 tptp.product_prod_nat_nat)) (=> (@ D4 X3) (=> (@ (@ R3 Z2) X3) (@ D4 Z2)))) (=> (@ D4 X) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ D4 X3) (=> (forall ((Z6 tptp.product_prod_nat_nat)) (=> (@ (@ R3 Z6) X3) (@ P2 Z6))) (@ P2 X3)))) (@ P2 X)))))))
% 8.20/8.60 (assert (forall ((D4 (-> tptp.product_prod_int_int Bool)) (R3 (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)) (X tptp.product_prod_int_int) (P2 (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o D4) (@ tptp.accp_P1096762738010456898nt_int R3)) (=> (forall ((X3 tptp.product_prod_int_int) (Z2 tptp.product_prod_int_int)) (=> (@ D4 X3) (=> (@ (@ R3 Z2) X3) (@ D4 Z2)))) (=> (@ D4 X) (=> (forall ((X3 tptp.product_prod_int_int)) (=> (@ D4 X3) (=> (forall ((Z6 tptp.product_prod_int_int)) (=> (@ (@ R3 Z6) X3) (@ P2 Z6))) (@ P2 X3)))) (@ P2 X)))))))
% 8.20/8.60 (assert (forall ((D4 (-> tptp.produc2732055786443039994et_nat Bool)) (R3 (-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)) (X tptp.produc2732055786443039994et_nat) (P2 (-> tptp.produc2732055786443039994et_nat Bool))) (=> (@ (@ tptp.ord_le1658592502415435381_nat_o D4) (@ tptp.accp_P1862375125659990705et_nat R3)) (=> (forall ((X3 tptp.produc2732055786443039994et_nat) (Z2 tptp.produc2732055786443039994et_nat)) (=> (@ D4 X3) (=> (@ (@ R3 Z2) X3) (@ D4 Z2)))) (=> (@ D4 X) (=> (forall ((X3 tptp.produc2732055786443039994et_nat)) (=> (@ D4 X3) (=> (forall ((Z6 tptp.produc2732055786443039994et_nat)) (=> (@ (@ R3 Z6) X3) (@ P2 Z6))) (@ P2 X3)))) (@ P2 X)))))))
% 8.20/8.60 (assert (forall ((D4 (-> tptp.nat Bool)) (R3 (-> tptp.nat tptp.nat Bool)) (X tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o D4) (@ tptp.accp_nat R3)) (=> (forall ((X3 tptp.nat) (Z2 tptp.nat)) (=> (@ D4 X3) (=> (@ (@ R3 Z2) X3) (@ D4 Z2)))) (=> (@ D4 X) (=> (forall ((X3 tptp.nat)) (=> (@ D4 X3) (=> (forall ((Z6 tptp.nat)) (=> (@ (@ R3 Z6) X3) (@ P2 Z6))) (@ P2 X3)))) (@ P2 X)))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.b Bool)) (X tptp.b) (H tptp.heap_e7401611519738050253t_unit)) (=> (not (@ P2 X)) (= (@ (@ tptp.heap_Time_execute_b (@ (@ tptp.heap_Time_assert_b P2) X)) H) tptp.none_P6779099274072355161it_nat))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.a Bool)) (X tptp.a) (H tptp.heap_e7401611519738050253t_unit)) (=> (not (@ P2 X)) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_assert_a P2) X)) H) tptp.none_P2651198173097904984it_nat))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (Q2 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 P2) Q2)) _let_1) (or (@ (@ tptp.rep_assn P2) _let_1) (@ (@ tptp.rep_assn Q2) _let_1))))))
% 8.20/8.60 (assert (= tptp.combin724284867043296059it_nat (lambda ((F3 (-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)) (X4 tptp.option4065278094766928714it_nat) (Y4 tptp.option4065278094766928714it_nat)) (@ (@ (@ tptp.case_o5901184372446974929it_nat Y4) (lambda ((Z tptp.produc7388388658123137530it_nat)) (@ (@ (@ tptp.case_o5901184372446974929it_nat (@ tptp.some_P2818173045054083285it_nat Z)) (lambda ((Aa tptp.produc7388388658123137530it_nat)) (@ tptp.some_P2818173045054083285it_nat (@ (@ F3 Z) Aa)))) Y4))) X4))))
% 8.20/8.60 (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 ((Z tptp.produc3260487557148687353it_nat)) (@ (@ (@ tptp.case_o6061097939050036047it_nat (@ tptp.some_P7913643980934408916it_nat Z)) (lambda ((Aa tptp.produc3260487557148687353it_nat)) (@ tptp.some_P7913643980934408916it_nat (@ (@ F3 Z) Aa)))) Y4))) X4))))
% 8.20/8.60 (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 ((Z tptp.produc8664842809031399944it_nat)) (@ (@ (@ tptp.case_o2963978774867076333it_nat (@ tptp.some_P1914260805536162275it_nat Z)) (lambda ((Aa tptp.produc8664842809031399944it_nat)) (@ tptp.some_P1914260805536162275it_nat (@ (@ F3 Z) Aa)))) Y4))) X4))))
% 8.20/8.60 (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 ((Z tptp.num)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num Z)) (lambda ((Aa tptp.num)) (@ tptp.some_num (@ (@ F3 Z) Aa)))) Y4))) X4))))
% 8.20/8.60 (assert (forall ((R2 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)) R2))) (lambda ((Y6 tptp.product_prod_nat_nat) (Z4 tptp.product_prod_nat_nat)) (= Y6 Z4))) (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 R2) tptp.id_Pro2258643101195443293at_nat))))))
% 8.20/8.60 (assert (forall ((R2 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)) R2))) (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y4)) (@ (@ tptp.sup_su6327502436637775413at_nat R2) tptp.id_nat2))))))
% 8.20/8.60 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.sup_sup_int_int_o (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y4)) R2))) (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y4)) (@ (@ tptp.sup_su6024340866399070445nt_int R2) tptp.id_int2))))))
% 8.20/8.60 (assert (forall ((R2 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)) R2))) (lambda ((Y6 tptp.multis2468970476368604999at_nat) (Z4 tptp.multis2468970476368604999at_nat)) (= Y6 Z4))) (lambda ((X4 tptp.multis2468970476368604999at_nat) (Y4 tptp.multis2468970476368604999at_nat)) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat X4) Y4)) (@ (@ tptp.sup_su3035147773818789531at_nat R2) tptp.id_mul2649389997224486051at_nat))))))
% 8.20/8.60 (assert (forall ((R2 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)) R2))) (lambda ((Y6 tptp.set_Pr1261947904930325089at_nat) (Z4 tptp.set_Pr1261947904930325089at_nat)) (= Y6 Z4))) (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X4) Y4)) (@ (@ tptp.sup_su5525570899277871387at_nat R2) tptp.id_set1796276052702428605at_nat))))))
% 8.20/8.60 (assert (forall ((X tptp.int) (Y tptp.int) (F (-> tptp.int tptp.nat))) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.measure_int F)) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (M tptp.heap_Time_Heap_a) (Q2 (-> tptp.a tptp.assn)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.hoare_hoare_triple_a P2))) (=> (@ (@ _let_1 M) Q2) (@ (@ _let_1 (@ (@ tptp.heap_T757603679106148408unit_a (@ tptp.heap_Time_wait N2)) (lambda ((Uu2 tptp.product_unit)) M))) Q2)))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (M tptp.heap_Time_Heap_b) (Q2 (-> tptp.b tptp.assn)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.hoare_hoare_triple_b P2))) (=> (@ (@ _let_1 M) Q2) (@ (@ _let_1 (@ (@ tptp.heap_T757603679106148409unit_b (@ tptp.heap_Time_wait N2)) (lambda ((Uu2 tptp.product_unit)) M))) Q2)))))
% 8.20/8.60 (assert (forall ((P2 tptp.assn) (M tptp.heap_T5738788834812785303t_unit) (Q2 (-> tptp.product_unit tptp.assn)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.hoare_8945653483474564448t_unit P2))) (=> (@ (@ _let_1 M) Q2) (@ (@ _let_1 (@ (@ tptp.heap_T2633723481742716231t_unit (@ tptp.heap_Time_wait N2)) (lambda ((Uu2 tptp.product_unit)) M))) Q2)))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.list_nat Bool))) (= (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat P2)) (forall ((X4 tptp.list_nat)) (not (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (= (= tptp.bot_bo1488462491386950373nt_int (@ tptp.collec5210948495886036740nt_int P2)) (forall ((X4 tptp.set_Pr958786334691620121nt_int)) (not (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.set_nat Bool))) (= (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat P2)) (forall ((X4 tptp.set_nat)) (not (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.product_prod_nat_nat Bool))) (= (= tptp.bot_bo2099793752762293965at_nat (@ tptp.collec3392354462482085612at_nat P2)) (forall ((X4 tptp.product_prod_nat_nat)) (not (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> Bool Bool))) (= (= tptp.bot_bot_set_o (@ tptp.collect_o P2)) (forall ((X4 Bool)) (not (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P2)) (forall ((X4 tptp.nat)) (not (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.int Bool))) (= (= tptp.bot_bot_set_int (@ tptp.collect_int P2)) (forall ((X4 tptp.int)) (not (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.list_nat Bool))) (= (= (@ tptp.collect_list_nat P2) tptp.bot_bot_set_list_nat) (forall ((X4 tptp.list_nat)) (not (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (= (= (@ tptp.collec5210948495886036740nt_int P2) tptp.bot_bo1488462491386950373nt_int) (forall ((X4 tptp.set_Pr958786334691620121nt_int)) (not (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.set_nat Bool))) (= (= (@ tptp.collect_set_nat P2) tptp.bot_bot_set_set_nat) (forall ((X4 tptp.set_nat)) (not (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.product_prod_nat_nat Bool))) (= (= (@ tptp.collec3392354462482085612at_nat P2) tptp.bot_bo2099793752762293965at_nat) (forall ((X4 tptp.product_prod_nat_nat)) (not (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> Bool Bool))) (= (= (@ tptp.collect_o P2) tptp.bot_bot_set_o) (forall ((X4 Bool)) (not (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P2) tptp.bot_bot_set_nat) (forall ((X4 tptp.nat)) (not (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((P2 (-> tptp.int Bool))) (= (= (@ tptp.collect_int P2) tptp.bot_bot_set_int) (forall ((X4 tptp.int)) (not (@ P2 X4))))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int)) (= (forall ((X4 tptp.set_Pr958786334691620121nt_int)) (not (@ (@ tptp.member2340774599025711042nt_int X4) A4))) (= A4 tptp.bot_bo1488462491386950373nt_int))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_set_nat)) (= (forall ((X4 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X4) A4))) (= A4 tptp.bot_bot_set_set_nat))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (= (forall ((X4 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat X4) A4))) (= A4 tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_o)) (= (forall ((X4 Bool)) (not (@ (@ tptp.member_o X4) A4))) (= A4 tptp.bot_bot_set_o))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat)) (= (forall ((X4 tptp.nat)) (not (@ (@ tptp.member_nat X4) A4))) (= A4 tptp.bot_bot_set_nat))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int)) (= (forall ((X4 tptp.int)) (not (@ (@ tptp.member_int X4) A4))) (= A4 tptp.bot_bot_set_int))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int)) (not (@ (@ tptp.member2340774599025711042nt_int C2) tptp.bot_bo1488462491386950373nt_int))))
% 8.20/8.60 (assert (forall ((C2 tptp.set_nat)) (not (@ (@ tptp.member_set_nat C2) tptp.bot_bot_set_set_nat))))
% 8.20/8.60 (assert (forall ((C2 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat C2) tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.60 (assert (forall ((C2 Bool)) (not (@ (@ tptp.member_o C2) tptp.bot_bot_set_o))))
% 8.20/8.60 (assert (forall ((C2 tptp.nat)) (not (@ (@ tptp.member_nat C2) tptp.bot_bot_set_nat))))
% 8.20/8.60 (assert (forall ((C2 tptp.int)) (not (@ (@ tptp.member_int C2) tptp.bot_bot_set_int))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A4) tptp.bot_bo2099793752762293965at_nat) (= A4 tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A4) tptp.bot_bot_set_o) (= A4 tptp.bot_bot_set_o))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A4) tptp.bot_bot_set_nat) (= A4 tptp.bot_bot_set_nat))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A4) tptp.bot_bot_set_int) (= A4 tptp.bot_bot_set_int))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat tptp.bot_bo2099793752762293965at_nat) A4)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o tptp.bot_bot_set_o) A4)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A4)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A4)))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat tptp.bot_bo8422036546324065075at_nat) X) X)))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) X) X)))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat) X) X)))
% 8.20/8.60 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) X) X)))
% 8.20/8.60 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) X) X)))
% 8.20/8.60 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) X) X)))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat X) tptp.bot_bo8422036546324065075at_nat) X)))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) tptp.bot_bo228742789529271731at_nat) X)))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat X) tptp.bot_bo2099793752762293965at_nat) X)))
% 8.20/8.60 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o X) tptp.bot_bot_set_o) X)))
% 8.20/8.60 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) tptp.bot_bot_set_nat) X)))
% 8.20/8.60 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X) tptp.bot_bot_set_int) X)))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat tptp.bot_bo8422036546324065075at_nat) A) A)))
% 8.20/8.60 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) A) A)))
% 8.20/8.60 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat) A) A)))
% 8.20/8.60 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) A) A)))
% 8.20/8.60 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) A) A)))
% 8.20/8.60 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) A) A)))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A) tptp.bot_bo8422036546324065075at_nat) A)))
% 8.20/8.60 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) tptp.bot_bo228742789529271731at_nat) A)))
% 8.20/8.60 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat A) tptp.bot_bo2099793752762293965at_nat) A)))
% 8.20/8.60 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o A) tptp.bot_bot_set_o) A)))
% 8.20/8.60 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) tptp.bot_bot_set_nat) A)))
% 8.20/8.60 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A) tptp.bot_bot_set_int) A)))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (= (= (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5) tptp.bot_bo8422036546324065075at_nat) (and (= A4 tptp.bot_bo8422036546324065075at_nat) (= B5 tptp.bot_bo8422036546324065075at_nat)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5) tptp.bot_bo228742789529271731at_nat) (and (= A4 tptp.bot_bo228742789529271731at_nat) (= B5 tptp.bot_bo228742789529271731at_nat)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat A4) B5) tptp.bot_bo2099793752762293965at_nat) (and (= A4 tptp.bot_bo2099793752762293965at_nat) (= B5 tptp.bot_bo2099793752762293965at_nat)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o)) (= (= (@ (@ tptp.sup_sup_set_o A4) B5) tptp.bot_bot_set_o) (and (= A4 tptp.bot_bot_set_o) (= B5 tptp.bot_bot_set_o)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (= (@ (@ tptp.sup_sup_set_nat A4) B5) tptp.bot_bot_set_nat) (and (= A4 tptp.bot_bot_set_nat) (= B5 tptp.bot_bot_set_nat)))))
% 8.20/8.60 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (= (= (@ (@ tptp.sup_sup_set_int A4) B5) tptp.bot_bot_set_int) (and (= A4 tptp.bot_bot_set_int) (= B5 tptp.bot_bot_set_int)))))
% 8.20/8.60 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat A) B)) tptp.id_Pro2258643101195443293at_nat) (= A B))))
% 8.20/8.60 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat A) B)) tptp.id_mul2649389997224486051at_nat) (= A B))))
% 8.20/8.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) tptp.id_nat2) (= A B))))
% 8.20/8.60 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A) B)) tptp.id_int2) (= A B))))
% 8.20/8.60 (assert (forall ((A tptp.product_prod_nat_nat)) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat A) A)) tptp.id_Pro2258643101195443293at_nat)))
% 8.20/8.60 (assert (forall ((A tptp.multis2468970476368604999at_nat)) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat A) A)) tptp.id_mul2649389997224486051at_nat)))
% 8.20/8.60 (assert (forall ((A tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) A)) tptp.id_nat2)))
% 8.20/8.60 (assert (forall ((A tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A) A)) tptp.id_int2)))
% 8.20/8.60 (assert (forall ((F (-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)) (A tptp.produc7388388658123137530it_nat) (B tptp.produc7388388658123137530it_nat)) (= (@ (@ (@ tptp.combin724284867043296059it_nat F) (@ tptp.some_P2818173045054083285it_nat A)) (@ tptp.some_P2818173045054083285it_nat B)) (@ tptp.some_P2818173045054083285it_nat (@ (@ F A) B)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((F (-> tptp.num tptp.num tptp.num)) (Y tptp.option_num)) (= (@ (@ (@ tptp.combine_options_num F) tptp.none_num) Y) Y)))
% 8.20/8.60 (assert (forall ((F (-> tptp.num tptp.num tptp.num)) (X tptp.option_num)) (= (@ (@ (@ tptp.combine_options_num F) X) tptp.none_num) X)))
% 8.20/8.60 (assert (@ tptp.biject3503750217840948301at_nat tptp.id_Pro2258643101195443293at_nat))
% 8.20/8.60 (assert (@ tptp.biject5714339216877808333at_nat tptp.id_mul2649389997224486051at_nat))
% 8.20/8.60 (assert (@ tptp.bijective_nat_nat tptp.id_nat2))
% 8.20/8.60 (assert (forall ((X tptp.set_Pr958786334691620121nt_int) (S tptp.set_se6260736226359567993nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X) S) (not (= S tptp.bot_bo1488462491386950373nt_int)))))
% 8.20/8.60 (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)))))
% 8.20/8.60 (assert (forall ((X tptp.product_prod_nat_nat) (S tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) S) (not (= S tptp.bot_bo2099793752762293965at_nat)))))
% 8.20/8.60 (assert (forall ((X Bool) (S tptp.set_o)) (=> (@ (@ tptp.member_o X) S) (not (= S tptp.bot_bot_set_o)))))
% 8.20/8.60 (assert (forall ((X tptp.nat) (S tptp.set_nat)) (=> (@ (@ tptp.member_nat X) S) (not (= S tptp.bot_bot_set_nat)))))
% 8.20/8.60 (assert (forall ((X tptp.int) (S tptp.set_int)) (=> (@ (@ tptp.member_int X) S) (not (= S tptp.bot_bot_set_int)))))
% 8.20/8.60 (assert (forall ((S tptp.set_se6260736226359567993nt_int)) (=> (not (= S tptp.bot_bo1488462491386950373nt_int)) (not (forall ((X3 tptp.set_Pr958786334691620121nt_int)) (not (@ (@ tptp.member2340774599025711042nt_int X3) S)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.60 (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)))))))
% 8.20/8.61 (assert (forall ((S tptp.set_o)) (=> (not (= S tptp.bot_bot_set_o)) (not (forall ((X3 Bool)) (not (@ (@ tptp.member_o X3) S)))))))
% 8.20/8.61 (assert (forall ((S tptp.set_nat)) (=> (not (= S tptp.bot_bot_set_nat)) (not (forall ((X3 tptp.nat)) (not (@ (@ tptp.member_nat X3) S)))))))
% 8.20/8.61 (assert (forall ((S tptp.set_int)) (=> (not (= S tptp.bot_bot_set_int)) (not (forall ((X3 tptp.int)) (not (@ (@ tptp.member_int X3) S)))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int)) (= (exists ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) A4)) (not (= A4 tptp.bot_bo1488462491386950373nt_int)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_set_nat)) (= (exists ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A4)) (not (= A4 tptp.bot_bot_set_set_nat)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (= (exists ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) A4)) (not (= A4 tptp.bot_bo2099793752762293965at_nat)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_o)) (= (exists ((X4 Bool)) (@ (@ tptp.member_o X4) A4)) (not (= A4 tptp.bot_bot_set_o)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A4)) (not (= A4 tptp.bot_bot_set_nat)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int)) (= (exists ((X4 tptp.int)) (@ (@ tptp.member_int X4) A4)) (not (= A4 tptp.bot_bot_set_int)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int)) (=> (forall ((Y3 tptp.set_Pr958786334691620121nt_int)) (not (@ (@ tptp.member2340774599025711042nt_int Y3) A4))) (= A4 tptp.bot_bo1488462491386950373nt_int))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_set_nat)) (=> (forall ((Y3 tptp.set_nat)) (not (@ (@ tptp.member_set_nat Y3) A4))) (= A4 tptp.bot_bot_set_set_nat))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat Y3) A4))) (= A4 tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_o)) (=> (forall ((Y3 Bool)) (not (@ (@ tptp.member_o Y3) A4))) (= A4 tptp.bot_bot_set_o))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat)) (=> (forall ((Y3 tptp.nat)) (not (@ (@ tptp.member_nat Y3) A4))) (= A4 tptp.bot_bot_set_nat))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int)) (=> (forall ((Y3 tptp.int)) (not (@ (@ tptp.member_int Y3) A4))) (= A4 tptp.bot_bot_set_int))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (A tptp.set_Pr958786334691620121nt_int)) (=> (= A4 tptp.bot_bo1488462491386950373nt_int) (not (@ (@ tptp.member2340774599025711042nt_int A) A4)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_set_nat) (A tptp.set_nat)) (=> (= A4 tptp.bot_bot_set_set_nat) (not (@ (@ tptp.member_set_nat A) A4)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat)) (=> (= A4 tptp.bot_bo2099793752762293965at_nat) (not (@ (@ tptp.member8440522571783428010at_nat A) A4)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_o) (A Bool)) (=> (= A4 tptp.bot_bot_set_o) (not (@ (@ tptp.member_o A) A4)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (A tptp.nat)) (=> (= A4 tptp.bot_bot_set_nat) (not (@ (@ tptp.member_nat A) A4)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int) (A tptp.int)) (=> (= A4 tptp.bot_bot_set_int) (not (@ (@ tptp.member_int A) A4)))))
% 8.20/8.61 (assert (forall ((A tptp.set_Pr958786334691620121nt_int)) (not (@ (@ tptp.member2340774599025711042nt_int A) tptp.bot_bo1488462491386950373nt_int))))
% 8.20/8.61 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.member_set_nat A) tptp.bot_bot_set_set_nat))))
% 8.20/8.61 (assert (forall ((A tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat A) tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.61 (assert (forall ((A Bool)) (not (@ (@ tptp.member_o A) tptp.bot_bot_set_o))))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.member_nat A) tptp.bot_bot_set_nat))))
% 8.20/8.61 (assert (forall ((A tptp.int)) (not (@ (@ tptp.member_int A) tptp.bot_bot_set_int))))
% 8.20/8.61 (assert (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) false))))
% 8.20/8.61 (assert (= tptp.bot_bo1488462491386950373nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) false))))
% 8.20/8.61 (assert (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) false))))
% 8.20/8.61 (assert (= tptp.bot_bo2099793752762293965at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) false))))
% 8.20/8.61 (assert (= tptp.bot_bot_set_o (@ tptp.collect_o (lambda ((X4 Bool)) false))))
% 8.20/8.61 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) false))))
% 8.20/8.61 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) false))))
% 8.20/8.61 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat tptp.bot_bo2099793752762293965at_nat) A)))
% 8.20/8.61 (assert (forall ((A tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o tptp.bot_bot_set_o) A)))
% 8.20/8.61 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 8.20/8.61 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)))
% 8.20/8.61 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A) tptp.bot_bo2099793752762293965at_nat) (= A tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.61 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A) tptp.bot_bot_set_o) (= A tptp.bot_bot_set_o))))
% 8.20/8.61 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 8.20/8.61 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 8.20/8.61 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) tptp.bot_bo2099793752762293965at_nat) (= A tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.61 (assert (forall ((A tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A) tptp.bot_bot_set_o) (= A tptp.bot_bot_set_o))))
% 8.20/8.61 (assert (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 8.20/8.61 (assert (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 8.20/8.61 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.ord_le7866589430770878221at_nat A) tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.61 (assert (forall ((A tptp.set_o)) (not (@ (@ tptp.ord_less_set_o A) tptp.bot_bot_set_o))))
% 8.20/8.61 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 8.20/8.61 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 8.20/8.61 (assert (forall ((A tptp.assn)) (not (@ (@ tptp.ord_less_assn A) tptp.bot_bot_assn))))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))))
% 8.20/8.61 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (not (= A tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.ord_le7866589430770878221at_nat tptp.bot_bo2099793752762293965at_nat) A))))
% 8.20/8.61 (assert (forall ((A tptp.set_o)) (= (not (= A tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_set_o tptp.bot_bot_set_o) A))))
% 8.20/8.61 (assert (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))))
% 8.20/8.61 (assert (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))))
% 8.20/8.61 (assert (forall ((A tptp.assn)) (= (not (= A tptp.bot_bot_assn)) (@ (@ tptp.ord_less_assn tptp.bot_bot_assn) A))))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat X) tptp.bot_bo8422036546324065075at_nat) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) tptp.bot_bo228742789529271731at_nat) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat X) tptp.bot_bo2099793752762293965at_nat) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o X) tptp.bot_bot_set_o) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) tptp.bot_bot_set_nat) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X) tptp.bot_bot_set_int) X)))
% 8.20/8.61 (assert (forall ((P3 tptp.produc859450856879609959at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat P3) tptp.id_Pro2258643101195443293at_nat) (not (forall ((X3 tptp.product_prod_nat_nat)) (not (= P3 (@ (@ tptp.produc6161850002892822231at_nat X3) X3))))))))
% 8.20/8.61 (assert (forall ((P3 tptp.produc4166570645942440679at_nat)) (=> (@ (@ tptp.member6689249552917799696at_nat P3) tptp.id_mul2649389997224486051at_nat) (not (forall ((X3 tptp.multis2468970476368604999at_nat)) (not (= P3 (@ (@ tptp.produc4348348721325984599at_nat X3) X3))))))))
% 8.20/8.61 (assert (forall ((P3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat P3) tptp.id_nat2) (not (forall ((X3 tptp.nat)) (not (= P3 (@ (@ tptp.product_Pair_nat_nat X3) X3))))))))
% 8.20/8.61 (assert (forall ((P3 tptp.product_prod_int_int)) (=> (@ (@ tptp.member5262025264175285858nt_int P3) tptp.id_int2) (not (forall ((X3 tptp.int)) (not (= P3 (@ (@ tptp.product_Pair_int_int X3) X3))))))))
% 8.20/8.61 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat A) B)) tptp.id_Pro2258643101195443293at_nat) (= A B))))
% 8.20/8.61 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat A) B)) tptp.id_mul2649389997224486051at_nat) (= A B))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) tptp.id_nat2) (= A B))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A) B)) tptp.id_int2) (= A B))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int)) (=> (forall ((X3 tptp.set_Pr958786334691620121nt_int)) (not (@ (@ tptp.member2340774599025711042nt_int X3) A4))) (@ (@ tptp.ord_le483042692224249369nt_int A4) tptp.bot_bo1488462491386950373nt_int))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X3) A4))) (@ (@ tptp.ord_le6893508408891458716et_nat A4) tptp.bot_bot_set_set_nat))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat X3) A4))) (@ (@ tptp.ord_le3146513528884898305at_nat A4) tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_o)) (=> (forall ((X3 Bool)) (not (@ (@ tptp.member_o X3) A4))) (@ (@ tptp.ord_less_eq_set_o A4) tptp.bot_bot_set_o))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (not (@ (@ tptp.member_nat X3) A4))) (@ (@ tptp.ord_less_eq_set_nat A4) tptp.bot_bot_set_nat))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int)) (=> (forall ((X3 tptp.int)) (not (@ (@ tptp.member_int X3) A4))) (@ (@ tptp.ord_less_eq_set_int A4) tptp.bot_bot_set_int))))
% 8.20/8.61 (assert (forall ((B5 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat tptp.bot_bo8422036546324065075at_nat) B5) B5)))
% 8.20/8.61 (assert (forall ((B5 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) B5) B5)))
% 8.20/8.61 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat) B5) B5)))
% 8.20/8.61 (assert (forall ((B5 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) B5) B5)))
% 8.20/8.61 (assert (forall ((B5 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) B5) B5)))
% 8.20/8.61 (assert (forall ((B5 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) B5) B5)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A4) tptp.bot_bo8422036546324065075at_nat) A4)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A4) tptp.bot_bo228742789529271731at_nat) A4)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat A4) tptp.bot_bo2099793752762293965at_nat) A4)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o A4) tptp.bot_bot_set_o) A4)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A4) tptp.bot_bot_set_nat) A4)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A4) tptp.bot_bot_set_int) A4)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.ord_le7866589430770878221at_nat A4) tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_o)) (not (@ (@ tptp.ord_less_set_o A4) tptp.bot_bot_set_o))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A4) tptp.bot_bot_set_nat))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A4) tptp.bot_bot_set_int))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (H tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.rep_assn P2))) (= (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H) tptp.bot_bot_set_nat)) (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H5) tptp.bot_bot_set_nat))))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.product_unit Bool)) (X tptp.product_unit) (H tptp.heap_e7401611519738050253t_unit)) (=> (@ P2 X) (= (@ (@ tptp.heap_T875086893843062177t_unit (@ (@ tptp.heap_T4208721593536448476t_unit P2) X)) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat X) (@ (@ tptp.produc584006145561248582it_nat H) tptp.one_one_nat)))))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.b Bool)) (X tptp.b) (H tptp.heap_e7401611519738050253t_unit)) (=> (@ P2 X) (= (@ (@ tptp.heap_Time_execute_b (@ (@ tptp.heap_Time_assert_b P2) X)) H) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat X) (@ (@ tptp.produc584006145561248582it_nat H) tptp.one_one_nat)))))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.a Bool)) (X tptp.a) (H tptp.heap_e7401611519738050253t_unit)) (=> (@ P2 X) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_assert_a P2) X)) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat X) (@ (@ tptp.produc584006145561248582it_nat H) tptp.one_one_nat)))))))
% 8.20/8.61 (assert (= (@ tptp.dflt_N6592383573632408824at_nat tptp.bot_bo2099793752762293965at_nat) tptp.none_s625347054029921090at_nat))
% 8.20/8.61 (assert (= (@ tptp.dflt_None_set_o tptp.bot_bot_set_o) tptp.none_set_o))
% 8.20/8.61 (assert (= (@ tptp.dflt_None_set_nat tptp.bot_bot_set_nat) tptp.none_set_nat))
% 8.20/8.61 (assert (= (@ tptp.dflt_None_set_int tptp.bot_bot_set_int) tptp.none_set_int))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat)) (=> (not (= S tptp.bot_bo2099793752762293965at_nat)) (= (@ tptp.dflt_N6592383573632408824at_nat S) (@ tptp.some_s147305329494351046at_nat S)))))
% 8.20/8.61 (assert (forall ((S tptp.set_o)) (=> (not (= S tptp.bot_bot_set_o)) (= (@ tptp.dflt_None_set_o S) (@ tptp.some_set_o S)))))
% 8.20/8.61 (assert (forall ((S tptp.set_nat)) (=> (not (= S tptp.bot_bot_set_nat)) (= (@ tptp.dflt_None_set_nat S) (@ tptp.some_set_nat S)))))
% 8.20/8.61 (assert (forall ((S tptp.set_int)) (=> (not (= S tptp.bot_bot_set_int)) (= (@ tptp.dflt_None_set_int S) (@ tptp.some_set_int S)))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.the_de3668382347305825784at_nat tptp.bot_bo2099793752762293965at_nat) (@ tptp.dflt_N6592383573632408824at_nat X)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.the_default_set_o tptp.bot_bot_set_o) (@ tptp.dflt_None_set_o X)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.the_default_set_nat tptp.bot_bot_set_nat) (@ tptp.dflt_None_set_nat X)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.the_default_set_int tptp.bot_bot_set_int) (@ tptp.dflt_None_set_int X)) X)))
% 8.20/8.61 (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))
% 8.20/8.61 (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))
% 8.20/8.61 (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))
% 8.20/8.61 (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))
% 8.20/8.61 (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))
% 8.20/8.61 (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))
% 8.20/8.61 (assert (forall ((C2 tptp.heap_Time_Heap_a) (Q2 (-> tptp.a tptp.assn))) (@ (@ (@ tptp.hoare_hoare_triple_a tptp.bot_bot_assn) C2) Q2)))
% 8.20/8.61 (assert (forall ((C2 tptp.heap_Time_Heap_b) (Q2 (-> tptp.b tptp.assn))) (@ (@ (@ tptp.hoare_hoare_triple_b tptp.bot_bot_assn) C2) Q2)))
% 8.20/8.61 (assert (forall ((C2 tptp.heap_T5738788834812785303t_unit) (Q2 (-> tptp.product_unit tptp.assn))) (@ (@ (@ tptp.hoare_8945653483474564448t_unit tptp.bot_bot_assn) C2) Q2)))
% 8.20/8.61 (assert (@ tptp.bijective_nat_nat tptp.bot_bo2099793752762293965at_nat))
% 8.20/8.61 (assert (= (@ tptp.set_to_map_nat_nat tptp.bot_bo2099793752762293965at_nat) (lambda ((X4 tptp.nat)) tptp.none_nat)))
% 8.20/8.61 (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))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (= tptp.bot_bot_int_int_o (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y4)) tptp.bot_bo1796632182523588997nt_int))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (= tptp.bot_bo5216386038637673661_nat_o (lambda ((X4 tptp.b) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat X4) Y4)) tptp.bot_bo8983147464310796868it_nat))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat tptp.bot_bot_list_nat_o)))
% 8.20/8.61 (assert (= tptp.bot_bo1488462491386950373nt_int (@ tptp.collec5210948495886036740nt_int tptp.bot_bo2686080419298087992_int_o)))
% 8.20/8.61 (assert (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat tptp.bot_bot_set_nat_o)))
% 8.20/8.61 (assert (= tptp.bot_bo2099793752762293965at_nat (@ tptp.collec3392354462482085612at_nat tptp.bot_bo482883023278783056_nat_o)))
% 8.20/8.61 (assert (= tptp.bot_bot_set_o (@ tptp.collect_o tptp.bot_bot_o_o)))
% 8.20/8.61 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat tptp.bot_bot_nat_o)))
% 8.20/8.61 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int tptp.bot_bot_int_o)))
% 8.20/8.61 (assert (= tptp.bot_bot_option_num tptp.none_num))
% 8.20/8.61 (assert (forall ((H tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn tptp.bot_bot_assn) H))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (= A4 tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5))))
% 8.20/8.61 (assert (forall ((S2 tptp.list_char) (Q2 (-> tptp.a tptp.assn))) (@ (@ (@ tptp.hoare_hoare_triple_a tptp.bot_bot_assn) (@ tptp.heap_Time_raise_a S2)) Q2)))
% 8.20/8.61 (assert (forall ((S2 tptp.list_char) (Q2 (-> tptp.b tptp.assn))) (@ (@ (@ tptp.hoare_hoare_triple_b tptp.bot_bot_assn) (@ tptp.heap_Time_raise_b S2)) Q2)))
% 8.20/8.61 (assert (forall ((S2 tptp.list_char) (Q2 (-> tptp.product_unit tptp.assn))) (@ (@ (@ tptp.hoare_8945653483474564448t_unit tptp.bot_bot_assn) (@ tptp.heap_T2927564422264180874t_unit S2)) Q2)))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (S2 tptp.list_char) (Q2 (-> tptp.a tptp.assn))) (= (@ (@ (@ tptp.hoare_hoare_triple_a P2) (@ tptp.heap_Time_raise_a S2)) Q2) (= P2 tptp.bot_bot_assn))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (S2 tptp.list_char) (Q2 (-> tptp.b tptp.assn))) (= (@ (@ (@ tptp.hoare_hoare_triple_b P2) (@ tptp.heap_Time_raise_b S2)) Q2) (= P2 tptp.bot_bot_assn))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (S2 tptp.list_char) (Q2 (-> tptp.product_unit tptp.assn))) (= (@ (@ (@ tptp.hoare_8945653483474564448t_unit P2) (@ tptp.heap_T2927564422264180874t_unit S2)) Q2) (= P2 tptp.bot_bot_assn))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (= tptp.dflt_N6592383573632408824at_nat (lambda ((S4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ (@ tptp.if_opt7704869406773131885at_nat (= S4 tptp.bot_bo2099793752762293965at_nat)) tptp.none_s625347054029921090at_nat) (@ tptp.some_s147305329494351046at_nat S4)))))
% 8.20/8.61 (assert (= tptp.dflt_None_set_o (lambda ((S4 tptp.set_o)) (@ (@ (@ tptp.if_option_set_o (= S4 tptp.bot_bot_set_o)) tptp.none_set_o) (@ tptp.some_set_o S4)))))
% 8.20/8.61 (assert (= tptp.dflt_None_set_nat (lambda ((S4 tptp.set_nat)) (@ (@ (@ tptp.if_option_set_nat (= S4 tptp.bot_bot_set_nat)) tptp.none_set_nat) (@ tptp.some_set_nat S4)))))
% 8.20/8.61 (assert (= tptp.dflt_None_set_int (lambda ((S4 tptp.set_int)) (@ (@ (@ tptp.if_option_set_int (= S4 tptp.bot_bot_set_int)) tptp.none_set_int) (@ tptp.some_set_int S4)))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.rel_of_nat_nat (lambda ((X4 tptp.nat)) tptp.none_nat)) P2) tptp.bot_bo2099793752762293965at_nat)))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (= tptp.heap_Time_tap_b (lambda ((F3 (-> tptp.heap_e7401611519738050253t_unit tptp.b))) (@ tptp.heap_Time_Heap_b2 (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat (@ F3 H6)) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.one_one_nat))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.b)) (H tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.heap_Time_execute_b (@ tptp.heap_Time_tap_b F)) H) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat (@ F H)) (@ (@ tptp.produc584006145561248582it_nat H) tptp.one_one_nat))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A) (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer))))
% 8.20/8.61 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 8.20/8.61 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 8.20/8.61 (assert (not (= tptp.bot_bot_assn tptp.one_one_assn)))
% 8.20/8.61 (assert (forall ((Q2 (-> tptp.a tptp.assn)) (X tptp.a)) (@ (@ (@ tptp.hoare_hoare_triple_a (@ Q2 X)) (@ tptp.heap_Time_return_a X)) Q2)))
% 8.20/8.61 (assert (forall ((Q2 (-> tptp.b tptp.assn)) (X tptp.b)) (@ (@ (@ tptp.hoare_hoare_triple_b (@ Q2 X)) (@ tptp.heap_Time_return_b X)) Q2)))
% 8.20/8.61 (assert (forall ((Q2 (-> tptp.product_unit tptp.assn)) (X tptp.product_unit)) (@ (@ (@ tptp.hoare_8945653483474564448t_unit (@ Q2 X)) (@ tptp.heap_T7507251653302230130t_unit X)) Q2)))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (@ (@ (@ tptp.hoare_8945653483474564448t_unit tptp.one_one_assn) (@ tptp.heap_Time_wait N2)) (lambda ((Uu2 tptp.product_unit)) tptp.one_one_assn))))
% 8.20/8.61 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.nat Bool)) (X tptp.nat) (M6 tptp.nat)) (=> (@ P2 X) (=> (forall ((X3 tptp.nat)) (=> (@ P2 X3) (@ (@ tptp.ord_less_eq_nat X3) M6))) (not (forall ((M5 tptp.nat)) (=> (@ P2 M5) (not (forall ((X6 tptp.nat)) (=> (@ P2 X6) (@ (@ tptp.ord_less_eq_nat X6) M5)))))))))))
% 8.20/8.61 (assert (forall ((H tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.rep_assn tptp.one_one_assn) (@ (@ tptp.produc7507926704131184380et_nat H) tptp.bot_bot_set_nat))))
% 8.20/8.61 (assert (= tptp.heap_Time_return_b (lambda ((X4 tptp.b)) (@ tptp.heap_Time_heap_b (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc4082563078715348724it_nat X4) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.one_one_nat)))))))
% 8.20/8.61 (assert (= tptp.heap_Time_return_a (lambda ((X4 tptp.a)) (@ tptp.heap_Time_heap_a (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc9178034014595674355it_nat X4) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.one_one_nat)))))))
% 8.20/8.61 (assert (forall ((R2 tptp.ref_Product_unit) (H tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.heap_T875086893843062177t_unit (@ tptp.ref_lo7930775386976318366t_unit R2)) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat (@ (@ tptp.ref_get_Product_unit H) R2)) (@ (@ tptp.produc584006145561248582it_nat H) tptp.one_one_nat))))))
% 8.20/8.61 (assert (forall ((X tptp.product_unit)) (= (@ tptp.heap_T875086893843062177t_unit (@ tptp.heap_T7507251653302230130t_unit X)) (@ (@ tptp.comp_P3118722334806803912t_unit tptp.some_P1914260805536162275it_nat) (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc7133225469290080770it_nat X) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.one_one_nat)))))))
% 8.20/8.61 (assert (forall ((X tptp.b)) (= (@ tptp.heap_Time_execute_b (@ tptp.heap_Time_return_b X)) (@ (@ tptp.comp_P6401406225962756324t_unit tptp.some_P2818173045054083285it_nat) (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc4082563078715348724it_nat X) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.one_one_nat)))))))
% 8.20/8.61 (assert (forall ((X tptp.a)) (= (@ tptp.heap_Time_execute_a (@ tptp.heap_Time_return_a X)) (@ (@ tptp.comp_P8552900652980440422t_unit tptp.some_P7913643980934408916it_nat) (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc9178034014595674355it_nat X) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.one_one_nat)))))))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 8.20/8.61 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 8.20/8.61 (assert (= (@ tptp.map_to_set_nat_nat (lambda ((X4 tptp.nat)) tptp.none_nat)) tptp.bot_bo2099793752762293965at_nat))
% 8.20/8.61 (assert (forall ((M6 (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (N7 (-> tptp.code_integer tptp.code_integer)) (H (-> tptp.code_integer tptp.code_integer)) (F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (let ((_let_1 (@ tptp.comp_C1593894019821074884nteger F))) (=> (= (@ M6 (@ G X)) (@ N7 (@ H X))) (= (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ _let_1 M6)) G) X) (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ _let_1 N7)) H) X))))))
% 8.20/8.61 (assert (forall ((M6 (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (N7 (-> (-> tptp.code_integer tptp.code_integer) tptp.code_integer)) (H (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (=> (= (@ M6 (@ G X)) (@ N7 (@ H X))) (= (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C1593894019821074884nteger F) M6)) G) X) (@ (@ (@ tptp.comp_C8797469213163452608nteger (@ (@ tptp.comp_C95226695241045696nteger F) N7)) H) X)))))
% 8.20/8.61 (assert (forall ((M6 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (N7 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (H (-> tptp.code_integer tptp.code_integer)) (F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (let ((_let_1 (@ tptp.comp_C8797469213163452608nteger F))) (=> (= (@ M6 (@ G X)) (@ N7 (@ H X))) (= (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ _let_1 M6)) G) X) (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ _let_1 N7)) H) X))))))
% 8.20/8.61 (assert (forall ((M6 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (N7 (-> (-> tptp.code_integer tptp.code_integer) tptp.code_integer tptp.code_integer)) (H (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (=> (= (@ M6 (@ G X)) (@ N7 (@ H X))) (= (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger F) M6)) G) X) (@ (@ (@ tptp.comp_C8797469213163452608nteger (@ (@ tptp.comp_C3983183376822107068nteger F) N7)) H) X)))))
% 8.20/8.61 (assert (forall ((M6 (-> (-> tptp.code_integer tptp.code_integer) tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (N7 (-> tptp.code_integer tptp.code_integer)) (H (-> tptp.code_integer tptp.code_integer)) (F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (=> (= (@ M6 (@ G X)) (@ N7 (@ H X))) (= (@ (@ (@ tptp.comp_C8797469213163452608nteger (@ (@ tptp.comp_C95226695241045696nteger F) M6)) G) X) (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C1593894019821074884nteger F) N7)) H) X)))))
% 8.20/8.61 (assert (forall ((M6 (-> (-> tptp.code_integer tptp.code_integer) tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (N7 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (H (-> tptp.code_integer tptp.code_integer)) (F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (=> (= (@ M6 (@ G X)) (@ N7 (@ H X))) (= (@ (@ (@ tptp.comp_C8797469213163452608nteger (@ (@ tptp.comp_C3983183376822107068nteger F) M6)) G) X) (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger F) N7)) H) X)))))
% 8.20/8.61 (assert (forall ((M6 (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (X tptp.int) (N7 (-> tptp.int tptp.int)) (H (-> tptp.int tptp.int)) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.comp_int_nat_int F))) (=> (= (@ M6 (@ G X)) (@ N7 (@ H X))) (= (@ (@ (@ tptp.comp_int_nat_int (@ _let_1 M6)) G) X) (@ (@ (@ tptp.comp_int_nat_int (@ _let_1 N7)) H) X))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (Y (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (F (-> tptp.code_integer tptp.code_integer))) (=> (= X Y) (= (@ (@ tptp.comp_C1593894019821074884nteger X) F) (@ (@ tptp.comp_C1593894019821074884nteger Y) F)))))
% 8.20/8.61 (assert (forall ((X (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (Y (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (F (-> tptp.code_integer tptp.code_integer tptp.code_integer))) (=> (= X Y) (= (@ (@ tptp.comp_C8797469213163452608nteger X) F) (@ (@ tptp.comp_C8797469213163452608nteger Y) F)))))
% 8.20/8.61 (assert (forall ((X (-> tptp.int tptp.nat)) (Y (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.int))) (=> (= X Y) (= (@ (@ tptp.comp_int_nat_int X) F) (@ (@ tptp.comp_int_nat_int Y) F)))))
% 8.20/8.61 (assert (forall ((X (-> tptp.code_integer tptp.code_integer)) (Y (-> tptp.code_integer tptp.code_integer)) (F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (let ((_let_1 (@ tptp.comp_C1593894019821074884nteger F))) (=> (= X Y) (= (@ _let_1 X) (@ _let_1 Y))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (Y (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (let ((_let_1 (@ tptp.comp_C8797469213163452608nteger F))) (=> (= X Y) (= (@ _let_1 X) (@ _let_1 Y))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int)) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.comp_int_nat_int F))) (=> (= X Y) (= (@ _let_1 X) (@ _let_1 Y))))))
% 8.20/8.61 (assert (forall ((F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer)) (Fg (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (= (= (@ (@ tptp.comp_C1593894019821074884nteger F) G) Fg) (forall ((X4 tptp.code_integer)) (= (@ F (@ G X4)) (@ Fg X4))))))
% 8.20/8.61 (assert (forall ((F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (Fg (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (= (= (@ (@ tptp.comp_C8797469213163452608nteger F) G) Fg) (forall ((X4 tptp.code_integer)) (= (@ F (@ G X4)) (@ Fg X4))))))
% 8.20/8.61 (assert (forall ((F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.int)) (Fg (-> tptp.int tptp.nat))) (= (= (@ (@ tptp.comp_int_nat_int F) G) Fg) (forall ((X4 tptp.int)) (= (@ F (@ G X4)) (@ Fg X4))))))
% 8.20/8.61 (assert (forall ((F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (F4 (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G2 (-> tptp.code_integer tptp.code_integer)) (X10 tptp.code_integer)) (=> (= (@ F (@ G X)) (@ F4 (@ G2 X10))) (= (@ (@ (@ tptp.comp_C1593894019821074884nteger F) G) X) (@ (@ (@ tptp.comp_C1593894019821074884nteger F4) G2) X10)))))
% 8.20/8.61 (assert (forall ((F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (F4 (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G2 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (X10 tptp.code_integer)) (=> (= (@ F (@ G X)) (@ F4 (@ G2 X10))) (= (@ (@ (@ tptp.comp_C1593894019821074884nteger F) G) X) (@ (@ (@ tptp.comp_C8797469213163452608nteger F4) G2) X10)))))
% 8.20/8.61 (assert (forall ((F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (F4 (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G2 (-> tptp.code_integer tptp.code_integer)) (X10 tptp.code_integer)) (=> (= (@ F (@ G X)) (@ F4 (@ G2 X10))) (= (@ (@ (@ tptp.comp_C8797469213163452608nteger F) G) X) (@ (@ (@ tptp.comp_C1593894019821074884nteger F4) G2) X10)))))
% 8.20/8.61 (assert (forall ((F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (F4 (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G2 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (X10 tptp.code_integer)) (=> (= (@ F (@ G X)) (@ F4 (@ G2 X10))) (= (@ (@ (@ tptp.comp_C8797469213163452608nteger F) G) X) (@ (@ (@ tptp.comp_C8797469213163452608nteger F4) G2) X10)))))
% 8.20/8.61 (assert (forall ((F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.int)) (X tptp.int) (F4 (-> tptp.int tptp.nat)) (G2 (-> tptp.int tptp.int)) (X10 tptp.int)) (=> (= (@ F (@ G X)) (@ F4 (@ G2 X10))) (= (@ (@ (@ tptp.comp_int_nat_int F) G) X) (@ (@ (@ tptp.comp_int_nat_int F4) G2) X10)))))
% 8.20/8.61 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat))) (= (@ tptp.heap_T875086893843062177t_unit (@ tptp.heap_T6927113302350381334t_unit F)) (@ (@ tptp.comp_P3118722334806803912t_unit tptp.some_P1914260805536162275it_nat) F))))
% 8.20/8.61 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat))) (= (@ tptp.heap_Time_execute_b (@ tptp.heap_Time_heap_b F)) (@ (@ tptp.comp_P6401406225962756324t_unit tptp.some_P2818173045054083285it_nat) F))))
% 8.20/8.61 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat))) (= (@ tptp.heap_Time_execute_a (@ tptp.heap_Time_heap_a F)) (@ (@ tptp.comp_P8552900652980440422t_unit tptp.some_P7913643980934408916it_nat) F))))
% 8.20/8.61 (assert (= tptp.heap_Time_heap_b (lambda ((F3 (-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat))) (@ tptp.heap_Time_Heap_b2 (@ (@ tptp.comp_P6401406225962756324t_unit tptp.some_P2818173045054083285it_nat) F3)))))
% 8.20/8.61 (assert (= tptp.heap_Time_heap_a (lambda ((F3 (-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat))) (@ tptp.heap_Time_Heap_a2 (@ (@ tptp.comp_P8552900652980440422t_unit tptp.some_P7913643980934408916it_nat) F3)))))
% 8.20/8.61 (assert (= tptp.heap_T6927113302350381334t_unit (lambda ((F3 (-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat))) (@ tptp.heap_T6183433275982383450t_unit (@ (@ tptp.comp_P3118722334806803912t_unit tptp.some_P1914260805536162275it_nat) F3)))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_int B) C2))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat) (Acc tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat F))) (let ((_let_2 (@ (@ (@ _let_1 A) B) Acc))) (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) Acc)))) (and (=> _let_3 (= _let_2 Acc)) (=> (not _let_3) (= _let_2 (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) B) (@ (@ F A) Acc)))))))))))
% 8.20/8.61 (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))))))))))
% 8.20/8.61 (assert (= tptp.is_emp1662574758705540307at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat)) (= A6 tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.61 (assert (= tptp.is_empty_o (lambda ((A6 tptp.set_o)) (= A6 tptp.bot_bot_set_o))))
% 8.20/8.61 (assert (= tptp.is_empty_nat (lambda ((A6 tptp.set_nat)) (= A6 tptp.bot_bot_set_nat))))
% 8.20/8.61 (assert (= tptp.is_empty_int (lambda ((A6 tptp.set_int)) (= A6 tptp.bot_bot_set_int))))
% 8.20/8.61 (assert (= (@ tptp.heap_T4436805183663264329t_unit tptp.bot_bo8105976889876132193t_unit) (@ tptp.heap_T6183433275982383450t_unit (lambda ((X4 tptp.heap_e7401611519738050253t_unit)) tptp.none_P9117596204409417319it_nat))))
% 8.20/8.61 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F3 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B4 tptp.nat) (Acc2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B4) A5)) Acc2) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F3) (@ (@ tptp.plus_plus_nat A5) tptp.one_one_nat)) B4) (@ (@ F3 A5) Acc2))))))
% 8.20/8.61 (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))))))))))
% 8.20/8.61 (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)))
% 8.20/8.61 (assert (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.pure_assn P2) (@ tptp.pure_assn Q2)) (= P2 Q2))))
% 8.20/8.61 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.sup_sup_assn (@ tptp.pure_assn A)) (@ tptp.pure_assn B)) (@ tptp.pure_assn (or A B)))))
% 8.20/8.61 (assert (forall ((P2 Bool)) (= (= (@ tptp.pure_assn P2) tptp.one_one_assn) P2)))
% 8.20/8.61 (assert (= (@ tptp.pure_assn true) tptp.one_one_assn))
% 8.20/8.61 (assert (forall ((P2 Bool)) (= (= (@ tptp.pure_assn P2) tptp.bot_bot_assn) (not P2))))
% 8.20/8.61 (assert (= (@ tptp.pure_assn false) tptp.bot_bot_assn))
% 8.20/8.61 (assert (forall ((B Bool) (F tptp.heap_Time_Heap_a) (Q2 (-> tptp.a tptp.assn))) (= (@ (@ (@ tptp.hoare_hoare_triple_a (@ tptp.pure_assn B)) F) Q2) (=> B (@ (@ (@ tptp.hoare_hoare_triple_a tptp.one_one_assn) F) Q2)))))
% 8.20/8.61 (assert (forall ((B Bool) (F tptp.heap_Time_Heap_b) (Q2 (-> tptp.b tptp.assn))) (= (@ (@ (@ tptp.hoare_hoare_triple_b (@ tptp.pure_assn B)) F) Q2) (=> B (@ (@ (@ tptp.hoare_hoare_triple_b tptp.one_one_assn) F) Q2)))))
% 8.20/8.61 (assert (forall ((B Bool) (F tptp.heap_T5738788834812785303t_unit) (Q2 (-> tptp.product_unit tptp.assn))) (= (@ (@ (@ tptp.hoare_8945653483474564448t_unit (@ tptp.pure_assn B)) F) Q2) (=> B (@ (@ (@ tptp.hoare_8945653483474564448t_unit tptp.one_one_assn) F) Q2)))))
% 8.20/8.61 (assert (forall ((B Bool) (F tptp.heap_Time_Heap_a) (Q2 (-> tptp.a tptp.assn))) (=> (=> B (@ (@ (@ tptp.hoare_hoare_triple_a tptp.one_one_assn) F) Q2)) (@ (@ (@ tptp.hoare_hoare_triple_a (@ tptp.pure_assn B)) F) Q2))))
% 8.20/8.61 (assert (forall ((B Bool) (F tptp.heap_Time_Heap_b) (Q2 (-> tptp.b tptp.assn))) (=> (=> B (@ (@ (@ tptp.hoare_hoare_triple_b tptp.one_one_assn) F) Q2)) (@ (@ (@ tptp.hoare_hoare_triple_b (@ tptp.pure_assn B)) F) Q2))))
% 8.20/8.61 (assert (forall ((B Bool) (F tptp.heap_T5738788834812785303t_unit) (Q2 (-> tptp.product_unit tptp.assn))) (=> (=> B (@ (@ (@ tptp.hoare_8945653483474564448t_unit tptp.one_one_assn) F) Q2)) (@ (@ (@ tptp.hoare_8945653483474564448t_unit (@ tptp.pure_assn B)) F) Q2))))
% 8.20/8.61 (assert (forall ((P3 tptp.ref_Product_unit) (X tptp.product_unit)) (@ (@ (@ tptp.hoare_8945653483474564448t_unit (@ (@ tptp.sngr_a5825115052027484668t_unit P3) X)) (@ tptp.ref_lo7930775386976318366t_unit P3)) (lambda ((R5 tptp.product_unit)) (@ (@ tptp.times_times_assn (@ (@ tptp.sngr_a5825115052027484668t_unit P3) X)) (@ tptp.pure_assn (= R5 X)))))))
% 8.20/8.61 (assert (forall ((C2 (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (F (-> tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.comp_C1593894019821074884nteger (lambda ((X4 tptp.code_integer) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ C2 __flatten_var_0))) F) (lambda ((X4 tptp.code_integer) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ C2 __flatten_var_0)))))
% 8.20/8.61 (assert (forall ((C2 (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (F (-> tptp.code_integer tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.comp_C8797469213163452608nteger (lambda ((X4 (-> tptp.code_integer tptp.code_integer)) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ C2 __flatten_var_0))) F) (lambda ((X4 tptp.code_integer) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ C2 __flatten_var_0)))))
% 8.20/8.61 (assert (forall ((C2 tptp.nat) (F (-> tptp.int tptp.int))) (= (@ (@ tptp.comp_int_nat_int (lambda ((X4 tptp.int)) C2)) F) (lambda ((X4 tptp.int)) C2))))
% 8.20/8.61 (assert (forall ((X tptp.product_unit)) (= (@ tptp.heap_T875086893843062177t_unit (@ tptp.heap_T4284346855313245393t_unit X)) (@ (@ tptp.comp_P3118722334806803912t_unit tptp.some_P1914260805536162275it_nat) (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc7133225469290080770it_nat X) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.zero_zero_nat)))))))
% 8.20/8.61 (assert (forall ((X tptp.b)) (= (@ tptp.heap_Time_execute_b (@ tptp.heap_Time_ureturn_b X)) (@ (@ tptp.comp_P6401406225962756324t_unit tptp.some_P2818173045054083285it_nat) (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc4082563078715348724it_nat X) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.zero_zero_nat)))))))
% 8.20/8.61 (assert (forall ((X tptp.a)) (= (@ tptp.heap_Time_execute_a (@ tptp.heap_Time_ureturn_a X)) (@ (@ tptp.comp_P8552900652980440422t_unit tptp.some_P7913643980934408916it_nat) (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc9178034014595674355it_nat X) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.zero_zero_nat)))))))
% 8.20/8.61 (assert (forall ((F (-> tptp.int tptp.nat)) (X tptp.int) (Y tptp.int) (R3 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)))) (=> (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y)) (=> (@ _let_1 R3) (@ _let_1 (@ (@ tptp.mlex_prod_int F) R3)))))))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int) (F (-> tptp.int tptp.nat)) (R3 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)))) (let ((_let_2 (@ F Y))) (let ((_let_3 (@ F X))) (= (@ _let_1 (@ (@ tptp.mlex_prod_int F) R3)) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 R3)))))))))
% 8.20/8.61 (assert (forall ((F (-> tptp.int tptp.nat)) (X tptp.int) (Y tptp.int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ tptp.mlex_prod_int F) R3)))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (B Bool)) (let ((_let_1 (@ tptp.entails P2))) (= (@ _let_1 (@ tptp.pure_assn B)) (and (forall ((H6 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H6) B)) (@ _let_1 tptp.one_one_assn))))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) Y) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (= Y (not (and (= As2 tptp.bot_bot_set_nat) X)))))))))
% 8.20/8.61 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (not (and (= As2 tptp.bot_bot_set_nat) X))))))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) A) A)))
% 8.20/8.61 (assert (forall ((A tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.plus_p7104986032573967614at_nat tptp.zero_z1048942125864253310at_nat) A) A)))
% 8.20/8.61 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 8.20/8.61 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (= B tptp.zero_z3403309356797280102nteger))))
% 8.20/8.61 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat)) (= (= A (@ (@ tptp.plus_p7104986032573967614at_nat A) B)) (= B tptp.zero_z1048942125864253310at_nat))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ (@ tptp.plus_p5714425477246183910nteger B) A)) (= B tptp.zero_z3403309356797280102nteger))))
% 8.20/8.61 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat)) (= (= A (@ (@ tptp.plus_p7104986032573967614at_nat B) A)) (= B tptp.zero_z1048942125864253310at_nat))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) A) (= B tptp.zero_z3403309356797280102nteger))))
% 8.20/8.61 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat)) (= (= (@ (@ tptp.plus_p7104986032573967614at_nat A) B) A) (= B tptp.zero_z1048942125864253310at_nat))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 8.20/8.61 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger B) A) A) (= B tptp.zero_z3403309356797280102nteger))))
% 8.20/8.61 (assert (forall ((B tptp.multis2468970476368604999at_nat) (A tptp.multis2468970476368604999at_nat)) (= (= (@ (@ tptp.plus_p7104986032573967614at_nat B) A) A) (= B tptp.zero_z1048942125864253310at_nat))))
% 8.20/8.61 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 8.20/8.61 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ (@ tptp.plus_p5714425477246183910nteger A) A)) (= A tptp.zero_z3403309356797280102nteger))))
% 8.20/8.61 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 8.20/8.61 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 8.20/8.61 (assert (forall ((A tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.plus_p7104986032573967614at_nat A) tptp.zero_z1048942125864253310at_nat) A)))
% 8.20/8.61 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 8.20/8.61 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 8.20/8.61 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.times_times_assn (@ tptp.pure_assn A)) (@ tptp.pure_assn B)) (@ tptp.pure_assn (and A B)))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.bot_bot_assn) P2) tptp.bot_bot_assn)))
% 8.20/8.61 (assert (forall ((P2 tptp.assn)) (= (@ (@ tptp.times_times_assn P2) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) tptp.one_one_nat) (= N2 tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (B Bool) (H tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P2) (@ tptp.pure_assn B))) H) (and (@ (@ tptp.rep_assn P2) H) B))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (B Bool) (Q2 tptp.assn)) (= (@ (@ tptp.entails (@ (@ tptp.times_times_assn P2) (@ tptp.pure_assn B))) Q2) (=> B (@ (@ tptp.entails P2) Q2)))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (B Bool) (F tptp.heap_Time_Heap_a) (Q2 (-> tptp.a tptp.assn))) (= (@ (@ (@ tptp.hoare_hoare_triple_a (@ (@ tptp.times_times_assn P2) (@ tptp.pure_assn B))) F) Q2) (=> B (@ (@ (@ tptp.hoare_hoare_triple_a P2) F) Q2)))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (B Bool) (F tptp.heap_Time_Heap_b) (Q2 (-> tptp.b tptp.assn))) (= (@ (@ (@ tptp.hoare_hoare_triple_b (@ (@ tptp.times_times_assn P2) (@ tptp.pure_assn B))) F) Q2) (=> B (@ (@ (@ tptp.hoare_hoare_triple_b P2) F) Q2)))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (B Bool) (F tptp.heap_T5738788834812785303t_unit) (Q2 (-> tptp.product_unit tptp.assn))) (= (@ (@ (@ tptp.hoare_8945653483474564448t_unit (@ (@ tptp.times_times_assn P2) (@ tptp.pure_assn B))) F) Q2) (=> B (@ (@ (@ tptp.hoare_8945653483474564448t_unit P2) F) Q2)))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn)) (= (@ (@ tptp.entails P2) tptp.bot_bot_assn) (forall ((H6 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn P2) H6))))))
% 8.20/8.61 (assert (forall ((B Bool) (Q2 tptp.assn)) (= (@ (@ tptp.entails (@ tptp.pure_assn B)) Q2) (=> B (@ (@ tptp.entails tptp.one_one_assn) Q2)))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (Q2 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 P2) Q2)) _let_1) (and (@ (@ tptp.rep_assn P2) _let_1) (@ (@ tptp.rep_assn Q2) _let_1))))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (B Bool)) (let ((_let_1 (@ tptp.entails P2))) (= (@ _let_1 (@ (@ tptp.times_times_assn Q2) (@ tptp.pure_assn B))) (and (forall ((H6 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H6) B)) (@ _let_1 Q2))))))
% 8.20/8.61 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 8.20/8.61 (assert (= (lambda ((H6 tptp.code_integer)) tptp.zero_z3403309356797280102nteger) (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger)))
% 8.20/8.61 (assert (= (lambda ((H6 tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 8.20/8.61 (assert (= (lambda ((H6 tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 8.20/8.61 (assert (= (lambda ((H6 tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) D2) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 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 C2) D2) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 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 C2) D2) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 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 C2) D2) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D2)))))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) D2) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 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 C2) D2) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 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 C2) D2) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 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 C2) D2) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D2)))))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A) A))))
% 8.20/8.61 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 8.20/8.61 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) (@ (@ tptp.times_3573771949741848930nteger B) C2))))))
% 8.20/8.61 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))))
% 8.20/8.61 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) (@ (@ tptp.times_3573771949741848930nteger B) C2))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((A4 tptp.assn) (B5 tptp.assn)) (=> (@ (@ tptp.entails A4) B5) (=> (@ (@ tptp.entails B5) A4) (= A4 B5)))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn)) (@ (@ tptp.entails P2) P2)))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (R3 tptp.assn)) (let ((_let_1 (@ tptp.entails P2))) (=> (@ _let_1 Q2) (=> (@ (@ tptp.entails Q2) R3) (@ _let_1 R3))))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (P6 tptp.assn) (Q2 tptp.assn) (Q4 tptp.assn)) (=> (@ (@ tptp.entails P2) P6) (=> (@ (@ tptp.entails Q2) Q4) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P2) Q2)) (@ (@ tptp.times_times_assn P6) Q4))))))
% 8.20/8.61 (assert (= tptp.times_times_assn (lambda ((P5 tptp.assn) (Q3 tptp.assn)) (@ (@ tptp.times_times_assn Q3) P5))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (R3 tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn P2))) (= (@ (@ tptp.times_times_assn (@ _let_1 Q2)) R3) (@ _let_1 (@ (@ tptp.times_times_assn Q2) R3))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) A)) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.61 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 8.20/8.61 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le6747313008572928689nteger B) A))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat B) A))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int B) A))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (and (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 8.20/8.61 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) (@ (@ tptp.times_3573771949741848930nteger B) C2))))))
% 8.20/8.61 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))))
% 8.20/8.61 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) (@ (@ tptp.times_3573771949741848930nteger B) C2))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (C2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) (@ (@ tptp.times_3573771949741848930nteger B) C2)) (or (and (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (and (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger A) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) A)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A)))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (C2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) (@ (@ tptp.times_3573771949741848930nteger B) C2)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger A) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) A))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B))))))
% 8.20/8.61 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat A) B))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) D2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D2))))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D2))))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C2) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D2))))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (C2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) (@ (@ tptp.times_3573771949741848930nteger B) C2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger A) B)))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat A) B)))))
% 8.20/8.61 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B)))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) D2) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 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 C2) D2) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 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 C2) D2) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 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 C2) D2) (=> (@ _let_1 A) (=> (@ _let_1 C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D2)))))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (C2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) (@ (@ tptp.times_3573771949741848930nteger B) C2)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le3102999989581377725nteger B) A))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int B) A))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 8.20/8.61 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C2))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) B))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (C2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) (@ (@ tptp.times_3573771949741848930nteger B) C2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger A) B)))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 8.20/8.61 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) B)))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) D2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D2))))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D2))))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C2) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D2))))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) D2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C2) D2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) D2))))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) D2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) D2))))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C2) D2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) D2))))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) A)))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) A)))))
% 8.20/8.61 (assert (forall ((C2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C2)) A)))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) A)))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (E tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E)) C2))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (E tptp.nat) (B tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E)) C2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E)) C2))))
% 8.20/8.61 (assert (forall ((A tptp.int) (E tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E)) C2))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C2))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C2))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2)))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C2))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C2))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2)))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2)))))
% 8.20/8.61 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 8.20/8.61 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= N2 tptp.zero_zero_nat)))))
% 8.20/8.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) A) A)))
% 8.20/8.61 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 8.20/8.61 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 8.20/8.61 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 8.20/8.61 (assert (forall ((A tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.plus_p7104986032573967614at_nat A) tptp.zero_z1048942125864253310at_nat) A)))
% 8.20/8.61 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 8.20/8.61 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 8.20/8.61 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) A) A)))
% 8.20/8.61 (assert (forall ((A tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.plus_p7104986032573967614at_nat tptp.zero_z1048942125864253310at_nat) A) A)))
% 8.20/8.61 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 8.20/8.61 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 8.20/8.61 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 8.20/8.61 (assert (forall ((A tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.plus_p7104986032573967614at_nat A) tptp.zero_z1048942125864253310at_nat) A)))
% 8.20/8.61 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 8.20/8.61 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (H tptp.produc3658429121746597890et_nat) (Q2 tptp.assn)) (=> (@ (@ tptp.rep_assn P2) H) (=> (@ (@ tptp.entails P2) Q2) (@ (@ tptp.rep_assn Q2) H)))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.entails P2) Q2) (=> (@ (@ tptp.rep_assn P2) H) (@ (@ tptp.rep_assn Q2) H)))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn)) (=> (forall ((H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H2) (@ (@ tptp.rep_assn Q2) H2))) (@ (@ tptp.entails P2) Q2))))
% 8.20/8.61 (assert (= tptp.entails (lambda ((P5 tptp.assn) (Q3 tptp.assn)) (forall ((H6 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P5) H6) (@ (@ tptp.rep_assn Q3) H6))))))
% 8.20/8.61 (assert (forall ((A4 tptp.assn) (B5 tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A4) B5)) H) (exists ((H12 tptp.produc3658429121746597890et_nat) (H23 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.rep_assn A4) H12) (@ (@ tptp.rep_assn B5) H23))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (=> (not (@ P2 N5)) (exists ((M4 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N5) (not (@ P2 M4))))))) (@ P2 N2)))))
% 8.20/8.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N2) N2)))
% 8.20/8.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N2) M) (= N2 tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_Time_Heap_a) (Q2 (-> tptp.a tptp.assn)) (Q4 (-> tptp.a tptp.assn))) (let ((_let_1 (@ (@ tptp.hoare_hoare_triple_a P2) C2))) (=> (@ _let_1 Q2) (=> (forall ((X3 tptp.a)) (@ (@ tptp.entails (@ Q2 X3)) (@ Q4 X3))) (@ _let_1 Q4))))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_Time_Heap_b) (Q2 (-> tptp.b tptp.assn)) (Q4 (-> tptp.b tptp.assn))) (let ((_let_1 (@ (@ tptp.hoare_hoare_triple_b P2) C2))) (=> (@ _let_1 Q2) (=> (forall ((X3 tptp.b)) (@ (@ tptp.entails (@ Q2 X3)) (@ Q4 X3))) (@ _let_1 Q4))))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_T5738788834812785303t_unit) (Q2 (-> tptp.product_unit tptp.assn)) (Q4 (-> tptp.product_unit tptp.assn))) (let ((_let_1 (@ (@ tptp.hoare_8945653483474564448t_unit P2) C2))) (=> (@ _let_1 Q2) (=> (forall ((X3 tptp.product_unit)) (@ (@ tptp.entails (@ Q2 X3)) (@ Q4 X3))) (@ _let_1 Q4))))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (P6 tptp.assn) (Q2 (-> tptp.a tptp.assn)) (Q4 (-> tptp.a tptp.assn)) (C2 tptp.heap_Time_Heap_a)) (=> (@ (@ tptp.entails P2) P6) (=> (forall ((X3 tptp.a)) (@ (@ tptp.entails (@ Q2 X3)) (@ Q4 X3))) (=> (@ (@ (@ tptp.hoare_hoare_triple_a P6) C2) Q2) (@ (@ (@ tptp.hoare_hoare_triple_a P2) C2) Q4))))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (P6 tptp.assn) (Q2 (-> tptp.b tptp.assn)) (Q4 (-> tptp.b tptp.assn)) (C2 tptp.heap_Time_Heap_b)) (=> (@ (@ tptp.entails P2) P6) (=> (forall ((X3 tptp.b)) (@ (@ tptp.entails (@ Q2 X3)) (@ Q4 X3))) (=> (@ (@ (@ tptp.hoare_hoare_triple_b P6) C2) Q2) (@ (@ (@ tptp.hoare_hoare_triple_b P2) C2) Q4))))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (P6 tptp.assn) (Q2 (-> tptp.product_unit tptp.assn)) (Q4 (-> tptp.product_unit tptp.assn)) (C2 tptp.heap_T5738788834812785303t_unit)) (=> (@ (@ tptp.entails P2) P6) (=> (forall ((X3 tptp.product_unit)) (@ (@ tptp.entails (@ Q2 X3)) (@ Q4 X3))) (=> (@ (@ (@ tptp.hoare_8945653483474564448t_unit P6) C2) Q2) (@ (@ (@ tptp.hoare_8945653483474564448t_unit P2) C2) Q4))))))
% 8.20/8.61 (assert (forall ((A4 tptp.assn) (C4 tptp.assn) (B5 tptp.assn)) (=> (@ (@ tptp.entails A4) C4) (=> (@ (@ tptp.entails B5) C4) (@ (@ tptp.entails (@ (@ tptp.sup_sup_assn A4) B5)) C4)))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (R3 tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.sup_sup_assn P2) Q2)) R3) (@ (@ tptp.entails P2) R3))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (R3 tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.sup_sup_assn P2) Q2)) R3) (@ (@ tptp.entails Q2) R3))))
% 8.20/8.61 (assert (forall ((A4 tptp.assn) (B5 tptp.assn) (C4 tptp.assn)) (let ((_let_1 (@ tptp.entails A4))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.sup_sup_assn B5) C4))))))
% 8.20/8.61 (assert (forall ((A4 tptp.assn) (C4 tptp.assn) (B5 tptp.assn)) (let ((_let_1 (@ tptp.entails A4))) (=> (@ _let_1 C4) (@ _let_1 (@ (@ tptp.sup_sup_assn B5) C4))))))
% 8.20/8.61 (assert (forall ((A4 tptp.assn) (B5 tptp.assn)) (@ (@ tptp.entails A4) (@ (@ tptp.sup_sup_assn A4) B5))))
% 8.20/8.61 (assert (forall ((B5 tptp.assn) (A4 tptp.assn)) (@ (@ tptp.entails B5) (@ (@ tptp.sup_sup_assn A4) B5))))
% 8.20/8.61 (assert (forall ((A4 tptp.assn) (B5 tptp.assn) (C4 tptp.assn)) (= (@ (@ tptp.times_times_assn (@ (@ tptp.sup_sup_assn A4) B5)) C4) (@ (@ tptp.sup_sup_assn (@ (@ tptp.times_times_assn A4) C4)) (@ (@ tptp.times_times_assn B5) C4)))))
% 8.20/8.61 (assert (forall ((C4 tptp.assn) (A4 tptp.assn) (B5 tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn C4))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn A4) B5)) (@ (@ tptp.sup_sup_assn (@ _let_1 A4)) (@ _let_1 B5))))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) P2) P2)))
% 8.20/8.61 (assert (forall ((P2 tptp.assn)) (@ (@ tptp.entails tptp.bot_bot_assn) P2)))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C2) (@ (@ tptp.times_3573771949741848930nteger C2) B)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C2) (@ (@ tptp.times_times_rat C2) B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C2) (@ (@ tptp.times_times_int C2) B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger C2) A)) C2) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C2) A)) C2) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C2) A)) C2) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C2) (@ (@ tptp.times_3573771949741848930nteger B) C2)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C2) (@ (@ tptp.times_times_rat B) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C2) (@ (@ tptp.times_times_int B) C2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (C2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) C2) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) C2) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C2)) C2) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C2) (@ (@ tptp.times_3573771949741848930nteger C2) B)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C2) (@ (@ tptp.times_times_rat C2) B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C2) (@ (@ tptp.times_times_int C2) B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger C2) A)) C2) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C2) A)) C2) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C2) A)) C2) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C2) (@ (@ tptp.times_3573771949741848930nteger B) C2)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C2) (@ (@ tptp.times_times_rat B) C2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C2) (@ (@ tptp.times_times_int B) C2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (C2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C2)) C2) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) C2) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C2)) C2) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 8.20/8.61 (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)))))))))
% 8.20/8.61 (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)))))))))
% 8.20/8.61 (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)))))))))
% 8.20/8.61 (assert (= (lambda ((X4 tptp.code_integer)) X4) (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer)))
% 8.20/8.61 (assert (= (lambda ((X4 tptp.assn)) X4) (@ tptp.times_times_assn tptp.one_one_assn)))
% 8.20/8.61 (assert (= (lambda ((X4 tptp.rat)) X4) (@ tptp.times_times_rat tptp.one_one_rat)))
% 8.20/8.61 (assert (= (lambda ((X4 tptp.nat)) X4) (@ tptp.times_times_nat tptp.one_one_nat)))
% 8.20/8.61 (assert (= (lambda ((X4 tptp.int)) X4) (@ tptp.times_times_int tptp.one_one_int)))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (P6 tptp.assn) (C2 tptp.heap_Time_Heap_a) (Q2 (-> tptp.a tptp.assn))) (=> (@ (@ tptp.entails P2) P6) (=> (@ (@ (@ tptp.hoare_hoare_triple_a P6) C2) Q2) (@ (@ (@ tptp.hoare_hoare_triple_a P2) C2) Q2)))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (P6 tptp.assn) (C2 tptp.heap_Time_Heap_b) (Q2 (-> tptp.b tptp.assn))) (=> (@ (@ tptp.entails P2) P6) (=> (@ (@ (@ tptp.hoare_hoare_triple_b P6) C2) Q2) (@ (@ (@ tptp.hoare_hoare_triple_b P2) C2) Q2)))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (P6 tptp.assn) (C2 tptp.heap_T5738788834812785303t_unit) (Q2 (-> tptp.product_unit tptp.assn))) (=> (@ (@ tptp.entails P2) P6) (=> (@ (@ (@ tptp.hoare_8945653483474564448t_unit P6) C2) Q2) (@ (@ (@ tptp.hoare_8945653483474564448t_unit P2) C2) Q2)))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_Time_Heap_a) (Q2 (-> tptp.a tptp.assn)) (R3 tptp.assn)) (=> (@ (@ (@ tptp.hoare_hoare_triple_a P2) C2) Q2) (@ (@ (@ tptp.hoare_hoare_triple_a (@ (@ tptp.times_times_assn P2) R3)) C2) (lambda ((X4 tptp.a)) (@ (@ tptp.times_times_assn (@ Q2 X4)) R3))))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_Time_Heap_b) (Q2 (-> tptp.b tptp.assn)) (R3 tptp.assn)) (=> (@ (@ (@ tptp.hoare_hoare_triple_b P2) C2) Q2) (@ (@ (@ tptp.hoare_hoare_triple_b (@ (@ tptp.times_times_assn P2) R3)) C2) (lambda ((X4 tptp.b)) (@ (@ tptp.times_times_assn (@ Q2 X4)) R3))))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (C2 tptp.heap_T5738788834812785303t_unit) (Q2 (-> tptp.product_unit tptp.assn)) (R3 tptp.assn)) (=> (@ (@ (@ tptp.hoare_8945653483474564448t_unit P2) C2) Q2) (@ (@ (@ tptp.hoare_8945653483474564448t_unit (@ (@ tptp.times_times_assn P2) R3)) C2) (lambda ((X4 tptp.product_unit)) (@ (@ tptp.times_times_assn (@ Q2 X4)) R3))))))
% 8.20/8.61 (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)))))))))
% 8.20/8.61 (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)))))))))
% 8.20/8.61 (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)))))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (C2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C2)) B)))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C2) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) B)))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C2) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) B)))))
% 8.20/8.61 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C2) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) B)))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int A) C2)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C2)) B)))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C2)) B)))))
% 8.20/8.61 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) B)))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C2)) B)))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) C2)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C2)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C2)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_int A) C2)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 8.20/8.61 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 8.20/8.61 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int A) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C)) (= C tptp.zero_zero_nat)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 8.20/8.61 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 8.20/8.61 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P2 N2) (=> (not (@ P2 tptp.zero_zero_nat)) (exists ((K tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K) N2) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (not (@ P2 I4)))) (@ P2 K)))))))
% 8.20/8.61 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (exists ((K tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.plus_plus_nat I2) K) J2))))))
% 8.20/8.61 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) X) (not (= X tptp.zero_zero_nat)))))
% 8.20/8.61 (assert (forall ((B Bool) (P2 tptp.assn) (F tptp.heap_Time_Heap_a) (Q2 (-> tptp.a tptp.assn))) (=> (=> B (@ (@ (@ tptp.hoare_hoare_triple_a P2) F) Q2)) (@ (@ (@ tptp.hoare_hoare_triple_a (@ (@ tptp.times_times_assn P2) (@ tptp.pure_assn B))) F) Q2))))
% 8.20/8.61 (assert (forall ((B Bool) (P2 tptp.assn) (F tptp.heap_Time_Heap_b) (Q2 (-> tptp.b tptp.assn))) (=> (=> B (@ (@ (@ tptp.hoare_hoare_triple_b P2) F) Q2)) (@ (@ (@ tptp.hoare_hoare_triple_b (@ (@ tptp.times_times_assn P2) (@ tptp.pure_assn B))) F) Q2))))
% 8.20/8.61 (assert (forall ((B Bool) (P2 tptp.assn) (F tptp.heap_T5738788834812785303t_unit) (Q2 (-> tptp.product_unit tptp.assn))) (=> (=> B (@ (@ (@ tptp.hoare_8945653483474564448t_unit P2) F) Q2)) (@ (@ (@ tptp.hoare_8945653483474564448t_unit (@ (@ tptp.times_times_assn P2) (@ tptp.pure_assn B))) F) Q2))))
% 8.20/8.61 (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))
% 8.20/8.61 (assert (= tptp.heap_Time_ureturn_b (lambda ((X4 tptp.b)) (@ tptp.heap_Time_heap_b (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc4082563078715348724it_nat X4) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.zero_zero_nat)))))))
% 8.20/8.61 (assert (= tptp.heap_Time_ureturn_a (lambda ((X4 tptp.a)) (@ tptp.heap_Time_heap_a (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc9178034014595674355it_nat X4) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.zero_zero_nat)))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) C2) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ (@ tptp.plus_p5714425477246183910nteger A) C2))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.plus_plus_rat A) C2))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ (@ tptp.ord_less_nat B) (@ (@ tptp.plus_plus_nat A) C2))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ (@ tptp.ord_less_int B) (@ (@ tptp.plus_plus_int A) C2))))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int A) C2)))))))
% 8.20/8.61 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 8.20/8.61 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (X tptp.a)) (@ (@ (@ tptp.hoare_hoare_triple_a P2) (@ tptp.heap_Time_return_a X)) (lambda ((R5 tptp.a)) (@ (@ tptp.times_times_assn P2) (@ tptp.pure_assn (= R5 X)))))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (X tptp.b)) (@ (@ (@ tptp.hoare_hoare_triple_b P2) (@ tptp.heap_Time_return_b X)) (lambda ((R5 tptp.b)) (@ (@ tptp.times_times_assn P2) (@ tptp.pure_assn (= R5 X)))))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (X tptp.product_unit)) (@ (@ (@ tptp.hoare_8945653483474564448t_unit P2) (@ tptp.heap_T7507251653302230130t_unit X)) (lambda ((R5 tptp.product_unit)) (@ (@ tptp.times_times_assn P2) (@ tptp.pure_assn (= R5 X)))))))
% 8.20/8.61 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ tptp.pure_a825153325127701367it_nat X) Xa)) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (and (= As2 tptp.bot_bot_set_nat) X)))))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((A tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 8.20/8.61 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 8.20/8.61 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((Z3 tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z3) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger X) Z3)) (@ (@ tptp.times_3573771949741848930nteger Y) Z3)) (@ (@ tptp.ord_le3102999989581377725nteger X) Y)))))
% 8.20/8.61 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat Y) Z3)) (@ (@ tptp.ord_less_eq_rat X) Y)))))
% 8.20/8.61 (assert (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z3)) (@ (@ tptp.times_times_int Y) Z3)) (@ (@ tptp.ord_less_eq_int X) Y)))))
% 8.20/8.61 (assert (forall ((Z3 tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger Z3))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z3) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_le3102999989581377725nteger X) Y))))))
% 8.20/8.61 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z3))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 8.20/8.61 (assert (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((Q6 tptp.code_integer) (R2 tptp.code_integer)) (= (@ tptp.unique5706413561485394159nteger (@ (@ tptp.produc1086072967326762835nteger Q6) R2)) (= R2 tptp.zero_z3403309356797280102nteger))))
% 8.20/8.61 (assert (forall ((Q6 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q6) R2)) (= R2 tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((Q6 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q6) R2)) (= R2 tptp.zero_zero_int))))
% 8.20/8.61 (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 ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= Xa _let_1) (=> (@ (@ tptp.accp_P8458817951426537472et_nat tptp.pure_a6022498039421069578it_nat) (@ (@ tptp.produc3762353314782720579et_nat X) _let_1)) (and (= As2 tptp.bot_bot_set_nat) X))))))))))
% 8.20/8.61 (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 ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= Xa _let_1) (=> (@ (@ tptp.accp_P8458817951426537472et_nat tptp.pure_a6022498039421069578it_nat) (@ (@ tptp.produc3762353314782720579et_nat X) _let_1)) (not (and (= As2 tptp.bot_bot_set_nat) X)))))))))))
% 8.20/8.61 (assert (forall ((M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K2) (@ (@ tptp.times_times_nat N2) K2)) (or (= M N2) (= K2 tptp.zero_zero_nat)))))
% 8.20/8.61 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (= (@ _let_1 M) (@ _let_1 N2)) (or (= M N2) (= K2 tptp.zero_zero_nat))))))
% 8.20/8.61 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (assert (forall ((M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K2)) (@ (@ tptp.times_times_nat N2) K2)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_nat M) N2)))))
% 8.20/8.61 (assert (forall ((M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K2)) (@ (@ tptp.times_times_nat N2) K2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 8.20/8.61 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 8.20/8.61 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 8.20/8.61 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_eq_nat K2) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K2)) (@ (@ tptp.times_times_nat J2) L))))))
% 8.20/8.61 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K2)) (@ (@ tptp.times_times_nat J2) K2)))))
% 8.20/8.61 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J2))))))
% 8.20/8.61 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 8.20/8.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N2)) K2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K2)) (@ (@ tptp.times_times_nat N2) K2)))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat N2) tptp.one_one_nat) N2)))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N2) N2)))
% 8.20/8.61 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J2)))))))
% 8.20/8.61 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I2) K2)) (@ (@ tptp.times_times_nat J2) K2))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (A4 tptp.nat) (B tptp.nat) (N7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) A4) (=> (@ (@ 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 A4) N7))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((X6 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X6))))
% 8.20/8.61 (assert (forall ((X6 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X6) X_1))))
% 8.20/8.61 (assert (forall ((Z3 tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z3) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger X) Z3)) (@ (@ tptp.times_3573771949741848930nteger Y) Z3)) (@ (@ tptp.ord_le6747313008572928689nteger X) Y)))))
% 8.20/8.61 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat Y) Z3)) (@ (@ tptp.ord_less_rat X) Y)))))
% 8.20/8.61 (assert (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z3)) (@ (@ tptp.times_times_int Y) Z3)) (@ (@ tptp.ord_less_int X) Y)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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 ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= Xa _let_1) (=> (= Y (and (= As2 tptp.bot_bot_set_nat) X)) (not (@ (@ tptp.accp_P8458817951426537472et_nat tptp.pure_a6022498039421069578it_nat) (@ (@ tptp.produc3762353314782720579et_nat X) _let_1))))))))))))
% 8.20/8.61 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 8.20/8.61 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_nat M) N2))))))
% 8.20/8.61 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 8.20/8.61 (assert (forall ((R2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger R2))) (=> (not (= R2 tptp.zero_z3403309356797280102nteger)) (=> (and (= A B) (not (= C2 D2))) (not (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ _let_1 C2)) (@ (@ tptp.plus_p5714425477246183910nteger B) (@ _let_1 D2)))))))))
% 8.20/8.61 (assert (forall ((R2 tptp.rat) (A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A B) (not (= C2 D2))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C2)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D2)))))))))
% 8.20/8.61 (assert (forall ((R2 tptp.nat) (A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A B) (not (= C2 D2))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C2)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D2)))))))))
% 8.20/8.61 (assert (forall ((R2 tptp.int) (A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A B) (not (= C2 D2))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C2)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D2)))))))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ P2 A3) B3) (@ (@ P2 B3) A3))) (=> (forall ((A3 tptp.nat)) (@ (@ P2 A3) tptp.zero_zero_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ P2 A3))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A3) B3))))) (@ (@ P2 A) B))))))
% 8.20/8.61 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 8.20/8.61 (assert (forall ((I2 tptp.nat) (U tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) K2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I2) J2)) U)) K2))))
% 8.20/8.61 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (= B (@ (@ tptp.plus_p5714425477246183910nteger B) A)) (= A tptp.zero_z3403309356797280102nteger))))
% 8.20/8.61 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 8.20/8.61 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 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 (= C2 D2))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C2)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_rat (@ _let_2 D2)) (@ _let_1 C2)))))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 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 (= C2 D2))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C2)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_nat (@ _let_2 D2)) (@ _let_1 C2)))))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 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 (= C2 D2))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C2)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_int (@ _let_2 D2)) (@ _let_1 C2)))))))))
% 8.20/8.61 (assert (forall ((W2 tptp.rat) (Y tptp.rat) (X tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (let ((_let_2 (@ tptp.times_times_rat W2))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))))
% 8.20/8.61 (assert (forall ((W2 tptp.nat) (Y tptp.nat) (X tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W2))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))))
% 8.20/8.61 (assert (forall ((W2 tptp.int) (Y tptp.int) (X tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W2))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z3)) (@ (@ tptp.plus_plus_int (@ _let_2 Z3)) (@ _let_1 Y))) (or (= W2 X) (= Y Z3)))))))
% 8.20/8.61 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P2) (@ (@ tptp.wand_assn P2) Q2))) Q2)))
% 8.20/8.61 (assert (forall ((Q2 tptp.assn) (P2 tptp.assn) (R3 tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn Q2) P2)) R3) (@ (@ tptp.entails P2) (@ (@ tptp.wand_assn Q2) R3)))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((A4 tptp.assn) (B5 tptp.assn) (H tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A4) B5)) H) (exists ((Hr tptp.heap_e7401611519738050253t_unit) (As1 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat Hr))) (and (= H (@ _let_1 (@ (@ tptp.sup_sup_set_nat As1) As22))) (= (@ (@ tptp.inf_inf_set_nat As1) As22) tptp.bot_bot_set_nat) (@ (@ tptp.rep_assn A4) (@ _let_1 As1)) (@ (@ tptp.rep_assn B5) (@ _let_1 As22))))))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat) (Q2 tptp.assn) (As5 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (=> (@ (@ tptp.rep_assn P2) (@ _let_1 As)) (=> (@ (@ tptp.rep_assn Q2) (@ _let_1 As5)) (=> (= (@ (@ tptp.inf_inf_set_nat As) As5) tptp.bot_bot_set_nat) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P2) Q2)) (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As5)))))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((C2 Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_o A4) B5)) (and (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.61 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (= (@ _let_1 (@ (@ tptp.inf_in8396524679539076455nt_int A4) B5)) (and (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.61 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A4) B5)) (and (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)) (and (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.61 (assert (forall ((C2 tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C2))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) (and (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.61 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)) (and (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.61 (assert (forall ((C2 Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (=> (@ _let_1 A4) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.inf_inf_set_o A4) B5)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (@ _let_1 A4) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.inf_in8396524679539076455nt_int A4) B5)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (@ _let_1 A4) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A4) B5)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 A4) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C2))) (=> (@ _let_1 A4) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)))))))
% 8.20/8.61 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 A4) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z3 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o X))) (= (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_rat Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (= (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z3)) (and (@ _let_1 Y) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))))
% 8.20/8.61 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))))
% 8.20/8.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))))
% 8.20/8.61 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool)) (C2 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o A))) (= (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))))
% 8.20/8.61 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_rat B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ (@ tptp.inf_inf_int B) C2)) (and (@ _let_1 B) (@ _let_1 C2))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) (@ (@ tptp.sup_sup_assn X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ (@ tptp.sup_su6327502436637775413at_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) (@ (@ tptp.sup_su8463660629351352368_int_o X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat X) (@ (@ tptp.sup_su3035147773818789531at_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.inf_inf_nat X) (@ (@ tptp.sup_sup_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.inf_inf_int X) (@ (@ tptp.sup_sup_int X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) (@ (@ tptp.inf_inf_assn X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat X) (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.sup_su8463660629351352368_int_o X) (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat X) (@ (@ tptp.inf_in1697001100524423349at_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) (@ (@ tptp.inf_in7913087082777306421at_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) (@ (@ tptp.inf_inf_set_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.sup_sup_nat X) (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.sup_sup_int X) (@ (@ tptp.inf_inf_int X) Y)) X)))
% 8.20/8.61 (assert (forall ((C4 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat C4))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) (and (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.61 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C4))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)) (and (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.61 (assert (forall ((C4 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C4))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)) (and (@ _let_1 A4) (@ _let_1 B5))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in7104746047340619750_int_o (@ tptp.some_P180497116919641311_int_o X)) (@ tptp.some_P180497116919641311_int_o Y)) (@ tptp.some_P180497116919641311_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)))))
% 8.20/8.61 (assert (forall ((T7 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat T7) (@ (@ tptp.inf_in2572325071724192079at_nat S) T7)) T7)))
% 8.20/8.61 (assert (forall ((T7 tptp.set_Pr8551490117392284871at_nat) (S tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat T7) (@ (@ tptp.inf_in1697001100524423349at_nat S) T7)) T7)))
% 8.20/8.61 (assert (forall ((T7 tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat T7) (@ (@ tptp.inf_in7913087082777306421at_nat S) T7)) T7)))
% 8.20/8.61 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat T7) (@ (@ tptp.inf_inf_set_nat S) T7)) T7)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat S) (@ (@ tptp.inf_in2572325071724192079at_nat S) T7)) S)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T7 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat S) (@ (@ tptp.inf_in1697001100524423349at_nat S) T7)) S)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T7 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat S) (@ (@ tptp.inf_in7913087082777306421at_nat S) T7)) S)))
% 8.20/8.61 (assert (forall ((S tptp.set_nat) (T7 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat S) (@ (@ tptp.inf_inf_set_nat S) T7)) S)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat S) T7)) T7) T7)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T7 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat S) T7)) T7) T7)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T7 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat S) T7)) T7) T7)))
% 8.20/8.61 (assert (forall ((S tptp.set_nat) (T7 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat S) T7)) T7) T7)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat S) T7)) S) S)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T7 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat S) T7)) S) S)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T7 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat S) T7)) S) S)))
% 8.20/8.61 (assert (forall ((S tptp.set_nat) (T7 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat S) T7)) S) S)))
% 8.20/8.61 (assert (forall ((T7 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat T7) (@ (@ tptp.sup_su6327502436637775413at_nat S) T7)) T7)))
% 8.20/8.61 (assert (forall ((T7 tptp.set_Pr8551490117392284871at_nat) (S tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat T7) (@ (@ tptp.sup_su3035147773818789531at_nat S) T7)) T7)))
% 8.20/8.61 (assert (forall ((T7 tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat T7) (@ (@ tptp.sup_su5525570899277871387at_nat S) T7)) T7)))
% 8.20/8.61 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat T7) (@ (@ tptp.sup_sup_set_nat S) T7)) T7)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat S) (@ (@ tptp.sup_su6327502436637775413at_nat S) T7)) S)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T7 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat S) (@ (@ tptp.sup_su3035147773818789531at_nat S) T7)) S)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T7 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat S) (@ (@ tptp.sup_su5525570899277871387at_nat S) T7)) S)))
% 8.20/8.61 (assert (forall ((S tptp.set_nat) (T7 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat S) (@ (@ tptp.sup_sup_set_nat S) T7)) S)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T7)) T7) T7)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T7 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat S) T7)) T7) T7)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T7 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T7)) T7) T7)))
% 8.20/8.61 (assert (forall ((S tptp.set_nat) (T7 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat S) T7)) T7) T7)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T7)) S) S)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T7 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat S) T7)) S) S)))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T7 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T7)) S) S)))
% 8.20/8.61 (assert (forall ((S tptp.set_nat) (T7 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat S) T7)) S) S)))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A4))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat B5))) (= (@ _let_1 (@ _let_2 C4)) (@ _let_2 (@ _let_1 C4)))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A4))) (let ((_let_2 (@ tptp.inf_inf_set_nat B5))) (= (@ _let_1 (@ _let_2 C4)) (@ _let_2 (@ _let_1 C4)))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A4))) (let ((_let_2 (@ _let_1 B5))) (= (@ _let_1 _let_2) _let_2)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A4))) (let ((_let_2 (@ _let_1 B5))) (= (@ _let_1 _let_2) _let_2)))))
% 8.20/8.61 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat B6) A6))))
% 8.20/8.61 (assert (= tptp.inf_inf_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat B6) A6))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) A4) A4)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A4) A4) A4)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A4))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B5) C4))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A4))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B5) C4))))))
% 8.20/8.61 (assert (forall ((C2 Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_o A4) B5)) (@ _let_1 B5)))))
% 8.20/8.61 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (@ _let_1 (@ (@ tptp.inf_in8396524679539076455nt_int A4) B5)) (@ _let_1 B5)))))
% 8.20/8.61 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A4) B5)) (@ _let_1 B5)))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)) (@ _let_1 B5)))))
% 8.20/8.61 (assert (forall ((C2 tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C2))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) (@ _let_1 B5)))))
% 8.20/8.61 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)) (@ _let_1 B5)))))
% 8.20/8.61 (assert (forall ((C2 Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_o A4) B5)) (@ _let_1 A4)))))
% 8.20/8.61 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (@ _let_1 (@ (@ tptp.inf_in8396524679539076455nt_int A4) B5)) (@ _let_1 A4)))))
% 8.20/8.61 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A4) B5)) (@ _let_1 A4)))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)) (@ _let_1 A4)))))
% 8.20/8.61 (assert (forall ((C2 tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C2))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) (@ _let_1 A4)))))
% 8.20/8.61 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)) (@ _let_1 A4)))))
% 8.20/8.61 (assert (forall ((C2 Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_o A4) B5)) (not (=> (@ _let_1 A4) (not (@ _let_1 B5))))))))
% 8.20/8.61 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (@ _let_1 (@ (@ tptp.inf_in8396524679539076455nt_int A4) B5)) (not (=> (@ _let_1 A4) (not (@ _let_1 B5))))))))
% 8.20/8.61 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A4) B5)) (not (=> (@ _let_1 A4) (not (@ _let_1 B5))))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)) (not (=> (@ _let_1 A4) (not (@ _let_1 B5))))))))
% 8.20/8.61 (assert (forall ((C2 tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C2))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) (not (=> (@ _let_1 A4) (not (@ _let_1 B5))))))))
% 8.20/8.61 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)) (not (=> (@ _let_1 A4) (not (@ _let_1 B5))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (assert (= tptp.inf_in8396524679539076455nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int X4))) (and (@ _let_1 A6) (@ _let_1 B6))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (assert (forall ((X Bool) (A4 tptp.set_o) (P2 (-> Bool Bool))) (let ((_let_1 (@ tptp.member_o X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_o A4) (@ tptp.collect_o P2))) (and (@ _let_1 A4) (@ P2 X))))))
% 8.20/8.61 (assert (forall ((X tptp.list_nat) (A4 tptp.set_list_nat) (P2 (-> tptp.list_nat Bool))) (let ((_let_1 (@ tptp.member_list_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_list_nat A4) (@ tptp.collect_list_nat P2))) (and (@ _let_1 A4) (@ P2 X))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (P2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (let ((_let_1 (@ tptp.member2340774599025711042nt_int X))) (= (@ _let_1 (@ (@ tptp.inf_in8396524679539076455nt_int A4) (@ tptp.collec5210948495886036740nt_int P2))) (and (@ _let_1 A4) (@ P2 X))))))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (A4 tptp.set_set_nat) (P2 (-> tptp.set_nat Bool))) (let ((_let_1 (@ tptp.member_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A4) (@ tptp.collect_set_nat P2))) (and (@ _let_1 A4) (@ P2 X))))))
% 8.20/8.61 (assert (forall ((X tptp.int) (A4 tptp.set_int) (P2 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2))) (and (@ _let_1 A4) (@ P2 X))))))
% 8.20/8.61 (assert (forall ((X tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (P2 (-> tptp.product_prod_nat_nat Bool))) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) (@ tptp.collec3392354462482085612at_nat P2))) (and (@ _let_1 A4) (@ P2 X))))))
% 8.20/8.61 (assert (forall ((X tptp.nat) (A4 tptp.set_nat) (P2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.collect_nat P2))) (and (@ _let_1 A4) (@ P2 X))))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.list_nat Bool)) (Q2 (-> tptp.list_nat Bool))) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.inf_inf_set_list_nat (@ tptp.collect_list_nat P2)) (@ tptp.collect_list_nat Q2)))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.set_Pr958786334691620121nt_int Bool)) (Q2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (= (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (and (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.inf_in8396524679539076455nt_int (@ tptp.collec5210948495886036740nt_int P2)) (@ tptp.collec5210948495886036740nt_int Q2)))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.set_nat Bool)) (Q2 (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.inf_inf_set_set_nat (@ tptp.collect_set_nat P2)) (@ tptp.collect_set_nat Q2)))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.inf_inf_set_int (@ tptp.collect_int P2)) (@ tptp.collect_int Q2)))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.product_prod_nat_nat Bool)) (Q2 (-> tptp.product_prod_nat_nat Bool))) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (and (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.collec3392354462482085612at_nat P2)) (@ tptp.collec3392354462482085612at_nat Q2)))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.inf_inf_set_nat (@ tptp.collect_nat P2)) (@ tptp.collect_nat Q2)))))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) Y)))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Y)))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Y)))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) Y)))
% 8.20/8.61 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X) Y)) Y)))
% 8.20/8.61 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) Y)))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) Y)))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) X)))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) Y)))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Y)))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Y)))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) Y)))
% 8.20/8.61 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X) Y)) Y)))
% 8.20/8.61 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) Y)))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) Y)))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o X))) (=> (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o A) B)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((A tptp.assn) (C2 tptp.assn) (B tptp.assn) (D2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) C2) (=> (@ (@ tptp.ord_less_eq_assn B) D2) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) (@ (@ tptp.inf_inf_assn C2) D2))))))
% 8.20/8.61 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (D2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) C2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) D2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ (@ tptp.inf_in2572325071724192079at_nat C2) D2))))))
% 8.20/8.61 (assert (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat) (D2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C2) (=> (@ (@ 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 C2) D2))))))
% 8.20/8.61 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (C2 (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool)) (D2 (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o A) C2) (=> (@ (@ tptp.ord_le8369615600986905444_int_o B) D2) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) (@ (@ tptp.inf_in3604695632404883862_int_o C2) D2))))))
% 8.20/8.61 (assert (forall ((A tptp.set_int) (C2 tptp.set_int) (B tptp.set_int) (D2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) C2) (=> (@ (@ 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 C2) D2))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) C2) (=> (@ (@ tptp.ord_less_eq_rat B) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) (@ (@ tptp.inf_inf_rat C2) D2))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C2) (=> (@ (@ tptp.ord_less_eq_nat B) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) (@ (@ tptp.inf_inf_nat C2) D2))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) C2) (=> (@ (@ tptp.ord_less_eq_int B) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) (@ (@ tptp.inf_inf_int C2) D2))))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o A) X) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) X))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((B (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o B) X) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) X))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) B) (= A (@ (@ tptp.inf_inf_assn A) B)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o A) B) (= A (@ (@ tptp.inf_in3604695632404883862_int_o A) B)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A (@ (@ tptp.inf_inf_rat A) B)))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A (@ (@ tptp.inf_inf_nat A) B)))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A (@ (@ tptp.inf_inf_int A) B)))))
% 8.20/8.61 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (= A (@ (@ tptp.inf_inf_assn A) B)) (@ (@ tptp.ord_less_eq_assn A) B))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (= A (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) (@ (@ tptp.ord_le8369615600986905444_int_o A) B))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.inf_inf_rat A) B)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.inf_inf_nat A) B)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.inf_inf_int A) B)) (@ (@ tptp.ord_less_eq_int A) B))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((F (-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (=> (forall ((X3 (-> tptp.product_prod_int_int Bool)) (Y3 (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ F X3) Y3)) X3)) (=> (forall ((X3 (-> tptp.product_prod_int_int Bool)) (Y3 (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ F X3) Y3)) Y3)) (=> (forall ((X3 (-> tptp.product_prod_int_int Bool)) (Y3 (-> tptp.product_prod_int_int Bool)) (Z2 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F Y3) Z2)))))) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) Y) (@ (@ F X) Y)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_assn (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (= (@ (@ tptp.inf_inf_assn X4) Y4) X4))))
% 8.20/8.61 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X4) Y4) X4))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X4) Y4) X4))))
% 8.20/8.61 (assert (= tptp.ord_le8369615600986905444_int_o (lambda ((X4 (-> tptp.product_prod_int_int Bool)) (Y4 (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o X4) Y4) X4))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_set_int (lambda ((X4 tptp.set_int) (Y4 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X4) Y4) X4))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.inf_inf_rat X4) Y4) X4))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.inf_inf_nat X4) Y4) X4))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.inf_inf_int X4) Y4) X4))))
% 8.20/8.61 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) B) (= (@ (@ tptp.inf_inf_assn A) B) A))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o A) B) (= (@ (@ tptp.inf_in3604695632404883862_int_o A) B) A))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.inf_inf_rat A) B) A))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.inf_inf_nat A) B) A))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.inf_inf_int A) B) A))))
% 8.20/8.61 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B) A) (= (@ (@ tptp.inf_inf_assn A) B) B))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((B (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o B) A) (= (@ (@ tptp.inf_in3604695632404883862_int_o A) B) B))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.inf_inf_rat A) B) B))))
% 8.20/8.61 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.inf_inf_nat A) B) B))))
% 8.20/8.61 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.inf_inf_int A) B) B))))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (= (@ (@ tptp.inf_inf_assn X) Y) X))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o X) Y) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) Y) X))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.inf_inf_rat X) Y) X))))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.inf_inf_nat X) Y) X))))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.inf_inf_int X) Y) X))))
% 8.20/8.61 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (= (@ (@ tptp.inf_inf_assn X) Y) Y))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((Y (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o Y) X) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) Y) Y))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.inf_inf_rat X) Y) Y))))
% 8.20/8.61 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.inf_inf_nat X) Y) Y))))
% 8.20/8.61 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.inf_inf_int X) Y) Y))))
% 8.20/8.61 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_assn B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 8.20/8.61 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 8.20/8.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 8.20/8.61 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool)) (C2 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o A))) (=> (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 8.20/8.61 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_rat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 8.20/8.61 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_assn B) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)))))))
% 8.20/8.61 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool)) (C2 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o B) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_set_int B) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_rat B) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_nat B) C2)))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_int B) C2)))))))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z3 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z3)))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_inf_set_int Y) Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_inf_rat Y) Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z3) (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z3)))))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_assn (lambda ((A5 tptp.assn) (B4 tptp.assn)) (= A5 (@ (@ tptp.inf_inf_assn A5) B4)))))
% 8.20/8.61 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (= A5 (@ (@ tptp.inf_in2572325071724192079at_nat A5) B4)))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (= A5 (@ (@ tptp.inf_inf_set_nat A5) B4)))))
% 8.20/8.61 (assert (= tptp.ord_le8369615600986905444_int_o (lambda ((A5 (-> tptp.product_prod_int_int Bool)) (B4 (-> tptp.product_prod_int_int Bool))) (= A5 (@ (@ tptp.inf_in3604695632404883862_int_o A5) B4)))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B4 tptp.set_int)) (= A5 (@ (@ tptp.inf_inf_set_int A5) B4)))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (= A5 (@ (@ tptp.inf_inf_rat A5) B4)))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (= A5 (@ (@ tptp.inf_inf_nat A5) B4)))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (= A5 (@ (@ tptp.inf_inf_int A5) B4)))))
% 8.20/8.61 (assert (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) A)))
% 8.20/8.61 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) A)))
% 8.20/8.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) A)))
% 8.20/8.61 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) A)))
% 8.20/8.61 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A) B)) A)))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) A)))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) A)))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) A)))
% 8.20/8.61 (assert (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) B)))
% 8.20/8.61 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) B)))
% 8.20/8.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) B)))
% 8.20/8.61 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) B)))
% 8.20/8.61 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A) B)) B)))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) B)))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) B)))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) B)))
% 8.20/8.61 (assert (= tptp.ord_less_eq_assn (lambda ((A5 tptp.assn) (B4 tptp.assn)) (= (@ (@ tptp.inf_inf_assn A5) B4) A5))))
% 8.20/8.61 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A5) B4) A5))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A5) B4) A5))))
% 8.20/8.61 (assert (= tptp.ord_le8369615600986905444_int_o (lambda ((A5 (-> tptp.product_prod_int_int Bool)) (B4 (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o A5) B4) A5))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B4 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A5) B4) A5))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.inf_inf_rat A5) B4) A5))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A5) B4) A5))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.inf_inf_int A5) B4) A5))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_assn (lambda ((B4 tptp.assn) (A5 tptp.assn)) (= (@ (@ tptp.inf_inf_assn A5) B4) B4))))
% 8.20/8.61 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((B4 tptp.set_Pr1261947904930325089at_nat) (A5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A5) B4) B4))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_set_nat (lambda ((B4 tptp.set_nat) (A5 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A5) B4) B4))))
% 8.20/8.61 (assert (= tptp.ord_le8369615600986905444_int_o (lambda ((B4 (-> tptp.product_prod_int_int Bool)) (A5 (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o A5) B4) B4))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_set_int (lambda ((B4 tptp.set_int) (A5 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A5) B4) B4))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (= (@ (@ tptp.inf_inf_rat A5) B4) B4))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A5) B4) B4))))
% 8.20/8.61 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (= (@ (@ tptp.inf_inf_int A5) B4) B4))))
% 8.20/8.61 (assert (forall ((A tptp.assn) (C2 tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) C2) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) C2))))
% 8.20/8.61 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) C2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C2))))
% 8.20/8.61 (assert (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C2))))
% 8.20/8.61 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (C2 (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o A) C2) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) C2))))
% 8.20/8.61 (assert (forall ((A tptp.set_int) (C2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) C2) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A) B)) C2))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) C2))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) C2))))
% 8.20/8.61 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) C2))))
% 8.20/8.61 (assert (forall ((B tptp.assn) (C2 tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B) C2) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) C2))))
% 8.20/8.61 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) C2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C2))))
% 8.20/8.61 (assert (forall ((B tptp.set_nat) (C2 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) C2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C2))))
% 8.20/8.61 (assert (forall ((B (-> tptp.product_prod_int_int Bool)) (C2 (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o B) C2) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) C2))))
% 8.20/8.61 (assert (forall ((B tptp.set_int) (C2 tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) C2) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A) B)) C2))))
% 8.20/8.61 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) C2))))
% 8.20/8.61 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) C2))))
% 8.20/8.61 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) C2))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8213806771718485336_int_o A) X) (@ (@ tptp.ord_le8213806771718485336_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) X))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((B (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8213806771718485336_int_o B) X) (@ (@ tptp.ord_le8213806771718485336_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) X))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8213806771718485336_int_o A) B) (= (@ (@ tptp.inf_in3604695632404883862_int_o A) B) A))))
% 8.20/8.61 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (= (@ (@ tptp.inf_inf_assn A) B) A))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.inf_inf_rat A) B) A))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.inf_inf_nat A) B) A))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.inf_inf_int A) B) A))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((B (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8213806771718485336_int_o B) A) (= (@ (@ tptp.inf_in3604695632404883862_int_o A) B) B))))
% 8.20/8.61 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A) (= (@ (@ tptp.inf_inf_assn A) B) B))))
% 8.20/8.61 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.inf_inf_rat A) B) B))))
% 8.20/8.61 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.inf_inf_nat A) B) B))))
% 8.20/8.61 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.inf_inf_int A) B) B))))
% 8.20/8.61 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le7866589430770878221at_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 8.20/8.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 8.20/8.61 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool)) (C2 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8213806771718485336_int_o A))) (=> (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 8.20/8.61 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_assn B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_rat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int B) C2)) (not (=> (@ _let_1 B) (not (@ _let_1 C2))))))))
% 8.20/8.61 (assert (= tptp.ord_le7866589430770878221at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (and (= A5 (@ (@ tptp.inf_in2572325071724192079at_nat A5) B4)) (not (= A5 B4))))))
% 8.20/8.61 (assert (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B4 tptp.set_nat)) (and (= A5 (@ (@ tptp.inf_inf_set_nat A5) B4)) (not (= A5 B4))))))
% 8.20/8.61 (assert (= tptp.ord_le8213806771718485336_int_o (lambda ((A5 (-> tptp.product_prod_int_int Bool)) (B4 (-> tptp.product_prod_int_int Bool))) (and (= A5 (@ (@ tptp.inf_in3604695632404883862_int_o A5) B4)) (not (= A5 B4))))))
% 8.20/8.61 (assert (= tptp.ord_less_assn (lambda ((A5 tptp.assn) (B4 tptp.assn)) (and (= A5 (@ (@ tptp.inf_inf_assn A5) B4)) (not (= A5 B4))))))
% 8.20/8.61 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (and (= A5 (@ (@ tptp.inf_inf_rat A5) B4)) (not (= A5 B4))))))
% 8.20/8.61 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (and (= A5 (@ (@ tptp.inf_inf_nat A5) B4)) (not (= A5 B4))))))
% 8.20/8.61 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B4 tptp.int)) (and (= A5 (@ (@ tptp.inf_inf_int A5) B4)) (not (= A5 B4))))))
% 8.20/8.61 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A) C2) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C2))))
% 8.20/8.61 (assert (forall ((A tptp.set_nat) (C2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) C2) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C2))))
% 8.20/8.61 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (C2 (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8213806771718485336_int_o A) C2) (@ (@ tptp.ord_le8213806771718485336_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) C2))))
% 8.20/8.61 (assert (forall ((A tptp.assn) (C2 tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) C2) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A) B)) C2))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.inf_inf_rat A) B)) C2))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A) B)) C2))))
% 8.20/8.61 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A) B)) C2))))
% 8.20/8.61 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B) C2) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C2))))
% 8.20/8.61 (assert (forall ((B tptp.set_nat) (C2 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) C2) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C2))))
% 8.20/8.61 (assert (forall ((B (-> tptp.product_prod_int_int Bool)) (C2 (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8213806771718485336_int_o B) C2) (@ (@ tptp.ord_le8213806771718485336_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) C2))))
% 8.20/8.61 (assert (forall ((B tptp.assn) (C2 tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) C2) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A) B)) C2))))
% 8.20/8.61 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.inf_inf_rat A) B)) C2))))
% 8.20/8.61 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) C2) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A) B)) C2))))
% 8.20/8.61 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A) B)) C2))))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z3 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) Z3)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (=> (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) Z3)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.sup_su8463660629351352368_int_o X))) (=> (forall ((X3 (-> tptp.product_prod_int_int Bool)) (Y3 (-> tptp.product_prod_int_int Bool)) (Z2 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X3))) (= (@ _let_1 (@ (@ tptp.sup_su8463660629351352368_int_o Y3) Z2)) (@ (@ tptp.sup_su8463660629351352368_int_o (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z3)) (@ (@ tptp.inf_in3604695632404883862_int_o (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z3 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) Z3)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z3 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) Z3)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 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) Z3)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 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) Z3)) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X))) (=> (forall ((X3 tptp.int) (Y3 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.inf_inf_int X3))) (= (@ _let_1 (@ (@ tptp.sup_sup_int Y3) Z2)) (@ (@ tptp.sup_sup_int (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z3)) (@ (@ tptp.inf_inf_int (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z3 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) Z3)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (=> (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) Z3)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X))) (=> (forall ((X3 (-> tptp.product_prod_int_int Bool)) (Y3 (-> tptp.product_prod_int_int Bool)) (Z2 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.sup_su8463660629351352368_int_o X3))) (= (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y3) Z2)) (@ (@ tptp.inf_in3604695632404883862_int_o (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_su8463660629351352368_int_o Y) Z3)) (@ (@ tptp.sup_su8463660629351352368_int_o (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z3 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) Z3)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z3 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) Z3)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 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) Z3)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 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) Z3)) (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.inf_inf_int X))) (=> (forall ((X3 tptp.int) (Y3 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X3))) (= (@ _let_1 (@ (@ tptp.inf_inf_int Y3) Z2)) (@ (@ tptp.inf_inf_int (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_sup_int Y) Z3)) (@ (@ tptp.sup_sup_int (@ _let_1 Y)) (@ _let_1 Z3)))))))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z3 tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z3)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z3)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X))) (= (@ _let_1 (@ (@ tptp.sup_su8463660629351352368_int_o Y) Z3)) (@ (@ tptp.sup_su8463660629351352368_int_o (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.inf_in1697001100524423349at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z3)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z3)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z3)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (= (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z3)) (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.inf_inf_int X))) (= (@ _let_1 (@ (@ tptp.sup_sup_int Y) Z3)) (@ (@ tptp.sup_sup_int (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((Y tptp.assn) (Z3 tptp.assn) (X tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) Z3)) X) (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) X)) (@ (@ tptp.inf_inf_assn Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z3)) X) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) X)) (@ (@ tptp.inf_in2572325071724192079at_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o (@ (@ tptp.sup_su8463660629351352368_int_o Y) Z3)) X) (@ (@ tptp.sup_su8463660629351352368_int_o (@ (@ tptp.inf_in3604695632404883862_int_o Y) X)) (@ (@ tptp.inf_in3604695632404883862_int_o Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z3)) X) (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat Y) X)) (@ (@ tptp.inf_in1697001100524423349at_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z3)) X) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat Y) X)) (@ (@ tptp.inf_in7913087082777306421at_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_nat) (Z3 tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) Z3)) X) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) X)) (@ (@ tptp.inf_inf_set_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.nat) (Z3 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.inf_inf_nat (@ (@ tptp.sup_sup_nat Y) Z3)) X) (@ (@ tptp.sup_sup_nat (@ (@ tptp.inf_inf_nat Y) X)) (@ (@ tptp.inf_inf_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.int) (Z3 tptp.int) (X tptp.int)) (= (@ (@ tptp.inf_inf_int (@ (@ tptp.sup_sup_int Y) Z3)) X) (@ (@ tptp.sup_sup_int (@ (@ tptp.inf_inf_int Y) X)) (@ (@ tptp.inf_inf_int Z3) X)))))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z3 tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z3)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z3)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.sup_su8463660629351352368_int_o X))) (= (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z3)) (@ (@ tptp.inf_in3604695632404883862_int_o (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat Y) Z3)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z3)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z3)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z3)) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X))) (= (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z3)) (@ (@ tptp.inf_inf_int (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((Y tptp.assn) (Z3 tptp.assn) (X tptp.assn)) (= (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) Z3)) X) (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) X)) (@ (@ tptp.sup_sup_assn Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z3)) X) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) X)) (@ (@ tptp.sup_su6327502436637775413at_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.sup_su8463660629351352368_int_o (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z3)) X) (@ (@ tptp.inf_in3604695632404883862_int_o (@ (@ tptp.sup_su8463660629351352368_int_o Y) X)) (@ (@ tptp.sup_su8463660629351352368_int_o Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat Y) Z3)) X) (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat Y) X)) (@ (@ tptp.sup_su3035147773818789531at_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z3)) X) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) X)) (@ (@ tptp.sup_su5525570899277871387at_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_nat) (Z3 tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) Z3)) X) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) X)) (@ (@ tptp.sup_sup_set_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.nat) (Z3 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.sup_sup_nat (@ (@ tptp.inf_inf_nat Y) Z3)) X) (@ (@ tptp.inf_inf_nat (@ (@ tptp.sup_sup_nat Y) X)) (@ (@ tptp.sup_sup_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.int) (Z3 tptp.int) (X tptp.int)) (= (@ (@ tptp.sup_sup_int (@ (@ tptp.inf_inf_int Y) Z3)) X) (@ (@ tptp.inf_inf_int (@ (@ tptp.sup_sup_int Y) X)) (@ (@ tptp.sup_sup_int Z3) X)))))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z3 tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z3)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z3)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X))) (= (@ _let_1 (@ (@ tptp.sup_su8463660629351352368_int_o Y) Z3)) (@ (@ tptp.sup_su8463660629351352368_int_o (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.inf_in1697001100524423349at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z3)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z3)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z3)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z3 tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z3)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z3)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.sup_su8463660629351352368_int_o X))) (= (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z3)) (@ (@ tptp.inf_in3604695632404883862_int_o (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat Y) Z3)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z3)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z3)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((Y tptp.assn) (Z3 tptp.assn) (X tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) Z3)) X) (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) X)) (@ (@ tptp.inf_inf_assn Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z3)) X) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) X)) (@ (@ tptp.inf_in2572325071724192079at_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o (@ (@ tptp.sup_su8463660629351352368_int_o Y) Z3)) X) (@ (@ tptp.sup_su8463660629351352368_int_o (@ (@ tptp.inf_in3604695632404883862_int_o Y) X)) (@ (@ tptp.inf_in3604695632404883862_int_o Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z3)) X) (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat Y) X)) (@ (@ tptp.inf_in1697001100524423349at_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z3)) X) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat Y) X)) (@ (@ tptp.inf_in7913087082777306421at_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_nat) (Z3 tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) Z3)) X) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) X)) (@ (@ tptp.inf_inf_set_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.assn) (Z3 tptp.assn) (X tptp.assn)) (= (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) Z3)) X) (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) X)) (@ (@ tptp.sup_sup_assn Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z3)) X) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) X)) (@ (@ tptp.sup_su6327502436637775413at_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.sup_su8463660629351352368_int_o (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z3)) X) (@ (@ tptp.inf_in3604695632404883862_int_o (@ (@ tptp.sup_su8463660629351352368_int_o Y) X)) (@ (@ tptp.sup_su8463660629351352368_int_o Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat Y) Z3)) X) (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat Y) X)) (@ (@ tptp.sup_su3035147773818789531at_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z3)) X) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) X)) (@ (@ tptp.sup_su5525570899277871387at_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((Y tptp.set_nat) (Z3 tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) Z3)) X) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) X)) (@ (@ tptp.sup_sup_set_nat Z3) X)))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2)))))
% 8.20/8.61 (assert (forall ((A tptp.set_se6260736226359567993nt_int) (B tptp.set_se6260736226359567993nt_int)) (=> (forall ((X3 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_in8396524679539076455nt_int A) B) tptp.bot_bo1488462491386950373nt_int))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5) tptp.bot_bo2099793752762293965at_nat) (forall ((X4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X4) A4) (forall ((Y4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y4) B5) (not (= X4 Y4)))))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A4) B5) tptp.bot_bot_set_o) (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A4) (forall ((Y4 Bool)) (=> (@ (@ tptp.member_o Y4) B5) (= X4 (not Y4)))))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) B5) (not (= X4 Y4)))))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) B5) (not (= X4 Y4)))))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A4) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A4) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A4) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 8.20/8.61 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) B5) tptp.bot_bo2099793752762293965at_nat)))
% 8.20/8.61 (assert (forall ((B5 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) B5) tptp.bot_bot_set_o)))
% 8.20/8.61 (assert (forall ((B5 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) B5) tptp.bot_bot_set_nat)))
% 8.20/8.61 (assert (forall ((B5 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) B5) tptp.bot_bot_set_int)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (= (= (@ (@ tptp.inf_in8396524679539076455nt_int A4) B5) tptp.bot_bo1488462491386950373nt_int) (forall ((X4 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int X4))) (=> (@ _let_1 A4) (not (@ _let_1 B5))))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (= (= (@ (@ tptp.inf_inf_set_set_nat A4) B5) tptp.bot_bot_set_set_nat) (forall ((X4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X4))) (=> (@ _let_1 A4) (not (@ _let_1 B5))))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5) tptp.bot_bo2099793752762293965at_nat) (forall ((X4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X4))) (=> (@ _let_1 A4) (not (@ _let_1 B5))))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A4) B5) tptp.bot_bot_set_o) (forall ((X4 Bool)) (let ((_let_1 (@ tptp.member_o X4))) (=> (@ _let_1 A4) (not (@ _let_1 B5))))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (=> (@ _let_1 A4) (not (@ _let_1 B5))))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (=> (@ _let_1 A4) (not (@ _let_1 B5))))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (=> (forall ((X3 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int X3))) (=> (@ _let_1 A4) (not (@ _let_1 B5))))) (= (@ (@ tptp.inf_in8396524679539076455nt_int A4) B5) tptp.bot_bo1488462491386950373nt_int))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (=> (@ _let_1 A4) (not (@ _let_1 B5))))) (= (@ (@ tptp.inf_inf_set_set_nat A4) B5) tptp.bot_bot_set_set_nat))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X3))) (=> (@ _let_1 A4) (not (@ _let_1 B5))))) (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5) tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o)) (=> (forall ((X3 Bool)) (let ((_let_1 (@ tptp.member_o X3))) (=> (@ _let_1 A4) (not (@ _let_1 B5))))) (= (@ (@ tptp.inf_inf_set_o A4) B5) tptp.bot_bot_set_o))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A4) (not (@ _let_1 B5))))) (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A4) (not (@ _let_1 B5))))) (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (D4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A4) C4) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B5) D4) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) (@ (@ tptp.inf_in2572325071724192079at_nat C4) D4))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (C4 tptp.set_nat) (B5 tptp.set_nat) (D4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A4) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) D4) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A4) B5)) (@ (@ tptp.inf_inf_set_nat C4) D4))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int) (C4 tptp.set_int) (B5 tptp.set_int) (D4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int B5) D4) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A4) B5)) (@ (@ tptp.inf_inf_set_int C4) D4))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) A4)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A4) B5)) A4)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A4) B5)) A4)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) B5)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A4) B5)) B5)))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A4) B5)) B5)))
% 8.20/8.61 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B5) A4) (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5) B5))))
% 8.20/8.61 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (= (@ (@ tptp.inf_inf_set_nat A4) B5) B5))))
% 8.20/8.61 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (= (@ (@ tptp.inf_inf_set_int A4) B5) B5))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5) (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5) A4))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (= (@ (@ tptp.inf_inf_set_nat A4) B5) A4))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (= (@ (@ tptp.inf_inf_set_int A4) B5) A4))))
% 8.20/8.61 (assert (forall ((C4 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat C4))) (=> (@ _let_1 A4) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)))))))
% 8.20/8.61 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C4))) (=> (@ _let_1 A4) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))
% 8.20/8.61 (assert (forall ((C4 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C4))) (=> (@ _let_1 A4) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o) (P2 (-> Bool Bool)) (Q2 (-> Bool Bool))) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (=> (@ P2 X3) (@ Q2 X3)))) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.inf_inf_set_o A4) (@ tptp.collect_o P2))) (@ (@ tptp.inf_inf_set_o B5) (@ tptp.collect_o Q2)))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_list_nat) (B5 tptp.set_list_nat) (P2 (-> tptp.list_nat Bool)) (Q2 (-> tptp.list_nat Bool))) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A4) B5) (=> (forall ((X3 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X3) A4) (=> (@ P2 X3) (@ Q2 X3)))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ (@ tptp.inf_inf_set_list_nat A4) (@ tptp.collect_list_nat P2))) (@ (@ tptp.inf_inf_set_list_nat B5) (@ tptp.collect_list_nat Q2)))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int) (P2 (-> tptp.set_Pr958786334691620121nt_int Bool)) (Q2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (=> (@ (@ tptp.ord_le483042692224249369nt_int A4) B5) (=> (forall ((X3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X3) A4) (=> (@ P2 X3) (@ Q2 X3)))) (@ (@ tptp.ord_le483042692224249369nt_int (@ (@ tptp.inf_in8396524679539076455nt_int A4) (@ tptp.collec5210948495886036740nt_int P2))) (@ (@ tptp.inf_in8396524679539076455nt_int B5) (@ tptp.collec5210948495886036740nt_int Q2)))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat) (P2 (-> tptp.set_nat Bool)) (Q2 (-> tptp.set_nat Bool))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A4) B5) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) A4) (=> (@ P2 X3) (@ Q2 X3)))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.inf_inf_set_set_nat A4) (@ tptp.collect_set_nat P2))) (@ (@ tptp.inf_inf_set_set_nat B5) (@ tptp.collect_set_nat Q2)))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (P2 (-> tptp.product_prod_nat_nat Bool)) (Q2 (-> tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A4) (=> (@ P2 X3) (@ Q2 X3)))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A4) (@ tptp.collec3392354462482085612at_nat P2))) (@ (@ tptp.inf_in2572325071724192079at_nat B5) (@ tptp.collec3392354462482085612at_nat Q2)))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (P2 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (=> (@ P2 X3) (@ Q2 X3)))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.collect_nat P2))) (@ (@ tptp.inf_inf_set_nat B5) (@ tptp.collect_nat Q2)))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (=> (@ P2 X3) (@ Q2 X3)))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2))) (@ (@ tptp.inf_inf_set_int B5) (@ tptp.collect_int Q2)))))))
% 8.20/8.61 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (S6 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat B5))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat A4))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) S6) (=> (= (@ _let_2 S6) (@ _let_1 S6)) (= (@ _let_2 S) (@ _let_1 S))))))))
% 8.20/8.61 (assert (forall ((S tptp.set_nat) (S6 tptp.set_nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B5))) (let ((_let_2 (@ tptp.inf_inf_set_nat A4))) (=> (@ (@ tptp.ord_less_eq_set_nat S) S6) (=> (= (@ _let_2 S6) (@ _let_1 S6)) (= (@ _let_2 S) (@ _let_1 S))))))))
% 8.20/8.61 (assert (forall ((S tptp.set_int) (S6 tptp.set_int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int B5))) (let ((_let_2 (@ tptp.inf_inf_set_int A4))) (=> (@ (@ tptp.ord_less_eq_set_int S) S6) (=> (= (@ _let_2 S6) (@ _let_1 S6)) (= (@ _let_2 S) (@ _let_1 S))))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) (@ (@ tptp.inf_in2572325071724192079at_nat B5) C4))) (@ (@ tptp.inf_in2572325071724192079at_nat C4) A4)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A4) B5)) (@ (@ tptp.sup_su6327502436637775413at_nat B5) C4))) (@ (@ tptp.sup_su6327502436637775413at_nat C4) A4)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat A4) B5)) (@ (@ tptp.inf_in1697001100524423349at_nat B5) C4))) (@ (@ tptp.inf_in1697001100524423349at_nat C4) A4)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5)) (@ (@ tptp.sup_su3035147773818789531at_nat B5) C4))) (@ (@ tptp.sup_su3035147773818789531at_nat C4) A4)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A4) B5)) (@ (@ tptp.inf_in7913087082777306421at_nat B5) C4))) (@ (@ tptp.inf_in7913087082777306421at_nat C4) A4)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5)) (@ (@ tptp.sup_su5525570899277871387at_nat B5) C4))) (@ (@ tptp.sup_su5525570899277871387at_nat C4) A4)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat A4) B5)) (@ (@ tptp.inf_inf_set_nat B5) C4))) (@ (@ tptp.inf_inf_set_nat C4) A4)) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.sup_sup_set_nat B5) C4))) (@ (@ tptp.sup_sup_set_nat C4) A4)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A4))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B5) C4)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.inf_in1697001100524423349at_nat A4))) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat B5) C4)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A4))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B5) C4)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A4))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat B5) C4)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat A4))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B5) C4)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat A4))) (= (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat B5) C4)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A4))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B5) C4)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A4))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B5) C4)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.61 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat B5) C4)) A4) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat B5) A4)) (@ (@ tptp.inf_in2572325071724192079at_nat C4) A4)))))
% 8.20/8.61 (assert (forall ((B5 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat) (A4 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat B5) C4)) A4) (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat B5) A4)) (@ (@ tptp.inf_in1697001100524423349at_nat C4) A4)))))
% 8.20/8.61 (assert (forall ((B5 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B5) C4)) A4) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat B5) A4)) (@ (@ tptp.inf_in7913087082777306421at_nat C4) A4)))))
% 8.20/8.61 (assert (forall ((B5 tptp.set_nat) (C4 tptp.set_nat) (A4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat B5) C4)) A4) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat B5) A4)) (@ (@ tptp.inf_inf_set_nat C4) A4)))))
% 8.20/8.61 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat B5) C4)) A4) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat B5) A4)) (@ (@ tptp.sup_su6327502436637775413at_nat C4) A4)))))
% 8.20/8.61 (assert (forall ((B5 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat) (A4 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat B5) C4)) A4) (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat B5) A4)) (@ (@ tptp.sup_su3035147773818789531at_nat C4) A4)))))
% 8.20/8.61 (assert (forall ((B5 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat B5) C4)) A4) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B5) A4)) (@ (@ tptp.sup_su5525570899277871387at_nat C4) A4)))))
% 8.20/8.61 (assert (forall ((B5 tptp.set_nat) (C4 tptp.set_nat) (A4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat B5) C4)) A4) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat B5) A4)) (@ (@ tptp.sup_sup_set_nat C4) A4)))))
% 8.20/8.61 (assert (= tptp.inf_inf_option_assn (lambda ((X4 tptp.option_assn) (Y4 tptp.option_assn)) (@ (@ (@ tptp.case_o4484465799723439917n_assn tptp.none_assn) (lambda ((Z tptp.assn)) (@ (@ (@ tptp.case_o4484465799723439917n_assn tptp.none_assn) (lambda ((Aa tptp.assn)) (@ tptp.some_assn (@ (@ tptp.inf_inf_assn Z) Aa)))) Y4))) X4))))
% 8.20/8.61 (assert (= tptp.inf_in777885744494410645at_nat (lambda ((X4 tptp.option8963830502488799655at_nat) (Y4 tptp.option8963830502488799655at_nat)) (@ (@ (@ tptp.case_o311359030874850053at_nat tptp.none_s625347054029921090at_nat) (lambda ((Z 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 Z) Aa)))) Y4))) X4))))
% 8.20/8.61 (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 ((Z 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 Z) Aa)))) Y4))) X4))))
% 8.20/8.61 (assert (= tptp.inf_inf_option_nat (lambda ((X4 tptp.option_nat) (Y4 tptp.option_nat)) (@ (@ (@ tptp.case_o7429725398727453821at_nat tptp.none_nat) (lambda ((Z tptp.nat)) (@ (@ (@ tptp.case_o7429725398727453821at_nat tptp.none_nat) (lambda ((Aa tptp.nat)) (@ tptp.some_nat (@ (@ tptp.inf_inf_nat Z) Aa)))) Y4))) X4))))
% 8.20/8.61 (assert (= tptp.inf_in7104746047340619750_int_o (lambda ((X4 tptp.option1893999432384633940_int_o) (Y4 tptp.option1893999432384633940_int_o)) (@ (@ (@ tptp.case_o670596351732880613_int_o tptp.none_P2320557853698873699_int_o) (lambda ((Z (-> tptp.product_prod_int_int Bool))) (@ (@ (@ tptp.case_o670596351732880613_int_o tptp.none_P2320557853698873699_int_o) (lambda ((Aa (-> tptp.product_prod_int_int Bool))) (@ tptp.some_P180497116919641311_int_o (@ (@ tptp.inf_in3604695632404883862_int_o Z) Aa)))) Y4))) X4))))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z3 tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (@ (@ tptp.ord_less_eq_assn (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z3))) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z3))) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.sup_su8463660629351352368_int_o X))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z3))) (@ (@ tptp.inf_in3604695632404883862_int_o (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (@ (@ tptp.ord_le8081472938463900775at_nat (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat Y) Z3))) (@ (@ tptp.inf_in1697001100524423349at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (@ (@ tptp.ord_le1268244103169919719at_nat (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z3))) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z3))) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z3 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) Z3))) (@ (@ tptp.inf_inf_set_int (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.sup_sup_rat X))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ (@ tptp.inf_inf_rat Y) Z3))) (@ (@ tptp.inf_inf_rat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z3))) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X))) (@ (@ tptp.ord_less_eq_int (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z3))) (@ (@ tptp.inf_inf_int (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z3 tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z3))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.sup_su8463660629351352368_int_o (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_su8463660629351352368_int_o Y) Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z3 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 Z3))) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat X))) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z3 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 Z3))) (@ _let_1 (@ (@ tptp.sup_sup_set_int Y) Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.inf_inf_rat X))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_sup_rat Y) Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z3))))))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.inf_inf_int X))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int (@ _let_1 Y)) (@ _let_1 Z3))) (@ _let_1 (@ (@ tptp.sup_sup_int Y) Z3))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.divide_divide_rat A) C2))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)) (not (= C2 tptp.zero_zero_rat))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2))))))
% 8.20/8.61 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A4))) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B5) C4))) (@ (@ tptp.ord_le3146513528884898305at_nat C4) A4)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.inf_in1697001100524423349at_nat A4))) (= (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat B5) C4))) (@ (@ tptp.ord_le8081472938463900775at_nat C4) A4)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A4))) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B5) C4))) (@ (@ tptp.ord_le1268244103169919719at_nat C4) A4)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A4))) (= (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B5) C4))) (@ (@ tptp.ord_less_eq_set_nat C4) A4)))))
% 8.20/8.61 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A4))) (= (= (@ (@ tptp.sup_sup_set_int (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_sup_set_int B5) C4))) (@ (@ tptp.ord_less_eq_set_int C4) A4)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C2)) (@ (@ tptp.divide_divide_rat B) C2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 8.20/8.61 (assert (forall ((X tptp.rat) (Y tptp.rat) (W2 tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ _let_1 W2) (=> (@ (@ tptp.ord_less_rat W2) Z3) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z3)) (@ (@ tptp.divide_divide_rat Y) W2)))))))))
% 8.20/8.61 (assert (forall ((X tptp.rat) (Y tptp.rat) (W2 tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W2) (=> (@ (@ tptp.ord_less_eq_rat W2) Z3) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z3)) (@ (@ tptp.divide_divide_rat Y) W2))))))))
% 8.20/8.61 (assert (forall ((Y tptp.rat) (X tptp.rat) (W2 tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W2) (=> (@ (@ tptp.ord_less_eq_rat W2) Z3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Z3)) (@ (@ tptp.divide_divide_rat Y) W2))))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C2) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C2)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C2))))))
% 8.20/8.61 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C2)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2))))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (= (@ _let_1 (@ (@ tptp.times_times_int B) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2))))))
% 8.20/8.61 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ _let_1 C2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (and (=> _let_4 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> _let_4 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) B)))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C2))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C2))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) B)))))
% 8.20/8.61 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.times_times_rat Z3) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) Z3)))))
% 8.20/8.61 (assert (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z3) Y)) X) (@ (@ tptp.ord_less_rat Z3) (@ (@ tptp.divide_divide_rat X) Y))))))
% 8.20/8.61 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_2 C2) (=> (@ _let_2 (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((Z3 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z3)) B))) (let ((_let_2 (= Z3 tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat B) Z3))) Z3))))))))
% 8.20/8.61 (assert (forall ((Z3 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z3)))) (let ((_let_2 (= Z3 tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) Z3)) B)) Z3))))))))
% 8.20/8.61 (assert (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z3)))))))
% 8.20/8.61 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z3 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) Z3) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z3) Y))) Y)))))
% 8.20/8.61 (assert (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z3) (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z3) Y))) Y)))))
% 8.20/8.61 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat Y) Z3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z3)) Y)) Z3)))))
% 8.20/8.61 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Z3)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Y) Z3))) Z3)))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) N2) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.divide_divide_nat M) N2))))))
% 8.20/8.61 (assert (@ (@ (@ tptp.lattic6529551498584149819at_nat tptp.inf_in2572325071724192079at_nat) tptp.ord_le3146513528884898305at_nat) tptp.ord_le7866589430770878221at_nat))
% 8.20/8.61 (assert (@ (@ (@ tptp.lattic3109210760196336428et_nat tptp.inf_inf_set_nat) tptp.ord_less_eq_set_nat) tptp.ord_less_set_nat))
% 8.20/8.61 (assert (@ (@ (@ tptp.lattic8660852769118194346_int_o tptp.inf_in3604695632404883862_int_o) tptp.ord_le8369615600986905444_int_o) tptp.ord_le8213806771718485336_int_o))
% 8.20/8.61 (assert (@ (@ (@ tptp.lattic5623431474481994958t_assn tptp.inf_inf_assn) tptp.ord_less_eq_assn) tptp.ord_less_assn))
% 8.20/8.61 (assert (@ (@ (@ tptp.lattic8154731777541915528et_int tptp.inf_inf_set_int) tptp.ord_less_eq_set_int) tptp.ord_less_set_int))
% 8.20/8.61 (assert (@ (@ (@ tptp.lattic5374021519246970238et_rat tptp.inf_inf_rat) tptp.ord_less_eq_rat) tptp.ord_less_rat))
% 8.20/8.61 (assert (@ (@ (@ tptp.lattic6009151579333465974et_nat tptp.inf_inf_nat) tptp.ord_less_eq_nat) tptp.ord_less_nat))
% 8.20/8.61 (assert (@ (@ (@ tptp.lattic6006661108824415698et_int tptp.inf_inf_int) tptp.ord_less_eq_int) tptp.ord_less_int))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 8.20/8.61 (assert (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z3) Y)) X) (@ (@ tptp.ord_less_eq_rat Z3) (@ (@ tptp.divide_divide_rat X) Y))))))
% 8.20/8.61 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.times_times_rat Z3) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) Z3)))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) B)))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C2))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C2)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C2))))))
% 8.20/8.61 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) B)))))
% 8.20/8.61 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 8.20/8.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 8.20/8.61 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_3 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C2) B))) B) (@ (@ tptp.plus_p5714425477246183910nteger C2) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C2) B))) B) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C2) B))) B) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C2 tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural C2) B))) B) (@ (@ tptp.plus_p4538020629002901425atural C2) (@ (@ tptp.divide5121882707175180666atural A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C2 tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C2))) B) (@ (@ tptp.plus_p5714425477246183910nteger C2) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C2))) B) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C2))) B) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C2 tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural B) C2))) B) (@ (@ tptp.plus_p4538020629002901425atural C2) (@ (@ tptp.divide5121882707175180666atural A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.code_integer) (C2 tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C2) B)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C2) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C2) B)) A)) B) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C2) B)) A)) B) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.code_natural) (C2 tptp.code_natural) (A tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural C2) B)) A)) B) (@ (@ tptp.plus_p4538020629002901425atural C2) (@ (@ tptp.divide5121882707175180666atural A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.code_integer) (C2 tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C2)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C2) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C2)) A)) B) (@ (@ tptp.plus_plus_nat C2) (@ (@ tptp.divide_divide_nat A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C2)) A)) B) (@ (@ tptp.plus_plus_int C2) (@ (@ tptp.divide_divide_int A) B))))))
% 8.20/8.61 (assert (forall ((B tptp.code_natural) (C2 tptp.code_natural) (A tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) C2)) A)) B) (@ (@ tptp.plus_p4538020629002901425atural C2) (@ (@ tptp.divide5121882707175180666atural A) B))))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.inf_inf_assn (@ tptp.pure_assn A)) (@ tptp.pure_assn B)) (@ tptp.pure_assn (and A B)))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (Q2 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 P2) Q2)) _let_1) (and (@ (@ tptp.rep_assn P2) _let_1) (@ (@ tptp.rep_assn Q2) _let_1))))))
% 8.20/8.61 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (S tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.inf_inf_int_int_o (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y4)) R3))) (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y4)) S))) (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y4)) (@ (@ tptp.inf_in2269163501485487111nt_int R3) S))))))
% 8.20/8.61 (assert (forall ((R3 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)) R3))) (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 R3) S))))))
% 8.20/8.61 (assert (forall ((R3 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)) R3))) (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 R3) S))))))
% 8.20/8.61 (assert (forall ((R3 tptp.set_Pr7600907837789447088it_nat) (S tptp.set_Pr7600907837789447088it_nat)) (= (@ (@ tptp.inf_in844129575377303227_nat_o (lambda ((X4 tptp.b) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat X4) Y4)) R3))) (lambda ((X4 tptp.b) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat X4) Y4)) S))) (lambda ((X4 tptp.b) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat X4) Y4)) (@ (@ tptp.inf_in3995795194662975554it_nat R3) S))))))
% 8.20/8.61 (assert (forall ((R3 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)) R3))) (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 R3) S))))))
% 8.20/8.61 (assert (forall ((R3 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)) R3))) (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 R3) S))))))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (H tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.inf_inf_assn P2) Q2)) H) (and (@ (@ tptp.rep_assn P2) H) (@ (@ tptp.rep_assn Q2) H)))))
% 8.20/8.61 (assert (forall ((A4 tptp.assn) (B5 tptp.assn) (C4 tptp.assn)) (let ((_let_1 (@ tptp.entails A4))) (=> (@ _let_1 B5) (=> (@ _let_1 C4) (@ _let_1 (@ (@ tptp.inf_inf_assn B5) C4)))))))
% 8.20/8.61 (assert (forall ((A4 tptp.assn) (C4 tptp.assn) (B5 tptp.assn)) (=> (@ (@ tptp.entails A4) C4) (@ (@ tptp.entails (@ (@ tptp.inf_inf_assn A4) B5)) C4))))
% 8.20/8.61 (assert (forall ((B5 tptp.assn) (C4 tptp.assn) (A4 tptp.assn)) (=> (@ (@ tptp.entails B5) C4) (@ (@ tptp.entails (@ (@ tptp.inf_inf_assn A4) B5)) C4))))
% 8.20/8.61 (assert (forall ((R3 tptp.set_o) (S tptp.set_o)) (= (@ (@ tptp.inf_inf_o_o (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) R3))) (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) S))) (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) (@ (@ tptp.inf_inf_set_o R3) S))))))
% 8.20/8.61 (assert (forall ((R3 tptp.set_se6260736226359567993nt_int) (S tptp.set_se6260736226359567993nt_int)) (= (@ (@ tptp.inf_in5102985939729578038_int_o (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) R3))) (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) S))) (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) (@ (@ tptp.inf_in8396524679539076455nt_int R3) S))))))
% 8.20/8.61 (assert (forall ((R3 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) R3))) (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 R3) S))))))
% 8.20/8.61 (assert (forall ((R3 tptp.set_int) (S tptp.set_int)) (= (@ (@ tptp.inf_inf_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) R3))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) S))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) (@ (@ tptp.inf_inf_set_int R3) S))))))
% 8.20/8.61 (assert (forall ((R3 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) R3))) (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 R3) S))))))
% 8.20/8.61 (assert (forall ((R3 tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.inf_inf_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) R3))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) S))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) (@ (@ tptp.inf_inf_set_nat R3) S))))))
% 8.20/8.61 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (S tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.inf_in3604695632404883862_int_o (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X4) R3))) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X4) S))) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X4) (@ (@ tptp.inf_in2269163501485487111nt_int R3) S))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (= tptp.inf_in8396524679539076455nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (@ tptp.collec5210948495886036740nt_int (@ (@ tptp.inf_in5102985939729578038_int_o (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) A6))) (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) B6)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) M)))
% 8.20/8.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K2)) (@ (@ tptp.divide_divide_nat N2) K2)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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)))
% 8.20/8.61 (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)))
% 8.20/8.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K2))) (=> (@ (@ 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)))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 8.20/8.61 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 8.20/8.61 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 8.20/8.61 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) B) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.divide5121882707175180666atural A) B)) tptp.one_one_Code_natural)))))
% 8.20/8.61 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 8.20/8.61 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 8.20/8.61 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 8.20/8.61 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural B) A)) B) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.divide5121882707175180666atural A) B)) tptp.one_one_Code_natural)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P2 (@ (@ tptp.divide_divide_nat M) N2)) (and (=> _let_1 (@ P2 tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I)) J)) (@ P2 I))))))))))
% 8.20/8.61 (assert (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat) (Q2 tptp.assn) (R3 tptp.assn)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (@ tptp.in_range _let_1) (=> (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H4))) (=> (= (@ (@ tptp.inf_inf_set_nat As) As6) tptp.bot_bot_set_nat) (=> (@ (@ (@ tptp.relH As) H) H4) (=> (@ tptp.in_range (@ _let_1 As)) (=> (@ (@ tptp.rep_assn Q2) (@ _let_1 As6)) (@ (@ tptp.rep_assn R3) (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As6))))))))) (@ (@ tptp.rep_assn (@ (@ tptp.wand_assn Q2) R3)) _let_1))))))
% 8.20/8.61 (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 ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (exists ((As12 tptp.set_nat) (As23 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (and (= As2 (@ (@ tptp.sup_sup_set_nat As12) As23)) (= (@ (@ tptp.inf_inf_set_nat As12) As23) tptp.bot_bot_set_nat) (@ X (@ _let_1 As12)) (@ Xa (@ _let_1 As23)))))))))))
% 8.20/8.61 (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 ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (not (exists ((As13 tptp.set_nat) (As24 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (and (= As2 (@ (@ tptp.sup_sup_set_nat As13) As24)) (= (@ (@ tptp.inf_inf_set_nat As13) As24) tptp.bot_bot_set_nat) (@ X (@ _let_1 As13)) (@ Xa (@ _let_1 As24))))))))))))
% 8.20/8.61 (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 ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (= Y (not (exists ((As1 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (and (= As2 (@ (@ tptp.sup_sup_set_nat As1) As22)) (= (@ (@ tptp.inf_inf_set_nat As1) As22) tptp.bot_bot_set_nat) (@ X (@ _let_1 As1)) (@ Xa (@ _let_1 As22)))))))))))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (@ (@ (@ tptp.times_assn_raw P2) Q2) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (exists ((As1 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As (@ (@ tptp.sup_sup_set_nat As1) As22)) (= (@ (@ tptp.inf_inf_set_nat As1) As22) tptp.bot_bot_set_nat) (@ P2 (@ _let_1 As1)) (@ Q2 (@ _let_1 As22))))))))
% 8.20/8.61 (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 ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (exists ((As12 tptp.set_nat) (As23 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (and (= As2 (@ (@ tptp.sup_sup_set_nat As12) As23)) (= (@ (@ tptp.inf_inf_set_nat As12) As23) tptp.bot_bot_set_nat) (@ X (@ _let_1 As12)) (@ Xa (@ _let_1 As23))))))))))))))
% 8.20/8.61 (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 ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (not (exists ((As13 tptp.set_nat) (As24 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (and (= As2 (@ (@ tptp.sup_sup_set_nat As13) As24)) (= (@ (@ tptp.inf_inf_set_nat As13) As24) tptp.bot_bot_set_nat) (@ X (@ _let_1 As13)) (@ Xa (@ _let_1 As24)))))))))))))))
% 8.20/8.61 (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 ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= Xb _let_1) (=> (= Y (exists ((As1 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (and (= As2 (@ (@ tptp.sup_sup_set_nat As1) As22)) (= (@ (@ tptp.inf_inf_set_nat As1) As22) tptp.bot_bot_set_nat) (@ X (@ _let_1 As1)) (@ Xa (@ _let_1 As22)))))) (not (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1)))))))))))))
% 8.20/8.61 (assert (forall ((H tptp.heap_e7401611519738050253t_unit)) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H) tptp.bot_bot_set_nat))))
% 8.20/8.61 (assert (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat) (As5 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (= (@ tptp.in_range (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As5))) (and (@ tptp.in_range (@ _let_1 As)) (@ tptp.in_range (@ _let_1 As5)))))))
% 8.20/8.61 (assert (= tptp.inf_inf_Product_unit (lambda ((Uu3 tptp.product_unit) (Uv tptp.product_unit)) tptp.product_Unity)))
% 8.20/8.61 (assert (= tptp.ord_less_eq_assn (lambda ((A5 tptp.assn) (B4 tptp.assn)) (= A5 (@ (@ tptp.inf_inf_assn A5) B4)))))
% 8.20/8.61 (assert (forall ((Y tptp.product_unit)) (= Y tptp.product_Unity)))
% 8.20/8.61 (assert (= tptp.sup_sup_Product_unit (lambda ((Uu3 tptp.product_unit) (Uv tptp.product_unit)) tptp.product_Unity)))
% 8.20/8.61 (assert (= tptp.bot_bot_Product_unit tptp.product_Unity))
% 8.20/8.61 (assert (forall ((P2 tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H) (@ tptp.in_range H))))
% 8.20/8.61 (assert (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ (@ tptp.relH As) H) H5) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H5) As)))))
% 8.20/8.61 (assert (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ (@ tptp.relH As) H) H5) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H) As)))))
% 8.20/8.61 (assert (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H) As)) (@ (@ (@ tptp.relH As) H) H))))
% 8.20/8.61 (assert (forall ((As tptp.set_nat) (As5 tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (=> (@ (@ tptp.ord_less_eq_set_nat As) As5) (=> (@ tptp.in_range (@ _let_1 As5)) (@ tptp.in_range (@ _let_1 As)))))))
% 8.20/8.61 (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))))))))
% 8.20/8.61 (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)))))))
% 8.20/8.61 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.in_range X) Y) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (= Y (not (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) As2) (@ (@ tptp.ord_less_nat X4) (@ tptp.lim_Product_unit H2))))))))))))
% 8.20/8.61 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.in_range X) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (not (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) As2) (@ (@ tptp.ord_less_nat X6) (@ tptp.lim_Product_unit H2)))))))))))
% 8.20/8.61 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.in_range X)) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) As2) (@ (@ tptp.ord_less_nat X3) (@ tptp.lim_Product_unit H2))))))))))
% 8.20/8.61 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (= (@ (@ (@ tptp.wand_raw P2) Q2) _let_1) (and (@ tptp.in_range _let_1) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As7 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H7))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As7) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H) H7) (@ tptp.in_range (@ _let_1 As)) (@ P2 (@ _let_1 As7))) (@ Q2 (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As7)))))))))))
% 8.20/8.61 (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 ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= Xb _let_1) (= Y (not (and (@ tptp.in_range _let_1) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As7 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H7))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As2) As7) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As2) H2) H7) (@ tptp.in_range (@ _let_1 As2)) (@ X (@ _let_1 As7))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As7))))))))))))))))
% 8.20/8.61 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.wand_raw X) Xa) Xb) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= Xb _let_1) (not (and (@ tptp.in_range _let_1) (forall ((H8 tptp.heap_e7401611519738050253t_unit) (As8 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H8))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As2) As8) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As2) H2) H8) (@ tptp.in_range (@ _let_1 As2)) (@ X (@ _let_1 As8))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As8)))))))))))))))
% 8.20/8.61 (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 ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= Xb _let_1) (and (@ tptp.in_range _let_1) (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H4))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As2) As6) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As2) H2) H4) (@ tptp.in_range (@ _let_1 As2)) (@ X (@ _let_1 As6))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As6))))))))))))))
% 8.20/8.61 (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 ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= Xb _let_1) (=> (= Y (and (@ tptp.in_range _let_1) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As7 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H7))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As2) As7) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As2) H2) H7) (@ tptp.in_range (@ _let_1 As2)) (@ X (@ _let_1 As7))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As7)))))))) (not (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1)))))))))))))
% 8.20/8.61 (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 ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= 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) (As8 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H8))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As2) As8) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As2) H2) H8) (@ tptp.in_range (@ _let_1 As2)) (@ X (@ _let_1 As8))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As8)))))))))))))))))
% 8.20/8.61 (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 ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= 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 ((H4 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H4))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As2) As6) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As2) H2) H4) (@ tptp.in_range (@ _let_1 As2)) (@ X (@ _let_1 As6))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As6))))))))))))))))
% 8.20/8.61 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.in_range X) Y) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) X) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= X _let_1) (=> (= Y (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) As2) (@ (@ tptp.ord_less_nat X4) (@ tptp.lim_Product_unit H2))))) (not (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) _let_1)))))))))))
% 8.20/8.61 (assert (= tptp.ord_less_assn (lambda ((A5 tptp.assn) (B4 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A5) B4) (not (= A5 B4))))))
% 8.20/8.61 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.in_range X)) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) X) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) _let_1) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) As2) (@ (@ tptp.ord_less_nat X3) (@ tptp.lim_Product_unit H2)))))))))))))
% 8.20/8.61 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.in_range X) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) X) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) _let_1) (not (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) As2) (@ (@ tptp.ord_less_nat X6) (@ tptp.lim_Product_unit H2))))))))))))))
% 8.20/8.61 (assert (= tptp.defaul566961228789861419t_unit tptp.product_Unity))
% 8.20/8.61 (assert (forall ((A4 tptp.nat) (B5 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A4) N2)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B5) N2) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B5) N2))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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))))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (= tptp.wand_assn (lambda ((P5 tptp.assn) (Q3 tptp.assn)) (@ tptp.abs_assn (@ (@ tptp.wand_raw (@ tptp.rep_assn P5)) (@ tptp.rep_assn Q3))))))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.rat) (B tptp.rat) (C2 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) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C2)))))))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.nat) (B tptp.nat) (C2 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) C2)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C2)))))))
% 8.20/8.61 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.int) (B tptp.int) (C2 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) C2)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C2)))))))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.rat) (B tptp.rat) (C2 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) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C2)))))))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.nat) (B tptp.nat) (C2 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) C2)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C2)))))))
% 8.20/8.61 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int) (C2 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) C2)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C2)))))))
% 8.20/8.61 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural) (A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (=> (@ (@ tptp.nO_MAT3836730678284324717al_rat (@ (@ tptp.divide5121882707175180666atural X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C2)))))))
% 8.20/8.61 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural) (A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.nO_MAT4471860738370820453al_nat (@ (@ tptp.divide5121882707175180666atural X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C2)))))))
% 8.20/8.61 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural) (A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.nO_MAT4469370267861770177al_int (@ (@ tptp.divide5121882707175180666atural X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C2)))))))
% 8.20/8.61 (assert (forall ((X tptp.rat) (Y tptp.rat) (A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (=> (@ (@ tptp.nO_MATCH_rat_rat (@ (@ tptp.divide_divide_rat X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C2)))))))
% 8.20/8.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N2)) (= M N2))))
% 8.20/8.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N2)) (= M N2))))
% 8.20/8.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger M) (@ tptp.semiri4939895301339042750nteger N2)) (= M N2))))
% 8.20/8.61 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 8.20/8.61 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 8.20/8.61 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural B) A)) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 8.20/8.61 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 8.20/8.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat M) N2) M))))
% 8.20/8.61 (assert (forall ((X tptp.assn)) (= (@ tptp.abs_assn (@ tptp.rep_assn X)) X)))
% 8.20/8.61 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 8.20/8.61 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 8.20/8.61 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 8.20/8.61 (assert (= (@ tptp.semiri4939895301339042750nteger tptp.zero_zero_nat) tptp.zero_z3403309356797280102nteger))
% 8.20/8.61 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger M) tptp.zero_z3403309356797280102nteger) (= M tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N2)) (= tptp.zero_zero_nat N2))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N2)) (= tptp.zero_zero_nat N2))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= tptp.zero_zero_nat N2))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.semiri4939895301339042750nteger N2)) (= tptp.zero_zero_nat N2))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C2) B))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 8.20/8.61 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C2) B))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 8.20/8.61 (assert (forall ((A tptp.code_natural) (C2 tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural C2) B))) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 8.20/8.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C2))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 8.20/8.61 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C2))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 8.20/8.61 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C2 tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural B) C2))) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 8.20/8.61 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C2) B)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 8.20/8.61 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C2) B)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 8.20/8.61 (assert (forall ((C2 tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural C2) B)) A)) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 8.20/8.61 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C2)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 8.20/8.61 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C2)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 8.20/8.61 (assert (forall ((B tptp.code_natural) (C2 tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) C2)) A)) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 8.20/8.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N2) tptp.one_one_rat) (= N2 tptp.one_one_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N2) tptp.one_one_int) (= N2 tptp.one_one_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N2) tptp.one_one_nat) (= N2 tptp.one_one_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger N2) tptp.one_one_Code_integer) (= N2 tptp.one_one_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N2)) (= N2 tptp.one_one_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N2)) (= N2 tptp.one_one_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= N2 tptp.one_one_nat))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_Code_integer (@ tptp.semiri4939895301339042750nteger N2)) (= N2 tptp.one_one_nat))))
% 8.20/8.61 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 8.20/8.61 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 8.20/8.61 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 8.20/8.61 (assert (= (@ tptp.semiri4939895301339042750nteger tptp.one_one_nat) tptp.one_one_Code_integer))
% 8.20/8.61 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger) (= M tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 8.20/8.61 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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)))))
% 8.20/8.61 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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))))
% 8.20/8.61 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C2))) C2) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C2)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C2))) C2) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C2)))))
% 8.20/8.62 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C2 tptp.code_natural)) (let ((_let_1 (@ tptp.plus_p4538020629002901425atural A))) (= (@ (@ tptp.modulo8411746178871703098atural (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural B) C2))) C2) (@ (@ tptp.modulo8411746178871703098atural (@ _let_1 B)) C2)))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C2)) B)) C2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C2))))
% 8.20/8.62 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C2)) B)) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C2))))
% 8.20/8.62 (assert (forall ((A tptp.code_natural) (C2 tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) C2)) B)) C2) (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) C2))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (C2 tptp.nat) (A2 tptp.nat) (B tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C2) (@ (@ tptp.modulo_modulo_nat A2) C2)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C2) (@ (@ tptp.modulo_modulo_nat B2) C2)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A2) B2)) C2))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (C2 tptp.int) (A2 tptp.int) (B tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C2) (@ (@ tptp.modulo_modulo_int A2) C2)) (=> (= (@ (@ tptp.modulo_modulo_int B) C2) (@ (@ tptp.modulo_modulo_int B2) C2)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A2) B2)) C2))))))
% 8.20/8.62 (assert (forall ((A tptp.code_natural) (C2 tptp.code_natural) (A2 tptp.code_natural) (B tptp.code_natural) (B2 tptp.code_natural)) (=> (= (@ (@ tptp.modulo8411746178871703098atural A) C2) (@ (@ tptp.modulo8411746178871703098atural A2) C2)) (=> (= (@ (@ tptp.modulo8411746178871703098atural B) C2) (@ (@ tptp.modulo8411746178871703098atural B2) C2)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) C2) (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural A2) B2)) C2))))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C2)) (@ (@ tptp.modulo_modulo_nat B) C2))) C2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C2))))
% 8.20/8.62 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C2)) (@ (@ tptp.modulo_modulo_int B) C2))) C2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C2))))
% 8.20/8.62 (assert (forall ((A tptp.code_natural) (C2 tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) C2)) (@ (@ tptp.modulo8411746178871703098atural B) C2))) C2) (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) C2))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) M)))
% 8.20/8.62 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 8.20/8.62 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) Z3)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N2))) Z3))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1314217659103216013at_int M)))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 8.20/8.62 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 8.20/8.62 (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)))))))))
% 8.20/8.62 (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)))))))))
% 8.20/8.62 (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)))))))))
% 8.20/8.62 (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)))))))))
% 8.20/8.62 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 8.20/8.62 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (Pr tptp.assn)) (=> (forall ((H2 tptp.produc3658429121746597890et_nat)) (= (@ P2 H2) (@ (@ tptp.rep_assn Pr) H2))) (= (@ tptp.abs_assn P2) Pr))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (Pr tptp.assn)) (=> (forall ((H2 tptp.produc3658429121746597890et_nat)) (= (@ P2 H2) (@ (@ tptp.rep_assn Pr) H2))) (= Pr (@ tptp.abs_assn P2)))))
% 8.20/8.62 (assert (= tptp.pure_assn (lambda ((B4 Bool)) (@ tptp.abs_assn (@ tptp.pure_a825153325127701367it_nat B4)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri4939895301339042750nteger N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2))))
% 8.20/8.62 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 8.20/8.62 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 8.20/8.62 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.62 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C2) (@ (@ tptp.modulo_modulo_int B) C2)) (not (forall ((D tptp.int)) (not (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C2) D)))))))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C2)) (@ (@ tptp.divide_divide_nat B) C2))) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C2)) (@ (@ tptp.modulo_modulo_nat B) C2))) C2)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C2)) (@ (@ tptp.divide_divide_int B) C2))) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C2)) (@ (@ tptp.modulo_modulo_int B) C2))) C2)))))
% 8.20/8.62 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C2 tptp.code_natural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) C2) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.divide5121882707175180666atural A) C2)) (@ (@ tptp.divide5121882707175180666atural B) C2))) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) C2)) (@ (@ tptp.modulo8411746178871703098atural B) C2))) C2)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger I2)) (@ tptp.semiri4939895301339042750nteger J2)))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I2)) (@ tptp.semiri681578069525770553at_rat J2)))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I2)) (@ tptp.semiri1316708129612266289at_nat J2)))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J2)))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((M5 tptp.nat)) (@ (@ P2 M5) tptp.zero_zero_nat)) (=> (forall ((M5 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (=> (@ (@ P2 N5) (@ (@ tptp.modulo_modulo_nat M5) N5)) (@ (@ P2 M5) N5)))) (@ (@ P2 M) N2)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K2)))) (=> (@ (@ tptp.ord_less_int I2) J2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J2)))))))
% 8.20/8.62 (assert (forall ((K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (not (forall ((N5 tptp.nat)) (=> (= K2 (@ tptp.semiri1314217659103216013at_int N5)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5))))))))
% 8.20/8.62 (assert (forall ((K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (exists ((N5 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (= K2 (@ tptp.semiri1314217659103216013at_int N5)))))))
% 8.20/8.62 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (= (@ (@ tptp.plus_plus_nat X) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))))
% 8.20/8.62 (assert (= tptp.bot_bot_assn (@ tptp.abs_assn (lambda ((Uu2 tptp.produc3658429121746597890et_nat)) false))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))
% 8.20/8.62 (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)))
% 8.20/8.62 (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)))
% 8.20/8.62 (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)))
% 8.20/8.62 (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)))
% 8.20/8.62 (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)))
% 8.20/8.62 (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)))
% 8.20/8.62 (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)))
% 8.20/8.62 (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)))
% 8.20/8.62 (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)))
% 8.20/8.62 (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)))
% 8.20/8.62 (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)))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))) C2) (@ (@ tptp.plus_plus_nat A) C2))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))) C2) (@ (@ tptp.plus_plus_int A) C2))))
% 8.20/8.62 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C2 tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B))) C2) (@ (@ tptp.plus_p4538020629002901425atural A) C2))))
% 8.20/8.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))) C2) (@ (@ tptp.plus_plus_nat A) C2))))
% 8.20/8.62 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))) C2) (@ (@ tptp.plus_plus_int A) C2))))
% 8.20/8.62 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C2 tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) (@ (@ tptp.modulo8411746178871703098atural A) B))) C2) (@ (@ tptp.plus_p4538020629002901425atural A) C2))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.divide_divide_nat B) C2))) (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C2))) C2))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.divide_divide_int B) C2))) (@ (@ tptp.divide_divide_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C2))) C2))))))
% 8.20/8.62 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C2 tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (= (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C2) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_1 (@ (@ tptp.divide5121882707175180666atural B) C2))) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural B) C2))) C2))))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))))
% 8.20/8.62 (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))))))))))
% 8.20/8.62 (assert (forall ((A4 tptp.nat) (B5 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ (@ tptp.modulo_modulo_nat A4) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B5) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A4) N2)) (@ (@ tptp.divide_divide_nat B5) N2))))))))
% 8.20/8.62 (assert (forall ((A4 tptp.nat) (N2 tptp.nat)) (= A4 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A4) N2)) N2)) (@ (@ tptp.modulo_modulo_nat A4) N2)))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q6 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N2))) (= (@ _let_1 (@ _let_2 Q6)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N2)) Q6))) (@ _let_1 N2)))))))
% 8.20/8.62 (assert (= tptp.sup_sup_assn (lambda ((P5 tptp.assn) (Q3 tptp.assn)) (@ tptp.abs_assn (lambda ((H6 tptp.produc3658429121746597890et_nat)) (or (@ (@ tptp.rep_assn P5) H6) (@ (@ tptp.rep_assn Q3) H6)))))))
% 8.20/8.62 (assert (= tptp.inf_inf_assn (lambda ((P5 tptp.assn) (Q3 tptp.assn)) (@ tptp.abs_assn (lambda ((H6 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.rep_assn P5) H6) (@ (@ tptp.rep_assn Q3) H6)))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P2 (@ (@ tptp.modulo_modulo_nat M) N2)) (and (=> _let_1 (@ P2 M)) (=> (not _let_1) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I)) J)) (@ P2 J))))))))))
% 8.20/8.62 (assert (forall ((C2 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) C2) (= (@ _let_1 (@ _let_2 C2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C2))) (@ _let_1 B))))))))
% 8.20/8.62 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C2) (= (@ _let_1 (@ _let_2 C2)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) B)) C2))) (@ _let_1 B))))))))
% 8.20/8.62 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (= (@ _let_1 (@ _let_2 C2)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C2))) (@ _let_1 B))))))))
% 8.20/8.62 (assert (= tptp.times_times_assn (lambda ((P5 tptp.assn) (Q3 tptp.assn)) (@ tptp.abs_assn (@ (@ tptp.times_assn_raw (@ tptp.rep_assn P5)) (@ tptp.rep_assn Q3))))))
% 8.20/8.62 (assert (forall ((X tptp.nat) (Y tptp.nat) (C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.nO_MATCH_nat_rat (@ (@ tptp.divide_divide_nat X) Y)) C2) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))))
% 8.20/8.62 (assert (forall ((X tptp.nat) (Y tptp.nat) (C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.nO_MATCH_nat_nat (@ (@ tptp.divide_divide_nat X) Y)) C2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2))))))
% 8.20/8.62 (assert (forall ((X tptp.nat) (Y tptp.nat) (C2 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.nO_MATCH_nat_int (@ (@ tptp.divide_divide_nat X) Y)) C2) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2))))))
% 8.20/8.62 (assert (forall ((X tptp.int) (Y tptp.int) (C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.nO_MATCH_int_rat (@ (@ tptp.divide_divide_int X) Y)) C2) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))))
% 8.20/8.62 (assert (forall ((X tptp.int) (Y tptp.int) (C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.nO_MATCH_int_nat (@ (@ tptp.divide_divide_int X) Y)) C2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2))))))
% 8.20/8.62 (assert (forall ((X tptp.int) (Y tptp.int) (C2 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.nO_MATCH_int_int (@ (@ tptp.divide_divide_int X) Y)) C2) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2))))))
% 8.20/8.62 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural) (C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.nO_MAT3836730678284324717al_rat (@ (@ tptp.divide5121882707175180666atural X) Y)) C2) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))))
% 8.20/8.62 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural) (C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.nO_MAT4471860738370820453al_nat (@ (@ tptp.divide5121882707175180666atural X) Y)) C2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C2)) (@ (@ tptp.times_times_nat B) C2))))))
% 8.20/8.62 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural) (C2 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.nO_MAT4469370267861770177al_int (@ (@ tptp.divide5121882707175180666atural X) Y)) C2) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C2)) (@ (@ tptp.times_times_int B) C2))))))
% 8.20/8.62 (assert (forall ((X tptp.rat) (Y tptp.rat) (C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.nO_MATCH_rat_rat (@ (@ tptp.divide_divide_rat X) Y)) C2) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C2)) (@ (@ tptp.times_times_rat B) C2))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I tptp.rat)) (@ (@ tptp.plus_plus_rat I) tptp.one_one_rat))) N) tptp.zero_zero_rat))))
% 8.20/8.62 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I tptp.int)) (@ (@ tptp.plus_plus_int I) tptp.one_one_int))) N) tptp.zero_zero_int))))
% 8.20/8.62 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat))) N) tptp.zero_zero_nat))))
% 8.20/8.62 (assert (= tptp.semiri4939895301339042750nteger (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri4055485073559036834nteger (lambda ((I tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger I) tptp.one_one_Code_integer))) N) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.62 (assert (forall ((X tptp.rat)) (exists ((N5 tptp.nat)) (@ (@ tptp.ord_less_rat X) (@ tptp.semiri681578069525770553at_rat N5)))))
% 8.20/8.62 (assert (forall ((X tptp.rat)) (exists ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.semiri681578069525770553at_rat N5)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X2) (@ tptp.suc Y2)) (= X2 Y2))))
% 8.20/8.62 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc N2))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (= N2 tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N2))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((K2 tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L) K2) (= (@ (@ tptp.modulo_modulo_int K2) L) K2)))))
% 8.20/8.62 (assert (forall ((K2 tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (=> (@ (@ tptp.ord_less_int K2) L) (= (@ (@ tptp.modulo_modulo_int K2) L) K2)))))
% 8.20/8.62 (assert (forall ((K2 tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (=> (@ (@ tptp.ord_less_int K2) L) (= (@ (@ tptp.divide_divide_int K2) L) tptp.zero_zero_int)))))
% 8.20/8.62 (assert (forall ((K2 tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L) K2) (= (@ (@ tptp.divide_divide_int K2) L) tptp.zero_zero_int)))))
% 8.20/8.62 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 8.20/8.62 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 8.20/8.62 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 8.20/8.62 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.suc M)) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.semiri4939895301339042750nteger M)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (K2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) K2)) M))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) N2)) M))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat N2) K2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat K2) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 8.20/8.62 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_int W2) (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W2) Z3))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((I2 tptp.int) (K2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int I2) K2) I2) (or (= K2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K2)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K2) I2))))))
% 8.20/8.62 (assert (forall ((M tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int M) K2)) M))))
% 8.20/8.62 (assert (forall ((K2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (exists ((N5 tptp.nat)) (= K2 (@ tptp.semiri1314217659103216013at_int N5))))))
% 8.20/8.62 (assert (forall ((K2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (not (forall ((N5 tptp.nat)) (not (= K2 (@ tptp.semiri1314217659103216013at_int N5))))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z3)))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3))))
% 8.20/8.62 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_int W2) Z3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W2) tptp.one_one_int)) Z3))))
% 8.20/8.62 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W2) tptp.one_one_int)) Z3) (@ (@ tptp.ord_less_int W2) Z3))))
% 8.20/8.62 (assert (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z tptp.int)) (exists ((N tptp.nat)) (= Z (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N)))))))
% 8.20/8.62 (assert (forall ((D2 tptp.int) (P2 (-> tptp.int Bool)) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int)) (=> (@ P2 X3) (@ P2 (@ (@ tptp.plus_plus_int X3) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (forall ((X6 tptp.int)) (=> (@ P2 X6) (@ P2 (@ (@ tptp.plus_plus_int X6) (@ (@ tptp.times_times_int K2) D2))))))))))
% 8.20/8.62 (assert (forall ((B tptp.int) (Q7 tptp.int) (R7 tptp.int) (Q6 tptp.int) (R2 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 Q7)) R7)) (@ (@ tptp.plus_plus_int (@ _let_2 Q6)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ _let_1 R2) (=> (@ _let_1 R7) (@ (@ tptp.ord_less_eq_int Q6) Q7)))))))))
% 8.20/8.62 (assert (forall ((B tptp.int) (Q7 tptp.int) (R7 tptp.int) (Q6 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q7)) R7)) (@ (@ tptp.plus_plus_int (@ _let_1 Q6)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R7) (=> (@ (@ tptp.ord_less_int R7) B) (=> (@ (@ tptp.ord_less_int R2) B) (@ (@ tptp.ord_less_eq_int Q7) Q6))))))))
% 8.20/8.62 (assert (forall ((B tptp.int) (Q6 tptp.int) (R2 tptp.int) (B2 tptp.int) (Q7 tptp.int) (R7 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q7)) R7))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q6)) R2) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R2) 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 Q7) Q6))))))))))
% 8.20/8.62 (assert (forall ((B tptp.int) (Q6 tptp.int) (R2 tptp.int) (B2 tptp.int) (Q7 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) Q7)) R7))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q6)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R7) B2) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int Q6) Q7)))))))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (Q6 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q6)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (Q6 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q6)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 8.20/8.62 (assert (forall ((B2 tptp.int) (Q7 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) Q7)) R7)) (=> (@ (@ tptp.ord_less_int R7) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ _let_1 Q7)))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.int Bool)) (N2 tptp.int) (K2 tptp.int)) (= (@ P2 (@ (@ tptp.modulo_modulo_int N2) K2)) (and (=> (= K2 tptp.zero_zero_int) (@ P2 N2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J) (@ (@ tptp.ord_less_int J) K2) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ P2 J)))) (=> (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_int K2) J) (@ (@ tptp.ord_less_eq_int J) tptp.zero_zero_int) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ P2 J))))))))
% 8.20/8.62 (assert (forall ((L tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int K2) L)) tptp.zero_zero_int))))
% 8.20/8.62 (assert (forall ((L tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int K2) L)))))
% 8.20/8.62 (assert (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int K2) L))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (=> (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int K2) L) _let_1))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.int) (K2 tptp.int)) (= (= (@ (@ tptp.divide_divide_int I2) K2) tptp.zero_zero_int) (or (= K2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K2)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K2) I2))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (assert (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K2) L)) (or (= K2 tptp.zero_zero_int) (= L tptp.zero_zero_int) (and (@ _let_1 K2) (@ _let_1 L)) (and (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))))
% 8.20/8.62 (assert (forall ((L tptp.int) (K2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int L) K2) (=> (@ _let_1 L) (@ _let_1 (@ (@ tptp.divide_divide_int K2) L)))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((K2 tptp.int) (I2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 K2) (= (@ _let_1 (@ (@ tptp.divide_divide_int I2) K2)) (@ (@ tptp.ord_less_eq_int K2) I2))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((A4 tptp.int) (B5 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int A4) B5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A4) N2)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B5) N2) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B5) N2))))))
% 8.20/8.62 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (= (@ _let_1 (@ _let_2 C2)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C2))) (@ _let_1 B))))))))
% 8.20/8.62 (assert (forall ((K2 tptp.int) (P2 (-> tptp.int tptp.int Bool)) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (= (@ (@ P2 (@ (@ tptp.divide_divide_int N2) K2)) (@ (@ tptp.modulo_modulo_int N2) K2)) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J) (@ (@ tptp.ord_less_int J) K2) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ (@ P2 I) J)))))))
% 8.20/8.62 (assert (forall ((K2 tptp.int) (P2 (-> tptp.int tptp.int Bool)) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (= (@ (@ P2 (@ (@ tptp.divide_divide_int N2) K2)) (@ (@ tptp.modulo_modulo_int N2) K2)) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_int K2) J) (@ (@ tptp.ord_less_eq_int J) tptp.zero_zero_int) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ (@ P2 I) J)))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (Q6 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q6)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.divide_divide_int A) B) Q6))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (Q6 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q6)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.divide_divide_int A) B) Q6))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.int Bool)) (N2 tptp.int) (K2 tptp.int)) (= (@ P2 (@ (@ tptp.divide_divide_int N2) K2)) (and (=> (= K2 tptp.zero_zero_int) (@ P2 tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J) (@ (@ tptp.ord_less_int J) K2) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ P2 I)))) (=> (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_int K2) J) (@ (@ tptp.ord_less_eq_int J) tptp.zero_zero_int) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K2) I)) J))) (@ P2 I))))))))
% 8.20/8.62 (assert (forall ((A4 tptp.int) (N2 tptp.int)) (= A4 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A4) N2)) N2)) (@ (@ tptp.modulo_modulo_int A4) N2)))))
% 8.20/8.62 (assert (forall ((X tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K2) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X) K2)) X)))))
% 8.20/8.62 (assert (forall ((A4 tptp.int) (B5 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int A4) B5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (=> (= (@ (@ tptp.modulo_modulo_int A4) N2) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B5) N2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A4) N2)) (@ (@ tptp.divide_divide_int B5) N2))))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((L tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int K2) L)) L))))
% 8.20/8.62 (assert (forall ((L tptp.int) (K2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (=> (@ _let_1 tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.modulo_modulo_int K2) L))))))
% 8.20/8.62 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K2))) (=> (@ (@ tptp.ord_less_int I2) J2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J2)))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))))
% 8.20/8.62 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 8.20/8.62 (assert (forall ((P2 Bool) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ (@ tptp.if_nat P2) A) B)))) (and (=> P2 (= _let_1 (@ tptp.semiri1314217659103216013at_int A))) (=> (not P2) (= _let_1 (@ tptp.semiri1314217659103216013at_int B)))))))
% 8.20/8.62 (assert (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (lambda ((A5 tptp.nat) (B4 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int A5) (@ tptp.semiri1314217659103216013at_int B4)))))
% 8.20/8.62 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z tptp.int)) (exists ((N tptp.nat)) (= Z (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N))))))))
% 8.20/8.62 (assert (forall ((K2 tptp.int) (I2 tptp.int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K2) I2) (=> (@ P2 (@ (@ tptp.plus_plus_int K2) tptp.one_one_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int K2) I3) (=> (@ P2 I3) (@ P2 (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P2 I2))))))
% 8.20/8.62 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)) (or (@ _let_1 Z3) (= W2 Z3))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z3)) Z3)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z3) tptp.zero_zero_int))))
% 8.20/8.62 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 8.20/8.62 (assert (forall ((K2 tptp.int)) (= (@ (@ tptp.plus_plus_int K2) tptp.zero_zero_int) K2)))
% 8.20/8.62 (assert (forall ((L tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L) L)))
% 8.20/8.62 (assert (forall ((Z3 tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z3)) Z3) tptp.zero_zero_int))))
% 8.20/8.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (not (= N2 (@ tptp.suc N2)))))
% 8.20/8.62 (assert (forall ((W2 tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 8.20/8.62 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z22)) W2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W2)) (@ (@ tptp.times_times_int Z22) W2)))))
% 8.20/8.62 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C2) (= (@ _let_1 (@ (@ tptp.times_times_int B) C2)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C2))))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((K2 tptp.int) (I2 tptp.int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int K2) I2) (=> (@ P2 K2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K2) I3) (=> (@ P2 I3) (@ P2 (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P2 I2))))))
% 8.20/8.62 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 8.20/8.62 (assert (forall ((X tptp.int) (X10 tptp.int) (P2 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 (= P2 P6)) (= (=> (@ _let_1 X) P2) (=> _let_2 P6))))))))
% 8.20/8.62 (assert (forall ((X tptp.int) (X10 tptp.int) (P2 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 (= P2 P6)) (= (and (@ _let_1 X) P2) (and _let_2 P6))))))))
% 8.20/8.62 (assert (forall ((X2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X2)))))
% 8.20/8.62 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 8.20/8.62 (assert (forall ((Nat tptp.nat) (X2 tptp.nat)) (=> (= Nat (@ tptp.suc X2)) (not (= Nat tptp.zero_zero_nat)))))
% 8.20/8.62 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (@ P2 N5) (@ P2 (@ tptp.suc N5)))) (@ P2 N2)))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((X3 tptp.nat)) (@ (@ P2 X3) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P2 tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P2 X3) Y3) (@ (@ P2 (@ tptp.suc X3)) (@ tptp.suc Y3)))) (@ (@ P2 M) N2))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (K2 tptp.nat)) (=> (@ P2 K2) (=> (forall ((N5 tptp.nat)) (=> (@ P2 (@ tptp.suc N5)) (@ P2 N5))) (@ P2 tptp.zero_zero_nat)))))
% 8.20/8.62 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 8.20/8.62 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (exists ((M5 tptp.nat)) (= N2 (@ tptp.suc M5))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (forall ((I3 tptp.nat)) (=> (= J2 (@ tptp.suc I3)) (@ P2 I3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (@ P2 (@ tptp.suc I3)) (@ P2 I3)))) (@ P2 I2))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (P2 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (forall ((I3 tptp.nat)) (@ (@ P2 I3) (@ tptp.suc I3))) (=> (forall ((I3 tptp.nat) (J3 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ P2 I3))) (=> (@ (@ tptp.ord_less_nat I3) J3) (=> (@ (@ tptp.ord_less_nat J3) K) (=> (@ _let_1 J3) (=> (@ (@ P2 J3) K) (@ _let_1 K))))))) (@ (@ P2 I2) J2))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K2)))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.suc N2)) (@ P2 I))) (and (@ P2 N2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N2) (@ P2 I)))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.suc N2)) (@ P2 I))) (or (@ P2 N2) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) N2) (@ P2 I)))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K2) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J3) (not (= K2 (@ tptp.suc J3)))))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K2) (=> (not (= K2 (@ tptp.suc I2))) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J3) (not (= K2 (@ tptp.suc J3))))))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (R3 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (forall ((X3 tptp.nat)) (@ (@ R3 X3) X3)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ R3 X3))) (=> (@ _let_1 Y3) (=> (@ (@ R3 Y3) Z2) (@ _let_1 Z2))))) (=> (forall ((N5 tptp.nat)) (@ (@ R3 N5) (@ tptp.suc N5))) (@ (@ R3 M) N2)))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ P2 M) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N5) (=> (@ P2 N5) (@ P2 (@ tptp.suc N5))))) (@ P2 N2))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M4)) N5) (@ P2 M4))) (@ P2 N5))) (@ P2 N2))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) N2))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 8.20/8.62 (assert (forall ((A4 tptp.nat) (K2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K2))) (=> (= A4 (@ _let_1 A)) (= (@ tptp.suc A4) (@ _let_1 (@ tptp.suc A)))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N2)))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N2)))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K2)))) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N2)) tptp.zero_zero_rat))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) tptp.zero_zero_int))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N2)) tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri4939895301339042750nteger (@ tptp.suc N2)) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) (@ tptp.suc N2)) (@ P2 I))) (or (@ P2 tptp.zero_zero_nat) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_nat I) N2) (@ P2 (@ tptp.suc I))))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M3 tptp.nat)) (= N2 (@ tptp.suc M3))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.suc N2)) (@ P2 I))) (and (@ P2 tptp.zero_zero_nat) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N2) (@ P2 (@ tptp.suc I))))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M5 tptp.nat)) (= N2 (@ tptp.suc M5))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (or (= M tptp.zero_zero_nat) (exists ((J tptp.nat)) (and (= M (@ tptp.suc J)) (@ (@ tptp.ord_less_nat J) N2)))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Nn) N5) (@ P2 Nn))) (@ P2 (@ tptp.suc N5)))) (@ P2 N2)))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Nn) N5) (@ P2 Nn))) (@ P2 (@ tptp.suc N5)))) (@ P2 N2)))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ P2 I2) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N5) (=> (@ (@ tptp.ord_less_nat N5) J2) (=> (@ P2 N5) (@ P2 (@ tptp.suc N5)))))) (@ P2 J2))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ P2 J2) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N5) (=> (@ (@ tptp.ord_less_nat N5) J2) (=> (@ P2 (@ tptp.suc N5)) (@ P2 N5))))) (@ P2 I2))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) M)))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I2)))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (exists ((K tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K)))))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K2)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 8.20/8.62 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K2)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (= tptp.suc (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))
% 8.20/8.62 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 8.20/8.62 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (N2 tptp.nat) (P3 tptp.nat) (M tptp.nat)) (=> (@ P2 N2) (=> (@ (@ tptp.ord_less_nat N2) P3) (=> (@ (@ tptp.ord_less_nat M) P3) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N5) P3) (=> (@ P2 N5) (@ P2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N5)) P3))))) (@ P2 M)))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N2))) N2)))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P2 N2) (=> (not (@ P2 tptp.zero_zero_nat)) (exists ((K tptp.nat)) (and (@ (@ tptp.ord_less_nat K) N2) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) K) (not (@ P2 I4)))) (@ P2 (@ tptp.suc K))))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ P2 tptp.one_one_nat) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (=> (@ P2 N5) (@ P2 (@ tptp.suc N5))))) (@ P2 N2))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat K2) (@ (@ tptp.power_power_nat N2) K2)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (= (@ P2 (@ (@ tptp.divide_divide_nat M) N2)) (or (and (= N2 tptp.zero_zero_nat) (@ P2 tptp.zero_zero_nat)) (exists ((Q8 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q8)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q8))) (@ P2 Q8))))))))
% 8.20/8.62 (assert (forall ((X (-> tptp.produc7388388658123137530it_nat tptp.nat)) (X2 tptp.produc7388388658123137530it_nat)) (= (@ (@ tptp.size_o5858930521590659991it_nat X) (@ tptp.some_P2818173045054083285it_nat X2)) (@ (@ tptp.plus_plus_nat (@ X X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((Xa (-> tptp.product_unit tptp.nat)) (X (-> tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat))) (= (@ (@ tptp.heap_T4142866422068808505t_unit Xa) (@ tptp.heap_T6183433275982383450t_unit X)) (@ tptp.suc tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((X (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((X (-> tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat))) (= (@ tptp.size_s1564113455978345259t_unit (@ tptp.heap_T6183433275982383450t_unit X)) (@ tptp.suc tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((K2 tptp.int) (L tptp.int) (Q6 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))) (= (@ (@ (@ tptp.eucl_rel_int K2) L) (@ (@ tptp.product_Pair_int_int Q6) R2)) (and (= K2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L) Q6)) R2)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (@ (@ tptp.ord_less_int R2) L))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R2) (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int))) (=> (not _let_2) (= Q6 tptp.zero_zero_int)))))))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y))) (not (= X Y)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X) (@ tptp.size_size_list_int Y))) (not (= X Y)))))
% 8.20/8.62 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P2 (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((I3 tptp.int) (J3 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I3) J3)) (=> (=> (@ (@ tptp.ord_less_eq_int I3) J3) (@ (@ P2 (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J3)) (@ (@ P2 I3) J3)))) (@ (@ P2 A0) A1)))))
% 8.20/8.62 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 8.20/8.62 (assert (forall ((X2 tptp.produc7388388658123137530it_nat)) (= (@ tptp.size_s2866289034186623454it_nat (@ tptp.some_P2818173045054083285it_nat X2)) (@ tptp.suc tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((X2 tptp.produc3260487557148687353it_nat)) (= (@ tptp.size_s2363601347547812957it_nat (@ tptp.some_P7913643980934408916it_nat X2)) (@ tptp.suc tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((X2 tptp.produc8664842809031399944it_nat)) (= (@ tptp.size_s8766407808098229740it_nat (@ tptp.some_P1914260805536162275it_nat X2)) (@ tptp.suc tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((X2 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X2)) (@ tptp.suc tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((K2 tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K2) L)) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int K2) L) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 8.20/8.62 (assert (forall ((L tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K2) (= (@ (@ tptp.divide_divide_int K2) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int K2) L)) L)) tptp.one_one_int))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K2) (= (@ (@ tptp.divide_divide_int (@ _let_1 M)) K2) (@ _let_1 (@ (@ tptp.minus_minus_nat M) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z3))))
% 8.20/8.62 (assert (forall ((B tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int B)) B)))
% 8.20/8.62 (assert (forall ((B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger B)) B)))
% 8.20/8.62 (assert (forall ((B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat B)) B)))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ (@ tptp.plus_p7104986032573967614at_nat A) B)) B) A)))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 8.20/8.62 (assert (forall ((A tptp.multis2468970476368604999at_nat) (C2 tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ (@ tptp.plus_p7104986032573967614at_nat A) C2)) (@ (@ tptp.plus_p7104986032573967614at_nat B) C2)) (@ (@ tptp.minus_4286766774447292334at_nat A) B))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C2)) (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.minus_minus_rat A) B))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.minus_minus_nat A) B))))
% 8.20/8.62 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C2)) (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.minus_minus_int A) B))))
% 8.20/8.62 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ (@ tptp.plus_p7104986032573967614at_nat A) B)) A) B)))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 8.20/8.62 (assert (forall ((C2 tptp.multis2468970476368604999at_nat) (A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat C2))) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_4286766774447292334at_nat A) B)))))
% 8.20/8.62 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_rat A) B)))))
% 8.20/8.62 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_nat A) B)))))
% 8.20/8.62 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_int A) B)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 8.20/8.62 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat M) N2))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2)) (@ tptp.suc K2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N2)) K2))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K2) (@ _let_1 (@ (@ tptp.plus_plus_nat J2) K2))))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat A) (@ (@ tptp.plus_p7104986032573967614at_nat A) B)) tptp.zero_z1048942125864253310at_nat)))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 8.20/8.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 8.20/8.62 (assert (forall ((B tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B) (@ tptp.uminus_uminus_int B))))
% 8.20/8.62 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B) (@ tptp.uminus1351360451143612070nteger B))))
% 8.20/8.62 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B) (@ tptp.uminus_uminus_rat B))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (@ tptp.uminus7117520113953359693_int_o (@ (@ tptp.sup_su8463660629351352368_int_o X) Y)) (@ (@ tptp.inf_in3604695632404883862_int_o (@ tptp.uminus7117520113953359693_int_o X)) (@ tptp.uminus7117520113953359693_int_o Y)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (@ tptp.uminus7117520113953359693_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) (@ (@ tptp.sup_su8463660629351352368_int_o (@ tptp.uminus7117520113953359693_int_o X)) (@ tptp.uminus7117520113953359693_int_o Y)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.minus_minus_nat I2) (@ (@ tptp.minus_minus_nat J2) K2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K2)) J2)))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J2) K2)) I2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J2) I2)) K2)))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J2) K2)) (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K2))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) tptp.one_one_nat) N2)))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 8.20/8.62 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 8.20/8.62 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 8.20/8.62 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 8.20/8.62 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 8.20/8.62 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.minus_minus_nat I2) (@ tptp.suc (@ (@ tptp.minus_minus_nat J2) K2))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K2)) (@ tptp.suc J2))))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J2) K2))) I2) (@ (@ tptp.minus_minus_nat (@ tptp.suc J2)) (@ (@ tptp.plus_plus_nat K2) I2))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z3) tptp.zero_zero_int) (= (@ tptp.nat2 Z3) tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((I2 tptp.int)) (= (= (@ tptp.nat2 I2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int))))
% 8.20/8.62 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z3)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (@ (@ tptp.ord_less_int W2) Z3)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z3)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3))) (and (=> _let_2 (= _let_1 Z3)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 8.20/8.62 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int W2) (@ (@ tptp.minus_minus_int Z3) tptp.one_one_int)) (@ (@ tptp.ord_less_int W2) Z3))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A B) (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= A B) (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A B) (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K2) (@ (@ tptp.minus_minus_nat (@ _let_1 K2)) J2)))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (assert (forall ((Z7 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z7) (=> (@ (@ tptp.ord_less_eq_int Z7) Z3) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z3) Z7)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z3)) (@ tptp.nat2 Z7)))))))
% 8.20/8.62 (assert (forall ((B5 tptp.int) (K2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B5 (@ (@ tptp.plus_plus_int K2) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K2)) (@ _let_1 B)))))))
% 8.20/8.62 (assert (forall ((B5 tptp.code_integer) (K2 tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B5 (@ (@ tptp.plus_p5714425477246183910nteger K2) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K2)) (@ _let_1 B)))))))
% 8.20/8.62 (assert (forall ((B5 tptp.rat) (K2 tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B5 (@ (@ tptp.plus_plus_rat K2) B)) (= (@ _let_1 B5) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K2)) (@ _let_1 B)))))))
% 8.20/8.62 (assert (= tptp.minus_minus_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A5) (@ tptp.uminus_uminus_int B4)))))
% 8.20/8.62 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A5 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.uminus1351360451143612070nteger B4)))))
% 8.20/8.62 (assert (= tptp.minus_minus_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.uminus_uminus_rat B4)))))
% 8.20/8.62 (assert (= tptp.minus_minus_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A5) (@ tptp.uminus_uminus_int B4)))))
% 8.20/8.62 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A5 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.uminus1351360451143612070nteger B4)))))
% 8.20/8.62 (assert (= tptp.minus_minus_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.uminus_uminus_rat B4)))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N2) M)) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1314217659103216013at_int M)))))))
% 8.20/8.62 (assert (= tptp.minus_minus_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((Z7 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z3) Z7))) (let ((_let_2 (@ tptp.nat2 Z3))) (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)))))))))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C2) D2)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C2) D2)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C2) D2)) (= (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int C2) D2)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C2)) (@ (@ tptp.minus_minus_rat B) C2)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C2)) (@ (@ tptp.minus_minus_int B) C2)))))
% 8.20/8.62 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C2))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 8.20/8.62 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C2))) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (D2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D2) C2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C2)) (@ (@ tptp.minus_minus_rat B) D2))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (D2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int D2) C2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C2)) (@ (@ tptp.minus_minus_int B) D2))))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C2)) (@ (@ tptp.minus_minus_rat B) C2)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C2)) (@ (@ tptp.minus_minus_int B) C2)))))
% 8.20/8.62 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C2))) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 8.20/8.62 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C2))) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C2) D2)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C2) D2)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C2) D2)) (= (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int C2) D2)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (D2 tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D2) C2) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C2)) (@ (@ tptp.minus_minus_rat B) D2))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (D2 tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int D2) C2) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C2)) (@ (@ tptp.minus_minus_int B) D2))))))
% 8.20/8.62 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat) (C2 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.minus_4286766774447292334at_nat A))) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_p7104986032573967614at_nat B) C2))))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2))))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_int B) C2))))))
% 8.20/8.62 (assert (forall ((C2 tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat) (A tptp.multis2468970476368604999at_nat)) (=> (= (@ (@ tptp.plus_p7104986032573967614at_nat C2) B) A) (= C2 (@ (@ tptp.minus_4286766774447292334at_nat A) B)))))
% 8.20/8.62 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C2) B) A) (= C2 (@ (@ tptp.minus_minus_rat A) B)))))
% 8.20/8.62 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C2) B) A) (= C2 (@ (@ tptp.minus_minus_nat A) B)))))
% 8.20/8.62 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C2) B) A) (= C2 (@ (@ tptp.minus_minus_int A) B)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 C2)) B)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 C2)) B)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) C2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C2)) B))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) C2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C2)) B))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.minus_minus_rat B) C2)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C2)) B))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.minus_minus_int B) C2)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C2)) B))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C2)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C2)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C2)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C2)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.minus_minus_rat C2) B)) (= (@ (@ tptp.plus_plus_rat A) B) C2))))
% 8.20/8.62 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.minus_minus_int C2) B)) (= (@ (@ tptp.plus_plus_int A) B) C2))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A) B) C2) (= A (@ (@ tptp.plus_plus_rat C2) B)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (= (@ (@ tptp.minus_minus_int A) B) C2) (= A (@ (@ tptp.plus_plus_int C2) B)))))
% 8.20/8.62 (assert (forall ((A4 tptp.rat) (K2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_rat A4) B) (@ _let_1 (@ (@ tptp.minus_minus_rat A) B)))))))
% 8.20/8.62 (assert (forall ((A4 tptp.int) (K2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K2))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A4) B) (@ _let_1 (@ (@ tptp.minus_minus_int A) B)))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.rat Bool)) (D4 tptp.rat) (Q2 (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D4))))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D4))))) (forall ((X6 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K4) D4)))) (= (or (@ P2 X6) (@ Q2 X6)) (or (@ P2 _let_1) (@ Q2 _let_1)))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.int Bool)) (D4 tptp.int) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D4))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D4))))) (forall ((X6 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K4) D4)))) (= (or (@ P2 X6) (@ Q2 X6)) (or (@ P2 _let_1) (@ Q2 _let_1)))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.rat Bool)) (D4 tptp.rat) (Q2 (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D4))))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D4))))) (forall ((X6 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K4) D4)))) (= (and (@ P2 X6) (@ Q2 X6)) (and (@ P2 _let_1) (@ Q2 _let_1)))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.int Bool)) (D4 tptp.int) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D4))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D4))))) (forall ((X6 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K4) D4)))) (= (and (@ P2 X6) (@ Q2 X6)) (and (@ P2 _let_1) (@ Q2 _let_1)))))))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 8.20/8.62 (assert (forall ((A4 tptp.int) (K2 tptp.int) (A tptp.int)) (=> (= A4 (@ (@ tptp.plus_plus_int K2) A)) (= (@ tptp.uminus_uminus_int A4) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K2)) (@ tptp.uminus_uminus_int A))))))
% 8.20/8.62 (assert (forall ((A4 tptp.code_integer) (K2 tptp.code_integer) (A tptp.code_integer)) (=> (= A4 (@ (@ tptp.plus_p5714425477246183910nteger K2) A)) (= (@ tptp.uminus1351360451143612070nteger A4) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K2)) (@ tptp.uminus1351360451143612070nteger A))))))
% 8.20/8.62 (assert (forall ((A4 tptp.rat) (K2 tptp.rat) (A tptp.rat)) (=> (= A4 (@ (@ tptp.plus_plus_rat K2) A)) (= (@ tptp.uminus_uminus_rat A4) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K2)) (@ tptp.uminus_uminus_rat A))))))
% 8.20/8.62 (assert (forall ((P2 (-> 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)) (@ P2 Ys))) (@ P2 Xs2))) (@ P2 Xs))))
% 8.20/8.62 (assert (forall ((P2 (-> 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)) (@ P2 Ys))) (@ P2 Xs2))) (@ P2 Xs))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (forall ((Xs2 tptp.list_int)) (=> (forall ((Ys tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys)) (@ tptp.size_size_list_int Xs2)) (@ P2 Ys))) (@ P2 Xs2))) (@ P2 Xs))))
% 8.20/8.62 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (K2 tptp.nat) (I2 tptp.nat)) (=> (@ P2 K2) (=> (forall ((N5 tptp.nat)) (=> (@ P2 (@ tptp.suc N5)) (@ P2 N5))) (@ P2 (@ (@ tptp.minus_minus_nat K2) I2))))))
% 8.20/8.62 (assert (forall ((J2 tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) K2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J2) N2)) K2))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) C2) (=> (@ _let_1 C2) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N2)) M)))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_2 M) (=> (@ _let_2 N2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K2)) (@ (@ tptp.minus_minus_nat N2) K2)) (@ _let_1 N2))))))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K2)) (@ (@ tptp.minus_minus_nat N2) K2)) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (= (@ (@ tptp.minus_minus_nat M) K2) (@ (@ tptp.minus_minus_nat N2) K2)) (= M N2)))))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.minus_minus_nat M) N2)))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K2)) (@ (@ tptp.plus_plus_nat N2) K2)) (@ (@ tptp.minus_minus_nat M) N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) M)) N2) M)))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) N2) M)))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N2)) K2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K2)) (@ (@ tptp.times_times_nat N2) K2)))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 8.20/8.62 (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))))))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z3) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z3) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z3))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z7)))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P2 tptp.zero_zero_int))))))
% 8.20/8.62 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((A5 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A5) B4)) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.62 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A5) B4)) tptp.zero_zero_rat))))
% 8.20/8.62 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A5) B4)) tptp.zero_zero_int))))
% 8.20/8.62 (assert (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)))
% 8.20/8.62 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((A5 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A5) B4)) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.62 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A5) B4)) tptp.zero_zero_rat))))
% 8.20/8.62 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A5) B4)) tptp.zero_zero_int))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) B)) C2) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat C2) B)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) B)) C2) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int C2) B)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.minus_minus_rat C2) B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) C2))))
% 8.20/8.62 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int C2) B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) C2))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat C2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C2)) A)))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_less_eq_nat C2) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C2) A)) B)))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A))))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)))))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C2)) A)))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C2)))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat C2) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C2) A)) B)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B) A) C2) (= B (@ (@ tptp.plus_plus_nat C2) A))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.rat) (K2 tptp.rat) (N2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K2)) N2) (@ (@ tptp.ord_less_eq_rat I2) (@ (@ tptp.minus_minus_rat N2) K2)))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) N2) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat N2) K2)))))
% 8.20/8.62 (assert (forall ((I2 tptp.int) (K2 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K2)) N2) (@ (@ tptp.ord_less_eq_int I2) (@ (@ tptp.minus_minus_int N2) K2)))))
% 8.20/8.62 (assert (forall ((I2 tptp.rat) (K2 tptp.rat) (N2 tptp.rat) (J2 tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N2) (@ (@ tptp.plus_plus_rat J2) K2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K2)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N2) K2)) J2)))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (K2 tptp.nat) (N2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat J2) K2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N2) K2)) J2)))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.int) (K2 tptp.int) (N2 tptp.int) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N2) (@ (@ tptp.plus_plus_int J2) K2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K2)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N2) K2)) J2)))))))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.minus_minus_rat C2) B)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) C2))))
% 8.20/8.62 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int C2) B)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) C2))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) B)) C2) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat C2) B)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) B)) C2) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int C2) B)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2) (@ (@ 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)) C2) D2))))
% 8.20/8.62 (assert (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2) (@ (@ 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)) C2) D2))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (= C2 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D2)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (= C2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D2)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (= (lambda ((P4 (-> tptp.nat Bool))) (exists ((X5 tptp.nat)) (@ P4 X5))) (lambda ((P5 (-> tptp.nat Bool))) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ P5 (@ tptp.nat2 X4)))))))
% 8.20/8.62 (assert (= (lambda ((P4 (-> tptp.nat Bool))) (forall ((X5 tptp.nat)) (@ P4 X5))) (lambda ((P5 (-> tptp.nat Bool))) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ P5 (@ tptp.nat2 X4)))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int) (Z7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z3) (=> (@ _let_1 Z7) (= (= (@ tptp.nat2 Z3) (@ tptp.nat2 Z7)) (= Z3 Z7)))))))
% 8.20/8.62 (assert (forall ((L tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K2)) L) (@ (@ tptp.minus_minus_int (@ (@ tptp.minus_minus_int L) tptp.one_one_int)) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K2) tptp.one_one_int)) L))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 8.20/8.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 8.20/8.62 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 8.20/8.62 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 8.20/8.62 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 8.20/8.62 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 8.20/8.62 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 8.20/8.62 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 8.20/8.62 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 8.20/8.62 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 8.20/8.62 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 8.20/8.62 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 8.20/8.62 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 8.20/8.62 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 8.20/8.62 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (= (@ tptp.suc N2) M) (= N2 (@ (@ tptp.minus_minus_nat M) (@ tptp.suc tptp.zero_zero_nat))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ tptp.suc M))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N2) (@ (@ tptp.plus_plus_nat N2) M)) tptp.zero_zero_nat)))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K2))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K2)) (@ (@ tptp.minus_minus_nat N2) K2)) (@ (@ tptp.ord_less_nat M) N2)))))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C2)) (@ (@ tptp.minus_minus_nat B) C2))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.minus_minus_nat J2) K2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K2)) J2))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (= (@ (@ tptp.minus_minus_nat J2) I2) K2) (= J2 (@ (@ tptp.plus_plus_nat K2) I2))))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J2) I2)) K2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J2) K2)) I2)))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K2) (@ _let_1 (@ (@ tptp.minus_minus_nat J2) K2)))))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat J2) K2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K2)) J2)))))
% 8.20/8.62 (assert (forall ((J2 tptp.nat) (K2 tptp.nat) (I2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J2) K2)) I2) (@ (@ tptp.ord_less_eq_nat J2) (@ (@ tptp.plus_plus_nat I2) K2)))))
% 8.20/8.62 (assert (forall ((I2 tptp.int) (K2 tptp.int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I2) K2) (=> (@ P2 K2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K2) (=> (@ P2 I3) (@ P2 (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P2 I2))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((I2 tptp.int) (K2 tptp.int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I2) K2) (=> (@ P2 (@ (@ tptp.minus_minus_int K2) tptp.one_one_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int I3) K2) (=> (@ P2 I3) (@ P2 (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P2 I2))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C2)) D2))))
% 8.20/8.62 (assert (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C2)) D2))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_eq_rat C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D2)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_eq_int C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D2)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_rat C2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D2)))))
% 8.20/8.62 (assert (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_int C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D2)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (E tptp.rat) (C2 tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C2)) D2))))
% 8.20/8.62 (assert (forall ((A tptp.int) (E tptp.int) (C2 tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C2)) D2))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int) (W2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int W2) Z3)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 8.20/8.62 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 8.20/8.62 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 8.20/8.62 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 8.20/8.62 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 8.20/8.62 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) Z3))))
% 8.20/8.62 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 8.20/8.62 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 8.20/8.62 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 8.20/8.62 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 8.20/8.62 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 8.20/8.62 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (Z3 tptp.int)) (= (= (@ tptp.semiri1314217659103216013at_int M) Z3) (and (= M (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3)))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z3)) Z3))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B))) (@ (@ tptp.plus_plus_nat A) B))))
% 8.20/8.62 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (= (@ (@ tptp.inf_in3604695632404883862_int_o X) Y) tptp.bot_bo8147686125503663512_int_o) (@ (@ tptp.ord_le8369615600986905444_int_o X) (@ tptp.uminus7117520113953359693_int_o Y)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Z3) (@ (@ tptp.ord_le3146513528884898305at_nat X) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.uminus6524753893492686040at_nat Y)) Z3)))))
% 8.20/8.62 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) Z3) (@ (@ tptp.ord_le8369615600986905444_int_o X) (@ (@ tptp.sup_su8463660629351352368_int_o (@ tptp.uminus7117520113953359693_int_o Y)) Z3)))))
% 8.20/8.62 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.inf_in1697001100524423349at_nat X) Y)) Z3) (@ (@ tptp.ord_le8081472938463900775at_nat X) (@ (@ tptp.sup_su3035147773818789531at_nat (@ tptp.uminus2330091110623919550at_nat Y)) Z3)))))
% 8.20/8.62 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.inf_in7913087082777306421at_nat X) Y)) Z3) (@ (@ tptp.ord_le1268244103169919719at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.uminus935396558254630718at_nat Y)) Z3)))))
% 8.20/8.62 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Z3) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) Z3)))))
% 8.20/8.62 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z3 tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) Z3) (@ (@ tptp.ord_less_eq_assn X) (@ (@ tptp.sup_sup_assn (@ tptp.uminus_uminus_assn Y)) Z3)))))
% 8.20/8.62 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z3 tptp.product_unit)) (= (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit X) Y)) Z3) (@ (@ tptp.ord_le3221252021190050221t_unit X) (@ (@ tptp.sup_sup_Product_unit (@ tptp.uminus2952777764628376836t_unit Y)) Z3)))))
% 8.20/8.62 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X) Y)) Z3) (@ (@ tptp.ord_less_eq_set_int X) (@ (@ tptp.sup_sup_set_int (@ tptp.uminus1532241313380277803et_int Y)) Z3)))))
% 8.20/8.62 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ tptp.uminus6524753893492686040at_nat Y))) Z3) (@ (@ tptp.ord_le3146513528884898305at_nat X) (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z3)))))
% 8.20/8.62 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z3 (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) (@ tptp.uminus7117520113953359693_int_o Y))) Z3) (@ (@ tptp.ord_le8369615600986905444_int_o X) (@ (@ tptp.sup_su8463660629351352368_int_o Y) Z3)))))
% 8.20/8.62 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.inf_in1697001100524423349at_nat X) (@ tptp.uminus2330091110623919550at_nat Y))) Z3) (@ (@ tptp.ord_le8081472938463900775at_nat X) (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z3)))))
% 8.20/8.62 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.inf_in7913087082777306421at_nat X) (@ tptp.uminus935396558254630718at_nat Y))) Z3) (@ (@ tptp.ord_le1268244103169919719at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z3)))))
% 8.20/8.62 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y))) Z3) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat Y) Z3)))))
% 8.20/8.62 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z3 tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) (@ tptp.uminus_uminus_assn Y))) Z3) (@ (@ tptp.ord_less_eq_assn X) (@ (@ tptp.sup_sup_assn Y) Z3)))))
% 8.20/8.62 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z3 tptp.product_unit)) (= (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit X) (@ tptp.uminus2952777764628376836t_unit Y))) Z3) (@ (@ tptp.ord_le3221252021190050221t_unit X) (@ (@ tptp.sup_sup_Product_unit Y) Z3)))))
% 8.20/8.62 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X) (@ tptp.uminus1532241313380277803et_int Y))) Z3) (@ (@ tptp.ord_less_eq_set_int X) (@ (@ tptp.sup_sup_set_int Y) Z3)))))
% 8.20/8.62 (assert (forall ((P3 tptp.set_Pr1261947904930325089at_nat) (Q6 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat P3) (@ (@ tptp.sup_su6327502436637775413at_nat Q6) R2)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat P3) (@ tptp.uminus6524753893492686040at_nat Q6))) R2))))
% 8.20/8.62 (assert (forall ((P3 (-> tptp.product_prod_int_int Bool)) (Q6 (-> tptp.product_prod_int_int Bool)) (R2 (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.ord_le8369615600986905444_int_o P3) (@ (@ tptp.sup_su8463660629351352368_int_o Q6) R2)) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o P3) (@ tptp.uminus7117520113953359693_int_o Q6))) R2))))
% 8.20/8.62 (assert (forall ((P3 tptp.set_Pr8551490117392284871at_nat) (Q6 tptp.set_Pr8551490117392284871at_nat) (R2 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.ord_le8081472938463900775at_nat P3) (@ (@ tptp.sup_su3035147773818789531at_nat Q6) R2)) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.inf_in1697001100524423349at_nat P3) (@ tptp.uminus2330091110623919550at_nat Q6))) R2))))
% 8.20/8.62 (assert (forall ((P3 tptp.set_Pr4329608150637261639at_nat) (Q6 tptp.set_Pr4329608150637261639at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat P3) (@ (@ tptp.sup_su5525570899277871387at_nat Q6) R2)) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.inf_in7913087082777306421at_nat P3) (@ tptp.uminus935396558254630718at_nat Q6))) R2))))
% 8.20/8.62 (assert (forall ((P3 tptp.set_nat) (Q6 tptp.set_nat) (R2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat P3) (@ (@ tptp.sup_sup_set_nat Q6) R2)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat P3) (@ tptp.uminus5710092332889474511et_nat Q6))) R2))))
% 8.20/8.62 (assert (forall ((P3 tptp.assn) (Q6 tptp.assn) (R2 tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn P3) (@ (@ tptp.sup_sup_assn Q6) R2)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn P3) (@ tptp.uminus_uminus_assn Q6))) R2))))
% 8.20/8.62 (assert (forall ((P3 tptp.product_unit) (Q6 tptp.product_unit) (R2 tptp.product_unit)) (= (@ (@ tptp.ord_le3221252021190050221t_unit P3) (@ (@ tptp.sup_sup_Product_unit Q6) R2)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit P3) (@ tptp.uminus2952777764628376836t_unit Q6))) R2))))
% 8.20/8.62 (assert (forall ((P3 tptp.set_int) (Q6 tptp.set_int) (R2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int P3) (@ (@ tptp.sup_sup_set_int Q6) R2)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int P3) (@ tptp.uminus1532241313380277803et_int Q6))) R2))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z3) N2)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z3)) N2)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P2 (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P2 tptp.zero_zero_nat))) (exists ((D5 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D5)) (not (@ P2 D5)))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P2 (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P2 tptp.zero_zero_nat)) (forall ((D5 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D5)) (@ P2 D5)))))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) J2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J2) K2)) I2) (@ (@ tptp.ord_less_nat J2) (@ (@ tptp.plus_plus_nat I2) K2))))))
% 8.20/8.62 (assert (forall ((D2 tptp.int) (P1 (-> tptp.int Bool)) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P1 X3) (@ P1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D2))))) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z6) (= (@ P2 X3) (@ P1 X3))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P2 X_1))))))))
% 8.20/8.62 (assert (forall ((D2 tptp.int) (P6 (-> tptp.int Bool)) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D2))))) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z6) X3) (= (@ P2 X3) (@ P6 X3))))) (=> (exists ((X_12 tptp.int)) (@ P6 X_12)) (exists ((X_1 tptp.int)) (@ P2 X_1))))))))
% 8.20/8.62 (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))))))))))
% 8.20/8.62 (assert (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N2)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M) N2)))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N2)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N2))))))
% 8.20/8.62 (assert (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) 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 J2) U)) N2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M)) N2)))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N2)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N2))))))
% 8.20/8.62 (assert (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M)) N2)))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N2)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N2))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.int Bool)) (K2 tptp.int) (I2 tptp.int)) (=> (@ P2 K2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K2) I3) (=> (@ P2 I3) (@ P2 (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K2) (=> (@ P2 I3) (@ P2 (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P2 I2))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((K2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K2) tptp.zero_zero_int) (not (forall ((N5 tptp.nat)) (not (= K2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N5)))))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) tptp.zero_zero_int)))
% 8.20/8.62 (assert (= tptp.plus_plus_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 8.20/8.62 (assert (= tptp.times_times_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 8.20/8.62 (assert (= tptp.divide_divide_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 8.20/8.62 (assert (= tptp.modulo_modulo_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 8.20/8.62 (assert (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z3)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z3))) tptp.zero_zero_rat))))))
% 8.20/8.62 (assert (forall ((Y tptp.rat) (Z3 tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z3)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z3)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z3))) tptp.zero_zero_rat))))))
% 8.20/8.62 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_int W2) Z3)))))
% 8.20/8.62 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z3)) (@ (@ tptp.ord_less_eq_int W2) Z3)))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (I2 tptp.int)) (= (@ P2 (@ tptp.nat2 I2)) (and (forall ((N tptp.nat)) (=> (= I2 (@ tptp.semiri1314217659103216013at_int N)) (@ P2 N))) (=> (@ (@ tptp.ord_less_int I2) tptp.zero_zero_int) (@ P2 tptp.zero_zero_nat))))))
% 8.20/8.62 (assert (forall ((K2 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (= (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.nat2 K2)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N2)) K2)))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int) (Z7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z3) (=> (@ _let_1 Z7) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z3) Z7)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z3)) (@ tptp.nat2 Z7))))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z3) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z3)) (@ tptp.nat2 Z7))))))
% 8.20/8.62 (assert (= tptp.suc (lambda ((A5 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A5)) tptp.one_one_int)))))
% 8.20/8.62 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C2))))))
% 8.20/8.62 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ tptp.uminus_uminus_rat B))))))
% 8.20/8.62 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C2)) (@ tptp.uminus_uminus_rat B))))))
% 8.20/8.62 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C2))))))
% 8.20/8.62 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.uminus_uminus_rat B))) (let ((_let_4 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_5 (@ _let_1 C2))) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z3))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z3))) Z3)))))
% 8.20/8.62 (assert (forall ((Z3 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z3))) B))) (let ((_let_2 (= Z3 tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z3))) Z3))))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (=> (@ (@ tptp.ord_less_eq_nat K2) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat K2) (@ tptp.suc tptp.zero_zero_nat))) M)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (assert (forall ((J2 tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J2)) U)) M)) N2)))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J2) U)) N2)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J2) I2)) U)) N2))))))
% 8.20/8.62 (assert (forall ((D2 tptp.int) (P2 (-> tptp.int Bool)) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int)) (=> (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (forall ((X6 tptp.int)) (=> (@ P2 X6) (@ P2 (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K2) D2))))))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((K2 tptp.int)) (=> (not (= K2 tptp.zero_zero_int)) (=> (forall ((N5 tptp.nat)) (=> (= K2 (@ tptp.semiri1314217659103216013at_int N5)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5)))) (not (forall ((N5 tptp.nat)) (=> (= K2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N5))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5)))))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) tptp.zero_zero_int)))
% 8.20/8.62 (assert (forall ((L tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K2) (= (@ (@ tptp.modulo_modulo_int K2) L) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K2) L)) L))))))
% 8.20/8.62 (assert (forall ((A4 tptp.int) (B5 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A4) B5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B5) N2)) (@ (@ tptp.divide_divide_int A4) N2))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((U tptp.rat) (V tptp.rat) (R2 tptp.rat) (S2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (=> (@ (@ tptp.ord_less_eq_rat R2) S2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R2) (@ (@ tptp.minus_minus_rat V) U))) S2))) V))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.suc (@ tptp.nat2 Z3)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int tptp.one_one_int) Z3))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C2))))))
% 8.20/8.62 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ tptp.uminus_uminus_rat B))))))
% 8.20/8.62 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C2)) (@ tptp.uminus_uminus_rat B))))))
% 8.20/8.62 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C2))))))
% 8.20/8.62 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.uminus_uminus_rat B))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C2))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C2))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 8.20/8.62 (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))))))))))))
% 8.20/8.62 (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))))))))))))
% 8.20/8.62 (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))))))))))))
% 8.20/8.62 (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))))))))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((K2 tptp.int)) (=> (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (not (forall ((N5 tptp.nat)) (=> (= K2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N5))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5))))))))
% 8.20/8.62 (assert (forall ((K2 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 K2) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K2)))))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K2)))))))
% 8.20/8.62 (assert (forall ((K2 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 K2) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K2)))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((M6 tptp.multis2468970476368604999at_nat) (N7 tptp.multis2468970476368604999at_nat)) (= (@ tptp.size_s8510653225128441779at_nat (@ (@ tptp.plus_p7104986032573967614at_nat M6) N7)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s8510653225128441779at_nat M6)) (@ tptp.size_s8510653225128441779at_nat N7)))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((A tptp.array_nat) (Xs tptp.list_nat)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ (@ tptp.snga_assn_nat A) Xs)) (@ tptp.array_len_nat A)) (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_nat A) Xs)) (@ tptp.pure_assn (= R5 (@ tptp.size_size_list_nat Xs))))))))
% 8.20/8.62 (assert (forall ((A tptp.array_o) (Xs tptp.list_o)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ (@ tptp.snga_assn_o A) Xs)) (@ tptp.array_len_o A)) (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_o A) Xs)) (@ tptp.pure_assn (= R5 (@ tptp.size_size_list_o Xs))))))))
% 8.20/8.62 (assert (forall ((A tptp.array_int) (Xs tptp.list_int)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ (@ tptp.snga_assn_int A) Xs)) (@ tptp.array_len_int A)) (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_int A) Xs)) (@ tptp.pure_assn (= R5 (@ tptp.size_size_list_int Xs))))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o A4) A4) tptp.bot_bot_set_o)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A4) A4) tptp.bot_bot_set_nat)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A4) A4) tptp.bot_bot_set_int)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat A4) A4) tptp.bot_bo2099793752762293965at_nat)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o tptp.bot_bot_set_o) A4) tptp.bot_bot_set_o)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A4) tptp.bot_bot_set_nat)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A4) tptp.bot_bot_set_int)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat tptp.bot_bo2099793752762293965at_nat) A4) tptp.bot_bo2099793752762293965at_nat)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o A4) tptp.bot_bot_set_o) A4)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A4) tptp.bot_bot_set_nat) A4)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A4) tptp.bot_bot_set_int) A4)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat A4) tptp.bot_bo2099793752762293965at_nat) A4)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int B5)) (@ tptp.uminus1532241313380277803et_int A4)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int A4)) (@ tptp.uminus1532241313380277803et_int B5)) (@ (@ tptp.ord_less_eq_set_int B5) A4))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A4) (@ tptp.uminus5710092332889474511et_nat B5)) (@ (@ tptp.inf_inf_set_nat A4) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat A4) (@ tptp.uminus6524753893492686040at_nat B5)) (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.uminus5710092332889474511et_nat B5)) (@ (@ tptp.minus_minus_set_nat A4) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) (@ tptp.uminus6524753893492686040at_nat B5)) (@ (@ tptp.minus_1356011639430497352at_nat A4) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (= (@ tptp.uminus2330091110623919550at_nat (@ (@ tptp.minus_5060654252129873198at_nat A4) B5)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ tptp.uminus2330091110623919550at_nat A4)) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.uminus935396558254630718at_nat (@ (@ tptp.minus_3314409938677909166at_nat A4) B5)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.uminus935396558254630718at_nat A4)) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.minus_minus_set_nat A4) B5)) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat A4)) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.uminus6524753893492686040at_nat A4)) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat A4))) (= (@ _let_1 (@ (@ tptp.minus_5060654252129873198at_nat B5) A4)) (@ _let_1 B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A4))) (= (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat B5) A4)) (@ _let_1 B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A4))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)) (@ _let_1 B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat A4))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat B5) A4)) (@ _let_1 B5)))))
% 8.20/8.62 (assert (forall ((B5 tptp.set_Pr8551490117392284871at_nat) (A4 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.minus_5060654252129873198at_nat B5) A4)) A4) (@ (@ tptp.sup_su3035147773818789531at_nat B5) A4))))
% 8.20/8.62 (assert (forall ((B5 tptp.set_Pr4329608150637261639at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.minus_3314409938677909166at_nat B5) A4)) A4) (@ (@ tptp.sup_su5525570899277871387at_nat B5) A4))))
% 8.20/8.62 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat B5) A4)) A4) (@ (@ tptp.sup_sup_set_nat B5) A4))))
% 8.20/8.62 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.minus_1356011639430497352at_nat B5) A4)) A4) (@ (@ tptp.sup_su6327502436637775413at_nat B5) A4))))
% 8.20/8.62 (assert (forall ((M6 tptp.multis2468970476368604999at_nat) (N7 tptp.multis2468970476368604999at_nat) (P2 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.minus_4286766774447292334at_nat M6))) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ _let_1 N7)) P2) (@ _let_1 (@ (@ tptp.plus_p7104986032573967614at_nat N7) P2))))))
% 8.20/8.62 (assert (forall ((M6 tptp.multis2468970476368604999at_nat) (N7 tptp.multis2468970476368604999at_nat)) (= (= (@ (@ tptp.plus_p7104986032573967614at_nat M6) N7) tptp.zero_z1048942125864253310at_nat) (and (= M6 tptp.zero_z1048942125864253310at_nat) (= N7 tptp.zero_z1048942125864253310at_nat)))))
% 8.20/8.62 (assert (forall ((M6 tptp.multis2468970476368604999at_nat) (N7 tptp.multis2468970476368604999at_nat)) (= (= tptp.zero_z1048942125864253310at_nat (@ (@ tptp.plus_p7104986032573967614at_nat M6) N7)) (and (= M6 tptp.zero_z1048942125864253310at_nat) (= N7 tptp.zero_z1048942125864253310at_nat)))))
% 8.20/8.62 (assert (forall ((X tptp.multis2468970476368604999at_nat) (Y tptp.multis2468970476368604999at_nat)) (= (= tptp.zero_z1048942125864253310at_nat (@ (@ tptp.plus_p7104986032573967614at_nat X) Y)) (and (= X tptp.zero_z1048942125864253310at_nat) (= Y tptp.zero_z1048942125864253310at_nat)))))
% 8.20/8.62 (assert (forall ((X tptp.multis2468970476368604999at_nat) (Y tptp.multis2468970476368604999at_nat)) (= (= (@ (@ tptp.plus_p7104986032573967614at_nat X) Y) tptp.zero_z1048942125864253310at_nat) (and (= X tptp.zero_z1048942125864253310at_nat) (= Y tptp.zero_z1048942125864253310at_nat)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o A4) B5) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o A4) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A4) B5) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A4) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat A4) B5) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A4) B5) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A4) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A4) (@ (@ tptp.minus_minus_set_o B5) A4)) tptp.bot_bot_set_o)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A4) (@ (@ tptp.minus_minus_set_nat B5) A4)) tptp.bot_bot_set_nat)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A4) (@ (@ tptp.minus_minus_set_int B5) A4)) tptp.bot_bot_set_int)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) (@ (@ tptp.minus_1356011639430497352at_nat B5) A4)) tptp.bot_bo2099793752762293965at_nat)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) (@ tptp.uminus6524753893492686040at_nat A4)) tptp.bot_bo2099793752762293965at_nat)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A4) (@ tptp.uminus_uminus_set_o A4)) tptp.bot_bot_set_o)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.uminus5710092332889474511et_nat A4)) tptp.bot_bot_set_nat)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A4) (@ tptp.uminus1532241313380277803et_int A4)) tptp.bot_bot_set_int)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat A4)) A4) tptp.bot_bo2099793752762293965at_nat)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o A4)) A4) tptp.bot_bot_set_o)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat A4)) A4) tptp.bot_bot_set_nat)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int A4)) A4) tptp.bot_bot_set_int)))
% 8.20/8.62 (assert (forall ((P2 tptp.assn) (H tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ tptp.uminus_uminus_assn P2)) H) (and (@ tptp.in_range H) (not (@ (@ tptp.rep_assn P2) H))))))
% 8.20/8.62 (assert (= tptp.minus_minus_assn (lambda ((A5 tptp.assn) (B4 tptp.assn)) (@ (@ tptp.inf_inf_assn A5) (@ tptp.uminus_uminus_assn B4)))))
% 8.20/8.62 (assert (forall ((M6 tptp.multis2468970476368604999at_nat) (N7 tptp.multis2468970476368604999at_nat) (Q2 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.minus_4286766774447292334at_nat M6))) (= (@ _let_1 (@ (@ tptp.plus_p7104986032573967614at_nat N7) Q2)) (@ (@ tptp.minus_4286766774447292334at_nat (@ _let_1 N7)) Q2)))))
% 8.20/8.62 (assert (forall ((N7 tptp.multis2468970476368604999at_nat) (M6 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ (@ tptp.plus_p7104986032573967614at_nat N7) M6)) N7) M6)))
% 8.20/8.62 (assert (forall ((M6 tptp.multis2468970476368604999at_nat) (N7 tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ (@ tptp.plus_p7104986032573967614at_nat M6) N7)) N7) M6)))
% 8.20/8.62 (assert (forall ((C4 tptp.multis2468970476368604999at_nat) (B5 tptp.multis2468970476368604999at_nat) (A4 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A4))) (=> (= (@ (@ tptp.minus_4286766774447292334at_nat C4) B5) tptp.zero_z1048942125864253310at_nat) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.minus_4286766774447292334at_nat B5) C4)))))))
% 8.20/8.62 (assert (forall ((X tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.plus_p7104986032573967614at_nat tptp.zero_z1048942125864253310at_nat) X) X)))
% 8.20/8.62 (assert (forall ((X tptp.multis2468970476368604999at_nat)) (= (@ (@ tptp.plus_p7104986032573967614at_nat X) tptp.zero_z1048942125864253310at_nat) X)))
% 8.20/8.62 (assert (forall ((A4 tptp.multis2468970476368604999at_nat) (B5 tptp.multis2468970476368604999at_nat) (M6 tptp.multis2468970476368604999at_nat) (N7 tptp.multis2468970476368604999at_nat)) (=> (= (@ (@ tptp.plus_p7104986032573967614at_nat A4) B5) (@ (@ tptp.plus_p7104986032573967614at_nat M6) N7)) (not (forall ((Am tptp.multis2468970476368604999at_nat) (An tptp.multis2468970476368604999at_nat)) (=> (= A4 (@ (@ tptp.plus_p7104986032573967614at_nat Am) An)) (forall ((Bm tptp.multis2468970476368604999at_nat) (Bn tptp.multis2468970476368604999at_nat)) (=> (= B5 (@ (@ tptp.plus_p7104986032573967614at_nat Bm) Bn)) (=> (= M6 (@ (@ tptp.plus_p7104986032573967614at_nat Am) Bm)) (not (= N7 (@ (@ tptp.plus_p7104986032573967614at_nat An) Bn))))))))))))
% 8.20/8.62 (assert (forall ((A4 tptp.multis2468970476368604999at_nat) (X7 tptp.multis2468970476368604999at_nat) (Y7 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A4))) (=> (= (@ _let_1 X7) (@ _let_1 Y7)) (= X7 Y7)))))
% 8.20/8.62 (assert (forall ((M6 tptp.multis2468970476368604999at_nat) (K5 tptp.multis2468970476368604999at_nat) (N7 tptp.multis2468970476368604999at_nat)) (= (= (@ (@ tptp.plus_p7104986032573967614at_nat M6) K5) (@ (@ tptp.plus_p7104986032573967614at_nat N7) K5)) (= M6 N7))))
% 8.20/8.62 (assert (forall ((K5 tptp.multis2468970476368604999at_nat) (M6 tptp.multis2468970476368604999at_nat) (N7 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat K5))) (= (= (@ _let_1 M6) (@ _let_1 N7)) (= M6 N7)))))
% 8.20/8.62 (assert (= tptp.plus_p7104986032573967614at_nat (lambda ((M9 tptp.multis2468970476368604999at_nat) (N8 tptp.multis2468970476368604999at_nat)) (@ (@ tptp.plus_p7104986032573967614at_nat N8) M9))))
% 8.20/8.62 (assert (forall ((M6 tptp.multis2468970476368604999at_nat) (N7 tptp.multis2468970476368604999at_nat) (K5 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat M6))) (let ((_let_2 (@ tptp.plus_p7104986032573967614at_nat N7))) (= (@ _let_1 (@ _let_2 K5)) (@ _let_2 (@ _let_1 K5)))))))
% 8.20/8.62 (assert (forall ((M6 tptp.multis2468970476368604999at_nat) (N7 tptp.multis2468970476368604999at_nat) (K5 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat M6))) (= (@ (@ tptp.plus_p7104986032573967614at_nat (@ _let_1 N7)) K5) (@ _let_1 (@ (@ tptp.plus_p7104986032573967614at_nat N7) K5))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat) (D4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A4) C4) (=> (@ (@ tptp.ord_le3146513528884898305at_nat D4) B5) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) (@ (@ tptp.minus_1356011639430497352at_nat C4) D4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (C4 tptp.set_int) (D4 tptp.set_int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A4) C4) (=> (@ (@ tptp.ord_less_eq_set_int D4) B5) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A4) B5)) (@ (@ tptp.minus_minus_set_int C4) D4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) A4)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A4) B5)) A4)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B5) C4) (= (@ (@ tptp.minus_1356011639430497352at_nat B5) (@ (@ tptp.minus_1356011639430497352at_nat C4) A4)) A4)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (C4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (@ (@ tptp.ord_less_eq_set_int B5) C4) (= (@ (@ tptp.minus_minus_set_int B5) (@ (@ tptp.minus_minus_set_int C4) A4)) A4)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.minus_minus_set_nat A4) B5)) C4) (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.inf_inf_set_nat A4) C4)) (@ (@ tptp.inf_inf_set_nat B5) C4)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) C4) (@ (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A4) C4)) (@ (@ tptp.inf_in2572325071724192079at_nat B5) C4)))))
% 8.20/8.62 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat C4))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5)) (@ (@ tptp.minus_minus_set_nat (@ _let_1 A4)) (@ _let_1 B5))))))
% 8.20/8.62 (assert (forall ((C4 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat C4))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 A4)) (@ _let_1 B5))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A4))) (= (@ _let_1 (@ _let_1 B5)) (@ (@ tptp.inf_inf_set_nat A4) B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A4))) (= (@ _let_1 (@ _let_1 B5)) (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (C4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat (@ (@ tptp.inf_inf_set_nat A4) C4)))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B5) C4)) (@ _let_1 B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A4) C4)))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B5) C4)) (@ _let_1 B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A4))) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) C4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A4))) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat B5) C4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.minus_5060654252129873198at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5)) C4) (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.minus_5060654252129873198at_nat A4) C4)) (@ (@ tptp.minus_5060654252129873198at_nat B5) C4)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.minus_3314409938677909166at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5)) C4) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.minus_3314409938677909166at_nat A4) C4)) (@ (@ tptp.minus_3314409938677909166at_nat B5) C4)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.sup_sup_set_nat A4) B5)) C4) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat A4) C4)) (@ (@ tptp.minus_minus_set_nat B5) C4)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A4) B5)) C4) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) C4)) (@ (@ tptp.minus_1356011639430497352at_nat B5) C4)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.minus_5060654252129873198at_nat A4))) (= (@ (@ tptp.minus_5060654252129873198at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat B5) C4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A4))) (= (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B5) C4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A4))) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B5) C4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A4))) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B5) C4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o)) (=> (@ (@ tptp.ord_less_set_o A4) B5) (exists ((B3 Bool)) (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o B5) A4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (=> (@ (@ tptp.ord_le1924305788584680229nt_int A4) B5) (exists ((B3 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int B3) (@ (@ tptp.minus_2612819937483484256nt_int B5) A4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_set_set_nat A4) B5) (exists ((B3 tptp.set_nat)) (@ (@ tptp.member_set_nat B3) (@ (@ tptp.minus_2163939370556025621et_nat B5) A4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A4) B5) (exists ((B3 tptp.nat)) (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat B5) A4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A4) B5) (exists ((B3 tptp.int)) (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A4) B5) (exists ((B3 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat B3) (@ (@ tptp.minus_1356011639430497352at_nat B5) A4))))))
% 8.20/8.62 (assert (= tptp.uminus2952777764628376836t_unit (lambda ((Uu3 tptp.product_unit)) tptp.product_Unity)))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.list_nat Bool)) (Q2 (-> tptp.list_nat Bool))) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (=> (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.sup_sup_set_list_nat (@ tptp.uminus3195874150345416415st_nat (@ tptp.collect_list_nat P2))) (@ tptp.collect_list_nat Q2)))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.set_Pr958786334691620121nt_int Bool)) (Q2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (= (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (=> (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.sup_su2047564715030645325nt_int (@ tptp.uminus6423885277529793776nt_int (@ tptp.collec5210948495886036740nt_int P2))) (@ tptp.collec5210948495886036740nt_int Q2)))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.set_nat Bool)) (Q2 (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (=> (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.sup_sup_set_set_nat (@ tptp.uminus613421341184616069et_nat (@ tptp.collect_set_nat P2))) (@ tptp.collect_set_nat Q2)))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (=> (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.sup_sup_set_int (@ tptp.uminus1532241313380277803et_int (@ tptp.collect_int P2))) (@ tptp.collect_int Q2)))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.produc4166570645942440679at_nat Bool)) (Q2 (-> tptp.produc4166570645942440679at_nat Bool))) (= (@ tptp.collec5204685387357076818at_nat (lambda ((X4 tptp.produc4166570645942440679at_nat)) (=> (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.sup_su3035147773818789531at_nat (@ tptp.uminus2330091110623919550at_nat (@ tptp.collec5204685387357076818at_nat P2))) (@ tptp.collec5204685387357076818at_nat Q2)))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.produc3843707927480180839at_nat Bool)) (Q2 (-> tptp.produc3843707927480180839at_nat Bool))) (= (@ tptp.collec6321179662152712658at_nat (lambda ((X4 tptp.produc3843707927480180839at_nat)) (=> (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.uminus935396558254630718at_nat (@ tptp.collec6321179662152712658at_nat P2))) (@ tptp.collec6321179662152712658at_nat Q2)))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (=> (@ P2 X4) (@ Q2 X4)))) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat (@ tptp.collect_nat P2))) (@ tptp.collect_nat Q2)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (= (@ (@ tptp.minus_minus_set_o A4) B5) tptp.bot_bot_set_o))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (= (@ (@ tptp.minus_minus_set_nat A4) B5) tptp.bot_bot_set_nat))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5) (= (@ (@ tptp.minus_1356011639430497352at_nat A4) B5) tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (= (@ (@ tptp.minus_minus_set_int A4) B5) tptp.bot_bot_set_int))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A4) (@ tptp.uminus6524753893492686040at_nat A4)) (= A4 tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A4) (@ tptp.uminus_uminus_set_o A4)) (= A4 tptp.bot_bot_set_o))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A4) (@ tptp.uminus5710092332889474511et_nat A4)) (= A4 tptp.bot_bot_set_nat))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A4) (@ tptp.uminus1532241313380277803et_int A4)) (= A4 tptp.bot_bot_set_int))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o)) (= (not (= (@ (@ tptp.minus_minus_set_o A4) B5) A4)) (not (= (@ (@ tptp.inf_inf_set_o A4) B5) tptp.bot_bot_set_o)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (not (= (@ (@ tptp.minus_minus_set_nat A4) B5) A4)) (not (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (= (not (= (@ (@ tptp.minus_minus_set_int A4) B5) A4)) (not (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (not (= (@ (@ tptp.minus_1356011639430497352at_nat A4) B5) A4)) (not (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5) tptp.bot_bo2099793752762293965at_nat)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o A4) B5) A4) (= (@ (@ tptp.inf_inf_set_o A4) B5) tptp.bot_bot_set_o))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A4) B5) A4) (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A4) B5) A4) (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat A4) B5) A4) (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5) tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.inf_inf_set_o A4) B5)) (@ (@ tptp.minus_minus_set_o A4) B5)) tptp.bot_bot_set_o)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat A4) B5)) (@ (@ tptp.minus_minus_set_nat A4) B5)) tptp.bot_bot_set_nat)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.inf_inf_set_int A4) B5)) (@ (@ tptp.minus_minus_set_int A4) B5)) tptp.bot_bot_set_int)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) tptp.bot_bo2099793752762293965at_nat)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o)) (=> (= (@ (@ tptp.inf_inf_set_o A4) B5) tptp.bot_bot_set_o) (= (@ (@ tptp.minus_minus_set_o A4) B5) A4))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat) (= (@ (@ tptp.minus_minus_set_nat A4) B5) A4))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int) (= (@ (@ tptp.minus_minus_set_int A4) B5) A4))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5) tptp.bot_bo2099793752762293965at_nat) (= (@ (@ tptp.minus_1356011639430497352at_nat A4) B5) A4))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.minus_5060654252129873198at_nat A4) B5)) C4) (@ (@ tptp.ord_le8081472938463900775at_nat A4) (@ (@ tptp.sup_su3035147773818789531at_nat B5) C4)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.minus_3314409938677909166at_nat A4) B5)) C4) (@ (@ tptp.ord_le1268244103169919719at_nat A4) (@ (@ tptp.sup_su5525570899277871387at_nat B5) C4)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A4) B5)) C4) (@ (@ tptp.ord_less_eq_set_nat A4) (@ (@ tptp.sup_sup_set_nat B5) C4)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) C4) (@ (@ tptp.ord_le3146513528884898305at_nat A4) (@ (@ tptp.sup_su6327502436637775413at_nat B5) C4)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (C4 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A4) B5)) C4) (@ (@ tptp.ord_less_eq_set_int A4) (@ (@ tptp.sup_sup_set_int B5) C4)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat A4) B5) (= (@ (@ tptp.sup_su3035147773818789531at_nat A4) (@ (@ tptp.minus_5060654252129873198at_nat B5) A4)) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A4) B5) (= (@ (@ tptp.sup_su5525570899277871387at_nat A4) (@ (@ tptp.minus_3314409938677909166at_nat B5) A4)) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (= (@ (@ tptp.sup_sup_set_nat A4) (@ (@ tptp.minus_minus_set_nat B5) A4)) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5) (= (@ (@ tptp.sup_su6327502436637775413at_nat A4) (@ (@ tptp.minus_1356011639430497352at_nat B5) A4)) B5))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (= (@ (@ tptp.sup_sup_set_int A4) (@ (@ tptp.minus_minus_set_int B5) A4)) B5))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.minus_5060654252129873198at_nat A4) B5)) (@ (@ tptp.inf_in1697001100524423349at_nat A4) B5)) A4)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.minus_3314409938677909166at_nat A4) B5)) (@ (@ tptp.inf_in7913087082777306421at_nat A4) B5)) A4)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat A4) B5)) (@ (@ tptp.inf_inf_set_nat A4) B5)) A4)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) A4)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat A4) B5)) (@ (@ tptp.minus_5060654252129873198at_nat A4) B5)) A4)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A4) B5)) (@ (@ tptp.minus_3314409938677909166at_nat A4) B5)) A4)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat A4) B5)) (@ (@ tptp.minus_minus_set_nat A4) B5)) A4)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) A4)))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.minus_5060654252129873198at_nat A4))) (= (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat B5) C4)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A4))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B5) C4)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A4))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B5) C4)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A4))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B5) C4)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.minus_5060654252129873198at_nat A4))) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat B5) C4)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A4))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B5) C4)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A4))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat B5) C4)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A4))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B5) C4)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B5)) (@ _let_1 C4))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.uminus6524753893492686040at_nat A4)) (@ tptp.uminus6524753893492686040at_nat B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (= (@ tptp.uminus2330091110623919550at_nat (@ (@ tptp.inf_in1697001100524423349at_nat A4) B5)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ tptp.uminus2330091110623919550at_nat A4)) (@ tptp.uminus2330091110623919550at_nat B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.uminus935396558254630718at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A4) B5)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.uminus935396558254630718at_nat A4)) (@ tptp.uminus935396558254630718at_nat B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.inf_inf_set_nat A4) B5)) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat A4)) (@ tptp.uminus5710092332889474511et_nat B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A4) B5)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat A4)) (@ tptp.uminus6524753893492686040at_nat B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (= (@ tptp.uminus2330091110623919550at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ tptp.uminus2330091110623919550at_nat A4)) (@ tptp.uminus2330091110623919550at_nat B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.uminus935396558254630718at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ tptp.uminus935396558254630718at_nat A4)) (@ tptp.uminus935396558254630718at_nat B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat A4)) (@ tptp.uminus5710092332889474511et_nat B5)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat A4) (@ tptp.uminus6524753893492686040at_nat B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A4) B5) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o A4) (@ tptp.uminus_uminus_set_o B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A4) (@ tptp.uminus5710092332889474511et_nat B5)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A4) (@ tptp.uminus1532241313380277803et_int B5)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o)) (= (@ (@ tptp.ord_less_set_o (@ (@ tptp.minus_minus_set_o A4) B5)) A4) (not (= (@ (@ tptp.inf_inf_set_o A4) B5) tptp.bot_bot_set_o)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A4) B5)) A4) (not (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A4) B5)) A4) (not (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int)))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) A4) (not (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5) tptp.bot_bo2099793752762293965at_nat)))))
% 8.20/8.62 (assert (= tptp.uminus_uminus_assn (lambda ((P5 tptp.assn)) (@ tptp.abs_assn (lambda ((H6 tptp.produc3658429121746597890et_nat)) (and (@ tptp.in_range H6) (not (@ (@ tptp.rep_assn P5) H6))))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z3))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z3) (@ tptp.semiri681578069525770553at_rat N2))) (@ _let_1 N2))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z3))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z3) (@ tptp.semiri1314217659103216013at_int N2))) (@ _let_1 N2))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z3))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z3) (@ tptp.semiri1316708129612266289at_nat N2))) (@ _let_1 N2))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z3))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger Z3) (@ tptp.semiri4939895301339042750nteger N2))) (@ _let_1 N2))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat N2) K2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K2) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N2) K2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N2) K2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K2) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K2) tptp.zero_zero_rat))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K2) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K2) tptp.zero_zero_int))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K2) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K2) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (not (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K2) tptp.zero_zero_rat)))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K2) tptp.zero_zero_int)))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K2) tptp.zero_z3403309356797280102nteger)))))
% 8.20/8.62 (assert (forall ((Z3 tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z3) (@ tptp.semiri681578069525770553at_rat N2))) M))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z3) (@ tptp.semiri1314217659103216013at_int N2))) M))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z3) (@ tptp.semiri1316708129612266289at_nat N2))) M))))))
% 8.20/8.62 (assert (forall ((Z3 tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N2)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger Z3) (@ tptp.semiri4939895301339042750nteger N2))) M))))))
% 8.20/8.62 (assert (forall ((R2 tptp.product_prod_int_int) (P3 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.normalize R2) (@ (@ tptp.product_Pair_int_int P3) Q6)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q6))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z3))) (=> (@ (@ 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 Z3) (@ tptp.semiri681578069525770553at_rat M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z3 tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z3))) (=> (@ (@ 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 Z3) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z3))) (=> (@ (@ 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 Z3) (@ tptp.semiri1316708129612266289at_nat M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z3 tptp.code_integer)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z3))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger Z3) (@ tptp.semiri4939895301339042750nteger M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 8.20/8.62 (assert (forall ((R2 tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R2))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R2) (@ tptp.semiri681578069525770553at_rat K2))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K2)) (@ (@ tptp.times_times_rat R2) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K2))))))
% 8.20/8.62 (assert (forall ((R2 tptp.int) (K2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R2))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R2) (@ tptp.semiri1314217659103216013at_int K2))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K2)) (@ (@ tptp.times_times_int R2) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K2))))))
% 8.20/8.62 (assert (forall ((R2 tptp.code_integer) (K2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R2) (@ tptp.semiri4939895301339042750nteger K2))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K2)) (@ (@ tptp.times_3573771949741848930nteger R2) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K2))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((B tptp.rat) (K2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K2))) tptp.one_one_rat)) K2)))))
% 8.20/8.62 (assert (forall ((B tptp.int) (K2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K2))) tptp.one_one_int)) K2)))))
% 8.20/8.62 (assert (forall ((B tptp.code_integer) (K2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K2)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K2))) tptp.one_one_Code_integer)) K2)))))
% 8.20/8.62 (assert (forall ((B tptp.rat) (K2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K2))) tptp.one_one_rat)) K2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K2)))))
% 8.20/8.62 (assert (forall ((B tptp.int) (K2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K2))) tptp.one_one_int)) K2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K2)))))
% 8.20/8.62 (assert (forall ((B tptp.code_integer) (K2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K2))) tptp.one_one_Code_integer)) K2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K2)) (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K2)))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K2 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)) K2) (=> (@ (@ tptp.ord_less_eq_int K2) (@ F N2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ F I3) K2))))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_eq_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_int Xs)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.slice_int From) To) Xs)) (@ (@ tptp.minus_minus_nat To) From))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K2 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)) K2) (=> (@ (@ tptp.ord_less_eq_int K2) (@ F N2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ F I3) K2))))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N2)) _let_1)))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.gbinomial_rat A) K2) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.semiri681578069525770553at_rat K2))) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((C2 Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (=> (@ _let_1 A4) (=> (not (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.minus_minus_set_o A4) B5)))))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (@ _let_1 A4) (=> (not (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.minus_2612819937483484256nt_int A4) B5)))))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (@ _let_1 A4) (=> (not (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A4) B5)))))))
% 8.20/8.62 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 A4) (=> (not (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5)))))))
% 8.20/8.62 (assert (forall ((C2 tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 A4) (=> (not (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5)))))))
% 8.20/8.62 (assert (forall ((C2 tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C2))) (=> (@ _let_1 A4) (=> (not (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)))))))
% 8.20/8.62 (assert (forall ((C2 Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A4) B5)) (and (@ _let_1 A4) (not (@ _let_1 B5)))))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (= (@ _let_1 (@ (@ tptp.minus_2612819937483484256nt_int A4) B5)) (and (@ _let_1 A4) (not (@ _let_1 B5)))))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A4) B5)) (and (@ _let_1 A4) (not (@ _let_1 B5)))))))
% 8.20/8.62 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5)) (and (@ _let_1 A4) (not (@ _let_1 B5)))))))
% 8.20/8.62 (assert (forall ((C2 tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5)) (and (@ _let_1 A4) (not (@ _let_1 B5)))))))
% 8.20/8.62 (assert (forall ((C2 tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C2))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) (and (@ _let_1 A4) (not (@ _let_1 B5)))))))
% 8.20/8.62 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) B5))) (= (@ (@ tptp.minus_1356011639430497352at_nat _let_1) B5) _let_1))))
% 8.20/8.62 (assert (forall ((C2 Bool) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (=> (not (@ _let_1 A4)) (@ _let_1 (@ tptp.uminus_uminus_set_o A4))))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (not (@ _let_1 A4)) (@ _let_1 (@ tptp.uminus6423885277529793776nt_int A4))))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (not (@ _let_1 A4)) (@ _let_1 (@ tptp.uminus613421341184616069et_nat A4))))))
% 8.20/8.62 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (not (@ _let_1 A4)) (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A4))))))
% 8.20/8.62 (assert (forall ((C2 tptp.int) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (not (@ _let_1 A4)) (@ _let_1 (@ tptp.uminus1532241313380277803et_int A4))))))
% 8.20/8.62 (assert (forall ((C2 Bool) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (= (@ _let_1 (@ tptp.uminus_uminus_set_o A4)) (not (@ _let_1 A4))))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (= (@ _let_1 (@ tptp.uminus6423885277529793776nt_int A4)) (not (@ _let_1 A4))))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (= (@ _let_1 (@ tptp.uminus613421341184616069et_nat A4)) (not (@ _let_1 A4))))))
% 8.20/8.62 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (= (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A4)) (not (@ _let_1 A4))))))
% 8.20/8.62 (assert (forall ((C2 tptp.int) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (= (@ _let_1 (@ tptp.uminus1532241313380277803et_int A4)) (not (@ _let_1 A4))))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 8.20/8.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 8.20/8.62 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 8.20/8.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ (@ tptp.slice_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)) Xs) Xs)))
% 8.20/8.62 (assert (forall ((Xs tptp.list_o)) (= (@ (@ (@ tptp.slice_o tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs)) Xs) Xs)))
% 8.20/8.62 (assert (forall ((Xs tptp.list_int)) (= (@ (@ (@ tptp.slice_int tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)) Xs) Xs)))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z3)) tptp.one_one_int) (= Z3 tptp.zero_zero_int))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((C2 Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_o A4) B5)) (not (=> (@ _let_1 A4) (@ _let_1 B5)))))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (@ _let_1 (@ (@ tptp.minus_2612819937483484256nt_int A4) B5)) (not (=> (@ _let_1 A4) (@ _let_1 B5)))))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A4) B5)) (not (=> (@ _let_1 A4) (@ _let_1 B5)))))))
% 8.20/8.62 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5)) (not (=> (@ _let_1 A4) (@ _let_1 B5)))))))
% 8.20/8.62 (assert (forall ((C2 tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5)) (not (=> (@ _let_1 A4) (@ _let_1 B5)))))))
% 8.20/8.62 (assert (forall ((C2 tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C2))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) (not (=> (@ _let_1 A4) (@ _let_1 B5)))))))
% 8.20/8.62 (assert (forall ((C2 Bool) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (=> (@ _let_1 (@ tptp.uminus_uminus_set_o A4)) (not (@ _let_1 A4))))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (@ _let_1 (@ tptp.uminus6423885277529793776nt_int A4)) (not (@ _let_1 A4))))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (@ _let_1 (@ tptp.uminus613421341184616069et_nat A4)) (not (@ _let_1 A4))))))
% 8.20/8.62 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A4)) (not (@ _let_1 A4))))))
% 8.20/8.62 (assert (forall ((C2 tptp.int) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 (@ tptp.uminus1532241313380277803et_int A4)) (not (@ _let_1 A4))))))
% 8.20/8.62 (assert (forall ((C2 Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_o A4) B5)) (@ _let_1 A4)))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (@ _let_1 (@ (@ tptp.minus_2612819937483484256nt_int A4) B5)) (@ _let_1 A4)))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A4) B5)) (@ _let_1 A4)))))
% 8.20/8.62 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5)) (@ _let_1 A4)))))
% 8.20/8.62 (assert (forall ((C2 tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5)) (@ _let_1 A4)))))
% 8.20/8.62 (assert (forall ((C2 tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C2))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) (@ _let_1 A4)))))
% 8.20/8.62 (assert (forall ((C2 Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_o A4) B5)) (not (@ _let_1 B5))))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int C2))) (=> (@ _let_1 (@ (@ tptp.minus_2612819937483484256nt_int A4) B5)) (not (@ _let_1 B5))))))
% 8.20/8.62 (assert (forall ((C2 tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C2))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A4) B5)) (not (@ _let_1 B5))))))
% 8.20/8.62 (assert (forall ((C2 tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5)) (not (@ _let_1 B5))))))
% 8.20/8.62 (assert (forall ((C2 tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5)) (not (@ _let_1 B5))))))
% 8.20/8.62 (assert (forall ((C2 tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C2))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) (not (@ _let_1 B5))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (= tptp.uminus6423885277529793776nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int)) (@ tptp.collec5210948495886036740nt_int (@ tptp.uminus8147837162492574189_int_o (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) A6)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (= tptp.minus_2612819937483484256nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (@ tptp.collec5210948495886036740nt_int (@ (@ tptp.minus_357216186751819389_int_o (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) A6))) (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) B6)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.list_nat Bool))) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (not (@ P2 X4)))) (@ tptp.uminus3195874150345416415st_nat (@ tptp.collect_list_nat P2)))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (= (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (not (@ P2 X4)))) (@ tptp.uminus6423885277529793776nt_int (@ tptp.collec5210948495886036740nt_int P2)))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (not (@ P2 X4)))) (@ tptp.uminus613421341184616069et_nat (@ tptp.collect_set_nat P2)))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (not (@ P2 X4)))) (@ tptp.uminus5710092332889474511et_nat (@ tptp.collect_nat P2)))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (not (@ P2 X4)))) (@ tptp.uminus1532241313380277803et_int (@ tptp.collect_int P2)))))
% 8.20/8.62 (assert (= tptp.uminus_uminus_set_o (lambda ((A6 tptp.set_o)) (@ tptp.collect_o (lambda ((X4 Bool)) (not (@ (@ tptp.member_o X4) A6)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (= tptp.uminus6423885277529793776nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int)) (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (not (@ (@ tptp.member2340774599025711042nt_int X4) A6)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (= tptp.uminus5710092332889474511et_nat (lambda ((A6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (not (@ (@ tptp.member_nat X4) A6)))))))
% 8.20/8.62 (assert (= tptp.uminus1532241313380277803et_int (lambda ((A6 tptp.set_int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (not (@ (@ tptp.member_int X4) A6)))))))
% 8.20/8.62 (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)))))))))
% 8.20/8.62 (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)))))))))
% 8.20/8.62 (assert (= tptp.minus_2612819937483484256nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int X4))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 8.20/8.62 (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)))))))))
% 8.20/8.62 (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)))))))))
% 8.20/8.62 (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)))))))))
% 8.20/8.62 (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)))))))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 8.20/8.62 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 8.20/8.62 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 8.20/8.62 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 8.20/8.62 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (C2 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) C2) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_1) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C2) D2))))))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (C2 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) C2) (=> (@ (@ tptp.ord_less_rat _let_1) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C2) D2))))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (C2 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) C2) (=> (@ (@ tptp.ord_less_int _let_1) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C2) D2))))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 8.20/8.62 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (= (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) _let_1) (@ (@ tptp.plus_plus_rat (@ _let_2 K2)) (@ _let_2 _let_1)))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri3624122377584611663nteger N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri3624122377584611663nteger N2)) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N2)) tptp.zero_zero_rat))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N2)) tptp.zero_zero_int))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N2)) tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri3624122377584611663nteger N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.semiri3624122377584611663nteger N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A5) (@ tptp.semiri681578069525770553at_rat K3))) tptp.one_one_rat)) K3)) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_rat A) _let_2) (@ (@ tptp.plus_plus_rat (@ _let_1 _let_2)) (@ _let_1 K2)))))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K2))) (= (@ (@ tptp.times_times_rat A) _let_3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K2)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K2))) (= (@ (@ tptp.times_times_rat _let_3) A) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K2)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat K2))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) _let_1)) K2)) (@ (@ tptp.gbinomial_rat A) K2))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 8.20/8.62 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 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 C2) D2)))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) C2))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) D2))))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 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 C2) D2)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) C2))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) D2))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (C2 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 C2) D2)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C2))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) D2))))))
% 8.20/8.62 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) A))) R2) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X) (@ (@ tptp.ord_le3102999989581377725nteger X) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 8.20/8.62 (assert (forall ((X tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R2) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R2)) X) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat A) R2))))))
% 8.20/8.62 (assert (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R2) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R2)) X) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.plus_plus_int A) R2))))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 8.20/8.62 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) A))) R2) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X) (@ (@ tptp.ord_le6747313008572928689nteger X) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 8.20/8.62 (assert (forall ((X tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R2) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R2)) X) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat A) R2))))))
% 8.20/8.62 (assert (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R2) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R2)) X) (@ (@ tptp.ord_less_int X) (@ (@ tptp.plus_plus_int A) R2))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 8.20/8.62 (assert (= tptp.abs_abs_int (lambda ((I tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int I) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int I)) I))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((L tptp.int) (K2 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.modulo_modulo_int K2) L))) (@ tptp.abs_abs_int L)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.power_power_nat N2) N2)))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N2)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N2) N2)))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N2) N2)))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N2) N2)))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (let ((_let_2 (@ tptp.suc K2))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_2)) (@ (@ tptp.gbinomial_rat _let_1) _let_2)) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.gbinomial_rat A) K2)))))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (M tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat A))) (=> (@ (@ tptp.ord_less_eq_nat K2) M) (= (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat M)) K2)) (@ (@ tptp.times_times_rat (@ _let_1 K2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat K2))) (@ (@ tptp.minus_minus_nat M) K2))))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((K2 tptp.int) (L tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int K2) L)))) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 (@ tptp.abs_abs_int L))))))
% 8.20/8.62 (assert (forall ((R2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) R2)))) (@ (@ tptp.power_power_nat N2) R2)))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))) (@ (@ tptp.gbinomial_rat A) K2)))))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K2)) (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))))))))
% 8.20/8.62 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (= (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K2))) tptp.one_one_rat)) K2)))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.gbinomial_rat A) K2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))) (@ _let_1 K2)))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K2 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)) K2) (=> (@ (@ tptp.ord_less_eq_int K2) (@ F N2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I3) (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ F I3) K2)))))))))
% 8.20/8.62 (assert (forall ((D2 tptp.int) (X tptp.int) (Z3 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 Z3))) tptp.one_one_int)) D2))) Z3)))))
% 8.20/8.62 (assert (forall ((D2 tptp.int) (Z3 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int Z3) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z3))) tptp.one_one_int)) D2))))))
% 8.20/8.62 (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) (Q8 tptp.int)) (and (= A12 K3) (= A22 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q8) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q8) L2)))) (exists ((R5 tptp.int) (L2 tptp.int) (K3 tptp.int) (Q8 tptp.int)) (and (= A12 K3) (= A22 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q8) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L2)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L2)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q8) L2)) R5))))))))
% 8.20/8.62 (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 ((R4 tptp.int) (Q5 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q5) R4)) (=> (= (@ tptp.sgn_sgn_int R4) (@ tptp.sgn_sgn_int A23)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R4)) (@ tptp.abs_abs_int A23)) (not (= A1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q5) A23)) R4)))))))))))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_int Xs) Xs))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (assert (forall ((R2 tptp.int) (L tptp.int) (K2 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R2) (@ tptp.sgn_sgn_int L)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R2)) (@ tptp.abs_abs_int L)) (=> (= K2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q6) L)) R2)) (@ (@ (@ tptp.eucl_rel_int K2) L) (@ (@ tptp.product_Pair_int_int Q6) R2)))))))
% 8.20/8.62 (assert (= tptp.neg_nu7757733837767384882nteger (lambda ((X4 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger X4) X4)) tptp.one_one_Code_integer))))
% 8.20/8.62 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X4) X4)) tptp.one_one_rat))))
% 8.20/8.62 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X4) X4)) tptp.one_one_int))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer))))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat))))
% 8.20/8.62 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.sgn_sgn_int A) tptp.one_one_int))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (=> (= (@ tptp.sgn_sgn_Code_integer B) _let_1) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B)) _let_1)))))
% 8.20/8.62 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (=> (= (@ tptp.sgn_sgn_rat B) _let_1) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1)))))
% 8.20/8.62 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (=> (= (@ tptp.sgn_sgn_int B) _let_1) (= (@ tptp.sgn_sgn_int (@ (@ tptp.plus_plus_int A) B)) _let_1)))))
% 8.20/8.62 (assert (= (lambda ((Y6 tptp.list_nat) (Z4 tptp.list_nat)) (= Y6 Z4)) (lambda ((Xs3 tptp.list_nat) (Ys2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) (@ tptp.size_size_list_nat Ys2)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs3)) (= (@ (@ tptp.nth_nat Xs3) I) (@ (@ tptp.nth_nat Ys2) I))))))))
% 8.20/8.62 (assert (= (lambda ((Y6 tptp.list_o) (Z4 tptp.list_o)) (= Y6 Z4)) (lambda ((Xs3 tptp.list_o) (Ys2 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs3) (@ tptp.size_size_list_o Ys2)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs3)) (= (@ (@ tptp.nth_o Xs3) I) (@ (@ tptp.nth_o Ys2) I))))))))
% 8.20/8.62 (assert (= (lambda ((Y6 tptp.list_int) (Z4 tptp.list_int)) (= Y6 Z4)) (lambda ((Xs3 tptp.list_int) (Ys2 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) (@ tptp.size_size_list_int Ys2)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs3)) (= (@ (@ tptp.nth_int Xs3) I) (@ (@ tptp.nth_int Ys2) I))))))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (P2 (-> tptp.nat tptp.nat Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (exists ((X11 tptp.nat)) (@ (@ P2 I) X11)))) (exists ((Xs3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) K2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (@ (@ P2 I) (@ (@ tptp.nth_nat Xs3) I)))))))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (P2 (-> tptp.nat Bool Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (exists ((X11 Bool)) (@ (@ P2 I) X11)))) (exists ((Xs3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs3) K2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (@ (@ P2 I) (@ (@ tptp.nth_o Xs3) I)))))))))
% 8.20/8.62 (assert (forall ((K2 tptp.nat) (P2 (-> tptp.nat tptp.int Bool))) (= (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (exists ((X11 tptp.int)) (@ (@ P2 I) X11)))) (exists ((Xs3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) K2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (@ (@ P2 I) (@ (@ tptp.nth_int Xs3) I)))))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (P2 (-> tptp.nat tptp.nat Bool))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (exists ((Li tptp.nat)) (@ (@ P2 Li) I3)))) (not (forall ((L3 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat L3) N2) (not (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (@ (@ P2 (@ (@ tptp.nth_nat L3) I4)) I4))))))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (P2 (-> Bool tptp.nat Bool))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (exists ((Li Bool)) (@ (@ P2 Li) I3)))) (not (forall ((L3 tptp.list_o)) (=> (= (@ tptp.size_size_list_o L3) N2) (not (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (@ (@ P2 (@ (@ tptp.nth_o L3) I4)) I4))))))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (P2 (-> tptp.int tptp.nat Bool))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (exists ((Li tptp.int)) (@ (@ P2 Li) I3)))) (not (forall ((L3 tptp.list_int)) (=> (= (@ tptp.size_size_list_int L3) N2) (not (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (@ (@ P2 (@ (@ tptp.nth_int L3) I4)) I4))))))))))
% 8.20/8.62 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (= (@ tptp.sgn_sgn_Code_integer B) (@ tptp.sgn_sgn_Code_integer A)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))))))
% 8.20/8.62 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (= (@ tptp.sgn_sgn_rat B) (@ tptp.sgn_sgn_rat A)) (= (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))))))
% 8.20/8.62 (assert (forall ((B tptp.int) (A tptp.int)) (=> (= (@ tptp.sgn_sgn_int B) (@ tptp.sgn_sgn_int A)) (= (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 8.20/8.62 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 8.20/8.62 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 8.20/8.62 (assert (= tptp.sgn_sgn_int (lambda ((I tptp.int)) (@ (@ (@ tptp.if_int (= I tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (Xs tptp.list_nat) (A tptp.array_nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat (@ (@ tptp.snga_assn_nat A) Xs)) (@ (@ tptp.array_nth_nat A) I2)) (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_nat A) Xs)) (@ tptp.pure_assn (= R5 (@ (@ tptp.nth_nat Xs) I2)))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (Xs tptp.list_o) (A tptp.array_o)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (@ (@ (@ tptp.hoare_hoare_triple_o (@ (@ tptp.snga_assn_o A) Xs)) (@ (@ tptp.array_nth_o A) I2)) (lambda ((R5 Bool)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_o A) Xs)) (@ tptp.pure_assn (= R5 (@ (@ tptp.nth_o Xs) I2)))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (Xs tptp.list_int) (A tptp.array_int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)) (@ (@ (@ tptp.hoare_3065115510600077593le_int (@ (@ tptp.snga_assn_int A) Xs)) (@ (@ tptp.array_nth_int A) I2)) (lambda ((R5 tptp.int)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_int A) Xs)) (@ tptp.pure_assn (= R5 (@ (@ tptp.nth_int Xs) I2)))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (Xs tptp.list_Product_unit) (A tptp.array_Product_unit)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s245203480648594047t_unit Xs)) (@ (@ (@ tptp.hoare_8945653483474564448t_unit (@ (@ tptp.snga_a4522542871529764173t_unit A) Xs)) (@ (@ tptp.array_7872002506669749220t_unit A) I2)) (lambda ((R5 tptp.product_unit)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_a4522542871529764173t_unit A) Xs)) (@ tptp.pure_assn (= R5 (@ (@ tptp.nth_Product_unit Xs) I2)))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (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))))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (Xs tptp.list_b) (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_b Xs)) _let_1)) (= (@ (@ tptp.nth_Pr3591576263217728691it_nat (@ (@ tptp.produc1870533552098665926it_nat Xs) Ys3)) N2) (@ (@ tptp.produc4082563078715348724it_nat (@ (@ tptp.nth_b Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_Pr4561283279332054789it_nat Ys3) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 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) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ 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 J2)) (not (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.nth_o L))) (=> (@ (@ tptp.ord_less_eq_nat I2) K) (=> (@ (@ tptp.ord_less_nat K) J2) (=> (@ (@ tptp.ord_less_eq_o (@ _let_1 K)) X) (not (@ (@ tptp.ord_less_o X) (@ _let_1 (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 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) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ 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 J2)) (not (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.nth_rat L))) (=> (@ (@ tptp.ord_less_eq_nat I2) K) (=> (@ (@ tptp.ord_less_nat K) J2) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 K)) X) (not (@ (@ tptp.ord_less_rat X) (@ _let_1 (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 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) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ 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 J2)) (not (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.nth_num L))) (=> (@ (@ tptp.ord_less_eq_nat I2) K) (=> (@ (@ tptp.ord_less_nat K) J2) (=> (@ (@ tptp.ord_less_eq_num (@ _let_1 K)) X) (not (@ (@ tptp.ord_less_num X) (@ _let_1 (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 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) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ 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 J2)) (not (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.nth_nat L))) (=> (@ (@ tptp.ord_less_eq_nat I2) K) (=> (@ (@ tptp.ord_less_nat K) J2) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) X) (not (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (J2 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) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ 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 J2)) (not (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.nth_int L))) (=> (@ (@ tptp.ord_less_eq_nat I2) K) (=> (@ (@ tptp.ord_less_nat K) J2) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 K)) X) (not (@ (@ tptp.ord_less_int X) (@ _let_1 (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))))))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (= tptp.array_of_list_nat (lambda ((Xs3 tptp.list_nat)) (@ (@ tptp.array_make_nat (@ tptp.size_size_list_nat Xs3)) (@ tptp.nth_nat Xs3)))))
% 8.20/8.62 (assert (= tptp.array_of_list_o (lambda ((Xs3 tptp.list_o)) (@ (@ tptp.array_make_o (@ tptp.size_size_list_o Xs3)) (@ tptp.nth_o Xs3)))))
% 8.20/8.62 (assert (= tptp.array_of_list_int (lambda ((Xs3 tptp.list_int)) (@ (@ tptp.array_make_int (@ tptp.size_size_list_int Xs3)) (@ tptp.nth_int Xs3)))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_o) (R3 tptp.set_Product_prod_o_o) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (=> (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (=> (@ (@ tptp.ord_less_nat N5) (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_o Xs)) tptp.one_one_nat)) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o (@ _let_1 (@ tptp.suc N5))) (@ _let_1 N5))) R3)))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o (@ _let_1 N2)) (@ _let_1 M))) (@ tptp.transitive_trancl_o R3))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_int) (R3 tptp.set_Pr958786334691620121nt_int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_nat N5) (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_int Xs)) tptp.one_one_nat)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ _let_1 (@ tptp.suc N5))) (@ _let_1 N5))) R3)))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ _let_1 N2)) (@ _let_1 M))) (@ tptp.transi6261509568448316235cl_int R3))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_nat) (R3 tptp.set_Pr1261947904930325089at_nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_nat N5) (@ (@ tptp.minus_minus_nat (@ tptp.size_size_list_nat Xs)) tptp.one_one_nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ _let_1 (@ tptp.suc N5))) (@ _let_1 N5))) R3)))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ _let_1 N2)) (@ _let_1 M))) (@ tptp.transi6264000038957366511cl_nat R3))))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat) (M tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat N2) _let_1) (= (@ (@ tptp.nth_nat (@ (@ tptp.rotate_nat M) Xs)) N2) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M) N2)) _let_1)))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o) (M tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_o Xs))) (=> (@ (@ tptp.ord_less_nat N2) _let_1) (= (@ (@ tptp.nth_o (@ (@ tptp.rotate_o M) Xs)) N2) (@ (@ tptp.nth_o Xs) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M) N2)) _let_1)))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int) (M tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat N2) _let_1) (= (@ (@ tptp.nth_int (@ (@ tptp.rotate_int M) Xs)) N2) (@ (@ tptp.nth_int Xs) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M) N2)) _let_1)))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) tptp.one_one_nat) (= (@ (@ tptp.rotate_nat N2) Xs) Xs))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_o) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) tptp.one_one_nat) (= (@ (@ tptp.rotate_o N2) Xs) Xs))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) tptp.one_one_nat) (= (@ (@ tptp.rotate_int N2) Xs) Xs))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_nat)) (@ (@ tptp.sorted_wrt_nat (lambda ((Uu2 tptp.nat) (Uv2 tptp.nat)) true)) Xs)))
% 8.20/8.62 (assert (forall ((Xs tptp.list_int)) (@ (@ tptp.sorted_wrt_int (lambda ((Uu2 tptp.int) (Uv2 tptp.int)) true)) Xs)))
% 8.20/8.62 (assert (forall ((A1 tptp.int) (A23 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A1) A23)))) (=> (@ _let_1 (@ tptp.transi6261509568448316235cl_int R2)) (=> (not (@ _let_1 R2)) (not (forall ((B3 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A1) B3)) (@ tptp.transi6261509568448316235cl_int R2)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B3) A23)) R2))))))))))
% 8.20/8.62 (assert (forall ((A1 tptp.nat) (A23 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) A23)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) B3)) (@ tptp.transi6264000038957366511cl_nat R2)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B3) A23)) R2))))))))))
% 8.20/8.62 (assert (forall ((A1 tptp.int) (A23 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A1) A23)) (@ tptp.transi6261509568448316235cl_int R2)) (or (exists ((A5 tptp.int) (B4 tptp.int)) (and (= A1 A5) (= A23 B4) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A5) B4)) R2))) (exists ((A5 tptp.int) (B4 tptp.int) (C3 tptp.int)) (and (= A1 A5) (= A23 C3) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A5) B4)) (@ tptp.transi6261509568448316235cl_int R2)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B4) C3)) R2)))))))
% 8.20/8.62 (assert (forall ((A1 tptp.nat) (A23 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) A23)) (@ tptp.transi6264000038957366511cl_nat R2)) (or (exists ((A5 tptp.nat) (B4 tptp.nat)) (and (= A1 A5) (= A23 B4) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A5) B4)) R2))) (exists ((A5 tptp.nat) (B4 tptp.nat) (C3 tptp.nat)) (and (= A1 A5) (= A23 C3) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A5) B4)) (@ tptp.transi6264000038957366511cl_nat R2)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B4) C3)) R2)))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A) B)))) (=> (@ _let_1 R2) (@ _let_1 (@ tptp.transi6261509568448316235cl_int R2))))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) B)))) (=> (@ _let_1 R2) (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A) B)))) (=> (@ _let_1 (@ tptp.transi6261509568448316235cl_int R2)) (=> (not (@ _let_1 R2)) (not (forall ((C tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A) C)) (@ tptp.transi6261509568448316235cl_int R2)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int C) B)) R2))))))))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) B)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((C tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) C)) (@ tptp.transi6264000038957366511cl_nat R2)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat C) B)) R2))))))))))
% 8.20/8.62 (assert (forall ((X tptp.int) (Y tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.transi6261509568448316235cl_int R2))) (let ((_let_2 (@ tptp.product_Pair_int_int X))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 Y)) _let_1) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y) Z3)) _let_1) (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 Z3)) _let_1)))))))
% 8.20/8.62 (assert (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.transi6264000038957366511cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat X))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 Y)) _let_1) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y) Z3)) _let_1) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 Z3)) _let_1)))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A) B)) (@ tptp.transi6261509568448316235cl_int R2)) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A) Y3)) R2) (@ P2 Y3))) (=> (forall ((Y3 tptp.int) (Z2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A) Y3)) (@ tptp.transi6261509568448316235cl_int R2)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y3) Z2)) R2) (=> (@ P2 Y3) (@ P2 Z2))))) (@ P2 B))))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) Y3)) R2) (@ P2 Y3))) (=> (forall ((Y3 tptp.nat) (Z2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) Y3)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y3) Z2)) R2) (=> (@ P2 Y3) (@ P2 Z2))))) (@ P2 B))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (R3 tptp.set_Pr958786334691620121nt_int) (C2 tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int A))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 B)) R3) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) C2)) R3) (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 C2)) (@ tptp.transi6261509568448316235cl_int R3)))))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat A))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 B)) R3) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) C2)) R3) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 C2)) (@ tptp.transi6264000038957366511cl_nat R3)))))))
% 8.20/8.62 (assert (forall ((X tptp.int) (Z3 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Z3)))) (=> (@ _let_1 (@ tptp.transi6261509568448316235cl_int R2)) (=> (not (@ _let_1 R2)) (not (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y3)) R2) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y3) Z3)) (@ tptp.transi6261509568448316235cl_int R2)))))))))))
% 8.20/8.62 (assert (forall ((X tptp.nat) (Z3 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Z3)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y3)) R2) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y3) Z3)) (@ tptp.transi6264000038957366511cl_nat R2)))))))))))
% 8.20/8.62 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int) (Y tptp.int)) (=> (forall ((X3 tptp.int)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) X3)) (@ tptp.transi6261509568448316235cl_int R2)))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2) (not (= X Y))))))
% 8.20/8.62 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X3 tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) X3)) (@ tptp.transi6264000038957366511cl_nat R2)))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2) (not (= X Y))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (C2 tptp.int)) (let ((_let_1 (@ tptp.transi6261509568448316235cl_int R2))) (let ((_let_2 (@ tptp.product_Pair_int_int A))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 B)) _let_1) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) C2)) R2) (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 C2)) _let_1)))))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.transi6264000038957366511cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat A))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 B)) _let_1) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) C2)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 C2)) _let_1)))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (C2 tptp.int)) (let ((_let_1 (@ tptp.transi6261509568448316235cl_int R2))) (let ((_let_2 (@ tptp.product_Pair_int_int A))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 B)) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) C2)) _let_1) (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 C2)) _let_1)))))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.transi6264000038957366511cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat A))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 B)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) C2)) _let_1) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 C2)) _let_1)))))))
% 8.20/8.62 (assert (forall ((X tptp.int) (Y tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (P2 (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.transi6261509568448316235cl_int R2)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y3)) R2) (@ (@ P2 X3) Y3))) (=> (forall ((X3 tptp.int) (Y3 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ P2 X3))) (let ((_let_2 (@ tptp.transi6261509568448316235cl_int R2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y3)) _let_2) (=> (@ _let_1 Y3) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y3) Z2)) _let_2) (=> (@ (@ P2 Y3) Z2) (@ _let_1 Z2)))))))) (@ (@ P2 X) Y))))))
% 8.20/8.62 (assert (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (P2 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y3)) R2) (@ (@ P2 X3) Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ P2 X3))) (let ((_let_2 (@ tptp.transi6264000038957366511cl_nat R2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y3)) _let_2) (=> (@ _let_1 Y3) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y3) Z2)) _let_2) (=> (@ (@ P2 Y3) Z2) (@ _let_1 Z2)))))))) (@ (@ P2 X) Y))))))
% 8.20/8.62 (assert (forall ((A tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A) B)) (@ tptp.transi6261509568448316235cl_int R2)) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y3) B)) R2) (@ P2 Y3))) (=> (forall ((Y3 tptp.int) (Z2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y3) Z2)) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Z2) B)) (@ tptp.transi6261509568448316235cl_int R2)) (=> (@ P2 Z2) (@ P2 Y3))))) (@ P2 A))))))
% 8.20/8.62 (assert (forall ((A tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y3) B)) R2) (@ P2 Y3))) (=> (forall ((Y3 tptp.nat) (Z2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y3) Z2)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Z2) B)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (@ P2 Z2) (@ P2 Y3))))) (@ P2 A))))))
% 8.20/8.62 (assert (forall ((Ax tptp.int) (Ay tptp.int) (Bx tptp.int) (By tptp.int) (R2 tptp.set_Pr2560585780119916871nt_int) (P2 (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int (@ (@ tptp.product_Pair_int_int Ax) Ay)) (@ (@ tptp.product_Pair_int_int Bx) By))) (@ tptp.transi6288783178788033498nt_int R2)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int (@ (@ tptp.product_Pair_int_int Ax) Ay)) (@ (@ tptp.product_Pair_int_int A3) B3))) R2) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.int) (B3 tptp.int) (Aa2 tptp.int) (Ba tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int A3) B3))) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int (@ (@ tptp.product_Pair_int_int Ax) Ay)) _let_1)) (@ tptp.transi6288783178788033498nt_int R2)) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int _let_1) (@ (@ tptp.product_Pair_int_int Aa2) Ba))) R2) (=> (@ (@ P2 A3) B3) (@ (@ P2 Aa2) Ba)))))) (@ (@ P2 Bx) By))))))
% 8.20/8.62 (assert (forall ((Ax (-> tptp.produc3658429121746597890et_nat Bool)) (Ay tptp.produc3658429121746597890et_nat) (Bx (-> tptp.produc3658429121746597890et_nat Bool)) (By tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr7928877670098842301et_nat) (P2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ (@ tptp.produc5001842942810119800et_nat Ax) Ay)) (@ (@ tptp.produc5001842942810119800et_nat Bx) By))) (@ tptp.transi3145040225084697757et_nat R2)) (=> (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ (@ tptp.produc5001842942810119800et_nat Ax) Ay)) (@ (@ tptp.produc5001842942810119800et_nat A3) B3))) R2) (@ (@ P2 A3) B3))) (=> (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3658429121746597890et_nat) (Aa2 (-> tptp.produc3658429121746597890et_nat Bool)) (Ba tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ (@ tptp.produc5001842942810119800et_nat A3) B3))) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ (@ tptp.produc5001842942810119800et_nat Ax) Ay)) _let_1)) (@ tptp.transi3145040225084697757et_nat R2)) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat _let_1) (@ (@ tptp.produc5001842942810119800et_nat Aa2) Ba))) R2) (=> (@ (@ P2 A3) B3) (@ (@ P2 Aa2) Ba)))))) (@ (@ P2 Bx) By))))))
% 8.20/8.62 (assert (forall ((Ax (-> tptp.produc3658429121746597890et_nat Bool)) (Ay tptp.produc3925858234332021118et_nat) (Bx (-> tptp.produc3658429121746597890et_nat Bool)) (By tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr3444600963470892981et_nat) (P2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool))) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ (@ tptp.produc2245416461498447860et_nat Ax) Ay)) (@ (@ tptp.produc2245416461498447860et_nat Bx) By))) (@ tptp.transi5221092739591632921et_nat R2)) (=> (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ (@ tptp.produc2245416461498447860et_nat Ax) Ay)) (@ (@ tptp.produc2245416461498447860et_nat A3) B3))) R2) (@ (@ P2 A3) B3))) (=> (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3925858234332021118et_nat) (Aa2 (-> tptp.produc3658429121746597890et_nat Bool)) (Ba tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ (@ tptp.produc2245416461498447860et_nat A3) B3))) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ (@ tptp.produc2245416461498447860et_nat Ax) Ay)) _let_1)) (@ tptp.transi5221092739591632921et_nat R2)) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat _let_1) (@ (@ tptp.produc2245416461498447860et_nat Aa2) Ba))) R2) (=> (@ (@ P2 A3) B3) (@ (@ P2 Aa2) Ba)))))) (@ (@ P2 Bx) By))))))
% 8.20/8.62 (assert (forall ((Ax tptp.b) (Ay tptp.produc6653097349344004940it_nat) (Bx tptp.b) (By tptp.produc6653097349344004940it_nat) (R2 tptp.set_Pr5508209795250834101it_nat) (P2 (-> tptp.b tptp.produc6653097349344004940it_nat Bool))) (=> (@ (@ tptp.member6820296301096096254it_nat (@ (@ tptp.produc6853161671299316109it_nat (@ (@ tptp.produc4082563078715348724it_nat Ax) Ay)) (@ (@ tptp.produc4082563078715348724it_nat Bx) By))) (@ tptp.transi2518514244971309593it_nat R2)) (=> (forall ((A3 tptp.b) (B3 tptp.produc6653097349344004940it_nat)) (=> (@ (@ tptp.member6820296301096096254it_nat (@ (@ tptp.produc6853161671299316109it_nat (@ (@ tptp.produc4082563078715348724it_nat Ax) Ay)) (@ (@ tptp.produc4082563078715348724it_nat A3) B3))) R2) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.b) (B3 tptp.produc6653097349344004940it_nat) (Aa2 tptp.b) (Ba tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ (@ tptp.produc4082563078715348724it_nat A3) B3))) (=> (@ (@ tptp.member6820296301096096254it_nat (@ (@ tptp.produc6853161671299316109it_nat (@ (@ tptp.produc4082563078715348724it_nat Ax) Ay)) _let_1)) (@ tptp.transi2518514244971309593it_nat R2)) (=> (@ (@ tptp.member6820296301096096254it_nat (@ (@ tptp.produc6853161671299316109it_nat _let_1) (@ (@ tptp.produc4082563078715348724it_nat Aa2) Ba))) R2) (=> (@ (@ P2 A3) B3) (@ (@ P2 Aa2) Ba)))))) (@ (@ P2 Bx) By))))))
% 8.20/8.62 (assert (forall ((Ax tptp.a) (Ay tptp.produc6653097349344004940it_nat) (Bx tptp.a) (By tptp.produc6653097349344004940it_nat) (R2 tptp.set_Pr2819221443900773171it_nat) (P2 (-> tptp.a tptp.produc6653097349344004940it_nat Bool))) (=> (@ (@ tptp.member5335690527091456380it_nat (@ (@ tptp.produc1743342482959036555it_nat (@ (@ tptp.produc9178034014595674355it_nat Ax) Ay)) (@ (@ tptp.produc9178034014595674355it_nat Bx) By))) (@ tptp.transi7613985180851635224it_nat R2)) (=> (forall ((A3 tptp.a) (B3 tptp.produc6653097349344004940it_nat)) (=> (@ (@ tptp.member5335690527091456380it_nat (@ (@ tptp.produc1743342482959036555it_nat (@ (@ tptp.produc9178034014595674355it_nat Ax) Ay)) (@ (@ tptp.produc9178034014595674355it_nat A3) B3))) R2) (@ (@ P2 A3) B3))) (=> (forall ((A3 tptp.a) (B3 tptp.produc6653097349344004940it_nat) (Aa2 tptp.a) (Ba tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ (@ tptp.produc9178034014595674355it_nat A3) B3))) (=> (@ (@ tptp.member5335690527091456380it_nat (@ (@ tptp.produc1743342482959036555it_nat (@ (@ tptp.produc9178034014595674355it_nat Ax) Ay)) _let_1)) (@ tptp.transi7613985180851635224it_nat R2)) (=> (@ (@ tptp.member5335690527091456380it_nat (@ (@ tptp.produc1743342482959036555it_nat _let_1) (@ (@ tptp.produc9178034014595674355it_nat Aa2) Ba))) R2) (=> (@ (@ P2 A3) B3) (@ (@ P2 Aa2) Ba)))))) (@ (@ P2 Bx) By))))))
% 8.20/8.62 (assert (forall ((P3 tptp.product_prod_nat_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat P3))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat R2) S2) (@ _let_1 (@ tptp.transi6264000038957366511cl_nat S2)))))))
% 8.20/8.62 (assert (forall ((U2 tptp.set_Pr1261947904930325089at_nat) (V3 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat U2) V3) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat U2)) (@ _let_1 (@ tptp.transi6264000038957366511cl_nat V3)))))))
% 8.20/8.62 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat R3) (@ tptp.transi6264000038957366511cl_nat R3))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (= tptp.sorted_wrt_nat (lambda ((P5 (-> tptp.nat tptp.nat Bool)) (Xs3 tptp.list_nat)) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs3))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs3)) (@ (@ P5 (@ _let_1 I)) (@ _let_1 J)))))))))
% 8.20/8.62 (assert (= tptp.sorted_wrt_o (lambda ((P5 (-> Bool Bool Bool)) (Xs3 tptp.list_o)) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs3))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_o Xs3)) (@ (@ P5 (@ _let_1 I)) (@ _let_1 J)))))))))
% 8.20/8.62 (assert (= tptp.sorted_wrt_int (lambda ((P5 (-> tptp.int tptp.int Bool)) (Xs3 tptp.list_int)) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs3))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int Xs3)) (@ (@ P5 (@ _let_1 I)) (@ _let_1 J)))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat tptp.nat Bool)) (Xs tptp.list_nat) (I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.sorted_wrt_nat P2) Xs) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs)) (@ (@ P2 (@ _let_1 I2)) (@ _let_1 J2))))))))
% 8.20/8.62 (assert (forall ((P2 (-> Bool Bool Bool)) (Xs tptp.list_o) (I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (=> (@ (@ tptp.sorted_wrt_o P2) Xs) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_o Xs)) (@ (@ P2 (@ _let_1 I2)) (@ _let_1 J2))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.int tptp.int Bool)) (Xs tptp.list_int) (I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.sorted_wrt_int P2) Xs) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_int Xs)) (@ (@ P2 (@ _let_1 I2)) (@ _let_1 J2))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_nat) (P2 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_nat P2) Xs))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_o) (P2 (-> Bool Bool Bool))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_o P2) Xs))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_int) (P2 (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_int P2) Xs))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_o)) (= (@ (@ tptp.sorted_wrt_o tptp.ord_less_eq_o) Xs) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.ord_less_eq_o (@ _let_1 I)) (@ _let_1 J)))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_rat)) (= (@ (@ tptp.sorted_wrt_rat tptp.ord_less_eq_rat) Xs) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_rat Xs))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_rat Xs)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 I)) (@ _let_1 J)))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_num)) (= (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) Xs) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_num Xs))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_num Xs)) (@ (@ tptp.ord_less_eq_num (@ _let_1 I)) (@ _let_1 J)))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J)))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 I)) (@ _let_1 J)))))))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_o)) (= (@ (@ tptp.sorted_wrt_o tptp.ord_less_eq_o) Xs) (forall ((I tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (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 I)) (@ _let_2 _let_1)))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_rat)) (= (@ (@ tptp.sorted_wrt_rat tptp.ord_less_eq_rat) Xs) (forall ((I tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (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 I)) (@ _let_2 _let_1)))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_num)) (= (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) Xs) (forall ((I tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (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 I)) (@ _let_2 _let_1)))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs) (forall ((I tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (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 I)) (@ _let_2 _let_1)))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs) (forall ((I tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (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 I)) (@ _let_2 _let_1)))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_o)) (= (@ (@ tptp.sorted_wrt_o tptp.ord_less_eq_o) Xs) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.ord_less_eq_o (@ _let_1 I)) (@ _let_1 J)))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_rat)) (= (@ (@ tptp.sorted_wrt_rat tptp.ord_less_eq_rat) Xs) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_rat Xs))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_rat Xs)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 I)) (@ _let_1 J)))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_num)) (= (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) Xs) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_num Xs))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_num Xs)) (@ (@ tptp.ord_less_eq_num (@ _let_1 I)) (@ _let_1 J)))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J)))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 I)) (@ _let_1 J)))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_o) (I2 tptp.nat) (J2 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) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.ord_less_eq_o (@ _let_1 I2)) (@ _let_1 J2))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_rat) (I2 tptp.nat) (J2 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) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_rat Xs)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 I2)) (@ _let_1 J2))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_num) (I2 tptp.nat) (J2 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) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_num Xs)) (@ (@ tptp.ord_less_eq_num (@ _let_1 I2)) (@ _let_1 J2))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_nat) (I2 tptp.nat) (J2 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) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J2))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_int) (I2 tptp.nat) (J2 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) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 I2)) (@ _let_1 J2))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (Xs tptp.list_nat) (Ys3 tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_nat Xs)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys3)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.zip_nat_nat Xs) Ys3)) I2) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.nth_nat Xs) I2)) (@ (@ tptp.nth_nat Ys3) I2))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (Xs tptp.list_nat) (Ys3 tptp.list_o)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_nat Xs)) (=> (@ _let_1 (@ tptp.size_size_list_o Ys3)) (= (@ (@ tptp.nth_Pr112076138515278198_nat_o (@ (@ tptp.zip_nat_o Xs) Ys3)) I2) (@ (@ tptp.product_Pair_nat_o (@ (@ tptp.nth_nat Xs) I2)) (@ (@ tptp.nth_o Ys3) I2))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (Xs tptp.list_nat) (Ys3 tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_nat Xs)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys3)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.zip_nat_int Xs) Ys3)) I2) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.nth_nat Xs) I2)) (@ (@ tptp.nth_int Ys3) I2))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (Xs tptp.list_o) (Ys3 tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_o Xs)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys3)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.zip_o_nat Xs) Ys3)) I2) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs) I2)) (@ (@ tptp.nth_nat Ys3) I2))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (Xs tptp.list_o) (Ys3 tptp.list_o)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_o Xs)) (=> (@ _let_1 (@ tptp.size_size_list_o Ys3)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.zip_o_o Xs) Ys3)) I2) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs) I2)) (@ (@ tptp.nth_o Ys3) I2))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (Xs tptp.list_o) (Ys3 tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_o Xs)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys3)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.zip_o_int Xs) Ys3)) I2) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs) I2)) (@ (@ tptp.nth_int Ys3) I2))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (Xs tptp.list_int) (Ys3 tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_int Xs)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys3)) (= (@ (@ tptp.nth_Pr8617346907841251940nt_nat (@ (@ tptp.zip_int_nat Xs) Ys3)) I2) (@ (@ tptp.product_Pair_int_nat (@ (@ tptp.nth_int Xs) I2)) (@ (@ tptp.nth_nat Ys3) I2))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (Xs tptp.list_int) (Ys3 tptp.list_o)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_int Xs)) (=> (@ _let_1 (@ tptp.size_size_list_o Ys3)) (= (@ (@ tptp.nth_Pr7514405829937366042_int_o (@ (@ tptp.zip_int_o Xs) Ys3)) I2) (@ (@ tptp.product_Pair_int_o (@ (@ tptp.nth_int Xs) I2)) (@ (@ tptp.nth_o Ys3) I2))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (Xs tptp.list_int) (Ys3 tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_int Xs)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys3)) (= (@ (@ tptp.nth_Pr4439495888332055232nt_int (@ (@ tptp.zip_int_int Xs) Ys3)) I2) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.nth_int Xs) I2)) (@ (@ tptp.nth_int Ys3) I2))))))))
% 8.20/8.62 (assert (forall ((I2 tptp.nat) (Xs tptp.list_b) (Ys3 tptp.list_P131111800688179804it_nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_b Xs)) (=> (@ _let_1 (@ tptp.size_s341701280123345136it_nat Ys3)) (= (@ (@ tptp.nth_Pr3591576263217728691it_nat (@ (@ tptp.zip_b_5987488365222434772it_nat Xs) Ys3)) I2) (@ (@ tptp.produc4082563078715348724it_nat (@ (@ tptp.nth_b Xs) I2)) (@ (@ tptp.nth_Pr4561283279332054789it_nat Ys3) I2))))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N2) (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N2) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.produc7388388658123137530it_nat Bool)) (Xs tptp.list_P7438302566501821706it_nat) (X tptp.produc7388388658123137530it_nat)) (= (= (@ (@ tptp.find_P8943372834735446238it_nat P2) Xs) (@ tptp.some_P2818173045054083285it_nat X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr3591576263217728691it_nat Xs) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s4572066133376685982it_nat Xs)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_Pr3591576263217728691it_nat Xs) J)))))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.produc3260487557148687353it_nat Bool)) (Xs tptp.list_P6935614879863011209it_nat) (X tptp.produc3260487557148687353it_nat)) (= (= (@ (@ tptp.find_P4815471733760996061it_nat P2) Xs) (@ tptp.some_P7913643980934408916it_nat X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr8687047199098054322it_nat Xs) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s4069378446737875485it_nat Xs)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_Pr8687047199098054322it_nat Xs) J)))))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.produc8664842809031399944it_nat Bool)) (Xs tptp.list_P626663023886443800it_nat) (X tptp.produc8664842809031399944it_nat)) (= (= (@ (@ tptp.find_P5317947125398478060it_nat P2) Xs) (@ tptp.some_P1914260805536162275it_nat X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr2956344619228612545it_nat Xs) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s4881146867534228396it_nat Xs)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_Pr2956344619228612545it_nat Xs) J)))))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.num Bool)) (Xs tptp.list_num) (X tptp.num)) (= (= (@ (@ tptp.find_num P2) Xs) (@ tptp.some_num X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_num Xs) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_num Xs)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_num Xs) J)))))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (Xs tptp.list_nat) (X tptp.nat)) (= (= (@ (@ tptp.find_nat P2) Xs) (@ tptp.some_nat X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xs) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_nat Xs) J)))))))))))
% 8.20/8.62 (assert (forall ((P2 (-> Bool Bool)) (Xs tptp.list_o) (X Bool)) (= (= (@ (@ tptp.find_o P2) Xs) (@ tptp.some_o X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_o Xs) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_o Xs) J)))))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.int Bool)) (Xs tptp.list_int) (X tptp.int)) (= (= (@ (@ tptp.find_int P2) Xs) (@ tptp.some_int X)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xs) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_int Xs) J)))))))))))
% 8.20/8.62 (assert (forall ((X tptp.produc7388388658123137530it_nat) (P2 (-> tptp.produc7388388658123137530it_nat Bool)) (Xs tptp.list_P7438302566501821706it_nat)) (= (= (@ tptp.some_P2818173045054083285it_nat X) (@ (@ tptp.find_P8943372834735446238it_nat P2) Xs)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr3591576263217728691it_nat Xs) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s4572066133376685982it_nat Xs)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_Pr3591576263217728691it_nat Xs) J)))))))))))
% 8.20/8.62 (assert (forall ((X tptp.produc3260487557148687353it_nat) (P2 (-> tptp.produc3260487557148687353it_nat Bool)) (Xs tptp.list_P6935614879863011209it_nat)) (= (= (@ tptp.some_P7913643980934408916it_nat X) (@ (@ tptp.find_P4815471733760996061it_nat P2) Xs)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr8687047199098054322it_nat Xs) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s4069378446737875485it_nat Xs)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_Pr8687047199098054322it_nat Xs) J)))))))))))
% 8.20/8.62 (assert (forall ((X tptp.produc8664842809031399944it_nat) (P2 (-> tptp.produc8664842809031399944it_nat Bool)) (Xs tptp.list_P626663023886443800it_nat)) (= (= (@ tptp.some_P1914260805536162275it_nat X) (@ (@ tptp.find_P5317947125398478060it_nat P2) Xs)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_Pr2956344619228612545it_nat Xs) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_s4881146867534228396it_nat Xs)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_Pr2956344619228612545it_nat Xs) J)))))))))))
% 8.20/8.62 (assert (forall ((X tptp.num) (P2 (-> tptp.num Bool)) (Xs tptp.list_num)) (= (= (@ tptp.some_num X) (@ (@ tptp.find_num P2) Xs)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_num Xs) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_num Xs)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_num Xs) J)))))))))))
% 8.20/8.62 (assert (forall ((X tptp.nat) (P2 (-> tptp.nat Bool)) (Xs tptp.list_nat)) (= (= (@ tptp.some_nat X) (@ (@ tptp.find_nat P2) Xs)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat Xs) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_nat Xs) J)))))))))))
% 8.20/8.62 (assert (forall ((X Bool) (P2 (-> Bool Bool)) (Xs tptp.list_o)) (= (= (@ tptp.some_o X) (@ (@ tptp.find_o P2) Xs)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_o Xs) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_o Xs) J)))))))))))
% 8.20/8.62 (assert (forall ((X tptp.int) (P2 (-> tptp.int Bool)) (Xs tptp.list_int)) (= (= (@ tptp.some_int X) (@ (@ tptp.find_int P2) Xs)) (exists ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_int Xs) I))) (and (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs)) (@ P2 _let_1) (= X _let_1) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) I) (not (@ P2 (@ (@ tptp.nth_int Xs) J)))))))))))
% 8.20/8.62 (assert (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 8.20/8.62 (assert (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le1926595141338095240atural (@ tptp.numera5444537566228673987atural M)) (@ tptp.numera5444537566228673987atural N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le5570908160329646204atural (@ tptp.numera5444537566228673987atural M)) (@ tptp.numera5444537566228673987atural N2)) (@ (@ tptp.ord_less_num M) N2))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)) (@ (@ tptp.ord_less_num M) N2))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N2)))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2)))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ tptp.numera5444537566228673987atural M)) (@ tptp.numera5444537566228673987atural N2)) (@ tptp.numera5444537566228673987atural (@ (@ tptp.plus_plus_num M) N2)))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N2)))))
% 8.20/8.62 (assert (forall ((V tptp.num) (W2 tptp.num) (Z3 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat W2)) Z3)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W2))) Z3))))
% 8.20/8.62 (assert (forall ((V tptp.num) (W2 tptp.num) (Z3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W2)) Z3)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) W2))) Z3))))
% 8.20/8.62 (assert (forall ((V tptp.num) (W2 tptp.num) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W2)) Z3)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W2))) Z3))))
% 8.20/8.62 (assert (forall ((V tptp.num) (W2 tptp.num) (Z3 tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ tptp.numera5444537566228673987atural V)) (@ (@ tptp.plus_p4538020629002901425atural (@ tptp.numera5444537566228673987atural W2)) Z3)) (@ (@ tptp.plus_p4538020629002901425atural (@ tptp.numera5444537566228673987atural (@ (@ tptp.plus_plus_num V) W2))) Z3))))
% 8.20/8.62 (assert (forall ((V tptp.num) (W2 tptp.num) (Z3 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger W2)) Z3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W2))) Z3))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (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)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_nat) (B tptp.list_nat) (A2 tptp.list_nat) (B2 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat A) (@ tptp.size_size_list_nat B)) (=> (= (@ tptp.size_size_list_nat A2) (@ tptp.size_size_list_nat B2)) (= (= (@ (@ tptp.zip_nat_nat A) B) (@ (@ tptp.zip_nat_nat A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_nat) (B tptp.list_o) (A2 tptp.list_nat) (B2 tptp.list_o)) (=> (= (@ tptp.size_size_list_nat A) (@ tptp.size_size_list_o B)) (=> (= (@ tptp.size_size_list_nat A2) (@ tptp.size_size_list_o B2)) (= (= (@ (@ tptp.zip_nat_o A) B) (@ (@ tptp.zip_nat_o A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_nat) (B tptp.list_int) (A2 tptp.list_nat) (B2 tptp.list_int)) (=> (= (@ tptp.size_size_list_nat A) (@ tptp.size_size_list_int B)) (=> (= (@ tptp.size_size_list_nat A2) (@ tptp.size_size_list_int B2)) (= (= (@ (@ tptp.zip_nat_int A) B) (@ (@ tptp.zip_nat_int A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_o) (B tptp.list_nat) (A2 tptp.list_o) (B2 tptp.list_nat)) (=> (= (@ tptp.size_size_list_o A) (@ tptp.size_size_list_nat B)) (=> (= (@ tptp.size_size_list_o A2) (@ tptp.size_size_list_nat B2)) (= (= (@ (@ tptp.zip_o_nat A) B) (@ (@ tptp.zip_o_nat A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_o) (B tptp.list_o) (A2 tptp.list_o) (B2 tptp.list_o)) (=> (= (@ tptp.size_size_list_o A) (@ tptp.size_size_list_o B)) (=> (= (@ tptp.size_size_list_o A2) (@ tptp.size_size_list_o B2)) (= (= (@ (@ tptp.zip_o_o A) B) (@ (@ tptp.zip_o_o A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_o) (B tptp.list_int) (A2 tptp.list_o) (B2 tptp.list_int)) (=> (= (@ tptp.size_size_list_o A) (@ tptp.size_size_list_int B)) (=> (= (@ tptp.size_size_list_o A2) (@ tptp.size_size_list_int B2)) (= (= (@ (@ tptp.zip_o_int A) B) (@ (@ tptp.zip_o_int A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_int) (B tptp.list_nat) (A2 tptp.list_int) (B2 tptp.list_nat)) (=> (= (@ tptp.size_size_list_int A) (@ tptp.size_size_list_nat B)) (=> (= (@ tptp.size_size_list_int A2) (@ tptp.size_size_list_nat B2)) (= (= (@ (@ tptp.zip_int_nat A) B) (@ (@ tptp.zip_int_nat A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_int) (B tptp.list_o) (A2 tptp.list_int) (B2 tptp.list_o)) (=> (= (@ tptp.size_size_list_int A) (@ tptp.size_size_list_o B)) (=> (= (@ tptp.size_size_list_int A2) (@ tptp.size_size_list_o B2)) (= (= (@ (@ tptp.zip_int_o A) B) (@ (@ tptp.zip_int_o A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_int) (B tptp.list_int) (A2 tptp.list_int) (B2 tptp.list_int)) (=> (= (@ tptp.size_size_list_int A) (@ tptp.size_size_list_int B)) (=> (= (@ tptp.size_size_list_int A2) (@ tptp.size_size_list_int B2)) (= (= (@ (@ tptp.zip_int_int A) B) (@ (@ tptp.zip_int_int A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((V tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C2))))))
% 8.20/8.62 (assert (forall ((V tptp.num) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C2))))))
% 8.20/8.62 (assert (forall ((V tptp.num) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C2))))))
% 8.20/8.62 (assert (forall ((V tptp.num) (B tptp.code_natural) (C2 tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural V)))) (= (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural B) C2)) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_1 B)) (@ _let_1 C2))))))
% 8.20/8.62 (assert (forall ((V tptp.num) (B tptp.code_integer) (C2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C2))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int _let_2) _let_1)))))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (let ((_let_2 (@ tptp.numeral_numeral_rat M))) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat _let_2)) (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat _let_2) _let_1)))))))
% 8.20/8.62 (assert (forall ((V tptp.num) (W2 tptp.num) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) Y)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W2)))) Y))))
% 8.20/8.62 (assert (forall ((V tptp.num) (W2 tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W2))) Y)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W2)))) Y))))
% 8.20/8.62 (assert (forall ((V tptp.num) (W2 tptp.num) (Y tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2))) Y)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W2)))) Y))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2))))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N2))))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N2))))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2)))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N2)))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N2)))))
% 8.20/8.62 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.nat) (Ys3 tptp.list_nat)) (= (@ (@ tptp.zip_int_nat (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_nat Y) Ys3)) (@ (@ tptp.cons_P7512249878480867347nt_nat (@ (@ tptp.product_Pair_int_nat X) Y)) (@ (@ tptp.zip_int_nat Xs) Ys3)))))
% 8.20/8.62 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.int) (Ys3 tptp.list_int)) (= (@ (@ tptp.zip_nat_int (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_int Y) Ys3)) (@ (@ tptp.cons_P2335045147070616083at_int (@ (@ tptp.product_Pair_nat_int X) Y)) (@ (@ tptp.zip_nat_int Xs) Ys3)))))
% 8.20/8.62 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.nat) (Ys3 tptp.list_nat)) (= (@ (@ tptp.zip_nat_nat (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_nat Y) Ys3)) (@ (@ tptp.cons_P6512896166579812791at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.zip_nat_nat Xs) Ys3)))))
% 8.20/8.62 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.int) (Ys3 tptp.list_int)) (= (@ (@ tptp.zip_int_int (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_int Y) Ys3)) (@ (@ tptp.cons_P3334398858971670639nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ tptp.zip_int_int Xs) Ys3)))))
% 8.20/8.62 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o) (Y tptp.produc3658429121746597890et_nat) (Ys3 tptp.list_P9062070895058802706et_nat)) (= (@ (@ tptp.zip_Pr7134870689397686104et_nat (@ (@ tptp.cons_P6219271836124797827_nat_o X) Xs)) (@ (@ tptp.cons_P2869003950965171916et_nat Y) Ys3)) (@ (@ tptp.cons_P3419706843779801160et_nat (@ (@ tptp.produc5001842942810119800et_nat X) Y)) (@ (@ tptp.zip_Pr7134870689397686104et_nat Xs) Ys3)))))
% 8.20/8.62 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o) (Y tptp.produc3925858234332021118et_nat) (Ys3 tptp.list_P2321686559999237006et_nat)) (= (@ (@ tptp.zip_Pr8136144321567152340et_nat (@ (@ tptp.cons_P6219271836124797827_nat_o X) Xs)) (@ (@ tptp.cons_P3419706843779801160et_nat Y) Ys3)) (@ (@ tptp.cons_P6329468272379687876et_nat (@ (@ tptp.produc2245416461498447860et_nat X) Y)) (@ (@ tptp.zip_Pr8136144321567152340et_nat Xs) Ys3)))))
% 8.20/8.62 (assert (forall ((X tptp.b) (Xs tptp.list_b) (Y tptp.produc6653097349344004940it_nat) (Ys3 tptp.list_P131111800688179804it_nat)) (= (@ (@ tptp.zip_b_5987488365222434772it_nat (@ (@ tptp.cons_b X) Xs)) (@ (@ tptp.cons_P7873165156130251286it_nat Y) Ys3)) (@ (@ tptp.cons_P6467324686191779524it_nat (@ (@ tptp.produc4082563078715348724it_nat X) Y)) (@ (@ tptp.zip_b_5987488365222434772it_nat Xs) Ys3)))))
% 8.20/8.62 (assert (forall ((X tptp.a) (Xs tptp.list_a) (Y tptp.produc6653097349344004940it_nat) (Ys3 tptp.list_P131111800688179804it_nat)) (= (@ (@ tptp.zip_a_1859587264247984595it_nat (@ (@ tptp.cons_a X) Xs)) (@ (@ tptp.cons_P7873165156130251286it_nat Y) Ys3)) (@ (@ tptp.cons_P2339423585217329347it_nat (@ (@ tptp.produc9178034014595674355it_nat X) Y)) (@ (@ tptp.zip_a_1859587264247984595it_nat Xs) Ys3)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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)))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (= tptp.numeral_numeral_nat (lambda ((I tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I)))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_int N2))))
% 8.20/8.62 (assert (forall ((N1 tptp.int) (R12 tptp.list_int) (N22 tptp.int) (R23 tptp.list_int)) (=> (= (@ (@ tptp.cons_int N1) R12) (@ (@ tptp.cons_int N22) R23)) (and (= N1 N22) (= R12 R23)))))
% 8.20/8.62 (assert (forall ((N1 tptp.nat) (R12 tptp.list_nat) (N22 tptp.nat) (R23 tptp.list_nat)) (=> (= (@ (@ tptp.cons_nat N1) R12) (@ (@ tptp.cons_nat N22) R23)) (and (= N1 N22) (= R12 R23)))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_int) (Ys3 tptp.list_nat) (Xy tptp.product_prod_int_nat) (Xys tptp.list_P8198026277950538467nt_nat)) (=> (= (@ (@ tptp.zip_int_nat Xs) Ys3) (@ (@ tptp.cons_P7512249878480867347nt_nat Xy) Xys)) (not (forall ((X3 tptp.int) (Xs4 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int X3) Xs4)) (forall ((Y3 tptp.nat) (Ys4 tptp.list_nat)) (=> (= Ys3 (@ (@ tptp.cons_nat Y3) Ys4)) (=> (= Xy (@ (@ tptp.product_Pair_int_nat X3) Y3)) (not (= Xys (@ (@ tptp.zip_int_nat Xs4) Ys4))))))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_nat) (Ys3 tptp.list_int) (Xy tptp.product_prod_nat_int) (Xys tptp.list_P3521021558325789923at_int)) (=> (= (@ (@ tptp.zip_nat_int Xs) Ys3) (@ (@ tptp.cons_P2335045147070616083at_int Xy) Xys)) (not (forall ((X3 tptp.nat) (Xs4 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Xs4)) (forall ((Y3 tptp.int) (Ys4 tptp.list_int)) (=> (= Ys3 (@ (@ tptp.cons_int Y3) Ys4)) (=> (= Xy (@ (@ tptp.product_Pair_nat_int X3) Y3)) (not (= Xys (@ (@ tptp.zip_nat_int Xs4) Ys4))))))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_nat) (Ys3 tptp.list_nat) (Xy tptp.product_prod_nat_nat) (Xys tptp.list_P6011104703257516679at_nat)) (=> (= (@ (@ tptp.zip_nat_nat Xs) Ys3) (@ (@ tptp.cons_P6512896166579812791at_nat Xy) Xys)) (not (forall ((X3 tptp.nat) (Xs4 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Xs4)) (forall ((Y3 tptp.nat) (Ys4 tptp.list_nat)) (=> (= Ys3 (@ (@ tptp.cons_nat Y3) Ys4)) (=> (= Xy (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (= Xys (@ (@ tptp.zip_nat_nat Xs4) Ys4))))))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_int) (Ys3 tptp.list_int) (Xy tptp.product_prod_int_int) (Xys tptp.list_P5707943133018811711nt_int)) (=> (= (@ (@ tptp.zip_int_int Xs) Ys3) (@ (@ tptp.cons_P3334398858971670639nt_int Xy) Xys)) (not (forall ((X3 tptp.int) (Xs4 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int X3) Xs4)) (forall ((Y3 tptp.int) (Ys4 tptp.list_int)) (=> (= Ys3 (@ (@ tptp.cons_int Y3) Ys4)) (=> (= Xy (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (= Xys (@ (@ tptp.zip_int_int Xs4) Ys4))))))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_P7985473006766602707_nat_o) (Ys3 tptp.list_P9062070895058802706et_nat) (Xy tptp.produc3925858234332021118et_nat) (Xys tptp.list_P2321686559999237006et_nat)) (=> (= (@ (@ tptp.zip_Pr7134870689397686104et_nat Xs) Ys3) (@ (@ tptp.cons_P3419706843779801160et_nat Xy) Xys)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Xs4 tptp.list_P7985473006766602707_nat_o)) (=> (= Xs (@ (@ tptp.cons_P6219271836124797827_nat_o X3) Xs4)) (forall ((Y3 tptp.produc3658429121746597890et_nat) (Ys4 tptp.list_P9062070895058802706et_nat)) (=> (= Ys3 (@ (@ tptp.cons_P2869003950965171916et_nat Y3) Ys4)) (=> (= Xy (@ (@ tptp.produc5001842942810119800et_nat X3) Y3)) (not (= Xys (@ (@ tptp.zip_Pr7134870689397686104et_nat Xs4) Ys4))))))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_P7985473006766602707_nat_o) (Ys3 tptp.list_P2321686559999237006et_nat) (Xy tptp.produc2732055786443039994et_nat) (Xys tptp.list_P362550909693114634et_nat)) (=> (= (@ (@ tptp.zip_Pr8136144321567152340et_nat Xs) Ys3) (@ (@ tptp.cons_P6329468272379687876et_nat Xy) Xys)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Xs4 tptp.list_P7985473006766602707_nat_o)) (=> (= Xs (@ (@ tptp.cons_P6219271836124797827_nat_o X3) Xs4)) (forall ((Y3 tptp.produc3925858234332021118et_nat) (Ys4 tptp.list_P2321686559999237006et_nat)) (=> (= Ys3 (@ (@ tptp.cons_P3419706843779801160et_nat Y3) Ys4)) (=> (= Xy (@ (@ tptp.produc2245416461498447860et_nat X3) Y3)) (not (= Xys (@ (@ tptp.zip_Pr8136144321567152340et_nat Xs4) Ys4))))))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_b) (Ys3 tptp.list_P131111800688179804it_nat) (Xy tptp.produc7388388658123137530it_nat) (Xys tptp.list_P7438302566501821706it_nat)) (=> (= (@ (@ tptp.zip_b_5987488365222434772it_nat Xs) Ys3) (@ (@ tptp.cons_P6467324686191779524it_nat Xy) Xys)) (not (forall ((X3 tptp.b) (Xs4 tptp.list_b)) (=> (= Xs (@ (@ tptp.cons_b X3) Xs4)) (forall ((Y3 tptp.produc6653097349344004940it_nat) (Ys4 tptp.list_P131111800688179804it_nat)) (=> (= Ys3 (@ (@ tptp.cons_P7873165156130251286it_nat Y3) Ys4)) (=> (= Xy (@ (@ tptp.produc4082563078715348724it_nat X3) Y3)) (not (= Xys (@ (@ tptp.zip_b_5987488365222434772it_nat Xs4) Ys4))))))))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_a) (Ys3 tptp.list_P131111800688179804it_nat) (Xy tptp.produc3260487557148687353it_nat) (Xys tptp.list_P6935614879863011209it_nat)) (=> (= (@ (@ tptp.zip_a_1859587264247984595it_nat Xs) Ys3) (@ (@ tptp.cons_P2339423585217329347it_nat Xy) Xys)) (not (forall ((X3 tptp.a) (Xs4 tptp.list_a)) (=> (= Xs (@ (@ tptp.cons_a X3) Xs4)) (forall ((Y3 tptp.produc6653097349344004940it_nat) (Ys4 tptp.list_P131111800688179804it_nat)) (=> (= Ys3 (@ (@ tptp.cons_P7873165156130251286it_nat Y3) Ys4)) (=> (= Xy (@ (@ tptp.produc9178034014595674355it_nat X3) Y3)) (not (= Xys (@ (@ tptp.zip_a_1859587264247984595it_nat Xs4) Ys4))))))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.int Bool)) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.find_int P2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.cons_int X) Xs)))) (let ((_let_3 (@ P2 X))) (and (=> _let_3 (= _let_2 (@ tptp.some_int X))) (=> (not _let_3) (= _let_2 (@ _let_1 Xs)))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.nat Bool)) (X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.find_nat P2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.cons_nat X) Xs)))) (let ((_let_3 (@ P2 X))) (and (=> _let_3 (= _let_2 (@ tptp.some_nat X))) (=> (not _let_3) (= _let_2 (@ _let_1 Xs)))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.produc7388388658123137530it_nat Bool)) (X tptp.produc7388388658123137530it_nat) (Xs tptp.list_P7438302566501821706it_nat)) (let ((_let_1 (@ tptp.find_P8943372834735446238it_nat P2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.cons_P6467324686191779524it_nat X) Xs)))) (let ((_let_3 (@ P2 X))) (and (=> _let_3 (= _let_2 (@ tptp.some_P2818173045054083285it_nat X))) (=> (not _let_3) (= _let_2 (@ _let_1 Xs)))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.produc3260487557148687353it_nat Bool)) (X tptp.produc3260487557148687353it_nat) (Xs tptp.list_P6935614879863011209it_nat)) (let ((_let_1 (@ tptp.find_P4815471733760996061it_nat P2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.cons_P2339423585217329347it_nat X) Xs)))) (let ((_let_3 (@ P2 X))) (and (=> _let_3 (= _let_2 (@ tptp.some_P7913643980934408916it_nat X))) (=> (not _let_3) (= _let_2 (@ _let_1 Xs)))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.produc8664842809031399944it_nat Bool)) (X tptp.produc8664842809031399944it_nat) (Xs tptp.list_P626663023886443800it_nat)) (let ((_let_1 (@ tptp.find_P5317947125398478060it_nat P2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.cons_P4136552807766418642it_nat X) Xs)))) (let ((_let_3 (@ P2 X))) (and (=> _let_3 (= _let_2 (@ tptp.some_P1914260805536162275it_nat X))) (=> (not _let_3) (= _let_2 (@ _let_1 Xs)))))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.num Bool)) (X tptp.num) (Xs tptp.list_num)) (let ((_let_1 (@ tptp.find_num P2))) (let ((_let_2 (@ _let_1 (@ (@ tptp.cons_num X) Xs)))) (let ((_let_3 (@ P2 X))) (and (=> _let_3 (= _let_2 (@ tptp.some_num X))) (=> (not _let_3) (= _let_2 (@ _let_1 Xs)))))))))
% 8.20/8.62 (assert (forall ((L tptp.list_P6011104703257516679at_nat)) (not (forall ((L1 tptp.list_nat) (L22 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat L22))) (=> (= L (@ (@ tptp.zip_nat_nat L1) L22)) (=> (= (@ tptp.size_size_list_nat L1) _let_1) (not (= (@ tptp.size_s5460976970255530739at_nat L) _let_1)))))))))
% 8.20/8.62 (assert (forall ((L tptp.list_P7333126701944960589_nat_o)) (not (forall ((L1 tptp.list_nat) (L22 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o L22))) (=> (= L (@ (@ tptp.zip_nat_o L1) L22)) (=> (= (@ tptp.size_size_list_nat L1) _let_1) (not (= (@ tptp.size_s6491369823275344609_nat_o L) _let_1)))))))))
% 8.20/8.62 (assert (forall ((L tptp.list_P3521021558325789923at_int)) (not (forall ((L1 tptp.list_nat) (L22 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int L22))) (=> (= L (@ (@ tptp.zip_nat_int L1) L22)) (=> (= (@ tptp.size_size_list_nat L1) _let_1) (not (= (@ tptp.size_s2970893825323803983at_int L) _let_1)))))))))
% 8.20/8.62 (assert (forall ((L tptp.list_P6285523579766656935_o_nat)) (not (forall ((L1 tptp.list_o) (L22 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat L22))) (=> (= L (@ (@ tptp.zip_o_nat L1) L22)) (=> (= (@ tptp.size_size_list_o L1) _let_1) (not (= (@ tptp.size_s5443766701097040955_o_nat L) _let_1)))))))))
% 8.20/8.62 (assert (forall ((L tptp.list_P4002435161011370285od_o_o)) (not (forall ((L1 tptp.list_o) (L22 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o L22))) (=> (= L (@ (@ tptp.zip_o_o L1) L22)) (=> (= (@ tptp.size_size_list_o L1) _let_1) (not (= (@ tptp.size_s1515746228057227161od_o_o L) _let_1)))))))))
% 8.20/8.62 (assert (forall ((L tptp.list_P3795440434834930179_o_int)) (not (forall ((L1 tptp.list_o) (L22 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int L22))) (=> (= L (@ (@ tptp.zip_o_int L1) L22)) (=> (= (@ tptp.size_size_list_o L1) _let_1) (not (= (@ tptp.size_s2953683556165314199_o_int L) _let_1)))))))))
% 8.20/8.62 (assert (forall ((L tptp.list_P8198026277950538467nt_nat)) (not (forall ((L1 tptp.list_int) (L22 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat L22))) (=> (= L (@ (@ tptp.zip_int_nat L1) L22)) (=> (= (@ tptp.size_size_list_int L1) _let_1) (not (= (@ tptp.size_s7647898544948552527nt_nat L) _let_1)))))))))
% 8.20/8.62 (assert (forall ((L tptp.list_P5087981734274514673_int_o)) (not (forall ((L1 tptp.list_int) (L22 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o L22))) (=> (= L (@ (@ tptp.zip_int_o L1) L22)) (=> (= (@ tptp.size_size_list_int L1) _let_1) (not (= (@ tptp.size_s4246224855604898693_int_o L) _let_1)))))))))
% 8.20/8.62 (assert (forall ((L tptp.list_P5707943133018811711nt_int)) (not (forall ((L1 tptp.list_int) (L22 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int L22))) (=> (= L (@ (@ tptp.zip_int_int L1) L22)) (=> (= (@ tptp.size_size_list_int L1) _let_1) (not (= (@ tptp.size_s5157815400016825771nt_int L) _let_1)))))))))
% 8.20/8.62 (assert (forall ((A tptp.list_nat) (B tptp.list_nat) (A2 tptp.list_nat) (B2 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat A) (@ tptp.size_size_list_nat B)) (=> (= (@ tptp.size_size_list_nat A2) (@ tptp.size_size_list_nat B2)) (=> (= (@ (@ tptp.zip_nat_nat A) B) (@ (@ tptp.zip_nat_nat A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_nat) (B tptp.list_o) (A2 tptp.list_nat) (B2 tptp.list_o)) (=> (= (@ tptp.size_size_list_nat A) (@ tptp.size_size_list_o B)) (=> (= (@ tptp.size_size_list_nat A2) (@ tptp.size_size_list_o B2)) (=> (= (@ (@ tptp.zip_nat_o A) B) (@ (@ tptp.zip_nat_o A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_nat) (B tptp.list_int) (A2 tptp.list_nat) (B2 tptp.list_int)) (=> (= (@ tptp.size_size_list_nat A) (@ tptp.size_size_list_int B)) (=> (= (@ tptp.size_size_list_nat A2) (@ tptp.size_size_list_int B2)) (=> (= (@ (@ tptp.zip_nat_int A) B) (@ (@ tptp.zip_nat_int A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_o) (B tptp.list_nat) (A2 tptp.list_o) (B2 tptp.list_nat)) (=> (= (@ tptp.size_size_list_o A) (@ tptp.size_size_list_nat B)) (=> (= (@ tptp.size_size_list_o A2) (@ tptp.size_size_list_nat B2)) (=> (= (@ (@ tptp.zip_o_nat A) B) (@ (@ tptp.zip_o_nat A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_o) (B tptp.list_o) (A2 tptp.list_o) (B2 tptp.list_o)) (=> (= (@ tptp.size_size_list_o A) (@ tptp.size_size_list_o B)) (=> (= (@ tptp.size_size_list_o A2) (@ tptp.size_size_list_o B2)) (=> (= (@ (@ tptp.zip_o_o A) B) (@ (@ tptp.zip_o_o A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_o) (B tptp.list_int) (A2 tptp.list_o) (B2 tptp.list_int)) (=> (= (@ tptp.size_size_list_o A) (@ tptp.size_size_list_int B)) (=> (= (@ tptp.size_size_list_o A2) (@ tptp.size_size_list_int B2)) (=> (= (@ (@ tptp.zip_o_int A) B) (@ (@ tptp.zip_o_int A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_int) (B tptp.list_nat) (A2 tptp.list_int) (B2 tptp.list_nat)) (=> (= (@ tptp.size_size_list_int A) (@ tptp.size_size_list_nat B)) (=> (= (@ tptp.size_size_list_int A2) (@ tptp.size_size_list_nat B2)) (=> (= (@ (@ tptp.zip_int_nat A) B) (@ (@ tptp.zip_int_nat A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_int) (B tptp.list_o) (A2 tptp.list_int) (B2 tptp.list_o)) (=> (= (@ tptp.size_size_list_int A) (@ tptp.size_size_list_o B)) (=> (= (@ tptp.size_size_list_int A2) (@ tptp.size_size_list_o B2)) (=> (= (@ (@ tptp.zip_int_o A) B) (@ (@ tptp.zip_int_o A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((A tptp.list_int) (B tptp.list_int) (A2 tptp.list_int) (B2 tptp.list_int)) (=> (= (@ tptp.size_size_list_int A) (@ tptp.size_size_list_int B)) (=> (= (@ tptp.size_size_list_int A2) (@ tptp.size_size_list_int B2)) (=> (= (@ (@ tptp.zip_int_int A) B) (@ (@ tptp.zip_int_int A2) B2)) (and (= A A2) (= B B2)))))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.produc7388388658123137530it_nat Bool)) (Xs tptp.list_P7438302566501821706it_nat) (X tptp.produc7388388658123137530it_nat)) (=> (= (@ (@ tptp.find_P8943372834735446238it_nat P2) Xs) (@ tptp.some_P2818173045054083285it_nat X)) (@ P2 X))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.produc3260487557148687353it_nat Bool)) (Xs tptp.list_P6935614879863011209it_nat) (X tptp.produc3260487557148687353it_nat)) (=> (= (@ (@ tptp.find_P4815471733760996061it_nat P2) Xs) (@ tptp.some_P7913643980934408916it_nat X)) (@ P2 X))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.produc8664842809031399944it_nat Bool)) (Xs tptp.list_P626663023886443800it_nat) (X tptp.produc8664842809031399944it_nat)) (=> (= (@ (@ tptp.find_P5317947125398478060it_nat P2) Xs) (@ tptp.some_P1914260805536162275it_nat X)) (@ P2 X))))
% 8.20/8.62 (assert (forall ((P2 (-> tptp.num Bool)) (Xs tptp.list_num) (X tptp.num)) (=> (= (@ (@ tptp.find_num P2) Xs) (@ tptp.some_num X)) (@ P2 X))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le1926595141338095240atural (@ tptp.numera5444537566228673987atural N2)) tptp.zero_z2226904508553997617atural))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger N2)) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) (@ tptp.numera5444537566228673987atural N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le5570908160329646204atural (@ tptp.numera5444537566228673987atural N2)) tptp.zero_z2226904508553997617atural))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger N2)) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) (@ tptp.numera5444537566228673987atural N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le5570908160329646204atural (@ tptp.numera5444537566228673987atural N2)) tptp.one_one_Code_natural))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger N2)) tptp.one_one_Code_integer))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 8.20/8.62 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 8.20/8.62 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 8.20/8.62 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera5444537566228673987atural X))) (= (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) _let_1) (@ (@ tptp.plus_p4538020629002901425atural _let_1) tptp.one_one_Code_natural)))))
% 8.20/8.62 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.cons_nat X) Xs)) (@ tptp.suc (@ tptp.size_size_list_nat Xs)))))
% 8.20/8.62 (assert (forall ((X Bool) (Xs tptp.list_o)) (= (@ tptp.size_size_list_o (@ (@ tptp.cons_o X) Xs)) (@ tptp.suc (@ tptp.size_size_list_o Xs)))))
% 8.20/8.62 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ tptp.size_size_list_int (@ (@ tptp.cons_int X) Xs)) (@ tptp.suc (@ tptp.size_size_list_int Xs)))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_nat) (Ys3 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_nat Ys3)) (not (= Xs (@ (@ tptp.cons_nat X) Ys3))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_o) (Ys3 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_o Ys3)) (not (= Xs (@ (@ tptp.cons_o X) Ys3))))))
% 8.20/8.62 (assert (forall ((Xs tptp.list_int) (Ys3 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) (@ tptp.size_size_list_int Ys3)) (not (= Xs (@ (@ tptp.cons_int X) Ys3))))))
% 8.20/8.62 (assert (forall ((X tptp.rat) (Y tptp.rat) (Zs tptp.list_rat)) (let ((_let_1 (@ (@ tptp.cons_rat Y) Zs))) (let ((_let_2 (@ tptp.sorted_wrt_rat tptp.ord_less_eq_rat))) (= (@ _let_2 (@ (@ tptp.cons_rat X) _let_1)) (and (@ (@ tptp.ord_less_eq_rat X) Y) (@ _let_2 _let_1)))))))
% 8.20/8.62 (assert (forall ((X tptp.num) (Y tptp.num) (Zs tptp.list_num)) (let ((_let_1 (@ (@ tptp.cons_num Y) Zs))) (let ((_let_2 (@ tptp.sorted_wrt_num tptp.ord_less_eq_num))) (= (@ _let_2 (@ (@ tptp.cons_num X) _let_1)) (and (@ (@ tptp.ord_less_eq_num X) Y) (@ _let_2 _let_1)))))))
% 8.20/8.62 (assert (forall ((X tptp.nat) (Y tptp.nat) (Zs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat Y) Zs))) (let ((_let_2 (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat))) (= (@ _let_2 (@ (@ tptp.cons_nat X) _let_1)) (and (@ (@ tptp.ord_less_eq_nat X) Y) (@ _let_2 _let_1)))))))
% 8.20/8.62 (assert (forall ((X tptp.int) (Y tptp.int) (Zs tptp.list_int)) (let ((_let_1 (@ (@ tptp.cons_int Y) Zs))) (let ((_let_2 (@ tptp.sorted_wrt_int tptp.ord_less_eq_int))) (= (@ _let_2 (@ (@ tptp.cons_int X) _let_1)) (and (@ (@ tptp.ord_less_eq_int X) Y) (@ _let_2 _let_1)))))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat)))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)))
% 8.20/8.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat)))
% 8.20/8.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 8.20/8.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 8.20/8.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 8.20/8.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 8.20/8.62 (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))))
% 8.20/8.62 (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))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 8.20/8.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 8.20/8.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 8.20/8.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 8.20/8.62 (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))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.size_size_list_nat Xs)) (exists ((X4 tptp.nat) (Ys2 tptp.list_nat)) (and (= Xs (@ (@ tptp.cons_nat X4) Ys2)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.size_size_list_nat Ys2)))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.size_size_list_o Xs)) (exists ((X4 Bool) (Ys2 tptp.list_o)) (and (= Xs (@ (@ tptp.cons_o X4) Ys2)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.size_size_list_o Ys2)))))))
% 8.20/8.62 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.size_size_list_int Xs)) (exists ((X4 tptp.int) (Ys2 tptp.list_int)) (and (= Xs (@ (@ tptp.cons_int X4) Ys2)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.size_size_list_int Ys2)))))))
% 8.20/8.62 (assert (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 8.20/8.62 (assert (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ _let_2 C2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C2)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 8.20/8.62 (assert (forall ((X21 tptp.nat) (X222 tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.cons_nat X21) X222)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_nat X222)) (@ tptp.suc tptp.zero_zero_nat)))))
% 8.20/8.62 (assert (forall ((X21 Bool) (X222 tptp.list_o)) (= (@ tptp.size_size_list_o (@ (@ tptp.cons_o X21) X222)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_o X222)) (@ tptp.suc tptp.zero_zero_nat)))))
% 8.20/8.62 (assert (forall ((X21 tptp.int) (X222 tptp.list_int)) (= (@ tptp.size_size_list_int (@ (@ tptp.cons_int X21) X222)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_int X222)) (@ tptp.suc tptp.zero_zero_nat)))))
% 8.20/8.62 (assert (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 8.20/8.62 (assert (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C2)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 8.20/8.62 (assert (forall ((W2 tptp.num) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C2))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C2)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 8.20/8.62 (assert (forall ((B tptp.rat) (C2 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C2) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C2))) (let ((_let_5 (@ _let_2 C2))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C2)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 8.20/8.62 (assert (forall ((X tptp.int) (Y tptp.int) (Xs tptp.list_int) (N2 tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N2) Y) (and (= (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 8.20/8.62 (assert (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (N2 tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N2) Y) (and (= (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 8.20/8.62 (assert (forall ((Begin tptp.nat) (End tptp.nat) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.minus_minus_nat End) tptp.one_one_nat))) (let ((_let_2 (@ tptp.cons_int X))) (let ((_let_3 (@ tptp.slice_int Begin))) (let ((_let_4 (@ (@ _let_3 End) (@ _let_2 Xs)))) (let ((_let_5 (and (= Begin tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) End)))) (and (=> _let_5 (= _let_4 (@ _let_2 (@ (@ _let_3 _let_1) Xs)))) (=> (not _let_5) (= _let_4 (@ (@ (@ tptp.slice_int (@ (@ tptp.minus_minus_nat Begin) tptp.one_one_nat)) _let_1) Xs)))))))))))
% 8.20/8.62 (assert (forall ((Begin tptp.nat) (End tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat End) tptp.one_one_nat))) (let ((_let_2 (@ tptp.cons_nat X))) (let ((_let_3 (@ tptp.slice_nat Begin))) (let ((_let_4 (@ (@ _let_3 End) (@ _let_2 Xs)))) (let ((_let_5 (and (= Begin tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) End)))) (and (=> _let_5 (= _let_4 (@ _let_2 (@ (@ _let_3 _let_1) Xs)))) (=> (not _let_5) (= _let_4 (@ (@ (@ tptp.slice_nat (@ (@ tptp.minus_minus_nat Begin) tptp.one_one_nat)) _let_1) Xs)))))))))))
% 8.20/8.62 (assert (forall ((P2 (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y8 tptp.produc3658429121746597890et_nat) (Y tptp.produc3658429121746597890et_nat) (R3 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr719794911490849221et_nat))) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat X))) (=> (@ P2 X) (=> (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat Y8) Y)) (@ R3 X)) (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ _let_1 Y8)) (@ _let_1 Y))) (@ (@ tptp.same_f7251492184213700963et_nat P2) R3)))))))
% 8.20/8.62 (assert (forall ((P2 (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y8 tptp.produc3925858234332021118et_nat) (Y tptp.produc3925858234332021118et_nat) (R3 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr7928877670098842301et_nat))) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat X))) (=> (@ P2 X) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat Y8) Y)) (@ R3 X)) (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ _let_1 Y8)) (@ _let_1 Y))) (@ (@ tptp.same_f1912051055550046943et_nat P2) R3)))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.b Bool)) (X tptp.b) (Y8 tptp.produc6653097349344004940it_nat) (Y tptp.produc6653097349344004940it_nat) (R3 (-> tptp.b tptp.set_Pr4389693562480114009it_nat))) (let ((_let_1 (@ tptp.produc4082563078715348724it_nat X))) (=> (@ P2 X) (=> (@ (@ tptp.member5617269971687963298it_nat (@ (@ tptp.produc3130510018828335921it_nat Y8) Y)) (@ R3 X)) (@ (@ tptp.member6820296301096096254it_nat (@ (@ tptp.produc6853161671299316109it_nat (@ _let_1 Y8)) (@ _let_1 Y))) (@ (@ tptp.same_f3722904161141537503it_nat P2) R3)))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.a Bool)) (X tptp.a) (Y8 tptp.produc6653097349344004940it_nat) (Y tptp.produc6653097349344004940it_nat) (R3 (-> tptp.a tptp.set_Pr4389693562480114009it_nat))) (let ((_let_1 (@ tptp.produc9178034014595674355it_nat X))) (=> (@ P2 X) (=> (@ (@ tptp.member5617269971687963298it_nat (@ (@ tptp.produc3130510018828335921it_nat Y8) Y)) (@ R3 X)) (@ (@ tptp.member5335690527091456380it_nat (@ (@ tptp.produc1743342482959036555it_nat (@ _let_1 Y8)) (@ _let_1 Y))) (@ (@ tptp.same_f8818375097021863134it_nat P2) R3)))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.int Bool)) (X tptp.int) (Y8 tptp.int) (Y tptp.int) (R3 (-> tptp.int tptp.set_Pr958786334691620121nt_int))) (let ((_let_1 (@ tptp.product_Pair_int_int X))) (=> (@ P2 X) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y8) Y)) (@ R3 X)) (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int (@ _let_1 Y8)) (@ _let_1 Y))) (@ (@ tptp.same_fst_int_int P2) R3)))))))
% 8.20/8.63 (assert (= tptp.upto_aux (lambda ((I tptp.int) (J tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J) I)) Js) (@ (@ (@ tptp.upto_aux I) (@ (@ tptp.minus_minus_int J) tptp.one_one_int)) (@ (@ tptp.cons_int J) Js))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat W2)) (@ tptp.ring_1_of_int_rat Z3)) (@ (@ tptp.ord_less_eq_int W2) Z3))))
% 8.20/8.63 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z3)) (@ (@ tptp.ord_less_eq_int W2) Z3))))
% 8.20/8.63 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat W2)) (@ tptp.ring_1_of_int_rat Z3)) (@ (@ tptp.ord_less_int W2) Z3))))
% 8.20/8.63 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z3)) (@ (@ tptp.ord_less_int W2) Z3))))
% 8.20/8.63 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.plus_plus_int W2) Z3)) (@ (@ tptp.plus_plus_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z3)))))
% 8.20/8.63 (assert (forall ((W2 tptp.int) (Z3 tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int W2) Z3)) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat W2)) (@ tptp.ring_1_of_int_rat Z3)))))
% 8.20/8.63 (assert (forall ((X tptp.rat) (Z3 tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) (@ tptp.ring_1_of_int_rat Z3))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger Z3)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_int Z3) tptp.zero_zero_int))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z3)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int Z3) tptp.zero_zero_int))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z3)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int Z3) tptp.zero_zero_int))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.ring_18347121197199848620nteger Z3)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z3)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger Z3)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_int Z3) tptp.zero_zero_int))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z3)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int Z3) tptp.zero_zero_int))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z3)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z3) tptp.zero_zero_int))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.ring_18347121197199848620nteger Z3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num) (Z3 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.ring_18347121197199848620nteger Z3)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) Z3))))
% 8.20/8.63 (assert (forall ((N2 tptp.num) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.ring_1_of_int_rat Z3)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) Z3))))
% 8.20/8.63 (assert (forall ((N2 tptp.num) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger Z3)) (@ tptp.numera6620942414471956472nteger N2)) (@ (@ tptp.ord_less_eq_int Z3) (@ tptp.numeral_numeral_int N2)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z3)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_eq_int Z3) (@ tptp.numeral_numeral_int N2)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z3)) _let_1) (@ (@ tptp.ord_less_eq_int Z3) _let_1)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.ring_1_of_int_rat Z3)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) Z3))))
% 8.20/8.63 (assert (forall ((N2 tptp.num) (Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num) (Z3 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.ring_18347121197199848620nteger Z3)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z3)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_int Z3) (@ tptp.numeral_numeral_int N2)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z3)) _let_1) (@ (@ tptp.ord_less_int Z3) _let_1)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger Z3)) (@ tptp.numera6620942414471956472nteger N2)) (@ (@ tptp.ord_less_int Z3) (@ tptp.numeral_numeral_int N2)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger Z3)) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_int Z3) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z3)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int Z3) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z3)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int Z3) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.ring_18347121197199848620nteger Z3)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z3)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger Z3)) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_int Z3) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z3)) tptp.one_one_rat) (@ (@ tptp.ord_less_int Z3) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z3)) tptp.one_one_int) (@ (@ tptp.ord_less_int Z3) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.ring_18347121197199848620nteger Z3)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z3)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z3)) (@ _let_1 Z3)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)))))
% 8.20/8.63 (assert (forall ((X tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 Z3)) (@ tptp.ring_1_of_int_rat Z3)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z3)) (@ tptp.ring_1_of_int_int Z3)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 Z3)) (@ tptp.ring_18347121197199848620nteger Z3)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)))))
% 8.20/8.63 (assert (forall ((X tptp.rat) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) Z3) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat Z3)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_int Z3) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z3)) X))))
% 8.20/8.63 (assert (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat Z2)))))
% 8.20/8.63 (assert (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) X))))
% 8.20/8.63 (assert (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat Z2)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z3))) (=> (@ (@ 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) Z3))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.int Bool)) (T6 tptp.rat)) (= (@ P2 (@ tptp.archim2889992004027027881ng_rat T6)) (forall ((I tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I))) (=> (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) T6) (@ (@ tptp.ord_less_eq_rat T6) _let_1)) (@ P2 I)))))))
% 8.20/8.63 (assert (forall ((X tptp.rat) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) Z3) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z3)) tptp.one_one_rat)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z3) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z3)) tptp.one_one_rat)) X))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat R2) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim2889992004027027881ng_rat R2))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.ring_18347121197199848620nteger Z3)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z3)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z3) (@ _let_1 (@ tptp.ring_1_of_int_int Z3))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.ring_18347121197199848620nteger Z3)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z3) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z3)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 Z3) (@ _let_1 (@ tptp.ring_1_of_int_int Z3))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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 ((Y5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y5)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y5) tptp.one_one_int)))) (= Y5 X3)))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int) (A2 tptp.int) (B2 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.product_Pair_int_int A))) (= (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int (@ _let_1 B)) (@ (@ tptp.product_Pair_int_int A2) B2))) (@ (@ tptp.lex_prod_int_int R2) S2)) (or (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 A2)) R2) (and (= A A2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) B2)) S2)))))))
% 8.20/8.63 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr2161125870931222855_nat_o) (S2 tptp.set_Pr719794911490849221et_nat)) (= (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ (@ tptp.produc5001842942810119800et_nat A) B)) (@ (@ tptp.produc5001842942810119800et_nat A2) B2))) (@ (@ tptp.lex_pr5340572901959109728et_nat R2) S2)) (or (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A) A2)) R2) (and (= A A2) (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat B) B2)) S2))))))
% 8.20/8.63 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr2161125870931222855_nat_o) (S2 tptp.set_Pr7928877670098842301et_nat)) (= (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ (@ tptp.produc2245416461498447860et_nat A) B)) (@ (@ tptp.produc2245416461498447860et_nat A2) B2))) (@ (@ tptp.lex_pr4722427456421979612et_nat R2) S2)) (or (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A) A2)) R2) (and (= A A2) (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat B) B2)) S2))))))
% 8.20/8.63 (assert (forall ((A tptp.b) (B tptp.produc6653097349344004940it_nat) (A2 tptp.b) (B2 tptp.produc6653097349344004940it_nat) (R2 tptp.set_Product_prod_b_b) (S2 tptp.set_Pr4389693562480114009it_nat)) (= (@ (@ tptp.member6820296301096096254it_nat (@ (@ tptp.produc6853161671299316109it_nat (@ (@ tptp.produc4082563078715348724it_nat A) B)) (@ (@ tptp.produc4082563078715348724it_nat A2) B2))) (@ (@ tptp.lex_pr2603589247317408988it_nat R2) S2)) (or (@ (@ tptp.member7862447936710763792od_b_b (@ (@ tptp.product_Pair_b_b A) A2)) R2) (and (= A A2) (@ (@ tptp.member5617269971687963298it_nat (@ (@ tptp.produc3130510018828335921it_nat B) B2)) S2))))))
% 8.20/8.63 (assert (forall ((A tptp.a) (B tptp.produc6653097349344004940it_nat) (A2 tptp.a) (B2 tptp.produc6653097349344004940it_nat) (R2 tptp.set_Product_prod_a_a) (S2 tptp.set_Pr4389693562480114009it_nat)) (= (@ (@ tptp.member5335690527091456380it_nat (@ (@ tptp.produc1743342482959036555it_nat (@ (@ tptp.produc9178034014595674355it_nat A) B)) (@ (@ tptp.produc9178034014595674355it_nat A2) B2))) (@ (@ tptp.lex_pr7699060183197734619it_nat R2) S2)) (or (@ (@ tptp.member1426531477525435216od_a_a (@ (@ tptp.product_Pair_a_a A) A2)) R2) (and (= A A2) (@ (@ tptp.member5617269971687963298it_nat (@ (@ tptp.produc3130510018828335921it_nat B) B2)) S2))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat) (A2 tptp.nat) (B2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat A))) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ _let_1 B)) (@ (@ tptp.product_Pair_nat_nat A2) B2))) (@ (@ tptp.lex_prod_nat_nat R2) S2)) (or (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 A2)) R2) (and (= A A2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) B2)) S2)))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (or (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat Y) tptp.ring_1_Ints_rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat B) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.ring_1_Ints_rat)))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int B) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int A) B)) tptp.ring_1_Ints_int)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X))) X)))
% 8.20/8.63 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim2889992004027027881ng_rat X))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A) tptp.ring_11222124179247155820nteger) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 8.20/8.63 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))))
% 8.20/8.63 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z3) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z3)) X))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((X tptp.rat) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) Z3) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat Z3)))))
% 8.20/8.63 (assert (forall ((X tptp.rat) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) Z3) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) (@ tptp.ring_1_of_int_rat Z3))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (X tptp.rat)) (= (@ (@ tptp.plus_plus_int Z3) (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z3)) X)))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A) tptp.ring_11222124179247155820nteger) (not (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) A) tptp.zero_z3403309356797280102nteger)))))
% 8.20/8.63 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (not (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A)) A) tptp.zero_zero_rat)))))
% 8.20/8.63 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) A) tptp.zero_zero_int)))))
% 8.20/8.63 (assert (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat R2)))) R2))))
% 8.20/8.63 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)))))
% 8.20/8.63 (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)))
% 8.20/8.63 (assert (= tptp.archim2889992004027027881ng_rat (lambda ((X4 tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X4))) (@ (@ (@ tptp.if_int (= X4 (@ tptp.ring_1_of_int_rat _let_1))) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z3))) (=> (@ (@ 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) Z3))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.int Bool)) (T6 tptp.rat)) (= (@ P2 (@ tptp.archim3151403230148437115or_rat T6)) (forall ((I tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I))) (=> (and (@ (@ tptp.ord_less_eq_rat _let_1) T6) (@ (@ tptp.ord_less_rat T6) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))) (@ P2 I)))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_int Z3) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z3)) tptp.one_one_rat)) X))))
% 8.20/8.63 (assert (forall ((X tptp.rat) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) Z3) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z3)) tptp.one_one_rat)))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 8.20/8.63 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 8.20/8.63 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N2))))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N2))))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N2))))))
% 8.20/8.63 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc M))))))
% 8.20/8.63 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc M))))))
% 8.20/8.63 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc M))))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N2)))
% 8.20/8.63 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural N2)) (@ tptp.numera5444537566228673987atural (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ tptp.numera5444537566228673987atural N2)) tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger N2)) tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le1926595141338095240atural (@ tptp.numera5444537566228673987atural N2)) tptp.one_one_Code_natural) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger N2)) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 8.20/8.63 (assert (forall ((X tptp.num)) (= (@ (@ tptp.plus_plus_num X) tptp.one) (@ tptp.inc X))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N2) (@ (@ tptp.plus_plus_num N2) tptp.one))))
% 8.20/8.63 (assert (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))))
% 8.20/8.63 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ tptp.inc (@ _let_1 Y))))))
% 8.20/8.63 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X)))))
% 8.20/8.63 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X))))
% 8.20/8.63 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat (@ tptp.archimedean_frac_rat X)) tptp.one_one_rat)))
% 8.20/8.63 (assert (forall ((X tptp.rat)) (= (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ tptp.archimedean_frac_rat X))))
% 8.20/8.63 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X)) tptp.one_one_rat))))
% 8.20/8.63 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X)) tptp.one_one_nat))))
% 8.20/8.63 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X)) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((X tptp.num)) (= (@ tptp.numera5444537566228673987atural (@ tptp.inc X)) (@ (@ tptp.plus_p4538020629002901425atural (@ tptp.numera5444537566228673987atural X)) tptp.one_one_Code_natural))))
% 8.20/8.63 (assert (forall ((X tptp.num)) (= (@ tptp.numera6620942414471956472nteger (@ tptp.inc X)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger X)) tptp.one_one_Code_integer))))
% 8.20/8.63 (assert (forall ((V tptp.num) (N2 tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N2))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (assert (forall ((Z3 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) Z3)) _let_4) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s4028243227959126397er_rat Z3) N2))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z3) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N2)))))))))
% 8.20/8.63 (assert (forall ((B tptp.int) (A tptp.int) (Q6 tptp.int) (R2 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 R2)) (@ (@ (@ 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 R2)) tptp.one_one_int)))))))))
% 8.20/8.63 (assert (forall ((F (-> tptp.product_unit tptp.product_unit)) (R2 tptp.ref_Product_unit) (H tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ F (@ (@ tptp.ref_get_Product_unit H) R2)))) (= (@ (@ tptp.heap_T875086893843062177t_unit (@ (@ tptp.ref_ch7259622376331601608t_unit F) R2)) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat _let_1) (@ (@ tptp.produc584006145561248582it_nat (@ (@ (@ tptp.ref_set_Product_unit R2) _let_1) H)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))))))
% 8.20/8.63 (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))))))))))
% 8.20/8.63 (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))))))))))
% 8.20/8.63 (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))))))))))
% 8.20/8.63 (assert (forall ((B tptp.int) (A tptp.int) (Q6 tptp.int) (R2 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 R2)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R2)))))))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.bit0 X2) (@ tptp.bit0 Y2)) (= X2 Y2))))
% 8.20/8.63 (assert (forall ((X32 tptp.num) (Y32 tptp.num)) (= (= (@ tptp.bit1 X32) (@ tptp.bit1 Y32)) (= X32 Y32))))
% 8.20/8.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N2)))))
% 8.20/8.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 8.20/8.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N2)))))
% 8.20/8.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N2)))))
% 8.20/8.63 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N2))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 8.20/8.63 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N2))))
% 8.20/8.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N2)) tptp.one)))))
% 8.20/8.63 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 8.20/8.63 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.bit1 N2))))
% 8.20/8.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N2)) (@ tptp.bit0 (@ (@ tptp.times_times_num M) N2)))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 8.20/8.63 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 8.20/8.63 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 8.20/8.63 (assert (= (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))
% 8.20/8.63 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ tptp.suc (@ tptp.suc N2)))))
% 8.20/8.63 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 8.20/8.63 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.plus_plus_int _let_1) _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 8.20/8.63 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 8.20/8.63 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) _let_1)))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) _let_1)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((V tptp.num) (W2 tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W2))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W2)))) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((X2 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X2) (@ tptp.bit1 X32)))))
% 8.20/8.63 (assert (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))))
% 8.20/8.63 (assert (forall ((X2 tptp.num)) (not (= tptp.one (@ tptp.bit0 X2)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera5444537566228673987atural N2))) (= (@ tptp.numera5444537566228673987atural (@ tptp.bit0 N2)) (@ (@ tptp.plus_p4538020629002901425atural _let_1) _let_1)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera5444537566228673987atural N2))) (= (@ tptp.numera5444537566228673987atural (@ tptp.bit0 N2)) (@ (@ tptp.plus_p4538020629002901425atural _let_1) _let_1)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 8.20/8.63 (assert (forall ((X2 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X2)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((Z3 tptp.assn) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_assn Z3))) (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 Z3) _let_2)) _let_2))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat Z3) _let_2)) _let_2))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.nat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Z3) _let_2)) _let_2))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int Z3) _let_2)) _let_2))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.assn) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_assn Z3))) (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))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_rat _let_2) _let_2))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.nat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_nat _let_2) _let_2))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z3))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_int _let_2) _let_2))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))
% 8.20/8.63 (assert (forall ((Z3 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_rat Z3) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_nat Z3) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_plus_int Z3) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_p4538020629002901425atural Z3) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Z3) (@ (@ tptp.plus_p5714425477246183910nteger Z3) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.rat)) (= (@ (@ tptp.times_times_rat Z3) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z3) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.nat)) (= (@ (@ tptp.times_times_nat Z3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z3) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int)) (= (@ (@ tptp.times_times_int Z3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z3) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural Z3) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p4538020629002901425atural Z3) Z3))))
% 8.20/8.63 (assert (forall ((Z3 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p5714425477246183910nteger Z3) Z3))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat K2) M)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N2))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N2))))
% 8.20/8.63 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ 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))))))
% 8.20/8.63 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 8.20/8.63 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (@ P2 tptp.one_one_nat) (=> (forall ((N5 tptp.nat)) (=> (@ P2 N5) (@ P2 (@ (@ tptp.plus_plus_nat N5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P2 N2))))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K2))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((B tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K2) (exists ((N5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N5)) K2) (@ (@ tptp.ord_less_nat K2) (@ _let_1 (@ (@ tptp.plus_plus_nat N5) tptp.one_one_nat))))))))))
% 8.20/8.63 (assert (forall ((B tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B) (=> (@ _let_1 K2) (exists ((N5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N5)) K2) (@ (@ tptp.ord_less_eq_nat K2) (@ _let_1 (@ (@ tptp.plus_plus_nat N5) tptp.one_one_nat)))))))))))
% 8.20/8.63 (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))))))))))
% 8.20/8.63 (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))))))))))
% 8.20/8.63 (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))))))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int))))
% 8.20/8.63 (assert (forall ((K2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ _let_1 K2)))))
% 8.20/8.63 (assert (forall ((L tptp.num) (R2 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) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R2))))))))))
% 8.20/8.63 (assert (forall ((L tptp.num) (R2 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) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_int L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R2))))))))))
% 8.20/8.63 (assert (forall ((L tptp.num) (R2 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) R2)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R2))))))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.int Bool)) (K2 tptp.int)) (=> (@ P2 tptp.zero_zero_int) (=> (@ P2 (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K tptp.int)) (=> (@ P2 K) (=> (not (= K tptp.zero_zero_int)) (@ P2 (@ (@ tptp.times_times_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K tptp.int)) (=> (@ P2 K) (=> (not (= K (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P2 (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P2 K2)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (@ P2 N5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (@ P2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N5))))) (=> (forall ((N5 tptp.nat)) (=> (@ P2 N5) (@ P2 (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N5))))) (@ P2 N2))))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 N2) tptp.zero_zero_nat))))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 N2) tptp.zero_zero_int))))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_z2226904508553997617atural)) (not (= (@ _let_1 N2) tptp.zero_z2226904508553997617atural))))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_z3403309356797280102nteger)) (not (= (@ _let_1 N2) tptp.zero_z3403309356797280102nteger))))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 M) tptp.zero_zero_nat))))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 M) tptp.zero_zero_int))))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_z2226904508553997617atural)) (not (= (@ _let_1 M) tptp.zero_z2226904508553997617atural))))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_z3403309356797280102nteger)) (not (= (@ _let_1 M) tptp.zero_z3403309356797280102nteger))))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide6298287555418463151nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_2 (@ _let_1 M))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 M))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_2 (@ _let_1 M))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))))
% 8.20/8.63 (assert (forall ((A tptp.code_natural) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide5121882707175180666atural A))) (= (@ (@ tptp.divide5121882707175180666atural (@ _let_2 (@ _let_1 M))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) tptp.zero_z3403309356797280102nteger)))))
% 8.20/8.63 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.modulo_modulo_nat A) _let_1)) tptp.zero_zero_nat)))))
% 8.20/8.63 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.modulo_modulo_int A) _let_1)) tptp.zero_zero_int)))))
% 8.20/8.63 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide5121882707175180666atural A) _let_1) A) (= (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) tptp.zero_z2226904508553997617atural)))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))))
% 8.20/8.63 (assert (forall ((A tptp.code_natural) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.divide5121882707175180666atural A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.modulo8411746178871703098atural A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))))
% 8.20/8.63 (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))))))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N2) K2)) (@ _let_1 K2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N2) K2)) (@ _let_1 K2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N2) K2)) (@ _let_1 K2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N2) K2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N2) K2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K2))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.numeral_numeral_int K2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K2)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K2))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K2)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.plus_plus_int K2) L))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K2)) K2)))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int K2) (@ (@ tptp.bit_se7879613467334960850it_int N2) K2))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim7778729529865785530nd_rat X))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 8.20/8.63 (assert (forall ((Z3 tptp.rat) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_rat Z3))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat Z3))))) (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat M)))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K2) (@ (@ tptp.bit_ri631733984087533419it_int N2) K2)) (@ (@ tptp.ord_less_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K2)) K2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K2))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 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) K2))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K2)) K2) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) K2))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K2))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N2) K2)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) K2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K2)) (@ (@ tptp.minus_minus_int K2) (@ _let_1 (@ tptp.suc N2))))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K2) K2) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K2) (@ (@ tptp.ord_less_int K2) _let_1))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 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)) K2) (=> (@ (@ tptp.ord_less_int K2) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K2) K2))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K2) (@ tptp.uminus_uminus_int (@ _let_1 N2))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K2) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.bit_ri631733984087533419it_int N2) K2))))))
% 8.20/8.63 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X4 tptp.rat)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))))))))))
% 8.20/8.63 (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)))))))))))))
% 8.20/8.63 (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)))))))))))))
% 8.20/8.63 (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)))))))))))))
% 8.20/8.63 (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)))))))))))))
% 8.20/8.63 (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)))))))))))))
% 8.20/8.63 (assert (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K2)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K2))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N2)) K2) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N2) (@ (@ tptp.divide_divide_int K2) _let_1)) L)))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (assert (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K2))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.nat)) (= (= (@ (@ tptp.binomial N2) K2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N2) K2))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (let ((_let_2 (@ tptp.binomial N2))) (= (@ (@ tptp.binomial (@ tptp.suc N2)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K2)) (@ _let_2 _let_1)))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N2) K2) L)) (@ _let_1 L)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N2) K2) L)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N2) K2)) (@ (@ tptp.ord_less_eq_nat K2) N2))))
% 8.20/8.63 (assert (forall ((K2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K2)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K2)) N2))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.pred_numeral K2)))))
% 8.20/8.63 (assert (forall ((K2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K2)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K2)) N2))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K2)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.pred_numeral K2)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int) (M tptp.nat) (L tptp.int) (R2 tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N2) K2))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L) R2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N2)) (@ _let_1 L)) R2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K2) (= (@ (@ tptp.binomial N2) K2) tptp.zero_zero_nat))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (= (@ _let_1 K2) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K2)))))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (R2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (let ((_let_2 (@ _let_1 R2))) (let ((_let_3 (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) K2)))) (let ((_let_4 (@ _let_1 K2))) (= (@ (@ tptp.times_times_nat (@ _let_3 _let_4)) (@ (@ tptp.binomial _let_4) K2)) (@ (@ tptp.times_times_nat (@ _let_3 K2)) (@ (@ tptp.binomial _let_2) M)))))))))
% 8.20/8.63 (assert (forall ((R2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) R2)) (@ (@ tptp.power_power_nat N2) R2)))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N2) K2)))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat A) B))))) (let ((_let_2 (@ tptp.suc A))) (= (@ (@ tptp.times_times_nat _let_2) (@ _let_1 _let_2)) (@ (@ tptp.times_times_nat (@ tptp.suc B)) (@ _let_1 A)))))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K2) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.binomial M) K2)) (@ (@ tptp.times_times_nat (@ _let_1 K2)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K2)) (@ (@ tptp.minus_minus_nat M) K2)))))))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K2)))) (@ (@ tptp.binomial N2) K2)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.semiri681578069525770553at_rat K2))) K2)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K2))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 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 K2) (= (@ (@ tptp.binomial N2) K2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))) (@ _let_1 K2)))))))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.times_times_nat K2) (@ (@ tptp.binomial N2) K2)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) K2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (= (@ (@ tptp.binomial N2) K2) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K2))))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.binomial N2) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K2))))))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (= (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K2)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K2))) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N2)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N2) K2)))))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K2)) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N2)) (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K2)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N2) K2))))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (assert (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K2)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K2))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 8.20/8.63 (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))))))))))
% 8.20/8.63 (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))))))))))
% 8.20/8.63 (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))))))))))
% 8.20/8.63 (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))))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q8 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q8) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_nat)))) (@ (@ tptp.unique5055182867167087721od_nat M) N2)))))
% 8.20/8.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q8 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q8) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_Code_integer)))) (@ (@ tptp.unique3479559517661332726nteger M) N2)))))
% 8.20/8.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q8 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q8) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_int)))) (@ (@ tptp.unique5052692396658037445od_int M) N2)))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 8.20/8.63 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)) (@ _let_1 B)))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (@ _let_1 B)))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (@ _let_1 B)))))
% 8.20/8.63 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) A)) (@ _let_1 B)))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) A)) (@ _let_1 B)))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) A)) (@ _let_1 B)))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K2)))
% 8.20/8.63 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))
% 8.20/8.63 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc3704529784387675049_nat_o (@ tptp.produc8739625826339149834_nat_o F)) F)))
% 8.20/8.63 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int))) (= (@ tptp.produc8249235968001453780nt_int (@ tptp.produc4245557441103728435nt_int F)) F)))
% 8.20/8.63 (assert (forall ((F (-> tptp.int tptp.int Bool))) (= (@ tptp.produc175634133007206835_int_o (@ tptp.produc4947309494688390418_int_o F)) F)))
% 8.20/8.63 (assert (forall ((F (-> tptp.int tptp.int tptp.int))) (= (@ tptp.produc1016772743285680337nt_int (@ tptp.produc8211389475949308722nt_int F)) F)))
% 8.20/8.63 (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)))
% 8.20/8.63 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc8739625826339149834_nat_o (@ tptp.produc3704529784387675049_nat_o F)) F)))
% 8.20/8.63 (assert (forall ((F (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (= (@ tptp.produc4245557441103728435nt_int (@ tptp.produc8249235968001453780nt_int F)) F)))
% 8.20/8.63 (assert (forall ((F (-> tptp.product_prod_int_int Bool))) (= (@ tptp.produc4947309494688390418_int_o (@ tptp.produc175634133007206835_int_o F)) F)))
% 8.20/8.63 (assert (forall ((F (-> tptp.product_prod_int_int tptp.int))) (= (@ tptp.produc8211389475949308722nt_int (@ tptp.produc1016772743285680337nt_int F)) F)))
% 8.20/8.63 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C2) A)) B)) (@ _let_1 B)))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C2) A)) B)) (@ _let_1 B)))))
% 8.20/8.63 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C2) A)) B)) (@ _let_1 B)))))
% 8.20/8.63 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.times_times_rat C2) A))) (@ _let_1 B)))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.times_times_nat C2) A))) (@ _let_1 B)))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) (@ (@ tptp.times_times_int C2) A))) (@ _let_1 B)))))
% 8.20/8.63 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C2)) (@ (@ tptp.divide_divide_nat B) C2))))))))
% 8.20/8.63 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C2)) (@ (@ tptp.divide_divide_int B) C2))))))))
% 8.20/8.63 (assert (forall ((C2 tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural C2))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) C2) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.divide5121882707175180666atural A) C2)) (@ (@ tptp.divide5121882707175180666atural B) C2))))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 8.20/8.63 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 8.20/8.63 (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.plus_p4538020629002901425atural A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 8.20/8.63 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (not (@ _let_1 A))))))
% 8.20/8.63 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (not (@ _let_1 A))))))
% 8.20/8.63 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural A) tptp.one_one_Code_natural)) (not (@ _let_1 A))))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) (not (@ _let_1 A))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int A) B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) tptp.one_one_Code_integer))))))
% 8.20/8.63 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) _let_1)) tptp.one_one_nat))))))
% 8.20/8.63 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) _let_1)) tptp.one_one_int))))))
% 8.20/8.63 (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.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) tptp.one_one_Code_natural)) _let_1) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.divide5121882707175180666atural A) _let_1)) tptp.one_one_Code_natural))))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 8.20/8.63 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 8.20/8.63 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 8.20/8.63 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_natural _let_1) A) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) tptp.one_one_Code_natural)) _let_1) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 8.20/8.63 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 8.20/8.63 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 8.20/8.63 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_natural _let_1) A) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) A)) _let_1) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q8 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q8) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5055182867167087721od_nat M) N2)))))
% 8.20/8.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q8 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q8) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique3479559517661332726nteger M) N2)))))
% 8.20/8.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q8 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q8) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5052692396658037445od_int M) N2)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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)))))))))
% 8.20/8.63 (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) (R5 tptp.nat)) (@ (@ (@ F3 L2) R5) Y4))) X4))))
% 8.20/8.63 (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) (R5 tptp.nat)) (@ (@ (@ F3 L2) R5) Y4))) X4))))
% 8.20/8.63 (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) (B4 tptp.nat)) (@ (@ (@ F3 A5) B4) Y4))) X4))))
% 8.20/8.63 (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) (B4 tptp.nat)) (@ (@ (@ F3 A5) B4) Y4))) X4))))
% 8.20/8.63 (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 ((X12 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X12) X23)))) Prod))))
% 8.20/8.63 (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 ((X12 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X12) X23)))) Prod))))
% 8.20/8.63 (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 ((X12 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X12) X23)))) Prod))))
% 8.20/8.63 (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 ((X12 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X12) X23)))) Prod))))
% 8.20/8.63 (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 ((X12 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X12) X23)))) Prod))))
% 8.20/8.63 (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 ((X12 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X12) X23)))) Prod))))
% 8.20/8.63 (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 ((X12 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X12) X23)))) Prod))))
% 8.20/8.63 (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 ((X12 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X12) X23)))) Prod))))
% 8.20/8.63 (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 ((X12 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X12) X23)))) Prod))))
% 8.20/8.63 (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 ((X12 tptp.nat) (X23 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ H (@ (@ F X12) X23)) __flatten_var_0))) Prod))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M)))
% 8.20/8.63 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)))))))
% 8.20/8.63 (assert (forall ((A tptp.rat) (C2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C2) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ _let_1 B))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)) (@ _let_1 B))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C2) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ _let_1 B))))))
% 8.20/8.63 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C2)) (@ _let_1 C2))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2)) (@ _let_1 C2))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C2)) (@ _let_1 C2))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K2))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))))))
% 8.20/8.63 (assert (= tptp.dvd_dvd_int (lambda ((D5 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int D5)) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.dvd_dvd_int (lambda ((D5 tptp.int) (T4 tptp.int)) (@ (@ tptp.dvd_dvd_int D5) (@ tptp.uminus_uminus_int T4)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2))))
% 8.20/8.63 (assert (forall ((P3 tptp.produc3925858234332021118et_nat)) (= (@ (@ tptp.produc4058941399401191971et_nat tptp.produc5001842942810119800et_nat) P3) P3)))
% 8.20/8.63 (assert (forall ((P3 tptp.produc2732055786443039994et_nat)) (= (@ (@ tptp.produc2377985495875741467et_nat tptp.produc2245416461498447860et_nat) P3) P3)))
% 8.20/8.63 (assert (forall ((P3 tptp.produc7388388658123137530it_nat)) (= (@ (@ tptp.produc7293086598567236123it_nat tptp.produc4082563078715348724it_nat) P3) P3)))
% 8.20/8.63 (assert (forall ((P3 tptp.produc3260487557148687353it_nat)) (= (@ (@ tptp.produc2183267410226956569it_nat tptp.produc9178034014595674355it_nat) P3) P3)))
% 8.20/8.63 (assert (forall ((P3 tptp.product_prod_int_int)) (= (@ (@ tptp.produc4245557441103728435nt_int tptp.product_Pair_int_int) P3) P3)))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N2) K2)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.nat2 K2))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.nat2 K2)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N2) K2))))))
% 8.20/8.63 (assert (forall ((Q2 (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)) (P2 (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Z3 tptp.product_prod_nat_nat)) (=> (@ Q2 (@ (@ tptp.produc27273713700761075at_nat P2) Z3)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= Z3 (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ Q2 (@ (@ P2 X3) Y3)))))))))
% 8.20/8.63 (assert (forall ((Q2 (-> (-> tptp.product_prod_nat_nat Bool) Bool)) (P2 (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (Z3 tptp.product_prod_nat_nat)) (=> (@ Q2 (@ (@ tptp.produc8739625826339149834_nat_o P2) Z3)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= Z3 (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ Q2 (@ (@ P2 X3) Y3)))))))))
% 8.20/8.63 (assert (forall ((Q2 (-> tptp.product_prod_int_int Bool)) (P2 (-> tptp.int tptp.int tptp.product_prod_int_int)) (Z3 tptp.product_prod_int_int)) (=> (@ Q2 (@ (@ tptp.produc4245557441103728435nt_int P2) Z3)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z3 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q2 (@ (@ P2 X3) Y3)))))))))
% 8.20/8.63 (assert (forall ((Q2 (-> Bool Bool)) (P2 (-> tptp.int tptp.int Bool)) (Z3 tptp.product_prod_int_int)) (=> (@ Q2 (@ (@ tptp.produc4947309494688390418_int_o P2) Z3)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z3 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q2 (@ (@ P2 X3) Y3)))))))))
% 8.20/8.63 (assert (forall ((Q2 (-> tptp.int Bool)) (P2 (-> tptp.int tptp.int tptp.int)) (Z3 tptp.product_prod_int_int)) (=> (@ Q2 (@ (@ tptp.produc8211389475949308722nt_int P2) Z3)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z3 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q2 (@ (@ P2 X3) Y3)))))))))
% 8.20/8.63 (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)))
% 8.20/8.63 (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)))
% 8.20/8.63 (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)))
% 8.20/8.63 (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)))
% 8.20/8.63 (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)))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) A)))) (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) B)))) (@ (@ tptp.dvd_dvd_nat A) B))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) A)))) (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) B)))) (@ (@ tptp.dvd_dvd_int A) B))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (= (@ _let_1 K2) (@ tptp.bit_se2000444600071755411sk_int N2)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K2) tptp.one_one_int)) tptp.zero_zero_int)))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) A)))) (@ tptp.collect_nat (lambda ((C3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C3) B)))) (and (@ (@ tptp.dvd_dvd_nat A) B) (not (@ (@ tptp.dvd_dvd_nat B) A))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) A)))) (@ tptp.collect_int (lambda ((C3 tptp.int)) (@ (@ tptp.dvd_dvd_int C3) B)))) (and (@ (@ tptp.dvd_dvd_int A) B) (not (@ (@ tptp.dvd_dvd_int B) A))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K2) (@ tptp.bit_se2000444600071755411sk_int N2)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.plus_plus_int K2) tptp.one_one_int)))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K2)) (@ (@ tptp.bit_se2923211474154528505it_int N2) K2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K2)) K2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K2))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K2))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) K2)) (@ _let_1 tptp.zero_zero_int)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K2)) tptp.zero_zero_int))))
% 8.20/8.63 (assert (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X6) S2)))) (=> (@ (@ tptp.ord_less_rat Z2) X6) (= _let_1 _let_1)))))))
% 8.20/8.63 (assert (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X6) S2)))) (=> (@ (@ tptp.ord_less_nat Z2) X6) (= _let_1 _let_1)))))))
% 8.20/8.63 (assert (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X6) S2)))) (=> (@ (@ tptp.ord_less_int Z2) X6) (= _let_1 _let_1)))))))
% 8.20/8.63 (assert (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X6) S2))))) (=> (@ (@ tptp.ord_less_rat Z2) X6) (= _let_1 _let_1)))))))
% 8.20/8.63 (assert (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X6) S2))))) (=> (@ (@ tptp.ord_less_nat Z2) X6) (= _let_1 _let_1)))))))
% 8.20/8.63 (assert (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X6) S2))))) (=> (@ (@ tptp.ord_less_int Z2) X6) (= _let_1 _let_1)))))))
% 8.20/8.63 (assert (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X6) S2)))) (=> (@ (@ tptp.ord_less_rat X6) Z2) (= _let_1 _let_1)))))))
% 8.20/8.63 (assert (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X6) S2)))) (=> (@ (@ tptp.ord_less_nat X6) Z2) (= _let_1 _let_1)))))))
% 8.20/8.63 (assert (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X6) S2)))) (=> (@ (@ tptp.ord_less_int X6) Z2) (= _let_1 _let_1)))))))
% 8.20/8.63 (assert (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X6 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X6) S2))))) (=> (@ (@ tptp.ord_less_rat X6) Z2) (= _let_1 _let_1)))))))
% 8.20/8.63 (assert (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X6 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X6) S2))))) (=> (@ (@ tptp.ord_less_nat X6) Z2) (= _let_1 _let_1)))))))
% 8.20/8.63 (assert (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X6 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X6) S2))))) (=> (@ (@ tptp.ord_less_int X6) Z2) (= _let_1 _let_1)))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C2) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C2)) (@ (@ tptp.divide_divide_nat B) C2))))))
% 8.20/8.63 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C2) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C2)) (@ (@ tptp.divide_divide_int B) C2))))))
% 8.20/8.63 (assert (forall ((C2 tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural C2) A) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) C2) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.divide5121882707175180666atural A) C2)) (@ (@ tptp.divide5121882707175180666atural B) C2))))))
% 8.20/8.63 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C2) B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C2)) (@ (@ tptp.divide_divide_nat B) C2))))))
% 8.20/8.63 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C2) B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C2)) (@ (@ tptp.divide_divide_int B) C2))))))
% 8.20/8.63 (assert (forall ((C2 tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural C2) B) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) C2) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.divide5121882707175180666atural A) C2)) (@ (@ tptp.divide5121882707175180666atural B) C2))))))
% 8.20/8.63 (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)))))))))))
% 8.20/8.63 (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)))))))))))
% 8.20/8.63 (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)))))))))))
% 8.20/8.63 (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)))))))))))
% 8.20/8.63 (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)))))))))))
% 8.20/8.63 (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)))))))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 N2)))))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K2))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 M)))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (M tptp.int) (T6 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K2))) (=> (not (= K2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int M) T6) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 T6)))))))
% 8.20/8.63 (assert (forall ((D2 tptp.nat) (A tptp.nat) (B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D2))) (=> (@ _let_3 A) (=> (@ _let_3 B) (=> (or (= (@ _let_1 X) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D2)) (= (@ _let_2 X) (@ (@ tptp.plus_plus_nat (@ _let_1 Y)) D2))) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A) B))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D2)) (= (@ _let_3 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D2)))))))))))))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D)) (= (@ _let_2 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D))))))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (N2 tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N2) (@ (@ tptp.times_times_int K2) M))) (@ _let_1 N2)))))
% 8.20/8.63 (assert (forall ((A tptp.int) (D2 tptp.int) (X tptp.int) (T6 tptp.int) (C2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int A))) (=> (@ _let_2 D2) (= (@ _let_2 (@ _let_1 T6)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.times_times_int C2) D2))) T6))))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (= tptp.uncurr8011562610307062878at_nat tptp.produc27273713700761075at_nat))
% 8.20/8.63 (assert (= tptp.uncurr7511940902602773877_nat_o tptp.produc8739625826339149834_nat_o))
% 8.20/8.63 (assert (= tptp.uncurr7650761721940715016nt_int tptp.produc4245557441103728435nt_int))
% 8.20/8.63 (assert (= tptp.uncurry_int_int_o tptp.produc4947309494688390418_int_o))
% 8.20/8.63 (assert (= tptp.uncurry_int_int_int tptp.produc8211389475949308722nt_int))
% 8.20/8.63 (assert (= tptp.produc1854806715440696265at_nat tptp.produc27273713700761075at_nat))
% 8.20/8.63 (assert (= tptp.produc4780622933104268256_nat_o tptp.produc8739625826339149834_nat_o))
% 8.20/8.63 (assert (= tptp.produc297006045350968285nt_int tptp.produc4245557441103728435nt_int))
% 8.20/8.63 (assert (= tptp.produc8005341501107743676_int_o tptp.produc4947309494688390418_int_o))
% 8.20/8.63 (assert (= tptp.produc7926200574084438792nt_int tptp.produc8211389475949308722nt_int))
% 8.20/8.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N2))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N2)) tptp.zero_zero_int))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z3))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 Z3)) M) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z3) (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.code_integer Bool)) (L tptp.code_integer)) (= (exists ((X4 tptp.code_integer)) (@ P2 (@ (@ tptp.times_3573771949741848930nteger L) X4))) (exists ((X4 tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L) (@ (@ tptp.plus_p5714425477246183910nteger X4) tptp.zero_z3403309356797280102nteger)) (@ P2 X4))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.rat Bool)) (L tptp.rat)) (= (exists ((X4 tptp.rat)) (@ P2 (@ (@ tptp.times_times_rat L) X4))) (exists ((X4 tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L) (@ (@ tptp.plus_plus_rat X4) tptp.zero_zero_rat)) (@ P2 X4))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X4 tptp.nat)) (@ P2 (@ (@ tptp.times_times_nat L) X4))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X4) tptp.zero_zero_nat)) (@ P2 X4))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X4 tptp.int)) (@ P2 (@ (@ tptp.times_times_int L) X4))) (exists ((X4 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X4) tptp.zero_zero_int)) (@ P2 X4))))))
% 8.20/8.63 (assert (forall ((D2 tptp.rat) (D4 tptp.rat) (T6 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D4) (forall ((X6 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X6) T6)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K4) D4))) T6))))))))
% 8.20/8.63 (assert (forall ((D2 tptp.int) (D4 tptp.int) (T6 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X6 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X6) T6)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K4) D4))) T6))))))))
% 8.20/8.63 (assert (forall ((D2 tptp.rat) (D4 tptp.rat) (T6 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D4) (forall ((X6 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X6) T6))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K4) D4))) T6)))))))))
% 8.20/8.63 (assert (forall ((D2 tptp.int) (D4 tptp.int) (T6 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X6 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X6) T6))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K4) D4))) T6)))))))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K2) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat K2) N2)))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D tptp.nat) (X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) D))))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z3) N2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (@ (@ tptp.ord_less_eq_int Z3) N2)))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K2)) (@ tptp.semiri773545260158071498ct_rat N2))) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.plus_plus_nat K2) N2)))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K2)) (@ tptp.semiri1406184849735516958ct_int N2))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K2) N2)))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K2)) (@ tptp.semiri1408675320244567234ct_nat N2))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K2) N2)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.nat2 K2)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) K2))))))
% 8.20/8.63 (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))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 8.20/8.63 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural A) B)))))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K2)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N2) K2)))) (@ tptp.semiri773545260158071498ct_rat N2)))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K2)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N2) K2)))) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K2)))) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N2) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))))
% 8.20/8.63 (assert (forall ((Q6 tptp.nat) (N2 tptp.nat) (R2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R2) 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)))))))))))
% 8.20/8.63 (assert (forall ((R2 tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R2) N2) (=> (@ (@ tptp.ord_less_eq_nat R2) M) (=> (@ (@ tptp.dvd_dvd_nat N2) (@ (@ tptp.minus_minus_nat M) R2)) (= (@ (@ tptp.modulo_modulo_nat M) N2) R2))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K2) L)) (or (@ (@ tptp.dvd_dvd_int L) K2) (and (= L tptp.zero_zero_int) (@ _let_1 K2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int K2) L)) (@ _let_1 (@ (@ tptp.plus_plus_int K2) L))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K2))) (let ((_let_2 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ _let_1 (@ tptp.abs_abs_int L))) (@ _let_2 (@ _let_1 L)))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int K2)) L)) (@ _let_1 (@ (@ tptp.plus_plus_int K2) L))))))
% 8.20/8.63 (assert (forall ((K2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K2))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K2) (@ (@ tptp.bit_se2923211474154528505it_int N2) K2)) (@ (@ tptp.ord_less_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K2)) K2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K2))))
% 8.20/8.63 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_nat))))))))
% 8.20/8.63 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_int))))))))
% 8.20/8.63 (assert (forall ((A tptp.code_natural)) (=> (not (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.code_natural)) (not (= A (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_Code_natural))))))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_Code_integer))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (=> (@ (@ tptp.ord_less_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K2) K2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K2) K2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (@ (@ tptp.ord_less_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 K2))) (=> (not (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int K2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_2)))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_se569199155075624693atural (@ tptp.suc N2)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 K2))) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural N2) (@ tptp.numera5444537566228673987atural K2))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_natural))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N2)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 K2))) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ tptp.numera6620942414471956472nteger K2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K2))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.numeral_numeral_int K2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K2))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat K2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q8 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q8))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 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) K2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K2)) (@ (@ tptp.minus_minus_int K2) _let_1)))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K2)))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc tptp.zero_zero_nat))) (=> (= (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) _let_3)) _let_2))))))))
% 8.20/8.63 (assert (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_se569199155075624693atural (@ tptp.numeral_numeral_nat L)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 K2))) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural (@ tptp.pred_numeral L)) (@ tptp.numera5444537566228673987atural K2))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_natural))))
% 8.20/8.63 (assert (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.numeral_numeral_nat L)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 K2))) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.pred_numeral L)) (@ tptp.numera6620942414471956472nteger K2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer))))
% 8.20/8.63 (assert (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K2))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((L tptp.num) (K2 tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K2))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 8.20/8.63 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q8 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q8))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 8.20/8.63 (assert (forall ((K2 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) K2) (=> (@ (@ tptp.ord_less_eq_int K2) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int K2)) (@ (@ tptp.minus_minus_int _let_1) K2)))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K2)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K2))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 8.20/8.63 (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)))))))))))))
% 8.20/8.63 (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)))))))))))))
% 8.20/8.63 (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)))))))))))))
% 8.20/8.63 (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)))))))))))))
% 8.20/8.63 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q8 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q8))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q8 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q8))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q8 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q8))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 8.20/8.63 (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 ((Q8 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 Q8)))))) (@ (@ tptp.bit_take_bit_num _let_1) N2))))))
% 8.20/8.63 (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 ((Q8 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q8)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M3) N)) N))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 8.20/8.63 (assert (forall ((X2 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X2)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 8.20/8.63 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K3 tptp.zero_zero_int) (= L2 tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K3 _let_2)) L2) (@ (@ (@ tptp.if_int (= L2 _let_2)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 8.20/8.63 (assert (forall ((P3 tptp.produc3925858234332021118et_nat) (C2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool))) (=> (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3658429121746597890et_nat)) (=> (= P3 (@ (@ tptp.produc5001842942810119800et_nat A3) B3)) (@ (@ C2 A3) B3))) (@ (@ tptp.produc1437786849005270451_nat_o C2) P3))))
% 8.20/8.63 (assert (forall ((P3 tptp.produc2732055786443039994et_nat) (C2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool))) (=> (forall ((A3 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3925858234332021118et_nat)) (=> (= P3 (@ (@ tptp.produc2245416461498447860et_nat A3) B3)) (@ (@ C2 A3) B3))) (@ (@ tptp.produc838355143741117751_nat_o C2) P3))))
% 8.20/8.63 (assert (forall ((P3 tptp.produc7388388658123137530it_nat) (C2 (-> tptp.b tptp.produc6653097349344004940it_nat Bool))) (=> (forall ((A3 tptp.b) (B3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc4082563078715348724it_nat A3) B3)) (@ (@ C2 A3) B3))) (@ (@ tptp.produc3971132677695353399_nat_o C2) P3))))
% 8.20/8.63 (assert (forall ((P3 tptp.produc3260487557148687353it_nat) (C2 (-> tptp.a tptp.produc6653097349344004940it_nat Bool))) (=> (forall ((A3 tptp.a) (B3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat A3) B3)) (@ (@ C2 A3) B3))) (@ (@ tptp.produc8860486935419594360_nat_o C2) P3))))
% 8.20/8.63 (assert (forall ((P3 tptp.product_prod_int_int) (C2 (-> tptp.int tptp.int Bool))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= P3 (@ (@ tptp.product_Pair_int_int A3) B3)) (@ (@ C2 A3) B3))) (@ (@ tptp.produc4947309494688390418_int_o C2) P3))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((F (-> tptp.b tptp.produc6653097349344004940it_nat Bool)) (A tptp.b) (B tptp.produc6653097349344004940it_nat)) (=> (@ (@ F A) B) (@ (@ tptp.produc3971132677695353399_nat_o F) (@ (@ tptp.produc4082563078715348724it_nat A) B)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((P3 tptp.product_prod_int_int) (Z3 Bool) (C2 (-> tptp.int tptp.int tptp.set_o))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= P3 (@ (@ tptp.product_Pair_int_int A3) B3)) (@ (@ tptp.member_o Z3) (@ (@ C2 A3) B3)))) (@ (@ tptp.member_o Z3) (@ (@ tptp.produc4257766111578684402_set_o C2) P3)))))
% 8.20/8.63 (assert (forall ((P3 tptp.product_prod_int_int) (Z3 tptp.nat) (C2 (-> tptp.int tptp.int tptp.set_nat))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= P3 (@ (@ tptp.product_Pair_int_int A3) B3)) (@ (@ tptp.member_nat Z3) (@ (@ C2 A3) B3)))) (@ (@ tptp.member_nat Z3) (@ (@ tptp.produc4251311855443802252et_nat C2) P3)))))
% 8.20/8.63 (assert (forall ((P3 tptp.product_prod_int_int) (Z3 tptp.int) (C2 (-> tptp.int tptp.int tptp.set_int))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= P3 (@ (@ tptp.product_Pair_int_int A3) B3)) (@ (@ tptp.member_int Z3) (@ (@ C2 A3) B3)))) (@ (@ tptp.member_int Z3) (@ (@ tptp.produc73460835934605544et_int C2) P3)))))
% 8.20/8.63 (assert (forall ((P3 tptp.product_prod_int_int) (Z3 tptp.set_nat) (C2 (-> tptp.int tptp.int tptp.set_set_nat))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= P3 (@ (@ tptp.product_Pair_int_int A3) B3)) (@ (@ tptp.member_set_nat Z3) (@ (@ C2 A3) B3)))) (@ (@ tptp.member_set_nat Z3) (@ (@ tptp.produc5233655623923918146et_nat C2) P3)))))
% 8.20/8.63 (assert (forall ((P3 tptp.product_prod_int_int) (Z3 tptp.set_Pr958786334691620121nt_int) (C2 (-> tptp.int tptp.int tptp.set_se6260736226359567993nt_int))) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= P3 (@ (@ tptp.product_Pair_int_int A3) B3)) (@ (@ tptp.member2340774599025711042nt_int Z3) (@ (@ C2 A3) B3)))) (@ (@ tptp.member2340774599025711042nt_int Z3) (@ (@ tptp.produc7771776839612048883nt_int C2) P3)))))
% 8.20/8.63 (assert (forall ((P3 tptp.produc7388388658123137530it_nat) (Z3 Bool) (C2 (-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_o))) (=> (forall ((A3 tptp.b) (B3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc4082563078715348724it_nat A3) B3)) (@ (@ tptp.member_o Z3) (@ (@ C2 A3) B3)))) (@ (@ tptp.member_o Z3) (@ (@ tptp.produc8188766211626073367_set_o C2) P3)))))
% 8.20/8.63 (assert (forall ((P3 tptp.produc7388388658123137530it_nat) (Z3 tptp.nat) (C2 (-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_nat))) (=> (forall ((A3 tptp.b) (B3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc4082563078715348724it_nat A3) B3)) (@ (@ tptp.member_nat Z3) (@ (@ C2 A3) B3)))) (@ (@ tptp.member_nat Z3) (@ (@ tptp.produc8058763169506871975et_nat C2) P3)))))
% 8.20/8.63 (assert (forall ((P3 tptp.produc7388388658123137530it_nat) (Z3 tptp.int) (C2 (-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_int))) (=> (forall ((A3 tptp.b) (B3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc4082563078715348724it_nat A3) B3)) (@ (@ tptp.member_int Z3) (@ (@ C2 A3) B3)))) (@ (@ tptp.member_int Z3) (@ (@ tptp.produc3880912149997675267et_int C2) P3)))))
% 8.20/8.63 (assert (forall ((P3 tptp.produc3260487557148687353it_nat) (Z3 Bool) (C2 (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_o))) (=> (forall ((A3 tptp.a) (B3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat A3) B3)) (@ (@ tptp.member_o Z3) (@ (@ C2 A3) B3)))) (@ (@ tptp.member_o Z3) (@ (@ tptp.produc5350075035600711000_set_o C2) P3)))))
% 8.20/8.63 (assert (forall ((P3 tptp.produc3260487557148687353it_nat) (Z3 tptp.nat) (C2 (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_nat))) (=> (forall ((A3 tptp.a) (B3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat A3) B3)) (@ (@ tptp.member_nat Z3) (@ (@ C2 A3) B3)))) (@ (@ tptp.member_nat Z3) (@ (@ tptp.produc7315013382793309350et_nat C2) P3)))))
% 8.20/8.63 (assert (forall ((Z3 Bool) (C2 (-> tptp.int tptp.int tptp.set_o)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_o Z3))) (=> (@ _let_1 (@ (@ C2 A) B)) (@ _let_1 (@ (@ tptp.produc4257766111578684402_set_o C2) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.nat) (C2 (-> tptp.int tptp.int tptp.set_nat)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_nat Z3))) (=> (@ _let_1 (@ (@ C2 A) B)) (@ _let_1 (@ (@ tptp.produc4251311855443802252et_nat C2) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (C2 (-> tptp.int tptp.int tptp.set_int)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_int Z3))) (=> (@ _let_1 (@ (@ C2 A) B)) (@ _let_1 (@ (@ tptp.produc73460835934605544et_int C2) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.set_nat) (C2 (-> tptp.int tptp.int tptp.set_set_nat)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_set_nat Z3))) (=> (@ _let_1 (@ (@ C2 A) B)) (@ _let_1 (@ (@ tptp.produc5233655623923918146et_nat C2) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.set_Pr958786334691620121nt_int) (C2 (-> tptp.int tptp.int tptp.set_se6260736226359567993nt_int)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int Z3))) (=> (@ _let_1 (@ (@ C2 A) B)) (@ _let_1 (@ (@ tptp.produc7771776839612048883nt_int C2) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 8.20/8.63 (assert (forall ((Z3 Bool) (C2 (-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_o)) (A tptp.b) (B tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.member_o Z3))) (=> (@ _let_1 (@ (@ C2 A) B)) (@ _let_1 (@ (@ tptp.produc8188766211626073367_set_o C2) (@ (@ tptp.produc4082563078715348724it_nat A) B)))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.nat) (C2 (-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_nat)) (A tptp.b) (B tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.member_nat Z3))) (=> (@ _let_1 (@ (@ C2 A) B)) (@ _let_1 (@ (@ tptp.produc8058763169506871975et_nat C2) (@ (@ tptp.produc4082563078715348724it_nat A) B)))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (C2 (-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_int)) (A tptp.b) (B tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.member_int Z3))) (=> (@ _let_1 (@ (@ C2 A) B)) (@ _let_1 (@ (@ tptp.produc3880912149997675267et_int C2) (@ (@ tptp.produc4082563078715348724it_nat A) B)))))))
% 8.20/8.63 (assert (forall ((Z3 Bool) (C2 (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_o)) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.member_o Z3))) (=> (@ _let_1 (@ (@ C2 A) B)) (@ _let_1 (@ (@ tptp.produc5350075035600711000_set_o C2) (@ (@ tptp.produc9178034014595674355it_nat A) B)))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.nat) (C2 (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_nat)) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.member_nat Z3))) (=> (@ _let_1 (@ (@ C2 A) B)) (@ _let_1 (@ (@ tptp.produc7315013382793309350et_nat C2) (@ (@ tptp.produc9178034014595674355it_nat A) B)))))))
% 8.20/8.63 (assert (forall ((P3 tptp.product_prod_nat_nat) (C2 (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A3) B3) P3) (@ (@ (@ C2 A3) B3) X))) (@ (@ (@ tptp.produc8739625826339149834_nat_o C2) P3) X))))
% 8.20/8.63 (assert (forall ((P2 Bool) (Q2 Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) (@ tptp.zero_n2052037380579107095ol_rat Q2)) (=> P2 Q2))))
% 8.20/8.63 (assert (forall ((P2 Bool) (Q2 Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n2687167440665602831ol_nat Q2)) (=> P2 Q2))))
% 8.20/8.63 (assert (forall ((P2 Bool) (Q2 Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P2)) (@ tptp.zero_n2684676970156552555ol_int Q2)) (=> P2 Q2))))
% 8.20/8.63 (assert (forall ((P2 Bool) (Q2 Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P2)) (@ tptp.zero_n356916108424825756nteger Q2)) (=> P2 Q2))))
% 8.20/8.63 (assert (forall ((P2 Bool) (Q2 Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) (@ tptp.zero_n2052037380579107095ol_rat Q2)) (and (not P2) Q2))))
% 8.20/8.63 (assert (forall ((P2 Bool) (Q2 Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n2687167440665602831ol_nat Q2)) (and (not P2) Q2))))
% 8.20/8.63 (assert (forall ((P2 Bool) (Q2 Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P2)) (@ tptp.zero_n2684676970156552555ol_int Q2)) (and (not P2) Q2))))
% 8.20/8.63 (assert (forall ((P2 Bool) (Q2 Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P2)) (@ tptp.zero_n356916108424825756nteger Q2)) (and (not P2) Q2))))
% 8.20/8.63 (assert (forall ((P2 Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 8.20/8.63 (assert (forall ((P2 Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n2684676970156552555ol_int P2))))
% 8.20/8.63 (assert (forall ((P2 Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n356916108424825756nteger P2))))
% 8.20/8.63 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P2)) P2)))
% 8.20/8.63 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P2)) P2)))
% 8.20/8.63 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P2)) P2)))
% 8.20/8.63 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P2)) P2)))
% 8.20/8.63 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) tptp.one_one_rat) (not P2))))
% 8.20/8.63 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) tptp.one_one_nat) (not P2))))
% 8.20/8.63 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P2)) tptp.one_one_int) (not P2))))
% 8.20/8.63 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P2)) tptp.one_one_Code_integer) (not P2))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K2) L)) (or (@ _let_1 K2) (@ _let_1 L))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int K2) L)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))
% 8.20/8.63 (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 ((Q8 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q8)))) (@ (@ tptp.bit_take_bit_num N2) M)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (assert (forall ((R2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q8 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q8)))) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R2)) M)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((R2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R2)) M))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se2773287842338716102atural (@ tptp.numera5444537566228673987atural (@ tptp.bit1 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_se2773287842338716102atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y)))))))
% 8.20/8.63 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y)))))))
% 8.20/8.63 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 8.20/8.63 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (= tptp.same_fst_int_int (lambda ((P5 (-> tptp.int Bool)) (R (-> tptp.int tptp.set_Pr958786334691620121nt_int))) (@ tptp.collec7447955092554649554nt_int (@ tptp.produc1676490119946744748_int_o (@ tptp.produc1459180154077124618_int_o (lambda ((X8 tptp.int) (Y9 tptp.int) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((X4 tptp.int) (Y4 tptp.int)) (and (= X8 X4) (@ P5 X4) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y9) Y4)) (@ R X4))))) __flatten_var_0))))))))
% 8.20/8.63 (assert (= tptp.same_fst_nat_nat (lambda ((P5 (-> tptp.nat Bool)) (R (-> tptp.nat tptp.set_Pr1261947904930325089at_nat))) (@ tptp.collec7088162979684241874at_nat (@ tptp.produc6590410687421337004_nat_o (@ tptp.produc8739625826339149834_nat_o (lambda ((X8 tptp.nat) (Y9 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (= X8 X4) (@ P5 X4) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y9) Y4)) (@ R X4))))) __flatten_var_0))))))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (=> (@ (@ tptp.dvd_dvd_nat N2) M) (= M N2)))))
% 8.20/8.63 (assert (= tptp.lex_prod_int_int (lambda ((Ra tptp.set_Pr958786334691620121nt_int) (Rb tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec7447955092554649554nt_int (@ tptp.produc1676490119946744748_int_o (@ tptp.produc1459180154077124618_int_o (lambda ((A5 tptp.int) (B4 tptp.int) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A8 tptp.int) (B8 tptp.int)) (or (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A5) A8)) Ra) (and (= A5 A8) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B4) B8)) Rb))))) __flatten_var_0))))))))
% 8.20/8.63 (assert (= tptp.lex_prod_nat_nat (lambda ((Ra tptp.set_Pr1261947904930325089at_nat) (Rb tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec7088162979684241874at_nat (@ tptp.produc6590410687421337004_nat_o (@ tptp.produc8739625826339149834_nat_o (lambda ((A5 tptp.nat) (B4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((A8 tptp.nat) (B8 tptp.nat)) (or (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A5) A8)) Ra) (and (= A5 A8) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B4) B8)) Rb))))) __flatten_var_0))))))))
% 8.20/8.63 (assert (forall ((Z3 Bool) (C2 (-> tptp.int tptp.int tptp.set_o)) (P3 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_o Z3) (@ (@ tptp.produc4257766111578684402_set_o C2) P3)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P3 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ tptp.member_o Z3) (@ (@ C2 X3) Y3)))))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.nat) (C2 (-> tptp.int tptp.int tptp.set_nat)) (P3 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_nat Z3) (@ (@ tptp.produc4251311855443802252et_nat C2) P3)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P3 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ tptp.member_nat Z3) (@ (@ C2 X3) Y3)))))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (C2 (-> tptp.int tptp.int tptp.set_int)) (P3 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_int Z3) (@ (@ tptp.produc73460835934605544et_int C2) P3)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P3 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ tptp.member_int Z3) (@ (@ C2 X3) Y3)))))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.set_nat) (C2 (-> tptp.int tptp.int tptp.set_set_nat)) (P3 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_set_nat Z3) (@ (@ tptp.produc5233655623923918146et_nat C2) P3)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P3 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ tptp.member_set_nat Z3) (@ (@ C2 X3) Y3)))))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.set_Pr958786334691620121nt_int) (C2 (-> tptp.int tptp.int tptp.set_se6260736226359567993nt_int)) (P3 tptp.product_prod_int_int)) (=> (@ (@ tptp.member2340774599025711042nt_int Z3) (@ (@ tptp.produc7771776839612048883nt_int C2) P3)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P3 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ tptp.member2340774599025711042nt_int Z3) (@ (@ C2 X3) Y3)))))))))
% 8.20/8.63 (assert (forall ((Z3 Bool) (C2 (-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_o)) (P3 tptp.produc7388388658123137530it_nat)) (=> (@ (@ tptp.member_o Z3) (@ (@ tptp.produc8188766211626073367_set_o C2) P3)) (not (forall ((X3 tptp.b) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc4082563078715348724it_nat X3) Y3)) (not (@ (@ tptp.member_o Z3) (@ (@ C2 X3) Y3)))))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.nat) (C2 (-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_nat)) (P3 tptp.produc7388388658123137530it_nat)) (=> (@ (@ tptp.member_nat Z3) (@ (@ tptp.produc8058763169506871975et_nat C2) P3)) (not (forall ((X3 tptp.b) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc4082563078715348724it_nat X3) Y3)) (not (@ (@ tptp.member_nat Z3) (@ (@ C2 X3) Y3)))))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.int) (C2 (-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_int)) (P3 tptp.produc7388388658123137530it_nat)) (=> (@ (@ tptp.member_int Z3) (@ (@ tptp.produc3880912149997675267et_int C2) P3)) (not (forall ((X3 tptp.b) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc4082563078715348724it_nat X3) Y3)) (not (@ (@ tptp.member_int Z3) (@ (@ C2 X3) Y3)))))))))
% 8.20/8.63 (assert (forall ((Z3 Bool) (C2 (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_o)) (P3 tptp.produc3260487557148687353it_nat)) (=> (@ (@ tptp.member_o Z3) (@ (@ tptp.produc5350075035600711000_set_o C2) P3)) (not (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat X3) Y3)) (not (@ (@ tptp.member_o Z3) (@ (@ C2 X3) Y3)))))))))
% 8.20/8.63 (assert (forall ((Z3 tptp.nat) (C2 (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_nat)) (P3 tptp.produc3260487557148687353it_nat)) (=> (@ (@ tptp.member_nat Z3) (@ (@ tptp.produc7315013382793309350et_nat C2) P3)) (not (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat X3) Y3)) (not (@ (@ tptp.member_nat Z3) (@ (@ C2 X3) Y3)))))))))
% 8.20/8.63 (assert (forall ((C2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool)) (P3 tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.produc1437786849005270451_nat_o C2) P3) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 tptp.produc3658429121746597890et_nat)) (=> (= P3 (@ (@ tptp.produc5001842942810119800et_nat X3) Y3)) (not (@ (@ C2 X3) Y3))))))))
% 8.20/8.63 (assert (forall ((C2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool)) (P3 tptp.produc2732055786443039994et_nat)) (=> (@ (@ tptp.produc838355143741117751_nat_o C2) P3) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 tptp.produc3925858234332021118et_nat)) (=> (= P3 (@ (@ tptp.produc2245416461498447860et_nat X3) Y3)) (not (@ (@ C2 X3) Y3))))))))
% 8.20/8.63 (assert (forall ((C2 (-> tptp.b tptp.produc6653097349344004940it_nat Bool)) (P3 tptp.produc7388388658123137530it_nat)) (=> (@ (@ tptp.produc3971132677695353399_nat_o C2) P3) (not (forall ((X3 tptp.b) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc4082563078715348724it_nat X3) Y3)) (not (@ (@ C2 X3) Y3))))))))
% 8.20/8.63 (assert (forall ((C2 (-> tptp.a tptp.produc6653097349344004940it_nat Bool)) (P3 tptp.produc3260487557148687353it_nat)) (=> (@ (@ tptp.produc8860486935419594360_nat_o C2) P3) (not (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat X3) Y3)) (not (@ (@ C2 X3) Y3))))))))
% 8.20/8.63 (assert (forall ((C2 (-> tptp.int tptp.int Bool)) (P3 tptp.product_prod_int_int)) (=> (@ (@ tptp.produc4947309494688390418_int_o C2) P3) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P3 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ C2 X3) Y3))))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((F (-> tptp.b tptp.produc6653097349344004940it_nat Bool)) (A tptp.b) (B tptp.produc6653097349344004940it_nat)) (=> (@ (@ tptp.produc3971132677695353399_nat_o F) (@ (@ tptp.produc4082563078715348724it_nat A) B)) (@ (@ F A) B))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((C2 (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (P3 tptp.product_prod_nat_nat) (Z3 tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o C2) P3) Z3) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P3 (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ (@ (@ C2 X3) Y3) Z3))))))))
% 8.20/8.63 (assert (forall ((R3 (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat) (C2 tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o R3) (@ (@ tptp.product_Pair_nat_nat A) B)) C2) (@ (@ (@ R3 A) B) C2))))
% 8.20/8.63 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P2))))
% 8.20/8.63 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P2))))
% 8.20/8.63 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P2))))
% 8.20/8.63 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P2))))
% 8.20/8.63 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) tptp.one_one_rat)))
% 8.20/8.63 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) tptp.one_one_nat)))
% 8.20/8.63 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P2)) tptp.one_one_int)))
% 8.20/8.63 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P2)) tptp.one_one_Code_integer)))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((Y tptp.int) (Z3 tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z3)))))
% 8.20/8.63 (assert (forall ((Y tptp.int) (Z3 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z3)))))
% 8.20/8.63 (assert (forall ((A4 (-> tptp.int tptp.int Bool)) (B5 (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.ord_le6741204236512500942_int_o A4) B5) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o A4))) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o B5))))))
% 8.20/8.63 (assert (forall ((F tptp.heap_Time_Heap_b) (G (-> tptp.b tptp.heap_Time_Heap_b)) (H tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.heap_Time_execute_b (@ (@ tptp.heap_Time_bind_b_b F) G)) H) (@ (@ (@ tptp.case_o5901184372446974929it_nat tptp.none_P6779099274072355161it_nat) (@ tptp.produc3931674313442123243it_nat (lambda ((X4 tptp.b) (__flatten_var_0 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.produc6148253707941125437it_nat (lambda ((H7 tptp.heap_e7401611519738050253t_unit) (N tptp.nat)) (@ (@ tptp.heap_T7616092557645711336rame_b N) (@ (@ tptp.heap_Time_execute_b (@ G X4)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_b F) H)))))
% 8.20/8.63 (assert (forall ((F tptp.heap_Time_Heap_a) (G (-> tptp.a tptp.heap_Time_Heap_b)) (H tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.heap_Time_execute_b (@ (@ tptp.heap_Time_bind_a_b F) G)) H) (@ (@ (@ tptp.case_o1773283271472524752it_nat tptp.none_P6779099274072355161it_nat) (@ tptp.produc8352694711413002346it_nat (lambda ((X4 tptp.a) (__flatten_var_0 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.produc6148253707941125437it_nat (lambda ((H7 tptp.heap_e7401611519738050253t_unit) (N tptp.nat)) (@ (@ tptp.heap_T7616092557645711336rame_b N) (@ (@ tptp.heap_Time_execute_b (@ G X4)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_a F) H)))))
% 8.20/8.63 (assert (forall ((F tptp.heap_Time_Heap_b) (G (-> tptp.b tptp.heap_Time_Heap_a)) (H tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_bind_b_a F) G)) H) (@ (@ (@ tptp.case_o965627003169710416it_nat tptp.none_P2651198173097904984it_nat) (@ tptp.produc3428986626803312746it_nat (lambda ((X4 tptp.b) (__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_b F) H)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 8.20/8.63 (assert (forall ((Y tptp.int) (Z3 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z3) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z3)))))
% 8.20/8.63 (assert (forall ((Y tptp.int) (Z3 tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z3) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z3)))))
% 8.20/8.63 (assert (forall ((L tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int K2) L)) K2))))
% 8.20/8.63 (assert (= tptp.heap_Time_bind_b_b (lambda ((F3 tptp.heap_Time_Heap_b) (G3 (-> tptp.b tptp.heap_Time_Heap_b))) (@ tptp.heap_Time_Heap_b2 (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ (@ tptp.case_o5901184372446974929it_nat tptp.none_P6779099274072355161it_nat) (@ tptp.produc3931674313442123243it_nat (lambda ((R5 tptp.b) (__flatten_var_0 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.produc6148253707941125437it_nat (lambda ((H7 tptp.heap_e7401611519738050253t_unit) (N tptp.nat)) (@ (@ tptp.heap_T7616092557645711336rame_b N) (@ (@ tptp.heap_Time_execute_b (@ G3 R5)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_b F3) H6)))))))
% 8.20/8.63 (assert (= tptp.heap_Time_bind_a_b (lambda ((F3 tptp.heap_Time_Heap_a) (G3 (-> tptp.a tptp.heap_Time_Heap_b))) (@ tptp.heap_Time_Heap_b2 (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ (@ tptp.case_o1773283271472524752it_nat tptp.none_P6779099274072355161it_nat) (@ tptp.produc8352694711413002346it_nat (lambda ((R5 tptp.a) (__flatten_var_0 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.produc6148253707941125437it_nat (lambda ((H7 tptp.heap_e7401611519738050253t_unit) (N tptp.nat)) (@ (@ tptp.heap_T7616092557645711336rame_b N) (@ (@ tptp.heap_Time_execute_b (@ G3 R5)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_a F3) H6)))))))
% 8.20/8.63 (assert (= tptp.heap_Time_bind_b_a (lambda ((F3 tptp.heap_Time_Heap_b) (G3 (-> tptp.b tptp.heap_Time_Heap_a))) (@ tptp.heap_Time_Heap_a2 (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ (@ tptp.case_o965627003169710416it_nat tptp.none_P2651198173097904984it_nat) (@ tptp.produc3428986626803312746it_nat (lambda ((R5 tptp.b) (__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 R5)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_b F3) H6)))))))
% 8.20/8.63 (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 ((R5 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 R5)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_a F3) H6)))))))
% 8.20/8.63 (assert (= tptp.heap_T3413130826733729493t_unit (lambda ((F3 tptp.heap_Time_Heap_b) (G3 (-> tptp.b tptp.heap_T5738788834812785303t_unit))) (@ tptp.heap_T6183433275982383450t_unit (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ (@ tptp.case_o2632329678403290591it_nat tptp.none_P9117596204409417319it_nat) (@ tptp.produc450363836004716793it_nat (lambda ((R5 tptp.b) (__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 R5)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_b F3) H6)))))))
% 8.20/8.63 (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 ((R5 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 R5)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_a F3) H6)))))))
% 8.20/8.63 (assert (= tptp.rel_of4838799251197538391et_nat (lambda ((M3 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.option936205604648967762et_nat)) (P5 (-> 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)) (@ P5 (@ (@ tptp.produc5001842942810119800et_nat K3) V2)))))))))
% 8.20/8.63 (assert (= tptp.rel_of7774016450764239315et_nat (lambda ((M3 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.option5190343406534369742et_nat)) (P5 (-> 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)) (@ P5 (@ (@ tptp.produc2245416461498447860et_nat K3) V2)))))))))
% 8.20/8.63 (assert (= tptp.rel_of6889123638293104083it_nat (lambda ((M3 (-> tptp.b tptp.option233860712434008220it_nat)) (P5 (-> tptp.produc7388388658123137530it_nat Bool))) (@ tptp.collec8276579174399660751it_nat (@ tptp.produc3971132677695353399_nat_o (lambda ((K3 tptp.b) (V2 tptp.produc6653097349344004940it_nat)) (and (= (@ M3 K3) (@ tptp.some_P1054239925786823975it_nat V2)) (@ P5 (@ (@ tptp.produc4082563078715348724it_nat K3) V2)))))))))
% 8.20/8.63 (assert (= tptp.rel_of2761222537318653906it_nat (lambda ((M3 (-> tptp.a tptp.option233860712434008220it_nat)) (P5 (-> 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)) (@ P5 (@ (@ tptp.produc9178034014595674355it_nat K3) V2)))))))))
% 8.20/8.63 (assert (= tptp.rel_of_int_int (lambda ((M3 (-> tptp.int tptp.option_int)) (P5 (-> 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)) (@ P5 (@ (@ tptp.product_Pair_int_int K3) V2)))))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.code_natural Bool)) (A tptp.code_natural)) (=> (forall ((A3 tptp.code_natural)) (=> (= (@ (@ tptp.divide5121882707175180666atural A3) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A3) (@ P2 A3))) (=> (forall ((A3 tptp.code_natural) (B3 Bool)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p4538020629002901425atural (@ tptp.zero_n8403883297036319079atural B3)) (@ (@ tptp.times_2397367101498566445atural _let_1) A3)))) (=> (@ P2 A3) (=> (= (@ (@ tptp.divide5121882707175180666atural _let_2) _let_1) A3) (@ P2 _let_2)))))) (@ P2 A)))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A3 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A3) (@ P2 A3))) (=> (forall ((A3 tptp.nat) (B3 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B3)) (@ (@ tptp.times_times_nat _let_1) A3)))) (=> (@ P2 A3) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A3) (@ P2 _let_2)))))) (@ P2 A)))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A3 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A3) (@ P2 A3))) (=> (forall ((A3 tptp.int) (B3 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B3)) (@ (@ tptp.times_times_int _let_1) A3)))) (=> (@ P2 A3) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A3) (@ P2 _let_2)))))) (@ P2 A)))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A3 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A3) (@ P2 A3))) (=> (forall ((A3 tptp.code_integer) (B3 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B3)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A3)))) (=> (@ P2 A3) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A3) (@ P2 _let_2)))))) (@ P2 A)))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (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))))))))
% 8.20/8.63 (assert (forall ((L tptp.int) (K2 tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M) N2))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.sgn_sgn_int K2))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int N2))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N2 tptp.zero_zero_nat)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (@ tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_5) (= _let_4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N2) M)))))))))))))))))))
% 8.20/8.63 (assert (= tptp.divide_divide_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 (@ tptp.abs_abs_int L2))))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) (@ tptp.sgn_sgn_int L2))) (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_int L2) K3))))))))))))
% 8.20/8.63 (assert (= tptp.mlex_prod_int (lambda ((F3 (-> tptp.int tptp.nat)) (R 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)) R)))))))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))))))))
% 8.20/8.63 (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)))))))))))))))
% 8.20/8.63 (assert (forall ((Q6 tptp.int) (R2 tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q6) R2)) (@ (@ tptp.plus_plus_int Q6) (@ tptp.zero_n2684676970156552555ol_int (not (= R2 tptp.zero_zero_int)))))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat X))) (let ((_let_2 (@ _let_1 A4))) (= (@ _let_1 _let_2) _let_2)))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_2 (@ _let_1 A4))) (= (@ _let_1 _let_2) _let_2)))))
% 8.20/8.63 (assert (forall ((X Bool) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ _let_1 A4))) (= (@ _let_1 _let_2) _let_2)))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ _let_1 A4))) (= (@ _let_1 _let_2) _let_2)))))
% 8.20/8.63 (assert (forall ((X tptp.int) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ _let_1 A4))) (= (@ _let_1 _let_2) _let_2)))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (B tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat A))) (= (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat B) A4)) (or (= A B) (@ _let_1 A4))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A))) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B) A4)) (or (= A B) (@ _let_1 A4))))))
% 8.20/8.63 (assert (forall ((A Bool) (B Bool) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o A))) (= (@ _let_1 (@ (@ tptp.insert_o B) A4)) (or (= A B) (@ _let_1 A4))))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (B tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int A))) (= (@ _let_1 (@ (@ tptp.insert8897473484851387113nt_int B) A4)) (or (= A B) (@ _let_1 A4))))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (A4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (= (@ _let_1 (@ (@ tptp.insert_set_nat B) A4)) (or (= A B) (@ _let_1 A4))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A))) (= (@ _let_1 (@ (@ tptp.insert_nat B) A4)) (or (= A B) (@ _let_1 A4))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A))) (= (@ _let_1 (@ (@ tptp.insert_int B) A4)) (or (= A B) (@ _let_1 A4))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (B tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat B) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B) B5))))))
% 8.20/8.63 (assert (forall ((A Bool) (B5 tptp.set_o) (B Bool)) (let ((_let_1 (@ tptp.member_o A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert_o B) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (B5 tptp.set_se6260736226359567993nt_int) (B tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert8897473484851387113nt_int B) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (B5 tptp.set_set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert_set_nat B) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B5 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert_nat B) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B5 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ tptp.member_int A))) (=> (=> (not (@ _let_1 B5)) (= A B)) (@ _let_1 (@ (@ tptp.insert_int B) B5))))))
% 8.20/8.63 (assert (forall ((P2 Bool) (Q2 (-> tptp.int tptp.int Bool))) (= (@ tptp.produc4947309494688390418_int_o (lambda ((A5 tptp.int) (B4 tptp.int)) (and P2 (@ (@ Q2 A5) B4)))) (lambda ((Ab tptp.product_prod_int_int)) (and P2 (@ (@ tptp.produc4947309494688390418_int_o Q2) Ab))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat A) (@ (@ tptp.insert9069300056098147895at_nat A) tptp.bot_bo228742789529271731at_nat))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int A) (@ (@ tptp.insert8897473484851387113nt_int A) tptp.bot_bo1488462491386950373nt_int))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.member_set_nat A) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat A) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.63 (assert (forall ((A Bool)) (@ (@ tptp.member_o A) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))
% 8.20/8.63 (assert (forall ((A tptp.nat)) (@ (@ tptp.member_nat A) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 8.20/8.63 (assert (forall ((A tptp.int)) (@ (@ tptp.member_int A) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.insert9069300056098147895at_nat X) A4)) B5) (and (@ (@ tptp.member8757157785044589968at_nat X) B5) (@ (@ tptp.ord_le1268244103169919719at_nat A4) B5)))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.insert8211810215607154385at_nat X) A4)) B5) (and (@ (@ tptp.member8440522571783428010at_nat X) B5) (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5)))))
% 8.20/8.63 (assert (forall ((X Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o X) A4)) B5) (and (@ (@ tptp.member_o X) B5) (@ (@ tptp.ord_less_eq_set_o A4) B5)))))
% 8.20/8.63 (assert (forall ((X tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (= (@ (@ tptp.ord_le483042692224249369nt_int (@ (@ tptp.insert8897473484851387113nt_int X) A4)) B5) (and (@ (@ tptp.member2340774599025711042nt_int X) B5) (@ (@ tptp.ord_le483042692224249369nt_int A4) B5)))))
% 8.20/8.63 (assert (forall ((X tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.insert_set_nat X) A4)) B5) (and (@ (@ tptp.member_set_nat X) B5) (@ (@ tptp.ord_le6893508408891458716et_nat A4) B5)))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X) A4)) B5) (and (@ (@ tptp.member_nat X) B5) (@ (@ tptp.ord_less_eq_set_nat A4) B5)))))
% 8.20/8.63 (assert (forall ((X tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X) A4)) B5) (and (@ (@ tptp.member_int X) B5) (@ (@ tptp.ord_less_eq_set_int A4) B5)))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A4))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat A))) (=> (@ (@ tptp.member8757157785044589968at_nat A) A4) (= (@ _let_1 (@ _let_2 B5)) (@ _let_2 (@ _let_1 B5))))))))
% 8.20/8.63 (assert (forall ((A Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A4))) (let ((_let_2 (@ tptp.insert_o A))) (=> (@ (@ tptp.member_o A) A4) (= (@ _let_1 (@ _let_2 B5)) (@ _let_2 (@ _let_1 B5))))))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.inf_in8396524679539076455nt_int A4))) (let ((_let_2 (@ tptp.insert8897473484851387113nt_int A))) (=> (@ (@ tptp.member2340774599025711042nt_int A) A4) (= (@ _let_1 (@ _let_2 B5)) (@ _let_2 (@ _let_1 B5))))))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_set_nat A4))) (let ((_let_2 (@ tptp.insert_set_nat A))) (=> (@ (@ tptp.member_set_nat A) A4) (= (@ _let_1 (@ _let_2 B5)) (@ _let_2 (@ _let_1 B5))))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A4))) (let ((_let_2 (@ tptp.insert_int A))) (=> (@ (@ tptp.member_int A) A4) (= (@ _let_1 (@ _let_2 B5)) (@ _let_2 (@ _let_1 B5))))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A4))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat A))) (=> (@ (@ tptp.member8440522571783428010at_nat A) A4) (= (@ _let_1 (@ _let_2 B5)) (@ _let_2 (@ _let_1 B5))))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A4))) (let ((_let_2 (@ tptp.insert_nat A))) (=> (@ (@ tptp.member_nat A) A4) (= (@ _let_1 (@ _let_2 B5)) (@ _let_2 (@ _let_1 B5))))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A4))) (=> (not (@ (@ tptp.member8757157785044589968at_nat A) A4)) (= (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat A) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((A Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A4))) (=> (not (@ (@ tptp.member_o A) A4)) (= (@ _let_1 (@ (@ tptp.insert_o A) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.inf_in8396524679539076455nt_int A4))) (=> (not (@ (@ tptp.member2340774599025711042nt_int A) A4)) (= (@ _let_1 (@ (@ tptp.insert8897473484851387113nt_int A) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_set_nat A4))) (=> (not (@ (@ tptp.member_set_nat A) A4)) (= (@ _let_1 (@ (@ tptp.insert_set_nat A) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A4))) (=> (not (@ (@ tptp.member_int A) A4)) (= (@ _let_1 (@ (@ tptp.insert_int A) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A4))) (=> (not (@ (@ tptp.member8440522571783428010at_nat A) A4)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat A) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A4))) (=> (not (@ (@ tptp.member_nat A) A4)) (= (@ _let_1 (@ (@ tptp.insert_nat A) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A))) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 A4)) (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A4) B5))))))
% 8.20/8.63 (assert (forall ((A Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A))) (= (@ (@ tptp.inf_inf_set_o (@ _let_1 A4)) (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.inf_inf_set_o A4) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (= (@ (@ tptp.inf_inf_set_int (@ _let_1 A4)) (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 A4)) (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 A4)) (@ _let_1 B5)) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (C4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A))) (=> (@ (@ tptp.member8757157785044589968at_nat A) C4) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B5) C4)))))))
% 8.20/8.63 (assert (forall ((A Bool) (C4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A))) (=> (@ (@ tptp.member_o A) C4) (= (@ (@ tptp.inf_inf_set_o (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.inf_inf_set_o B5) C4)))))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (C4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.insert8897473484851387113nt_int A))) (=> (@ (@ tptp.member2340774599025711042nt_int A) C4) (= (@ (@ tptp.inf_in8396524679539076455nt_int (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.inf_in8396524679539076455nt_int B5) C4)))))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (C4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat A))) (=> (@ (@ tptp.member_set_nat A) C4) (= (@ (@ tptp.inf_inf_set_set_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat B5) C4)))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (C4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.member_int A) C4) (= (@ (@ tptp.inf_inf_set_int (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.inf_inf_set_int B5) C4)))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (C4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (=> (@ (@ tptp.member8440522571783428010at_nat A) C4) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B5) C4)))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (C4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.member_nat A) C4) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B5) C4)))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (C4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat A) C4)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.insert9069300056098147895at_nat A) B5)) C4) (@ (@ tptp.inf_in7913087082777306421at_nat B5) C4)))))
% 8.20/8.63 (assert (forall ((A Bool) (C4 tptp.set_o) (B5 tptp.set_o)) (=> (not (@ (@ tptp.member_o A) C4)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.insert_o A) B5)) C4) (@ (@ tptp.inf_inf_set_o B5) C4)))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (C4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (=> (not (@ (@ tptp.member2340774599025711042nt_int A) C4)) (= (@ (@ tptp.inf_in8396524679539076455nt_int (@ (@ tptp.insert8897473484851387113nt_int A) B5)) C4) (@ (@ tptp.inf_in8396524679539076455nt_int B5) C4)))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (C4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (=> (not (@ (@ tptp.member_set_nat A) C4)) (= (@ (@ tptp.inf_inf_set_set_nat (@ (@ tptp.insert_set_nat A) B5)) C4) (@ (@ tptp.inf_inf_set_set_nat B5) C4)))))
% 8.20/8.63 (assert (forall ((A tptp.int) (C4 tptp.set_int) (B5 tptp.set_int)) (=> (not (@ (@ tptp.member_int A) C4)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int A) B5)) C4) (@ (@ tptp.inf_inf_set_int B5) C4)))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (C4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat A) C4)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.insert8211810215607154385at_nat A) B5)) C4) (@ (@ tptp.inf_in2572325071724192079at_nat B5) C4)))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (C4 tptp.set_nat) (B5 tptp.set_nat)) (=> (not (@ (@ tptp.member_nat A) C4)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat A) B5)) C4) (@ (@ tptp.inf_inf_set_nat B5) C4)))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B5) C4))))))
% 8.20/8.63 (assert (forall ((A Bool) (B5 tptp.set_o) (C4 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A))) (= (@ (@ tptp.sup_sup_set_o (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_sup_set_o B5) C4))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B5 tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (= (@ (@ tptp.sup_sup_set_int (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_sup_set_int B5) C4))))))
% 8.20/8.63 (assert (forall ((A tptp.produc4166570645942440679at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (C4 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.insert6337962749363155127at_nat A))) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat B5) C4))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (C4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B5) C4))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B5 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B5)) C4) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B5) C4))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat A4))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat A))) (= (@ _let_1 (@ _let_2 B5)) (@ _let_2 (@ _let_1 B5)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_o) (A Bool) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.sup_sup_set_o A4))) (let ((_let_2 (@ tptp.insert_o A))) (= (@ _let_1 (@ _let_2 B5)) (@ _let_2 (@ _let_1 B5)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_int) (A tptp.int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.sup_sup_set_int A4))) (let ((_let_2 (@ tptp.insert_int A))) (= (@ _let_1 (@ _let_2 B5)) (@ _let_2 (@ _let_1 B5)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (A tptp.produc4166570645942440679at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat A4))) (let ((_let_2 (@ tptp.insert6337962749363155127at_nat A))) (= (@ _let_1 (@ _let_2 B5)) (@ _let_2 (@ _let_1 B5)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (A tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A4))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat A))) (= (@ _let_1 (@ _let_2 B5)) (@ _let_2 (@ _let_1 B5)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_nat) (A tptp.nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A4))) (let ((_let_2 (@ tptp.insert_nat A))) (= (@ _let_1 (@ _let_2 B5)) (@ _let_2 (@ _let_1 B5)))))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) B5) (= (@ (@ tptp.minus_3314409938677909166at_nat (@ (@ tptp.insert9069300056098147895at_nat X) A4)) B5) (@ (@ tptp.minus_3314409938677909166at_nat A4) B5)))))
% 8.20/8.63 (assert (forall ((X Bool) (B5 tptp.set_o) (A4 tptp.set_o)) (=> (@ (@ tptp.member_o X) B5) (= (@ (@ tptp.minus_minus_set_o (@ (@ tptp.insert_o X) A4)) B5) (@ (@ tptp.minus_minus_set_o A4) B5)))))
% 8.20/8.63 (assert (forall ((X tptp.set_Pr958786334691620121nt_int) (B5 tptp.set_se6260736226359567993nt_int) (A4 tptp.set_se6260736226359567993nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X) B5) (= (@ (@ tptp.minus_2612819937483484256nt_int (@ (@ tptp.insert8897473484851387113nt_int X) A4)) B5) (@ (@ tptp.minus_2612819937483484256nt_int A4) B5)))))
% 8.20/8.63 (assert (forall ((X tptp.set_nat) (B5 tptp.set_set_nat) (A4 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) B5) (= (@ (@ tptp.minus_2163939370556025621et_nat (@ (@ tptp.insert_set_nat X) A4)) B5) (@ (@ tptp.minus_2163939370556025621et_nat A4) B5)))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (B5 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) B5) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.insert_nat X) A4)) B5) (@ (@ tptp.minus_minus_set_nat A4) B5)))))
% 8.20/8.63 (assert (forall ((X tptp.int) (B5 tptp.set_int) (A4 tptp.set_int)) (=> (@ (@ tptp.member_int X) B5) (= (@ (@ tptp.minus_minus_set_int (@ (@ tptp.insert_int X) A4)) B5) (@ (@ tptp.minus_minus_set_int A4) B5)))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) B5) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.insert8211810215607154385at_nat X) A4)) B5) (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A4))) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) A4)) (= (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat X) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((X Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o A4))) (=> (not (@ (@ tptp.member_o X) A4)) (= (@ _let_1 (@ (@ tptp.insert_o X) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((X tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.minus_2612819937483484256nt_int A4))) (=> (not (@ (@ tptp.member2340774599025711042nt_int X) A4)) (= (@ _let_1 (@ (@ tptp.insert8897473484851387113nt_int X) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((X tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat A4))) (=> (not (@ (@ tptp.member_set_nat X) A4)) (= (@ _let_1 (@ (@ tptp.insert_set_nat X) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A4))) (=> (not (@ (@ tptp.member_nat X) A4)) (= (@ _let_1 (@ (@ tptp.insert_nat X) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((X tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A4))) (=> (not (@ (@ tptp.member_int X) A4)) (= (@ _let_1 (@ (@ tptp.insert_int X) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A4))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A4)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat)) (= (@ tptp.collec6321179662152712658at_nat (lambda ((X4 tptp.produc3843707927480180839at_nat)) (= X4 A))) (@ (@ tptp.insert9069300056098147895at_nat A) tptp.bot_bo228742789529271731at_nat))))
% 8.20/8.63 (assert (forall ((A tptp.list_nat)) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (= X4 A))) (@ (@ tptp.insert_list_nat A) tptp.bot_bot_set_list_nat))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int)) (= (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (= X4 A))) (@ (@ tptp.insert8897473484851387113nt_int A) tptp.bot_bo1488462491386950373nt_int))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat)) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (= X4 A))) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (= X4 A))) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.63 (assert (forall ((A Bool)) (= (@ tptp.collect_o (lambda ((X4 Bool)) (= X4 A))) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))
% 8.20/8.63 (assert (forall ((A tptp.nat)) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (= X4 A))) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 8.20/8.63 (assert (forall ((A tptp.int)) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (= X4 A))) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat)) (= (@ tptp.collec6321179662152712658at_nat (@ (lambda ((Y6 tptp.produc3843707927480180839at_nat) (Z4 tptp.produc3843707927480180839at_nat)) (= Y6 Z4)) A)) (@ (@ tptp.insert9069300056098147895at_nat A) tptp.bot_bo228742789529271731at_nat))))
% 8.20/8.63 (assert (forall ((A tptp.list_nat)) (= (@ tptp.collect_list_nat (@ (lambda ((Y6 tptp.list_nat) (Z4 tptp.list_nat)) (= Y6 Z4)) A)) (@ (@ tptp.insert_list_nat A) tptp.bot_bot_set_list_nat))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int)) (= (@ tptp.collec5210948495886036740nt_int (@ (lambda ((Y6 tptp.set_Pr958786334691620121nt_int) (Z4 tptp.set_Pr958786334691620121nt_int)) (= Y6 Z4)) A)) (@ (@ tptp.insert8897473484851387113nt_int A) tptp.bot_bo1488462491386950373nt_int))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat)) (= (@ tptp.collect_set_nat (@ (lambda ((Y6 tptp.set_nat) (Z4 tptp.set_nat)) (= Y6 Z4)) A)) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat)) (= (@ tptp.collec3392354462482085612at_nat (@ (lambda ((Y6 tptp.product_prod_nat_nat) (Z4 tptp.product_prod_nat_nat)) (= Y6 Z4)) A)) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.63 (assert (forall ((A Bool)) (= (@ tptp.collect_o (@ (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)) A)) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))
% 8.20/8.63 (assert (forall ((A tptp.nat)) (= (@ tptp.collect_nat (@ (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) A)) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 8.20/8.63 (assert (forall ((A tptp.int)) (= (@ tptp.collect_int (@ (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) A)) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat B) tptp.bot_bo228742789529271731at_nat))) (= (= (@ (@ tptp.insert9069300056098147895at_nat A) A4) _let_1) (and (= A B) (@ (@ tptp.ord_le1268244103169919719at_nat A4) _let_1))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat B) tptp.bot_bo2099793752762293965at_nat))) (= (= (@ (@ tptp.insert8211810215607154385at_nat A) A4) _let_1) (and (= A B) (@ (@ tptp.ord_le3146513528884898305at_nat A4) _let_1))))))
% 8.20/8.63 (assert (forall ((A Bool) (A4 tptp.set_o) (B Bool)) (let ((_let_1 (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (= (= (@ (@ tptp.insert_o A) A4) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_o A4) _let_1))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (A4 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= (@ (@ tptp.insert_nat A) A4) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A4) _let_1))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (A4 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= (= (@ (@ tptp.insert_int A) A4) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_int A4) _let_1))))))
% 8.20/8.63 (assert (forall ((B tptp.produc3843707927480180839at_nat) (A tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat B) tptp.bot_bo228742789529271731at_nat))) (= (= _let_1 (@ (@ tptp.insert9069300056098147895at_nat A) A4)) (and (= A B) (@ (@ tptp.ord_le1268244103169919719at_nat A4) _let_1))))))
% 8.20/8.63 (assert (forall ((B tptp.product_prod_nat_nat) (A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat B) tptp.bot_bo2099793752762293965at_nat))) (= (= _let_1 (@ (@ tptp.insert8211810215607154385at_nat A) A4)) (and (= A B) (@ (@ tptp.ord_le3146513528884898305at_nat A4) _let_1))))))
% 8.20/8.63 (assert (forall ((B Bool) (A Bool) (A4 tptp.set_o)) (let ((_let_1 (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (= (= _let_1 (@ (@ tptp.insert_o A) A4)) (and (= A B) (@ (@ tptp.ord_less_eq_set_o A4) _let_1))))))
% 8.20/8.63 (assert (forall ((B tptp.nat) (A tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= _let_1 (@ (@ tptp.insert_nat A) A4)) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A4) _let_1))))))
% 8.20/8.63 (assert (forall ((B tptp.int) (A tptp.int) (A4 tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= (= _let_1 (@ (@ tptp.insert_int A) A4)) (and (= A B) (@ (@ tptp.ord_less_eq_set_int A4) _let_1))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A4))) (= (= tptp.bot_bo228742789529271731at_nat (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat B) B5))) (and (not (@ (@ tptp.member8757157785044589968at_nat B) A4)) (= tptp.bot_bo228742789529271731at_nat (@ _let_1 B5)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (B tptp.set_Pr958786334691620121nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.inf_in8396524679539076455nt_int A4))) (= (= tptp.bot_bo1488462491386950373nt_int (@ _let_1 (@ (@ tptp.insert8897473484851387113nt_int B) B5))) (and (not (@ (@ tptp.member2340774599025711042nt_int B) A4)) (= tptp.bot_bo1488462491386950373nt_int (@ _let_1 B5)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_set_nat) (B tptp.set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_set_nat A4))) (= (= tptp.bot_bot_set_set_nat (@ _let_1 (@ (@ tptp.insert_set_nat B) B5))) (and (not (@ (@ tptp.member_set_nat B) A4)) (= tptp.bot_bot_set_set_nat (@ _let_1 B5)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A4))) (= (= tptp.bot_bo2099793752762293965at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B) B5))) (and (not (@ (@ tptp.member8440522571783428010at_nat B) A4)) (= tptp.bot_bo2099793752762293965at_nat (@ _let_1 B5)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_o) (B Bool) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A4))) (= (= tptp.bot_bot_set_o (@ _let_1 (@ (@ tptp.insert_o B) B5))) (and (not (@ (@ tptp.member_o B) A4)) (= tptp.bot_bot_set_o (@ _let_1 B5)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_nat) (B tptp.nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A4))) (= (= tptp.bot_bot_set_nat (@ _let_1 (@ (@ tptp.insert_nat B) B5))) (and (not (@ (@ tptp.member_nat B) A4)) (= tptp.bot_bot_set_nat (@ _let_1 B5)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_int) (B tptp.int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A4))) (= (= tptp.bot_bot_set_int (@ _let_1 (@ (@ tptp.insert_int B) B5))) (and (not (@ (@ tptp.member_int B) A4)) (= tptp.bot_bot_set_int (@ _let_1 B5)))))))
% 8.20/8.63 (assert (forall ((B5 tptp.set_Pr4329608150637261639at_nat) (A tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat B5))) (= (= (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat A) A4)) tptp.bot_bo228742789529271731at_nat) (and (not (@ (@ tptp.member8757157785044589968at_nat A) B5)) (= (@ _let_1 A4) tptp.bot_bo228742789529271731at_nat))))))
% 8.20/8.63 (assert (forall ((B5 tptp.set_se6260736226359567993nt_int) (A tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.inf_in8396524679539076455nt_int B5))) (= (= (@ _let_1 (@ (@ tptp.insert8897473484851387113nt_int A) A4)) tptp.bot_bo1488462491386950373nt_int) (and (not (@ (@ tptp.member2340774599025711042nt_int A) B5)) (= (@ _let_1 A4) tptp.bot_bo1488462491386950373nt_int))))))
% 8.20/8.63 (assert (forall ((B5 tptp.set_set_nat) (A tptp.set_nat) (A4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_set_nat B5))) (= (= (@ _let_1 (@ (@ tptp.insert_set_nat A) A4)) tptp.bot_bot_set_set_nat) (and (not (@ (@ tptp.member_set_nat A) B5)) (= (@ _let_1 A4) tptp.bot_bot_set_set_nat))))))
% 8.20/8.63 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat B5))) (= (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat A) A4)) tptp.bot_bo2099793752762293965at_nat) (and (not (@ (@ tptp.member8440522571783428010at_nat A) B5)) (= (@ _let_1 A4) tptp.bot_bo2099793752762293965at_nat))))))
% 8.20/8.63 (assert (forall ((B5 tptp.set_o) (A Bool) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o B5))) (= (= (@ _let_1 (@ (@ tptp.insert_o A) A4)) tptp.bot_bot_set_o) (and (not (@ (@ tptp.member_o A) B5)) (= (@ _let_1 A4) tptp.bot_bot_set_o))))))
% 8.20/8.63 (assert (forall ((B5 tptp.set_nat) (A tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B5))) (= (= (@ _let_1 (@ (@ tptp.insert_nat A) A4)) tptp.bot_bot_set_nat) (and (not (@ (@ tptp.member_nat A) B5)) (= (@ _let_1 A4) tptp.bot_bot_set_nat))))))
% 8.20/8.63 (assert (forall ((B5 tptp.set_int) (A tptp.int) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int B5))) (= (= (@ _let_1 (@ (@ tptp.insert_int A) A4)) tptp.bot_bot_set_int) (and (not (@ (@ tptp.member_int A) B5)) (= (@ _let_1 A4) tptp.bot_bot_set_int))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (= (= tptp.bot_bo228742789529271731at_nat (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.insert9069300056098147895at_nat A) A4)) B5)) (and (not (@ (@ tptp.member8757157785044589968at_nat A) B5)) (= tptp.bot_bo228742789529271731at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A4) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (= (= tptp.bot_bo1488462491386950373nt_int (@ (@ tptp.inf_in8396524679539076455nt_int (@ (@ tptp.insert8897473484851387113nt_int A) A4)) B5)) (and (not (@ (@ tptp.member2340774599025711042nt_int A) B5)) (= tptp.bot_bo1488462491386950373nt_int (@ (@ tptp.inf_in8396524679539076455nt_int A4) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (= (= tptp.bot_bot_set_set_nat (@ (@ tptp.inf_inf_set_set_nat (@ (@ tptp.insert_set_nat A) A4)) B5)) (and (not (@ (@ tptp.member_set_nat A) B5)) (= tptp.bot_bot_set_set_nat (@ (@ tptp.inf_inf_set_set_nat A4) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (= tptp.bot_bo2099793752762293965at_nat (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.insert8211810215607154385at_nat A) A4)) B5)) (and (not (@ (@ tptp.member8440522571783428010at_nat A) B5)) (= tptp.bot_bo2099793752762293965at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5))))))
% 8.20/8.63 (assert (forall ((A Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (= (= tptp.bot_bot_set_o (@ (@ tptp.inf_inf_set_o (@ (@ tptp.insert_o A) A4)) B5)) (and (not (@ (@ tptp.member_o A) B5)) (= tptp.bot_bot_set_o (@ (@ tptp.inf_inf_set_o A4) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat A) A4)) B5)) (and (not (@ (@ tptp.member_nat A) B5)) (= tptp.bot_bot_set_nat (@ (@ tptp.inf_inf_set_nat A4) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int A) A4)) B5)) (and (not (@ (@ tptp.member_int A) B5)) (= tptp.bot_bot_set_int (@ (@ tptp.inf_inf_set_int A4) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.insert9069300056098147895at_nat A) A4)) B5) tptp.bot_bo228742789529271731at_nat) (and (not (@ (@ tptp.member8757157785044589968at_nat A) B5)) (= (@ (@ tptp.inf_in7913087082777306421at_nat A4) B5) tptp.bot_bo228742789529271731at_nat)))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (= (= (@ (@ tptp.inf_in8396524679539076455nt_int (@ (@ tptp.insert8897473484851387113nt_int A) A4)) B5) tptp.bot_bo1488462491386950373nt_int) (and (not (@ (@ tptp.member2340774599025711042nt_int A) B5)) (= (@ (@ tptp.inf_in8396524679539076455nt_int A4) B5) tptp.bot_bo1488462491386950373nt_int)))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (= (= (@ (@ tptp.inf_inf_set_set_nat (@ (@ tptp.insert_set_nat A) A4)) B5) tptp.bot_bot_set_set_nat) (and (not (@ (@ tptp.member_set_nat A) B5)) (= (@ (@ tptp.inf_inf_set_set_nat A4) B5) tptp.bot_bot_set_set_nat)))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.insert8211810215607154385at_nat A) A4)) B5) tptp.bot_bo2099793752762293965at_nat) (and (not (@ (@ tptp.member8440522571783428010at_nat A) B5)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5) tptp.bot_bo2099793752762293965at_nat)))))
% 8.20/8.63 (assert (forall ((A Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.insert_o A) A4)) B5) tptp.bot_bot_set_o) (and (not (@ (@ tptp.member_o A) B5)) (= (@ (@ tptp.inf_inf_set_o A4) B5) tptp.bot_bot_set_o)))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat A) A4)) B5) tptp.bot_bot_set_nat) (and (not (@ (@ tptp.member_nat A) B5)) (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat)))))
% 8.20/8.63 (assert (forall ((A tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int A) A4)) B5) tptp.bot_bot_set_int) (and (not (@ (@ tptp.member_int A) B5)) (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int)))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A))) (= (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A4) (@ _let_1 tptp.bot_bo228742789529271731at_nat))) (@ _let_1 A4)))))
% 8.20/8.63 (assert (forall ((A Bool) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A4) (@ _let_1 tptp.bot_bot_set_o))) (@ _let_1 A4)))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ _let_1 tptp.bot_bot_set_nat))) (@ _let_1 A4)))))
% 8.20/8.63 (assert (forall ((A tptp.int) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ _let_1 tptp.bot_bot_set_int))) (@ _let_1 A4)))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) (@ _let_1 A4)))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B tptp.produc3843707927480180839at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat A4) (@ tptp.uminus935396558254630718at_nat (@ (@ tptp.insert9069300056098147895at_nat B) tptp.bot_bo228742789529271731at_nat))) (not (@ (@ tptp.member8757157785044589968at_nat B) A4)))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (B tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.ord_le483042692224249369nt_int A4) (@ tptp.uminus6423885277529793776nt_int (@ (@ tptp.insert8897473484851387113nt_int B) tptp.bot_bo1488462491386950373nt_int))) (not (@ (@ tptp.member2340774599025711042nt_int B) A4)))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat A4) (@ tptp.uminus613421341184616069et_nat (@ (@ tptp.insert_set_nat B) tptp.bot_bot_set_set_nat))) (not (@ (@ tptp.member_set_nat B) A4)))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A4) (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.insert8211810215607154385at_nat B) tptp.bot_bo2099793752762293965at_nat))) (not (@ (@ tptp.member8440522571783428010at_nat B) A4)))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_o) (B Bool)) (= (@ (@ tptp.ord_less_eq_set_o A4) (@ tptp.uminus_uminus_set_o (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (not (@ (@ tptp.member_o B) A4)))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat A4) (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (not (@ (@ tptp.member_nat B) A4)))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int A4) (@ tptp.uminus1532241313380277803et_int (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (not (@ (@ tptp.member_int B) A4)))))
% 8.20/8.63 (assert (forall ((Prod tptp.product_prod_int_int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((Uu2 tptp.int) (Uv2 tptp.int)) true)) Prod)))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat A) A4) (exists ((B9 tptp.set_Pr4329608150637261639at_nat)) (and (= A4 (@ (@ tptp.insert9069300056098147895at_nat A) B9)) (not (@ (@ tptp.member8757157785044589968at_nat A) B9)))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat A) A4) (exists ((B9 tptp.set_Pr1261947904930325089at_nat)) (and (= A4 (@ (@ tptp.insert8211810215607154385at_nat A) B9)) (not (@ (@ tptp.member8440522571783428010at_nat A) B9)))))))
% 8.20/8.63 (assert (forall ((A Bool) (A4 tptp.set_o)) (=> (@ (@ tptp.member_o A) A4) (exists ((B9 tptp.set_o)) (and (= A4 (@ (@ tptp.insert_o A) B9)) (not (@ (@ tptp.member_o A) B9)))))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int A) A4) (exists ((B9 tptp.set_se6260736226359567993nt_int)) (and (= A4 (@ (@ tptp.insert8897473484851387113nt_int A) B9)) (not (@ (@ tptp.member2340774599025711042nt_int A) B9)))))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (A4 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat A) A4) (exists ((B9 tptp.set_set_nat)) (and (= A4 (@ (@ tptp.insert_set_nat A) B9)) (not (@ (@ tptp.member_set_nat A) B9)))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.member_nat A) A4) (exists ((B9 tptp.set_nat)) (and (= A4 (@ (@ tptp.insert_nat A) B9)) (not (@ (@ tptp.member_nat A) B9)))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (A4 tptp.set_int)) (=> (@ (@ tptp.member_int A) A4) (exists ((B9 tptp.set_int)) (and (= A4 (@ (@ tptp.insert_int A) B9)) (not (@ (@ tptp.member_int A) B9)))))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Y tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat X))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat Y))) (= (@ _let_1 (@ _let_2 A4)) (@ _let_2 (@ _let_1 A4)))))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat Y))) (= (@ _let_1 (@ _let_2 A4)) (@ _let_2 (@ _let_1 A4)))))))
% 8.20/8.63 (assert (forall ((X Bool) (Y Bool) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.insert_o Y))) (= (@ _let_1 (@ _let_2 A4)) (@ _let_2 (@ _let_1 A4)))))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (Y tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.insert_nat Y))) (= (@ _let_1 (@ _let_2 A4)) (@ _let_2 (@ _let_1 A4)))))))
% 8.20/8.63 (assert (forall ((X tptp.int) (Y tptp.int) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.insert_int Y))) (= (@ _let_1 (@ _let_2 A4)) (@ _let_2 (@ _let_1 A4)))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (= A B))) (=> (not (@ (@ tptp.member8757157785044589968at_nat A) A4)) (=> (not (@ (@ tptp.member8757157785044589968at_nat B) B5)) (= (= (@ (@ tptp.insert9069300056098147895at_nat A) A4) (@ (@ tptp.insert9069300056098147895at_nat B) B5)) (and (=> _let_1 (= A4 B5)) (=> (not _let_1) (exists ((C5 tptp.set_Pr4329608150637261639at_nat)) (and (= A4 (@ (@ tptp.insert9069300056098147895at_nat B) C5)) (not (@ (@ tptp.member8757157785044589968at_nat B) C5)) (= B5 (@ (@ tptp.insert9069300056098147895at_nat A) C5)) (not (@ (@ tptp.member8757157785044589968at_nat A) C5))))))))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (= A B))) (=> (not (@ (@ tptp.member8440522571783428010at_nat A) A4)) (=> (not (@ (@ tptp.member8440522571783428010at_nat B) B5)) (= (= (@ (@ tptp.insert8211810215607154385at_nat A) A4) (@ (@ tptp.insert8211810215607154385at_nat B) B5)) (and (=> _let_1 (= A4 B5)) (=> (not _let_1) (exists ((C5 tptp.set_Pr1261947904930325089at_nat)) (and (= A4 (@ (@ tptp.insert8211810215607154385at_nat B) C5)) (not (@ (@ tptp.member8440522571783428010at_nat B) C5)) (= B5 (@ (@ tptp.insert8211810215607154385at_nat A) C5)) (not (@ (@ tptp.member8440522571783428010at_nat A) C5))))))))))))
% 8.20/8.63 (assert (forall ((A Bool) (A4 tptp.set_o) (B Bool) (B5 tptp.set_o)) (=> (not (@ (@ tptp.member_o A) A4)) (=> (not (@ (@ tptp.member_o B) B5)) (= (= (@ (@ tptp.insert_o A) A4) (@ (@ tptp.insert_o B) B5)) (and (=> (= A B) (= A4 B5)) (=> (= A (not B)) (exists ((C5 tptp.set_o)) (and (= A4 (@ (@ tptp.insert_o B) C5)) (not (@ (@ tptp.member_o B) C5)) (= B5 (@ (@ tptp.insert_o A) C5)) (not (@ (@ tptp.member_o A) C5)))))))))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B tptp.set_Pr958786334691620121nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (= A B))) (=> (not (@ (@ tptp.member2340774599025711042nt_int A) A4)) (=> (not (@ (@ tptp.member2340774599025711042nt_int B) B5)) (= (= (@ (@ tptp.insert8897473484851387113nt_int A) A4) (@ (@ tptp.insert8897473484851387113nt_int B) B5)) (and (=> _let_1 (= A4 B5)) (=> (not _let_1) (exists ((C5 tptp.set_se6260736226359567993nt_int)) (and (= A4 (@ (@ tptp.insert8897473484851387113nt_int B) C5)) (not (@ (@ tptp.member2340774599025711042nt_int B) C5)) (= B5 (@ (@ tptp.insert8897473484851387113nt_int A) C5)) (not (@ (@ tptp.member2340774599025711042nt_int A) C5))))))))))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (A4 tptp.set_set_nat) (B tptp.set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (= A B))) (=> (not (@ (@ tptp.member_set_nat A) A4)) (=> (not (@ (@ tptp.member_set_nat B) B5)) (= (= (@ (@ tptp.insert_set_nat A) A4) (@ (@ tptp.insert_set_nat B) B5)) (and (=> _let_1 (= A4 B5)) (=> (not _let_1) (exists ((C5 tptp.set_set_nat)) (and (= A4 (@ (@ tptp.insert_set_nat B) C5)) (not (@ (@ tptp.member_set_nat B) C5)) (= B5 (@ (@ tptp.insert_set_nat A) C5)) (not (@ (@ tptp.member_set_nat A) C5))))))))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (A4 tptp.set_nat) (B tptp.nat) (B5 tptp.set_nat)) (let ((_let_1 (= A B))) (=> (not (@ (@ tptp.member_nat A) A4)) (=> (not (@ (@ tptp.member_nat B) B5)) (= (= (@ (@ tptp.insert_nat A) A4) (@ (@ tptp.insert_nat B) B5)) (and (=> _let_1 (= A4 B5)) (=> (not _let_1) (exists ((C5 tptp.set_nat)) (and (= A4 (@ (@ tptp.insert_nat B) C5)) (not (@ (@ tptp.member_nat B) C5)) (= B5 (@ (@ tptp.insert_nat A) C5)) (not (@ (@ tptp.member_nat A) C5))))))))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (A4 tptp.set_int) (B tptp.int) (B5 tptp.set_int)) (let ((_let_1 (= A B))) (=> (not (@ (@ tptp.member_int A) A4)) (=> (not (@ (@ tptp.member_int B) B5)) (= (= (@ (@ tptp.insert_int A) A4) (@ (@ tptp.insert_int B) B5)) (and (=> _let_1 (= A4 B5)) (=> (not _let_1) (exists ((C5 tptp.set_int)) (and (= A4 (@ (@ tptp.insert_int B) C5)) (not (@ (@ tptp.member_int B) C5)) (= B5 (@ (@ tptp.insert_int A) C5)) (not (@ (@ tptp.member_int A) C5))))))))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat A) A4) (= (@ (@ tptp.insert9069300056098147895at_nat A) A4) A4))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat A) A4) (= (@ (@ tptp.insert8211810215607154385at_nat A) A4) A4))))
% 8.20/8.63 (assert (forall ((A Bool) (A4 tptp.set_o)) (=> (@ (@ tptp.member_o A) A4) (= (@ (@ tptp.insert_o A) A4) A4))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int A) A4) (= (@ (@ tptp.insert8897473484851387113nt_int A) A4) A4))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (A4 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat A) A4) (= (@ (@ tptp.insert_set_nat A) A4) A4))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.member_nat A) A4) (= (@ (@ tptp.insert_nat A) A4) A4))))
% 8.20/8.63 (assert (forall ((A tptp.int) (A4 tptp.set_int)) (=> (@ (@ tptp.member_int A) A4) (= (@ (@ tptp.insert_int A) A4) A4))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat X))) (let ((_let_2 (@ tptp.member8757157785044589968at_nat X))) (=> (not (@ _let_2 A4)) (=> (not (@ _let_2 B5)) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_2 (@ tptp.member8440522571783428010at_nat X))) (=> (not (@ _let_2 A4)) (=> (not (@ _let_2 B5)) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))))))
% 8.20/8.63 (assert (forall ((X Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.member_o X))) (=> (not (@ _let_2 A4)) (=> (not (@ _let_2 B5)) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))))))
% 8.20/8.63 (assert (forall ((X tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.insert8897473484851387113nt_int X))) (let ((_let_2 (@ tptp.member2340774599025711042nt_int X))) (=> (not (@ _let_2 A4)) (=> (not (@ _let_2 B5)) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))))))
% 8.20/8.63 (assert (forall ((X tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X))) (let ((_let_2 (@ tptp.member_set_nat X))) (=> (not (@ _let_2 A4)) (=> (not (@ _let_2 B5)) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.member_nat X))) (=> (not (@ _let_2 A4)) (=> (not (@ _let_2 B5)) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))))))
% 8.20/8.63 (assert (forall ((X tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.member_int X))) (=> (not (@ _let_2 A4)) (=> (not (@ _let_2 B5)) (= (= (@ _let_1 A4) (@ _let_1 B5)) (= A4 B5))))))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) A4) (not (forall ((B9 tptp.set_Pr4329608150637261639at_nat)) (=> (= A4 (@ (@ tptp.insert9069300056098147895at_nat X) B9)) (@ (@ tptp.member8757157785044589968at_nat X) B9)))))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) A4) (not (forall ((B9 tptp.set_Pr1261947904930325089at_nat)) (=> (= A4 (@ (@ tptp.insert8211810215607154385at_nat X) B9)) (@ (@ tptp.member8440522571783428010at_nat X) B9)))))))
% 8.20/8.63 (assert (forall ((X Bool) (A4 tptp.set_o)) (=> (@ (@ tptp.member_o X) A4) (not (forall ((B9 tptp.set_o)) (=> (= A4 (@ (@ tptp.insert_o X) B9)) (@ (@ tptp.member_o X) B9)))))))
% 8.20/8.63 (assert (forall ((X tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X) A4) (not (forall ((B9 tptp.set_se6260736226359567993nt_int)) (=> (= A4 (@ (@ tptp.insert8897473484851387113nt_int X) B9)) (@ (@ tptp.member2340774599025711042nt_int X) B9)))))))
% 8.20/8.63 (assert (forall ((X tptp.set_nat) (A4 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) A4) (not (forall ((B9 tptp.set_set_nat)) (=> (= A4 (@ (@ tptp.insert_set_nat X) B9)) (@ (@ tptp.member_set_nat X) B9)))))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A4) (not (forall ((B9 tptp.set_nat)) (=> (= A4 (@ (@ tptp.insert_nat X) B9)) (@ (@ tptp.member_nat X) B9)))))))
% 8.20/8.63 (assert (forall ((X tptp.int) (A4 tptp.set_int)) (=> (@ (@ tptp.member_int X) A4) (not (forall ((B9 tptp.set_int)) (=> (= A4 (@ (@ tptp.insert_int X) B9)) (@ (@ tptp.member_int X) B9)))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (B tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat A))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat B) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B) B5))))))
% 8.20/8.63 (assert (forall ((A Bool) (B5 tptp.set_o) (B Bool)) (let ((_let_1 (@ tptp.member_o A))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.insert_o B) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (B5 tptp.set_se6260736226359567993nt_int) (B tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int A))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.insert8897473484851387113nt_int B) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (B5 tptp.set_set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.insert_set_nat B) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B5 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.insert_nat B) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B5 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ tptp.member_int A))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.insert_int B) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.member8757157785044589968at_nat A) (@ (@ tptp.insert9069300056098147895at_nat A) B5))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8440522571783428010at_nat A) (@ (@ tptp.insert8211810215607154385at_nat A) B5))))
% 8.20/8.63 (assert (forall ((A Bool) (B5 tptp.set_o)) (@ (@ tptp.member_o A) (@ (@ tptp.insert_o A) B5))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (@ (@ tptp.member2340774599025711042nt_int A) (@ (@ tptp.insert8897473484851387113nt_int A) B5))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (B5 tptp.set_set_nat)) (@ (@ tptp.member_set_nat A) (@ (@ tptp.insert_set_nat A) B5))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B5 tptp.set_nat)) (@ (@ tptp.member_nat A) (@ (@ tptp.insert_nat A) B5))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B5 tptp.set_int)) (@ (@ tptp.member_int A) (@ (@ tptp.insert_int A) B5))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (B tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat A))) (=> (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat B) A4)) (=> (not (= A B)) (@ _let_1 A4))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A))) (=> (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B) A4)) (=> (not (= A B)) (@ _let_1 A4))))))
% 8.20/8.63 (assert (forall ((A Bool) (B Bool) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o A))) (=> (@ _let_1 (@ (@ tptp.insert_o B) A4)) (=> (= A (not B)) (@ _let_1 A4))))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (B tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int A))) (=> (@ _let_1 (@ (@ tptp.insert8897473484851387113nt_int B) A4)) (=> (not (= A B)) (@ _let_1 A4))))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (A4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A))) (=> (@ _let_1 (@ (@ tptp.insert_set_nat B) A4)) (=> (not (= A B)) (@ _let_1 A4))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A))) (=> (@ _let_1 (@ (@ tptp.insert_nat B) A4)) (=> (not (= A B)) (@ _let_1 A4))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A))) (=> (@ _let_1 (@ (@ tptp.insert_int B) A4)) (=> (not (= A B)) (@ _let_1 A4))))))
% 8.20/8.63 (assert (= tptp.insert9069300056098147895at_nat (lambda ((A5 tptp.produc3843707927480180839at_nat) (B6 tptp.set_Pr4329608150637261639at_nat)) (@ tptp.collec6321179662152712658at_nat (lambda ((X4 tptp.produc3843707927480180839at_nat)) (or (= X4 A5) (@ (@ tptp.member8757157785044589968at_nat X4) B6)))))))
% 8.20/8.63 (assert (= tptp.insert8211810215607154385at_nat (lambda ((A5 tptp.product_prod_nat_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (or (= X4 A5) (@ (@ tptp.member8440522571783428010at_nat X4) B6)))))))
% 8.20/8.63 (assert (= tptp.insert_o (lambda ((A5 Bool) (B6 tptp.set_o)) (@ tptp.collect_o (lambda ((X4 Bool)) (or (= X4 A5) (@ (@ tptp.member_o X4) B6)))))))
% 8.20/8.63 (assert (= tptp.insert_list_nat (lambda ((A5 tptp.list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (or (= X4 A5) (@ (@ tptp.member_list_nat X4) B6)))))))
% 8.20/8.63 (assert (= tptp.insert8897473484851387113nt_int (lambda ((A5 tptp.set_Pr958786334691620121nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (or (= X4 A5) (@ (@ tptp.member2340774599025711042nt_int X4) B6)))))))
% 8.20/8.63 (assert (= tptp.insert_set_nat (lambda ((A5 tptp.set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (or (= X4 A5) (@ (@ tptp.member_set_nat X4) B6)))))))
% 8.20/8.63 (assert (= tptp.insert_nat (lambda ((A5 tptp.nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (or (= X4 A5) (@ (@ tptp.member_nat X4) B6)))))))
% 8.20/8.63 (assert (= tptp.insert_int (lambda ((A5 tptp.int) (B6 tptp.set_int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (or (= X4 A5) (@ (@ tptp.member_int X4) B6)))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (P2 (-> tptp.produc3843707927480180839at_nat Bool))) (= (@ (@ tptp.insert9069300056098147895at_nat A) (@ tptp.collec6321179662152712658at_nat P2)) (@ tptp.collec6321179662152712658at_nat (lambda ((U3 tptp.produc3843707927480180839at_nat)) (=> (not (= U3 A)) (@ P2 U3)))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (P2 (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.insert8211810215607154385at_nat A) (@ tptp.collec3392354462482085612at_nat P2)) (@ tptp.collec3392354462482085612at_nat (lambda ((U3 tptp.product_prod_nat_nat)) (=> (not (= U3 A)) (@ P2 U3)))))))
% 8.20/8.63 (assert (forall ((A Bool) (P2 (-> Bool Bool))) (= (@ (@ tptp.insert_o A) (@ tptp.collect_o P2)) (@ tptp.collect_o (lambda ((U3 Bool)) (=> (not (= U3 A)) (@ P2 U3)))))))
% 8.20/8.63 (assert (forall ((A tptp.list_nat) (P2 (-> tptp.list_nat Bool))) (= (@ (@ tptp.insert_list_nat A) (@ tptp.collect_list_nat P2)) (@ tptp.collect_list_nat (lambda ((U3 tptp.list_nat)) (=> (not (= U3 A)) (@ P2 U3)))))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (P2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (= (@ (@ tptp.insert8897473484851387113nt_int A) (@ tptp.collec5210948495886036740nt_int P2)) (@ tptp.collec5210948495886036740nt_int (lambda ((U3 tptp.set_Pr958786334691620121nt_int)) (=> (not (= U3 A)) (@ P2 U3)))))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (P2 (-> tptp.set_nat Bool))) (= (@ (@ tptp.insert_set_nat A) (@ tptp.collect_set_nat P2)) (@ tptp.collect_set_nat (lambda ((U3 tptp.set_nat)) (=> (not (= U3 A)) (@ P2 U3)))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (P2 (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A) (@ tptp.collect_nat P2)) (@ tptp.collect_nat (lambda ((U3 tptp.nat)) (=> (not (= U3 A)) (@ P2 U3)))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (P2 (-> tptp.int Bool))) (= (@ (@ tptp.insert_int A) (@ tptp.collect_int P2)) (@ tptp.collect_int (lambda ((U3 tptp.int)) (=> (not (= U3 A)) (@ P2 U3)))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (B tptp.produc3843707927480180839at_nat)) (=> (= (@ (@ tptp.insert9069300056098147895at_nat A) tptp.bot_bo228742789529271731at_nat) (@ (@ tptp.insert9069300056098147895at_nat B) tptp.bot_bo228742789529271731at_nat)) (= A B))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (=> (= (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.insert8211810215607154385at_nat B) tptp.bot_bo2099793752762293965at_nat)) (= A B))))
% 8.20/8.63 (assert (forall ((A Bool) (B Bool)) (=> (= (@ (@ tptp.insert_o A) tptp.bot_bot_set_o) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o)) (= A B))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat) (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat)) (= A B))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.insert_int A) tptp.bot_bot_set_int) (@ (@ tptp.insert_int B) tptp.bot_bot_set_int)) (= A B))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (not (= (@ (@ tptp.insert9069300056098147895at_nat A) A4) tptp.bot_bo228742789529271731at_nat))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (not (= (@ (@ tptp.insert8211810215607154385at_nat A) A4) tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.63 (assert (forall ((A Bool) (A4 tptp.set_o)) (not (= (@ (@ tptp.insert_o A) A4) tptp.bot_bot_set_o))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (A4 tptp.set_nat)) (not (= (@ (@ tptp.insert_nat A) A4) tptp.bot_bot_set_nat))))
% 8.20/8.63 (assert (forall ((A tptp.int) (A4 tptp.set_int)) (not (= (@ (@ tptp.insert_int A) A4) tptp.bot_bot_set_int))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (B tptp.produc3843707927480180839at_nat) (C2 tptp.produc3843707927480180839at_nat) (D2 tptp.produc3843707927480180839at_nat)) (= (= (@ (@ tptp.insert9069300056098147895at_nat A) (@ (@ tptp.insert9069300056098147895at_nat B) tptp.bot_bo228742789529271731at_nat)) (@ (@ tptp.insert9069300056098147895at_nat C2) (@ (@ tptp.insert9069300056098147895at_nat D2) tptp.bot_bo228742789529271731at_nat))) (or (and (= A C2) (= B D2)) (and (= A D2) (= B C2))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat) (C2 tptp.product_prod_nat_nat) (D2 tptp.product_prod_nat_nat)) (= (= (@ (@ tptp.insert8211810215607154385at_nat A) (@ (@ tptp.insert8211810215607154385at_nat B) tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.insert8211810215607154385at_nat C2) (@ (@ tptp.insert8211810215607154385at_nat D2) tptp.bot_bo2099793752762293965at_nat))) (or (and (= A C2) (= B D2)) (and (= A D2) (= B C2))))))
% 8.20/8.63 (assert (forall ((A Bool) (B Bool) (C2 Bool) (D2 Bool)) (= (= (@ (@ tptp.insert_o A) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o)) (@ (@ tptp.insert_o C2) (@ (@ tptp.insert_o D2) tptp.bot_bot_set_o))) (or (and (= A C2) (= B D2)) (and (= A D2) (= B C2))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (= (= (@ (@ tptp.insert_nat A) (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat)) (@ (@ tptp.insert_nat C2) (@ (@ tptp.insert_nat D2) tptp.bot_bot_set_nat))) (or (and (= A C2) (= B D2)) (and (= A D2) (= B C2))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.insert_int A) (@ (@ tptp.insert_int B) tptp.bot_bot_set_int)) (@ (@ tptp.insert_int C2) (@ (@ tptp.insert_int D2) tptp.bot_bot_set_int))) (or (and (= A C2) (= B D2)) (and (= A D2) (= B C2))))))
% 8.20/8.63 (assert (forall ((B tptp.produc3843707927480180839at_nat) (A tptp.produc3843707927480180839at_nat)) (= (@ (@ tptp.member8757157785044589968at_nat B) (@ (@ tptp.insert9069300056098147895at_nat A) tptp.bot_bo228742789529271731at_nat)) (= B A))))
% 8.20/8.63 (assert (forall ((B tptp.set_Pr958786334691620121nt_int) (A tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member2340774599025711042nt_int B) (@ (@ tptp.insert8897473484851387113nt_int A) tptp.bot_bo1488462491386950373nt_int)) (= B A))))
% 8.20/8.63 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.member_set_nat B) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat)) (= B A))))
% 8.20/8.63 (assert (forall ((B tptp.product_prod_nat_nat) (A tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8440522571783428010at_nat B) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat)) (= B A))))
% 8.20/8.63 (assert (forall ((B Bool) (A Bool)) (= (@ (@ tptp.member_o B) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o)) (= B A))))
% 8.20/8.63 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.member_nat B) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)) (= B A))))
% 8.20/8.63 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.member_int B) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)) (= B A))))
% 8.20/8.63 (assert (forall ((B tptp.produc3843707927480180839at_nat) (A tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat B) (@ (@ tptp.insert9069300056098147895at_nat A) tptp.bot_bo228742789529271731at_nat)) (= B A))))
% 8.20/8.63 (assert (forall ((B tptp.set_Pr958786334691620121nt_int) (A tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int B) (@ (@ tptp.insert8897473484851387113nt_int A) tptp.bot_bo1488462491386950373nt_int)) (= B A))))
% 8.20/8.63 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_set_nat B) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat)) (= B A))))
% 8.20/8.63 (assert (forall ((B tptp.product_prod_nat_nat) (A tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat B) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat)) (= B A))))
% 8.20/8.63 (assert (forall ((B Bool) (A Bool)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o)) (= B A))))
% 8.20/8.63 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)) (= B A))))
% 8.20/8.63 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.member_int B) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)) (= B A))))
% 8.20/8.63 (assert (forall ((C4 tptp.set_Pr4329608150637261639at_nat) (D4 tptp.set_Pr4329608150637261639at_nat) (A tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C4) D4) (@ (@ tptp.ord_le1268244103169919719at_nat (@ _let_1 C4)) (@ _let_1 D4))))))
% 8.20/8.63 (assert (forall ((C4 tptp.set_Pr1261947904930325089at_nat) (D4 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat C4) D4) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 C4)) (@ _let_1 D4))))))
% 8.20/8.63 (assert (forall ((C4 tptp.set_o) (D4 tptp.set_o) (A Bool)) (let ((_let_1 (@ tptp.insert_o A))) (=> (@ (@ tptp.ord_less_eq_set_o C4) D4) (@ (@ tptp.ord_less_eq_set_o (@ _let_1 C4)) (@ _let_1 D4))))))
% 8.20/8.63 (assert (forall ((C4 tptp.set_nat) (D4 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.ord_less_eq_set_nat C4) D4) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 C4)) (@ _let_1 D4))))))
% 8.20/8.63 (assert (forall ((C4 tptp.set_int) (D4 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.ord_less_eq_set_int C4) D4) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 C4)) (@ _let_1 D4))))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat A4))) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) A4)) (= (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat X) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A4))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A4)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((X Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A4))) (=> (not (@ (@ tptp.member_o X) A4)) (= (@ _let_1 (@ (@ tptp.insert_o X) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((X tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.ord_le483042692224249369nt_int A4))) (=> (not (@ (@ tptp.member2340774599025711042nt_int X) A4)) (= (@ _let_1 (@ (@ tptp.insert8897473484851387113nt_int X) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((X tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat A4))) (=> (not (@ (@ tptp.member_set_nat X) A4)) (= (@ _let_1 (@ (@ tptp.insert_set_nat X) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A4))) (=> (not (@ (@ tptp.member_nat X) A4)) (= (@ _let_1 (@ (@ tptp.insert_nat X) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((X tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A4))) (=> (not (@ (@ tptp.member_int X) A4)) (= (@ _let_1 (@ (@ tptp.insert_int X) B5)) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((B5 tptp.set_Pr4329608150637261639at_nat) (A tptp.produc3843707927480180839at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat B5) (@ (@ tptp.insert9069300056098147895at_nat A) B5))))
% 8.20/8.63 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat B5) (@ (@ tptp.insert8211810215607154385at_nat A) B5))))
% 8.20/8.63 (assert (forall ((B5 tptp.set_o) (A Bool)) (@ (@ tptp.ord_less_eq_set_o B5) (@ (@ tptp.insert_o A) B5))))
% 8.20/8.63 (assert (forall ((B5 tptp.set_nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat B5) (@ (@ tptp.insert_nat A) B5))))
% 8.20/8.63 (assert (forall ((B5 tptp.set_int) (A tptp.int)) (@ (@ tptp.ord_less_eq_set_int B5) (@ (@ tptp.insert_int A) B5))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (B tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat A4))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat B) B5))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A4))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B) B5))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o) (B Bool)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A4))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.insert_o B) B5))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A4))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.insert_nat B) B5))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A4))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.insert_int B) B5))))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (X7 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) A4) (=> (@ (@ tptp.ord_le1268244103169919719at_nat X7) A4) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.insert9069300056098147895at_nat X) X7)) A4)))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (X7 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) A4) (=> (@ (@ tptp.ord_le3146513528884898305at_nat X7) A4) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.insert8211810215607154385at_nat X) X7)) A4)))))
% 8.20/8.63 (assert (forall ((X Bool) (A4 tptp.set_o) (X7 tptp.set_o)) (=> (@ (@ tptp.member_o X) A4) (=> (@ (@ tptp.ord_less_eq_set_o X7) A4) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o X) X7)) A4)))))
% 8.20/8.63 (assert (forall ((X tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (X7 tptp.set_se6260736226359567993nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X) A4) (=> (@ (@ tptp.ord_le483042692224249369nt_int X7) A4) (@ (@ tptp.ord_le483042692224249369nt_int (@ (@ tptp.insert8897473484851387113nt_int X) X7)) A4)))))
% 8.20/8.63 (assert (forall ((X tptp.set_nat) (A4 tptp.set_set_nat) (X7 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) A4) (=> (@ (@ tptp.ord_le6893508408891458716et_nat X7) A4) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.insert_set_nat X) X7)) A4)))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (A4 tptp.set_nat) (X7 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A4) (=> (@ (@ tptp.ord_less_eq_set_nat X7) A4) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X) X7)) A4)))))
% 8.20/8.63 (assert (forall ((X tptp.int) (A4 tptp.set_int) (X7 tptp.set_int)) (=> (@ (@ tptp.member_int X) A4) (=> (@ (@ tptp.ord_less_eq_set_int X7) A4) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X) X7)) A4)))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A4))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ tptp.insert9069300056098147895at_nat A))) (let ((_let_4 (@ _let_1 (@ _let_3 B5)))) (let ((_let_5 (@ (@ tptp.member8757157785044589968at_nat A) A4))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 8.20/8.63 (assert (forall ((A Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A4))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ tptp.insert_o A))) (let ((_let_4 (@ _let_1 (@ _let_3 B5)))) (let ((_let_5 (@ (@ tptp.member_o A) A4))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.inf_in8396524679539076455nt_int A4))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ tptp.insert8897473484851387113nt_int A))) (let ((_let_4 (@ _let_1 (@ _let_3 B5)))) (let ((_let_5 (@ (@ tptp.member2340774599025711042nt_int A) A4))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_set_nat A4))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ tptp.insert_set_nat A))) (let ((_let_4 (@ _let_1 (@ _let_3 B5)))) (let ((_let_5 (@ (@ tptp.member_set_nat A) A4))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A4))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ tptp.insert_int A))) (let ((_let_4 (@ _let_1 (@ _let_3 B5)))) (let ((_let_5 (@ (@ tptp.member_int A) A4))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A4))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat A))) (let ((_let_4 (@ _let_1 (@ _let_3 B5)))) (let ((_let_5 (@ (@ tptp.member8440522571783428010at_nat A) A4))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A4))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (@ tptp.insert_nat A))) (let ((_let_4 (@ _let_1 (@ _let_3 B5)))) (let ((_let_5 (@ (@ tptp.member_nat A) A4))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (C4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B5) C4))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat A))) (let ((_let_3 (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_2 B5)) C4))) (let ((_let_4 (@ (@ tptp.member8757157785044589968at_nat A) C4))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.63 (assert (forall ((A Bool) (C4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ (@ tptp.inf_inf_set_o B5) C4))) (let ((_let_2 (@ tptp.insert_o A))) (let ((_let_3 (@ (@ tptp.inf_inf_set_o (@ _let_2 B5)) C4))) (let ((_let_4 (@ (@ tptp.member_o A) C4))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (C4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ (@ tptp.inf_in8396524679539076455nt_int B5) C4))) (let ((_let_2 (@ tptp.insert8897473484851387113nt_int A))) (let ((_let_3 (@ (@ tptp.inf_in8396524679539076455nt_int (@ _let_2 B5)) C4))) (let ((_let_4 (@ (@ tptp.member2340774599025711042nt_int A) C4))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (C4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_set_nat B5) C4))) (let ((_let_2 (@ tptp.insert_set_nat A))) (let ((_let_3 (@ (@ tptp.inf_inf_set_set_nat (@ _let_2 B5)) C4))) (let ((_let_4 (@ (@ tptp.member_set_nat A) C4))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (C4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ (@ tptp.inf_inf_set_int B5) C4))) (let ((_let_2 (@ tptp.insert_int A))) (let ((_let_3 (@ (@ tptp.inf_inf_set_int (@ _let_2 B5)) C4))) (let ((_let_4 (@ (@ tptp.member_int A) C4))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (C4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B5) C4))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat A))) (let ((_let_3 (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_2 B5)) C4))) (let ((_let_4 (@ (@ tptp.member8440522571783428010at_nat A) C4))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (C4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat B5) C4))) (let ((_let_2 (@ tptp.insert_nat A))) (let ((_let_3 (@ (@ tptp.inf_inf_set_nat (@ _let_2 B5)) C4))) (let ((_let_4 (@ (@ tptp.member_nat A) C4))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.minus_3314409938677909166at_nat A4) B5))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat X))) (let ((_let_3 (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_2 A4)) B5))) (let ((_let_4 (@ (@ tptp.member8757157785044589968at_nat X) B5))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 8.20/8.63 (assert (forall ((X Bool) (B5 tptp.set_o) (A4 tptp.set_o)) (let ((_let_1 (@ (@ tptp.minus_minus_set_o A4) B5))) (let ((_let_2 (@ tptp.insert_o X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_o (@ _let_2 A4)) B5))) (let ((_let_4 (@ (@ tptp.member_o X) B5))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 8.20/8.63 (assert (forall ((X tptp.set_Pr958786334691620121nt_int) (B5 tptp.set_se6260736226359567993nt_int) (A4 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ (@ tptp.minus_2612819937483484256nt_int A4) B5))) (let ((_let_2 (@ tptp.insert8897473484851387113nt_int X))) (let ((_let_3 (@ (@ tptp.minus_2612819937483484256nt_int (@ _let_2 A4)) B5))) (let ((_let_4 (@ (@ tptp.member2340774599025711042nt_int X) B5))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 8.20/8.63 (assert (forall ((X tptp.set_nat) (B5 tptp.set_set_nat) (A4 tptp.set_set_nat)) (let ((_let_1 (@ (@ tptp.minus_2163939370556025621et_nat A4) B5))) (let ((_let_2 (@ tptp.insert_set_nat X))) (let ((_let_3 (@ (@ tptp.minus_2163939370556025621et_nat (@ _let_2 A4)) B5))) (let ((_let_4 (@ (@ tptp.member_set_nat X) B5))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (B5 tptp.set_nat) (A4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (let ((_let_2 (@ tptp.insert_nat X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_nat (@ _let_2 A4)) B5))) (let ((_let_4 (@ (@ tptp.member_nat X) B5))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 8.20/8.63 (assert (forall ((X tptp.int) (B5 tptp.set_int) (A4 tptp.set_int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (let ((_let_2 (@ tptp.insert_int X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_int (@ _let_2 A4)) B5))) (let ((_let_4 (@ (@ tptp.member_int X) B5))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) B5))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_3 (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 A4)) B5))) (let ((_let_4 (@ (@ tptp.member8440522571783428010at_nat X) B5))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.produc3843707927480180839at_nat Bool)) (A tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collec6321179662152712658at_nat (lambda ((X4 tptp.produc3843707927480180839at_nat)) (and (= X4 A) (@ P2 X4)))) (@ (@ tptp.insert9069300056098147895at_nat A) tptp.bot_bo228742789529271731at_nat))) (=> (not _let_1) (= (@ tptp.collec6321179662152712658at_nat (lambda ((X4 tptp.produc3843707927480180839at_nat)) (and (= X4 A) (@ P2 X4)))) tptp.bot_bo228742789529271731at_nat))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.list_nat Bool)) (A tptp.list_nat)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (= X4 A) (@ P2 X4)))) (@ (@ tptp.insert_list_nat A) tptp.bot_bot_set_list_nat))) (=> (not _let_1) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (= X4 A) (@ P2 X4)))) tptp.bot_bot_set_list_nat))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.set_Pr958786334691620121nt_int Bool)) (A tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (and (= X4 A) (@ P2 X4)))) (@ (@ tptp.insert8897473484851387113nt_int A) tptp.bot_bo1488462491386950373nt_int))) (=> (not _let_1) (= (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (and (= X4 A) (@ P2 X4)))) tptp.bot_bo1488462491386950373nt_int))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.set_nat Bool)) (A tptp.set_nat)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (= X4 A) (@ P2 X4)))) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))) (=> (not _let_1) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (= X4 A) (@ P2 X4)))) tptp.bot_bot_set_set_nat))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.product_prod_nat_nat Bool)) (A tptp.product_prod_nat_nat)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (and (= X4 A) (@ P2 X4)))) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))) (=> (not _let_1) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (and (= X4 A) (@ P2 X4)))) tptp.bot_bo2099793752762293965at_nat))))))
% 8.20/8.63 (assert (forall ((P2 (-> Bool Bool)) (A Bool)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collect_o (lambda ((X4 Bool)) (and (= X4 A) (@ P2 X4)))) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))) (=> (not _let_1) (= (@ tptp.collect_o (lambda ((X4 Bool)) (and (= X4 A) (@ P2 X4)))) tptp.bot_bot_set_o))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.nat Bool)) (A tptp.nat)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (= X4 A) (@ P2 X4)))) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (= X4 A) (@ P2 X4)))) tptp.bot_bot_set_nat))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.int Bool)) (A tptp.int)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (= X4 A) (@ P2 X4)))) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (= X4 A) (@ P2 X4)))) tptp.bot_bot_set_int))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.produc3843707927480180839at_nat Bool)) (A tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collec6321179662152712658at_nat (lambda ((X4 tptp.produc3843707927480180839at_nat)) (and (= A X4) (@ P2 X4)))) (@ (@ tptp.insert9069300056098147895at_nat A) tptp.bot_bo228742789529271731at_nat))) (=> (not _let_1) (= (@ tptp.collec6321179662152712658at_nat (lambda ((X4 tptp.produc3843707927480180839at_nat)) (and (= A X4) (@ P2 X4)))) tptp.bot_bo228742789529271731at_nat))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.list_nat Bool)) (A tptp.list_nat)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (= A X4) (@ P2 X4)))) (@ (@ tptp.insert_list_nat A) tptp.bot_bot_set_list_nat))) (=> (not _let_1) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (= A X4) (@ P2 X4)))) tptp.bot_bot_set_list_nat))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.set_Pr958786334691620121nt_int Bool)) (A tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (and (= A X4) (@ P2 X4)))) (@ (@ tptp.insert8897473484851387113nt_int A) tptp.bot_bo1488462491386950373nt_int))) (=> (not _let_1) (= (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (and (= A X4) (@ P2 X4)))) tptp.bot_bo1488462491386950373nt_int))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.set_nat Bool)) (A tptp.set_nat)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (= A X4) (@ P2 X4)))) (@ (@ tptp.insert_set_nat A) tptp.bot_bot_set_set_nat))) (=> (not _let_1) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (= A X4) (@ P2 X4)))) tptp.bot_bot_set_set_nat))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.product_prod_nat_nat Bool)) (A tptp.product_prod_nat_nat)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (and (= A X4) (@ P2 X4)))) (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))) (=> (not _let_1) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (and (= A X4) (@ P2 X4)))) tptp.bot_bo2099793752762293965at_nat))))))
% 8.20/8.63 (assert (forall ((P2 (-> Bool Bool)) (A Bool)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collect_o (lambda ((X4 Bool)) (and (= A X4) (@ P2 X4)))) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))) (=> (not _let_1) (= (@ tptp.collect_o (lambda ((X4 Bool)) (and (= A X4) (@ P2 X4)))) tptp.bot_bot_set_o))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.nat Bool)) (A tptp.nat)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (= A X4) (@ P2 X4)))) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (= A X4) (@ P2 X4)))) tptp.bot_bot_set_nat))))))
% 8.20/8.63 (assert (forall ((P2 (-> tptp.int Bool)) (A tptp.int)) (let ((_let_1 (@ P2 A))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (= A X4) (@ P2 X4)))) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (= A X4) (@ P2 X4)))) tptp.bot_bot_set_int))))))
% 8.20/8.63 (assert (= tptp.insert8211810215607154385at_nat (lambda ((A5 tptp.product_prod_nat_nat) (__flatten_var_0 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (= X4 A5)))) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.insert_o (lambda ((A5 Bool) (__flatten_var_0 tptp.set_o)) (@ (@ tptp.sup_sup_set_o (@ tptp.collect_o (lambda ((X4 Bool)) (= X4 A5)))) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.insert_list_nat (lambda ((A5 tptp.list_nat) (__flatten_var_0 tptp.set_list_nat)) (@ (@ tptp.sup_sup_set_list_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (= X4 A5)))) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.insert8897473484851387113nt_int (lambda ((A5 tptp.set_Pr958786334691620121nt_int) (__flatten_var_0 tptp.set_se6260736226359567993nt_int)) (@ (@ tptp.sup_su2047564715030645325nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (= X4 A5)))) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.insert_set_nat (lambda ((A5 tptp.set_nat) (__flatten_var_0 tptp.set_set_nat)) (@ (@ tptp.sup_sup_set_set_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (= X4 A5)))) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.insert_int (lambda ((A5 tptp.int) (__flatten_var_0 tptp.set_int)) (@ (@ tptp.sup_sup_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (= X4 A5)))) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.insert6337962749363155127at_nat (lambda ((A5 tptp.produc4166570645942440679at_nat) (__flatten_var_0 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ tptp.collec5204685387357076818at_nat (lambda ((X4 tptp.produc4166570645942440679at_nat)) (= X4 A5)))) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.insert9069300056098147895at_nat (lambda ((A5 tptp.produc3843707927480180839at_nat) (__flatten_var_0 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.collec6321179662152712658at_nat (lambda ((X4 tptp.produc3843707927480180839at_nat)) (= X4 A5)))) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.insert_nat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (= X4 A5)))) __flatten_var_0))))
% 8.20/8.63 (assert (forall ((X7 tptp.set_Pr4329608150637261639at_nat) (A tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat A) tptp.bot_bo228742789529271731at_nat))) (= (@ (@ tptp.ord_le1268244103169919719at_nat X7) _let_1) (or (= X7 tptp.bot_bo228742789529271731at_nat) (= X7 _let_1))))))
% 8.20/8.63 (assert (forall ((X7 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat A) tptp.bot_bo2099793752762293965at_nat))) (= (@ (@ tptp.ord_le3146513528884898305at_nat X7) _let_1) (or (= X7 tptp.bot_bo2099793752762293965at_nat) (= X7 _let_1))))))
% 8.20/8.63 (assert (forall ((X7 tptp.set_o) (A Bool)) (let ((_let_1 (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))) (= (@ (@ tptp.ord_less_eq_set_o X7) _let_1) (or (= X7 tptp.bot_bot_set_o) (= X7 _let_1))))))
% 8.20/8.63 (assert (forall ((X7 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (= (@ (@ tptp.ord_less_eq_set_nat X7) _let_1) (or (= X7 tptp.bot_bot_set_nat) (= X7 _let_1))))))
% 8.20/8.63 (assert (forall ((X7 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (= (@ (@ tptp.ord_less_eq_set_int X7) _let_1) (or (= X7 tptp.bot_bot_set_int) (= X7 _let_1))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A4) _let_1) (or (= A4 tptp.bot_bo228742789529271731at_nat) (= A4 _let_1))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A4) _let_1) (or (= A4 tptp.bot_bo2099793752762293965at_nat) (= A4 _let_1))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_o) (X Bool)) (let ((_let_1 (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) (=> (@ (@ tptp.ord_less_eq_set_o A4) _let_1) (or (= A4 tptp.bot_bot_set_o) (= A4 _let_1))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A4) _let_1) (or (= A4 tptp.bot_bot_set_nat) (= A4 _let_1))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (=> (@ (@ tptp.ord_less_eq_set_int A4) _let_1) (or (= A4 tptp.bot_bot_set_int) (= A4 _let_1))))))
% 8.20/8.63 (assert (= tptp.insert6337962749363155127at_nat (lambda ((A5 tptp.produc4166570645942440679at_nat) (__flatten_var_0 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.insert6337962749363155127at_nat A5) tptp.bot_bo8422036546324065075at_nat)) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.insert9069300056098147895at_nat (lambda ((A5 tptp.produc3843707927480180839at_nat) (__flatten_var_0 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.insert9069300056098147895at_nat A5) tptp.bot_bo228742789529271731at_nat)) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.insert8211810215607154385at_nat (lambda ((A5 tptp.product_prod_nat_nat) (__flatten_var_0 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.insert8211810215607154385at_nat A5) tptp.bot_bo2099793752762293965at_nat)) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.insert_o (lambda ((A5 Bool) (__flatten_var_0 tptp.set_o)) (@ (@ tptp.sup_sup_set_o (@ (@ tptp.insert_o A5) tptp.bot_bot_set_o)) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.insert_nat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.insert_nat A5) tptp.bot_bot_set_nat)) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.insert_int (lambda ((A5 tptp.int) (__flatten_var_0 tptp.set_int)) (@ (@ tptp.sup_sup_set_int (@ (@ tptp.insert_int A5) tptp.bot_bot_set_int)) __flatten_var_0))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (X tptp.produc4166570645942440679at_nat)) (let ((_let_1 (@ (@ tptp.insert6337962749363155127at_nat X) tptp.bot_bo8422036546324065075at_nat))) (let ((_let_2 (= B5 _let_1))) (let ((_let_3 (= A4 _let_1))) (= (= (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5) _let_1) (or (and (= A4 tptp.bot_bo8422036546324065075at_nat) _let_2) (and _let_3 (= B5 tptp.bot_bo8422036546324065075at_nat)) (and _let_3 _let_2))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat))) (let ((_let_2 (= B5 _let_1))) (let ((_let_3 (= A4 _let_1))) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5) _let_1) (or (and (= A4 tptp.bot_bo228742789529271731at_nat) _let_2) (and _let_3 (= B5 tptp.bot_bo228742789529271731at_nat)) (and _let_3 _let_2))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))) (let ((_let_2 (= B5 _let_1))) (let ((_let_3 (= A4 _let_1))) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat A4) B5) _let_1) (or (and (= A4 tptp.bot_bo2099793752762293965at_nat) _let_2) (and _let_3 (= B5 tptp.bot_bo2099793752762293965at_nat)) (and _let_3 _let_2))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o) (X Bool)) (let ((_let_1 (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) (let ((_let_2 (= B5 _let_1))) (let ((_let_3 (= A4 _let_1))) (= (= (@ (@ tptp.sup_sup_set_o A4) B5) _let_1) (or (and (= A4 tptp.bot_bot_set_o) _let_2) (and _let_3 (= B5 tptp.bot_bot_set_o)) (and _let_3 _let_2))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (let ((_let_2 (= B5 _let_1))) (let ((_let_3 (= A4 _let_1))) (= (= (@ (@ tptp.sup_sup_set_nat A4) B5) _let_1) (or (and (= A4 tptp.bot_bot_set_nat) _let_2) (and _let_3 (= B5 tptp.bot_bot_set_nat)) (and _let_3 _let_2))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (let ((_let_2 (= B5 _let_1))) (let ((_let_3 (= A4 _let_1))) (= (= (@ (@ tptp.sup_sup_set_int A4) B5) _let_1) (or (and (= A4 tptp.bot_bot_set_int) _let_2) (and _let_3 (= B5 tptp.bot_bot_set_int)) (and _let_3 _let_2))))))))
% 8.20/8.63 (assert (forall ((X tptp.produc4166570645942440679at_nat) (A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ (@ tptp.insert6337962749363155127at_nat X) tptp.bot_bo8422036546324065075at_nat))) (let ((_let_2 (= B5 _let_1))) (let ((_let_3 (= A4 _let_1))) (= (= _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5)) (or (and (= A4 tptp.bot_bo8422036546324065075at_nat) _let_2) (and _let_3 (= B5 tptp.bot_bo8422036546324065075at_nat)) (and _let_3 _let_2))))))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat))) (let ((_let_2 (= B5 _let_1))) (let ((_let_3 (= A4 _let_1))) (= (= _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5)) (or (and (= A4 tptp.bot_bo228742789529271731at_nat) _let_2) (and _let_3 (= B5 tptp.bot_bo228742789529271731at_nat)) (and _let_3 _let_2))))))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))) (let ((_let_2 (= B5 _let_1))) (let ((_let_3 (= A4 _let_1))) (= (= _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A4) B5)) (or (and (= A4 tptp.bot_bo2099793752762293965at_nat) _let_2) (and _let_3 (= B5 tptp.bot_bo2099793752762293965at_nat)) (and _let_3 _let_2))))))))
% 8.20/8.63 (assert (forall ((X Bool) (A4 tptp.set_o) (B5 tptp.set_o)) (let ((_let_1 (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) (let ((_let_2 (= B5 _let_1))) (let ((_let_3 (= A4 _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_o A4) B5)) (or (and (= A4 tptp.bot_bot_set_o) _let_2) (and _let_3 (= B5 tptp.bot_bot_set_o)) (and _let_3 _let_2))))))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (A4 tptp.set_nat) (B5 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (let ((_let_2 (= B5 _let_1))) (let ((_let_3 (= A4 _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (or (and (= A4 tptp.bot_bot_set_nat) _let_2) (and _let_3 (= B5 tptp.bot_bot_set_nat)) (and _let_3 _let_2))))))))
% 8.20/8.63 (assert (forall ((X tptp.int) (A4 tptp.set_int) (B5 tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (let ((_let_2 (= B5 _let_1))) (let ((_let_3 (= A4 _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (or (and (= A4 tptp.bot_bot_set_int) _let_2) (and _let_3 (= B5 tptp.bot_bot_set_int)) (and _let_3 _let_2))))))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (X7 tptp.set_Pr4329608150637261639at_nat)) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) X7)) (= (@ (@ tptp.minus_3314409938677909166at_nat X7) (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat)) X7))))
% 8.20/8.63 (assert (forall ((X tptp.set_Pr958786334691620121nt_int) (X7 tptp.set_se6260736226359567993nt_int)) (=> (not (@ (@ tptp.member2340774599025711042nt_int X) X7)) (= (@ (@ tptp.minus_2612819937483484256nt_int X7) (@ (@ tptp.insert8897473484851387113nt_int X) tptp.bot_bo1488462491386950373nt_int)) X7))))
% 8.20/8.63 (assert (forall ((X tptp.set_nat) (X7 tptp.set_set_nat)) (=> (not (@ (@ tptp.member_set_nat X) X7)) (= (@ (@ tptp.minus_2163939370556025621et_nat X7) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat)) X7))))
% 8.20/8.63 (assert (forall ((X Bool) (X7 tptp.set_o)) (=> (not (@ (@ tptp.member_o X) X7)) (= (@ (@ tptp.minus_minus_set_o X7) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) X7))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (X7 tptp.set_nat)) (=> (not (@ (@ tptp.member_nat X) X7)) (= (@ (@ tptp.minus_minus_set_nat X7) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) X7))))
% 8.20/8.63 (assert (forall ((X tptp.int) (X7 tptp.set_int)) (=> (not (@ (@ tptp.member_int X) X7)) (= (@ (@ tptp.minus_minus_set_int X7) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) X7))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (X7 tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) X7)) (= (@ (@ tptp.minus_1356011639430497352at_nat X7) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)) X7))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (Y tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat Y) tptp.bot_bo228742789529271731at_nat))) (let ((_let_2 (@ tptp.insert9069300056098147895at_nat X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_2 A4)) _let_1) (@ _let_2 (@ (@ tptp.minus_3314409938677909166at_nat A4) _let_1))))))))
% 8.20/8.63 (assert (forall ((X Bool) (Y Bool) (A4 tptp.set_o)) (let ((_let_1 (@ (@ tptp.insert_o Y) tptp.bot_bot_set_o))) (let ((_let_2 (@ tptp.insert_o X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_minus_set_o (@ _let_2 A4)) _let_1) (@ _let_2 (@ (@ tptp.minus_minus_set_o A4) _let_1))))))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (Y tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat Y) tptp.bot_bot_set_nat))) (let ((_let_2 (@ tptp.insert_nat X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_2 A4)) _let_1) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A4) _let_1))))))))
% 8.20/8.63 (assert (forall ((X tptp.int) (Y tptp.int) (A4 tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int Y) tptp.bot_bot_set_int))) (let ((_let_2 (@ tptp.insert_int X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_minus_set_int (@ _let_2 A4)) _let_1) (@ _let_2 (@ (@ tptp.minus_minus_set_int A4) _let_1))))))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat Y) tptp.bot_bo2099793752762293965at_nat))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 A4)) _let_1) (@ _let_2 (@ (@ tptp.minus_1356011639430497352at_nat A4) _let_1))))))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat X))) (=> (not (@ (@ tptp.member8757157785044589968at_nat X) A4)) (= (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_1 A4)) (@ _let_1 tptp.bot_bo228742789529271731at_nat)) A4)))))
% 8.20/8.63 (assert (forall ((X tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.insert8897473484851387113nt_int X))) (=> (not (@ (@ tptp.member2340774599025711042nt_int X) A4)) (= (@ (@ tptp.minus_2612819937483484256nt_int (@ _let_1 A4)) (@ _let_1 tptp.bot_bo1488462491386950373nt_int)) A4)))))
% 8.20/8.63 (assert (forall ((X tptp.set_nat) (A4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X))) (=> (not (@ (@ tptp.member_set_nat X) A4)) (= (@ (@ tptp.minus_2163939370556025621et_nat (@ _let_1 A4)) (@ _let_1 tptp.bot_bot_set_set_nat)) A4)))))
% 8.20/8.63 (assert (forall ((X Bool) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (=> (not (@ (@ tptp.member_o X) A4)) (= (@ (@ tptp.minus_minus_set_o (@ _let_1 A4)) (@ _let_1 tptp.bot_bot_set_o)) A4)))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (not (@ (@ tptp.member_nat X) A4)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 A4)) (@ _let_1 tptp.bot_bot_set_nat)) A4)))))
% 8.20/8.63 (assert (forall ((X tptp.int) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (not (@ (@ tptp.member_int X) A4)) (= (@ (@ tptp.minus_minus_set_int (@ _let_1 A4)) (@ _let_1 tptp.bot_bot_set_int)) A4)))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (=> (not (@ (@ tptp.member8440522571783428010at_nat X) A4)) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 A4)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)) A4)))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (A tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A))) (let ((_let_2 (@ tptp.minus_3314409938677909166at_nat A4))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_2 (@ _let_1 tptp.bot_bo228742789529271731at_nat))) B5))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_o) (A Bool) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A))) (let ((_let_2 (@ tptp.minus_minus_set_o A4))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_minus_set_o (@ _let_2 (@ _let_1 tptp.bot_bot_set_o))) B5))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_nat) (A tptp.nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (let ((_let_2 (@ tptp.minus_minus_set_nat A4))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 (@ _let_1 tptp.bot_bot_set_nat))) B5))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_int) (A tptp.int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (let ((_let_2 (@ tptp.minus_minus_set_int A4))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_minus_set_int (@ _let_2 (@ _let_1 tptp.bot_bot_set_int))) B5))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (let ((_let_2 (@ tptp.minus_1356011639430497352at_nat A4))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) B5))))))
% 8.20/8.63 (assert (forall ((A tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A))) (=> (@ (@ tptp.member8757157785044589968at_nat A) A4) (= (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat A4) (@ _let_1 tptp.bot_bo228742789529271731at_nat))) A4)))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (A4 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.insert8897473484851387113nt_int A))) (=> (@ (@ tptp.member2340774599025711042nt_int A) A4) (= (@ _let_1 (@ (@ tptp.minus_2612819937483484256nt_int A4) (@ _let_1 tptp.bot_bo1488462491386950373nt_int))) A4)))))
% 8.20/8.63 (assert (forall ((A tptp.set_nat) (A4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.insert_set_nat A))) (=> (@ (@ tptp.member_set_nat A) A4) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A4) (@ _let_1 tptp.bot_bot_set_set_nat))) A4)))))
% 8.20/8.63 (assert (forall ((A Bool) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A))) (=> (@ (@ tptp.member_o A) A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A4) (@ _let_1 tptp.bot_bot_set_o))) A4)))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.member_nat A) A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ _let_1 tptp.bot_bot_set_nat))) A4)))))
% 8.20/8.63 (assert (forall ((A tptp.int) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.member_int A) A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ _let_1 tptp.bot_bot_set_int))) A4)))))
% 8.20/8.63 (assert (forall ((A tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (=> (@ (@ tptp.member8440522571783428010at_nat A) A4) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) A4)))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (A tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat A))) (let ((_let_2 (@ tptp.minus_3314409938677909166at_nat A4))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_2 B5)) (@ _let_1 tptp.bot_bo228742789529271731at_nat)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_o) (A Bool) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A))) (let ((_let_2 (@ tptp.minus_minus_set_o A4))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_minus_set_o (@ _let_2 B5)) (@ _let_1 tptp.bot_bot_set_o)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_nat) (A tptp.nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (let ((_let_2 (@ tptp.minus_minus_set_nat A4))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 B5)) (@ _let_1 tptp.bot_bot_set_nat)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_int) (A tptp.int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (let ((_let_2 (@ tptp.minus_minus_set_int A4))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_minus_set_int (@ _let_2 B5)) (@ _let_1 tptp.bot_bot_set_int)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (let ((_let_2 (@ tptp.minus_1356011639430497352at_nat A4))) (= (@ _let_2 (@ _let_1 B5)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_2 B5)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat)))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat) (C4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat B5))) (let ((_let_2 (@ tptp.ord_le1268244103169919719at_nat A4))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert9069300056098147895at_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member8757157785044589968at_nat X) A4))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o) (X Bool) (C4 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o B5))) (let ((_let_2 (@ tptp.ord_less_eq_set_o A4))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_o X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_o X) A4))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (B5 tptp.set_se6260736226359567993nt_int) (X tptp.set_Pr958786334691620121nt_int) (C4 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.minus_2612819937483484256nt_int B5))) (let ((_let_2 (@ tptp.ord_le483042692224249369nt_int A4))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert8897473484851387113nt_int X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member2340774599025711042nt_int X) A4))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat) (X tptp.set_nat) (C4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat B5))) (let ((_let_2 (@ tptp.ord_le6893508408891458716et_nat A4))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_set_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_set_nat X) A4))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (X tptp.nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B5))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A4))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_nat X) A4))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (C4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat B5))) (let ((_let_2 (@ tptp.ord_le3146513528884898305at_nat A4))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member8440522571783428010at_nat X) A4))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (X tptp.int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B5))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A4))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_int X) A4))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat A4))) (let ((_let_2 (@ (@ tptp.member8757157785044589968at_nat X) A4))) (let ((_let_3 (@ tptp.insert9069300056098147895at_nat X))) (= (@ _let_1 (@ _let_3 B5)) (and (=> _let_2 (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.minus_3314409938677909166at_nat A4) (@ _let_3 tptp.bot_bo228742789529271731at_nat))) B5)) (=> (not _let_2) (@ _let_1 B5)))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (X tptp.set_Pr958786334691620121nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.ord_le483042692224249369nt_int A4))) (let ((_let_2 (@ (@ tptp.member2340774599025711042nt_int X) A4))) (let ((_let_3 (@ tptp.insert8897473484851387113nt_int X))) (= (@ _let_1 (@ _let_3 B5)) (and (=> _let_2 (@ (@ tptp.ord_le483042692224249369nt_int (@ (@ tptp.minus_2612819937483484256nt_int A4) (@ _let_3 tptp.bot_bo1488462491386950373nt_int))) B5)) (=> (not _let_2) (@ _let_1 B5)))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_set_nat) (X tptp.set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat A4))) (let ((_let_2 (@ (@ tptp.member_set_nat X) A4))) (let ((_let_3 (@ tptp.insert_set_nat X))) (= (@ _let_1 (@ _let_3 B5)) (and (=> _let_2 (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) (@ _let_3 tptp.bot_bot_set_set_nat))) B5)) (=> (not _let_2) (@ _let_1 B5)))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_o) (X Bool) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A4))) (let ((_let_2 (@ (@ tptp.member_o X) A4))) (let ((_let_3 (@ tptp.insert_o X))) (= (@ _let_1 (@ _let_3 B5)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.minus_minus_set_o A4) (@ _let_3 tptp.bot_bot_set_o))) B5)) (=> (not _let_2) (@ _let_1 B5)))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_nat) (X tptp.nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A4))) (let ((_let_2 (@ (@ tptp.member_nat X) A4))) (let ((_let_3 (@ tptp.insert_nat X))) (= (@ _let_1 (@ _let_3 B5)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A4) (@ _let_3 tptp.bot_bot_set_nat))) B5)) (=> (not _let_2) (@ _let_1 B5)))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A4))) (let ((_let_2 (@ (@ tptp.member8440522571783428010at_nat X) A4))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X))) (= (@ _let_1 (@ _let_3 B5)) (and (=> _let_2 (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B5)) (=> (not _let_2) (@ _let_1 B5)))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_int) (X tptp.int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A4))) (let ((_let_2 (@ (@ tptp.member_int X) A4))) (let ((_let_3 (@ tptp.insert_int X))) (= (@ _let_1 (@ _let_3 B5)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A4) (@ _let_3 tptp.bot_bot_set_int))) B5)) (=> (not _let_2) (@ _let_1 B5)))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat X))) (=> (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.minus_3314409938677909166at_nat A4) (@ _let_1 tptp.bot_bo228742789529271731at_nat))) B5) (@ (@ tptp.ord_le1268244103169919719at_nat A4) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_o) (X Bool) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (=> (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.minus_minus_set_o A4) (@ _let_1 tptp.bot_bot_set_o))) B5) (@ (@ tptp.ord_less_eq_set_o A4) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_nat) (X tptp.nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A4) (@ _let_1 tptp.bot_bot_set_nat))) B5) (@ (@ tptp.ord_less_eq_set_nat A4) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))) B5) (@ (@ tptp.ord_le3146513528884898305at_nat A4) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_int) (X tptp.int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A4) (@ _let_1 tptp.bot_bot_set_int))) B5) (@ (@ tptp.ord_less_eq_set_int A4) (@ _let_1 B5))))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X) S) (@ (@ tptp.ord_le2604355607129572851at_nat (@ (@ tptp.minus_3314409938677909166at_nat S) (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat))) S))))
% 8.20/8.63 (assert (forall ((X tptp.set_Pr958786334691620121nt_int) (S tptp.set_se6260736226359567993nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X) S) (@ (@ tptp.ord_le1924305788584680229nt_int (@ (@ tptp.minus_2612819937483484256nt_int S) (@ (@ tptp.insert8897473484851387113nt_int X) tptp.bot_bo1488462491386950373nt_int))) S))))
% 8.20/8.63 (assert (forall ((X tptp.set_nat) (S tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) S) (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.minus_2163939370556025621et_nat S) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat))) S))))
% 8.20/8.63 (assert (forall ((X Bool) (S tptp.set_o)) (=> (@ (@ tptp.member_o X) S) (@ (@ tptp.ord_less_set_o (@ (@ tptp.minus_minus_set_o S) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) S))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (S tptp.set_nat)) (=> (@ (@ tptp.member_nat X) S) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat S) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) S))))
% 8.20/8.63 (assert (forall ((X tptp.int) (S tptp.set_int)) (=> (@ (@ tptp.member_int X) S) (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) S))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (S tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) S) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat S) (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))) S))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat) (A4 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.insert9069300056098147895at_nat X))) (= (@ tptp.uminus935396558254630718at_nat (@ _let_1 A4)) (@ (@ tptp.minus_3314409938677909166at_nat (@ tptp.uminus935396558254630718at_nat A4)) (@ _let_1 tptp.bot_bo228742789529271731at_nat))))))
% 8.20/8.63 (assert (forall ((X Bool) (A4 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (= (@ tptp.uminus_uminus_set_o (@ _let_1 A4)) (@ (@ tptp.minus_minus_set_o (@ tptp.uminus_uminus_set_o A4)) (@ _let_1 tptp.bot_bot_set_o))))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (= (@ tptp.uminus5710092332889474511et_nat (@ _let_1 A4)) (@ (@ tptp.minus_minus_set_nat (@ tptp.uminus5710092332889474511et_nat A4)) (@ _let_1 tptp.bot_bot_set_nat))))))
% 8.20/8.63 (assert (forall ((X tptp.int) (A4 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (= (@ tptp.uminus1532241313380277803et_int (@ _let_1 A4)) (@ (@ tptp.minus_minus_set_int (@ tptp.uminus1532241313380277803et_int A4)) (@ _let_1 tptp.bot_bot_set_int))))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat X))) (= (@ tptp.uminus6524753893492686040at_nat (@ _let_1 A4)) (@ (@ tptp.minus_1356011639430497352at_nat (@ tptp.uminus6524753893492686040at_nat A4)) (@ _let_1 tptp.bot_bo2099793752762293965at_nat))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ tptp.insert9069300056098147895at_nat X))) (let ((_let_4 (@ _let_1 B5))) (let ((_let_5 (@ tptp.ord_le2604355607129572851at_nat A4))) (= (@ _let_5 (@ _let_3 B5)) (and (=> _let_4 (@ _let_5 B5)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le2604355607129572851at_nat (@ (@ tptp.minus_3314409938677909166at_nat A4) (@ _let_3 tptp.bot_bo228742789529271731at_nat))) B5)) (=> (not _let_2) (@ (@ tptp.ord_le1268244103169919719at_nat A4) B5)))))))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (X tptp.set_Pr958786334691620121nt_int) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int X))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ tptp.insert8897473484851387113nt_int X))) (let ((_let_4 (@ _let_1 B5))) (let ((_let_5 (@ tptp.ord_le1924305788584680229nt_int A4))) (= (@ _let_5 (@ _let_3 B5)) (and (=> _let_4 (@ _let_5 B5)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le1924305788584680229nt_int (@ (@ tptp.minus_2612819937483484256nt_int A4) (@ _let_3 tptp.bot_bo1488462491386950373nt_int))) B5)) (=> (not _let_2) (@ (@ tptp.ord_le483042692224249369nt_int A4) B5)))))))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_set_nat) (X tptp.set_nat) (B5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ tptp.insert_set_nat X))) (let ((_let_4 (@ _let_1 B5))) (let ((_let_5 (@ tptp.ord_less_set_set_nat A4))) (= (@ _let_5 (@ _let_3 B5)) (and (=> _let_4 (@ _let_5 B5)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) (@ _let_3 tptp.bot_bot_set_set_nat))) B5)) (=> (not _let_2) (@ (@ tptp.ord_le6893508408891458716et_nat A4) B5)))))))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_o) (X Bool) (B5 tptp.set_o)) (let ((_let_1 (@ tptp.member_o X))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ tptp.insert_o X))) (let ((_let_4 (@ _let_1 B5))) (let ((_let_5 (@ tptp.ord_less_set_o A4))) (= (@ _let_5 (@ _let_3 B5)) (and (=> _let_4 (@ _let_5 B5)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_o (@ (@ tptp.minus_minus_set_o A4) (@ _let_3 tptp.bot_bot_set_o))) B5)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_o A4) B5)))))))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_nat) (X tptp.nat) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ tptp.insert_nat X))) (let ((_let_4 (@ _let_1 B5))) (let ((_let_5 (@ tptp.ord_less_set_nat A4))) (= (@ _let_5 (@ _let_3 B5)) (and (=> _let_4 (@ _let_5 B5)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A4) (@ _let_3 tptp.bot_bot_set_nat))) B5)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A4) B5)))))))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X))) (let ((_let_4 (@ _let_1 B5))) (let ((_let_5 (@ tptp.ord_le7866589430770878221at_nat A4))) (= (@ _let_5 (@ _let_3 B5)) (and (=> _let_4 (@ _let_5 B5)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B5)) (=> (not _let_2) (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5)))))))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_int) (X tptp.int) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ tptp.insert_int X))) (let ((_let_4 (@ _let_1 B5))) (let ((_let_5 (@ tptp.ord_less_set_int A4))) (= (@ _let_5 (@ _let_3 B5)) (and (=> _let_4 (@ _let_5 B5)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A4) (@ _let_3 tptp.bot_bot_set_int))) B5)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A4) B5)))))))))))))
% 8.20/8.63 (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 ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_and_not_num M) N2)))))
% 8.20/8.63 (assert (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q8 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q8) (@ tptp.zero_n2684676970156552555ol_int (not (= R5 tptp.zero_zero_int))))))))
% 8.20/8.63 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M3)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 8.20/8.63 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M3 tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 8.20/8.63 (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)))))))))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K2)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K2) L))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int K2) _let_5) (@ (@ tptp.member_int L) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K2) L)) (and (=> _let_6 (= _let_4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (assert (= tptp.int_ge_less_than2 (lambda ((D5 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z8 tptp.int) (Z tptp.int)) (and (@ (@ tptp.ord_less_eq_int D5) Z) (@ (@ tptp.ord_less_int Z8) Z))))))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.produc2922128104949294807at_nat A) B)) tptp.bot_bo228742789529271731at_nat))) (= (@ tptp.transi2703068831062848130at_nat _let_1) _let_1))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int A) B)) tptp.bot_bo1796632182523588997nt_int))) (= (@ tptp.transi6261509568448316235cl_int _let_1) _let_1))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) tptp.bot_bo2099793752762293965at_nat))) (= (@ tptp.transi6264000038957366511cl_nat _let_1) _let_1))))
% 8.20/8.63 (assert (forall ((R3 tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat (@ tptp.transi2703068831062848130at_nat R3)) (@ tptp.transi2703068831062848130at_nat (@ (@ tptp.insert9069300056098147895at_nat X) R3)))))
% 8.20/8.63 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.transi6264000038957366511cl_nat R3)) (@ tptp.transi6264000038957366511cl_nat (@ (@ tptp.insert8211810215607154385at_nat X) R3)))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N2)) (@ tptp.bit0 N2))))
% 8.20/8.63 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N2)) tptp.one) (@ tptp.bit0 N2))))
% 8.20/8.63 (assert (forall ((A tptp.multis2468970476368604999at_nat) (B tptp.multis2468970476368604999at_nat) (R2 tptp.set_Pr8551490117392284871at_nat)) (= (@ tptp.transi5749863603491437800at_nat (@ (@ tptp.insert6337962749363155127at_nat (@ (@ tptp.produc4348348721325984599at_nat A) B)) R2)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ tptp.transi5749863603491437800at_nat R2)) (@ tptp.collec5204685387357076818at_nat (@ tptp.produc5410597840814988588_nat_o (lambda ((X4 tptp.multis2468970476368604999at_nat) (Y4 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.transi5749863603491437800at_nat R2))) (and (or (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat X4) A)) _let_1) (= X4 A)) (or (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat B) Y4)) _let_1) (= Y4 B)))))))))))
% 8.20/8.63 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.transi2703068831062848130at_nat (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.produc2922128104949294807at_nat A) B)) R2)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.transi2703068831062848130at_nat R2)) (@ tptp.collec6321179662152712658at_nat (@ tptp.produc410239310623530412_nat_o (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.transi2703068831062848130at_nat R2))) (and (or (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X4) A)) _let_1) (= X4 A)) (or (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat B) Y4)) _let_1) (= Y4 B)))))))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.transi6264000038957366511cl_nat (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) R2)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.transi6264000038957366511cl_nat R2)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.transi6264000038957366511cl_nat R2))) (and (or (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) A)) _let_1) (= X4 A)) (or (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) Y4)) _let_1) (= Y4 B)))))))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ tptp.transi6261509568448316235cl_int (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int A) B)) R2)) (@ (@ tptp.sup_su6024340866399070445nt_int (@ tptp.transi6261509568448316235cl_int R2)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((X4 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.transi6261509568448316235cl_int R2))) (and (or (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) A)) _let_1) (= X4 A)) (or (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) Y4)) _let_1) (= Y4 B)))))))))))
% 8.20/8.63 (assert (= tptp.int_ge_less_than (lambda ((D5 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z8 tptp.int) (Z tptp.int)) (and (@ (@ tptp.ord_less_eq_int D5) Z8) (@ (@ tptp.ord_less_int Z8) Z))))))))
% 8.20/8.63 (assert (= tptp.log (lambda ((B4 tptp.code_natural) (I tptp.code_natural)) (@ (@ (@ tptp.if_Code_natural (or (@ (@ tptp.ord_le1926595141338095240atural B4) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural I) B4))) tptp.one_one_Code_natural) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.log B4) (@ (@ tptp.divide5121882707175180666atural I) B4)))))))
% 8.20/8.63 (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)))))))))))
% 8.20/8.63 (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))))))))))
% 8.20/8.63 (assert (= tptp.minus_shift (lambda ((R5 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 R5) K3)) L2)) (@ (@ tptp.minus_7197305767214868737atural K3) L2)))))
% 8.20/8.63 (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))))))))))))))))
% 8.20/8.63 (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))))))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z3))) (=> (not (@ (@ tptp.member_nat N2) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) Z3)) (@ (@ tptp.insert_nat N2) _let_1))))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) K2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N2)))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K2)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 8.20/8.63 (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))))))
% 8.20/8.63 (assert (= tptp.produc5538323210962509403atural (lambda ((F3 (-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)) (G3 (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)) (X4 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc8638916746724166107atural G3) (@ F3 X4)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N2) K2)) (not (@ (@ tptp.bit_se1146084159140164899it_int K2) N2)))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K2)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K2) N2))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (assert (forall ((F (-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)) (G (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)) (H (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural))) (let ((_let_1 (@ tptp.produc5538323210962509403atural F))) (= (@ (@ tptp.produc5538323210962509403atural (@ _let_1 G)) H) (@ _let_1 (lambda ((X4 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ (@ tptp.produc5538323210962509403atural (@ G X4)) H) __flatten_var_0)))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N5)) (not (@ (@ tptp.bit_se1146084159140164899it_int B) N5)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) B)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N5)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B) N5)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2))))))
% 8.20/8.63 (assert (forall ((X (-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural))) (= (@ (@ tptp.produc5538323210962509403atural X) tptp.produc6639722614265839536atural) X)))
% 8.20/8.63 (assert (forall ((X tptp.code_natural) (F (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural))) (= (@ (@ tptp.produc5538323210962509403atural (@ tptp.produc6639722614265839536atural X)) F) (@ F X))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se2923211474154528505it_int M) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))))
% 8.20/8.63 (assert (= tptp.produc5538323210962509403atural (lambda ((F3 (-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)) (G3 (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)) (X4 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc8638916746724166107atural G3) (@ F3 X4)))))
% 8.20/8.63 (assert (forall ((Bs tptp.list_o) (N2 tptp.nat)) (= (@ (@ tptp.bit_se8040316288895769887atural (@ (@ (@ tptp.groups2241214984954800037atural tptp.zero_n8403883297036319079atural) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) Bs)) N2) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Bs)) (@ (@ tptp.nth_o Bs) N2)))))
% 8.20/8.63 (assert (forall ((Bs tptp.list_o) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ (@ tptp.groups3417619833198082522nteger tptp.zero_n356916108424825756nteger) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Bs)) N2) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Bs)) (@ (@ tptp.nth_o Bs) N2)))))
% 8.20/8.63 (assert (forall ((Bs tptp.list_o) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ (@ tptp.groups9119017779487936845_o_nat tptp.zero_n2687167440665602831ol_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Bs)) N2) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Bs)) (@ (@ tptp.nth_o Bs) N2)))))
% 8.20/8.63 (assert (forall ((Bs tptp.list_o) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.groups9116527308978886569_o_int tptp.zero_n2684676970156552555ol_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Bs)) N2) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Bs)) (@ (@ tptp.nth_o Bs) N2)))))
% 8.20/8.63 (assert (= tptp.iterate_int_int (lambda ((K3 tptp.code_natural) (F3 (-> tptp.int tptp.int tptp.product_prod_int_int)) (X4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ (@ (@ tptp.if_int2409958687428134794nt_int (= K3 tptp.zero_z2226904508553997617atural)) (@ tptp.product_Pair_int_int X4)) (@ (@ tptp.produc6963641260316735276nt_int (@ F3 X4)) (@ (@ tptp.iterate_int_int (@ (@ tptp.minus_7197305767214868737atural K3) tptp.one_one_Code_natural)) F3))) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.iterat1233435593421607556et_nat (lambda ((K3 tptp.code_natural) (F3 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)) (X4 (-> tptp.produc3658429121746597890et_nat Bool)) (__flatten_var_0 tptp.produc3658429121746597890et_nat)) (@ (@ (@ (@ tptp.if_Pro6440128116348121305et_nat (= K3 tptp.zero_z2226904508553997617atural)) (@ tptp.produc5001842942810119800et_nat X4)) (@ (@ tptp.produc2318911012118706502et_nat (@ F3 X4)) (@ (@ tptp.iterat1233435593421607556et_nat (@ (@ tptp.minus_7197305767214868737atural K3) tptp.one_one_Code_natural)) F3))) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.iterat2702368289246022656et_nat (lambda ((K3 tptp.code_natural) (F3 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)) (X4 (-> tptp.produc3658429121746597890et_nat Bool)) (__flatten_var_0 tptp.produc3925858234332021118et_nat)) (@ (@ (@ (@ tptp.if_Pro5796790085669187537et_nat (= K3 tptp.zero_z2226904508553997617atural)) (@ tptp.produc2245416461498447860et_nat X4)) (@ (@ tptp.produc7537777246833756098et_nat (@ F3 X4)) (@ (@ tptp.iterat2702368289246022656et_nat (@ (@ tptp.minus_7197305767214868737atural K3) tptp.one_one_Code_natural)) F3))) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.iterat9120928542346325760it_nat (lambda ((K3 tptp.code_natural) (F3 (-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)) (X4 tptp.b) (__flatten_var_0 tptp.produc6653097349344004940it_nat)) (@ (@ (@ (@ tptp.if_Pro4080778131203054751it_nat (= K3 tptp.zero_z2226904508553997617atural)) (@ tptp.produc4082563078715348724it_nat X4)) (@ (@ tptp.produc8824551317683396724it_nat (@ F3 X4)) (@ (@ tptp.iterat9120928542346325760it_nat (@ (@ tptp.minus_7197305767214868737atural K3) tptp.one_one_Code_natural)) F3))) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.iterat4993027441371875583it_nat (lambda ((K3 tptp.code_natural) (F3 (-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)) (X4 tptp.a) (__flatten_var_0 tptp.produc6653097349344004940it_nat)) (@ (@ (@ (@ tptp.if_Pro3578090444564244254it_nat (= K3 tptp.zero_z2226904508553997617atural)) (@ tptp.produc9178034014595674355it_nat X4)) (@ (@ tptp.produc3714732129343117170it_nat (@ F3 X4)) (@ (@ tptp.iterat4993027441371875583it_nat (@ (@ tptp.minus_7197305767214868737atural K3) tptp.one_one_Code_natural)) F3))) __flatten_var_0))))
% 8.20/8.63 (assert (= tptp.iterat8892046348760725948atural (lambda ((K3 tptp.code_natural) (F3 (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)) (X4 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ (@ (@ tptp.if_Pro2760142802149639654atural (= K3 tptp.zero_z2226904508553997617atural)) (@ tptp.produc6639722614265839536atural X4)) (@ (@ tptp.produc5538323210962509403atural (@ F3 X4)) (@ (@ tptp.iterat8892046348760725948atural (@ (@ tptp.minus_7197305767214868737atural K3) tptp.one_one_Code_natural)) F3))) __flatten_var_0))))
% 8.20/8.63 (assert (forall ((X tptp.code_natural) (Xa (-> tptp.int tptp.int tptp.product_prod_int_int)) (Xb tptp.int) (Y (-> tptp.int tptp.product_prod_int_int))) (let ((_let_1 (= X tptp.zero_z2226904508553997617atural))) (=> (= (@ (@ (@ tptp.iterate_int_int X) Xa) Xb) Y) (and (=> _let_1 (= Y (@ tptp.product_Pair_int_int Xb))) (=> (not _let_1) (= Y (@ (@ tptp.produc6963641260316735276nt_int (@ Xa Xb)) (@ (@ tptp.iterate_int_int (@ (@ tptp.minus_7197305767214868737atural X) tptp.one_one_Code_natural)) Xa)))))))))
% 8.20/8.63 (assert (forall ((X tptp.code_natural) (Xa (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)) (Xb (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat))) (let ((_let_1 (= X tptp.zero_z2226904508553997617atural))) (=> (= (@ (@ (@ tptp.iterat1233435593421607556et_nat X) Xa) Xb) Y) (and (=> _let_1 (= Y (@ tptp.produc5001842942810119800et_nat Xb))) (=> (not _let_1) (= Y (@ (@ tptp.produc2318911012118706502et_nat (@ Xa Xb)) (@ (@ tptp.iterat1233435593421607556et_nat (@ (@ tptp.minus_7197305767214868737atural X) tptp.one_one_Code_natural)) Xa)))))))))
% 8.20/8.63 (assert (forall ((X tptp.code_natural) (Xa (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)) (Xb (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat))) (let ((_let_1 (= X tptp.zero_z2226904508553997617atural))) (=> (= (@ (@ (@ tptp.iterat2702368289246022656et_nat X) Xa) Xb) Y) (and (=> _let_1 (= Y (@ tptp.produc2245416461498447860et_nat Xb))) (=> (not _let_1) (= Y (@ (@ tptp.produc7537777246833756098et_nat (@ Xa Xb)) (@ (@ tptp.iterat2702368289246022656et_nat (@ (@ tptp.minus_7197305767214868737atural X) tptp.one_one_Code_natural)) Xa)))))))))
% 8.20/8.63 (assert (forall ((X tptp.code_natural) (Xa (-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)) (Xb tptp.b) (Y (-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat))) (let ((_let_1 (= X tptp.zero_z2226904508553997617atural))) (=> (= (@ (@ (@ tptp.iterat9120928542346325760it_nat X) Xa) Xb) Y) (and (=> _let_1 (= Y (@ tptp.produc4082563078715348724it_nat Xb))) (=> (not _let_1) (= Y (@ (@ tptp.produc8824551317683396724it_nat (@ Xa Xb)) (@ (@ tptp.iterat9120928542346325760it_nat (@ (@ tptp.minus_7197305767214868737atural X) tptp.one_one_Code_natural)) Xa)))))))))
% 8.20/8.63 (assert (forall ((X tptp.code_natural) (Xa (-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)) (Xb tptp.a) (Y (-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat))) (let ((_let_1 (= X tptp.zero_z2226904508553997617atural))) (=> (= (@ (@ (@ tptp.iterat4993027441371875583it_nat X) Xa) Xb) Y) (and (=> _let_1 (= Y (@ tptp.produc9178034014595674355it_nat Xb))) (=> (not _let_1) (= Y (@ (@ tptp.produc3714732129343117170it_nat (@ Xa Xb)) (@ (@ tptp.iterat4993027441371875583it_nat (@ (@ tptp.minus_7197305767214868737atural X) tptp.one_one_Code_natural)) Xa)))))))))
% 8.20/8.63 (assert (forall ((X tptp.code_natural) (Xa (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)) (Xb tptp.code_natural) (Y (-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural))) (let ((_let_1 (= X tptp.zero_z2226904508553997617atural))) (=> (= (@ (@ (@ tptp.iterat8892046348760725948atural X) Xa) Xb) Y) (and (=> _let_1 (= Y (@ tptp.produc6639722614265839536atural Xb))) (=> (not _let_1) (= Y (@ (@ tptp.produc5538323210962509403atural (@ Xa Xb)) (@ (@ tptp.iterat8892046348760725948atural (@ (@ tptp.minus_7197305767214868737atural X) tptp.one_one_Code_natural)) Xa)))))))))
% 8.20/8.63 (assert (forall ((N2 tptp.nat) (M tptp.nat) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K2) N2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K2))))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (K2 tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K2) L)) N2) (or (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1146084159140164899it_int K2) N2)) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) (@ (@ tptp.minus_minus_nat N2) M)))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int)) (not (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K2))) (=> (forall ((M4 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K2))) (=> (@ (@ 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)))))))))))
% 8.20/8.63 (assert (forall ((A tptp.code_natural) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se8040316288895769887atural (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) A)) N2) (or (@ (@ tptp.bit_se8040316288895769887atural A) N2) (= N2 tptp.zero_zero_nat))))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) N2) (or (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (= N2 tptp.zero_zero_nat))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (= N2 tptp.zero_zero_nat))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (= N2 tptp.zero_zero_nat))))))
% 8.20/8.63 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_2397367101498566445atural _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (not (@ (@ tptp.bit_se8040316288895769887atural A) (@ tptp.suc J3)))) (= (@ (@ tptp.bit_se8040316288895769887atural (@ (@ tptp.plus_p4538020629002901425atural A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_Code_natural _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se8040316288895769887atural _let_2) N2))))))))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (not (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc J3)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N2))))))))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc J3)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N2))))))))))
% 8.20/8.63 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc J3)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1148574629649215175it_nat _let_2) N2))))))))))
% 8.20/8.63 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) M3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))
% 8.20/8.63 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M3)) (not (@ _let_2 N)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 8.20/8.63 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se2046307713759805098atural A) tptp.one_one_Code_natural) (@ (@ tptp.minus_7197305767214868737atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ tptp.zero_n8403883297036319079atural _let_1))) (@ tptp.zero_n8403883297036319079atural (not _let_1)))))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se3222712562003087583nteger A) tptp.one_one_Code_integer) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger _let_1))) (@ tptp.zero_n356916108424825756nteger (not _let_1)))))))
% 8.20/8.63 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) tptp.one_one_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 8.20/8.63 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6526347334894502574or_int A) tptp.one_one_int) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int _let_1))) (@ tptp.zero_n2684676970156552555ol_int (not _let_1)))))))
% 8.20/8.63 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se2046307713759805098atural tptp.one_one_Code_natural) A) (@ (@ tptp.minus_7197305767214868737atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ tptp.zero_n8403883297036319079atural _let_1))) (@ tptp.zero_n8403883297036319079atural (not _let_1)))))))
% 8.20/8.63 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se3222712562003087583nteger tptp.one_one_Code_integer) A) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger _let_1))) (@ tptp.zero_n356916108424825756nteger (not _let_1)))))))
% 8.20/8.63 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 8.20/8.63 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int _let_1))) (@ tptp.zero_n2684676970156552555ol_int (not _let_1)))))))
% 8.20/8.63 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))
% 8.20/8.63 (assert (forall ((F (-> tptp.int tptp.rat)) (A tptp.rat) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.groups7852591826665563233nt_rat F) A))) (= (@ _let_1 (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.plus_plus_rat (@ F X)) (@ (@ tptp.times_times_rat A) (@ _let_1 Xs)))))))
% 8.20/8.63 (assert (forall ((F (-> tptp.nat tptp.rat)) (A tptp.rat) (X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.groups6853238114764508677at_rat F) A))) (= (@ _let_1 (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.plus_plus_rat (@ F X)) (@ (@ tptp.times_times_rat A) (@ _let_1 Xs)))))))
% 8.20/8.63 (assert (forall ((F (-> tptp.int tptp.nat)) (A tptp.nat) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.groups8487721886752058969nt_nat F) A))) (= (@ _let_1 (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.plus_plus_nat (@ F X)) (@ (@ tptp.times_times_nat A) (@ _let_1 Xs)))))))
% 8.20/8.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.groups7488368174851004413at_nat F) A))) (= (@ _let_1 (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.plus_plus_nat (@ F X)) (@ (@ tptp.times_times_nat A) (@ _let_1 Xs)))))))
% 8.20/8.63 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.groups8485231416243008693nt_int F) A))) (= (@ _let_1 (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.plus_plus_int (@ F X)) (@ (@ tptp.times_times_int A) (@ _let_1 Xs)))))))
% 8.20/8.63 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.groups7485877704341954137at_int F) A))) (= (@ _let_1 (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.plus_plus_int (@ F X)) (@ (@ tptp.times_times_int A) (@ _let_1 Xs)))))))
% 8.20/8.63 (assert (forall ((F (-> Bool tptp.int)) (A tptp.int) (X Bool) (Xs tptp.list_o)) (let ((_let_1 (@ (@ tptp.groups9116527308978886569_o_int F) A))) (= (@ _let_1 (@ (@ tptp.cons_o X) Xs)) (@ (@ tptp.plus_plus_int (@ F X)) (@ (@ tptp.times_times_int A) (@ _let_1 Xs)))))))
% 8.20/8.63 (assert (forall ((X tptp.code_natural) (Xa (-> tptp.int tptp.int tptp.product_prod_int_int)) (Xb tptp.int) (Y (-> tptp.int tptp.product_prod_int_int))) (let ((_let_1 (@ (@ tptp.accp_P5309764456724190780nt_int tptp.iterate_rel_int_int) (@ (@ tptp.produc6480503542405096427nt_int X) (@ (@ tptp.produc8811497915304161060nt_int Xa) Xb))))) (let ((_let_2 (= X tptp.zero_z2226904508553997617atural))) (=> (= (@ (@ (@ tptp.iterate_int_int X) Xa) Xb) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ tptp.product_Pair_int_int Xb))) (=> (not _let_2) (= Y (@ (@ tptp.produc6963641260316735276nt_int (@ Xa Xb)) (@ (@ tptp.iterate_int_int (@ (@ tptp.minus_7197305767214868737atural X) tptp.one_one_Code_natural)) Xa))))) (not _let_1)))))))))
% 8.20/8.63 (assert (forall ((X tptp.code_natural) (Xa (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)) (Xb (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat))) (let ((_let_1 (@ (@ tptp.accp_P2863604582003348699_nat_o tptp.iterat2000369294365210145et_nat) (@ (@ tptp.produc1685672994636548566_nat_o X) (@ (@ tptp.produc417064122970982599_nat_o Xa) Xb))))) (let ((_let_2 (= X tptp.zero_z2226904508553997617atural))) (=> (= (@ (@ (@ tptp.iterat1233435593421607556et_nat X) Xa) Xb) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ tptp.produc5001842942810119800et_nat Xb))) (=> (not _let_2) (= Y (@ (@ tptp.produc2318911012118706502et_nat (@ Xa Xb)) (@ (@ tptp.iterat1233435593421607556et_nat (@ (@ tptp.minus_7197305767214868737atural X) tptp.one_one_Code_natural)) Xa))))) (not _let_1)))))))))
% 8.20/8.63 (assert (forall ((X tptp.code_natural) (Xa (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)) (Xb (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat))) (let ((_let_1 (@ (@ tptp.accp_P5472185023545635811_nat_o tptp.iterat7486693702726674333et_nat) (@ (@ tptp.produc722914403947760862_nat_o X) (@ (@ tptp.produc5247183594425207759_nat_o Xa) Xb))))) (let ((_let_2 (= X tptp.zero_z2226904508553997617atural))) (=> (= (@ (@ (@ tptp.iterat2702368289246022656et_nat X) Xa) Xb) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ tptp.produc2245416461498447860et_nat Xb))) (=> (not _let_2) (= Y (@ (@ tptp.produc7537777246833756098et_nat (@ Xa Xb)) (@ (@ tptp.iterat2702368289246022656et_nat (@ (@ tptp.minus_7197305767214868737atural X) tptp.one_one_Code_natural)) Xa))))) (not _let_1)))))))))
% 8.20/8.63 (assert (forall ((X tptp.code_natural) (Xa (-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)) (Xb tptp.b) (Y (-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat))) (let ((_let_1 (@ (@ tptp.accp_P8256022550677833493_nat_b tptp.iterat7179843830775474589it_nat) (@ (@ tptp.produc7509976829882447632_nat_b X) (@ (@ tptp.produc5258162843807585025_nat_b Xa) Xb))))) (let ((_let_2 (= X tptp.zero_z2226904508553997617atural))) (=> (= (@ (@ (@ tptp.iterat9120928542346325760it_nat X) Xa) Xb) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ tptp.produc4082563078715348724it_nat Xb))) (=> (not _let_2) (= Y (@ (@ tptp.produc8824551317683396724it_nat (@ Xa Xb)) (@ (@ tptp.iterat9120928542346325760it_nat (@ (@ tptp.minus_7197305767214868737atural X) tptp.one_one_Code_natural)) Xa))))) (not _let_1)))))))))
% 8.20/8.63 (assert (forall ((X tptp.code_natural) (Xa (-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)) (Xb tptp.a) (Y (-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat))) (let ((_let_1 (@ (@ tptp.accp_P7857408453303007510_nat_a tptp.iterat3051942729801024412it_nat) (@ (@ tptp.produc1823638919063574929_nat_a X) (@ (@ tptp.produc8795196974146716930_nat_a Xa) Xb))))) (let ((_let_2 (= X tptp.zero_z2226904508553997617atural))) (=> (= (@ (@ (@ tptp.iterat4993027441371875583it_nat X) Xa) Xb) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ tptp.produc9178034014595674355it_nat Xb))) (=> (not _let_2) (= Y (@ (@ tptp.produc3714732129343117170it_nat (@ Xa Xb)) (@ (@ tptp.iterat4993027441371875583it_nat (@ (@ tptp.minus_7197305767214868737atural X) tptp.one_one_Code_natural)) Xa))))) (not _let_1)))))))))
% 8.20/8.63 (assert (forall ((X tptp.code_natural) (Xa (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)) (Xb tptp.code_natural) (Y (-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural))) (let ((_let_1 (@ (@ tptp.accp_P9117636446167716760atural tptp.iterat8136814461032266713atural) (@ (@ tptp.produc7296465590736685127atural X) (@ (@ tptp.produc2044891599319335296atural Xa) Xb))))) (let ((_let_2 (= X tptp.zero_z2226904508553997617atural))) (=> (= (@ (@ (@ tptp.iterat8892046348760725948atural X) Xa) Xb) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ tptp.produc6639722614265839536atural Xb))) (=> (not _let_2) (= Y (@ (@ tptp.produc5538323210962509403atural (@ Xa Xb)) (@ (@ tptp.iterat8892046348760725948atural (@ (@ tptp.minus_7197305767214868737atural X) tptp.one_one_Code_natural)) Xa))))) (not _let_1)))))))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat)) (= (@ tptp.the_el221668144340439132at_nat (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat)) X)))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.the_el2281957884133575798at_nat (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat)) X)))
% 8.20/8.63 (assert (forall ((X Bool)) (= (@ tptp.the_elem_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) X)))
% 8.20/8.63 (assert (forall ((X tptp.nat)) (= (@ tptp.the_elem_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) X)))
% 8.20/8.63 (assert (forall ((X tptp.int)) (= (@ tptp.the_elem_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) X)))
% 8.20/8.63 (assert (= tptp.inc_shift (lambda ((V2 tptp.code_natural) (K3 tptp.code_natural)) (@ (@ (@ tptp.if_Code_natural (= V2 K3)) tptp.one_one_Code_natural) (@ (@ tptp.plus_p4538020629002901425atural K3) tptp.one_one_Code_natural)))))
% 8.20/8.63 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q8 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q8))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int K2) L)) (= (@ _let_1 K2) (@ _let_1 L))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int K2) L)) tptp.zero_zero_int) (not (= (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))))
% 8.20/8.63 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 8.20/8.63 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) L) L)))
% 8.20/8.63 (assert (forall ((K2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger K2) tptp.zero_z3403309356797280102nteger) K2)))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (assert (forall ((K2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K2)) N2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2) (@ (@ tptp.bit_se1146084159140164899it_int K2) N2)))))
% 8.20/8.63 (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)))))))
% 8.20/8.63 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (not (= (not (@ _let_2 K3)) (not (@ _let_2 L2)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 8.20/8.63 (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))))))))))
% 8.20/8.63 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (= K3 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L2)) (@ (@ (@ tptp.if_int (= L2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))))))
% 8.20/8.63 (assert (= tptp.is_sin2937591304547752795at_nat (lambda ((A6 tptp.set_Pr4329608150637261639at_nat)) (= A6 (@ (@ tptp.insert9069300056098147895at_nat (@ tptp.the_el221668144340439132at_nat A6)) tptp.bot_bo228742789529271731at_nat)))))
% 8.20/8.63 (assert (= tptp.is_sin2850979758926227957at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat)) (= A6 (@ (@ tptp.insert8211810215607154385at_nat (@ tptp.the_el2281957884133575798at_nat A6)) tptp.bot_bo2099793752762293965at_nat)))))
% 8.20/8.63 (assert (= tptp.is_singleton_o (lambda ((A6 tptp.set_o)) (= A6 (@ (@ tptp.insert_o (@ tptp.the_elem_o A6)) tptp.bot_bot_set_o)))))
% 8.20/8.63 (assert (= tptp.is_singleton_nat (lambda ((A6 tptp.set_nat)) (= A6 (@ (@ tptp.insert_nat (@ tptp.the_elem_nat A6)) tptp.bot_bot_set_nat)))))
% 8.20/8.63 (assert (= tptp.is_singleton_int (lambda ((A6 tptp.set_int)) (= A6 (@ (@ tptp.insert_int (@ tptp.the_elem_int A6)) tptp.bot_bot_set_int)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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 ((Q8 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q8)))) (@ (@ 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)))))
% 8.20/8.63 (assert (forall ((X tptp.produc3843707927480180839at_nat)) (@ tptp.is_sin2937591304547752795at_nat (@ (@ tptp.insert9069300056098147895at_nat X) tptp.bot_bo228742789529271731at_nat))))
% 8.20/8.63 (assert (forall ((X tptp.product_prod_nat_nat)) (@ tptp.is_sin2850979758926227957at_nat (@ (@ tptp.insert8211810215607154385at_nat X) tptp.bot_bo2099793752762293965at_nat))))
% 8.20/8.63 (assert (forall ((X Bool)) (@ tptp.is_singleton_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))
% 8.20/8.63 (assert (forall ((X tptp.nat)) (@ tptp.is_singleton_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))
% 8.20/8.63 (assert (forall ((X tptp.int)) (@ tptp.is_singleton_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (assert (forall ((K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_ri7919022796975470100ot_int K2)) (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int))))
% 8.20/8.63 (assert (forall ((K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit_ri7919022796975470100ot_int K2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K2))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((H (-> tptp.option_num tptp.option_num)) (F1 tptp.option_num) (F2 (-> tptp.nat tptp.option_num)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_option_num F1) F2) Nat)) (@ (@ (@ tptp.case_nat_option_num (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F2 X4)))) Nat))))
% 8.20/8.63 (assert (forall ((H (-> tptp.option_num tptp.nat)) (F1 tptp.option_num) (F2 (-> tptp.nat tptp.option_num)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_option_num F1) F2) Nat)) (@ (@ (@ tptp.case_nat_nat (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F2 X4)))) Nat))))
% 8.20/8.63 (assert (forall ((H (-> tptp.option_num Bool)) (F1 tptp.option_num) (F2 (-> tptp.nat tptp.option_num)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_option_num F1) F2) Nat)) (@ (@ (@ tptp.case_nat_o (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F2 X4)))) Nat))))
% 8.20/8.63 (assert (forall ((H (-> tptp.nat tptp.option_num)) (F1 tptp.nat) (F2 (-> tptp.nat tptp.nat)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_nat F1) F2) Nat)) (@ (@ (@ tptp.case_nat_option_num (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F2 X4)))) Nat))))
% 8.20/8.63 (assert (forall ((H (-> tptp.nat tptp.nat)) (F1 tptp.nat) (F2 (-> tptp.nat tptp.nat)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_nat F1) F2) Nat)) (@ (@ (@ tptp.case_nat_nat (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F2 X4)))) Nat))))
% 8.20/8.63 (assert (forall ((H (-> tptp.nat Bool)) (F1 tptp.nat) (F2 (-> tptp.nat tptp.nat)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_nat F1) F2) Nat)) (@ (@ (@ tptp.case_nat_o (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F2 X4)))) Nat))))
% 8.20/8.63 (assert (forall ((H (-> Bool tptp.option_num)) (F1 Bool) (F2 (-> tptp.nat Bool)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_o F1) F2) Nat)) (@ (@ (@ tptp.case_nat_option_num (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F2 X4)))) Nat))))
% 8.20/8.63 (assert (forall ((H (-> Bool tptp.nat)) (F1 Bool) (F2 (-> tptp.nat Bool)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_o F1) F2) Nat)) (@ (@ (@ tptp.case_nat_nat (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F2 X4)))) Nat))))
% 8.20/8.63 (assert (forall ((H (-> Bool Bool)) (F1 Bool) (F2 (-> tptp.nat Bool)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_o F1) F2) Nat)) (@ (@ (@ tptp.case_nat_o (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F2 X4)))) Nat))))
% 8.20/8.63 (assert (forall ((H (-> tptp.option_num tptp.option_num)) (F1 tptp.option_num) (F2 (-> tptp.num tptp.option_num)) (F32 (-> tptp.num tptp.option_num)) (Num tptp.num)) (= (@ H (@ (@ (@ (@ tptp.case_num_option_num F1) F2) F32) Num)) (@ (@ (@ (@ tptp.case_num_option_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F2 X4)))) (lambda ((X4 tptp.num)) (@ H (@ F32 X4)))) Num))))
% 8.20/8.63 (assert (forall ((F1 tptp.option_num) (F2 (-> tptp.nat tptp.option_num))) (= (@ (@ (@ tptp.case_nat_option_num F1) F2) tptp.zero_zero_nat) F1)))
% 8.20/8.63 (assert (forall ((F1 tptp.nat) (F2 (-> tptp.nat tptp.nat))) (= (@ (@ (@ tptp.case_nat_nat F1) F2) tptp.zero_zero_nat) F1)))
% 8.20/8.63 (assert (forall ((F1 Bool) (F2 (-> tptp.nat Bool))) (= (@ (@ (@ tptp.case_nat_o F1) F2) tptp.zero_zero_nat) F1)))
% 8.20/8.63 (assert (forall ((F1 tptp.option_num) (F2 (-> tptp.nat tptp.option_num)) (X2 tptp.nat)) (= (@ (@ (@ tptp.case_nat_option_num F1) F2) (@ tptp.suc X2)) (@ F2 X2))))
% 8.20/8.63 (assert (forall ((F1 tptp.nat) (F2 (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (= (@ (@ (@ tptp.case_nat_nat F1) F2) (@ tptp.suc X2)) (@ F2 X2))))
% 8.20/8.63 (assert (forall ((F1 Bool) (F2 (-> tptp.nat Bool)) (X2 tptp.nat)) (= (@ (@ (@ tptp.case_nat_o F1) F2) (@ tptp.suc X2)) (@ F2 X2))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.minus_minus_int (@ tptp.bit_ri7919022796975470100ot_int A)) B))))
% 8.20/8.63 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A)) B))))
% 8.20/8.63 (assert (forall ((Xa tptp.int) (X tptp.int)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.plus_plus_int Xa) X)))))
% 8.20/8.63 (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))))
% 8.20/8.63 (assert (forall ((F1 tptp.option_num) (F2 (-> tptp.num tptp.option_num)) (F32 (-> tptp.num tptp.option_num)) (X2 tptp.num)) (= (@ (@ (@ (@ tptp.case_num_option_num F1) F2) F32) (@ tptp.bit0 X2)) (@ F2 X2))))
% 8.20/8.63 (assert (forall ((F1 tptp.option_num) (F2 (-> tptp.num tptp.option_num)) (F32 (-> tptp.num tptp.option_num))) (= (@ (@ (@ (@ tptp.case_num_option_num F1) F2) F32) tptp.one) F1)))
% 8.20/8.63 (assert (forall ((F1 tptp.option_num) (F2 (-> tptp.num tptp.option_num)) (F32 (-> tptp.num tptp.option_num)) (X32 tptp.num)) (= (@ (@ (@ (@ tptp.case_num_option_num F1) F2) F32) (@ tptp.bit1 X32)) (@ F32 X32))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int)) (=> (not (= A4 tptp.bot_bo1488462491386950373nt_int)) (=> (forall ((X3 tptp.set_Pr958786334691620121nt_int) (Y3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X3) A4) (=> (@ (@ tptp.member2340774599025711042nt_int Y3) A4) (= X3 Y3)))) (@ tptp.is_sin6299389887212142093nt_int A4)))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_set_nat)) (=> (not (= A4 tptp.bot_bot_set_set_nat)) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) A4) (=> (@ (@ tptp.member_set_nat Y3) A4) (= X3 Y3)))) (@ tptp.is_singleton_set_nat A4)))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (=> (not (= A4 tptp.bot_bo2099793752762293965at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A4) (=> (@ (@ tptp.member8440522571783428010at_nat Y3) A4) (= X3 Y3)))) (@ tptp.is_sin2850979758926227957at_nat A4)))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_o)) (=> (not (= A4 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool) (Y3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (=> (@ (@ tptp.member_o Y3) A4) (= X3 Y3)))) (@ tptp.is_singleton_o A4)))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_nat)) (=> (not (= A4 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (=> (@ (@ tptp.member_nat Y3) A4) (= X3 Y3)))) (@ tptp.is_singleton_nat A4)))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_int)) (=> (not (= A4 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (=> (@ (@ tptp.member_int Y3) A4) (= X3 Y3)))) (@ tptp.is_singleton_int A4)))))
% 8.20/8.63 (assert (= tptp.uminus1351360451143612070nteger (lambda ((A5 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.bit_ri7632146776885996613nteger A5)) tptp.one_one_Code_integer))))
% 8.20/8.63 (assert (= tptp.uminus_uminus_int (lambda ((A5 tptp.int)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A5)) tptp.one_one_int))))
% 8.20/8.63 (assert (forall ((X tptp.int) (Xs tptp.list_int) (N2 tptp.nat)) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N2) (@ (@ (@ tptp.case_nat_int X) (@ tptp.nth_int Xs)) N2))))
% 8.20/8.63 (assert (forall ((X tptp.option_num) (Xs tptp.list_option_num) (N2 tptp.nat)) (= (@ (@ tptp.nth_option_num (@ (@ tptp.cons_option_num X) Xs)) N2) (@ (@ (@ tptp.case_nat_option_num X) (@ tptp.nth_option_num Xs)) N2))))
% 8.20/8.63 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (N2 tptp.nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N2) (@ (@ (@ tptp.case_nat_nat X) (@ tptp.nth_nat Xs)) N2))))
% 8.20/8.63 (assert (forall ((X Bool) (Xs tptp.list_o) (N2 tptp.nat)) (= (@ (@ tptp.nth_o (@ (@ tptp.cons_o X) Xs)) N2) (@ (@ (@ tptp.case_nat_o X) (@ tptp.nth_o Xs)) N2))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.bit_se1745604003318907178nteger M) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.bit_se2119862282449309892nteger N2))) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N2))) tptp.zero_zero_int))))
% 8.20/8.63 (assert (= tptp.is_sin2937591304547752795at_nat (lambda ((A6 tptp.set_Pr4329608150637261639at_nat)) (exists ((X4 tptp.produc3843707927480180839at_nat)) (= A6 (@ (@ tptp.insert9069300056098147895at_nat X4) tptp.bot_bo228742789529271731at_nat))))))
% 8.20/8.63 (assert (= tptp.is_sin2850979758926227957at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat)) (exists ((X4 tptp.product_prod_nat_nat)) (= A6 (@ (@ tptp.insert8211810215607154385at_nat X4) tptp.bot_bo2099793752762293965at_nat))))))
% 8.20/8.63 (assert (= tptp.is_singleton_o (lambda ((A6 tptp.set_o)) (exists ((X4 Bool)) (= A6 (@ (@ tptp.insert_o X4) tptp.bot_bot_set_o))))))
% 8.20/8.63 (assert (= tptp.is_singleton_nat (lambda ((A6 tptp.set_nat)) (exists ((X4 tptp.nat)) (= A6 (@ (@ tptp.insert_nat X4) tptp.bot_bot_set_nat))))))
% 8.20/8.63 (assert (= tptp.is_singleton_int (lambda ((A6 tptp.set_int)) (exists ((X4 tptp.int)) (= A6 (@ (@ tptp.insert_int X4) tptp.bot_bot_set_int))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat)) (=> (@ tptp.is_sin2937591304547752795at_nat A4) (not (forall ((X3 tptp.produc3843707927480180839at_nat)) (not (= A4 (@ (@ tptp.insert9069300056098147895at_nat X3) tptp.bot_bo228742789529271731at_nat))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.is_sin2850979758926227957at_nat A4) (not (forall ((X3 tptp.product_prod_nat_nat)) (not (= A4 (@ (@ tptp.insert8211810215607154385at_nat X3) tptp.bot_bo2099793752762293965at_nat))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_o)) (=> (@ tptp.is_singleton_o A4) (not (forall ((X3 Bool)) (not (= A4 (@ (@ tptp.insert_o X3) tptp.bot_bot_set_o))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.is_singleton_nat A4) (not (forall ((X3 tptp.nat)) (not (= A4 (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))))))))
% 8.20/8.63 (assert (forall ((A4 tptp.set_int)) (=> (@ tptp.is_singleton_int A4) (not (forall ((X3 tptp.int)) (not (= A4 (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))))))))
% 8.20/8.63 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 8.20/8.64 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) K3))) (@ (@ tptp.times_times_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K3) _let_1))))))))
% 8.20/8.64 (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) (J 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 (= J tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_num _let_2) tptp.one)))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 8.20/8.64 (assert (= tptp.code_int_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K3)))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((L2 tptp.code_integer) (J tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.code_int_of_integer L2)))) (@ (@ (@ tptp.if_int (= J tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 8.20/8.64 (assert (forall ((P2 (-> tptp.option_num Bool)) (F1 tptp.option_num) (F2 (-> tptp.nat tptp.option_num)) (Nat tptp.nat)) (let ((_let_1 (@ tptp.pred Nat))) (= (@ P2 (@ (@ (@ tptp.case_nat_option_num F1) F2) Nat)) (not (or (and (= Nat tptp.zero_zero_nat) (not (@ P2 F1))) (and (= Nat (@ tptp.suc _let_1)) (not (@ P2 (@ F2 _let_1))))))))))
% 8.20/8.64 (assert (forall ((P2 (-> tptp.nat Bool)) (F1 tptp.nat) (F2 (-> tptp.nat tptp.nat)) (Nat tptp.nat)) (let ((_let_1 (@ tptp.pred Nat))) (= (@ P2 (@ (@ (@ tptp.case_nat_nat F1) F2) Nat)) (not (or (and (= Nat tptp.zero_zero_nat) (not (@ P2 F1))) (and (= Nat (@ tptp.suc _let_1)) (not (@ P2 (@ F2 _let_1))))))))))
% 8.20/8.64 (assert (forall ((P2 (-> Bool Bool)) (F1 Bool) (F2 (-> tptp.nat Bool)) (Nat tptp.nat)) (let ((_let_1 (@ tptp.pred Nat))) (= (@ P2 (@ (@ (@ tptp.case_nat_o F1) F2) Nat)) (not (or (and (= Nat tptp.zero_zero_nat) (not (@ P2 F1))) (and (= Nat (@ tptp.suc _let_1)) (not (@ P2 (@ F2 _let_1))))))))))
% 8.20/8.64 (assert (forall ((P2 (-> tptp.option_num Bool)) (F1 tptp.option_num) (F2 (-> tptp.nat tptp.option_num)) (Nat tptp.nat)) (let ((_let_1 (@ tptp.pred Nat))) (= (@ P2 (@ (@ (@ tptp.case_nat_option_num F1) F2) Nat)) (and (=> (= Nat tptp.zero_zero_nat) (@ P2 F1)) (=> (= Nat (@ tptp.suc _let_1)) (@ P2 (@ F2 _let_1))))))))
% 8.20/8.64 (assert (forall ((P2 (-> tptp.nat Bool)) (F1 tptp.nat) (F2 (-> tptp.nat tptp.nat)) (Nat tptp.nat)) (let ((_let_1 (@ tptp.pred Nat))) (= (@ P2 (@ (@ (@ tptp.case_nat_nat F1) F2) Nat)) (and (=> (= Nat tptp.zero_zero_nat) (@ P2 F1)) (=> (= Nat (@ tptp.suc _let_1)) (@ P2 (@ F2 _let_1))))))))
% 8.20/8.64 (assert (forall ((P2 (-> Bool Bool)) (F1 Bool) (F2 (-> tptp.nat Bool)) (Nat tptp.nat)) (let ((_let_1 (@ tptp.pred Nat))) (= (@ P2 (@ (@ (@ tptp.case_nat_o F1) F2) Nat)) (and (=> (= Nat tptp.zero_zero_nat) (@ P2 F1)) (=> (= Nat (@ tptp.suc _let_1)) (@ P2 (@ F2 _let_1))))))))
% 8.20/8.64 (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 ((Q8 tptp.nat)) (@ (@ tptp.ord_less_nat Q8) N2))))))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups4538972089207619220nt_int F) A4)) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_rat (@ F X4)))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups4538972089207619220nt_int F) A4)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_int (@ F X4)))) A4))))
% 8.20/8.64 (assert (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.plus_p5714425477246183910nteger X) Xa)) (@ (@ tptp.plus_plus_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa)))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.nat)) (A4 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A4)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((X4 tptp.nat)) (@ tptp.semiri4939895301339042750nteger (@ F X4)))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X4)))) A4))))
% 8.20/8.64 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X23 tptp.nat)) X23))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A4 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I)) A))) A4)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat F) A4)) A))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A4 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I)) A))) A4)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int F) A4)) A))))
% 8.20/8.64 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu2 tptp.nat)) true)) Nat))))
% 8.20/8.64 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu2 tptp.nat)) false)) Nat))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((X4 tptp.code_integer) (Xa2 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer X4)) (@ tptp.code_int_of_integer Xa2)))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((X4 tptp.code_integer) (Xa2 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer X4)) (@ tptp.code_int_of_integer Xa2)))))
% 8.20/8.64 (assert (forall ((X tptp.rat) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.plus_plus_nat M) I)))) I5) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I5))))))
% 8.20/8.64 (assert (forall ((X tptp.int) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.plus_plus_nat M) I)))) I5) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I5))))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (assert (forall ((W2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se8040316288895769887atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 W2))) N2) (@ (@ (@ tptp.case_nat_o false) (@ tptp.bit_se8040316288895769887atural (@ tptp.numera5444537566228673987atural W2))) N2))))
% 8.20/8.64 (assert (forall ((W2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 W2))) N2) (@ (@ (@ tptp.case_nat_o false) (@ tptp.bit_se9216721137139052372nteger (@ tptp.numera6620942414471956472nteger W2))) N2))))
% 8.20/8.64 (assert (forall ((W2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W2))) N2) (@ (@ (@ tptp.case_nat_o false) (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W2))) N2))))
% 8.20/8.64 (assert (forall ((W2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) N2) (@ (@ (@ tptp.case_nat_o false) (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W2))) N2))))
% 8.20/8.64 (assert (forall ((W2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se8040316288895769887atural (@ tptp.numera5444537566228673987atural (@ tptp.bit1 W2))) N2) (@ (@ (@ tptp.case_nat_o true) (@ tptp.bit_se8040316288895769887atural (@ tptp.numera5444537566228673987atural W2))) N2))))
% 8.20/8.64 (assert (forall ((W2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 W2))) N2) (@ (@ (@ tptp.case_nat_o true) (@ tptp.bit_se9216721137139052372nteger (@ tptp.numera6620942414471956472nteger W2))) N2))))
% 8.20/8.64 (assert (forall ((W2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W2))) N2) (@ (@ (@ tptp.case_nat_o true) (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W2))) N2))))
% 8.20/8.64 (assert (forall ((W2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) N2) (@ (@ (@ tptp.case_nat_o true) (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W2))) N2))))
% 8.20/8.64 (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 ((Q8 tptp.nat)) (@ (@ tptp.ord_less_nat Q8) N2))))))))
% 8.20/8.64 (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 ((Q8 tptp.nat)) (@ (@ tptp.ord_less_nat Q8) N2))))))))
% 8.20/8.64 (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 ((Q8 tptp.nat)) (@ (@ tptp.ord_less_nat Q8) N2))))))))
% 8.20/8.64 (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 ((Q8 tptp.nat)) (@ (@ tptp.ord_less_nat Q8) N2))))))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I tptp.int)) (@ tptp.abs_abs_int (@ F I)))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A4))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I tptp.int)) (@ tptp.abs_abs_int (@ F I)))) A4))))
% 8.20/8.64 (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 ((I Bool)) (@ (@ tptp.times_3573771949741848930nteger (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.code_integer)) (A (-> tptp.nat tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.code_integer)) (A (-> tptp.int tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((I tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 8.20/8.64 (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 ((I Bool)) (@ (@ tptp.times_times_rat (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 8.20/8.64 (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 ((I tptp.int)) (@ (@ tptp.times_times_rat (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 8.20/8.64 (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 ((I Bool)) (@ (@ tptp.times_times_int (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.times_times_int (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 8.20/8.64 (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 ((I tptp.int)) (@ (@ tptp.times_times_int (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 8.20/8.64 (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 ((I tptp.set_nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I)) (@ X I)))) I5)) B))) Delta))))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((A5 tptp.int)) (@ tptp.abs_abs_int (@ F A5)))) A4)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((A5 tptp.int)) (@ tptp.abs_abs_int (@ F A5)))) A4))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Uu2 tptp.nat)) tptp.zero_zero_nat)) A4) tptp.zero_zero_nat)))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Uu2 tptp.int)) tptp.zero_zero_int)) A4) tptp.zero_zero_int)))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.nat)) (A4 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A4)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A4))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (B5 tptp.set_nat) (A4 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ G I)) B5))) A4) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ G I) J))) A4))) B5))))
% 8.20/8.64 (assert (forall ((G (-> tptp.int tptp.int tptp.int)) (B5 tptp.set_int) (A4 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (@ G I)) B5))) A4) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I tptp.int)) (@ (@ G I) J))) A4))) B5))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X4)) (@ H X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A4)) (@ (@ tptp.groups3542108847815614940at_nat H) A4)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.int tptp.int)) (H (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ (@ tptp.plus_plus_int (@ G X4)) (@ H X4)))) A4) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A4)) (@ (@ tptp.groups4538972089207619220nt_int H) A4)))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B5 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups3542108847815614940at_nat G) B5)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ tptp.times_times_nat (@ F I)) (@ G J)))) B5))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int) (G (-> tptp.int tptp.int)) (B5 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A4)) (@ (@ tptp.groups4538972089207619220nt_int G) B5)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J tptp.int)) (@ (@ tptp.times_times_int (@ F I)) (@ G J)))) B5))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (R2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A4)) R2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_nat (@ F N)) R2))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int) (R2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A4)) R2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N tptp.int)) (@ (@ tptp.times_times_int (@ F N)) R2))) A4))))
% 8.20/8.64 (assert (forall ((R2 tptp.nat) (F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R2) (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_nat R2) (@ F N)))) A4))))
% 8.20/8.64 (assert (forall ((R2 tptp.int) (F (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ (@ tptp.times_times_int R2) (@ (@ tptp.groups4538972089207619220nt_int F) A4)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N tptp.int)) (@ (@ tptp.times_times_int R2) (@ F N)))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_int (@ F X4)) (@ G X4)))) A4) (@ (@ tptp.minus_minus_int (@ (@ tptp.groups4538972089207619220nt_int F) A4)) (@ (@ tptp.groups4538972089207619220nt_int G) A4)))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.uminus_uminus_int (@ F X4)))) A4) (@ tptp.uminus_uminus_int (@ (@ tptp.groups4538972089207619220nt_int F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups4406642042086082107nteger F) A4)) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7501900531339628137nteger F) A4)) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7873554091576472773nteger F) A4)) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.rat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups7872700643590313910_o_rat F) A4)) tptp.zero_zero_rat))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A4)) tptp.zero_zero_rat))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A4)) tptp.zero_zero_rat))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups8507830703676809646_o_nat F) A4)) tptp.zero_zero_nat))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A4)) tptp.zero_zero_nat))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ tptp.ord_less_eq_int (@ F X3)) tptp.zero_zero_int))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups8505340233167759370_o_int F) A4)) tptp.zero_zero_int))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_int (@ F X3)) tptp.zero_zero_int))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) A4)) tptp.zero_zero_int))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.groups4406642042086082107nteger F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.groups7501900531339628137nteger F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.groups7873554091576472773nteger F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.rat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ 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) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ 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) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ 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) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups3539618377306564664at_int F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.nat)) (F (-> Bool tptp.nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X4 Bool)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8507830703676809646_o_nat F) A4)) (@ (@ tptp.groups8507830703676809646_o_nat G) A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (G (-> tptp.set_Pr958786334691620121nt_int tptp.nat)) (F (-> tptp.set_Pr958786334691620121nt_int tptp.nat))) (=> (forall ((X3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X3) A4) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups185207323561075247nt_nat (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups185207323561075247nt_nat F) A4)) (@ (@ tptp.groups185207323561075247nt_nat G) A4))))))
% 8.20/8.64 (assert (forall ((A4 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) A4) (@ (@ 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)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8294997508430121362at_nat F) A4)) (@ (@ tptp.groups8294997508430121362at_nat G) A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A4)) (@ (@ tptp.groups4541462559716669496nt_nat G) A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups3542108847815614940at_nat G) A4))))))
% 8.20/8.64 (assert (forall ((H (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (=> (= (@ H tptp.zero_zero_nat) tptp.zero_z3403309356797280102nteger) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ H (@ (@ tptp.plus_plus_nat X3) Y3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ H X3)) (@ H Y3)))) (= (@ (@ tptp.groups7501900531339628137nteger (@ (@ tptp.comp_n3898172953802868194er_nat H) G)) A4) (@ H (@ (@ tptp.groups3542108847815614940at_nat G) A4)))))))
% 8.20/8.64 (assert (forall ((H (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (=> (= (@ H tptp.zero_zero_nat) tptp.zero_zero_rat) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ H (@ (@ tptp.plus_plus_nat X3) Y3)) (@ (@ tptp.plus_plus_rat (@ H X3)) (@ H Y3)))) (= (@ (@ tptp.groups2906978787729119204at_rat (@ (@ tptp.comp_nat_rat_nat H) G)) A4) (@ H (@ (@ tptp.groups3542108847815614940at_nat G) A4)))))))
% 8.20/8.64 (assert (forall ((H (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (=> (= (@ H tptp.zero_zero_nat) tptp.zero_zero_int) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ H (@ (@ tptp.plus_plus_nat X3) Y3)) (@ (@ tptp.plus_plus_int (@ H X3)) (@ H Y3)))) (= (@ (@ tptp.groups3539618377306564664at_int (@ (@ tptp.comp_nat_int_nat H) G)) A4) (@ H (@ (@ tptp.groups3542108847815614940at_nat G) A4)))))))
% 8.20/8.64 (assert (forall ((H (-> tptp.int tptp.code_integer)) (G (-> tptp.int tptp.int)) (A4 tptp.set_int)) (=> (= (@ H tptp.zero_zero_int) tptp.zero_z3403309356797280102nteger) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ H (@ (@ tptp.plus_plus_int X3) Y3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ H X3)) (@ H Y3)))) (= (@ (@ tptp.groups7873554091576472773nteger (@ (@ tptp.comp_i1585864551200866970er_int H) G)) A4) (@ H (@ (@ tptp.groups4538972089207619220nt_int G) A4)))))))
% 8.20/8.64 (assert (forall ((H (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.int)) (A4 tptp.set_int)) (=> (= (@ H tptp.zero_zero_int) tptp.zero_zero_rat) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ H (@ (@ tptp.plus_plus_int X3) Y3)) (@ (@ tptp.plus_plus_rat (@ H X3)) (@ H Y3)))) (= (@ (@ tptp.groups3906332499630173760nt_rat (@ (@ tptp.comp_int_rat_int H) G)) A4) (@ H (@ (@ tptp.groups4538972089207619220nt_int G) A4)))))))
% 8.20/8.64 (assert (forall ((H (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.int)) (A4 tptp.set_int)) (=> (= (@ H tptp.zero_zero_int) tptp.zero_zero_nat) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ H (@ (@ tptp.plus_plus_int X3) Y3)) (@ (@ tptp.plus_plus_nat (@ H X3)) (@ H Y3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (@ (@ tptp.comp_int_nat_int H) G)) A4) (@ H (@ (@ tptp.groups4538972089207619220nt_int G) A4)))))))
% 8.20/8.64 (assert (forall ((H (-> tptp.code_integer tptp.nat)) (G (-> tptp.nat tptp.code_integer)) (A4 tptp.set_nat)) (=> (= (@ H tptp.zero_z3403309356797280102nteger) tptp.zero_zero_nat) (=> (forall ((X3 tptp.code_integer) (Y3 tptp.code_integer)) (= (@ H (@ (@ tptp.plus_p5714425477246183910nteger X3) Y3)) (@ (@ tptp.plus_plus_nat (@ H X3)) (@ H Y3)))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ (@ tptp.comp_C4049556595663050210at_nat H) G)) A4) (@ H (@ (@ tptp.groups7501900531339628137nteger G) A4)))))))
% 8.20/8.64 (assert (forall ((H (-> tptp.rat tptp.nat)) (G (-> tptp.nat tptp.rat)) (A4 tptp.set_nat)) (=> (= (@ H tptp.zero_zero_rat) tptp.zero_zero_nat) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (= (@ H (@ (@ tptp.plus_plus_rat X3) Y3)) (@ (@ tptp.plus_plus_nat (@ H X3)) (@ H Y3)))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ (@ tptp.comp_rat_nat_nat H) G)) A4) (@ H (@ (@ tptp.groups2906978787729119204at_rat G) A4)))))))
% 8.20/8.64 (assert (forall ((H (-> tptp.int tptp.nat)) (G (-> tptp.nat tptp.int)) (A4 tptp.set_nat)) (=> (= (@ H tptp.zero_zero_int) tptp.zero_zero_nat) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ H (@ (@ tptp.plus_plus_int X3) Y3)) (@ (@ tptp.plus_plus_nat (@ H X3)) (@ H Y3)))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ (@ tptp.comp_int_nat_nat H) G)) A4) (@ H (@ (@ tptp.groups3539618377306564664at_int G) A4)))))))
% 8.20/8.64 (assert (forall ((H (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (=> (= (@ H tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ H (@ (@ tptp.plus_plus_nat X3) Y3)) (@ (@ tptp.plus_plus_nat (@ H X3)) (@ H Y3)))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ (@ tptp.comp_nat_nat_nat H) G)) A4) (@ H (@ (@ tptp.groups3542108847815614940at_nat G) A4)))))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A4) (@ tptp.suc N2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3)))))))
% 8.20/8.64 (assert (= tptp.code_nat_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K3) tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_nat) (@ (@ tptp.produc1555791787009142072er_nat (lambda ((L2 tptp.code_integer) (J tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_nat _let_1) _let_1))) (@ (@ (@ tptp.if_nat (= J tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ (@ tptp.if_rat (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) I))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_rat _let_1) N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ (@ tptp.if_int (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_int _let_1) N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ (@ tptp.if_Code_integer (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I))) tptp.zero_z3403309356797280102nteger))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) I))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_rat _let_1) N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_int _let_1) N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I))) tptp.zero_z3403309356797280102nteger))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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)))))))))))))
% 8.20/8.64 (assert (forall ((L tptp.set_int) (H tptp.set_int) (L4 tptp.set_int) (H5 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int L) H) (@ (@ tptp.set_or370866239135849197et_int L4) H5)) (or (and (= L L4) (= H H5)) (and (not (@ (@ tptp.ord_less_eq_set_int L) H)) (not (@ (@ tptp.ord_less_eq_set_int L4) H5)))))))
% 8.20/8.64 (assert (forall ((L tptp.rat) (H tptp.rat) (L4 tptp.rat) (H5 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L) H) (@ (@ tptp.set_or633870826150836451st_rat L4) H5)) (or (and (= L L4) (= H H5)) (and (not (@ (@ tptp.ord_less_eq_rat L) H)) (not (@ (@ tptp.ord_less_eq_rat L4) H5)))))))
% 8.20/8.64 (assert (forall ((L tptp.num) (H tptp.num) (L4 tptp.num) (H5 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L) H) (@ (@ tptp.set_or7049704709247886629st_num L4) H5)) (or (and (= L L4) (= H H5)) (and (not (@ (@ tptp.ord_less_eq_num L) H)) (not (@ (@ tptp.ord_less_eq_num L4) H5)))))))
% 8.20/8.64 (assert (forall ((L tptp.nat) (H tptp.nat) (L4 tptp.nat) (H5 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L) H) (@ (@ tptp.set_or1269000886237332187st_nat L4) H5)) (or (and (= L L4) (= H H5)) (and (not (@ (@ tptp.ord_less_eq_nat L) H)) (not (@ (@ tptp.ord_less_eq_nat L4) H5)))))))
% 8.20/8.64 (assert (forall ((L tptp.int) (H tptp.int) (L4 tptp.int) (H5 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L) H) (@ (@ tptp.set_or1266510415728281911st_int L4) H5)) (or (and (= L L4) (= H H5)) (and (not (@ (@ tptp.ord_less_eq_int L) H)) (not (@ (@ tptp.ord_less_eq_int L4) H5)))))))
% 8.20/8.64 (assert (forall ((L tptp.code_integer) (H tptp.code_integer) (L4 tptp.code_integer) (H5 tptp.code_integer)) (= (= (@ (@ tptp.set_or189985376899183464nteger L) H) (@ (@ tptp.set_or189985376899183464nteger L4) H5)) (or (and (= L L4) (= H H5)) (and (not (@ (@ tptp.ord_le3102999989581377725nteger L) H)) (not (@ (@ tptp.ord_le3102999989581377725nteger L4) H5)))))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((I2 tptp.set_Pr958786334691620121nt_int) (L tptp.set_Pr958786334691620121nt_int) (U tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member2340774599025711042nt_int I2) (@ (@ tptp.set_or2481441762145802318nt_int L) U)) (and (@ (@ tptp.ord_le2843351958646193337nt_int L) I2) (@ (@ tptp.ord_le2843351958646193337nt_int I2) U)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((I2 Bool) (K2 Bool)) (= (@ (@ tptp.member_o I2) (@ tptp.set_ord_atMost_o K2)) (@ (@ tptp.ord_less_eq_o I2) K2))))
% 8.20/8.64 (assert (forall ((I2 tptp.set_Pr958786334691620121nt_int) (K2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member2340774599025711042nt_int I2) (@ tptp.set_or2459421552957432928nt_int K2)) (@ (@ tptp.ord_le2843351958646193337nt_int I2) K2))))
% 8.20/8.64 (assert (forall ((I2 tptp.set_nat) (K2 tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ tptp.set_or4236626031148496127et_nat K2)) (@ (@ tptp.ord_less_eq_set_nat I2) K2))))
% 8.20/8.64 (assert (forall ((I2 tptp.set_int) (K2 tptp.set_int)) (= (@ (@ tptp.member_set_int I2) (@ tptp.set_or58775011639299419et_int K2)) (@ (@ tptp.ord_less_eq_set_int I2) K2))))
% 8.20/8.64 (assert (forall ((I2 tptp.rat) (K2 tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_atMost_rat K2)) (@ (@ tptp.ord_less_eq_rat I2) K2))))
% 8.20/8.64 (assert (forall ((I2 tptp.num) (K2 tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_atMost_num K2)) (@ (@ tptp.ord_less_eq_num I2) K2))))
% 8.20/8.64 (assert (forall ((I2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_atMost_nat K2)) (@ (@ tptp.ord_less_eq_nat I2) K2))))
% 8.20/8.64 (assert (forall ((I2 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_atMost_int K2)) (@ (@ tptp.ord_less_eq_int I2) K2))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.set_or189985376899183464nteger A) B) tptp.bot_bo3990330152332043303nteger) (not (@ (@ tptp.ord_le3102999989581377725nteger A) B)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= tptp.bot_bo3990330152332043303nteger (@ (@ tptp.set_or189985376899183464nteger A) B)) (not (@ (@ tptp.ord_le3102999989581377725nteger A) B)))))
% 8.20/8.64 (assert (forall ((B Bool) (A Bool)) (=> (@ (@ tptp.ord_less_o B) A) (= (@ (@ tptp.set_or8904488021354931149Most_o A) B) tptp.bot_bot_set_o))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (= (@ (@ tptp.set_or189985376899183464nteger A) B) tptp.bot_bo3990330152332043303nteger))))
% 8.20/8.64 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C2 tptp.set_int) (D2 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or370866239135849197et_int C2) D2)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (and (@ (@ tptp.ord_less_eq_set_int C2) A) (@ (@ tptp.ord_less_eq_set_int B) D2))))))
% 8.20/8.64 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C2) D2)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat C2) A) (@ (@ tptp.ord_less_eq_rat B) D2))))))
% 8.20/8.64 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num) (D2 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C2) D2)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num C2) A) (@ (@ tptp.ord_less_eq_num B) D2))))))
% 8.20/8.64 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C2) D2)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat C2) A) (@ (@ tptp.ord_less_eq_nat B) D2))))))
% 8.20/8.64 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C2) D2)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int C2) A) (@ (@ tptp.ord_less_eq_int B) D2))))))
% 8.20/8.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.set_or189985376899183464nteger A) B)) (@ (@ tptp.set_or189985376899183464nteger C2) D2)) (or (not (@ (@ tptp.ord_le3102999989581377725nteger A) B)) (and (@ (@ tptp.ord_le3102999989581377725nteger C2) A) (@ (@ tptp.ord_le3102999989581377725nteger B) D2))))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (assert (forall ((L tptp.set_int) (H tptp.set_int) (H5 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int L) H)) (@ tptp.set_or58775011639299419et_int H5)) (or (not (@ (@ tptp.ord_less_eq_set_int L) H)) (@ (@ tptp.ord_less_eq_set_int H) H5)))))
% 8.20/8.64 (assert (forall ((L tptp.rat) (H tptp.rat) (H5 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat L) H)) (@ tptp.set_ord_atMost_rat H5)) (or (not (@ (@ tptp.ord_less_eq_rat L) H)) (@ (@ tptp.ord_less_eq_rat H) H5)))))
% 8.20/8.64 (assert (forall ((L tptp.num) (H tptp.num) (H5 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num L) H)) (@ tptp.set_ord_atMost_num H5)) (or (not (@ (@ tptp.ord_less_eq_num L) H)) (@ (@ tptp.ord_less_eq_num H) H5)))))
% 8.20/8.64 (assert (forall ((L tptp.nat) (H tptp.nat) (H5 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat L) H)) (@ tptp.set_ord_atMost_nat H5)) (or (not (@ (@ tptp.ord_less_eq_nat L) H)) (@ (@ tptp.ord_less_eq_nat H) H5)))))
% 8.20/8.64 (assert (forall ((L tptp.int) (H tptp.int) (H5 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int L) H)) (@ tptp.set_ord_atMost_int H5)) (or (not (@ (@ tptp.ord_less_eq_int L) H)) (@ (@ tptp.ord_less_eq_int H) H5)))))
% 8.20/8.64 (assert (forall ((L tptp.code_integer) (H tptp.code_integer) (H5 tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.set_or189985376899183464nteger L) H)) (@ tptp.set_or9101266186257409494nteger H5)) (or (not (@ (@ tptp.ord_le3102999989581377725nteger L) H)) (@ (@ tptp.ord_le3102999989581377725nteger H) H5)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.multis2468970476368604999at_nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups6857163185585827899at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_p7104986032573967614at_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 8.20/8.64 (assert (forall ((K2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K2) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K2) tptp.zero_zero_nat))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (assert (forall ((H tptp.int) (L4 tptp.int) (H5 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int H)) (@ (@ tptp.set_or1266510415728281911st_int L4) H5)))))
% 8.20/8.64 (assert (= tptp.set_or2459421552957432928nt_int (lambda ((U3 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.ord_le2843351958646193337nt_int X4) U3))))))
% 8.20/8.64 (assert (= tptp.set_or4236626031148496127et_nat (lambda ((U3 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X4) U3))))))
% 8.20/8.64 (assert (= tptp.set_or58775011639299419et_int (lambda ((U3 tptp.set_int)) (@ tptp.collect_set_int (lambda ((X4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X4) U3))))))
% 8.20/8.64 (assert (= tptp.set_ord_atMost_rat (lambda ((U3 tptp.rat)) (@ tptp.collect_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X4) U3))))))
% 8.20/8.64 (assert (= tptp.set_ord_atMost_num (lambda ((U3 tptp.num)) (@ tptp.collect_num (lambda ((X4 tptp.num)) (@ (@ tptp.ord_less_eq_num X4) U3))))))
% 8.20/8.64 (assert (= tptp.set_ord_atMost_nat (lambda ((U3 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X4) U3))))))
% 8.20/8.64 (assert (= tptp.set_ord_atMost_int (lambda ((U3 tptp.int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_eq_int X4) U3))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N2) (@ P2 M3))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P2 X4))))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N2) (@ P2 M3))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P2 X4))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K2)) (@ (@ tptp.plus_plus_nat N2) K2))) (@ (@ tptp.groups3542108847815614940at_nat (@ (@ tptp.comp_nat_nat_nat G) (@ tptp.plus_plus_nat K2))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K2)) (@ (@ tptp.plus_plus_nat N2) K2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I) K2)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn) (D2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn C2))) (= (@ (@ tptp.ord_less_set_assn (@ (@ tptp.set_or7959216805967363635t_assn A) B)) (@ (@ tptp.set_or7959216805967363635t_assn C2) 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 C2) A) (@ (@ tptp.ord_less_assn B) D2)))) (@ _let_1 D2))))))
% 8.20/8.64 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C2 tptp.set_int) (D2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C2))) (= (@ (@ tptp.ord_less_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or370866239135849197et_int C2) 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 C2) A) (@ (@ tptp.ord_less_set_int B) D2)))) (@ _let_1 D2))))))
% 8.20/8.64 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C2) 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 C2) A) (@ (@ tptp.ord_less_rat B) D2)))) (@ _let_1 D2))))))
% 8.20/8.64 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num) (D2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (= (@ (@ tptp.ord_less_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C2) 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 C2) A) (@ (@ tptp.ord_less_num B) D2)))) (@ _let_1 D2))))))
% 8.20/8.64 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C2) 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 C2) A) (@ (@ tptp.ord_less_nat B) D2)))) (@ _let_1 D2))))))
% 8.20/8.64 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C2) 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 C2) A) (@ (@ tptp.ord_less_int B) D2)))) (@ _let_1 D2))))))
% 8.20/8.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger C2))) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ (@ tptp.set_or189985376899183464nteger A) B)) (@ (@ tptp.set_or189985376899183464nteger C2) D2)) (and (or (not (@ (@ tptp.ord_le3102999989581377725nteger A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger B) D2) (or (@ (@ tptp.ord_le6747313008572928689nteger C2) A) (@ (@ tptp.ord_le6747313008572928689nteger B) D2)))) (@ _let_1 D2))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I)))) _let_1)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.multis2468970476368604999at_nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ (@ tptp.groups6857163185585827899at_nat G) (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.plus_p7104986032573967614at_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6857163185585827899at_nat (@ (@ tptp.comp_n8698576032424989604at_nat G) tptp.suc)) (@ _let_1 N2)))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (@ (@ tptp.comp_nat_rat_nat G) tptp.suc)) (@ _let_1 N2)))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (@ (@ tptp.comp_nat_int_nat G) tptp.suc)) (@ _let_1 N2)))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ (@ tptp.comp_nat_nat_nat G) tptp.suc)) (@ _let_1 N2)))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.multis2468970476368604999at_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.groups6857163185585827899at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_p7104986032573967614at_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N2))))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I)) (@ F (@ tptp.suc I))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.int)) (I2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I)) (@ F (@ tptp.suc I))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) _let_1)))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) _let_1)))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) _let_1)))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) _let_1)))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I))) (@ F I)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I))) (@ F I)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ (@ tptp.comp_nat_nat_nat G) (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 8.20/8.64 (assert (forall ((R2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R2) K3)) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R2) N2))) N2))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J)) 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))))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J)) N2))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N2) M)) tptp.one_one_nat)) M))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.groups3542108847815614940at_nat (@ (@ tptp.comp_nat_nat_nat G) (@ tptp.plus_plus_nat M))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) M)))))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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 ((I tptp.nat) (J tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) J)) N2))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ G I) (@ (@ tptp.minus_minus_nat K3) I)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (R2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K3)) (@ (@ tptp.binomial N2) (@ (@ tptp.minus_minus_nat R2) K3))))) (@ tptp.set_ord_atMost_nat R2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N2)) R2))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_p7104986032573967614at_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_p7104986032573967614at_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 8.20/8.64 (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))))
% 8.20/8.64 (assert (forall ((P3 tptp.nat) (K2 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 K2) P3) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ (@ (@ tptp.if_Code_integer (= J K2)) tptp.zero_z3403309356797280102nteger) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 8.20/8.64 (assert (forall ((P3 tptp.nat) (K2 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 K2) P3) (= (@ (@ tptp.groups6857163185585827899at_nat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_mul8430962117462786573at_nat (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ (@ (@ tptp.if_mul8430962117462786573at_nat (= J K2)) tptp.zero_z1048942125864253310at_nat) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups6857163185585827899at_nat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_mul8430962117462786573at_nat (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 8.20/8.64 (assert (forall ((P3 tptp.nat) (K2 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 K2) P3) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ (@ (@ tptp.if_rat (= J K2)) tptp.zero_zero_rat) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 8.20/8.64 (assert (forall ((P3 tptp.nat) (K2 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 K2) P3) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ (@ (@ tptp.if_int (= J K2)) tptp.zero_zero_int) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 8.20/8.64 (assert (forall ((P3 tptp.nat) (K2 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 K2) P3) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ (@ (@ tptp.if_nat (= J K2)) tptp.zero_zero_nat) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J tptp.nat)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat J)) K2))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N2)) tptp.one_one_rat)) (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat)))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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)))))))))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I)) (@ tptp.semiri681578069525770553at_rat I))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) I))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I)) (@ tptp.semiri1314217659103216013at_int I))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I)) (@ tptp.semiri4939895301339042750nteger I))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I)) 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))))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural (@ tptp.semiri3763490453095760265atural I)) 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))))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I)) 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))))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I)) 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))))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I)) 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))))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_nat I) (@ (@ tptp.binomial N2) I)))) (@ 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))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I) 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)))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) I))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural (@ tptp.semiri3763490453095760265atural I)) 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))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I)) 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))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I)) 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))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I)) 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))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (assert (forall ((R2 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 R2) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R2) (@ 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 R2) _let_1))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (assert (forall ((Z3 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 Z3) _let_2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z3) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat _let_1)))) _let_2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_rat Z3) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K3)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))))
% 8.20/8.64 (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 ((R5 tptp.code_integer) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 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)) S5)))))) _let_1))))))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (assert (forall ((K2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K2)) (@ (@ tptp.minus_minus_nat (@ _let_1 K2)) tptp.one_one_nat)))))
% 8.20/8.64 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) N)))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.int)) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int X))) (= (@ (@ tptp.produc4463282112584876420nt_int F) (@ _let_1 Y)) (@ _let_1 (@ F Y))))))
% 8.20/8.64 (assert (forall ((F (-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat X))) (= (@ (@ tptp.produc8750854537940449737_nat_o F) (@ _let_1 Y)) (@ _let_1 (@ F Y))))))
% 8.20/8.64 (assert (forall ((F (-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.produc7714581247149323085_nat_o F) (@ (@ tptp.produc5001842942810119800et_nat X) Y)) (@ (@ tptp.produc2245416461498447860et_nat X) (@ F Y)))))
% 8.20/8.64 (assert (forall ((F (-> tptp.produc3925858234332021118et_nat tptp.produc3658429121746597890et_nat)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat)) (= (@ (@ tptp.produc1515462096303866701_nat_o F) (@ (@ tptp.produc2245416461498447860et_nat X) Y)) (@ (@ tptp.produc5001842942810119800et_nat X) (@ F Y)))))
% 8.20/8.64 (assert (forall ((F (-> tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat X))) (= (@ (@ tptp.produc969530845752564945_nat_o F) (@ _let_1 Y)) (@ _let_1 (@ F Y))))))
% 8.20/8.64 (assert (forall ((F (-> tptp.produc6653097349344004940it_nat tptp.produc6653097349344004940it_nat)) (X tptp.b) (Y tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.produc4082563078715348724it_nat X))) (= (@ (@ tptp.produc701890989253350759_nat_b F) (@ _let_1 Y)) (@ _let_1 (@ F Y))))))
% 8.20/8.64 (assert (forall ((F (-> tptp.produc6653097349344004940it_nat tptp.produc6653097349344004940it_nat)) (X tptp.a) (Y tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.produc9178034014595674355it_nat X))) (= (@ (@ tptp.produc701890989253350758_nat_a F) (@ _let_1 Y)) (@ _let_1 (@ F Y))))))
% 8.20/8.64 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.produc1086072967326762835nteger X))) (= (@ (@ tptp.produc6499014454317279255nteger F) (@ _let_1 Y)) (@ _let_1 (@ F Y))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu2 tptp.nat)) tptp.one_one_nat)) A4) tptp.one_one_nat)))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu2 tptp.nat)) tptp.one_one_int)) A4) tptp.one_one_int)))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu2 tptp.int)) tptp.one_one_int)) A4) tptp.one_one_int)))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.nat)) (A4 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups1707563613775114915nt_nat F) A4)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.groups708209901874060359at_nat F) A4)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((X4 tptp.nat)) (@ tptp.semiri4939895301339042750nteger (@ F X4)))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat F) A4)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X4)))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat F) A4)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.int)) (A4 tptp.set_nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups705719431365010083at_int F) A4)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((X4 tptp.nat)) (@ tptp.ring_1_of_int_rat (@ F X4)))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.int)) (A4 tptp.set_nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups705719431365010083at_int F) A4)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ tptp.ring_1_of_int_int (@ F X4)))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups1705073143266064639nt_int F) A4)) (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_rat (@ F X4)))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups1705073143266064639nt_int F) A4)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_int (@ F X4)))) A4))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((I2 tptp.set_Pr958786334691620121nt_int) (L tptp.set_Pr958786334691620121nt_int) (U tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member2340774599025711042nt_int I2) (@ (@ tptp.set_or2826562449856406570nt_int L) U)) (and (@ (@ tptp.ord_le2843351958646193337nt_int L) I2) (@ (@ tptp.ord_le7563427860532173253nt_int I2) U)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((B Bool) (A Bool)) (=> (@ (@ tptp.ord_less_eq_o B) A) (= (@ (@ tptp.set_or7139685690850216873Than_o A) B) tptp.bot_bot_set_o))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (= (@ (@ tptp.set_or8404916559141939852nteger A) B) tptp.bot_bo3990330152332043303nteger))))
% 8.20/8.64 (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))))
% 8.20/8.64 (assert (forall ((A Bool) (B Bool)) (= (= tptp.bot_bot_set_o (@ (@ tptp.set_or7139685690850216873Than_o A) B)) (not (@ (@ tptp.ord_less_o A) B)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= tptp.bot_bo3990330152332043303nteger (@ (@ tptp.set_or8404916559141939852nteger A) B)) (not (@ (@ tptp.ord_le6747313008572928689nteger A) B)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((A Bool) (B Bool)) (= (= (@ (@ tptp.set_or7139685690850216873Than_o A) B) tptp.bot_bot_set_o) (not (@ (@ tptp.ord_less_o A) B)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.set_or8404916559141939852nteger A) B) tptp.bot_bo3990330152332043303nteger) (not (@ (@ tptp.ord_le6747313008572928689nteger A) B)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((I2 tptp.rat) (J2 tptp.rat) (M tptp.rat) (N2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat J2))) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or4029947393144176647an_rat I2) J2)) (@ (@ tptp.set_or4029947393144176647an_rat M) N2)) (or (@ _let_1 I2) (and (@ (@ tptp.ord_less_eq_rat M) I2) (@ _let_1 N2)))))))
% 8.20/8.64 (assert (forall ((I2 tptp.num) (J2 tptp.num) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num J2))) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or1222409239386451017an_num I2) J2)) (@ (@ tptp.set_or1222409239386451017an_num M) N2)) (or (@ _let_1 I2) (and (@ (@ tptp.ord_less_eq_num M) I2) (@ _let_1 N2)))))))
% 8.20/8.64 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat J2))) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or4665077453230672383an_nat I2) J2)) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (or (@ _let_1 I2) (and (@ (@ tptp.ord_less_eq_nat M) I2) (@ _let_1 N2)))))))
% 8.20/8.64 (assert (forall ((I2 tptp.code_integer) (J2 tptp.code_integer) (M tptp.code_integer) (N2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger J2))) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.set_or8404916559141939852nteger I2) J2)) (@ (@ tptp.set_or8404916559141939852nteger M) N2)) (or (@ _let_1 I2) (and (@ (@ tptp.ord_le3102999989581377725nteger M) I2) (@ _let_1 N2)))))))
% 8.20/8.64 (assert (forall ((I2 tptp.int) (J2 tptp.int) (M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int J2))) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or4662586982721622107an_int I2) J2)) (@ (@ tptp.set_or4662586982721622107an_int M) N2)) (or (@ _let_1 I2) (and (@ (@ tptp.ord_less_eq_int M) I2) (@ _let_1 N2)))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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)))))))))))
% 8.20/8.64 (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)))))))))))
% 8.20/8.64 (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)))))))))))
% 8.20/8.64 (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)))))))))))
% 8.20/8.64 (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)))))))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (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)))))))))))
% 8.20/8.64 (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)))))))))))
% 8.20/8.64 (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)))))))))))
% 8.20/8.64 (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)))))))))))
% 8.20/8.64 (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)))))))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.plus_plus_nat M) K2)) (@ (@ tptp.plus_plus_nat N2) K2))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I) K2)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.plus_plus_nat M) K2)) (@ (@ tptp.plus_plus_nat N2) K2))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I) K2)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.plus_plus_nat M) K2)) (@ (@ tptp.plus_plus_nat N2) K2))) (@ (@ tptp.groups708209901874060359at_nat (@ (@ tptp.comp_nat_nat_nat G) (@ tptp.plus_plus_nat K2))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.plus_plus_nat M) K2)) (@ (@ tptp.plus_plus_nat N2) K2))) (@ (@ tptp.groups705719431365010083at_int (@ (@ tptp.comp_nat_int_nat G) (@ tptp.plus_plus_nat K2))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 8.20/8.64 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) D2) (= (= (@ (@ tptp.set_or4029947393144176647an_rat A) B) (@ (@ tptp.set_or4029947393144176647an_rat C2) D2)) (and (= A C2) (= B D2)))))))
% 8.20/8.64 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num) (D2 tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_num C2) D2) (= (= (@ (@ tptp.set_or1222409239386451017an_num A) B) (@ (@ tptp.set_or1222409239386451017an_num C2) D2)) (and (= A C2) (= B D2)))))))
% 8.20/8.64 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D2) (= (= (@ (@ tptp.set_or4665077453230672383an_nat A) B) (@ (@ tptp.set_or4665077453230672383an_nat C2) D2)) (and (= A C2) (= B D2)))))))
% 8.20/8.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) D2) (= (= (@ (@ tptp.set_or8404916559141939852nteger A) B) (@ (@ tptp.set_or8404916559141939852nteger C2) D2)) (and (= A C2) (= B D2)))))))
% 8.20/8.64 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C2) D2) (= (= (@ (@ tptp.set_or4662586982721622107an_int A) B) (@ (@ tptp.set_or4662586982721622107an_int C2) D2)) (and (= A C2) (= B D2)))))))
% 8.20/8.64 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.set_or4029947393144176647an_rat A) B) (@ (@ tptp.set_or4029947393144176647an_rat C2) D2)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) D2) (= A C2))))))
% 8.20/8.64 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num) (D2 tptp.num)) (=> (= (@ (@ tptp.set_or1222409239386451017an_num A) B) (@ (@ tptp.set_or1222409239386451017an_num C2) D2)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_num C2) D2) (= A C2))))))
% 8.20/8.64 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (= (@ (@ tptp.set_or4665077453230672383an_nat A) B) (@ (@ tptp.set_or4665077453230672383an_nat C2) D2)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D2) (= A C2))))))
% 8.20/8.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (=> (= (@ (@ tptp.set_or8404916559141939852nteger A) B) (@ (@ tptp.set_or8404916559141939852nteger C2) D2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) D2) (= A C2))))))
% 8.20/8.64 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.set_or4662586982721622107an_int A) B) (@ (@ tptp.set_or4662586982721622107an_int C2) D2)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C2) D2) (= A C2))))))
% 8.20/8.64 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.set_or4029947393144176647an_rat A) B) (@ (@ tptp.set_or4029947393144176647an_rat C2) D2)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C2) D2) (= B D2))))))
% 8.20/8.64 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num) (D2 tptp.num)) (=> (= (@ (@ tptp.set_or1222409239386451017an_num A) B) (@ (@ tptp.set_or1222409239386451017an_num C2) D2)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_num C2) D2) (= B D2))))))
% 8.20/8.64 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (= (@ (@ tptp.set_or4665077453230672383an_nat A) B) (@ (@ tptp.set_or4665077453230672383an_nat C2) D2)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D2) (= B D2))))))
% 8.20/8.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (=> (= (@ (@ tptp.set_or8404916559141939852nteger A) B) (@ (@ tptp.set_or8404916559141939852nteger C2) D2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C2) D2) (= B D2))))))
% 8.20/8.64 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.set_or4662586982721622107an_int A) B) (@ (@ tptp.set_or4662586982721622107an_int C2) D2)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C2) D2) (= B D2))))))
% 8.20/8.64 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat) (D2 tptp.nat) (G (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat))) (=> (= A C2) (=> (= B D2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) 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 C2) D2))))))))
% 8.20/8.64 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat) (D2 tptp.nat) (G (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int))) (=> (= A C2) (=> (= B D2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) 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 C2) D2))))))))
% 8.20/8.64 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int) (D2 tptp.int) (G (-> tptp.int tptp.int)) (H (-> tptp.int tptp.int))) (=> (= A C2) (=> (= B D2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) 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 C2) D2))))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (B5 tptp.set_nat) (A4 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ G I)) B5))) A4) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ G I) J))) A4))) B5))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (B5 tptp.set_nat) (A4 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ G I)) B5))) A4) (@ (@ tptp.groups705719431365010083at_int (lambda ((J tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ G I) J))) A4))) B5))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int tptp.int)) (B5 tptp.set_int) (A4 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.groups1705073143266064639nt_int (@ G I)) B5))) A4) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((J tptp.int)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ G I) J))) A4))) B5))))
% 8.20/8.64 (assert (forall ((G (-> tptp.int tptp.nat tptp.int)) (B5 tptp.set_nat) (A4 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I tptp.int)) (@ (@ tptp.groups705719431365010083at_int (@ G I)) B5))) A4) (@ (@ tptp.groups705719431365010083at_int (lambda ((J tptp.nat)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I tptp.int)) (@ (@ G I) J))) A4))) B5))))
% 8.20/8.64 (assert (forall ((G (-> tptp.int tptp.int tptp.int)) (B5 tptp.set_int) (A4 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I tptp.int)) (@ (@ tptp.groups1705073143266064639nt_int (@ G I)) B5))) A4) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((J tptp.int)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I tptp.int)) (@ (@ G I) J))) A4))) B5))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_nat (@ G X4)) (@ H X4)))) A4) (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) A4)) (@ (@ tptp.groups708209901874060359at_nat H) A4)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int)) (A4 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_int (@ G X4)) (@ H X4)))) A4) (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) A4)) (@ (@ tptp.groups705719431365010083at_int H) A4)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.int tptp.int)) (H (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_int (@ G X4)) (@ H X4)))) A4) (@ (@ tptp.times_times_int (@ (@ tptp.groups1705073143266064639nt_int G) A4)) (@ (@ tptp.groups1705073143266064639nt_int H) A4)))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A4)) N2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.power_power_nat (@ F X4)) N2))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.int)) (A4 tptp.set_nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A4)) N2) (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ (@ tptp.power_power_int (@ F X4)) N2))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A4)) N2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ (@ tptp.power_power_int (@ F X4)) N2))) A4))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.groups708209901874060359at_nat (@ (@ tptp.comp_nat_nat_nat G) (@ tptp.plus_plus_nat M))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) M))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.groups705719431365010083at_int (@ (@ tptp.comp_nat_int_nat G) (@ tptp.plus_plus_nat M))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) M))))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A4 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I)) A))) A4)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat F) A4)) A))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (A4 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.modulo_modulo_int (@ F I)) A))) A4)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int F) A4)) A))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A4 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I)) A))) A4)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int F) A4)) A))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (@ (@ tptp.comp_nat_nat_nat G) (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (@ (@ tptp.comp_nat_int_nat G) (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ tptp.suc I))))) _let_1)))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ tptp.suc I))))) _let_1)))))
% 8.20/8.64 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ A I) J))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N2)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))))
% 8.20/8.64 (assert (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ A I) J))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N2)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))))
% 8.20/8.64 (assert (forall ((F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer)) (X tptp.produc8923325533196201883nteger)) (= (@ (@ tptp.produc9020447175693601247nteger F) (@ (@ tptp.produc6499014454317279255nteger G) X)) (@ (@ tptp.produc9020447175693601247nteger (@ (@ tptp.comp_C1593894019821074884nteger F) G)) X))))
% 8.20/8.64 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer)) (X tptp.produc8923325533196201883nteger)) (= (@ (@ tptp.produc6499014454317279255nteger F) (@ (@ tptp.produc6499014454317279255nteger G) X)) (@ (@ tptp.produc6499014454317279255nteger (@ (@ tptp.comp_C7449957260575251196nteger F) G)) X))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A4)))))
% 8.20/8.64 (assert (forall ((A4 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) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) (@ G I3)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7694694392188491536nteger F) A4)) (@ (@ tptp.groups7694694392188491536nteger G) A4)))))
% 8.20/8.64 (assert (forall ((A4 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) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) (@ G I3)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3455450783089532116nteger F) A4)) (@ (@ tptp.groups3455450783089532116nteger G) A4)))))
% 8.20/8.64 (assert (forall ((A4 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) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) (@ G I3)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3827104343326376752nteger F) A4)) (@ (@ tptp.groups3827104343326376752nteger G) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.rat)) (G (-> Bool tptp.rat))) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A4) (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) A4)) (@ (@ tptp.groups2869687844427037835_o_rat G) A4)))))
% 8.20/8.64 (assert (forall ((A4 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) A4) (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) A4)) (@ (@ tptp.groups73079841787564623at_rat G) A4)))))
% 8.20/8.64 (assert (forall ((A4 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) A4) (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) A4)) (@ (@ tptp.groups1072433553688619179nt_rat G) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A4) (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) A4)) (@ (@ tptp.groups3504817904513533571_o_nat G) A4)))))
% 8.20/8.64 (assert (forall ((A4 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) A4) (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) A4)) (@ (@ tptp.groups1707563613775114915nt_nat G) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A4) (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) A4)) (@ (@ tptp.groups3502327434004483295_o_int G) A4)))))
% 8.20/8.64 (assert (forall ((A4 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) A4) (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) A4)) (@ (@ tptp.groups708209901874060359at_nat G) A4)))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups7694694392188491536nteger F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3455450783089532116nteger F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3827104343326376752nteger F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.rat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ 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) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ 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) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ 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) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups708209901874060359at_nat F) A4)))))
% 8.20/8.64 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 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 C2) D2)) (or (@ _let_1 A) (and (@ (@ tptp.ord_less_eq_rat C2) A) (@ _let_1 D2)))))))
% 8.20/8.64 (assert (forall ((A tptp.num) (B tptp.num) (C2 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 C2) D2)) (or (@ _let_1 A) (and (@ (@ tptp.ord_less_eq_num C2) A) (@ _let_1 D2)))))))
% 8.20/8.64 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 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 C2) D2)) (or (@ _let_1 A) (and (@ (@ tptp.ord_less_eq_nat C2) A) (@ _let_1 D2)))))))
% 8.20/8.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 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 C2) D2)) (or (@ _let_1 A) (and (@ (@ tptp.ord_le3102999989581377725nteger C2) A) (@ _let_1 D2)))))))
% 8.20/8.64 (assert (forall ((A tptp.int) (B tptp.int) (C2 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 C2) D2)) (or (@ _let_1 A) (and (@ (@ tptp.ord_less_eq_int C2) A) (@ _let_1 D2)))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K2)) (@ (@ tptp.plus_plus_nat N2) K2))) (@ (@ tptp.groups708209901874060359at_nat (@ (@ tptp.comp_nat_nat_nat G) (@ tptp.plus_plus_nat K2))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K2)) (@ (@ tptp.plus_plus_nat N2) K2))) (@ (@ tptp.groups705719431365010083at_int (@ (@ tptp.comp_nat_int_nat G) (@ tptp.plus_plus_nat K2))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N2) (@ P2 M3))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P2 X4))))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N2) (@ P2 M3))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P2 X4))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I)))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M)))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I)))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M)))))
% 8.20/8.64 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A5 tptp.rat) (N tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.semiri681578069525770553at_rat I)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 8.20/8.64 (assert (= tptp.comm_s8582702949713902594nteger (lambda ((A5 tptp.code_integer) (N tptp.nat)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.semiri4939895301339042750nteger I)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 8.20/8.64 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A5 tptp.nat) (N tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A5) (@ tptp.semiri1316708129612266289at_nat I)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 8.20/8.64 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A5 tptp.int) (N tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_int A5) (@ tptp.semiri1314217659103216013at_int I)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.plus_plus_nat M) K2)) (@ (@ tptp.plus_plus_nat N2) K2))) (@ (@ tptp.groups3542108847815614940at_nat (@ (@ tptp.comp_nat_nat_nat G) (@ tptp.plus_plus_nat K2))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 8.20/8.64 (assert (forall ((C2 tptp.nat) (F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.power_power_nat C2) (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((A5 tptp.nat)) (@ (@ tptp.power_power_nat C2) (@ F A5)))) A4))))
% 8.20/8.64 (assert (forall ((C2 tptp.int) (F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.power_power_int C2) (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups705719431365010083at_int (lambda ((A5 tptp.nat)) (@ (@ tptp.power_power_int C2) (@ F A5)))) A4))))
% 8.20/8.64 (assert (forall ((C2 tptp.int) (F (-> tptp.int tptp.nat)) (A4 tptp.set_int)) (= (@ (@ tptp.power_power_int C2) (@ (@ tptp.groups4541462559716669496nt_nat F) A4)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((A5 tptp.int)) (@ (@ tptp.power_power_int C2) (@ F A5)))) A4))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K2)) (@ (@ tptp.plus_plus_nat N2) K2))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I) K2)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K2)) (@ (@ tptp.plus_plus_nat N2) K2))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I) K2)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.plus_plus_nat M) K2)) (@ (@ tptp.plus_plus_nat N2) K2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I) K2)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (forall ((X3 Bool)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_o X3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7694694392188491536nteger F) A4)) tptp.one_one_Code_integer))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3455450783089532116nteger F) A4)) tptp.one_one_Code_integer))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3827104343326376752nteger F) A4)) tptp.one_one_Code_integer))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.rat))) (=> (forall ((X3 Bool)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_o X3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2869687844427037835_o_rat F) A4)) tptp.one_one_rat))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A4)) tptp.one_one_rat))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A4)) tptp.one_one_rat))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.nat))) (=> (forall ((X3 Bool)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_o X3) A4) (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) A4)) tptp.one_one_nat))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A4) (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) A4)) tptp.one_one_nat))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.int))) (=> (forall ((X3 Bool)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_o X3) A4) (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) A4)) tptp.one_one_int))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A4) (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) A4)) tptp.one_one_nat))))
% 8.20/8.64 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K2))) (=> (@ (@ tptp.ord_less_eq_nat K2) 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)))))))
% 8.20/8.64 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K2))) (=> (@ (@ tptp.ord_less_eq_nat K2) 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)))))))
% 8.20/8.64 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K2))) (=> (@ (@ tptp.ord_less_eq_nat K2) 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)))))))
% 8.20/8.64 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K2))) (=> (@ (@ tptp.ord_less_eq_nat K2) 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)))))))
% 8.20/8.64 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat) (D2 tptp.nat) (G (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat))) (=> (= A C2) (=> (= B D2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) 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 C2) D2))))))))
% 8.20/8.64 (assert (forall ((A tptp.int) (C2 tptp.int) (B tptp.int) (D2 tptp.int) (G (-> tptp.int tptp.int)) (H (-> tptp.int tptp.int))) (=> (= A C2) (=> (= B D2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) 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 C2) D2))))))))
% 8.20/8.64 (assert (= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A5) (@ tptp.semiri681578069525770553at_rat I))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat K3) I))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3)))))
% 8.20/8.64 (assert (forall ((K2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N2) I))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat K2) I))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K2))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (assert (forall ((K2 tptp.nat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K2)) (@ (@ tptp.gbinomial_rat A) K2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K2)))))
% 8.20/8.64 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K2)) (@ tptp.semiri773545260158071498ct_rat K2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K2)))))
% 8.20/8.64 (assert (= tptp.gbinom7368847122466276068atural (lambda ((A5 tptp.code_natural) (K3 tptp.nat)) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.groups2279045934846249631atural (lambda ((I tptp.nat)) (@ (@ tptp.minus_7197305767214868737atural A5) (@ tptp.semiri3763490453095760265atural I)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3))) (@ tptp.semiri2447717529341329178atural K3)))))
% 8.20/8.64 (assert (= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_rat A5) (@ tptp.semiri681578069525770553at_rat I)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3))) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 8.20/8.64 (assert (= tptp.gbinom8545251970709558553nteger (lambda ((A5 tptp.code_integer) (K3 tptp.nat)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.groups3455450783089532116nteger (lambda ((I tptp.nat)) (@ (@ tptp.minus_8373710615458151222nteger A5) (@ tptp.semiri4939895301339042750nteger I)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3))) (@ tptp.semiri3624122377584611663nteger K3)))))
% 8.20/8.64 (assert (= tptp.gbinomial_nat (lambda ((A5 tptp.nat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_nat A5) (@ tptp.semiri1316708129612266289at_nat I)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3))) (@ tptp.semiri1408675320244567234ct_nat K3)))))
% 8.20/8.64 (assert (= tptp.gbinomial_int (lambda ((A5 tptp.int) (K3 tptp.nat)) (@ (@ tptp.divide_divide_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_int A5) (@ tptp.semiri1314217659103216013at_int I)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3))) (@ tptp.semiri1406184849735516958ct_int K3)))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (B5 tptp.set_int) (P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_minus_int X3) D4))))) (forall ((X6 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X6) D4))) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B5) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa4))))))) (=> (and (@ P2 X6) (@ Q2 X6)) (and (@ P2 _let_1) (@ Q2 _let_1))))))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (B5 tptp.set_int) (P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_minus_int X3) D4))))) (forall ((X6 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X6) D4))) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B5) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa4))))))) (=> (or (@ P2 X6) (@ Q2 X6)) (or (@ P2 _let_1) (@ Q2 _let_1))))))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (A4 tptp.set_int) (P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A4) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A4) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ Q2 X3) (@ Q2 (@ (@ tptp.plus_plus_int X3) D4))))) (forall ((X6 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X6) D4))) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A4) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa4))))))) (=> (and (@ P2 X6) (@ Q2 X6)) (and (@ P2 _let_1) (@ Q2 _let_1))))))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (A4 tptp.set_int) (P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A4) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A4) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ Q2 X3) (@ Q2 (@ (@ tptp.plus_plus_int X3) D4))))) (forall ((X6 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X6) D4))) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A4) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa4))))))) (=> (or (@ P2 X6) (@ Q2 X6)) (or (@ P2 _let_1) (@ Q2 _let_1))))))))))
% 8.20/8.64 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J2) K2))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J2)) (@ (@ tptp.set_or4665077453230672383an_nat J2) _let_1))))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I)))) _let_1)))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I)))) _let_1)))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (assert (forall ((A tptp.assn) (B tptp.assn) (C2 tptp.assn) (D2 tptp.assn)) (= (@ (@ tptp.ord_less_eq_set_assn (@ (@ tptp.set_or7959216805967363635t_assn A) B)) (@ (@ tptp.set_or5523502641901747543n_assn C2) D2)) (=> (@ (@ tptp.ord_less_eq_assn A) B) (and (@ (@ tptp.ord_less_eq_assn C2) A) (@ (@ tptp.ord_less_assn B) D2))))))
% 8.20/8.64 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C2 tptp.set_int) (D2 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or8585797421378605585et_int C2) D2)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (and (@ (@ tptp.ord_less_eq_set_int C2) A) (@ (@ tptp.ord_less_set_int B) D2))))))
% 8.20/8.64 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or4029947393144176647an_rat C2) D2)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (and (@ (@ tptp.ord_less_eq_rat C2) A) (@ (@ tptp.ord_less_rat B) D2))))))
% 8.20/8.64 (assert (forall ((A tptp.num) (B tptp.num) (C2 tptp.num) (D2 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or1222409239386451017an_num C2) D2)) (=> (@ (@ tptp.ord_less_eq_num A) B) (and (@ (@ tptp.ord_less_eq_num C2) A) (@ (@ tptp.ord_less_num B) D2))))))
% 8.20/8.64 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or4665077453230672383an_nat C2) D2)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (and (@ (@ tptp.ord_less_eq_nat C2) A) (@ (@ tptp.ord_less_nat B) D2))))))
% 8.20/8.64 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C2 tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.set_or189985376899183464nteger A) B)) (@ (@ tptp.set_or8404916559141939852nteger C2) D2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (and (@ (@ tptp.ord_le3102999989581377725nteger C2) A) (@ (@ tptp.ord_le6747313008572928689nteger B) D2))))))
% 8.20/8.64 (assert (forall ((A tptp.int) (B tptp.int) (C2 tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or4662586982721622107an_int C2) D2)) (=> (@ (@ tptp.ord_less_eq_int A) B) (and (@ (@ tptp.ord_less_eq_int C2) A) (@ (@ tptp.ord_less_int B) D2))))))
% 8.20/8.64 (assert (forall ((A tptp.rat) (B tptp.rat) (C2 tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or4029947393144176647an_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C2) D2)) (=> (@ (@ tptp.ord_less_rat A) B) (and (@ (@ tptp.ord_less_eq_rat C2) A) (@ (@ tptp.ord_less_eq_rat B) D2))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.multis2468970476368604999at_nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.groups6857163185585827899at_nat G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.plus_p7104986032573967614at_nat (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))
% 8.20/8.64 (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.groups2906978787729119204at_rat G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))
% 8.20/8.64 (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.groups3539618377306564664at_int G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))
% 8.20/8.64 (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.groups3542108847815614940at_nat G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.multis2468970476368604999at_nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ (@ tptp.groups6857163185585827899at_nat G) (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.plus_p7104986032573967614at_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6857163185585827899at_nat (@ (@ tptp.comp_n8698576032424989604at_nat G) tptp.suc)) (@ _let_1 N2)))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (@ (@ tptp.comp_nat_rat_nat G) tptp.suc)) (@ _let_1 N2)))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (@ (@ tptp.comp_nat_int_nat G) tptp.suc)) (@ _let_1 N2)))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ (@ tptp.comp_nat_nat_nat G) tptp.suc)) (@ _let_1 N2)))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.groups3542108847815614940at_nat (@ (@ tptp.comp_nat_nat_nat G) (@ tptp.plus_plus_nat M))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) M))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (assert (forall ((D2 tptp.int) (D4 tptp.int) (A4 tptp.set_int) (T6 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X6 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X6))) (let ((_let_2 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A4) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa4))))))) (=> (not (@ _let_2 (@ _let_1 T6))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T6)))))))))))
% 8.20/8.64 (assert (forall ((D2 tptp.int) (D4 tptp.int) (A4 tptp.set_int) (T6 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X6 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X6))) (let ((_let_2 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A4) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa4))))))) (=> (@ _let_2 (@ _let_1 T6)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T6))))))))))
% 8.20/8.64 (assert (forall ((D2 tptp.int) (D4 tptp.int) (B5 tptp.set_int) (T6 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X6 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B5) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa4))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X6) T6))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X6) D4)) T6))))))))))
% 8.20/8.64 (assert (forall ((D2 tptp.int) (D4 tptp.int) (B5 tptp.set_int) (T6 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X6 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B5) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa4))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X6) T6)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X6) D4)) T6)))))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) _let_1)))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) _let_1)))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) _let_1)))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) _let_1)))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_atMost_nat N2))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (@ (@ tptp.comp_nat_nat_nat G) (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (@ (@ tptp.comp_nat_int_nat G) (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I))) (@ F I)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.minus_minus_rat (@ F N2)) (@ F M))))))
% 8.20/8.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I))) (@ F I)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F M))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ (@ tptp.comp_nat_nat_nat G) (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ tptp.suc I))))) _let_1)))))
% 8.20/8.64 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ A I)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ A I) J))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N2)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.groups708209901874060359at_nat (@ (@ tptp.comp_nat_nat_nat G) (@ tptp.plus_plus_nat M))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) M)))))))
% 8.20/8.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.groups705719431365010083at_int (@ (@ tptp.comp_nat_int_nat G) (@ tptp.plus_plus_nat M))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) M)))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (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))))))))))))
% 8.20/8.64 (assert (forall ((L Bool) (U Bool)) (=> (@ (@ tptp.ord_less_eq_o L) U) (= (@ (@ tptp.sup_sup_set_o (@ (@ tptp.set_or7139685690850216873Than_o L) U)) (@ (@ tptp.insert_o U) tptp.bot_bot_set_o)) (@ (@ tptp.set_or8904488021354931149Most_o L) U)))))
% 8.20/8.64 (assert (forall ((L tptp.rat) (U tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat L) U) (= (@ (@ tptp.sup_sup_set_rat (@ (@ tptp.set_or4029947393144176647an_rat L) U)) (@ (@ tptp.insert_rat U) tptp.bot_bot_set_rat)) (@ (@ tptp.set_or633870826150836451st_rat L) U)))))
% 8.20/8.64 (assert (forall ((L tptp.num) (U tptp.num)) (=> (@ (@ tptp.ord_less_eq_num L) U) (= (@ (@ tptp.sup_sup_set_num (@ (@ tptp.set_or1222409239386451017an_num L) U)) (@ (@ tptp.insert_num U) tptp.bot_bot_set_num)) (@ (@ tptp.set_or7049704709247886629st_num L) U)))))
% 8.20/8.64 (assert (forall ((L tptp.nat) (U tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat L) U) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U)) (@ (@ tptp.insert_nat U) tptp.bot_bot_set_nat)) (@ (@ tptp.set_or1269000886237332187st_nat L) U)))))
% 8.20/8.64 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger L) U) (= (@ (@ tptp.sup_su848401254843788991nteger (@ (@ tptp.set_or8404916559141939852nteger L) U)) (@ (@ tptp.insert_Code_integer U) tptp.bot_bo3990330152332043303nteger)) (@ (@ tptp.set_or189985376899183464nteger L) U)))))
% 8.20/8.64 (assert (forall ((L tptp.int) (U tptp.int)) (=> (@ (@ tptp.ord_less_eq_int L) U) (= (@ (@ tptp.sup_sup_set_int (@ (@ tptp.set_or4662586982721622107an_int L) U)) (@ (@ tptp.insert_int U) tptp.bot_bot_set_int)) (@ (@ tptp.set_or1266510415728281911st_int L) U)))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (assert (forall ((D2 tptp.int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D2))))) (= (exists ((X11 tptp.int)) (@ P2 X11)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D2)) (@ P2 X4))))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (T6 tptp.int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T6) tptp.one_one_int)) B5) (forall ((X6 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B5) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa4))))))) (=> (= X6 T6) (= (@ (@ tptp.minus_minus_int X6) D4) T6))))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (T6 tptp.int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T6) B5) (forall ((X6 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B5) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa4))))))) (=> (not (= X6 T6)) (not (= (@ (@ tptp.minus_minus_int X6) D4) T6)))))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (B5 tptp.set_int) (T6 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X6 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B5) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa4))))))) (=> (@ (@ tptp.ord_less_int X6) T6) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X6) D4)) T6)))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (T6 tptp.int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T6) B5) (forall ((X6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T6))) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B5) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa4))))))) (=> (@ _let_1 X6) (@ _let_1 (@ (@ tptp.minus_minus_int X6) D4))))))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (T6 tptp.int) (A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T6) tptp.one_one_int)) A4) (forall ((X6 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A4) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa4))))))) (=> (= X6 T6) (= (@ (@ tptp.plus_plus_int X6) D4) T6))))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (T6 tptp.int) (A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T6) A4) (forall ((X6 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A4) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa4))))))) (=> (not (= X6 T6)) (not (= (@ (@ tptp.plus_plus_int X6) D4) T6)))))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (T6 tptp.int) (A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T6) A4) (forall ((X6 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A4) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa4))))))) (=> (@ (@ tptp.ord_less_int X6) T6) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X6) D4)) T6))))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (A4 tptp.set_int) (T6 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T6))) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A4) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa4))))))) (=> (@ _let_1 X6) (@ _let_1 (@ (@ tptp.plus_plus_int X6) D4)))))))))
% 8.20/8.64 (assert (forall ((M tptp.nat) (K2 tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat K2)))) (let ((_let_3 (@ tptp.pred_numeral K2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat 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)))))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I)))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M)))))
% 8.20/8.64 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I tptp.int) (J tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J) I)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (A4 tptp.set_int) (T6 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T6))) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A4) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa4))))))) (=> (@ _let_1 X6) (@ _let_1 (@ (@ tptp.plus_plus_int X6) D4)))))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (T6 tptp.int) (A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T6) tptp.one_one_int)) A4) (forall ((X6 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A4) (not (= X6 (@ (@ tptp.minus_minus_int Xb3) Xa4))))))) (=> (@ (@ tptp.ord_less_eq_int X6) T6) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X6) D4)) T6))))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (T6 tptp.int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T6) tptp.one_one_int)) B5) (forall ((X6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T6))) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B5) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa4))))))) (=> (@ _let_1 X6) (@ _let_1 (@ (@ tptp.minus_minus_int X6) D4))))))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (B5 tptp.set_int) (T6 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X6 tptp.int)) (=> (forall ((Xa4 tptp.int)) (=> (@ (@ tptp.member_int Xa4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B5) (not (= X6 (@ (@ tptp.plus_plus_int Xb3) Xa4))))))) (=> (@ (@ tptp.ord_less_eq_int X6) T6) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X6) D4)) T6)))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (P2 (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z6) (= (@ P2 X3) (@ P6 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B5) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D4))))) (= (exists ((X11 tptp.int)) (@ P2 X11)) (or (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X4))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B5) (@ P2 (@ (@ tptp.plus_plus_int Y4) X4))))))))))))))
% 8.20/8.64 (assert (forall ((D4 tptp.int) (P2 (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z6) X3) (= (@ P2 X3) (@ P6 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A4) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D4))))) (= (exists ((X11 tptp.int)) (@ P2 X11)) (or (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X4))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) A4) (@ P2 (@ (@ tptp.minus_minus_int Y4) X4))))))))))))))
% 8.20/8.64 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 8.20/8.64 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger A) (@ tptp.suc N2)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.semiri4939895301339042750nteger I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 8.20/8.64 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 8.20/8.64 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 8.20/8.64 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A5 tptp.rat) (N tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 8.20/8.64 (assert (= tptp.comm_s8582702949713902594nteger (lambda ((A5 tptp.code_integer) (N tptp.nat)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.minus_minus_nat N) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 8.20/8.64 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A5 tptp.nat) (N tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A5) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 8.20/8.64 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A5 tptp.int) (N tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_int A5) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_assn (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_assn (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 8.20/8.64 (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 ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 8.20/8.64 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N2) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 8.20/8.64 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger A) (@ tptp.suc N2)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.minus_minus_nat N2) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 8.20/8.64 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N2) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 8.20/8.64 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N2) I))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 8.20/8.64 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L2)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K3)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 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) S5)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 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)) S5)))))) _let_1))))))))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (assert (= tptp.groups9119017779487936845_o_nat (lambda ((F3 (-> Bool tptp.nat)) (A5 tptp.nat) (Xs3 tptp.list_o)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_nat (@ F3 (@ (@ tptp.nth_o Xs3) N))) (@ (@ tptp.power_power_nat A5) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs3))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (assert (= tptp.groups9116527308978886569_o_int (lambda ((F3 (-> Bool tptp.int)) (A5 tptp.int) (Xs3 tptp.list_o)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ F3 (@ (@ tptp.nth_o Xs3) N))) (@ (@ tptp.power_power_int A5) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs3))))))
% 8.20/8.64 (assert (forall ((P3 tptp.nat) (K2 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 K2) P3) (= (@ (@ tptp.groups3455450783089532116nteger (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ (@ (@ tptp.if_Code_integer (= J K2)) tptp.one_one_Code_integer) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 8.20/8.64 (assert (forall ((P3 tptp.nat) (K2 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 K2) P3) (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_assn (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ (@ (@ tptp.if_assn (= J K2)) tptp.one_one_assn) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups6906906614972039071t_assn (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_assn (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 8.20/8.64 (assert (forall ((P3 tptp.nat) (K2 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 K2) P3) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ (@ (@ tptp.if_rat (= J K2)) tptp.one_one_rat) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 8.20/8.64 (assert (forall ((P3 tptp.nat) (K2 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 K2) P3) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ (@ (@ tptp.if_nat (= J K2)) tptp.one_one_nat) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 8.20/8.64 (assert (forall ((P3 tptp.nat) (K2 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 K2) P3) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ (@ (@ tptp.if_int (= J K2)) tptp.one_one_int) (@ H (@ (@ tptp.minus_minus_nat J) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J) K2)) (@ G J)) (@ H J)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 8.20/8.64 (assert (forall ((A tptp.code_natural) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.gbinom7368847122466276068atural A) _let_1) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.groups2279045934846249631atural (lambda ((I tptp.nat)) (@ (@ tptp.minus_7197305767214868737atural A) (@ tptp.semiri3763490453095760265atural I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2))) (@ tptp.semiri2447717529341329178atural _let_1))))))
% 8.20/8.64 (assert (forall ((A tptp.rat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_rat A) _let_1) (@ (@ tptp.divide_divide_rat (@ (@ tptp.groups73079841787564623at_rat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2))) (@ tptp.semiri773545260158071498ct_rat _let_1))))))
% 8.20/8.64 (assert (forall ((A tptp.code_integer) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.gbinom8545251970709558553nteger A) _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.groups3455450783089532116nteger (lambda ((I tptp.nat)) (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.semiri4939895301339042750nteger I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2))) (@ tptp.semiri3624122377584611663nteger _let_1))))))
% 8.20/8.64 (assert (forall ((A tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_nat A) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))))
% 8.20/8.64 (assert (forall ((A tptp.int) (K2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (= (@ (@ tptp.gbinomial_int A) _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K2))) (@ tptp.semiri1406184849735516958ct_int _let_1))))))
% 8.20/8.64 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K3 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R5 tptp.code_integer) (S5 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K3)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S5))) (= S5 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 8.20/8.64 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 8.20/8.64 (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 ((I tptp.nat) (J tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) N2))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ G I) (@ (@ tptp.minus_minus_nat K3) I)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (assert (forall ((I2 Bool) (K2 Bool)) (= (@ (@ tptp.member_o I2) (@ tptp.set_ord_lessThan_o K2)) (@ (@ tptp.ord_less_o I2) K2))))
% 8.20/8.64 (assert (forall ((I2 tptp.set_Pr958786334691620121nt_int) (K2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member2340774599025711042nt_int I2) (@ tptp.set_or4940836740269066044nt_int K2)) (@ (@ tptp.ord_le7563427860532173253nt_int I2) K2))))
% 8.20/8.64 (assert (forall ((I2 tptp.set_nat) (K2 tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ tptp.set_or890127255671739683et_nat K2)) (@ (@ tptp.ord_less_set_nat I2) K2))))
% 8.20/8.64 (assert (forall ((I2 tptp.assn) (K2 tptp.assn)) (= (@ (@ tptp.member_assn I2) (@ tptp.set_or7637083652282234053n_assn K2)) (@ (@ tptp.ord_less_assn I2) K2))))
% 8.20/8.64 (assert (forall ((I2 tptp.rat) (K2 tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_lessThan_rat K2)) (@ (@ tptp.ord_less_rat I2) K2))))
% 8.20/8.64 (assert (forall ((I2 tptp.num) (K2 tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_lessThan_num K2)) (@ (@ tptp.ord_less_num I2) K2))))
% 8.20/8.64 (assert (forall ((I2 tptp.nat) (K2 tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_lessThan_nat K2)) (@ (@ tptp.ord_less_nat I2) K2))))
% 8.20/8.64 (assert (forall ((I2 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_lessThan_int K2)) (@ (@ tptp.ord_less_int I2) K2))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.multis2468970476368604999at_nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups6857163185585827899at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_p7104986032573967614at_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 8.20/8.64 (assert (forall ((F (-> tptp.int tptp.nat)) (A4 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups1707563613775114915nt_nat F) A4)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A4))))
% 8.20/8.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat F) A4)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A4))))
% 8.20/8.64 (assert (= tptp.set_or4940836740269066044nt_int (lambda ((U3 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.ord_le7563427860532173253nt_int X4) U3))))))
% 8.20/8.64 (assert (= tptp.set_or890127255671739683et_nat (lambda ((U3 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_set_nat X4) U3))))))
% 8.20/8.64 (assert (= tptp.set_or7637083652282234053n_assn (lambda ((U3 tptp.assn)) (@ tptp.collect_assn (lambda ((X4 tptp.assn)) (@ (@ tptp.ord_less_assn X4) U3))))))
% 8.20/8.64 (assert (= tptp.set_ord_lessThan_rat (lambda ((U3 tptp.rat)) (@ tptp.collect_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.ord_less_rat X4) U3))))))
% 8.20/8.64 (assert (= tptp.set_ord_lessThan_num (lambda ((U3 tptp.num)) (@ tptp.collect_num (lambda ((X4 tptp.num)) (@ (@ tptp.ord_less_num X4) U3))))))
% 8.20/8.64 (assert (= tptp.set_ord_lessThan_nat (lambda ((U3 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) U3))))))
% 8.20/8.64 (assert (= tptp.set_ord_lessThan_int (lambda ((U3 tptp.int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_int X4) U3))))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L) (@ (@ tptp.plus_plus_int U) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L) U))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I))))) _let_1) (@ (@ tptp.groups708209901874060359at_nat G) _let_1)))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I))))) _let_1) (@ (@ tptp.groups705719431365010083at_int G) _let_1)))))
% 8.20/8.64 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) J2)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J2))))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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 ((I tptp.nat) (J tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) N2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ G I) (@ (@ tptp.minus_minus_nat K3) I)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 8.20/8.64 (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 ((I tptp.nat) (J tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) N2))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ G I) (@ (@ tptp.minus_minus_nat K3) I)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (assert (forall ((Q2 (-> tptp.int tptp.nat)) (P2 (-> 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 (@ Q2 X3)) (@ P2 X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat P2) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat Q2) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_nat (@ P2 X4)) (@ Q2 X4)))) _let_1))))))
% 8.20/8.64 (assert (forall ((Q2 (-> tptp.nat tptp.nat)) (P2 (-> 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 (@ Q2 X3)) (@ P2 X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P2) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q2) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P2 X4)) (@ Q2 X4)))) _let_1))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) J2))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((M3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat M3) K2))) (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) K2)))))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat N2) K2))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.nat)) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((M3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat M3) K2))) (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) K2)))))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat N2) K2))))))
% 8.20/8.64 (assert (forall ((G (-> tptp.nat tptp.int)) (K2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((M3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat M3) K2))) (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) K2)))))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat N2) K2))))))
% 8.20/8.64 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ A I)) (@ tptp.set_ord_lessThan_nat I)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I tptp.nat)) (@ (@ A I) J))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 8.20/8.64 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I)) (@ tptp.set_ord_lessThan_nat I)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ A I) J))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 8.20/8.64 (assert (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I)) (@ tptp.set_ord_lessThan_nat I)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ A I) J))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 8.20/8.64 (assert (forall ((X Bool) (K2 Bool)) (let ((_let_1 (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) (let ((_let_2 (@ (@ tptp.inf_inf_set_o (@ tptp.set_ord_lessThan_o K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_o X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_o))))))))
% 8.20/8.64 (assert (forall ((X tptp.assn) (K2 tptp.assn)) (let ((_let_1 (@ (@ tptp.insert_assn X) tptp.bot_bot_set_assn))) (let ((_let_2 (@ (@ tptp.inf_inf_set_assn (@ tptp.set_or7637083652282234053n_assn K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_assn X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_assn))))))))
% 8.20/8.64 (assert (forall ((X tptp.rat) (K2 tptp.rat)) (let ((_let_1 (@ (@ tptp.insert_rat X) tptp.bot_bot_set_rat))) (let ((_let_2 (@ (@ tptp.inf_inf_set_rat (@ tptp.set_ord_lessThan_rat K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_rat))))))))
% 8.20/8.64 (assert (forall ((X tptp.num) (K2 tptp.num)) (let ((_let_1 (@ (@ tptp.insert_num X) tptp.bot_bot_set_num))) (let ((_let_2 (@ (@ tptp.inf_inf_set_num (@ tptp.set_ord_lessThan_num K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_num X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_num))))))))
% 8.20/8.64 (assert (forall ((X tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (let ((_let_2 (@ (@ tptp.inf_inf_set_nat (@ tptp.set_ord_lessThan_nat K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 8.20/8.64 (assert (forall ((X tptp.int) (K2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (let ((_let_2 (@ (@ tptp.inf_inf_set_int (@ tptp.set_ord_lessThan_int K2)) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_int X) K2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_int))))))))
% 8.20/8.64 (assert (forall ((U Bool)) (= (@ (@ tptp.sup_sup_set_o (@ tptp.set_ord_lessThan_o U)) (@ (@ tptp.insert_o U) tptp.bot_bot_set_o)) (@ tptp.set_ord_atMost_o U))))
% 8.20/8.64 (assert (forall ((U tptp.nat)) (= (@ (@ tptp.sup_sup_set_nat (@ tptp.set_ord_lessThan_nat U)) (@ (@ tptp.insert_nat U) tptp.bot_bot_set_nat)) (@ tptp.set_ord_atMost_nat U))))
% 8.20/8.64 (assert (forall ((U tptp.int)) (= (@ (@ tptp.sup_sup_set_int (@ tptp.set_ord_lessThan_int U)) (@ (@ tptp.insert_int U) tptp.bot_bot_set_int)) (@ tptp.set_ord_atMost_int U))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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)))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ G (@ tptp.suc I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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)))))))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I)))) (@ (@ tptp.power_power_rat X) I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I)))) (@ (@ tptp.power_power_int X) I)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.power_8256067586552552935nteger X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 8.20/8.64 (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 ((I tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 8.20/8.64 (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 ((I tptp.nat) (J tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) J)) N2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ G I) (@ (@ tptp.minus_minus_nat K3) I)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 8.20/8.64 (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 ((I tptp.nat) (J tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) J)) N2))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ G I) (@ (@ tptp.minus_minus_nat K3) I)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (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))))))))))
% 8.20/8.64 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N tptp.nat) (A5 tptp.code_integer)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger _let_1) A5))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.bit_se7788150548672797655nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) _let_2))))))
% 8.20/8.64 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (A5 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int _let_1) A5))) (@ (@ (@ tptp.if_int (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.bit_se545348938243370406it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)))) _let_2))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (C2 (-> tptp.nat tptp.rat)) (D2 (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I))) (@ D2 I)))) A4) (@ (@ tptp.divide_divide_rat (@ C2 tptp.zero_zero_nat)) (@ D2 tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I))) (@ D2 I)))) A4) tptp.zero_zero_rat))))))
% 8.20/8.64 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (or (not (@ _let_2 K3)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 8.20/8.64 (assert (forall ((Xs tptp.list_nat) (H tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.heap_T2203789307644377761ay_nat (@ tptp.array_of_list_nat Xs)) H) (@ tptp.some_P8206036975937309155it_nat (@ (@ tptp.produc8657510640128716596it_nat (lambda ((R5 tptp.array_nat) (H7 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc4907525368653469954it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.size_size_list_nat Xs)))))) (@ (@ tptp.array_alloc_nat Xs) H))))))
% 8.20/8.64 (assert (forall ((Xs tptp.list_o) (H tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.heap_T8140152426084121245rray_o (@ tptp.array_of_list_o Xs)) H) (@ tptp.some_P3509045262911171395it_nat (@ (@ tptp.produc5512802776183222702it_nat (lambda ((R5 tptp.array_o) (H7 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc2890842502232952598it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.size_size_list_o Xs)))))) (@ (@ tptp.array_alloc_o Xs) H))))))
% 8.20/8.64 (assert (forall ((Xs tptp.list_int) (H tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.heap_T7249310324989956861ay_int (@ tptp.array_of_list_int Xs)) H) (@ tptp.some_P8650484732927216191it_nat (@ (@ tptp.produc3016605123915955252it_nat (lambda ((R5 tptp.array_int) (H7 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc5351973125643376990it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.size_size_list_int Xs)))))) (@ (@ tptp.array_alloc_int Xs) H))))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N2) K2)) (@ _let_1 K2)))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N2) K2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int))))
% 8.20/8.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.bit_se545348938243370406it_int M) (@ (@ tptp.bit_se545348938243370406it_int N2) A)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.plus_plus_nat M) N2)) A))))
% 8.20/8.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat M) (@ (@ tptp.bit_se547839408752420682it_nat N2) A)) (@ (@ tptp.bit_se547839408752420682it_nat (@ (@ tptp.plus_plus_nat M) N2)) A))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (assert (forall ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int K2) L)) (and (@ _let_1 K2) (@ _let_1 L))))))
% 8.20/8.64 (assert (forall ((K2 tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int K2) L)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (X Bool) (G (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat G))) (=> (@ tptp.finite_finite_o A4) (=> (not (@ (@ tptp.member_o X) A4)) (= (@ _let_1 (@ (@ tptp.insert_o X) A4)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A4))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A4) (=> (not (@ (@ tptp.member_nat X) A4)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A4)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A4))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A4) (=> (not (@ (@ tptp.member_int X) A4)) (= (@ _let_1 (@ (@ tptp.insert_int X) A4)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A4))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (not (@ (@ tptp.member_Code_integer X) A4)) (= (@ _let_1 (@ (@ tptp.insert_Code_integer X) A4)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A4))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (X Bool) (G (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups8507830703676809646_o_nat G))) (=> (@ tptp.finite_finite_o A4) (=> (not (@ (@ tptp.member_o X) A4)) (= (@ _let_1 (@ (@ tptp.insert_o X) A4)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A4))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A4) (=> (not (@ (@ tptp.member_int X) A4)) (= (@ _let_1 (@ (@ tptp.insert_int X) A4)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A4))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (not (@ (@ tptp.member_Code_integer X) A4)) (= (@ _let_1 (@ (@ tptp.insert_Code_integer X) A4)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A4))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (X Bool) (G (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups8505340233167759370_o_int G))) (=> (@ tptp.finite_finite_o A4) (=> (not (@ (@ tptp.member_o X) A4)) (= (@ _let_1 (@ (@ tptp.insert_o X) A4)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 A4))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A4) (=> (not (@ (@ tptp.member_nat X) A4)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A4)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 A4))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (not (@ (@ tptp.member_Code_integer X) A4)) (= (@ _let_1 (@ (@ tptp.insert_Code_integer X) A4)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 A4))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A4)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups3190895334310489300er_nat F) A4)) (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (=> (@ tptp.finite6177210948735845034at_nat A4) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4077766827762148844at_nat F) A4)) (forall ((X4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X4) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A4)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))) (@ F X4)))) A4) (@ (@ tptp.groups3906332499630173760nt_rat F) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.code_integer Bool)) (F (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups6602215022474089585er_rat (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))) (@ F X4)))) A4) (@ (@ tptp.groups6602215022474089585er_rat F) (@ (@ tptp.inf_in1364745209274528805nteger A4) (@ tptp.collect_Code_integer P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))) (@ F X4)))) A4) (@ (@ tptp.groups2906978787729119204at_rat F) (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.collect_nat P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))) (@ F X4)))) A4) (@ (@ tptp.groups4541462559716669496nt_nat F) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.code_integer Bool)) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))) (@ F X4)))) A4) (@ (@ tptp.groups7237345082560585321er_nat F) (@ (@ tptp.inf_in1364745209274528805nteger A4) (@ tptp.collect_Code_integer P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.code_integer Bool)) (F (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups7234854612051535045er_int (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ P2 X4))) (@ F X4)))) A4) (@ (@ tptp.groups7234854612051535045er_int F) (@ (@ tptp.inf_in1364745209274528805nteger A4) (@ tptp.collect_Code_integer P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ P2 X4))) (@ F X4)))) A4) (@ (@ tptp.groups3539618377306564664at_int F) (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.collect_nat P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (F (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups7873554091576472773nteger (lambda ((X4 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ P2 X4))) (@ F X4)))) A4) (@ (@ tptp.groups7873554091576472773nteger F) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.code_integer Bool)) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups879477027807139574nteger (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ P2 X4))) (@ F X4)))) A4) (@ (@ tptp.groups879477027807139574nteger F) (@ (@ tptp.inf_in1364745209274528805nteger A4) (@ tptp.collect_Code_integer P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (F (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((X4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ P2 X4))) (@ F X4)))) A4) (@ (@ tptp.groups7501900531339628137nteger F) (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.collect_nat P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_rat (@ F X4)) (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))))) A4) (@ (@ tptp.groups3906332499630173760nt_rat F) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (P2 (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups6602215022474089585er_rat (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_times_rat (@ F X4)) (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))))) A4) (@ (@ tptp.groups6602215022474089585er_rat F) (@ (@ tptp.inf_in1364745209274528805nteger A4) (@ tptp.collect_Code_integer P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (P2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_rat (@ F X4)) (@ tptp.zero_n2052037380579107095ol_rat (@ P2 X4))))) A4) (@ (@ tptp.groups2906978787729119204at_rat F) (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.collect_nat P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_nat (@ F X4)) (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))))) A4) (@ (@ tptp.groups4541462559716669496nt_nat F) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (P2 (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_times_nat (@ F X4)) (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4))))) A4) (@ (@ tptp.groups7237345082560585321er_nat F) (@ (@ tptp.inf_in1364745209274528805nteger A4) (@ tptp.collect_Code_integer P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int)) (P2 (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups7234854612051535045er_int (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_times_int (@ F X4)) (@ tptp.zero_n2684676970156552555ol_int (@ P2 X4))))) A4) (@ (@ tptp.groups7234854612051535045er_int F) (@ (@ tptp.inf_in1364745209274528805nteger A4) (@ tptp.collect_Code_integer P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.int)) (P2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_int (@ F X4)) (@ tptp.zero_n2684676970156552555ol_int (@ P2 X4))))) A4) (@ (@ tptp.groups3539618377306564664at_int F) (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.collect_nat P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.code_integer)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups7873554091576472773nteger (lambda ((X4 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ F X4)) (@ tptp.zero_n356916108424825756nteger (@ P2 X4))))) A4) (@ (@ tptp.groups7873554091576472773nteger F) (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (P2 (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups879477027807139574nteger (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger (@ F X4)) (@ tptp.zero_n356916108424825756nteger (@ P2 X4))))) A4) (@ (@ tptp.groups879477027807139574nteger F) (@ (@ tptp.inf_in1364745209274528805nteger A4) (@ tptp.collect_Code_integer P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (P2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((X4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ F X4)) (@ tptp.zero_n356916108424825756nteger (@ P2 X4))))) A4) (@ (@ tptp.groups7501900531339628137nteger F) (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.collect_nat P2)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (C2 (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I)))) A4) (@ C2 tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I tptp.nat)) (@ (@ tptp.times_times_rat (@ C2 I)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I)))) A4) tptp.zero_zero_rat))))))
% 8.20/8.64 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se9127793120404214118atural (@ 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_se9127793120404214118atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y)))))))
% 8.20/8.64 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1080825931792720795nteger (@ 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_se1080825931792720795nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y)))))))
% 8.20/8.64 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_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_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 8.20/8.64 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_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_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 8.20/8.64 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se9127793120404214118atural (@ 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_se9127793120404214118atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y)))))))
% 8.20/8.64 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1080825931792720795nteger (@ 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_se1080825931792720795nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y)))))))
% 8.20/8.64 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_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_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 8.20/8.64 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_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_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 8.20/8.64 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se9127793120404214118atural (@ tptp.numera5444537566228673987atural (@ tptp.bit1 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_se9127793120404214118atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y)))))))
% 8.20/8.64 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y)))))))
% 8.20/8.64 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 8.20/8.64 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))))))
% 8.20/8.64 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))))))
% 8.20/8.64 (assert (forall ((S tptp.set_Pr958786334691620121nt_int) (S3 tptp.set_Pr958786334691620121nt_int)) (=> (@ tptp.finite2998713641127702882nt_int S) (@ tptp.finite8744585540193469122nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((S5 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.minus_1052850069191792384nt_int S5) S) (@ (@ tptp.minus_1052850069191792384nt_int S3) S))))))))
% 8.20/8.64 (assert (forall ((S tptp.set_nat) (S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((S5 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat S5) S) (@ (@ tptp.minus_minus_set_nat S3) S))))))))
% 8.20/8.64 (assert (forall ((S tptp.set_int) (S3 tptp.set_int)) (=> (@ tptp.finite_finite_int S) (@ tptp.finite6197958912794628473et_int (@ tptp.collect_set_int (lambda ((S5 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int S5) S) (@ (@ tptp.minus_minus_set_int S3) S))))))))
% 8.20/8.64 (assert (forall ((S tptp.set_Code_integer) (S3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S) (@ tptp.finite6931041176100689706nteger (@ tptp.collec574505750873337192nteger (lambda ((S5 tptp.set_Code_integer)) (= (@ (@ tptp.minus_2355218937544613996nteger S5) S) (@ (@ tptp.minus_2355218937544613996nteger S3) S))))))))
% 8.20/8.64 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat S) (@ tptp.finite9047747110432174090at_nat (@ tptp.collec5514110066124741708at_nat (lambda ((S5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat S5) S) (@ (@ tptp.minus_1356011639430497352at_nat S3) S))))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (assert (forall ((P2 (-> tptp.nat Bool)) (I2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ P2 K3) (@ (@ tptp.ord_less_nat K3) I2)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_nat) (G (-> Bool tptp.nat tptp.nat)) (R3 (-> Bool tptp.nat Bool))) (=> (@ tptp.finite_finite_o A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X4 Bool)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_nat) (G (-> tptp.int tptp.nat tptp.nat)) (R3 (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_nat) (G (-> tptp.code_integer tptp.nat tptp.nat)) (R3 (-> tptp.code_integer tptp.nat Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ 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) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_int) (G (-> Bool tptp.int tptp.int)) (R3 (-> Bool tptp.int Bool))) (=> (@ tptp.finite_finite_o A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.groups8505340233167759370_o_int (lambda ((X4 Bool)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_int) (G (-> tptp.nat tptp.int tptp.int)) (R3 (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_int) (G (-> tptp.code_integer tptp.int tptp.int)) (R3 (-> tptp.code_integer tptp.int Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ 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) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_o) (G (-> tptp.nat Bool tptp.nat)) (R3 (-> tptp.nat Bool Bool))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_o B5) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.groups8507830703676809646_o_nat (@ G X4)) (@ tptp.collect_o (lambda ((Y4 Bool)) (and (@ (@ tptp.member_o Y4) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_int) (G (-> tptp.nat tptp.int tptp.nat)) (R3 (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.groups4541462559716669496nt_nat (@ G X4)) (@ tptp.collect_int (lambda ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_Code_integer) (G (-> tptp.nat tptp.code_integer tptp.nat)) (R3 (-> tptp.nat tptp.code_integer Bool))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ (@ 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) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.nat tptp.nat)) (R3 (-> tptp.nat tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_nat) (G (-> Bool tptp.nat tptp.nat)) (R3 (-> Bool tptp.nat Bool))) (=> (@ tptp.finite_finite_o A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.groups3504817904513533571_o_nat (lambda ((X4 Bool)) (@ (@ tptp.groups708209901874060359at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_nat) (G (-> tptp.int tptp.nat tptp.nat)) (R3 (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.groups708209901874060359at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_nat) (G (-> tptp.code_integer tptp.nat tptp.nat)) (R3 (-> tptp.code_integer tptp.nat Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ 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) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_nat) (G (-> Bool tptp.nat tptp.int)) (R3 (-> Bool tptp.nat Bool))) (=> (@ tptp.finite_finite_o A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.groups3502327434004483295_o_int (lambda ((X4 Bool)) (@ (@ tptp.groups705719431365010083at_int (@ G X4)) (@ tptp.collect_nat (lambda ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_nat) (G (-> tptp.code_integer tptp.nat tptp.int)) (R3 (-> tptp.code_integer tptp.nat Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ 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) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_int) (G (-> Bool tptp.int tptp.int)) (R3 (-> Bool tptp.int Bool))) (=> (@ tptp.finite_finite_o A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.groups3502327434004483295_o_int (lambda ((X4 Bool)) (@ (@ tptp.groups1705073143266064639nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_int) (G (-> tptp.code_integer tptp.int tptp.int)) (R3 (-> tptp.code_integer tptp.int Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ 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) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_o) (G (-> tptp.nat Bool tptp.nat)) (R3 (-> tptp.nat Bool Bool))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_o B5) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.groups3504817904513533571_o_nat (@ G X4)) (@ tptp.collect_o (lambda ((Y4 Bool)) (and (@ (@ tptp.member_o Y4) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_int) (G (-> tptp.nat tptp.int tptp.nat)) (R3 (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.groups1707563613775114915nt_nat (@ G X4)) (@ tptp.collect_int (lambda ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_Code_integer) (G (-> tptp.nat tptp.code_integer tptp.nat)) (R3 (-> tptp.nat tptp.code_integer Bool))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ (@ 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) B5) (@ (@ R3 X4) Y4))))))) A4) (@ (@ 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) A4) (@ (@ R3 X4) Y4))))))) B5))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (assert (forall ((L tptp.int) (K2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_eq_int K2) (@ (@ tptp.bit_se1409905431419307370or_int K2) L)))))
% 8.20/8.64 (assert (forall ((A tptp.int) (B tptp.int)) (=> (forall ((N5 tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N5)) (not (@ (@ tptp.bit_se1146084159140164899it_int B) N5)))) (= (@ (@ tptp.plus_plus_int A) B) (@ (@ tptp.bit_se1409905431419307370or_int A) B)))))
% 8.20/8.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (forall ((N5 tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N5)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B) N5)))) (= (@ (@ tptp.plus_plus_nat A) B) (@ (@ tptp.bit_se1412395901928357646or_nat A) B)))))
% 8.20/8.64 (assert (forall ((X7 tptp.set_Code_integer)) (=> (not (= X7 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) X7) (exists ((Xa3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa3) X7) (@ (@ tptp.ord_le6747313008572928689nteger X3) Xa3))))) (not (@ tptp.finite6017078050557962740nteger X7))))))
% 8.20/8.64 (assert (forall ((X7 tptp.set_o)) (=> (not (= X7 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) X7) (exists ((Xa3 Bool)) (and (@ (@ tptp.member_o Xa3) X7) (@ (@ tptp.ord_less_o X3) Xa3))))) (not (@ tptp.finite_finite_o X7))))))
% 8.20/8.64 (assert (forall ((X7 tptp.set_rat)) (=> (not (= X7 tptp.bot_bot_set_rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.member_rat X3) X7) (exists ((Xa3 tptp.rat)) (and (@ (@ tptp.member_rat Xa3) X7) (@ (@ tptp.ord_less_rat X3) Xa3))))) (not (@ tptp.finite_finite_rat X7))))))
% 8.20/8.64 (assert (forall ((X7 tptp.set_num)) (=> (not (= X7 tptp.bot_bot_set_num)) (=> (forall ((X3 tptp.num)) (=> (@ (@ tptp.member_num X3) X7) (exists ((Xa3 tptp.num)) (and (@ (@ tptp.member_num Xa3) X7) (@ (@ tptp.ord_less_num X3) Xa3))))) (not (@ tptp.finite_finite_num X7))))))
% 8.20/8.64 (assert (forall ((X7 tptp.set_nat)) (=> (not (= X7 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) X7) (exists ((Xa3 tptp.nat)) (and (@ (@ tptp.member_nat Xa3) X7) (@ (@ tptp.ord_less_nat X3) Xa3))))) (not (@ tptp.finite_finite_nat X7))))))
% 8.20/8.64 (assert (forall ((X7 tptp.set_int)) (=> (not (= X7 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) X7) (exists ((Xa3 tptp.int)) (and (@ (@ tptp.member_int Xa3) X7) (@ (@ tptp.ord_less_int X3) Xa3))))) (not (@ tptp.finite_finite_int X7))))))
% 8.20/8.64 (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 ((Xa3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa3) S) (@ (@ tptp.ord_le6747313008572928689nteger Xa3) X3))))))))))
% 8.20/8.64 (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 ((Xa3 Bool)) (and (@ (@ tptp.member_o Xa3) S) (@ (@ tptp.ord_less_o Xa3) X3))))))))))
% 8.20/8.64 (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 ((Xa3 tptp.assn)) (and (@ (@ tptp.member_assn Xa3) S) (@ (@ tptp.ord_less_assn Xa3) X3))))))))))
% 8.20/8.64 (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 ((Xa3 tptp.rat)) (and (@ (@ tptp.member_rat Xa3) S) (@ (@ tptp.ord_less_rat Xa3) X3))))))))))
% 8.20/8.64 (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 ((Xa3 tptp.num)) (and (@ (@ tptp.member_num Xa3) S) (@ (@ tptp.ord_less_num Xa3) X3))))))))))
% 8.20/8.64 (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 ((Xa3 tptp.nat)) (and (@ (@ tptp.member_nat Xa3) S) (@ (@ tptp.ord_less_nat Xa3) X3))))))))))
% 8.20/8.64 (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 ((Xa3 tptp.int)) (and (@ (@ tptp.member_int Xa3) S) (@ (@ tptp.ord_less_int Xa3) X3))))))))))
% 8.20/8.64 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) (@ (@ tptp.bit_se1409905431419307370or_int X) Y)) (@ (@ tptp.plus_plus_int X) Y))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int M))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) A)) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.plus_plus_nat M) N2)) (@ _let_1 A))))))
% 8.20/8.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat M))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) A)) (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ _let_1 A))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.code_integer)) (Y (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ X I) tptp.zero_z3403309356797280102nteger)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ Y I) tptp.zero_z3403309356797280102nteger)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ (@ tptp.plus_p5714425477246183910nteger (@ X I)) (@ Y I)) tptp.zero_z3403309356797280102nteger))))))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.code_integer)) (Y (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.zero_z3403309356797280102nteger)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.zero_z3403309356797280102nteger)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.plus_p5714425477246183910nteger (@ X I)) (@ Y I)) tptp.zero_z3403309356797280102nteger))))))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.code_integer)) (Y (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ X I) tptp.zero_z3403309356797280102nteger)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ Y I) tptp.zero_z3403309356797280102nteger)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ (@ tptp.plus_p5714425477246183910nteger (@ X I)) (@ Y I)) tptp.zero_z3403309356797280102nteger))))))))))
% 8.20/8.64 (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 ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) I5) (not (= (@ X I) tptp.zero_z3403309356797280102nteger)))))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) I5) (not (= (@ Y I) tptp.zero_z3403309356797280102nteger)))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) I5) (not (= (@ (@ tptp.plus_p5714425477246183910nteger (@ X I)) (@ Y I)) tptp.zero_z3403309356797280102nteger))))))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.rat)) (Y (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ X I) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ Y I) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I)) (@ Y I)) tptp.zero_zero_rat))))))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I)) (@ Y I)) tptp.zero_zero_rat))))))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.rat)) (Y (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ X I) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ Y I) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I)) (@ Y I)) tptp.zero_zero_rat))))))))))
% 8.20/8.64 (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 ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) I5) (not (= (@ X I) tptp.zero_zero_rat)))))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) I5) (not (= (@ Y I) tptp.zero_zero_rat)))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I)) (@ Y I)) tptp.zero_zero_rat))))))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.nat)) (Y (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ X I) tptp.zero_zero_nat)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ Y I) tptp.zero_zero_nat)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ (@ tptp.plus_plus_nat (@ X I)) (@ Y I)) tptp.zero_zero_nat))))))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.zero_zero_nat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.zero_zero_nat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.plus_plus_nat (@ X I)) (@ Y I)) tptp.zero_zero_nat))))))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.code_integer)) (Y (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ X I) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ Y I) tptp.one_one_Code_integer)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I)) (@ Y I)) tptp.one_one_Code_integer))))))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.code_integer)) (Y (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.one_one_Code_integer)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I)) (@ Y I)) tptp.one_one_Code_integer))))))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.code_integer)) (Y (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ X I) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ Y I) tptp.one_one_Code_integer)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I)) (@ Y I)) tptp.one_one_Code_integer))))))))))
% 8.20/8.64 (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 ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) I5) (not (= (@ X I) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) I5) (not (= (@ Y I) tptp.one_one_Code_integer)))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I)) (@ Y I)) tptp.one_one_Code_integer))))))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.assn)) (Y (-> Bool tptp.assn))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ X I) tptp.one_one_assn)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ Y I) tptp.one_one_assn)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ (@ tptp.times_times_assn (@ X I)) (@ Y I)) tptp.one_one_assn))))))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.assn)) (Y (-> tptp.nat tptp.assn))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.one_one_assn)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.one_one_assn)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.times_times_assn (@ X I)) (@ Y I)) tptp.one_one_assn))))))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.assn)) (Y (-> tptp.int tptp.assn))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ X I) tptp.one_one_assn)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ Y I) tptp.one_one_assn)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ (@ tptp.times_times_assn (@ X I)) (@ Y I)) tptp.one_one_assn))))))))))
% 8.20/8.64 (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 ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) I5) (not (= (@ X I) tptp.one_one_assn)))))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) I5) (not (= (@ Y I) tptp.one_one_assn)))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) I5) (not (= (@ (@ tptp.times_times_assn (@ X I)) (@ Y I)) tptp.one_one_assn))))))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.rat)) (Y (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ X I) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ Y I) tptp.one_one_rat)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ (@ tptp.times_times_rat (@ X I)) (@ Y I)) tptp.one_one_rat))))))))))
% 8.20/8.64 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ X I) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ Y I) tptp.one_one_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ (@ tptp.times_times_rat (@ X I)) (@ Y I)) tptp.one_one_rat))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.code_integer)) (P2 (-> Bool Bool))) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.groups4406642042086082107nteger G) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A4) (@ P2 X4))))) (@ (@ tptp.groups4406642042086082107nteger (lambda ((X4 Bool)) (@ (@ (@ tptp.if_Code_integer (@ P2 X4)) (@ G X4)) tptp.zero_z3403309356797280102nteger))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.code_integer)) (P2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups7501900531339628137nteger G) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ P2 X4))))) (@ (@ tptp.groups7501900531339628137nteger (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ P2 X4)) (@ G X4)) tptp.zero_z3403309356797280102nteger))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.code_integer)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups7873554091576472773nteger G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ P2 X4))))) (@ (@ tptp.groups7873554091576472773nteger (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ P2 X4)) (@ G X4)) tptp.zero_z3403309356797280102nteger))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (P2 (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups879477027807139574nteger G) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A4) (@ P2 X4))))) (@ (@ tptp.groups879477027807139574nteger (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ P2 X4)) (@ G X4)) tptp.zero_z3403309356797280102nteger))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.rat)) (P2 (-> Bool Bool))) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.groups7872700643590313910_o_rat G) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A4) (@ P2 X4))))) (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((X4 Bool)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ G X4)) tptp.zero_zero_rat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (P2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ P2 X4))))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ G X4)) tptp.zero_zero_rat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.rat)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3906332499630173760nt_rat G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ P2 X4))))) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ G X4)) tptp.zero_zero_rat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (P2 (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups6602215022474089585er_rat G) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A4) (@ P2 X4))))) (@ (@ tptp.groups6602215022474089585er_rat (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ G X4)) tptp.zero_zero_rat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.nat)) (P2 (-> Bool Bool))) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.groups8507830703676809646_o_nat G) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A4) (@ P2 X4))))) (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X4 Bool)) (@ (@ (@ tptp.if_nat (@ P2 X4)) (@ G X4)) tptp.zero_zero_nat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.nat)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups4541462559716669496nt_nat G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ P2 X4))))) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_nat (@ P2 X4)) (@ G X4)) tptp.zero_zero_nat))) A4)))))
% 8.20/8.64 (assert (forall ((M6 (-> tptp.list_nat tptp.nat)) (P2 (-> 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 (@ P2 X4)) (@ M6 X4)) tptp.zero_zero_nat))))))))
% 8.20/8.64 (assert (forall ((M6 (-> tptp.set_Pr958786334691620121nt_int tptp.nat)) (P2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (=> (@ tptp.finite8744585540193469122nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite8744585540193469122nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P2 X4)) (@ M6 X4)) tptp.zero_zero_nat))))))))
% 8.20/8.64 (assert (forall ((M6 (-> tptp.set_nat tptp.nat)) (P2 (-> 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 (@ P2 X4)) (@ M6 X4)) tptp.zero_zero_nat))))))))
% 8.20/8.64 (assert (forall ((M6 (-> tptp.nat tptp.nat)) (P2 (-> 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 (@ P2 X4)) (@ M6 X4)) tptp.zero_zero_nat))))))))
% 8.20/8.64 (assert (forall ((M6 (-> tptp.int tptp.nat)) (P2 (-> 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 (@ P2 X4)) (@ M6 X4)) tptp.zero_zero_nat))))))))
% 8.20/8.64 (assert (forall ((M6 (-> tptp.code_integer tptp.nat)) (P2 (-> 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 (@ P2 X4)) (@ M6 X4)) tptp.zero_zero_nat))))))))
% 8.20/8.64 (assert (forall ((M6 (-> tptp.product_prod_nat_nat tptp.nat)) (P2 (-> 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 (@ P2 X4)) (@ M6 X4)) tptp.zero_zero_nat))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.code_integer)) (P2 (-> Bool Bool))) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.groups7694694392188491536nteger G) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A4) (@ P2 X4))))) (@ (@ tptp.groups7694694392188491536nteger (lambda ((X4 Bool)) (@ (@ (@ tptp.if_Code_integer (@ P2 X4)) (@ G X4)) tptp.one_one_Code_integer))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.code_integer)) (P2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups3455450783089532116nteger G) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ P2 X4))))) (@ (@ tptp.groups3455450783089532116nteger (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ P2 X4)) (@ G X4)) tptp.one_one_Code_integer))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.code_integer)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3827104343326376752nteger G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ P2 X4))))) (@ (@ tptp.groups3827104343326376752nteger (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ P2 X4)) (@ G X4)) tptp.one_one_Code_integer))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (P2 (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups3674199335183972705nteger G) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A4) (@ P2 X4))))) (@ (@ tptp.groups3674199335183972705nteger (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ P2 X4)) (@ G X4)) tptp.one_one_Code_integer))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.assn)) (P2 (-> Bool Bool))) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.groups5301882518646026715o_assn G) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A4) (@ P2 X4))))) (@ (@ tptp.groups5301882518646026715o_assn (lambda ((X4 Bool)) (@ (@ (@ tptp.if_assn (@ P2 X4)) (@ G X4)) tptp.one_one_assn))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.assn)) (P2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups6906906614972039071t_assn G) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ P2 X4))))) (@ (@ tptp.groups6906906614972039071t_assn (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_assn (@ P2 X4)) (@ G X4)) tptp.one_one_assn))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.assn)) (P2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups7882442080178216443t_assn G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ P2 X4))))) (@ (@ tptp.groups7882442080178216443t_assn (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_assn (@ P2 X4)) (@ G X4)) tptp.one_one_assn))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (P2 (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups1304777262505850412r_assn G) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A4) (@ P2 X4))))) (@ (@ tptp.groups1304777262505850412r_assn (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_assn (@ P2 X4)) (@ G X4)) tptp.one_one_assn))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.rat)) (P2 (-> Bool Bool))) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.groups2869687844427037835_o_rat G) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A4) (@ P2 X4))))) (@ (@ tptp.groups2869687844427037835_o_rat (lambda ((X4 Bool)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ G X4)) tptp.one_one_rat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (P2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ P2 X4))))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ G X4)) tptp.one_one_rat))) A4)))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o A4) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (= (= (@ (@ tptp.groups4406642042086082107nteger F) A4) tptp.zero_z3403309356797280102nteger) (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A4) (= (@ F X4) tptp.zero_z3403309356797280102nteger))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (= (= (@ (@ tptp.groups7501900531339628137nteger F) A4) tptp.zero_z3403309356797280102nteger) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (= (@ F X4) tptp.zero_z3403309356797280102nteger))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (= (= (@ (@ tptp.groups7873554091576472773nteger F) A4) tptp.zero_z3403309356797280102nteger) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (= (@ F X4) tptp.zero_z3403309356797280102nteger))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (= (= (@ (@ tptp.groups879477027807139574nteger F) A4) tptp.zero_z3403309356797280102nteger) (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) A4) (= (@ F X4) tptp.zero_z3403309356797280102nteger))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o A4) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups7872700643590313910_o_rat F) A4) tptp.zero_zero_rat) (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A4) (= (@ F X4) tptp.zero_zero_rat))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups2906978787729119204at_rat F) A4) tptp.zero_zero_rat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (= (@ F X4) tptp.zero_zero_rat))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups3906332499630173760nt_rat F) A4) tptp.zero_zero_rat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (= (@ F X4) tptp.zero_zero_rat))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups6602215022474089585er_rat F) A4) tptp.zero_zero_rat) (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) A4) (= (@ F X4) tptp.zero_zero_rat))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o A4) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (= (= (@ (@ tptp.groups8507830703676809646_o_nat F) A4) tptp.zero_zero_nat) (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A4) (= (@ F X4) tptp.zero_zero_nat))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A4) tptp.zero_zero_nat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (= (@ F X4) tptp.zero_zero_nat))))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_nat) (T6 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 T6) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa3 tptp.nat)) (and (@ (@ tptp.member_nat Xa3) T6) (= (@ I2 Xa3) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa3)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7501900531339628137nteger F) S2)) (@ (@ tptp.groups7501900531339628137nteger G) T6))))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_nat) (T6 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 T6) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa3 tptp.int)) (and (@ (@ tptp.member_int Xa3) T6) (= (@ I2 Xa3) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa3)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7501900531339628137nteger F) S2)) (@ (@ tptp.groups7873554091576472773nteger G) T6))))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_nat) (T6 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 T6) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa3) T6) (= (@ I2 Xa3) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa3)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7501900531339628137nteger F) S2)) (@ (@ tptp.groups879477027807139574nteger G) T6))))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_int) (T6 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 T6) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa3 tptp.nat)) (and (@ (@ tptp.member_nat Xa3) T6) (= (@ I2 Xa3) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa3)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7873554091576472773nteger F) S2)) (@ (@ tptp.groups7501900531339628137nteger G) T6))))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_int) (T6 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 T6) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa3 tptp.int)) (and (@ (@ tptp.member_int Xa3) T6) (= (@ I2 Xa3) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa3)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7873554091576472773nteger F) S2)) (@ (@ tptp.groups7873554091576472773nteger G) T6))))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_int) (T6 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 T6) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa3) T6) (= (@ I2 Xa3) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa3)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7873554091576472773nteger F) S2)) (@ (@ tptp.groups879477027807139574nteger G) T6))))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_Code_integer) (T6 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 T6) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S2) (exists ((Xa3 tptp.nat)) (and (@ (@ tptp.member_nat Xa3) T6) (= (@ I2 Xa3) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa3)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups879477027807139574nteger F) S2)) (@ (@ tptp.groups7501900531339628137nteger G) T6))))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_Code_integer) (T6 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 T6) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S2) (exists ((Xa3 tptp.int)) (and (@ (@ tptp.member_int Xa3) T6) (= (@ I2 Xa3) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa3)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups879477027807139574nteger F) S2)) (@ (@ tptp.groups7873554091576472773nteger G) T6))))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_Code_integer) (T6 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 T6) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S2) (exists ((Xa3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa3) T6) (= (@ I2 Xa3) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa3)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups879477027807139574nteger F) S2)) (@ (@ tptp.groups879477027807139574nteger G) T6))))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_nat) (T6 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 T6) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa3 tptp.nat)) (and (@ (@ tptp.member_nat Xa3) T6) (= (@ I2 Xa3) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S2)) (@ (@ tptp.groups2906978787729119204at_rat G) T6))))))))
% 8.20/8.64 (assert (forall ((S tptp.set_Code_integer) (P2 (-> tptp.set_Code_integer Bool)) (F (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ P2 tptp.bot_bo3990330152332043303nteger) (=> (forall ((X3 tptp.code_integer) (S8 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S8) (=> (forall ((Y5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y5) S8) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X3)))) (=> (@ P2 S8) (@ P2 (@ (@ tptp.insert_Code_integer X3) S8)))))) (@ P2 S))))))
% 8.20/8.64 (assert (forall ((S tptp.set_o) (P2 (-> tptp.set_o Bool)) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o S) (=> (@ P2 tptp.bot_bot_set_o) (=> (forall ((X3 Bool) (S8 tptp.set_o)) (=> (@ tptp.finite_finite_o S8) (=> (forall ((Y5 Bool)) (=> (@ (@ tptp.member_o Y5) S8) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X3)))) (=> (@ P2 S8) (@ P2 (@ (@ tptp.insert_o X3) S8)))))) (@ P2 S))))))
% 8.20/8.64 (assert (forall ((S tptp.set_nat) (P2 (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (@ P2 tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S8 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S8) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) S8) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X3)))) (=> (@ P2 S8) (@ P2 (@ (@ tptp.insert_nat X3) S8)))))) (@ P2 S))))))
% 8.20/8.64 (assert (forall ((S tptp.set_int) (P2 (-> tptp.set_int Bool)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S) (=> (@ P2 tptp.bot_bot_set_int) (=> (forall ((X3 tptp.int) (S8 tptp.set_int)) (=> (@ tptp.finite_finite_int S8) (=> (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) S8) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X3)))) (=> (@ P2 S8) (@ P2 (@ (@ tptp.insert_int X3) S8)))))) (@ P2 S))))))
% 8.20/8.64 (assert (forall ((S tptp.set_Code_integer) (P2 (-> tptp.set_Code_integer Bool)) (F (-> tptp.code_integer tptp.num))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ P2 tptp.bot_bo3990330152332043303nteger) (=> (forall ((X3 tptp.code_integer) (S8 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S8) (=> (forall ((Y5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y5) S8) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X3)))) (=> (@ P2 S8) (@ P2 (@ (@ tptp.insert_Code_integer X3) S8)))))) (@ P2 S))))))
% 8.20/8.64 (assert (forall ((S tptp.set_o) (P2 (-> tptp.set_o Bool)) (F (-> Bool tptp.num))) (=> (@ tptp.finite_finite_o S) (=> (@ P2 tptp.bot_bot_set_o) (=> (forall ((X3 Bool) (S8 tptp.set_o)) (=> (@ tptp.finite_finite_o S8) (=> (forall ((Y5 Bool)) (=> (@ (@ tptp.member_o Y5) S8) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X3)))) (=> (@ P2 S8) (@ P2 (@ (@ tptp.insert_o X3) S8)))))) (@ P2 S))))))
% 8.20/8.64 (assert (forall ((S tptp.set_nat) (P2 (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.num))) (=> (@ tptp.finite_finite_nat S) (=> (@ P2 tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S8 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S8) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) S8) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X3)))) (=> (@ P2 S8) (@ P2 (@ (@ tptp.insert_nat X3) S8)))))) (@ P2 S))))))
% 8.20/8.64 (assert (forall ((S tptp.set_int) (P2 (-> tptp.set_int Bool)) (F (-> tptp.int tptp.num))) (=> (@ tptp.finite_finite_int S) (=> (@ P2 tptp.bot_bot_set_int) (=> (forall ((X3 tptp.int) (S8 tptp.set_int)) (=> (@ tptp.finite_finite_int S8) (=> (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) S8) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X3)))) (=> (@ P2 S8) (@ P2 (@ (@ tptp.insert_int X3) S8)))))) (@ P2 S))))))
% 8.20/8.64 (assert (forall ((S tptp.set_Code_integer) (P2 (-> tptp.set_Code_integer Bool)) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ P2 tptp.bot_bo3990330152332043303nteger) (=> (forall ((X3 tptp.code_integer) (S8 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S8) (=> (forall ((Y5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y5) S8) (@ (@ tptp.ord_less_eq_nat (@ F Y5)) (@ F X3)))) (=> (@ P2 S8) (@ P2 (@ (@ tptp.insert_Code_integer X3) S8)))))) (@ P2 S))))))
% 8.20/8.64 (assert (forall ((S tptp.set_o) (P2 (-> tptp.set_o Bool)) (F (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o S) (=> (@ P2 tptp.bot_bot_set_o) (=> (forall ((X3 Bool) (S8 tptp.set_o)) (=> (@ tptp.finite_finite_o S8) (=> (forall ((Y5 Bool)) (=> (@ (@ tptp.member_o Y5) S8) (@ (@ tptp.ord_less_eq_nat (@ F Y5)) (@ F X3)))) (=> (@ P2 S8) (@ P2 (@ (@ tptp.insert_o X3) S8)))))) (@ P2 S))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A4) (@ (@ tptp.ord_less_rat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A4)) (@ (@ tptp.groups2906978787729119204at_rat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) A4) (@ (@ tptp.ord_less_rat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A4)) (@ (@ tptp.groups3906332499630173760nt_rat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X6 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X6) A4) (@ (@ tptp.ord_less_rat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups6602215022474089585er_rat F) A4)) (@ (@ tptp.groups6602215022474089585er_rat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (=> (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) A4) (@ (@ tptp.ord_less_nat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A4)) (@ (@ tptp.groups4541462559716669496nt_nat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (=> (exists ((X6 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X6) A4) (@ (@ tptp.ord_less_nat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups7237345082560585321er_nat F) A4)) (@ (@ tptp.groups7237345082560585321er_nat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (=> (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A4) (@ (@ tptp.ord_less_int (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A4)) (@ (@ tptp.groups3539618377306564664at_int G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A4) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (=> (exists ((X6 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X6) A4) (@ (@ tptp.ord_less_int (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups7234854612051535045er_int F) A4)) (@ (@ tptp.groups7234854612051535045er_int G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (=> (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A4) (@ (@ tptp.ord_less_nat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups3542108847815614940at_nat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (=> (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) A4) (@ (@ tptp.ord_less_int (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups4538972089207619220nt_int F) A4)) (@ (@ tptp.groups4538972089207619220nt_int G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.rat)) (G (-> tptp.product_prod_nat_nat tptp.rat))) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X6 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X6) A4) (@ (@ tptp.ord_less_rat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups342789780944988191at_rat F) A4)) (@ (@ tptp.groups342789780944988191at_rat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ P2 tptp.bot_bo3990330152332043303nteger) (=> (forall ((B3 tptp.code_integer) (A9 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A9) (=> (forall ((X6 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X6) A9) (@ (@ tptp.ord_le6747313008572928689nteger X6) B3))) (=> (@ P2 A9) (@ P2 (@ (@ tptp.insert_Code_integer B3) A9)))))) (@ P2 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (P2 (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o A4) (=> (@ P2 tptp.bot_bot_set_o) (=> (forall ((B3 Bool) (A9 tptp.set_o)) (=> (@ tptp.finite_finite_o A9) (=> (forall ((X6 Bool)) (=> (@ (@ tptp.member_o X6) A9) (@ (@ tptp.ord_less_o X6) B3))) (=> (@ P2 A9) (@ P2 (@ (@ tptp.insert_o B3) A9)))))) (@ P2 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_rat) (P2 (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A4) (=> (@ P2 tptp.bot_bot_set_rat) (=> (forall ((B3 tptp.rat) (A9 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A9) (=> (forall ((X6 tptp.rat)) (=> (@ (@ tptp.member_rat X6) A9) (@ (@ tptp.ord_less_rat X6) B3))) (=> (@ P2 A9) (@ P2 (@ (@ tptp.insert_rat B3) A9)))))) (@ P2 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_num) (P2 (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A4) (=> (@ P2 tptp.bot_bot_set_num) (=> (forall ((B3 tptp.num) (A9 tptp.set_num)) (=> (@ tptp.finite_finite_num A9) (=> (forall ((X6 tptp.num)) (=> (@ (@ tptp.member_num X6) A9) (@ (@ tptp.ord_less_num X6) B3))) (=> (@ P2 A9) (@ P2 (@ (@ tptp.insert_num B3) A9)))))) (@ P2 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A4) (=> (@ P2 tptp.bot_bot_set_nat) (=> (forall ((B3 tptp.nat) (A9 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A9) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A9) (@ (@ tptp.ord_less_nat X6) B3))) (=> (@ P2 A9) (@ P2 (@ (@ tptp.insert_nat B3) A9)))))) (@ P2 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A4) (=> (@ P2 tptp.bot_bot_set_int) (=> (forall ((B3 tptp.int) (A9 tptp.set_int)) (=> (@ tptp.finite_finite_int A9) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A9) (@ (@ tptp.ord_less_int X6) B3))) (=> (@ P2 A9) (@ P2 (@ (@ tptp.insert_int B3) A9)))))) (@ P2 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ P2 tptp.bot_bo3990330152332043303nteger) (=> (forall ((B3 tptp.code_integer) (A9 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A9) (=> (forall ((X6 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X6) A9) (@ (@ tptp.ord_le6747313008572928689nteger B3) X6))) (=> (@ P2 A9) (@ P2 (@ (@ tptp.insert_Code_integer B3) A9)))))) (@ P2 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (P2 (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o A4) (=> (@ P2 tptp.bot_bot_set_o) (=> (forall ((B3 Bool) (A9 tptp.set_o)) (=> (@ tptp.finite_finite_o A9) (=> (forall ((X6 Bool)) (=> (@ (@ tptp.member_o X6) A9) (@ (@ tptp.ord_less_o B3) X6))) (=> (@ P2 A9) (@ P2 (@ (@ tptp.insert_o B3) A9)))))) (@ P2 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_rat) (P2 (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A4) (=> (@ P2 tptp.bot_bot_set_rat) (=> (forall ((B3 tptp.rat) (A9 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A9) (=> (forall ((X6 tptp.rat)) (=> (@ (@ tptp.member_rat X6) A9) (@ (@ tptp.ord_less_rat B3) X6))) (=> (@ P2 A9) (@ P2 (@ (@ tptp.insert_rat B3) A9)))))) (@ P2 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_num) (P2 (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A4) (=> (@ P2 tptp.bot_bot_set_num) (=> (forall ((B3 tptp.num) (A9 tptp.set_num)) (=> (@ tptp.finite_finite_num A9) (=> (forall ((X6 tptp.num)) (=> (@ (@ tptp.member_num X6) A9) (@ (@ tptp.ord_less_num B3) X6))) (=> (@ P2 A9) (@ P2 (@ (@ tptp.insert_num B3) A9)))))) (@ P2 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A4) (=> (@ P2 tptp.bot_bot_set_nat) (=> (forall ((B3 tptp.nat) (A9 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A9) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A9) (@ (@ tptp.ord_less_nat B3) X6))) (=> (@ P2 A9) (@ P2 (@ (@ tptp.insert_nat B3) A9)))))) (@ P2 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A4) (=> (@ P2 tptp.bot_bot_set_int) (=> (forall ((B3 tptp.int) (A9 tptp.set_int)) (=> (@ tptp.finite_finite_int A9) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A9) (@ (@ tptp.ord_less_int B3) X6))) (=> (@ P2 A9) (@ P2 (@ (@ tptp.insert_int B3) A9)))))) (@ P2 A4))))))
% 8.20/8.64 (assert (forall ((R3 (-> tptp.code_integer tptp.code_integer Bool)) (S tptp.set_nat) (H (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (@ (@ R3 tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger) (=> (forall ((X13 tptp.code_integer) (Y12 tptp.code_integer) (X22 tptp.code_integer) (Y22 tptp.code_integer)) (=> (and (@ (@ R3 X13) X22) (@ (@ R3 Y12) Y22)) (@ (@ R3 (@ (@ tptp.plus_p5714425477246183910nteger X13) Y12)) (@ (@ tptp.plus_p5714425477246183910nteger X22) Y22)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (@ (@ R3 (@ H X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups7501900531339628137nteger H) S)) (@ (@ tptp.groups7501900531339628137nteger G) S))))))))
% 8.20/8.64 (assert (forall ((R3 (-> tptp.code_integer tptp.code_integer Bool)) (S tptp.set_int) (H (-> tptp.int tptp.code_integer)) (G (-> tptp.int tptp.code_integer))) (=> (@ (@ R3 tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger) (=> (forall ((X13 tptp.code_integer) (Y12 tptp.code_integer) (X22 tptp.code_integer) (Y22 tptp.code_integer)) (=> (and (@ (@ R3 X13) X22) (@ (@ R3 Y12) Y22)) (@ (@ R3 (@ (@ tptp.plus_p5714425477246183910nteger X13) Y12)) (@ (@ tptp.plus_p5714425477246183910nteger X22) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (@ (@ R3 (@ H X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups7873554091576472773nteger H) S)) (@ (@ tptp.groups7873554091576472773nteger G) S))))))))
% 8.20/8.64 (assert (forall ((R3 (-> 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))) (=> (@ (@ R3 tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger) (=> (forall ((X13 tptp.code_integer) (Y12 tptp.code_integer) (X22 tptp.code_integer) (Y22 tptp.code_integer)) (=> (and (@ (@ R3 X13) X22) (@ (@ R3 Y12) Y22)) (@ (@ R3 (@ (@ tptp.plus_p5714425477246183910nteger X13) Y12)) (@ (@ tptp.plus_p5714425477246183910nteger X22) Y22)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (@ (@ R3 (@ H X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups879477027807139574nteger H) S)) (@ (@ tptp.groups879477027807139574nteger G) S))))))))
% 8.20/8.64 (assert (forall ((R3 (-> tptp.rat tptp.rat Bool)) (S tptp.set_nat) (H (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R3 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X13 tptp.rat) (Y12 tptp.rat) (X22 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R3 X13) X22) (@ (@ R3 Y12) Y22)) (@ (@ R3 (@ (@ tptp.plus_plus_rat X13) Y12)) (@ (@ tptp.plus_plus_rat X22) Y22)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (@ (@ R3 (@ H X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups2906978787729119204at_rat H) S)) (@ (@ tptp.groups2906978787729119204at_rat G) S))))))))
% 8.20/8.64 (assert (forall ((R3 (-> tptp.rat tptp.rat Bool)) (S tptp.set_int) (H (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ R3 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X13 tptp.rat) (Y12 tptp.rat) (X22 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R3 X13) X22) (@ (@ R3 Y12) Y22)) (@ (@ R3 (@ (@ tptp.plus_plus_rat X13) Y12)) (@ (@ tptp.plus_plus_rat X22) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (@ (@ R3 (@ H X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups3906332499630173760nt_rat H) S)) (@ (@ tptp.groups3906332499630173760nt_rat G) S))))))))
% 8.20/8.64 (assert (forall ((R3 (-> tptp.rat tptp.rat Bool)) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ (@ R3 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X13 tptp.rat) (Y12 tptp.rat) (X22 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R3 X13) X22) (@ (@ R3 Y12) Y22)) (@ (@ R3 (@ (@ tptp.plus_plus_rat X13) Y12)) (@ (@ tptp.plus_plus_rat X22) Y22)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (@ (@ R3 (@ H X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups6602215022474089585er_rat H) S)) (@ (@ tptp.groups6602215022474089585er_rat G) S))))))))
% 8.20/8.64 (assert (forall ((R3 (-> tptp.nat tptp.nat Bool)) (S tptp.set_int) (H (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ (@ R3 tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X13 tptp.nat) (Y12 tptp.nat) (X22 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R3 X13) X22) (@ (@ R3 Y12) Y22)) (@ (@ R3 (@ (@ tptp.plus_plus_nat X13) Y12)) (@ (@ tptp.plus_plus_nat X22) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (@ (@ R3 (@ H X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups4541462559716669496nt_nat H) S)) (@ (@ tptp.groups4541462559716669496nt_nat G) S))))))))
% 8.20/8.64 (assert (forall ((R3 (-> tptp.nat tptp.nat Bool)) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ (@ R3 tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X13 tptp.nat) (Y12 tptp.nat) (X22 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R3 X13) X22) (@ (@ R3 Y12) Y22)) (@ (@ R3 (@ (@ tptp.plus_plus_nat X13) Y12)) (@ (@ tptp.plus_plus_nat X22) Y22)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (@ (@ R3 (@ H X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups7237345082560585321er_nat H) S)) (@ (@ tptp.groups7237345082560585321er_nat G) S))))))))
% 8.20/8.64 (assert (forall ((R3 (-> tptp.int tptp.int Bool)) (S tptp.set_nat) (H (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ R3 tptp.zero_zero_int) tptp.zero_zero_int) (=> (forall ((X13 tptp.int) (Y12 tptp.int) (X22 tptp.int) (Y22 tptp.int)) (=> (and (@ (@ R3 X13) X22) (@ (@ R3 Y12) Y22)) (@ (@ R3 (@ (@ tptp.plus_plus_int X13) Y12)) (@ (@ tptp.plus_plus_int X22) Y22)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (@ (@ R3 (@ H X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups3539618377306564664at_int H) S)) (@ (@ tptp.groups3539618377306564664at_int G) S))))))))
% 8.20/8.64 (assert (forall ((R3 (-> tptp.int tptp.int Bool)) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (=> (@ (@ R3 tptp.zero_zero_int) tptp.zero_zero_int) (=> (forall ((X13 tptp.int) (Y12 tptp.int) (X22 tptp.int) (Y22 tptp.int)) (=> (and (@ (@ R3 X13) X22) (@ (@ R3 Y12) Y22)) (@ (@ R3 (@ (@ tptp.plus_plus_int X13) Y12)) (@ (@ tptp.plus_plus_int X22) Y22)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (@ (@ R3 (@ H X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups7234854612051535045er_int H) S)) (@ (@ tptp.groups7234854612051535045er_int G) S))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (not (= A4 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups6602215022474089585er_rat F) A4)) (@ (@ tptp.groups6602215022474089585er_rat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.rat)) (G (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o A4) (=> (not (= A4 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups7872700643590313910_o_rat F) A4)) (@ (@ tptp.groups7872700643590313910_o_rat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A4)) (@ (@ tptp.groups2906978787729119204at_rat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A4)) (@ (@ tptp.groups3906332499630173760nt_rat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (not (= A4 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A4) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups7237345082560585321er_nat F) A4)) (@ (@ tptp.groups7237345082560585321er_nat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o A4) (=> (not (= A4 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups8507830703676809646_o_nat F) A4)) (@ (@ tptp.groups8507830703676809646_o_nat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A4)) (@ (@ tptp.groups4541462559716669496nt_nat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (not (= A4 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A4) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups7234854612051535045er_int F) A4)) (@ (@ tptp.groups7234854612051535045er_int G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o A4) (=> (not (= A4 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups8505340233167759370_o_int F) A4)) (@ (@ tptp.groups8505340233167759370_o_int G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A4)) (@ (@ tptp.groups3539618377306564664at_int G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (X Bool) (G (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o X) A4)))) (let ((_let_4 (@ (@ tptp.member_o X) A4))) (=> (@ tptp.finite_finite_o A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X)) _let_2)))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A4)))) (let ((_let_4 (@ (@ tptp.member_nat X) A4))) (=> (@ tptp.finite_finite_nat A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X)) _let_2)))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A4)))) (let ((_let_4 (@ (@ tptp.member_int X) A4))) (=> (@ tptp.finite_finite_int A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X)) _let_2)))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Code_integer X) A4)))) (let ((_let_4 (@ (@ tptp.member_Code_integer X) A4))) (=> (@ tptp.finite6017078050557962740nteger A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X)) _let_2)))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (X Bool) (G (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups8507830703676809646_o_nat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o X) A4)))) (let ((_let_4 (@ (@ tptp.member_o X) A4))) (=> (@ tptp.finite_finite_o A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A4)))) (let ((_let_4 (@ (@ tptp.member_int X) A4))) (=> (@ tptp.finite_finite_int A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Code_integer X) A4)))) (let ((_let_4 (@ (@ tptp.member_Code_integer X) A4))) (=> (@ tptp.finite6017078050557962740nteger A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (X Bool) (G (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups8505340233167759370_o_int G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o X) A4)))) (let ((_let_4 (@ (@ tptp.member_o X) A4))) (=> (@ tptp.finite_finite_o A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_int (@ G X)) _let_2)))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A4)))) (let ((_let_4 (@ (@ tptp.member_nat X) A4))) (=> (@ tptp.finite_finite_nat A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_int (@ G X)) _let_2)))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Code_integer X) A4)))) (let ((_let_4 (@ (@ tptp.member_Code_integer X) A4))) (=> (@ tptp.finite6017078050557962740nteger A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_int (@ G X)) _let_2)))))))))))
% 8.20/8.64 (assert (forall ((M tptp.nat) (K2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K2)) N2) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1146084159140164899it_int K2) (@ (@ tptp.minus_minus_nat N2) M))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat F))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A4)) (@ _let_1 B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (let ((_let_1 (@ tptp.groups4077766827762148844at_nat F))) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A4)) (@ _let_1 B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int F))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (@ (@ tptp.dvd_dvd_int (@ _let_1 A4)) (@ _let_1 B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.int))) (let ((_let_1 (@ tptp.groups4075276357253098568at_int F))) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5) (@ (@ tptp.dvd_dvd_int (@ _let_1 A4)) (@ _let_1 B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat F))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A4)) (@ _let_1 B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat F))) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A4)) (@ _let_1 B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int F))) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (@ (@ tptp.dvd_dvd_int (@ _let_1 A4)) (@ _let_1 B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int F))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (@ (@ tptp.dvd_dvd_int (@ _let_1 A4)) (@ _let_1 B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (F (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o B5) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) A4) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups3504817904513533571_o_nat F) A4)) (@ (@ tptp.groups3504817904513533571_o_nat G) B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) A4) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups3190895334310489300er_nat F) A4)) (@ (@ tptp.groups3190895334310489300er_nat G) B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (F (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o B5) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) A4) (@ (@ tptp.dvd_dvd_int (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups3502327434004483295_o_int F) A4)) (@ (@ tptp.groups3502327434004483295_o_int G) B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) A4) (@ (@ tptp.dvd_dvd_int (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups3188404863801439024er_int F) A4)) (@ (@ tptp.groups3188404863801439024er_int G) B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A4)) (@ (@ tptp.groups1707563613775114915nt_nat G) B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups708209901874060359at_nat F) A4)) (@ (@ tptp.groups708209901874060359at_nat G) B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (@ (@ tptp.dvd_dvd_int (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups705719431365010083at_int F) A4)) (@ (@ tptp.groups705719431365010083at_int G) B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (@ (@ tptp.dvd_dvd_int (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups1705073143266064639nt_int F) A4)) (@ (@ tptp.groups1705073143266064639nt_int G) B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_set_nat) (A4 tptp.set_set_nat) (F (-> tptp.set_nat tptp.nat)) (G (-> tptp.set_nat tptp.nat))) (=> (@ tptp.finite1152437895449049373et_nat B5) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A4) B5) (=> (forall ((A3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat A3) A4) (@ (@ tptp.dvd_dvd_nat (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups4248547760180025341at_nat F) A4)) (@ (@ tptp.groups4248547760180025341at_nat G) B5)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_set_nat) (A4 tptp.set_set_nat) (F (-> tptp.set_nat tptp.int)) (G (-> tptp.set_nat tptp.int))) (=> (@ tptp.finite1152437895449049373et_nat B5) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A4) B5) (=> (forall ((A3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat A3) A4) (@ (@ tptp.dvd_dvd_int (@ F A3)) (@ G A3)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups4246057289670975065at_int F) A4)) (@ (@ tptp.groups4246057289670975065at_int G) B5)))))))
% 8.20/8.64 (assert (= tptp.bit_concat_bit (lambda ((N tptp.nat) (K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N) K3)) (@ (@ tptp.bit_se545348938243370406it_int N) L2)))))
% 8.20/8.64 (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))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.code_integer)) (B5 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) B5) (=> (@ (@ tptp.member_o I2) S2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) B5)))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (B5 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) B5) (=> (@ (@ tptp.member_nat I2) S2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) B5)))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.code_integer)) (B5 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) B5) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) B5)))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (B5 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) B5) (=> (@ (@ tptp.member_Code_integer I2) S2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) B5)))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.rat)) (B5 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) B5) (=> (@ (@ tptp.member_o I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B5)))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (B5 tptp.rat) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S2) B5) (=> (@ (@ tptp.member_nat I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B5)))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.rat)) (B5 tptp.rat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S2) B5) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B5)))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (B5 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) B5) (=> (@ (@ tptp.member_Code_integer I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B5)))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.nat)) (B5 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) B5) (=> (@ (@ tptp.member_o I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B5)))))))
% 8.20/8.64 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.nat)) (B5 tptp.nat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S2) B5) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B5)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (assert (forall ((M6 (-> tptp.set_Pr958786334691620121nt_int tptp.nat)) (A tptp.set_Pr958786334691620121nt_int)) (=> (@ tptp.finite8744585540193469122nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite8744585540193469122nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.code_integer)) (B5 tptp.set_o)) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.groups4406642042086082107nteger G) (@ (@ tptp.inf_inf_set_o A4) B5)) (@ (@ tptp.groups4406642042086082107nteger (lambda ((X4 Bool)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.member_o X4) B5)) (@ G X4)) tptp.zero_z3403309356797280102nteger))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.code_integer)) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups7873554091576472773nteger G) (@ (@ tptp.inf_inf_set_int A4) B5)) (@ (@ tptp.groups7873554091576472773nteger (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.member_int X4) B5)) (@ G X4)) tptp.zero_z3403309356797280102nteger))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (B5 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups879477027807139574nteger G) (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)) (@ (@ tptp.groups879477027807139574nteger (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.member_Code_integer X4) B5)) (@ G X4)) tptp.zero_z3403309356797280102nteger))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.rat)) (B5 tptp.set_o)) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.groups7872700643590313910_o_rat G) (@ (@ tptp.inf_inf_set_o A4) B5)) (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((X4 Bool)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_o X4) B5)) (@ G X4)) tptp.zero_zero_rat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.rat)) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3906332499630173760nt_rat G) (@ (@ tptp.inf_inf_set_int A4) B5)) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_int X4) B5)) (@ G X4)) tptp.zero_zero_rat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (B5 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups6602215022474089585er_rat G) (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)) (@ (@ tptp.groups6602215022474089585er_rat (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_Code_integer X4) B5)) (@ G X4)) tptp.zero_zero_rat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.nat)) (B5 tptp.set_o)) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.groups8507830703676809646_o_nat G) (@ (@ tptp.inf_inf_set_o A4) B5)) (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X4 Bool)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_o X4) B5)) (@ G X4)) tptp.zero_zero_nat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.nat)) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups4541462559716669496nt_nat G) (@ (@ tptp.inf_inf_set_int A4) B5)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_int X4) B5)) (@ G X4)) tptp.zero_zero_nat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (B5 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups7237345082560585321er_nat G) (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)) (@ (@ tptp.groups7237345082560585321er_nat (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_Code_integer X4) B5)) (@ G X4)) tptp.zero_zero_nat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.int)) (B5 tptp.set_o)) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.groups8505340233167759370_o_int G) (@ (@ tptp.inf_inf_set_o A4) B5)) (@ (@ tptp.groups8505340233167759370_o_int (lambda ((X4 Bool)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_o X4) B5)) (@ G X4)) tptp.zero_zero_int))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger G))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (= (@ G X4) tptp.zero_z3403309356797280102nteger))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups7873554091576472773nteger G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.zero_z3403309356797280102nteger))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger G))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.zero_z3403309356797280102nteger))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (= (@ G X4) tptp.zero_zero_rat))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.zero_zero_rat))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.zero_zero_rat))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.zero_zero_nat))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.zero_zero_nat))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (= (@ G X4) tptp.zero_zero_int))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.zero_zero_int))))) (@ _let_1 A4))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (assert (forall ((M6 (-> tptp.set_Pr958786334691620121nt_int tptp.nat)) (N7 (-> tptp.set_Pr958786334691620121nt_int tptp.nat))) (=> (@ tptp.finite8744585540193469122nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite8744585540193469122nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M6 X4)) (@ N7 X4)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.code_integer)) (B5 tptp.set_o)) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.groups7694694392188491536nteger G) (@ (@ tptp.inf_inf_set_o A4) B5)) (@ (@ tptp.groups7694694392188491536nteger (lambda ((X4 Bool)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.member_o X4) B5)) (@ G X4)) tptp.one_one_Code_integer))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.code_integer)) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3827104343326376752nteger G) (@ (@ tptp.inf_inf_set_int A4) B5)) (@ (@ tptp.groups3827104343326376752nteger (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.member_int X4) B5)) (@ G X4)) tptp.one_one_Code_integer))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (B5 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups3674199335183972705nteger G) (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)) (@ (@ tptp.groups3674199335183972705nteger (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.member_Code_integer X4) B5)) (@ G X4)) tptp.one_one_Code_integer))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.assn)) (B5 tptp.set_o)) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.groups5301882518646026715o_assn G) (@ (@ tptp.inf_inf_set_o A4) B5)) (@ (@ tptp.groups5301882518646026715o_assn (lambda ((X4 Bool)) (@ (@ (@ tptp.if_assn (@ (@ tptp.member_o X4) B5)) (@ G X4)) tptp.one_one_assn))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.assn)) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups7882442080178216443t_assn G) (@ (@ tptp.inf_inf_set_int A4) B5)) (@ (@ tptp.groups7882442080178216443t_assn (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_assn (@ (@ tptp.member_int X4) B5)) (@ G X4)) tptp.one_one_assn))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (B5 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups1304777262505850412r_assn G) (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)) (@ (@ tptp.groups1304777262505850412r_assn (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_assn (@ (@ tptp.member_Code_integer X4) B5)) (@ G X4)) tptp.one_one_assn))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.rat)) (B5 tptp.set_o)) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.groups2869687844427037835_o_rat G) (@ (@ tptp.inf_inf_set_o A4) B5)) (@ (@ tptp.groups2869687844427037835_o_rat (lambda ((X4 Bool)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_o X4) B5)) (@ G X4)) tptp.one_one_rat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.rat)) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups1072433553688619179nt_rat G) (@ (@ tptp.inf_inf_set_int A4) B5)) (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_int X4) B5)) (@ G X4)) tptp.one_one_rat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (B5 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups2555765274223993564er_rat G) (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)) (@ (@ tptp.groups2555765274223993564er_rat (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_Code_integer X4) B5)) (@ G X4)) tptp.one_one_rat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.nat)) (B5 tptp.set_o)) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.groups3504817904513533571_o_nat G) (@ (@ tptp.inf_inf_set_o A4) B5)) (@ (@ tptp.groups3504817904513533571_o_nat (lambda ((X4 Bool)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_o X4) B5)) (@ G X4)) tptp.one_one_nat))) A4)))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (= (@ G X4) tptp.one_one_Code_integer))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.one_one_Code_integer))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.one_one_Code_integer))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (= (@ G X4) tptp.one_one_assn))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.one_one_assn))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.one_one_assn))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (= (@ G X4) tptp.one_one_rat))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.one_one_rat))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.one_one_rat))))) (@ _let_1 A4))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.one_one_nat))))) (@ _let_1 A4))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (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)))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.code_integer)) (H (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups4406642042086082107nteger G) T7) (@ (@ tptp.groups4406642042086082107nteger H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.code_integer)) (H (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7501900531339628137nteger G) T7) (@ (@ tptp.groups7501900531339628137nteger H) S))))))))
% 8.20/8.64 (assert (forall ((T7 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 T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups879477027807139574nteger G) T7) (@ (@ tptp.groups879477027807139574nteger H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.rat)) (H (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) S)) (= (@ G X3) tptp.zero_zero_rat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7872700643590313910_o_rat G) T7) (@ (@ tptp.groups7872700643590313910_o_rat H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.rat)) (H (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups2906978787729119204at_rat G) T7) (@ (@ tptp.groups2906978787729119204at_rat H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (H (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) 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) T7) (@ (@ tptp.groups6602215022474089585er_rat H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.nat)) (H (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) S)) (= (@ G X3) tptp.zero_zero_nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups8507830703676809646_o_nat G) T7) (@ (@ tptp.groups8507830703676809646_o_nat H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (H (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) 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) T7) (@ (@ tptp.groups7237345082560585321er_nat H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.int)) (H (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) S)) (= (@ G X3) tptp.zero_zero_int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups8505340233167759370_o_int G) T7) (@ (@ tptp.groups8505340233167759370_o_int H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3539618377306564664at_int G) T7) (@ (@ tptp.groups3539618377306564664at_int H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.code_integer)) (G (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (H (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 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 T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.rat)) (G (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (H (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (H (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ H X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3539618377306564664at_int G) S) (@ (@ tptp.groups3539618377306564664at_int H) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger G))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups7873554091576472773nteger G))) (=> (@ tptp.finite_finite_int T7) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int T7) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int T7) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger G))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups7873554091576472773nteger G))) (=> (@ tptp.finite_finite_int T7) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int T7) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int T7) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.zero_z3403309356797280102nteger))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) C4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C4) A4)) (= (@ G A3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat C4) B5)) (= (@ H B3) tptp.zero_z3403309356797280102nteger))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (B5 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 C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) C4) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C4) A4)) (= (@ G A3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C4) B5)) (= (@ H B3) tptp.zero_z3403309356797280102nteger))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) C4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C4) A4)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (B5 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 C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) C4) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C4) A4)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (B5 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 C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) C4) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C4) A4)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C4) B5)) (= (@ H B3) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.zero_zero_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int H))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat C4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) C4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C4) A4)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat C4) B5)) (= (@ H B3) tptp.zero_zero_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.zero_z3403309356797280102nteger))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) C4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C4) A4)) (= (@ G A3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat C4) B5)) (= (@ H B3) tptp.zero_z3403309356797280102nteger))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (B5 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 C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) C4) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C4) A4)) (= (@ G A3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C4) B5)) (= (@ H B3) tptp.zero_z3403309356797280102nteger))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) C4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C4) A4)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (B5 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 C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) C4) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C4) A4)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C4) B5)) (= (@ H B3) tptp.zero_zero_rat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.zero_zero_nat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (B5 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 C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) C4) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C4) A4)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C4) B5)) (= (@ H B3) tptp.zero_zero_nat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.zero_zero_int))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int H))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat C4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) C4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C4) A4)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat C4) B5)) (= (@ H B3) tptp.zero_zero_int))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) A4) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) A4) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) A4) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int G))) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups342789780944988191at_rat G))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B5) A4) (=> (@ tptp.finite6177210948735845034at_nat A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5)) (@ (@ tptp.minus_minus_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat F))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) A4) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5)) (@ (@ tptp.minus_minus_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5)) (@ (@ tptp.minus_minus_int (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int F))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) A4) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5)) (@ (@ tptp.minus_minus_int (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups342789780944988191at_rat F))) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B5) A4) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) (@ (@ tptp.minus_minus_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.int))) (let ((_let_1 (@ tptp.groups975429370522433651at_int F))) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B5) A4) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) (@ (@ tptp.minus_minus_int (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5)) (@ (@ tptp.minus_minus_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5)) (@ (@ tptp.minus_minus_int (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) A4) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) A4) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) A4) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) A4) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.code_integer)) (H (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) S)) (= (@ G X3) tptp.one_one_Code_integer))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7694694392188491536nteger G) T7) (@ (@ tptp.groups7694694392188491536nteger H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.code_integer)) (H (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.one_one_Code_integer))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3455450783089532116nteger G) T7) (@ (@ tptp.groups3455450783089532116nteger H) S))))))))
% 8.20/8.64 (assert (forall ((T7 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 T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) 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) T7) (@ (@ tptp.groups3674199335183972705nteger H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.assn)) (H (-> Bool tptp.assn))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) S)) (= (@ G X3) tptp.one_one_assn))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups5301882518646026715o_assn G) T7) (@ (@ tptp.groups5301882518646026715o_assn H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.assn)) (H (-> tptp.nat tptp.assn))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups6906906614972039071t_assn G) T7) (@ (@ tptp.groups6906906614972039071t_assn H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (H (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) 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) T7) (@ (@ tptp.groups1304777262505850412r_assn H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.rat)) (H (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) S)) (= (@ G X3) tptp.one_one_rat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups2869687844427037835_o_rat G) T7) (@ (@ tptp.groups2869687844427037835_o_rat H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.rat)) (H (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups73079841787564623at_rat G) T7) (@ (@ tptp.groups73079841787564623at_rat H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (H (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) 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) T7) (@ (@ tptp.groups2555765274223993564er_rat H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.nat)) (H (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) S)) (= (@ G X3) tptp.one_one_nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3504817904513533571_o_nat G) T7) (@ (@ tptp.groups3504817904513533571_o_nat H) S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.code_integer)) (G (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (H (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ H X3) tptp.one_one_Code_integer))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3455450783089532116nteger G) S) (@ (@ tptp.groups3455450783089532116nteger H) T7))))))))
% 8.20/8.64 (assert (forall ((T7 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 T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.assn)) (G (-> Bool tptp.assn))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (H (-> tptp.nat tptp.assn)) (G (-> tptp.nat tptp.assn))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ H X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups6906906614972039071t_assn G) S) (@ (@ tptp.groups6906906614972039071t_assn H) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.assn)) (G (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.rat)) (G (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (H (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ H X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups73079841787564623at_rat G) S) (@ (@ tptp.groups73079841787564623at_rat H) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T7) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T7) 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) T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.one_one_int))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger G))) (=> (@ tptp.finite_finite_int T7) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int T7) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 T7) (@ _let_1 S))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat T7) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T7) S)) (= (@ G X3) tptp.one_one_int))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger G))) (=> (@ tptp.finite_finite_int T7) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((T7 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int T7) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 S) (@ _let_1 T7))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.one_one_Code_integer))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.one_one_Code_integer))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.code_integer)) (H (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger H))) (let ((_let_2 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat C4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) C4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C4) A4)) (= (@ G A3) tptp.one_one_Code_integer))) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat C4) B5)) (= (@ H B3) tptp.one_one_Code_integer))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (B5 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 C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) C4) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C4) A4)) (= (@ G A3) tptp.one_one_Code_integer))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C4) B5)) (= (@ H B3) tptp.one_one_Code_integer))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.one_one_assn))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.assn)) (H (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn H))) (let ((_let_2 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat C4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) C4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C4) A4)) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat C4) B5)) (= (@ H B3) tptp.one_one_assn))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (B5 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 C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) C4) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C4) A4)) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C4) B5)) (= (@ H B3) tptp.one_one_assn))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.one_one_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (H (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat H))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat C4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) C4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C4) A4)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat C4) B5)) (= (@ H B3) tptp.one_one_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (B5 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 C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) C4) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C4) A4)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C4) B5)) (= (@ H B3) tptp.one_one_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.one_one_nat))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.one_one_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A4) (@ _let_1 B5))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.one_one_Code_integer))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.one_one_Code_integer))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.code_integer)) (H (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger H))) (let ((_let_2 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat C4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) C4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C4) A4)) (= (@ G A3) tptp.one_one_Code_integer))) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat C4) B5)) (= (@ H B3) tptp.one_one_Code_integer))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (B5 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 C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) C4) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C4) A4)) (= (@ G A3) tptp.one_one_Code_integer))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C4) B5)) (= (@ H B3) tptp.one_one_Code_integer))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.one_one_assn))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.assn)) (H (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn H))) (let ((_let_2 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat C4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) C4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C4) A4)) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat C4) B5)) (= (@ H B3) tptp.one_one_assn))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (B5 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 C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) C4) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C4) A4)) (= (@ G A3) tptp.one_one_assn))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C4) B5)) (= (@ H B3) tptp.one_one_assn))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.one_one_rat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_nat) (A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (H (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat H))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat C4) (=> (@ (@ tptp.ord_less_eq_set_nat A4) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B5) C4) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C4) A4)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat C4) B5)) (= (@ H B3) tptp.one_one_rat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (B5 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 C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) C4) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) C4) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) (@ (@ tptp.minus_2355218937544613996nteger C4) A4)) (= (@ G A3) tptp.one_one_rat))) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger C4) B5)) (= (@ H B3) tptp.one_one_rat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((C4 tptp.set_o) (A4 tptp.set_o) (B5 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 C4) (=> (@ (@ tptp.ord_less_eq_set_o A4) C4) (=> (@ (@ tptp.ord_less_eq_set_o B5) C4) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) (@ (@ tptp.minus_minus_set_o C4) A4)) (= (@ G A3) tptp.one_one_nat))) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o C4) B5)) (= (@ H B3) tptp.one_one_nat))) (= (= (@ _let_2 A4) (@ _let_1 B5)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5))) (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5))) (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5))) (@ (@ tptp.plus_plus_int (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ (@ tptp.plus_plus_int (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ (@ tptp.plus_plus_int (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups342789780944988191at_rat G))) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ tptp.finite6177210948735845034at_nat B5) (= (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A4) B5))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5))) (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.rat)) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (B5 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.nat)) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (B5 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int)) (B5 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.int)) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B5 tptp.set_nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.int)) (B5 tptp.set_int)) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.rat)) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.groups342789780944988191at_rat G))) (=> (@ tptp.finite6177210948735845034at_nat A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ (@ tptp.times_times_assn (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5))) (@ (@ tptp.times_times_assn (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ (@ tptp.times_times_assn (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5))) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))) (@ (@ tptp.times_times_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5))) (@ (@ tptp.times_times_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5))) (@ (@ tptp.times_times_int (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))) (@ (@ tptp.times_times_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat F))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger B5) A4) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5)) (@ (@ tptp.minus_minus_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (let ((_let_1 (@ tptp.groups977919841031483927at_nat F))) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B5) A4) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) B5)) (@ (@ tptp.minus_minus_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int B5) A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5)) (@ (@ tptp.minus_minus_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat B5) A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5)) (@ (@ tptp.minus_minus_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int M) (@ tptp.bit_se2000444600071755411sk_int N2)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.plus_plus_nat N2) M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int M))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (H (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.collect_int P2))) (let ((_let_2 (@ tptp.inf_inf_set_int A4))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups3906332499630173760nt_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups3906332499630173760nt_rat G) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.code_integer Bool)) (H (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.collect_Code_integer P2))) (let ((_let_2 (@ tptp.inf_in1364745209274528805nteger A4))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups6602215022474089585er_rat (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups6602215022474089585er_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups6602215022474089585er_rat G) (@ _let_2 (@ tptp.uminus804700908173204444nteger _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (H (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.collect_int P2))) (let ((_let_2 (@ tptp.inf_inf_set_int A4))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_nat (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups4541462559716669496nt_nat H) (@ _let_2 _let_1))) (@ (@ tptp.groups4541462559716669496nt_nat G) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.code_integer Bool)) (H (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.collect_Code_integer P2))) (let ((_let_2 (@ tptp.inf_in1364745209274528805nteger A4))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups7237345082560585321er_nat H) (@ _let_2 _let_1))) (@ (@ tptp.groups7237345082560585321er_nat G) (@ _let_2 (@ tptp.uminus804700908173204444nteger _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.code_integer Bool)) (H (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.collect_Code_integer P2))) (let ((_let_2 (@ tptp.inf_in1364745209274528805nteger A4))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups7234854612051535045er_int (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups7234854612051535045er_int H) (@ _let_2 _let_1))) (@ (@ tptp.groups7234854612051535045er_int G) (@ _let_2 (@ tptp.uminus804700908173204444nteger _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (H (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.collect_nat P2))) (let ((_let_2 (@ tptp.inf_inf_set_nat A4))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups2906978787729119204at_rat G) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (H (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.collect_nat P2))) (let ((_let_2 (@ tptp.inf_inf_set_nat A4))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_int (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int H) (@ _let_2 _let_1))) (@ (@ tptp.groups3539618377306564664at_int G) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (H (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.collect_nat P2))) (let ((_let_2 (@ tptp.inf_inf_set_nat A4))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat H) (@ _let_2 _let_1))) (@ (@ tptp.groups3542108847815614940at_nat G) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (H (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.collect_int P2))) (let ((_let_2 (@ tptp.inf_inf_set_int A4))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_int (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int H) (@ _let_2 _let_1))) (@ (@ tptp.groups4538972089207619220nt_int G) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_list_nat) (P2 (-> tptp.list_nat Bool)) (H (-> tptp.list_nat tptp.rat)) (G (-> tptp.list_nat tptp.rat))) (let ((_let_1 (@ tptp.collect_list_nat P2))) (let ((_let_2 (@ tptp.inf_inf_set_list_nat A4))) (=> (@ tptp.finite8100373058378681591st_nat A4) (= (@ (@ tptp.groups3760926236672600436at_rat (lambda ((X4 tptp.list_nat)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups3760926236672600436at_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups3760926236672600436at_rat G) (@ _let_2 (@ tptp.uminus3195874150345416415st_nat _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (H (-> tptp.int tptp.assn)) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.collect_int P2))) (let ((_let_2 (@ tptp.inf_inf_set_int A4))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_assn (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.times_times_assn (@ (@ tptp.groups7882442080178216443t_assn H) (@ _let_2 _let_1))) (@ (@ tptp.groups7882442080178216443t_assn G) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.code_integer Bool)) (H (-> tptp.code_integer tptp.assn)) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.collect_Code_integer P2))) (let ((_let_2 (@ tptp.inf_in1364745209274528805nteger A4))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_assn (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.times_times_assn (@ (@ tptp.groups1304777262505850412r_assn H) (@ _let_2 _let_1))) (@ (@ tptp.groups1304777262505850412r_assn G) (@ _let_2 (@ tptp.uminus804700908173204444nteger _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (H (-> tptp.nat tptp.assn)) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.collect_nat P2))) (let ((_let_2 (@ tptp.inf_inf_set_nat A4))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_assn (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.times_times_assn (@ (@ tptp.groups6906906614972039071t_assn H) (@ _let_2 _let_1))) (@ (@ tptp.groups6906906614972039071t_assn G) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (H (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.collect_int P2))) (let ((_let_2 (@ tptp.inf_inf_set_int A4))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.times_times_rat (@ (@ tptp.groups1072433553688619179nt_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups1072433553688619179nt_rat G) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.code_integer Bool)) (H (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.collect_Code_integer P2))) (let ((_let_2 (@ tptp.inf_in1364745209274528805nteger A4))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups2555765274223993564er_rat (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2555765274223993564er_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups2555765274223993564er_rat G) (@ _let_2 (@ tptp.uminus804700908173204444nteger _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (H (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.collect_nat P2))) (let ((_let_2 (@ tptp.inf_inf_set_nat A4))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.times_times_rat (@ (@ tptp.groups73079841787564623at_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups73079841787564623at_rat G) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool)) (H (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.collect_int P2))) (let ((_let_2 (@ tptp.inf_inf_set_int A4))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_nat (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.times_times_nat (@ (@ tptp.groups1707563613775114915nt_nat H) (@ _let_2 _let_1))) (@ (@ tptp.groups1707563613775114915nt_nat G) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.code_integer Bool)) (H (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.collect_Code_integer P2))) (let ((_let_2 (@ tptp.inf_in1364745209274528805nteger A4))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups3190895334310489300er_nat (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3190895334310489300er_nat H) (@ _let_2 _let_1))) (@ (@ tptp.groups3190895334310489300er_nat G) (@ _let_2 (@ tptp.uminus804700908173204444nteger _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.code_integer Bool)) (H (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.collect_Code_integer P2))) (let ((_let_2 (@ tptp.inf_in1364745209274528805nteger A4))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.groups3188404863801439024er_int (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.times_times_int (@ (@ tptp.groups3188404863801439024er_int H) (@ _let_2 _let_1))) (@ (@ tptp.groups3188404863801439024er_int G) (@ _let_2 (@ tptp.uminus804700908173204444nteger _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool)) (H (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.collect_nat P2))) (let ((_let_2 (@ tptp.inf_inf_set_nat A4))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ P2 X4)) (@ H X4)) (@ G X4)))) A4) (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat H) (@ _let_2 _let_1))) (@ (@ tptp.groups708209901874060359at_nat G) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (forall ((I3 tptp.code_integer)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Code_integer I3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ G I3)))))) (=> (not (= A4 tptp.bot_bo3990330152332043303nteger)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.groups3674199335183972705nteger F) A4)) (@ (@ tptp.groups3674199335183972705nteger G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.code_integer)) (G (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o A4) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ G I3)))))) (=> (not (= A4 tptp.bot_bot_set_o)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.groups7694694392188491536nteger F) A4)) (@ (@ tptp.groups7694694392188491536nteger G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ G I3)))))) (=> (not (= A4 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.groups3455450783089532116nteger F) A4)) (@ (@ tptp.groups3455450783089532116nteger G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.code_integer)) (G (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ G I3)))))) (=> (not (= A4 tptp.bot_bot_set_int)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.groups3827104343326376752nteger F) A4)) (@ (@ tptp.groups3827104343326376752nteger G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (forall ((I3 tptp.code_integer)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Code_integer I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A4 tptp.bot_bo3990330152332043303nteger)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2555765274223993564er_rat F) A4)) (@ (@ tptp.groups2555765274223993564er_rat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.rat)) (G (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o A4) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A4 tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2869687844427037835_o_rat F) A4)) (@ (@ tptp.groups2869687844427037835_o_rat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A4 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups73079841787564623at_rat F) A4)) (@ (@ tptp.groups73079841787564623at_rat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A4 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A4)) (@ (@ tptp.groups1072433553688619179nt_rat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (forall ((I3 tptp.code_integer)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Code_integer I3) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I3)))))) (=> (not (= A4 tptp.bot_bo3990330152332043303nteger)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3190895334310489300er_nat F) A4)) (@ (@ tptp.groups3190895334310489300er_nat G) A4)))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o A4) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I3)))))) (=> (not (= A4 tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3504817904513533571_o_nat F) A4)) (@ (@ tptp.groups3504817904513533571_o_nat G) A4)))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (F (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups4406642042086082107nteger F))) (=> (@ tptp.finite_finite_o B5) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o B5) A4)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F B3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger F))) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat B5) A4)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F B3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger F))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger B5) A4)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F B3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat F))) (=> (@ tptp.finite_finite_o B5) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat F))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (F (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups8507830703676809646_o_nat F))) (=> (@ tptp.finite_finite_o B5) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o B5) A4)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B3)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat F))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger B5) A4)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B3)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (F (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups8505340233167759370_o_int F))) (=> (@ tptp.finite_finite_o B5) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o B5) A4)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat B5) A4)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A4)) (@ _let_1 B5))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups7873554091576472773nteger G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.plus_plus_int (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.plus_plus_int (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (X tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X))) (let ((_let_2 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A4) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (X tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X))) (let ((_let_2 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A4) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int)) (X tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X))) (let ((_let_2 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A4) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.rat)) (X Bool)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.groups7872700643590313910_o_rat G))) (=> (@ tptp.finite_finite_o A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_o A4) (@ _let_1 tptp.bot_bot_set_o))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.nat)) (X Bool)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.groups8507830703676809646_o_nat G))) (=> (@ tptp.finite_finite_o A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_o A4) (@ _let_1 tptp.bot_bot_set_o))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (G (-> Bool tptp.int)) (X Bool)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.groups8505340233167759370_o_int G))) (=> (@ tptp.finite_finite_o A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_o A4) (@ _let_1 tptp.bot_bot_set_o))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A4) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.int)) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A4) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.rat)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A4) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.nat)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A4) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ (@ tptp.member_Code_integer X) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ (@ tptp.member_Code_integer X) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ (@ tptp.member_Code_integer X) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger))))))))))
% 8.20/8.64 (assert (forall ((A4 tptp.set_o) (X Bool) (G (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat G))) (=> (@ tptp.finite_finite_o A4) (=> (@ (@ tptp.member_o X) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_o A4) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (X Bool) (G (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups8507830703676809646_o_nat G))) (=> (@ tptp.finite_finite_o A4) (=> (@ (@ tptp.member_o X) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_o A4) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (X Bool) (G (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups8505340233167759370_o_int G))) (=> (@ tptp.finite_finite_o A4) (=> (@ (@ tptp.member_o X) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_o A4) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat X) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat X) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int X) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int X) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat F))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int F))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups342789780944988191at_rat F))) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ tptp.finite6177210948735845034at_nat B5) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A4) B5)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.int))) (let ((_let_1 (@ tptp.groups975429370522433651at_int F))) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ tptp.finite6177210948735845034at_nat B5) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A4) B5)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (F (-> tptp.produc4166570645942440679at_nat tptp.rat))) (let ((_let_1 (@ tptp.groups6424767709179651461at_rat F))) (=> (@ tptp.finite1918287321285529104at_nat A4) (=> (@ tptp.finite1918287321285529104at_nat B5) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (F (-> tptp.produc3843707927480180839at_nat tptp.rat))) (let ((_let_1 (@ tptp.groups3225780264831618053at_rat F))) (=> (@ tptp.finite4343798906461161616at_nat A4) (=> (@ tptp.finite4343798906461161616at_nat B5) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A4) B5) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A4) B5) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A4) B5) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.plus_plus_int (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o) (G (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat G))) (=> (@ tptp.finite_finite_o A4) (=> (@ tptp.finite_finite_o B5) (=> (= (@ (@ tptp.inf_inf_set_o A4) B5) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A4) B5)) (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o) (G (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups8507830703676809646_o_nat G))) (=> (@ tptp.finite_finite_o A4) (=> (@ tptp.finite_finite_o B5) (=> (= (@ (@ tptp.inf_inf_set_o A4) B5) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A4) B5)) (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o) (G (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups8505340233167759370_o_int G))) (=> (@ tptp.finite_finite_o A4) (=> (@ tptp.finite_finite_o B5) (=> (= (@ (@ tptp.inf_inf_set_o A4) B5) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A4) B5)) (@ (@ tptp.plus_plus_int (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.plus_plus_int (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_plus_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_assn (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.times_times_assn (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_assn (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_nat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A4) B5) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.times_times_assn (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o) (G (-> Bool tptp.assn))) (let ((_let_1 (@ tptp.groups5301882518646026715o_assn G))) (=> (@ tptp.finite_finite_o A4) (=> (@ tptp.finite_finite_o B5) (=> (= (@ (@ tptp.inf_inf_set_o A4) B5) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A4) B5)) (@ (@ tptp.times_times_assn (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_assn (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_assn (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A4) B5) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o) (G (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat G))) (=> (@ tptp.finite_finite_o A4) (=> (@ tptp.finite_finite_o B5) (=> (= (@ (@ tptp.inf_inf_set_o A4) B5) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (= (@ (@ tptp.inf_inf_set_nat A4) B5) tptp.bot_bot_set_nat) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (= (@ (@ tptp.inf_inf_set_int A4) B5) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A4) B5) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.times_times_nat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_o) (G (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups3504817904513533571_o_nat G))) (=> (@ tptp.finite_finite_o A4) (=> (@ tptp.finite_finite_o B5) (=> (= (@ (@ tptp.inf_inf_set_o A4) B5) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A4) B5)) (@ (@ tptp.times_times_nat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B5) A4)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B5) A4)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B5) A4)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups342789780944988191at_rat G))) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ tptp.finite6177210948735845034at_nat B5) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A4) B5)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_int A4) B5))) (=> (@ 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 A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat F))) (let ((_let_2 (@ (@ tptp.sup_su848401254843788991nteger A4) B5))) (=> (@ tptp.finite6017078050557962740nteger _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B5) A4)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_int A4) B5))) (=> (@ 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 A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat F))) (let ((_let_2 (@ (@ tptp.sup_su848401254843788991nteger A4) B5))) (=> (@ tptp.finite6017078050557962740nteger _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B5) A4)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int F))) (let ((_let_2 (@ (@ tptp.sup_su848401254843788991nteger A4) B5))) (=> (@ tptp.finite6017078050557962740nteger _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B5) A4)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_nat A4) B5))) (=> (@ 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 A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_nat A4) B5))) (=> (@ 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 A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_nat A4) B5))) (=> (@ 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 A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_int A4) B5))) (=> (@ 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 A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 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 A4) B5))) (=> (@ tptp.finite6177210948735845034at_nat _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B5) A4)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B5) A4)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B5) A4)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B5) A4)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B5) A4)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat F))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (let ((_let_1 (@ tptp.groups977919841031483927at_nat F))) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ tptp.finite6177210948735845034at_nat B5) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A4) B5)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (F (-> tptp.produc4166570645942440679at_nat tptp.nat))) (let ((_let_1 (@ tptp.groups7059897769266147197at_nat F))) (=> (@ tptp.finite1918287321285529104at_nat A4) (=> (@ tptp.finite1918287321285529104at_nat B5) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (F (-> tptp.produc3843707927480180839at_nat tptp.nat))) (let ((_let_1 (@ tptp.groups3860910324918113789at_nat F))) (=> (@ tptp.finite4343798906461161616at_nat A4) (=> (@ tptp.finite4343798906461161616at_nat B5) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5)))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.rat)) (C2 (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ (@ tptp.groups6602215022474089585er_rat C2) (@ (@ tptp.minus_2355218937544613996nteger S) (@ (@ tptp.insert_Code_integer A) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_2 (@ (@ tptp.member_Code_integer A) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_2 (= (@ (@ tptp.groups6602215022474089585er_rat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups6602215022474089585er_rat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.nat)) (C2 (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ (@ tptp.groups7237345082560585321er_nat C2) (@ (@ tptp.minus_2355218937544613996nteger S) (@ (@ tptp.insert_Code_integer A) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_2 (@ (@ tptp.member_Code_integer A) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_2 (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.int)) (C2 (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ (@ tptp.groups7234854612051535045er_int C2) (@ (@ tptp.minus_2355218937544613996nteger S) (@ (@ tptp.insert_Code_integer A) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_2 (@ (@ tptp.member_Code_integer A) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_2 (= (@ (@ tptp.groups7234854612051535045er_int (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_int (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_int (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups7234854612051535045er_int (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_int (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.rat)) (C2 (-> Bool tptp.rat))) (let ((_let_1 (@ (@ tptp.groups7872700643590313910_o_rat C2) (@ (@ tptp.minus_minus_set_o S) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))) (let ((_let_2 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_2 (= (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.nat)) (C2 (-> Bool tptp.nat))) (let ((_let_1 (@ (@ tptp.groups8507830703676809646_o_nat C2) (@ (@ tptp.minus_minus_set_o S) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))) (let ((_let_2 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_2 (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.int)) (C2 (-> Bool tptp.int))) (let ((_let_1 (@ (@ tptp.groups8505340233167759370_o_int C2) (@ (@ tptp.minus_minus_set_o S) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))) (let ((_let_2 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_2 (= (@ (@ tptp.groups8505340233167759370_o_int (lambda ((K3 Bool)) (@ (@ (@ tptp.if_int (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_int (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups8505340233167759370_o_int (lambda ((K3 Bool)) (@ (@ (@ tptp.if_int (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat)) (C2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.groups2906978787729119204at_rat C2) (@ (@ tptp.minus_minus_set_nat S) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_2 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_2 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.int)) (C2 (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.groups3539618377306564664at_int C2) (@ (@ tptp.minus_minus_set_nat S) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_2 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_int (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_int (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_int (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat)) (C2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.groups3906332499630173760nt_rat C2) (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_2 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.nat)) (C2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.groups4541462559716669496nt_nat C2) (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_2 (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat)) (B tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_set_int A4))) (let ((_let_2 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.divide_divide_nat (@ _let_2 A4)) 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))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (B tptp.nat)) (let ((_let_1 (@ tptp.inf_in1364745209274528805nteger A4))) (let ((_let_2 (@ tptp.groups7237345082560585321er_nat F))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.divide_divide_nat (@ _let_2 A4)) 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))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int)) (B tptp.int)) (let ((_let_1 (@ tptp.inf_in1364745209274528805nteger A4))) (let ((_let_2 (@ tptp.groups7234854612051535045er_int F))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.divide_divide_int (@ _let_2 A4)) 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))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.int)) (B tptp.int)) (let ((_let_1 (@ tptp.inf_inf_set_nat A4))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.divide_divide_int (@ _let_2 A4)) 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))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.code_natural)) (B tptp.code_natural)) (let ((_let_1 (@ tptp.inf_inf_set_int A4))) (let ((_let_2 (@ tptp.groups6697149243333190288atural F))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.divide5121882707175180666atural (@ _let_2 A4)) 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))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_natural)) (B tptp.code_natural)) (let ((_let_1 (@ tptp.inf_in1364745209274528805nteger A4))) (let ((_let_2 (@ tptp.groups8926444216418632897atural F))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.divide5121882707175180666atural (@ _let_2 A4)) 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))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.code_natural)) (B tptp.code_natural)) (let ((_let_1 (@ tptp.inf_inf_set_nat A4))) (let ((_let_2 (@ tptp.groups6325495683096345652atural F))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.divide5121882707175180666atural (@ _let_2 A4)) 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))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A4))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.divide_divide_nat (@ _let_2 A4)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((A5 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ F A5)) B))) (@ _let_1 (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ F A5))))))) (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (not (@ (@ tptp.dvd_dvd_nat B) (@ F A5)))))))) B))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.int)) (B tptp.int)) (let ((_let_1 (@ tptp.inf_inf_set_int A4))) (let ((_let_2 (@ tptp.groups4538972089207619220nt_int F))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.divide_divide_int (@ _let_2 A4)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((A5 tptp.int)) (@ (@ tptp.divide_divide_int (@ F A5)) B))) (@ _let_1 (@ tptp.collect_int (lambda ((A5 tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ F A5))))))) (@ (@ tptp.divide_divide_int (@ _let_2 (@ _let_1 (@ tptp.collect_int (lambda ((A5 tptp.int)) (not (@ (@ tptp.dvd_dvd_int B) (@ F A5)))))))) B))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_list_nat) (F (-> tptp.list_nat tptp.nat)) (B tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_set_list_nat A4))) (let ((_let_2 (@ tptp.groups4396056296759096172at_nat F))) (=> (@ tptp.finite8100373058378681591st_nat A4) (= (@ (@ tptp.divide_divide_nat (@ _let_2 A4)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups4396056296759096172at_nat (lambda ((A5 tptp.list_nat)) (@ (@ tptp.divide_divide_nat (@ F A5)) B))) (@ _let_1 (@ tptp.collect_list_nat (lambda ((A5 tptp.list_nat)) (@ (@ tptp.dvd_dvd_nat B) (@ F A5))))))) (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 (@ tptp.collect_list_nat (lambda ((A5 tptp.list_nat)) (not (@ (@ tptp.dvd_dvd_nat B) (@ F A5)))))))) B))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.assn)) (C2 (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ (@ tptp.groups1304777262505850412r_assn C2) (@ (@ tptp.minus_2355218937544613996nteger S) (@ (@ tptp.insert_Code_integer A) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_2 (@ (@ tptp.member_Code_integer A) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_2 (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_assn (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.assn)) (C2 (-> Bool tptp.assn))) (let ((_let_1 (@ (@ tptp.groups5301882518646026715o_assn C2) (@ (@ tptp.minus_minus_set_o S) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))) (let ((_let_2 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_2 (= (@ (@ tptp.groups5301882518646026715o_assn (lambda ((K3 Bool)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_assn (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5301882518646026715o_assn (lambda ((K3 Bool)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.assn)) (C2 (-> tptp.nat tptp.assn))) (let ((_let_1 (@ (@ tptp.groups6906906614972039071t_assn C2) (@ (@ tptp.minus_minus_set_nat S) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_2 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_2 (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_assn (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.assn)) (C2 (-> tptp.int tptp.assn))) (let ((_let_1 (@ (@ tptp.groups7882442080178216443t_assn C2) (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_2 (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_assn (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.rat)) (C2 (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ (@ tptp.groups2555765274223993564er_rat C2) (@ (@ tptp.minus_2355218937544613996nteger S) (@ (@ tptp.insert_Code_integer A) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_2 (@ (@ tptp.member_Code_integer A) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_2 (= (@ (@ tptp.groups2555765274223993564er_rat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2555765274223993564er_rat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.rat)) (C2 (-> Bool tptp.rat))) (let ((_let_1 (@ (@ tptp.groups2869687844427037835_o_rat C2) (@ (@ tptp.minus_minus_set_o S) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))) (let ((_let_2 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_2 (= (@ (@ tptp.groups2869687844427037835_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2869687844427037835_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat)) (C2 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.groups73079841787564623at_rat C2) (@ (@ tptp.minus_minus_set_nat S) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_2 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_2 (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat)) (C2 (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.groups1072433553688619179nt_rat C2) (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_2 (= (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.nat)) (C2 (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ (@ tptp.groups3190895334310489300er_nat C2) (@ (@ tptp.minus_2355218937544613996nteger S) (@ (@ tptp.insert_Code_integer A) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_2 (@ (@ tptp.member_Code_integer A) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_2 (= (@ (@ tptp.groups3190895334310489300er_nat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups3190895334310489300er_nat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.nat)) (C2 (-> Bool tptp.nat))) (let ((_let_1 (@ (@ tptp.groups3504817904513533571_o_nat C2) (@ (@ tptp.minus_minus_set_o S) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))) (let ((_let_2 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_2 (= (@ (@ tptp.groups3504817904513533571_o_nat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) (@ (@ tptp.times_times_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups3504817904513533571_o_nat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) (@ C2 K3)))) S) _let_1))))))))
% 8.20/8.65 (assert (forall ((A tptp.array_nat) (H5 tptp.heap_e7401611519738050253t_unit) (Xs tptp.list_nat) (H tptp.heap_e7401611519738050253t_unit)) (=> (= (@ (@ tptp.produc1210945592254923927t_unit A) H5) (@ (@ tptp.array_alloc_nat Xs) H)) (@ (@ (@ (@ (@ tptp.heap_T1188250621483087889ay_nat (@ tptp.array_of_list_nat Xs)) H) H5) A) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.size_size_list_nat Xs))))))
% 8.20/8.65 (assert (forall ((A tptp.array_o) (H5 tptp.heap_e7401611519738050253t_unit) (Xs tptp.list_o) (H tptp.heap_e7401611519738050253t_unit)) (=> (= (@ (@ tptp.produc3742984184817956739t_unit A) H5) (@ (@ tptp.array_alloc_o Xs) H)) (@ (@ (@ (@ (@ tptp.heap_T1873992626244518189rray_o (@ tptp.array_of_list_o Xs)) H) H5) A) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.size_size_list_o Xs))))))
% 8.20/8.65 (assert (forall ((A tptp.array_int) (H5 tptp.heap_e7401611519738050253t_unit) (Xs tptp.list_int) (H tptp.heap_e7401611519738050253t_unit)) (=> (= (@ (@ tptp.produc2888458824036673339t_unit A) H5) (@ (@ tptp.array_alloc_int Xs) H)) (@ (@ (@ (@ (@ tptp.heap_T6233771638828666989ay_int (@ tptp.array_of_list_int Xs)) H) H5) A) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.size_size_list_int Xs))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (B Bool) (F (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups4406642042086082107nteger F))) (=> (@ tptp.finite_finite_o B5) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o B5) A4)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ F B)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) B5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger F))) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B5) A4)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ F B)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) B5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (B tptp.code_integer) (F (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger F))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (=> (@ (@ tptp.member_Code_integer B) (@ (@ tptp.minus_2355218937544613996nteger B5) A4)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ F B)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) B5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (B Bool) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat F))) (=> (@ tptp.finite_finite_o B5) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o B5) A4)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) B5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B5) A4)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) B5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (B tptp.code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat F))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (=> (@ (@ tptp.member_Code_integer B) (@ (@ tptp.minus_2355218937544613996nteger B5) A4)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) B5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (B Bool) (F (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups8507830703676809646_o_nat F))) (=> (@ tptp.finite_finite_o B5) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o B5) A4)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) B5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (B tptp.code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat F))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (=> (@ (@ tptp.member_Code_integer B) (@ (@ tptp.minus_2355218937544613996nteger B5) A4)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) B5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (B Bool) (F (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups8505340233167759370_o_int F))) (=> (@ tptp.finite_finite_o B5) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o B5) A4)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) B5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B5) A4)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) B5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int (@ _let_1 A4)) (@ _let_1 B5))))))))))
% 8.20/8.65 (assert (forall ((I2 tptp.code_integer) (A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ (@ tptp.member_Code_integer I2) A4) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger A4) (@ (@ tptp.insert_Code_integer I2) tptp.bot_bo3990330152332043303nteger))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (=> (@ tptp.finite6017078050557962740nteger A4) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) (@ (@ tptp.groups879477027807139574nteger F) A4)))))))
% 8.20/8.65 (assert (forall ((I2 Bool) (A4 tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (@ (@ tptp.member_o I2) A4) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o A4) (@ (@ tptp.insert_o I2) tptp.bot_bot_set_o))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (=> (@ tptp.finite_finite_o A4) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) (@ (@ tptp.groups4406642042086082107nteger F) A4)))))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (A4 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (@ (@ tptp.member_nat I2) A4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat I2) tptp.bot_bot_set_nat))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) (@ (@ tptp.groups7501900531339628137nteger F) A4)))))))
% 8.20/8.65 (assert (forall ((I2 tptp.int) (A4 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (@ (@ tptp.member_int I2) A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (=> (@ tptp.finite_finite_int A4) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) (@ (@ tptp.groups7873554091576472773nteger F) A4)))))))
% 8.20/8.65 (assert (forall ((I2 tptp.code_integer) (A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (=> (@ (@ tptp.member_Code_integer I2) A4) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger A4) (@ (@ tptp.insert_Code_integer I2) tptp.bot_bo3990330152332043303nteger))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite6017078050557962740nteger A4) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ (@ tptp.groups6602215022474089585er_rat F) A4)))))))
% 8.20/8.65 (assert (forall ((I2 Bool) (A4 tptp.set_o) (F (-> Bool tptp.rat))) (=> (@ (@ tptp.member_o I2) A4) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o A4) (@ (@ tptp.insert_o I2) tptp.bot_bot_set_o))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite_finite_o A4) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ (@ tptp.groups7872700643590313910_o_rat F) A4)))))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (A4 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.member_nat I2) A4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat I2) tptp.bot_bot_set_nat))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ (@ tptp.groups2906978787729119204at_rat F) A4)))))))
% 8.20/8.65 (assert (forall ((I2 tptp.int) (A4 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ (@ tptp.member_int I2) A4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite_finite_int A4) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ (@ tptp.groups3906332499630173760nt_rat F) A4)))))))
% 8.20/8.65 (assert (forall ((I2 tptp.code_integer) (A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ (@ tptp.member_Code_integer I2) A4) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger A4) (@ (@ tptp.insert_Code_integer I2) tptp.bot_bo3990330152332043303nteger))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (=> (@ tptp.finite6017078050557962740nteger A4) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ (@ tptp.groups7237345082560585321er_nat F) A4)))))))
% 8.20/8.65 (assert (forall ((I2 Bool) (A4 tptp.set_o) (F (-> Bool tptp.nat))) (=> (@ (@ tptp.member_o I2) A4) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o A4) (@ (@ tptp.insert_o I2) tptp.bot_bot_set_o))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (=> (@ tptp.finite_finite_o A4) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ (@ tptp.groups8507830703676809646_o_nat F) A4)))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (F (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups7694694392188491536nteger F))) (=> (@ tptp.finite_finite_o B5) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o B5) A4)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F B3)))) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F A3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger F))) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat B5) A4)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F B3)))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F A3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger F))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger B5) A4)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F B3)))) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F A3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat F))) (=> (@ tptp.finite_finite_o B5) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B3)))) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat F))) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B3)))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat F))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B3)))) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (F (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups3502327434004483295_o_int F))) (=> (@ tptp.finite_finite_o B5) (=> (@ (@ tptp.ord_less_eq_set_o A4) B5) (=> (forall ((B3 Bool)) (=> (@ (@ tptp.member_o B3) (@ (@ tptp.minus_minus_set_o B5) A4)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B3)))) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int F))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (=> (forall ((B3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B3) (@ (@ tptp.minus_2355218937544613996nteger B5) A4)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B3)))) (=> (forall ((A3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A3) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A3)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger F))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A4)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F B3)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F A3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F))) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B5) A4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B3)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A3)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B5)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F))) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A4) B5)) (not (= (@ F X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A4) B5)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A4) B5))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat F))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A4) B5)) (not (= (@ F X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A4) B5)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A4) B5))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups3442636767675653108at_rat F))) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5)) (not (= (@ F X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A4) B5)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A4) B5))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat) (F (-> tptp.produc4166570645942440679at_nat tptp.rat))) (let ((_let_1 (@ tptp.groups5938585286922990810at_rat F))) (=> (@ tptp.finite1918287321285529104at_nat A4) (=> (@ tptp.finite1918287321285529104at_nat B5) (=> (forall ((X3 tptp.produc4166570645942440679at_nat)) (=> (@ (@ tptp.member6689249552917799696at_nat X3) (@ (@ tptp.inf_in1697001100524423349at_nat A4) B5)) (not (= (@ F X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat A4) B5))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat) (F (-> tptp.produc3843707927480180839at_nat tptp.rat))) (let ((_let_1 (@ tptp.groups8874911130973611098at_rat F))) (=> (@ tptp.finite4343798906461161616at_nat A4) (=> (@ tptp.finite4343798906461161616at_nat B5) (=> (forall ((X3 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X3) (@ (@ tptp.inf_in7913087082777306421at_nat A4) B5)) (not (= (@ F X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A4) B5))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat F))) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A4) B5)) (not (= (@ F X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A4) B5)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A4)) (@ _let_1 B5))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A4) B5))))))))))
% 8.20/8.65 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.bit_se9127793120404214118atural A) tptp.one_one_Code_natural) (@ (@ tptp.plus_p4538020629002901425atural A) (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A))))))
% 8.20/8.65 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger A) tptp.one_one_Code_integer) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))))
% 8.20/8.65 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) tptp.one_one_int) (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))))
% 8.20/8.65 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))))
% 8.20/8.65 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.bit_se9127793120404214118atural tptp.one_one_Code_natural) A) (@ (@ tptp.plus_p4538020629002901425atural A) (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A))))))
% 8.20/8.65 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger tptp.one_one_Code_integer) A) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))))
% 8.20/8.65 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) A) (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))))
% 8.20/8.65 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) A) (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 8.20/8.65 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N tptp.nat) (A5 tptp.code_integer)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ tptp.bit_se7788150548672797655nteger K3) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.bit_se9216721137139052372nteger A5) K3))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 8.20/8.65 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (A5 tptp.int)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.bit_se545348938243370406it_int K3) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int A5) K3))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 8.20/8.65 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (A5 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.bit_se547839408752420682it_nat K3) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.bit_se1148574629649215175it_nat A5) K3))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 8.20/8.65 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 8.20/8.65 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 8.20/8.65 (assert (= tptp.array_of_list_nat (lambda ((Xs3 tptp.list_nat)) (@ tptp.heap_T4325564685996367510ay_nat (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc8657510640128716596it_nat (lambda ((R5 tptp.array_nat) (H7 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc4907525368653469954it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.size_size_list_nat Xs3)))))) (@ (@ tptp.array_alloc_nat Xs3) H6)))))))
% 8.20/8.65 (assert (= tptp.array_of_list_o (lambda ((Xs3 tptp.list_o)) (@ tptp.heap_T8367841184088661864rray_o (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc5512802776183222702it_nat (lambda ((R5 tptp.array_o) (H7 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc2890842502232952598it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.size_size_list_o Xs3)))))) (@ (@ tptp.array_alloc_o Xs3) H6)))))))
% 8.20/8.65 (assert (= tptp.array_of_list_int (lambda ((Xs3 tptp.list_int)) (@ tptp.heap_T147713666487170802ay_int (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc3016605123915955252it_nat (lambda ((R5 tptp.array_int) (H7 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc5351973125643376990it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.size_size_list_int Xs3)))))) (@ (@ tptp.array_alloc_int Xs3) H6)))))))
% 8.20/8.65 (assert (forall ((K2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) K2))))))
% 8.20/8.65 (assert (forall ((K2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) K2))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr958786334691620121nt_int)) (=> (@ tptp.finite2998713641127702882nt_int A4) (@ tptp.finite8744585540193469122nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((B6 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.ord_le2843351958646193337nt_int B6) A4)))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((B6 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B6) A4)))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A4) (@ tptp.finite6931041176100689706nteger (@ tptp.collec574505750873337192nteger (lambda ((B6 tptp.set_Code_integer)) (@ (@ tptp.ord_le7084787975880047091nteger B6) A4)))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A4) (@ tptp.finite9047747110432174090at_nat (@ tptp.collec5514110066124741708at_nat (lambda ((B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat B6) A4)))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (@ tptp.finite6197958912794628473et_int (@ tptp.collect_set_int (lambda ((B6 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B6) A4)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (P2 (-> tptp.set_Pr4329608150637261639at_nat Bool))) (=> (@ tptp.finite4343798906461161616at_nat S) (=> (@ P2 tptp.bot_bo228742789529271731at_nat) (=> (forall ((T8 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le2604355607129572851at_nat T8) S) (=> (@ P2 T8) (exists ((X6 tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X6) (@ (@ tptp.minus_3314409938677909166at_nat S) T8)) (@ P2 (@ (@ tptp.insert9069300056098147895at_nat X6) T8))))))) (@ P2 S))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Code_integer) (P2 (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ P2 tptp.bot_bo3990330152332043303nteger) (=> (forall ((T8 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le1307284697595431911nteger T8) S) (=> (@ P2 T8) (exists ((X6 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X6) (@ (@ tptp.minus_2355218937544613996nteger S) T8)) (@ P2 (@ (@ tptp.insert_Code_integer X6) T8))))))) (@ P2 S))))))
% 8.20/8.65 (assert (forall ((S tptp.set_o) (P2 (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o S) (=> (@ P2 tptp.bot_bot_set_o) (=> (forall ((T8 tptp.set_o)) (=> (@ (@ tptp.ord_less_set_o T8) S) (=> (@ P2 T8) (exists ((X6 Bool)) (and (@ (@ tptp.member_o X6) (@ (@ tptp.minus_minus_set_o S) T8)) (@ P2 (@ (@ tptp.insert_o X6) T8))))))) (@ P2 S))))))
% 8.20/8.65 (assert (forall ((S tptp.set_nat) (P2 (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat S) (=> (@ P2 tptp.bot_bot_set_nat) (=> (forall ((T8 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat T8) S) (=> (@ P2 T8) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) (@ (@ tptp.minus_minus_set_nat S) T8)) (@ P2 (@ (@ tptp.insert_nat X6) T8))))))) (@ P2 S))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (P2 (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int S) (=> (@ P2 tptp.bot_bot_set_int) (=> (forall ((T8 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int T8) S) (=> (@ P2 T8) (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) (@ (@ tptp.minus_minus_set_int S) T8)) (@ P2 (@ (@ tptp.insert_int X6) T8))))))) (@ P2 S))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (P2 (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat S) (=> (@ P2 tptp.bot_bo2099793752762293965at_nat) (=> (forall ((T8 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat T8) S) (=> (@ P2 T8) (exists ((X6 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X6) (@ (@ tptp.minus_1356011639430497352at_nat S) T8)) (@ P2 (@ (@ tptp.insert8211810215607154385at_nat X6) T8))))))) (@ P2 S))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_int) (G4 tptp.set_int)) (= (@ tptp.finite_finite_int (@ (@ tptp.sup_sup_set_int F5) G4)) (and (@ tptp.finite_finite_int F5) (@ tptp.finite_finite_int G4)))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Code_integer) (G4 tptp.set_Code_integer)) (= (@ tptp.finite6017078050557962740nteger (@ (@ tptp.sup_su848401254843788991nteger F5) G4)) (and (@ tptp.finite6017078050557962740nteger F5) (@ tptp.finite6017078050557962740nteger G4)))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Pr1261947904930325089at_nat) (G4 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.sup_su6327502436637775413at_nat F5) G4)) (and (@ tptp.finite6177210948735845034at_nat F5) (@ tptp.finite6177210948735845034at_nat G4)))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Pr8551490117392284871at_nat) (G4 tptp.set_Pr8551490117392284871at_nat)) (= (@ tptp.finite1918287321285529104at_nat (@ (@ tptp.sup_su3035147773818789531at_nat F5) G4)) (and (@ tptp.finite1918287321285529104at_nat F5) (@ tptp.finite1918287321285529104at_nat G4)))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Pr4329608150637261639at_nat) (G4 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.finite4343798906461161616at_nat (@ (@ tptp.sup_su5525570899277871387at_nat F5) G4)) (and (@ tptp.finite4343798906461161616at_nat F5) (@ tptp.finite4343798906461161616at_nat G4)))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_nat) (G4 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.sup_sup_set_nat F5) G4)) (and (@ tptp.finite_finite_nat F5) (@ tptp.finite_finite_nat G4)))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.list_nat Bool)) (Q2 (-> tptp.list_nat Bool))) (=> (or (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat P2)) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat Q2))) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ P2 X4) (@ Q2 X4))))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.set_Pr958786334691620121nt_int Bool)) (Q2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (=> (or (@ tptp.finite8744585540193469122nt_int (@ tptp.collec5210948495886036740nt_int P2)) (@ tptp.finite8744585540193469122nt_int (@ tptp.collec5210948495886036740nt_int Q2))) (@ tptp.finite8744585540193469122nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (and (@ P2 X4) (@ Q2 X4))))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.set_nat Bool)) (Q2 (-> tptp.set_nat Bool))) (=> (or (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P2)) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat Q2))) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ P2 X4) (@ Q2 X4))))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P2)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q2))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ P2 X4) (@ Q2 X4))))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (or (@ tptp.finite_finite_int (@ tptp.collect_int P2)) (@ tptp.finite_finite_int (@ tptp.collect_int Q2))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ P2 X4) (@ Q2 X4))))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.code_integer Bool)) (Q2 (-> tptp.code_integer Bool))) (=> (or (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer P2)) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer Q2))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ P2 X4) (@ Q2 X4))))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.product_prod_nat_nat Bool)) (Q2 (-> tptp.product_prod_nat_nat Bool))) (=> (or (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat P2)) (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat Q2))) (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (and (@ P2 X4) (@ Q2 X4))))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.list_nat Bool)) (Q2 (-> tptp.list_nat Bool))) (= (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (or (@ P2 X4) (@ Q2 X4))))) (and (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat P2)) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat Q2))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.set_Pr958786334691620121nt_int Bool)) (Q2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (= (@ tptp.finite8744585540193469122nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (or (@ P2 X4) (@ Q2 X4))))) (and (@ tptp.finite8744585540193469122nt_int (@ tptp.collec5210948495886036740nt_int P2)) (@ tptp.finite8744585540193469122nt_int (@ tptp.collec5210948495886036740nt_int Q2))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.set_nat Bool)) (Q2 (-> tptp.set_nat Bool))) (= (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (or (@ P2 X4) (@ Q2 X4))))) (and (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P2)) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat Q2))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (or (@ P2 X4) (@ Q2 X4))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P2)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q2))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (= (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (or (@ P2 X4) (@ Q2 X4))))) (and (@ tptp.finite_finite_int (@ tptp.collect_int P2)) (@ tptp.finite_finite_int (@ tptp.collect_int Q2))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.code_integer Bool)) (Q2 (-> tptp.code_integer Bool))) (= (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (or (@ P2 X4) (@ Q2 X4))))) (and (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer P2)) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer Q2))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.product_prod_nat_nat Bool)) (Q2 (-> tptp.product_prod_nat_nat Bool))) (= (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (or (@ P2 X4) (@ Q2 X4))))) (and (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat P2)) (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat Q2))))))
% 8.20/8.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I) (@ (@ tptp.ord_less_eq_int I) B)))))))
% 8.20/8.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.ord_less_int A) I) (@ (@ tptp.ord_less_int I) B)))))))
% 8.20/8.65 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or8404916559141939852nteger L) U))))
% 8.20/8.65 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or189985376899183464nteger L) U))))
% 8.20/8.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I) (@ (@ tptp.ord_less_int I) B)))))))
% 8.20/8.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.ord_less_int A) I) (@ (@ tptp.ord_less_eq_int I) B)))))))
% 8.20/8.65 (assert (forall ((M6 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M6) (exists ((N5 tptp.nat)) (forall ((X6 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X6) M6) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X6)) N5)))))))
% 8.20/8.65 (assert (forall ((M6 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M6) (exists ((N5 tptp.nat)) (forall ((X6 tptp.list_o)) (=> (@ (@ tptp.member_list_o X6) M6) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X6)) N5)))))))
% 8.20/8.65 (assert (forall ((M6 tptp.set_list_int)) (=> (@ tptp.finite3922522038869484883st_int M6) (exists ((N5 tptp.nat)) (forall ((X6 tptp.list_int)) (=> (@ (@ tptp.member_list_int X6) M6) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int X6)) N5)))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (assert (forall ((U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger) U))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.list_nat Bool))) (=> (not (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat P2))) (exists ((X_1 tptp.list_nat)) (@ P2 X_1)))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (=> (not (@ tptp.finite8744585540193469122nt_int (@ tptp.collec5210948495886036740nt_int P2))) (exists ((X_1 tptp.set_Pr958786334691620121nt_int)) (@ P2 X_1)))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.set_nat Bool))) (=> (not (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P2))) (exists ((X_1 tptp.set_nat)) (@ P2 X_1)))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat (@ tptp.collect_nat P2))) (exists ((X_1 tptp.nat)) (@ P2 X_1)))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int (@ tptp.collect_int P2))) (exists ((X_1 tptp.int)) (@ P2 X_1)))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.code_integer Bool))) (=> (not (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer P2))) (exists ((X_1 tptp.code_integer)) (@ P2 X_1)))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.product_prod_nat_nat Bool))) (=> (not (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat P2))) (exists ((X_1 tptp.product_prod_nat_nat)) (@ P2 X_1)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_nat) (R3 (-> Bool tptp.nat Bool))) (=> (not (@ tptp.finite_finite_o A4)) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (exists ((Xa3 tptp.nat)) (and (@ (@ tptp.member_nat Xa3) B5) (@ (@ R3 X3) Xa3))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B5) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A5 Bool)) (and (@ (@ tptp.member_o A5) A4) (@ (@ R3 A5) X3)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_int) (R3 (-> Bool tptp.int Bool))) (=> (not (@ tptp.finite_finite_o A4)) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (exists ((Xa3 tptp.int)) (and (@ (@ tptp.member_int Xa3) B5) (@ (@ R3 X3) Xa3))))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) B5) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A5 Bool)) (and (@ (@ tptp.member_o A5) A4) (@ (@ R3 A5) X3)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (B5 tptp.set_Code_integer) (R3 (-> Bool tptp.code_integer Bool))) (=> (not (@ tptp.finite_finite_o A4)) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A4) (exists ((Xa3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa3) B5) (@ (@ R3 X3) Xa3))))) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) B5) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A5 Bool)) (and (@ (@ tptp.member_o A5) A4) (@ (@ R3 A5) X3)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat) (R3 (-> tptp.nat tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A4)) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (exists ((Xa3 tptp.nat)) (and (@ (@ tptp.member_nat Xa3) B5) (@ (@ R3 X3) Xa3))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B5) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.member_nat A5) A4) (@ (@ R3 A5) X3)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_int) (R3 (-> tptp.nat tptp.int Bool))) (=> (not (@ tptp.finite_finite_nat A4)) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (exists ((Xa3 tptp.int)) (and (@ (@ tptp.member_int Xa3) B5) (@ (@ R3 X3) Xa3))))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) B5) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.member_nat A5) A4) (@ (@ R3 A5) X3)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_Code_integer) (R3 (-> tptp.nat tptp.code_integer Bool))) (=> (not (@ tptp.finite_finite_nat A4)) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A4) (exists ((Xa3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa3) B5) (@ (@ R3 X3) Xa3))))) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) B5) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.member_nat A5) A4) (@ (@ R3 A5) X3)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_nat) (R3 (-> tptp.int tptp.nat Bool))) (=> (not (@ tptp.finite_finite_int A4)) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (exists ((Xa3 tptp.nat)) (and (@ (@ tptp.member_nat Xa3) B5) (@ (@ R3 X3) Xa3))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B5) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A5 tptp.int)) (and (@ (@ tptp.member_int A5) A4) (@ (@ R3 A5) X3)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int) (R3 (-> tptp.int tptp.int Bool))) (=> (not (@ tptp.finite_finite_int A4)) (=> (@ tptp.finite_finite_int B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (exists ((Xa3 tptp.int)) (and (@ (@ tptp.member_int Xa3) B5) (@ (@ R3 X3) Xa3))))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) B5) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A5 tptp.int)) (and (@ (@ tptp.member_int A5) A4) (@ (@ R3 A5) X3)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_Code_integer) (R3 (-> tptp.int tptp.code_integer Bool))) (=> (not (@ tptp.finite_finite_int A4)) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A4) (exists ((Xa3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa3) B5) (@ (@ R3 X3) Xa3))))) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) B5) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A5 tptp.int)) (and (@ (@ tptp.member_int A5) A4) (@ (@ R3 A5) X3)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_nat) (R3 (-> tptp.code_integer tptp.nat Bool))) (=> (not (@ tptp.finite6017078050557962740nteger A4)) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A4) (exists ((Xa3 tptp.nat)) (and (@ (@ tptp.member_nat Xa3) B5) (@ (@ R3 X3) Xa3))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B5) (not (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((A5 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer A5) A4) (@ (@ R3 A5) X3)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (A Bool)) (=> (@ tptp.finite_finite_o A4) (=> (@ (@ tptp.member_o A) A4) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) A4) (@ (@ tptp.ord_less_eq_o X3) A) (forall ((Xa3 Bool)) (=> (@ (@ tptp.member_o Xa3) A4) (=> (@ (@ tptp.ord_less_eq_o Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (A tptp.set_Pr958786334691620121nt_int)) (=> (@ tptp.finite8744585540193469122nt_int A4) (=> (@ (@ tptp.member2340774599025711042nt_int A) A4) (exists ((X3 tptp.set_Pr958786334691620121nt_int)) (and (@ (@ tptp.member2340774599025711042nt_int X3) A4) (@ (@ tptp.ord_le2843351958646193337nt_int X3) A) (forall ((Xa3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int Xa3) A4) (=> (@ (@ tptp.ord_le2843351958646193337nt_int Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ (@ tptp.member_set_nat A) A4) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A4) (@ (@ tptp.ord_less_eq_set_nat X3) A) (forall ((Xa3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa3) A4) (=> (@ (@ tptp.ord_less_eq_set_nat Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (A tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ (@ tptp.member_Code_integer A) A4) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger X3) A) (forall ((Xa3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Xa3) A4) (=> (@ (@ tptp.ord_le3102999989581377725nteger Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A4) (=> (@ (@ tptp.member_set_int A) A4) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A4) (@ (@ tptp.ord_less_eq_set_int X3) A) (forall ((Xa3 tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa3) A4) (=> (@ (@ tptp.ord_less_eq_set_int Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A4) (=> (@ (@ tptp.member_rat A) A4) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A4) (@ (@ tptp.ord_less_eq_rat X3) A) (forall ((Xa3 tptp.rat)) (=> (@ (@ tptp.member_rat Xa3) A4) (=> (@ (@ tptp.ord_less_eq_rat Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A4) (=> (@ (@ tptp.member_num A) A4) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A4) (@ (@ tptp.ord_less_eq_num X3) A) (forall ((Xa3 tptp.num)) (=> (@ (@ tptp.member_num Xa3) A4) (=> (@ (@ tptp.ord_less_eq_num Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat A) A4) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat X3) A) (forall ((Xa3 tptp.nat)) (=> (@ (@ tptp.member_nat Xa3) A4) (=> (@ (@ tptp.ord_less_eq_nat Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int A) A4) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_int X3) A) (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) A4) (=> (@ (@ tptp.ord_less_eq_int Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (A Bool)) (=> (@ tptp.finite_finite_o A4) (=> (@ (@ tptp.member_o A) A4) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) A4) (@ (@ tptp.ord_less_eq_o A) X3) (forall ((Xa3 Bool)) (=> (@ (@ tptp.member_o Xa3) A4) (=> (@ (@ tptp.ord_less_eq_o X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_se6260736226359567993nt_int) (A tptp.set_Pr958786334691620121nt_int)) (=> (@ tptp.finite8744585540193469122nt_int A4) (=> (@ (@ tptp.member2340774599025711042nt_int A) A4) (exists ((X3 tptp.set_Pr958786334691620121nt_int)) (and (@ (@ tptp.member2340774599025711042nt_int X3) A4) (@ (@ tptp.ord_le2843351958646193337nt_int A) X3) (forall ((Xa3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int Xa3) A4) (=> (@ (@ tptp.ord_le2843351958646193337nt_int X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ (@ tptp.member_set_nat A) A4) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A4) (@ (@ tptp.ord_less_eq_set_nat A) X3) (forall ((Xa3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa3) A4) (=> (@ (@ tptp.ord_less_eq_set_nat X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (A tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ (@ tptp.member_Code_integer A) A4) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A4) (@ (@ tptp.ord_le3102999989581377725nteger A) X3) (forall ((Xa3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Xa3) A4) (=> (@ (@ tptp.ord_le3102999989581377725nteger X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A4) (=> (@ (@ tptp.member_set_int A) A4) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A4) (@ (@ tptp.ord_less_eq_set_int A) X3) (forall ((Xa3 tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa3) A4) (=> (@ (@ tptp.ord_less_eq_set_int X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A4) (=> (@ (@ tptp.member_rat A) A4) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A4) (@ (@ tptp.ord_less_eq_rat A) X3) (forall ((Xa3 tptp.rat)) (=> (@ (@ tptp.member_rat Xa3) A4) (=> (@ (@ tptp.ord_less_eq_rat X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A4) (=> (@ (@ tptp.member_num A) A4) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A4) (@ (@ tptp.ord_less_eq_num A) X3) (forall ((Xa3 tptp.num)) (=> (@ (@ tptp.member_num Xa3) A4) (=> (@ (@ tptp.ord_less_eq_num X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat A) A4) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_eq_nat A) X3) (forall ((Xa3 tptp.nat)) (=> (@ (@ tptp.member_nat Xa3) A4) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int A) A4) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_eq_int A) X3) (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) A4) (=> (@ (@ tptp.ord_less_eq_int X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (@ tptp.finite_finite_nat A4)))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (@ tptp.finite6017078050557962740nteger A4)))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5) (@ tptp.finite6177210948735845034at_nat A4)))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int)) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (@ tptp.finite_finite_int A4)))))
% 8.20/8.65 (assert (forall ((S tptp.set_nat) (T7 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat T7))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Code_integer) (T7 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T7) (=> (not (@ tptp.finite6017078050557962740nteger S)) (not (@ tptp.finite6017078050557962740nteger T7))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) T7) (=> (not (@ tptp.finite6177210948735845034at_nat S)) (not (@ tptp.finite6177210948735845034at_nat T7))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int T7))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (@ tptp.finite_finite_nat B5) (@ tptp.finite_finite_nat A4)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (=> (@ tptp.finite6017078050557962740nteger B5) (@ tptp.finite6017078050557962740nteger A4)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5) (=> (@ tptp.finite6177210948735845034at_nat B5) (@ tptp.finite6177210948735845034at_nat A4)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (@ tptp.finite_finite_int B5) (@ tptp.finite_finite_int A4)))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_int) (G4 tptp.set_int)) (=> (@ tptp.finite_finite_int F5) (=> (@ tptp.finite_finite_int G4) (@ tptp.finite_finite_int (@ (@ tptp.sup_sup_set_int F5) G4))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Code_integer) (G4 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger F5) (=> (@ tptp.finite6017078050557962740nteger G4) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.sup_su848401254843788991nteger F5) G4))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Pr1261947904930325089at_nat) (G4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat F5) (=> (@ tptp.finite6177210948735845034at_nat G4) (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.sup_su6327502436637775413at_nat F5) G4))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Pr8551490117392284871at_nat) (G4 tptp.set_Pr8551490117392284871at_nat)) (=> (@ tptp.finite1918287321285529104at_nat F5) (=> (@ tptp.finite1918287321285529104at_nat G4) (@ tptp.finite1918287321285529104at_nat (@ (@ tptp.sup_su3035147773818789531at_nat F5) G4))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Pr4329608150637261639at_nat) (G4 tptp.set_Pr4329608150637261639at_nat)) (=> (@ tptp.finite4343798906461161616at_nat F5) (=> (@ tptp.finite4343798906461161616at_nat G4) (@ tptp.finite4343798906461161616at_nat (@ (@ tptp.sup_su5525570899277871387at_nat F5) G4))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_nat) (G4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F5) (=> (@ tptp.finite_finite_nat G4) (@ tptp.finite_finite_nat (@ (@ tptp.sup_sup_set_nat F5) G4))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int)) (=> (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int (@ (@ tptp.sup_sup_set_int S) T7))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Code_integer) (T7 tptp.set_Code_integer)) (=> (not (@ tptp.finite6017078050557962740nteger S)) (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.sup_su848401254843788991nteger S) T7))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ tptp.finite6177210948735845034at_nat S)) (not (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T7))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T7 tptp.set_Pr8551490117392284871at_nat)) (=> (not (@ tptp.finite1918287321285529104at_nat S)) (not (@ tptp.finite1918287321285529104at_nat (@ (@ tptp.sup_su3035147773818789531at_nat S) T7))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T7 tptp.set_Pr4329608150637261639at_nat)) (=> (not (@ tptp.finite4343798906461161616at_nat S)) (not (@ tptp.finite4343798906461161616at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T7))))))
% 8.20/8.65 (assert (forall ((S tptp.set_nat) (T7 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat (@ (@ tptp.sup_sup_set_nat S) T7))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int)) (= (not (@ tptp.finite_finite_int (@ (@ tptp.sup_sup_set_int S) T7))) (or (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int T7))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Code_integer) (T7 tptp.set_Code_integer)) (= (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.sup_su848401254843788991nteger S) T7))) (or (not (@ tptp.finite6017078050557962740nteger S)) (not (@ tptp.finite6017078050557962740nteger T7))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat)) (= (not (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T7))) (or (not (@ tptp.finite6177210948735845034at_nat S)) (not (@ tptp.finite6177210948735845034at_nat T7))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T7 tptp.set_Pr8551490117392284871at_nat)) (= (not (@ tptp.finite1918287321285529104at_nat (@ (@ tptp.sup_su3035147773818789531at_nat S) T7))) (or (not (@ tptp.finite1918287321285529104at_nat S)) (not (@ tptp.finite1918287321285529104at_nat T7))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T7 tptp.set_Pr4329608150637261639at_nat)) (= (not (@ tptp.finite4343798906461161616at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T7))) (or (not (@ tptp.finite4343798906461161616at_nat S)) (not (@ tptp.finite4343798906461161616at_nat T7))))))
% 8.20/8.65 (assert (forall ((S tptp.set_nat) (T7 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat (@ (@ tptp.sup_sup_set_nat S) T7))) (or (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat T7))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((A9 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A9) (=> (forall ((B10 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B10) A9) (@ P2 B10))) (@ P2 A9)))) (@ P2 A4)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((A9 tptp.set_int)) (=> (@ tptp.finite_finite_int A9) (=> (forall ((B10 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B10) A9) (@ P2 B10))) (@ P2 A9)))) (@ P2 A4)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (forall ((A9 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A9) (=> (forall ((B10 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le1307284697595431911nteger B10) A9) (@ P2 B10))) (@ P2 A9)))) (@ P2 A4)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (P2 (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (forall ((A9 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A9) (=> (forall ((B10 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B10) A9) (@ P2 B10))) (@ P2 A9)))) (@ P2 A4)))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 8.20/8.65 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M3)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (not (= A4 tptp.bot_bo3990330152332043303nteger)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A4) (forall ((Xa3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Xa3) A4) (=> (@ (@ tptp.ord_le3102999989581377725nteger X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o)) (=> (@ tptp.finite_finite_o A4) (=> (not (= A4 tptp.bot_bot_set_o)) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) A4) (forall ((Xa3 Bool)) (=> (@ (@ tptp.member_o Xa3) A4) (=> (@ (@ tptp.ord_less_eq_o X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A4) (=> (not (= A4 tptp.bot_bot_set_set_int)) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A4) (forall ((Xa3 tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa3) A4) (=> (@ (@ tptp.ord_less_eq_set_int X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A4) (=> (not (= A4 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A4) (forall ((Xa3 tptp.rat)) (=> (@ (@ tptp.member_rat Xa3) A4) (=> (@ (@ tptp.ord_less_eq_rat X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_num)) (=> (@ tptp.finite_finite_num A4) (=> (not (= A4 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A4) (forall ((Xa3 tptp.num)) (=> (@ (@ tptp.member_num Xa3) A4) (=> (@ (@ tptp.ord_less_eq_num X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (forall ((Xa3 tptp.nat)) (=> (@ (@ tptp.member_nat Xa3) A4) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) A4) (=> (@ (@ tptp.ord_less_eq_int X3) Xa3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (not (= A4 tptp.bot_bo3990330152332043303nteger)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A4) (forall ((Xa3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Xa3) A4) (=> (@ (@ tptp.ord_le3102999989581377725nteger Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o)) (=> (@ tptp.finite_finite_o A4) (=> (not (= A4 tptp.bot_bot_set_o)) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) A4) (forall ((Xa3 Bool)) (=> (@ (@ tptp.member_o Xa3) A4) (=> (@ (@ tptp.ord_less_eq_o Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A4) (=> (not (= A4 tptp.bot_bot_set_set_int)) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A4) (forall ((Xa3 tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa3) A4) (=> (@ (@ tptp.ord_less_eq_set_int Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A4) (=> (not (= A4 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A4) (forall ((Xa3 tptp.rat)) (=> (@ (@ tptp.member_rat Xa3) A4) (=> (@ (@ tptp.ord_less_eq_rat Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_num)) (=> (@ tptp.finite_finite_num A4) (=> (not (= A4 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A4) (forall ((Xa3 tptp.num)) (=> (@ (@ tptp.member_num Xa3) A4) (=> (@ (@ tptp.ord_less_eq_num Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (forall ((Xa3 tptp.nat)) (=> (@ (@ tptp.member_nat Xa3) A4) (=> (@ (@ tptp.ord_less_eq_nat Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) A4) (=> (@ (@ tptp.ord_less_eq_int Xa3) X3) (= X3 Xa3))))))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Pr4329608150637261639at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (P2 (-> tptp.set_Pr4329608150637261639at_nat Bool))) (=> (@ tptp.finite4343798906461161616at_nat F5) (=> (@ (@ tptp.ord_le1268244103169919719at_nat F5) A4) (=> (@ P2 tptp.bot_bo228742789529271731at_nat) (=> (forall ((A3 tptp.produc3843707927480180839at_nat) (F6 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat A3))) (=> (@ tptp.finite4343798906461161616at_nat F6) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_le1268244103169919719at_nat F6) A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert9069300056098147895at_nat A3) F6))))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_se6260736226359567993nt_int) (A4 tptp.set_se6260736226359567993nt_int) (P2 (-> tptp.set_se6260736226359567993nt_int Bool))) (=> (@ tptp.finite8744585540193469122nt_int F5) (=> (@ (@ tptp.ord_le483042692224249369nt_int F5) A4) (=> (@ P2 tptp.bot_bo1488462491386950373nt_int) (=> (forall ((A3 tptp.set_Pr958786334691620121nt_int) (F6 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int A3))) (=> (@ tptp.finite8744585540193469122nt_int F6) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_le483042692224249369nt_int F6) A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert8897473484851387113nt_int A3) F6))))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_set_nat) (A4 tptp.set_set_nat) (P2 (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F5) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F5) A4) (=> (@ P2 tptp.bot_bot_set_set_nat) (=> (forall ((A3 tptp.set_nat) (F6 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A3))) (=> (@ tptp.finite1152437895449049373et_nat F6) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F6) A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert_set_nat A3) F6))))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (P2 (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger F5) (=> (@ (@ tptp.ord_le7084787975880047091nteger F5) A4) (=> (@ P2 tptp.bot_bo3990330152332043303nteger) (=> (forall ((A3 tptp.code_integer) (F6 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.member_Code_integer A3))) (=> (@ tptp.finite6017078050557962740nteger F6) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_le7084787975880047091nteger F6) A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert_Code_integer A3) F6))))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (P2 (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat F5) (=> (@ (@ tptp.ord_le3146513528884898305at_nat F5) A4) (=> (@ P2 tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A3 tptp.product_prod_nat_nat) (F6 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A3))) (=> (@ tptp.finite6177210948735845034at_nat F6) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_le3146513528884898305at_nat F6) A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert8211810215607154385at_nat A3) F6))))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_o) (A4 tptp.set_o) (P2 (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o F5) (=> (@ (@ tptp.ord_less_eq_set_o F5) A4) (=> (@ P2 tptp.bot_bot_set_o) (=> (forall ((A3 Bool) (F6 tptp.set_o)) (let ((_let_1 (@ tptp.member_o A3))) (=> (@ tptp.finite_finite_o F6) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_less_eq_set_o F6) A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert_o A3) F6))))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_nat) (A4 tptp.set_nat) (P2 (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F5) (=> (@ (@ tptp.ord_less_eq_set_nat F5) A4) (=> (@ P2 tptp.bot_bot_set_nat) (=> (forall ((A3 tptp.nat) (F6 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A3))) (=> (@ tptp.finite_finite_nat F6) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_less_eq_set_nat F6) A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert_nat A3) F6))))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_int) (A4 tptp.set_int) (P2 (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F5) (=> (@ (@ tptp.ord_less_eq_set_int F5) A4) (=> (@ P2 tptp.bot_bot_set_int) (=> (forall ((A3 tptp.int) (F6 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A3))) (=> (@ tptp.finite_finite_int F6) (=> (@ _let_1 A4) (=> (@ (@ tptp.ord_less_eq_set_int F6) A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert_int A3) F6))))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Pr4329608150637261639at_nat) (A4 tptp.set_Pr4329608150637261639at_nat) (P2 (-> tptp.set_Pr4329608150637261639at_nat Bool))) (=> (@ tptp.finite4343798906461161616at_nat F5) (=> (@ (@ tptp.ord_le1268244103169919719at_nat F5) A4) (=> (@ P2 tptp.bot_bo228742789529271731at_nat) (=> (forall ((A3 tptp.produc3843707927480180839at_nat) (F6 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat A3))) (=> (@ tptp.finite4343798906461161616at_nat F6) (=> (@ _let_1 A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert9069300056098147895at_nat A3) F6)))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_se6260736226359567993nt_int) (A4 tptp.set_se6260736226359567993nt_int) (P2 (-> tptp.set_se6260736226359567993nt_int Bool))) (=> (@ tptp.finite8744585540193469122nt_int F5) (=> (@ (@ tptp.ord_le483042692224249369nt_int F5) A4) (=> (@ P2 tptp.bot_bo1488462491386950373nt_int) (=> (forall ((A3 tptp.set_Pr958786334691620121nt_int) (F6 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int A3))) (=> (@ tptp.finite8744585540193469122nt_int F6) (=> (@ _let_1 A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert8897473484851387113nt_int A3) F6)))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_set_nat) (A4 tptp.set_set_nat) (P2 (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat F5) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F5) A4) (=> (@ P2 tptp.bot_bot_set_set_nat) (=> (forall ((A3 tptp.set_nat) (F6 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A3))) (=> (@ tptp.finite1152437895449049373et_nat F6) (=> (@ _let_1 A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert_set_nat A3) F6)))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Code_integer) (A4 tptp.set_Code_integer) (P2 (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger F5) (=> (@ (@ tptp.ord_le7084787975880047091nteger F5) A4) (=> (@ P2 tptp.bot_bo3990330152332043303nteger) (=> (forall ((A3 tptp.code_integer) (F6 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.member_Code_integer A3))) (=> (@ tptp.finite6017078050557962740nteger F6) (=> (@ _let_1 A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert_Code_integer A3) F6)))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (P2 (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat F5) (=> (@ (@ tptp.ord_le3146513528884898305at_nat F5) A4) (=> (@ P2 tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A3 tptp.product_prod_nat_nat) (F6 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat A3))) (=> (@ tptp.finite6177210948735845034at_nat F6) (=> (@ _let_1 A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert8211810215607154385at_nat A3) F6)))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_o) (A4 tptp.set_o) (P2 (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o F5) (=> (@ (@ tptp.ord_less_eq_set_o F5) A4) (=> (@ P2 tptp.bot_bot_set_o) (=> (forall ((A3 Bool) (F6 tptp.set_o)) (let ((_let_1 (@ tptp.member_o A3))) (=> (@ tptp.finite_finite_o F6) (=> (@ _let_1 A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert_o A3) F6)))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_nat) (A4 tptp.set_nat) (P2 (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F5) (=> (@ (@ tptp.ord_less_eq_set_nat F5) A4) (=> (@ P2 tptp.bot_bot_set_nat) (=> (forall ((A3 tptp.nat) (F6 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A3))) (=> (@ tptp.finite_finite_nat F6) (=> (@ _let_1 A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert_nat A3) F6)))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_int) (A4 tptp.set_int) (P2 (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F5) (=> (@ (@ tptp.ord_less_eq_set_int F5) A4) (=> (@ P2 tptp.bot_bot_set_int) (=> (forall ((A3 tptp.int) (F6 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A3))) (=> (@ tptp.finite_finite_int F6) (=> (@ _let_1 A4) (=> (not (@ _let_1 F6)) (=> (@ P2 F6) (@ P2 (@ (@ tptp.insert_int A3) F6)))))))) (@ P2 F5)))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Pr4329608150637261639at_nat) (P2 (-> tptp.set_Pr4329608150637261639at_nat Bool))) (=> (@ tptp.finite4343798906461161616at_nat B5) (=> (@ P2 tptp.bot_bo228742789529271731at_nat) (=> (forall ((A9 tptp.set_Pr4329608150637261639at_nat)) (=> (@ tptp.finite4343798906461161616at_nat A9) (=> (not (= A9 tptp.bot_bo228742789529271731at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A9) B5) (=> (forall ((X6 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X6) A9) (@ P2 (@ (@ tptp.minus_3314409938677909166at_nat A9) (@ (@ tptp.insert9069300056098147895at_nat X6) tptp.bot_bo228742789529271731at_nat))))) (@ P2 A9)))))) (@ P2 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_se6260736226359567993nt_int) (P2 (-> tptp.set_se6260736226359567993nt_int Bool))) (=> (@ tptp.finite8744585540193469122nt_int B5) (=> (@ P2 tptp.bot_bo1488462491386950373nt_int) (=> (forall ((A9 tptp.set_se6260736226359567993nt_int)) (=> (@ tptp.finite8744585540193469122nt_int A9) (=> (not (= A9 tptp.bot_bo1488462491386950373nt_int)) (=> (@ (@ tptp.ord_le483042692224249369nt_int A9) B5) (=> (forall ((X6 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X6) A9) (@ P2 (@ (@ tptp.minus_2612819937483484256nt_int A9) (@ (@ tptp.insert8897473484851387113nt_int X6) tptp.bot_bo1488462491386950373nt_int))))) (@ P2 A9)))))) (@ P2 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_set_nat) (P2 (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat B5) (=> (@ P2 tptp.bot_bot_set_set_nat) (=> (forall ((A9 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A9) (=> (not (= A9 tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A9) B5) (=> (forall ((X6 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X6) A9) (@ P2 (@ (@ tptp.minus_2163939370556025621et_nat A9) (@ (@ tptp.insert_set_nat X6) tptp.bot_bot_set_set_nat))))) (@ P2 A9)))))) (@ P2 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Code_integer) (P2 (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ P2 tptp.bot_bo3990330152332043303nteger) (=> (forall ((A9 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A9) (=> (not (= A9 tptp.bot_bo3990330152332043303nteger)) (=> (@ (@ tptp.ord_le7084787975880047091nteger A9) B5) (=> (forall ((X6 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X6) A9) (@ P2 (@ (@ tptp.minus_2355218937544613996nteger A9) (@ (@ tptp.insert_Code_integer X6) tptp.bot_bo3990330152332043303nteger))))) (@ P2 A9)))))) (@ P2 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_o) (P2 (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o B5) (=> (@ P2 tptp.bot_bot_set_o) (=> (forall ((A9 tptp.set_o)) (=> (@ tptp.finite_finite_o A9) (=> (not (= A9 tptp.bot_bot_set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A9) B5) (=> (forall ((X6 Bool)) (=> (@ (@ tptp.member_o X6) A9) (@ P2 (@ (@ tptp.minus_minus_set_o A9) (@ (@ tptp.insert_o X6) tptp.bot_bot_set_o))))) (@ P2 A9)))))) (@ P2 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_nat) (P2 (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat B5) (=> (@ P2 tptp.bot_bot_set_nat) (=> (forall ((A9 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A9) (=> (not (= A9 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A9) B5) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A9) (@ P2 (@ (@ tptp.minus_minus_set_nat A9) (@ (@ tptp.insert_nat X6) tptp.bot_bot_set_nat))))) (@ P2 A9)))))) (@ P2 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (P2 (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (@ P2 tptp.bot_bo2099793752762293965at_nat) (=> (forall ((A9 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A9) (=> (not (= A9 tptp.bot_bo2099793752762293965at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A9) B5) (=> (forall ((X6 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X6) A9) (@ P2 (@ (@ tptp.minus_1356011639430497352at_nat A9) (@ (@ tptp.insert8211810215607154385at_nat X6) tptp.bot_bo2099793752762293965at_nat))))) (@ P2 A9)))))) (@ P2 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_int) (P2 (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int B5) (=> (@ P2 tptp.bot_bot_set_int) (=> (forall ((A9 tptp.set_int)) (=> (@ tptp.finite_finite_int A9) (=> (not (= A9 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A9) B5) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A9) (@ P2 (@ (@ tptp.minus_minus_set_int A9) (@ (@ tptp.insert_int X6) tptp.bot_bot_set_int))))) (@ P2 A9)))))) (@ P2 B5))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.set_Pr4329608150637261639at_nat Bool)) (B5 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ P2 B5))) (=> (@ P2 tptp.bot_bo228742789529271731at_nat) (=> (=> (not (@ tptp.finite4343798906461161616at_nat B5)) _let_1) (=> (forall ((A9 tptp.set_Pr4329608150637261639at_nat)) (=> (@ tptp.finite4343798906461161616at_nat A9) (=> (not (= A9 tptp.bot_bo228742789529271731at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A9) B5) (=> (forall ((X6 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X6) A9) (@ P2 (@ (@ tptp.minus_3314409938677909166at_nat A9) (@ (@ tptp.insert9069300056098147895at_nat X6) tptp.bot_bo228742789529271731at_nat))))) (@ P2 A9)))))) _let_1))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.set_se6260736226359567993nt_int Bool)) (B5 tptp.set_se6260736226359567993nt_int)) (let ((_let_1 (@ P2 B5))) (=> (@ P2 tptp.bot_bo1488462491386950373nt_int) (=> (=> (not (@ tptp.finite8744585540193469122nt_int B5)) _let_1) (=> (forall ((A9 tptp.set_se6260736226359567993nt_int)) (=> (@ tptp.finite8744585540193469122nt_int A9) (=> (not (= A9 tptp.bot_bo1488462491386950373nt_int)) (=> (@ (@ tptp.ord_le483042692224249369nt_int A9) B5) (=> (forall ((X6 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X6) A9) (@ P2 (@ (@ tptp.minus_2612819937483484256nt_int A9) (@ (@ tptp.insert8897473484851387113nt_int X6) tptp.bot_bo1488462491386950373nt_int))))) (@ P2 A9)))))) _let_1))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.set_set_nat Bool)) (B5 tptp.set_set_nat)) (let ((_let_1 (@ P2 B5))) (=> (@ P2 tptp.bot_bot_set_set_nat) (=> (=> (not (@ tptp.finite1152437895449049373et_nat B5)) _let_1) (=> (forall ((A9 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A9) (=> (not (= A9 tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A9) B5) (=> (forall ((X6 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X6) A9) (@ P2 (@ (@ tptp.minus_2163939370556025621et_nat A9) (@ (@ tptp.insert_set_nat X6) tptp.bot_bot_set_set_nat))))) (@ P2 A9)))))) _let_1))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.set_Code_integer Bool)) (B5 tptp.set_Code_integer)) (let ((_let_1 (@ P2 B5))) (=> (@ P2 tptp.bot_bo3990330152332043303nteger) (=> (=> (not (@ tptp.finite6017078050557962740nteger B5)) _let_1) (=> (forall ((A9 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A9) (=> (not (= A9 tptp.bot_bo3990330152332043303nteger)) (=> (@ (@ tptp.ord_le7084787975880047091nteger A9) B5) (=> (forall ((X6 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X6) A9) (@ P2 (@ (@ tptp.minus_2355218937544613996nteger A9) (@ (@ tptp.insert_Code_integer X6) tptp.bot_bo3990330152332043303nteger))))) (@ P2 A9)))))) _let_1))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.set_o Bool)) (B5 tptp.set_o)) (let ((_let_1 (@ P2 B5))) (=> (@ P2 tptp.bot_bot_set_o) (=> (=> (not (@ tptp.finite_finite_o B5)) _let_1) (=> (forall ((A9 tptp.set_o)) (=> (@ tptp.finite_finite_o A9) (=> (not (= A9 tptp.bot_bot_set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A9) B5) (=> (forall ((X6 Bool)) (=> (@ (@ tptp.member_o X6) A9) (@ P2 (@ (@ tptp.minus_minus_set_o A9) (@ (@ tptp.insert_o X6) tptp.bot_bot_set_o))))) (@ P2 A9)))))) _let_1))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.set_nat Bool)) (B5 tptp.set_nat)) (let ((_let_1 (@ P2 B5))) (=> (@ P2 tptp.bot_bot_set_nat) (=> (=> (not (@ tptp.finite_finite_nat B5)) _let_1) (=> (forall ((A9 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A9) (=> (not (= A9 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A9) B5) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A9) (@ P2 (@ (@ tptp.minus_minus_set_nat A9) (@ (@ tptp.insert_nat X6) tptp.bot_bot_set_nat))))) (@ P2 A9)))))) _let_1))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.set_Pr1261947904930325089at_nat Bool)) (B5 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ P2 B5))) (=> (@ P2 tptp.bot_bo2099793752762293965at_nat) (=> (=> (not (@ tptp.finite6177210948735845034at_nat B5)) _let_1) (=> (forall ((A9 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A9) (=> (not (= A9 tptp.bot_bo2099793752762293965at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A9) B5) (=> (forall ((X6 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X6) A9) (@ P2 (@ (@ tptp.minus_1356011639430497352at_nat A9) (@ (@ tptp.insert8211810215607154385at_nat X6) tptp.bot_bo2099793752762293965at_nat))))) (@ P2 A9)))))) _let_1))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.set_int Bool)) (B5 tptp.set_int)) (let ((_let_1 (@ P2 B5))) (=> (@ P2 tptp.bot_bot_set_int) (=> (=> (not (@ tptp.finite_finite_int B5)) _let_1) (=> (forall ((A9 tptp.set_int)) (=> (@ tptp.finite_finite_int A9) (=> (not (= A9 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A9) B5) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A9) (@ P2 (@ (@ tptp.minus_minus_set_int A9) (@ (@ tptp.insert_int X6) tptp.bot_bot_set_int))))) (@ P2 A9)))))) _let_1))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (@ (@ tptp.member_nat N2) A4)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N2) A4)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.nat_set_encode A4)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (exists ((K tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S) (@ tptp.set_ord_lessThan_nat K))))))
% 8.20/8.65 (assert (= tptp.finite_finite_nat (lambda ((S4 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S4) (@ tptp.set_ord_lessThan_nat K3))))))
% 8.20/8.65 (assert (= tptp.finite_finite_nat (lambda ((S4 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S4) (@ tptp.set_ord_atMost_nat K3))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (= (@ (@ tptp.member8277197624267554838et_nat (@ (@ tptp.produc4532415448927165861et_nat A4) B5)) tptp.finite_psubset_nat) (and (@ (@ tptp.ord_less_set_nat A4) B5) (@ tptp.finite_finite_nat B5)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (= (@ (@ tptp.member2572552093476627150et_int (@ (@ tptp.produc6363374080413544029et_int A4) B5)) tptp.finite_psubset_int) (and (@ (@ tptp.ord_less_set_int A4) B5) (@ tptp.finite_finite_int B5)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer)) (= (@ (@ tptp.member4307123515891402160nteger (@ (@ tptp.produc7443773368509356479nteger A4) B5)) tptp.finite2416775604798480986nteger) (and (@ (@ tptp.ord_le1307284697595431911nteger A4) B5) (@ tptp.finite6017078050557962740nteger B5)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A4) B5)) tptp.finite469560695537375940at_nat) (and (@ (@ tptp.ord_le7866589430770878221at_nat A4) B5) (@ tptp.finite6177210948735845034at_nat B5)))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (assert (forall ((K2 tptp.nat) (S tptp.set_nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) M5) (exists ((N10 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N10) (@ (@ tptp.member_nat N10) S))))) (not (@ tptp.finite_finite_nat S)))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K3 _let_2) (= L2 _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 8.20/8.65 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) M3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Code_integer) (I5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (I2 tptp.code_integer)) (let ((_let_1 (@ tptp.groups910942671188738463nteger F))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger I5) (@ (@ tptp.insert_Code_integer I2) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_4 (@ (@ tptp.member_Code_integer I2) I5))) (=> (@ tptp.finite6017078050557962740nteger F5) (=> (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) I5) (not (= (@ F I) tptp.zero_z3403309356797280102nteger)))))) F5) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_8373710615458151222nteger _let_2) (@ F I2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_o) (I5 tptp.set_o) (F (-> Bool tptp.code_integer)) (I2 Bool)) (let ((_let_1 (@ tptp.groups1402912129352969042nteger F))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_o I5) (@ (@ tptp.insert_o I2) tptp.bot_bot_set_o))))) (let ((_let_4 (@ (@ tptp.member_o I2) I5))) (=> (@ tptp.finite_finite_o F5) (=> (@ (@ tptp.ord_less_eq_set_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ F I) tptp.zero_z3403309356797280102nteger)))))) F5) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_8373710615458151222nteger _let_2) (@ F I2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_nat) (I5 tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.groups555127423416065298nteger F))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat I5) (@ (@ tptp.insert_nat I2) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat I2) I5))) (=> (@ tptp.finite_finite_nat F5) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ F I) tptp.zero_z3403309356797280102nteger)))))) F5) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_8373710615458151222nteger _let_2) (@ F I2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Code_integer) (I5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (I2 tptp.code_integer)) (let ((_let_1 (@ tptp.groups8878813951405302554er_rat F))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger I5) (@ (@ tptp.insert_Code_integer I2) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_4 (@ (@ tptp.member_Code_integer I2) I5))) (=> (@ tptp.finite6017078050557962740nteger F5) (=> (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) I5) (not (= (@ F I) tptp.zero_zero_rat)))))) F5) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F I2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_o) (I5 tptp.set_o) (F (-> Bool tptp.rat)) (I2 Bool)) (let ((_let_1 (@ tptp.groups3921277224699582669_o_rat F))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_o I5) (@ (@ tptp.insert_o I2) tptp.bot_bot_set_o))))) (let ((_let_4 (@ (@ tptp.member_o I2) I5))) (=> (@ tptp.finite_finite_o F5) (=> (@ (@ tptp.ord_less_eq_set_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ F I) tptp.zero_zero_rat)))))) F5) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F I2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_nat) (I5 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.groups1351286907653491341at_rat F))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat I5) (@ (@ tptp.insert_nat I2) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat I2) I5))) (=> (@ tptp.finite_finite_nat F5) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ F I) tptp.zero_zero_rat)))))) F5) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F I2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Code_integer) (I5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int)) (I2 tptp.code_integer)) (let ((_let_1 (@ tptp.groups288081504127972206er_int F))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger I5) (@ (@ tptp.insert_Code_integer I2) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_4 (@ (@ tptp.member_Code_integer I2) I5))) (=> (@ tptp.finite6017078050557962740nteger F5) (=> (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) I5) (not (= (@ F I) tptp.zero_zero_int)))))) F5) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F I2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_o) (I5 tptp.set_o) (F (-> Bool tptp.int)) (I2 Bool)) (let ((_let_1 (@ tptp.groups4553916814277028129_o_int F))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_o I5) (@ (@ tptp.insert_o I2) tptp.bot_bot_set_o))))) (let ((_let_4 (@ (@ tptp.member_o I2) I5))) (=> (@ tptp.finite_finite_o F5) (=> (@ (@ tptp.ord_less_eq_set_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) I5) (not (= (@ F I) tptp.zero_zero_int)))))) F5) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F I2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_nat) (I5 tptp.set_nat) (F (-> tptp.nat tptp.int)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.groups1983926497230936801at_int F))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat I5) (@ (@ tptp.insert_nat I2) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat I2) I5))) (=> (@ tptp.finite_finite_nat F5) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (and (@ (@ tptp.member_nat I) I5) (not (= (@ F I) tptp.zero_zero_int)))))) F5) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F I2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_int) (I5 tptp.set_int) (F (-> tptp.int tptp.code_integer)) (I2 tptp.int)) (let ((_let_1 (@ tptp.groups926780983652909934nteger F))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int I5) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int I2) I5))) (=> (@ tptp.finite_finite_int F5) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) I5) (not (= (@ F I) tptp.zero_z3403309356797280102nteger)))))) F5) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_8373710615458151222nteger _let_2) (@ F I2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))))
% 8.20/8.65 (assert (forall ((A4 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 A4) (= (@ _let_1 (@ (@ tptp.groups8507830703676809646_o_nat F) A4)) (@ _let_1 (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((A5 Bool)) (and (@ (@ tptp.member_o A5) A4) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 8.20/8.65 (assert (forall ((A4 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 A4) (= (@ _let_1 (@ (@ tptp.groups4541462559716669496nt_nat F) A4)) (@ _let_1 (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((A5 tptp.int)) (and (@ (@ tptp.member_int A5) A4) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 8.20/8.65 (assert (forall ((A4 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 A4) (= (@ _let_1 (@ (@ tptp.groups7237345082560585321er_nat F) A4)) (@ _let_1 (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((A5 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer A5) A4) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.int))) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ (@ tptp.groups8505340233167759370_o_int F) A4)) (@ (@ 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) A4) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ (@ tptp.groups3539618377306564664at_int F) A4)) (@ (@ 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) A4) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ (@ tptp.groups7234854612051535045er_int F) A4)) (@ (@ 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) A4) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (F (-> Bool tptp.code_natural))) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ tptp.finite_finite_o A4) (= (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural _let_1)) (@ (@ tptp.groups3230237193842799622atural F) A4)) (@ (@ 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) A4) (not (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.code_natural))) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural _let_1)) (@ (@ tptp.groups6325495683096345652atural F) A4)) (@ (@ 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) A4) (not (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.code_natural))) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural _let_1)) (@ (@ tptp.groups6697149243333190288atural F) A4)) (@ (@ 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) A4) (not (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_natural))) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural _let_1)) (@ (@ tptp.groups8926444216418632897atural F) A4)) (@ (@ 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) A4) (not (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 8.20/8.65 (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 ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ 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))))))))))))))))))))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (@ (@ tptp.ord_less_nat I) N2)))) N2)))
% 8.20/8.65 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C2)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C2) A)))))
% 8.20/8.65 (assert (forall ((B tptp.num) (C2 tptp.num) (A tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C2)) A) (and (@ (@ tptp.ord_less_eq_num B) A) (@ (@ tptp.ord_less_eq_num C2) A)))))
% 8.20/8.65 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C2)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C2) A)))))
% 8.20/8.65 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C2)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C2) A)))))
% 8.20/8.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 8.20/8.65 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 8.20/8.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 8.20/8.65 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 8.20/8.65 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 8.20/8.65 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 8.20/8.65 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 8.20/8.65 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 8.20/8.65 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat X) Y)) Z3) (and (@ (@ tptp.ord_less_rat X) Z3) (@ (@ tptp.ord_less_rat Y) Z3)))))
% 8.20/8.65 (assert (forall ((X tptp.num) (Y tptp.num) (Z3 tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X) Y)) Z3) (and (@ (@ tptp.ord_less_num X) Z3) (@ (@ tptp.ord_less_num Y) Z3)))))
% 8.20/8.65 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X) Y)) Z3) (and (@ (@ tptp.ord_less_nat X) Z3) (@ (@ tptp.ord_less_nat Y) Z3)))))
% 8.20/8.65 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X) Y)) Z3) (and (@ (@ tptp.ord_less_int X) Z3) (@ (@ tptp.ord_less_int Y) Z3)))))
% 8.20/8.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 8.20/8.65 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 8.20/8.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 8.20/8.65 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 8.20/8.65 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 8.20/8.65 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 8.20/8.65 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 8.20/8.65 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 8.20/8.65 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_ma7524802468073614006at_nat X) tptp.bot_bo2099793752762293965at_nat) X)))
% 8.20/8.65 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.ord_max_set_o X) tptp.bot_bot_set_o) X)))
% 8.20/8.65 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X) tptp.bot_bot_set_nat) X)))
% 8.20/8.65 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X) tptp.bot_bot_set_int) X)))
% 8.20/8.65 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat X) tptp.bot_bot_nat) X)))
% 8.20/8.65 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_ma7524802468073614006at_nat tptp.bot_bo2099793752762293965at_nat) X) X)))
% 8.20/8.65 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.ord_max_set_o tptp.bot_bot_set_o) X) X)))
% 8.20/8.65 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.bot_bot_set_nat) X) X)))
% 8.20/8.65 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.bot_bot_set_int) X) X)))
% 8.20/8.65 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.bot_bot_nat) X) X)))
% 8.20/8.65 (assert (forall ((F (-> tptp.num tptp.num)) (Xo tptp.option_num) (Y tptp.num)) (= (= (@ (@ tptp.map_option_num_num F) Xo) (@ tptp.some_num Y)) (exists ((Z tptp.num)) (and (= Xo (@ tptp.some_num Z)) (= (@ F Z) Y))))))
% 8.20/8.65 (assert (forall ((F (-> tptp.num tptp.produc7388388658123137530it_nat)) (Xo tptp.option_num) (Y tptp.produc7388388658123137530it_nat)) (= (= (@ (@ tptp.map_op2490657901765117089it_nat F) Xo) (@ tptp.some_P2818173045054083285it_nat Y)) (exists ((Z tptp.num)) (and (= Xo (@ tptp.some_num Z)) (= (@ F Z) Y))))))
% 8.20/8.65 (assert (forall ((F (-> tptp.num tptp.produc3260487557148687353it_nat)) (Xo tptp.option_num) (Y tptp.produc3260487557148687353it_nat)) (= (= (@ (@ tptp.map_op7586128837645442720it_nat F) Xo) (@ tptp.some_P7913643980934408916it_nat Y)) (exists ((Z tptp.num)) (and (= Xo (@ tptp.some_num Z)) (= (@ F Z) Y))))))
% 8.20/8.65 (assert (forall ((F (-> tptp.num tptp.produc8664842809031399944it_nat)) (Xo tptp.option_num) (Y tptp.produc8664842809031399944it_nat)) (= (= (@ (@ tptp.map_op8118133509425879471it_nat F) Xo) (@ tptp.some_P1914260805536162275it_nat Y)) (exists ((Z tptp.num)) (and (= Xo (@ tptp.some_num Z)) (= (@ F Z) Y))))))
% 8.20/8.65 (assert (forall ((F (-> tptp.produc7388388658123137530it_nat tptp.num)) (Xo tptp.option4065278094766928714it_nat) (Y tptp.num)) (= (= (@ (@ tptp.map_op6233829773304596897at_num F) Xo) (@ tptp.some_num Y)) (exists ((Z tptp.produc7388388658123137530it_nat)) (and (= Xo (@ tptp.some_P2818173045054083285it_nat Z)) (= (@ F Z) Y))))))
% 8.20/8.65 (assert (forall ((F (-> tptp.produc3260487557148687353it_nat tptp.num)) (Xo tptp.option3562590408128118217it_nat) (Y tptp.num)) (= (= (@ (@ tptp.map_op5165227558541518752at_num F) Xo) (@ tptp.some_num Y)) (exists ((Z tptp.produc3260487557148687353it_nat)) (and (= Xo (@ tptp.some_P7913643980934408916it_nat Z)) (= (@ F Z) Y))))))
% 8.20/8.65 (assert (forall ((F (-> tptp.produc8664842809031399944it_nat tptp.num)) (Xo tptp.option8956607266484857688it_nat) (Y tptp.num)) (= (= (@ (@ tptp.map_op2731889312448867759at_num F) Xo) (@ tptp.some_num Y)) (exists ((Z tptp.produc8664842809031399944it_nat)) (and (= Xo (@ tptp.some_P1914260805536162275it_nat Z)) (= (@ F Z) Y))))))
% 8.20/8.65 (assert (forall ((F (-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)) (Xo tptp.option4065278094766928714it_nat) (Y tptp.produc7388388658123137530it_nat)) (= (= (@ (@ tptp.map_op8581638957091552385it_nat F) Xo) (@ tptp.some_P2818173045054083285it_nat Y)) (exists ((Z tptp.produc7388388658123137530it_nat)) (and (= Xo (@ tptp.some_P2818173045054083285it_nat Z)) (= (@ F Z) Y))))))
% 8.20/8.65 (assert (forall ((F (-> tptp.produc3260487557148687353it_nat tptp.produc7388388658123137530it_nat)) (Xo tptp.option3562590408128118217it_nat) (Y tptp.produc7388388658123137530it_nat)) (= (= (@ (@ tptp.map_op7599720869725723008it_nat F) Xo) (@ tptp.some_P2818173045054083285it_nat Y)) (exists ((Z tptp.produc3260487557148687353it_nat)) (and (= Xo (@ tptp.some_P7913643980934408916it_nat Z)) (= (@ F Z) Y))))))
% 8.20/8.65 (assert (forall ((F (-> tptp.produc8664842809031399944it_nat tptp.produc7388388658123137530it_nat)) (Xo tptp.option8956607266484857688it_nat) (Y tptp.produc7388388658123137530it_nat)) (= (= (@ (@ tptp.map_op604423251913076367it_nat F) Xo) (@ tptp.some_P2818173045054083285it_nat Y)) (exists ((Z tptp.produc8664842809031399944it_nat)) (and (= Xo (@ tptp.some_P1914260805536162275it_nat Z)) (= (@ F Z) Y))))))
% 8.20/8.65 (assert (forall ((F (-> tptp.num tptp.num)) (X tptp.option_num)) (= (= tptp.none_num (@ (@ tptp.map_option_num_num F) X)) (= X tptp.none_num))))
% 8.20/8.65 (assert (forall ((F (-> tptp.num tptp.num)) (Opt tptp.option_num)) (= (= (@ (@ tptp.map_option_num_num F) Opt) tptp.none_num) (= Opt tptp.none_num))))
% 8.20/8.65 (assert (forall ((F (-> tptp.num tptp.num)) (A tptp.option_num)) (= (= (@ (@ tptp.map_option_num_num F) A) tptp.none_num) (= A tptp.none_num))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat N2) tptp.zero_zero_nat) N2)))
% 8.20/8.65 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N2) N2)))
% 8.20/8.65 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (@ (@ tptp.ord_less_eq_nat I) N2)))) (@ tptp.suc N2))))
% 8.20/8.65 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera5444537566228673987atural U))) (let ((_let_2 (@ tptp.numera5444537566228673987atural V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_natural _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le1926595141338095240atural _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.65 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.65 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.65 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat U))) (let ((_let_2 (@ tptp.numeral_numeral_nat V))) (let ((_let_3 (@ (@ tptp.ord_max_nat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.65 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.65 (assert (forall ((G (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (H (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (F (-> tptp.code_integer tptp.code_integer)) (X tptp.option_Code_integer)) (let ((_let_1 (@ tptp.case_o7134296353695833103nteger G))) (= (@ (@ _let_1 H) (@ (@ tptp.map_op3669829223712506439nteger F) X)) (@ (@ _let_1 (@ (@ tptp.comp_C1593894019821074884nteger H) F)) X)))))
% 8.20/8.65 (assert (forall ((G (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (H (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (F (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (X tptp.option_Code_integer)) (= (@ (@ (@ tptp.case_o1441893360019914891nteger G) H) (@ (@ tptp.map_op370346339404370627nteger F) X)) (@ (@ (@ tptp.case_o7134296353695833103nteger G) (@ (@ tptp.comp_C8797469213163452608nteger H) F)) X))))
% 8.20/8.65 (assert (forall ((G tptp.nat) (H (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.int)) (X tptp.option_int)) (let ((_let_1 (@ tptp.case_option_nat_int G))) (= (@ (@ _let_1 H) (@ (@ tptp.map_option_int_int F) X)) (@ (@ _let_1 (@ (@ tptp.comp_int_nat_int H) F)) X)))))
% 8.20/8.65 (assert (forall ((G tptp.int) (H (-> tptp.num tptp.int)) (F (-> tptp.num tptp.num)) (X tptp.option_num)) (let ((_let_1 (@ tptp.case_option_int_num G))) (= (@ (@ _let_1 H) (@ (@ tptp.map_option_num_num F) X)) (@ (@ _let_1 (@ (@ tptp.comp_num_int_num H) F)) X)))))
% 8.20/8.65 (assert (forall ((G tptp.option_num) (H (-> tptp.num tptp.option_num)) (F (-> tptp.num tptp.num)) (X tptp.option_num)) (let ((_let_1 (@ tptp.case_o6005452278849405969um_num G))) (= (@ (@ _let_1 H) (@ (@ tptp.map_option_num_num F) X)) (@ (@ _let_1 (@ (@ tptp.comp_n6731957995704128387um_num H) F)) X)))))
% 8.20/8.65 (assert (forall ((G tptp.num) (H (-> tptp.num tptp.num)) (F (-> tptp.num tptp.num)) (X tptp.option_num)) (let ((_let_1 (@ tptp.case_option_num_num G))) (= (@ (@ _let_1 H) (@ (@ tptp.map_option_num_num F) X)) (@ (@ _let_1 (@ (@ tptp.comp_num_num_num H) F)) X)))))
% 8.20/8.65 (assert (forall ((Y tptp.nat) (A4 tptp.set_int)) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X4 tptp.int)) Y)) A4) (@ (@ tptp.power_power_nat Y) (@ tptp.finite_card_int A4)))))
% 8.20/8.65 (assert (forall ((Y tptp.nat) (A4 tptp.set_list_nat)) (= (@ (@ tptp.groups2907647131375434839at_nat (lambda ((X4 tptp.list_nat)) Y)) A4) (@ (@ tptp.power_power_nat Y) (@ tptp.finite_card_list_nat A4)))))
% 8.20/8.65 (assert (forall ((Y tptp.nat) (A4 tptp.set_set_nat)) (= (@ (@ tptp.groups4248547760180025341at_nat (lambda ((X4 tptp.set_nat)) Y)) A4) (@ (@ tptp.power_power_nat Y) (@ tptp.finite_card_set_nat A4)))))
% 8.20/8.65 (assert (forall ((Y tptp.int) (A4 tptp.set_list_nat)) (= (@ (@ tptp.groups2905156660866384563at_int (lambda ((X4 tptp.list_nat)) Y)) A4) (@ (@ tptp.power_power_int Y) (@ tptp.finite_card_list_nat A4)))))
% 8.20/8.65 (assert (forall ((Y tptp.int) (A4 tptp.set_set_nat)) (= (@ (@ tptp.groups4246057289670975065at_int (lambda ((X4 tptp.set_nat)) Y)) A4) (@ (@ tptp.power_power_int Y) (@ tptp.finite_card_set_nat A4)))))
% 8.20/8.65 (assert (forall ((Y tptp.nat) (A4 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) Y)) A4) (@ (@ tptp.power_power_nat Y) (@ tptp.finite_card_nat A4)))))
% 8.20/8.65 (assert (forall ((Y tptp.int) (A4 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) Y)) A4) (@ (@ tptp.power_power_int Y) (@ tptp.finite_card_nat A4)))))
% 8.20/8.65 (assert (forall ((Y tptp.int) (A4 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) Y)) A4) (@ (@ tptp.power_power_int Y) (@ tptp.finite_card_int A4)))))
% 8.20/8.65 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.65 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.65 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.65 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.65 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.65 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.65 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.65 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.65 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 8.20/8.65 (assert (forall ((Y tptp.rat) (A4 tptp.set_nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) Y)) A4) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A4))) Y))))
% 8.20/8.65 (assert (forall ((Y tptp.rat) (A4 tptp.set_int)) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) Y)) A4) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_int A4))) Y))))
% 8.20/8.65 (assert (forall ((Y tptp.int) (A4 tptp.set_nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) Y)) A4) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_nat A4))) Y))))
% 8.20/8.65 (assert (forall ((Y tptp.nat) (A4 tptp.set_int)) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) Y)) A4) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_int A4))) Y))))
% 8.20/8.65 (assert (forall ((Y tptp.code_integer) (A4 tptp.set_nat)) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((X4 tptp.nat)) Y)) A4) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.finite_card_nat A4))) Y))))
% 8.20/8.65 (assert (forall ((Y tptp.code_integer) (A4 tptp.set_int)) (= (@ (@ tptp.groups7873554091576472773nteger (lambda ((X4 tptp.int)) Y)) A4) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.finite_card_int A4))) Y))))
% 8.20/8.65 (assert (forall ((Y tptp.nat) (A4 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) Y)) A4) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_nat A4))) Y))))
% 8.20/8.65 (assert (forall ((Y tptp.int) (A4 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) Y)) A4) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_int A4))) Y))))
% 8.20/8.65 (assert (forall ((Y tptp.rat) (A4 tptp.set_list_nat)) (= (@ (@ tptp.groups3760926236672600436at_rat (lambda ((X4 tptp.list_nat)) Y)) A4) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_list_nat A4))) Y))))
% 8.20/8.65 (assert (forall ((Y tptp.rat) (A4 tptp.set_set_nat)) (= (@ (@ tptp.groups7659867448343625626at_rat (lambda ((X4 tptp.set_nat)) Y)) A4) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_set_nat A4))) Y))))
% 8.20/8.65 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or1266510415728281911st_int L) U)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int U) L)) tptp.one_one_int)))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_o) (P3 (-> Bool tptp.code_integer)) (I2 Bool)) (let ((_let_1 (@ tptp.groups1402912129352969042nteger P3))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o I2) I5)))) (let ((_let_4 (@ (@ tptp.member_o I2) I5))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) I5) (not (= (@ P3 X4) tptp.zero_z3403309356797280102nteger)))))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger (@ P3 I2)) _let_2)))))))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_nat) (P3 (-> tptp.nat tptp.code_integer)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.groups555127423416065298nteger P3))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat I2) I5)))) (let ((_let_4 (@ (@ tptp.member_nat I2) I5))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) I5) (not (= (@ P3 X4) tptp.zero_z3403309356797280102nteger)))))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger (@ P3 I2)) _let_2)))))))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_int) (P3 (-> tptp.int tptp.code_integer)) (I2 tptp.int)) (let ((_let_1 (@ tptp.groups926780983652909934nteger P3))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int I2) I5)))) (let ((_let_4 (@ (@ tptp.member_int I2) I5))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) I5) (not (= (@ P3 X4) tptp.zero_z3403309356797280102nteger)))))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger (@ P3 I2)) _let_2)))))))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_Code_integer) (P3 (-> tptp.code_integer tptp.code_integer)) (I2 tptp.code_integer)) (let ((_let_1 (@ tptp.groups910942671188738463nteger P3))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Code_integer I2) I5)))) (let ((_let_4 (@ (@ tptp.member_Code_integer I2) I5))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) I5) (not (= (@ P3 X4) tptp.zero_z3403309356797280102nteger)))))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger (@ P3 I2)) _let_2)))))))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_o) (P3 (-> Bool tptp.rat)) (I2 Bool)) (let ((_let_1 (@ tptp.groups3921277224699582669_o_rat P3))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o I2) I5)))) (let ((_let_4 (@ (@ tptp.member_o I2) I5))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) I5) (not (= (@ P3 X4) tptp.zero_zero_rat)))))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ P3 I2)) _let_2)))))))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_nat) (P3 (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.groups1351286907653491341at_rat P3))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat I2) I5)))) (let ((_let_4 (@ (@ tptp.member_nat I2) I5))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) I5) (not (= (@ P3 X4) tptp.zero_zero_rat)))))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ P3 I2)) _let_2)))))))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_int) (P3 (-> tptp.int tptp.rat)) (I2 tptp.int)) (let ((_let_1 (@ tptp.groups2350640619554545897nt_rat P3))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int I2) I5)))) (let ((_let_4 (@ (@ tptp.member_int I2) I5))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) I5) (not (= (@ P3 X4) tptp.zero_zero_rat)))))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ P3 I2)) _let_2)))))))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_Code_integer) (P3 (-> tptp.code_integer tptp.rat)) (I2 tptp.code_integer)) (let ((_let_1 (@ tptp.groups8878813951405302554er_rat P3))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Code_integer I2) I5)))) (let ((_let_4 (@ (@ tptp.member_Code_integer I2) I5))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) I5) (not (= (@ P3 X4) tptp.zero_zero_rat)))))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ P3 I2)) _let_2)))))))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_o) (P3 (-> Bool tptp.nat)) (I2 Bool)) (let ((_let_1 (@ tptp.groups4556407284786078405_o_nat P3))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o I2) I5)))) (let ((_let_4 (@ (@ tptp.member_o I2) I5))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) I5) (not (= (@ P3 X4) tptp.zero_zero_nat)))))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ P3 I2)) _let_2)))))))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_nat) (P3 (-> tptp.nat tptp.nat)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.groups1986416967739987077at_nat P3))) (let ((_let_2 (@ _let_1 I5))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat I2) I5)))) (let ((_let_4 (@ (@ tptp.member_nat I2) I5))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) I5) (not (= (@ P3 X4) tptp.zero_zero_nat)))))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ P3 I2)) _let_2)))))))))))
% 8.20/8.65 (assert (forall ((A tptp.produc3843707927480180839at_nat) (B tptp.produc3843707927480180839at_nat)) (= (= (@ tptp.finite3771342082235030671at_nat (@ (@ tptp.insert9069300056098147895at_nat A) (@ (@ tptp.insert9069300056098147895at_nat B) tptp.bot_bo228742789529271731at_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (= A B)))))
% 8.20/8.65 (assert (forall ((A tptp.list_nat) (B tptp.list_nat)) (= (= (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat A) (@ (@ tptp.insert_list_nat B) tptp.bot_bot_set_list_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (= A B)))))
% 8.20/8.65 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat A) (@ (@ tptp.insert_set_nat B) tptp.bot_bot_set_set_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (= A B)))))
% 8.20/8.65 (assert (forall ((A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (= (= (@ tptp.finite711546835091564841at_nat (@ (@ tptp.insert8211810215607154385at_nat A) (@ (@ tptp.insert8211810215607154385at_nat B) tptp.bot_bo2099793752762293965at_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (= A B)))))
% 8.20/8.65 (assert (forall ((A Bool) (B Bool)) (= (= (@ tptp.finite_card_o (@ (@ tptp.insert_o A) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (= A B)))))
% 8.20/8.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ tptp.finite_card_nat (@ (@ tptp.insert_nat A) (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (= A B)))))
% 8.20/8.65 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.finite_card_int (@ (@ tptp.insert_int A) (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (= A B)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.finite_finite_int A4))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4)))) A4) (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_int (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.code_integer Bool))) (let ((_let_1 (@ tptp.finite6017078050557962740nteger A4))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((X4 tptp.code_integer)) (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4)))) A4) (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite4902975817058060853nteger (@ (@ tptp.inf_in1364745209274528805nteger A4) (@ tptp.collect_Code_integer P2))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.code_integer Bool))) (let ((_let_1 (@ tptp.finite6017078050557962740nteger A4))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups7234854612051535045er_int (lambda ((X4 tptp.code_integer)) (@ tptp.zero_n2684676970156552555ol_int (@ P2 X4)))) A4) (@ tptp.semiri1314217659103216013at_int (@ tptp.finite4902975817058060853nteger (@ (@ tptp.inf_in1364745209274528805nteger A4) (@ tptp.collect_Code_integer P2))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.finite_finite_nat A4))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ tptp.zero_n2684676970156552555ol_int (@ P2 X4)))) A4) (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_nat (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.collect_nat P2))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.finite_finite_int A4))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups7873554091576472773nteger (lambda ((X4 tptp.int)) (@ tptp.zero_n356916108424825756nteger (@ P2 X4)))) A4) (@ tptp.semiri4939895301339042750nteger (@ tptp.finite_card_int (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (P2 (-> tptp.code_integer Bool))) (let ((_let_1 (@ tptp.finite6017078050557962740nteger A4))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups879477027807139574nteger (lambda ((X4 tptp.code_integer)) (@ tptp.zero_n356916108424825756nteger (@ P2 X4)))) A4) (@ tptp.semiri4939895301339042750nteger (@ tptp.finite4902975817058060853nteger (@ (@ tptp.inf_in1364745209274528805nteger A4) (@ tptp.collect_Code_integer P2))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.finite_finite_nat A4))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((X4 tptp.nat)) (@ tptp.zero_n356916108424825756nteger (@ P2 X4)))) A4) (@ tptp.semiri4939895301339042750nteger (@ tptp.finite_card_nat (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.collect_nat P2))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (P2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.finite_finite_nat A4))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4)))) A4) (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_nat (@ (@ tptp.inf_inf_set_nat A4) (@ tptp.collect_nat P2))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (P2 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.finite_finite_int A4))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.zero_n2684676970156552555ol_int (@ P2 X4)))) A4) (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_int (@ (@ tptp.inf_inf_set_int A4) (@ tptp.collect_int P2))))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_list_nat) (P2 (-> tptp.list_nat Bool))) (let ((_let_1 (@ tptp.finite8100373058378681591st_nat A4))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups4396056296759096172at_nat (lambda ((X4 tptp.list_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ P2 X4)))) A4) (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_list_nat (@ (@ tptp.inf_inf_set_list_nat A4) (@ tptp.collect_list_nat P2))))))))))
% 8.20/8.65 (assert (forall ((F (-> tptp.num tptp.num)) (X2 tptp.num)) (= (@ (@ tptp.map_option_num_num F) (@ tptp.some_num X2)) (@ tptp.some_num (@ F X2)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.produc7388388658123137530it_nat tptp.num)) (X2 tptp.produc7388388658123137530it_nat)) (= (@ (@ tptp.map_op6233829773304596897at_num F) (@ tptp.some_P2818173045054083285it_nat X2)) (@ tptp.some_num (@ F X2)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.produc3260487557148687353it_nat tptp.num)) (X2 tptp.produc3260487557148687353it_nat)) (= (@ (@ tptp.map_op5165227558541518752at_num F) (@ tptp.some_P7913643980934408916it_nat X2)) (@ tptp.some_num (@ F X2)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.produc8664842809031399944it_nat tptp.num)) (X2 tptp.produc8664842809031399944it_nat)) (= (@ (@ tptp.map_op2731889312448867759at_num F) (@ tptp.some_P1914260805536162275it_nat X2)) (@ tptp.some_num (@ F X2)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.num tptp.produc7388388658123137530it_nat)) (X2 tptp.num)) (= (@ (@ tptp.map_op2490657901765117089it_nat F) (@ tptp.some_num X2)) (@ tptp.some_P2818173045054083285it_nat (@ F X2)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.num tptp.produc3260487557148687353it_nat)) (X2 tptp.num)) (= (@ (@ tptp.map_op7586128837645442720it_nat F) (@ tptp.some_num X2)) (@ tptp.some_P7913643980934408916it_nat (@ F X2)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.num tptp.produc8664842809031399944it_nat)) (X2 tptp.num)) (= (@ (@ tptp.map_op8118133509425879471it_nat F) (@ tptp.some_num X2)) (@ tptp.some_P1914260805536162275it_nat (@ F X2)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)) (X2 tptp.produc7388388658123137530it_nat)) (= (@ (@ tptp.map_op8581638957091552385it_nat F) (@ tptp.some_P2818173045054083285it_nat X2)) (@ tptp.some_P2818173045054083285it_nat (@ F X2)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.produc7388388658123137530it_nat tptp.produc3260487557148687353it_nat)) (X2 tptp.produc7388388658123137530it_nat)) (= (@ (@ tptp.map_op4453737856117102208it_nat F) (@ tptp.some_P2818173045054083285it_nat X2)) (@ tptp.some_P7913643980934408916it_nat (@ F X2)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.produc7388388658123137530it_nat tptp.produc8664842809031399944it_nat)) (X2 tptp.produc7388388658123137530it_nat)) (= (@ (@ tptp.map_op8924890681001947535it_nat F) (@ tptp.some_P2818173045054083285it_nat X2)) (@ tptp.some_P1914260805536162275it_nat (@ F X2)))))
% 8.20/8.65 (assert (forall ((X tptp.option_num) (Y tptp.option_num) (F (-> tptp.num tptp.num)) (G (-> tptp.num tptp.num))) (=> (= X Y) (=> (forall ((A3 tptp.num)) (=> (= Y (@ tptp.some_num A3)) (= (@ F A3) (@ G A3)))) (= (@ (@ tptp.map_option_num_num F) X) (@ (@ tptp.map_option_num_num G) Y))))))
% 8.20/8.65 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))))
% 8.20/8.65 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ tptp.semiri1316708129612266289at_nat Y)))))
% 8.20/8.65 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_Code_integer (@ tptp.semiri4939895301339042750nteger X)) (@ tptp.semiri4939895301339042750nteger Y)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.comp_o9011007105448239796nteger (@ tptp.map_op9146685272036663823nteger F)) (@ tptp.map_op3669829223712506439nteger G)) (@ tptp.map_op9146685272036663823nteger (@ (@ tptp.comp_C1593894019821074884nteger F) G)))))
% 8.20/8.65 (assert (forall ((F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.comp_o7188567781464924208nteger (@ tptp.map_op3563471509957180299nteger F)) (@ tptp.map_op370346339404370627nteger G)) (@ tptp.map_op9146685272036663823nteger (@ (@ tptp.comp_C8797469213163452608nteger F) G)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.int))) (= (@ (@ tptp.comp_o4824269118391204861on_int (@ tptp.map_option_int_nat F)) (@ tptp.map_option_int_int G)) (@ tptp.map_option_int_nat (@ (@ tptp.comp_int_nat_int F) G)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.num tptp.num)) (G (-> tptp.num tptp.num))) (= (@ (@ tptp.comp_o8931257242830428707on_num (@ tptp.map_option_num_num F)) (@ tptp.map_option_num_num G)) (@ tptp.map_option_num_num (@ (@ tptp.comp_num_num_num F) G)))))
% 8.20/8.65 (assert (forall ((G (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (F (-> tptp.code_integer tptp.code_integer)) (V tptp.option_Code_integer)) (= (@ (@ tptp.map_op9146685272036663823nteger G) (@ (@ tptp.map_op3669829223712506439nteger F) V)) (@ (@ tptp.map_op9146685272036663823nteger (@ (@ tptp.comp_C1593894019821074884nteger G) F)) V))))
% 8.20/8.65 (assert (forall ((G (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (F (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (V tptp.option_Code_integer)) (= (@ (@ tptp.map_op3563471509957180299nteger G) (@ (@ tptp.map_op370346339404370627nteger F) V)) (@ (@ tptp.map_op9146685272036663823nteger (@ (@ tptp.comp_C8797469213163452608nteger G) F)) V))))
% 8.20/8.65 (assert (forall ((G (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.int)) (V tptp.option_int)) (= (@ (@ tptp.map_option_int_nat G) (@ (@ tptp.map_option_int_int F) V)) (@ (@ tptp.map_option_int_nat (@ (@ tptp.comp_int_nat_int G) F)) V))))
% 8.20/8.65 (assert (forall ((G (-> tptp.num tptp.num)) (F (-> tptp.num tptp.num)) (V tptp.option_num)) (= (@ (@ tptp.map_option_num_num G) (@ (@ tptp.map_option_num_num F) V)) (@ (@ tptp.map_option_num_num (@ (@ tptp.comp_num_num_num G) F)) V))))
% 8.20/8.65 (assert (forall ((F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer)) (Option tptp.option_Code_integer)) (= (@ (@ tptp.map_op9146685272036663823nteger F) (@ (@ tptp.map_op3669829223712506439nteger G) Option)) (@ (@ tptp.map_op9146685272036663823nteger (@ (@ tptp.comp_C1593894019821074884nteger F) G)) Option))))
% 8.20/8.65 (assert (forall ((F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (Option tptp.option_Code_integer)) (= (@ (@ tptp.map_op3563471509957180299nteger F) (@ (@ tptp.map_op370346339404370627nteger G) Option)) (@ (@ tptp.map_op9146685272036663823nteger (@ (@ tptp.comp_C8797469213163452608nteger F) G)) Option))))
% 8.20/8.65 (assert (forall ((F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.int)) (Option tptp.option_int)) (= (@ (@ tptp.map_option_int_nat F) (@ (@ tptp.map_option_int_int G) Option)) (@ (@ tptp.map_option_int_nat (@ (@ tptp.comp_int_nat_int F) G)) Option))))
% 8.20/8.65 (assert (forall ((F (-> tptp.num tptp.num)) (G (-> tptp.num tptp.num)) (Option tptp.option_num)) (= (@ (@ tptp.map_option_num_num F) (@ (@ tptp.map_option_num_num G) Option)) (@ (@ tptp.map_option_num_num (@ (@ tptp.comp_num_num_num F) G)) Option))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 8.20/8.65 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (and (= A5 (@ (@ tptp.ord_max_rat A5) B4)) (not (= A5 B4))))))
% 8.20/8.65 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A5 tptp.num)) (and (= A5 (@ (@ tptp.ord_max_num A5) B4)) (not (= A5 B4))))))
% 8.20/8.65 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (and (= A5 (@ (@ tptp.ord_max_nat A5) B4)) (not (= A5 B4))))))
% 8.20/8.65 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A5 tptp.int)) (and (= A5 (@ (@ tptp.ord_max_int A5) B4)) (not (= A5 B4))))))
% 8.20/8.65 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat B) C2)) A) (not (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat C2) A)))))))
% 8.20/8.65 (assert (forall ((B tptp.num) (C2 tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num B) C2)) A) (not (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num C2) A)))))))
% 8.20/8.65 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat B) C2)) A) (not (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat C2) A)))))))
% 8.20/8.65 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int B) C2)) A) (not (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int C2) A)))))))
% 8.20/8.65 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 8.20/8.65 (assert (forall ((Z3 tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 8.20/8.65 (assert (forall ((Z3 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 8.20/8.65 (assert (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (assert (= tptp.sup_sup_int tptp.ord_max_int))
% 8.20/8.65 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 8.20/8.65 (assert (= tptp.sup_sup_int tptp.ord_max_int))
% 8.20/8.65 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 8.20/8.65 (assert (forall ((T6 tptp.option_num)) (= (@ (@ tptp.map_option_num_num (lambda ((X4 tptp.num)) X4)) T6) T6)))
% 8.20/8.65 (assert (forall ((C2 tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C2))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 8.20/8.65 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.ord_max_rat A5) B4) B4))))
% 8.20/8.65 (assert (= tptp.ord_less_eq_num (lambda ((A5 tptp.num) (B4 tptp.num)) (= (@ (@ tptp.ord_max_num A5) B4) B4))))
% 8.20/8.65 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A5) B4) B4))))
% 8.20/8.65 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.ord_max_int A5) B4) B4))))
% 8.20/8.65 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (= (@ (@ tptp.ord_max_rat A5) B4) A5))))
% 8.20/8.65 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A5 tptp.num)) (= (@ (@ tptp.ord_max_num A5) B4) A5))))
% 8.20/8.65 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (= (@ (@ tptp.ord_max_nat A5) B4) A5))))
% 8.20/8.65 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (= (@ (@ tptp.ord_max_int A5) B4) A5))))
% 8.20/8.65 (assert (forall ((Z3 tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 8.20/8.65 (assert (forall ((Z3 tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 8.20/8.65 (assert (forall ((Z3 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 8.20/8.65 (assert (forall ((Z3 tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z3))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 8.20/8.65 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat A) B))))
% 8.20/8.65 (assert (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))))
% 8.20/8.65 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))))
% 8.20/8.65 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))))
% 8.20/8.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat A) B))))
% 8.20/8.65 (assert (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))))
% 8.20/8.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))))
% 8.20/8.65 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))))
% 8.20/8.65 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A5 tptp.rat)) (= A5 (@ (@ tptp.ord_max_rat A5) B4)))))
% 8.20/8.65 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A5 tptp.num)) (= A5 (@ (@ tptp.ord_max_num A5) B4)))))
% 8.20/8.65 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A5 tptp.nat)) (= A5 (@ (@ tptp.ord_max_nat A5) B4)))))
% 8.20/8.65 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A5 tptp.int)) (= A5 (@ (@ tptp.ord_max_int A5) B4)))))
% 8.20/8.65 (assert (forall ((B tptp.rat) (A tptp.rat) (C2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C2) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C2)) A)))))
% 8.20/8.65 (assert (forall ((B tptp.num) (A tptp.num) (C2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num C2) A) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C2)) A)))))
% 8.20/8.65 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C2) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C2)) A)))))
% 8.20/8.65 (assert (forall ((B tptp.int) (A tptp.int) (C2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C2) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C2)) A)))))
% 8.20/8.65 (assert (forall ((B tptp.rat) (C2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C2) A)))))))
% 8.20/8.65 (assert (forall ((B tptp.num) (C2 tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_num B) A) (not (@ (@ tptp.ord_less_eq_num C2) A)))))))
% 8.20/8.65 (assert (forall ((B tptp.nat) (C2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C2) A)))))))
% 8.20/8.65 (assert (forall ((B tptp.int) (C2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C2)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C2) A)))))))
% 8.20/8.65 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 8.20/8.65 (assert (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))))
% 8.20/8.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 8.20/8.65 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 8.20/8.65 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat A) B)))))
% 8.20/8.65 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))))
% 8.20/8.65 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))))
% 8.20/8.65 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))))
% 8.20/8.65 (assert (forall ((C2 tptp.rat) (A tptp.rat) (D2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C2) A) (=> (@ (@ tptp.ord_less_eq_rat D2) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C2) D2)) (@ (@ tptp.ord_max_rat A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.num) (A tptp.num) (D2 tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num C2) A) (=> (@ (@ tptp.ord_less_eq_num D2) B) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num C2) D2)) (@ (@ tptp.ord_max_num A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.nat) (A tptp.nat) (D2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) A) (=> (@ (@ tptp.ord_less_eq_nat D2) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C2) D2)) (@ (@ tptp.ord_max_nat A) B))))))
% 8.20/8.65 (assert (forall ((C2 tptp.int) (A tptp.int) (D2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C2) A) (=> (@ (@ tptp.ord_less_eq_int D2) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C2) D2)) (@ (@ tptp.ord_max_int A) B))))))
% 8.20/8.65 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (= (@ (@ tptp.ord_max_set_int X) Y) Y))))
% 8.20/8.65 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.ord_max_rat X) Y) Y))))
% 8.20/8.65 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (@ (@ tptp.ord_max_num X) Y) Y))))
% 8.20/8.65 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.ord_max_nat X) Y) Y))))
% 8.20/8.65 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.ord_max_int X) Y) Y))))
% 8.20/8.65 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (= (@ (@ tptp.ord_max_set_int X) Y) X))))
% 8.20/8.65 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.ord_max_rat X) Y) X))))
% 8.20/8.65 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_max_num X) Y) X))))
% 8.20/8.65 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_max_nat X) Y) X))))
% 8.20/8.65 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_max_int X) Y) X))))
% 8.20/8.65 (assert (= tptp.ord_max_set_int (lambda ((A5 tptp.set_int) (B4 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A5) B4)) B4) A5))))
% 8.20/8.65 (assert (= tptp.ord_max_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A5) B4)) B4) A5))))
% 8.20/8.65 (assert (= tptp.ord_max_num (lambda ((A5 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A5) B4)) B4) A5))))
% 8.20/8.65 (assert (= tptp.ord_max_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A5) B4)) B4) A5))))
% 8.20/8.65 (assert (= tptp.ord_max_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A5) B4)) B4) A5))))
% 8.20/8.65 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y) Z3)) (@ (@ tptp.ord_max_rat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.65 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z3)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.65 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z3)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z3))))))
% 8.20/8.65 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z3 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X) Y)) Z3) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X) Z3)) (@ (@ tptp.plus_plus_rat Y) Z3)))))
% 8.20/8.65 (assert (forall ((X tptp.int) (Y tptp.int) (Z3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y)) Z3) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z3)) (@ (@ tptp.plus_plus_int Y) Z3)))))
% 8.20/8.65 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y)) Z3) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z3)) (@ (@ tptp.plus_plus_nat Y) Z3)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.num tptp.num))) (= (@ (@ tptp.map_option_num_num F) tptp.none_num) tptp.none_num)))
% 8.20/8.65 (assert (= tptp.ord_max_set_int (lambda ((A5 tptp.set_int) (B4 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A5) B4)) B4) A5))))
% 8.20/8.65 (assert (= tptp.ord_max_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A5) B4)) B4) A5))))
% 8.20/8.65 (assert (= tptp.ord_max_num (lambda ((A5 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A5) B4)) B4) A5))))
% 8.20/8.65 (assert (= tptp.ord_max_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A5) B4)) B4) A5))))
% 8.20/8.65 (assert (= tptp.ord_max_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A5) B4)) B4) A5))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr958786334691620121nt_int) (K2 tptp.nat)) (=> (@ tptp.finite2998713641127702882nt_int A4) (= (@ tptp.finite4053189226111446337nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((B6 tptp.set_Pr958786334691620121nt_int)) (and (@ (@ tptp.ord_le2843351958646193337nt_int B6) A4) (= (@ tptp.finite6756421564338198497nt_int B6) K2))))) (@ (@ tptp.binomial (@ tptp.finite6756421564338198497nt_int A4)) K2)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_list_nat) (K2 tptp.nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (= (@ tptp.finite2364142230527598318st_nat (@ tptp.collect_set_list_nat (lambda ((B6 tptp.set_list_nat)) (and (@ (@ tptp.ord_le6045566169113846134st_nat B6) A4) (= (@ tptp.finite_card_list_nat B6) K2))))) (@ (@ tptp.binomial (@ tptp.finite_card_list_nat A4)) K2)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_set_nat) (K2 tptp.nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (= (@ tptp.finite1149291290879098388et_nat (@ tptp.collect_set_set_nat (lambda ((B6 tptp.set_set_nat)) (and (@ (@ tptp.ord_le6893508408891458716et_nat B6) A4) (= (@ tptp.finite_card_set_nat B6) K2))))) (@ (@ tptp.binomial (@ tptp.finite_card_set_nat A4)) K2)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (K2 tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (= (@ tptp.finite_card_set_nat (@ tptp.collect_set_nat (lambda ((B6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B6) A4) (= (@ tptp.finite_card_nat B6) K2))))) (@ (@ tptp.binomial (@ tptp.finite_card_nat A4)) K2)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (K2 tptp.nat)) (=> (@ tptp.finite6017078050557962740nteger A4) (= (@ tptp.finite1340570857867686763nteger (@ tptp.collec574505750873337192nteger (lambda ((B6 tptp.set_Code_integer)) (and (@ (@ tptp.ord_le7084787975880047091nteger B6) A4) (= (@ tptp.finite4902975817058060853nteger B6) K2))))) (@ (@ tptp.binomial (@ tptp.finite4902975817058060853nteger A4)) K2)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (K2 tptp.nat)) (=> (@ tptp.finite6177210948735845034at_nat A4) (= (@ tptp.finite4356350796350151305at_nat (@ tptp.collec5514110066124741708at_nat (lambda ((B6 tptp.set_Pr1261947904930325089at_nat)) (and (@ (@ tptp.ord_le3146513528884898305at_nat B6) A4) (= (@ tptp.finite711546835091564841at_nat B6) K2))))) (@ (@ tptp.binomial (@ tptp.finite711546835091564841at_nat A4)) K2)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (K2 tptp.nat)) (=> (@ tptp.finite_finite_int A4) (= (@ tptp.finite_card_set_int (@ tptp.collect_set_int (lambda ((B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B6) A4) (= (@ tptp.finite_card_int B6) K2))))) (@ (@ tptp.binomial (@ tptp.finite_card_int A4)) K2)))))
% 8.20/8.65 (assert (forall ((G (-> Bool tptp.code_integer)) (I5 tptp.set_o)) (let ((_let_1 (@ tptp.groups1402912129352969042nteger G))) (= (@ _let_1 (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) I5) (not (= (@ G X4) tptp.zero_z3403309356797280102nteger)))))) (@ _let_1 I5)))))
% 8.20/8.65 (assert (forall ((G (-> tptp.nat tptp.code_integer)) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.groups555127423416065298nteger G))) (= (@ _let_1 (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) I5) (not (= (@ G X4) tptp.zero_z3403309356797280102nteger)))))) (@ _let_1 I5)))))
% 8.20/8.65 (assert (forall ((G (-> tptp.int tptp.code_integer)) (I5 tptp.set_int)) (let ((_let_1 (@ tptp.groups926780983652909934nteger G))) (= (@ _let_1 (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) I5) (not (= (@ G X4) tptp.zero_z3403309356797280102nteger)))))) (@ _let_1 I5)))))
% 8.20/8.65 (assert (forall ((G (-> Bool tptp.rat)) (I5 tptp.set_o)) (let ((_let_1 (@ tptp.groups3921277224699582669_o_rat G))) (= (@ _let_1 (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) I5) (not (= (@ G X4) tptp.zero_zero_rat)))))) (@ _let_1 I5)))))
% 8.20/8.65 (assert (forall ((G (-> tptp.nat tptp.rat)) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.groups1351286907653491341at_rat G))) (= (@ _let_1 (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) I5) (not (= (@ G X4) tptp.zero_zero_rat)))))) (@ _let_1 I5)))))
% 8.20/8.65 (assert (forall ((G (-> tptp.int tptp.rat)) (I5 tptp.set_int)) (let ((_let_1 (@ tptp.groups2350640619554545897nt_rat G))) (= (@ _let_1 (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) I5) (not (= (@ G X4) tptp.zero_zero_rat)))))) (@ _let_1 I5)))))
% 8.20/8.65 (assert (forall ((G (-> Bool tptp.nat)) (I5 tptp.set_o)) (let ((_let_1 (@ tptp.groups4556407284786078405_o_nat G))) (= (@ _let_1 (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) I5) (not (= (@ G X4) tptp.zero_zero_nat)))))) (@ _let_1 I5)))))
% 8.20/8.65 (assert (forall ((G (-> tptp.nat tptp.nat)) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.groups1986416967739987077at_nat G))) (= (@ _let_1 (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) I5) (not (= (@ G X4) tptp.zero_zero_nat)))))) (@ _let_1 I5)))))
% 8.20/8.65 (assert (forall ((G (-> tptp.int tptp.nat)) (I5 tptp.set_int)) (let ((_let_1 (@ tptp.groups2985770679641041633nt_nat G))) (= (@ _let_1 (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) I5) (not (= (@ G X4) tptp.zero_zero_nat)))))) (@ _let_1 I5)))))
% 8.20/8.65 (assert (forall ((G (-> Bool tptp.int)) (I5 tptp.set_o)) (let ((_let_1 (@ tptp.groups4553916814277028129_o_int G))) (= (@ _let_1 (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) I5) (not (= (@ G X4) tptp.zero_zero_int)))))) (@ _let_1 I5)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.int))) (= (@ (@ tptp.comp_o5073597352248849069on_int (@ tptp.size_option_int F)) (@ tptp.map_option_int_int G)) (@ tptp.size_option_int (@ (@ tptp.comp_int_nat_int F) G)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.num tptp.nat)) (G (-> tptp.num tptp.num))) (= (@ (@ tptp.comp_o6878144249584144265on_num (@ tptp.size_option_num F)) (@ tptp.map_option_num_num G)) (@ tptp.size_option_num (@ (@ tptp.comp_num_nat_num F) G)))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_list_nat) (A4 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B5) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A4) B5) (=> (= (@ tptp.finite_card_list_nat A4) (@ tptp.finite_card_list_nat B5)) (= A4 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_set_nat) (A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B5) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A4) B5) (=> (= (@ tptp.finite_card_set_nat A4) (@ tptp.finite_card_set_nat B5)) (= A4 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (= (@ tptp.finite_card_nat A4) (@ tptp.finite_card_nat B5)) (= A4 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (=> (= (@ tptp.finite4902975817058060853nteger A4) (@ tptp.finite4902975817058060853nteger B5)) (= A4 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5) (=> (= (@ tptp.finite711546835091564841at_nat A4) (@ tptp.finite711546835091564841at_nat B5)) (= A4 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int)) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (= (@ tptp.finite_card_int A4) (@ tptp.finite_card_int B5)) (= A4 B5))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_list_nat) (N2 tptp.nat)) (=> (not (@ tptp.finite8100373058378681591st_nat A4)) (exists ((B9 tptp.set_list_nat)) (and (@ tptp.finite8100373058378681591st_nat B9) (= (@ tptp.finite_card_list_nat B9) N2) (@ (@ tptp.ord_le6045566169113846134st_nat B9) A4))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_set_nat) (N2 tptp.nat)) (=> (not (@ tptp.finite1152437895449049373et_nat A4)) (exists ((B9 tptp.set_set_nat)) (and (@ tptp.finite1152437895449049373et_nat B9) (= (@ tptp.finite_card_set_nat B9) N2) (@ (@ tptp.ord_le6893508408891458716et_nat B9) A4))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (N2 tptp.nat)) (=> (not (@ tptp.finite_finite_nat A4)) (exists ((B9 tptp.set_nat)) (and (@ tptp.finite_finite_nat B9) (= (@ tptp.finite_card_nat B9) N2) (@ (@ tptp.ord_less_eq_set_nat B9) A4))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (N2 tptp.nat)) (=> (not (@ tptp.finite6017078050557962740nteger A4)) (exists ((B9 tptp.set_Code_integer)) (and (@ tptp.finite6017078050557962740nteger B9) (= (@ tptp.finite4902975817058060853nteger B9) N2) (@ (@ tptp.ord_le7084787975880047091nteger B9) A4))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (N2 tptp.nat)) (=> (not (@ tptp.finite6177210948735845034at_nat A4)) (exists ((B9 tptp.set_Pr1261947904930325089at_nat)) (and (@ tptp.finite6177210948735845034at_nat B9) (= (@ tptp.finite711546835091564841at_nat B9) N2) (@ (@ tptp.ord_le3146513528884898305at_nat B9) A4))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (N2 tptp.nat)) (=> (not (@ tptp.finite_finite_int A4)) (exists ((B9 tptp.set_int)) (and (@ tptp.finite_finite_int B9) (= (@ tptp.finite_card_int B9) N2) (@ (@ tptp.ord_less_eq_set_int B9) A4))))))
% 8.20/8.65 (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))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_o) (R2 (-> Bool Bool Bool))) (=> (@ tptp.finite_finite_o B5) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) A4) (exists ((B11 Bool)) (and (@ (@ tptp.member_o B11) B5) (@ (@ R2 A3) B11))))) (=> (forall ((A13 Bool) (A24 Bool) (B3 Bool)) (=> (@ (@ tptp.member_o A13) A4) (=> (@ (@ tptp.member_o A24) A4) (=> (@ (@ tptp.member_o B3) B5) (=> (@ (@ R2 A13) B3) (=> (@ (@ R2 A24) B3) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A4)) (@ tptp.finite_card_o B5)))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_nat) (R2 (-> tptp.nat Bool Bool))) (=> (@ tptp.finite_finite_o B5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (exists ((B11 Bool)) (and (@ (@ tptp.member_o B11) B5) (@ (@ R2 A3) B11))))) (=> (forall ((A13 tptp.nat) (A24 tptp.nat) (B3 Bool)) (=> (@ (@ tptp.member_nat A13) A4) (=> (@ (@ tptp.member_nat A24) A4) (=> (@ (@ tptp.member_o B3) B5) (=> (@ (@ R2 A13) B3) (=> (@ (@ R2 A24) B3) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_o B5)))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_o) (A4 tptp.set_int) (R2 (-> tptp.int Bool Bool))) (=> (@ tptp.finite_finite_o B5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (exists ((B11 Bool)) (and (@ (@ tptp.member_o B11) B5) (@ (@ R2 A3) B11))))) (=> (forall ((A13 tptp.int) (A24 tptp.int) (B3 Bool)) (=> (@ (@ tptp.member_int A13) A4) (=> (@ (@ tptp.member_int A24) A4) (=> (@ (@ tptp.member_o B3) B5) (=> (@ (@ R2 A13) B3) (=> (@ (@ R2 A24) B3) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_o B5)))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_o) (R2 (-> Bool tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) A4) (exists ((B11 tptp.nat)) (and (@ (@ tptp.member_nat B11) B5) (@ (@ R2 A3) B11))))) (=> (forall ((A13 Bool) (A24 Bool) (B3 tptp.nat)) (=> (@ (@ tptp.member_o A13) A4) (=> (@ (@ tptp.member_o A24) A4) (=> (@ (@ tptp.member_nat B3) B5) (=> (@ (@ R2 A13) B3) (=> (@ (@ R2 A24) B3) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A4)) (@ tptp.finite_card_nat B5)))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat) (R2 (-> tptp.nat tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (exists ((B11 tptp.nat)) (and (@ (@ tptp.member_nat B11) B5) (@ (@ R2 A3) B11))))) (=> (forall ((A13 tptp.nat) (A24 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.member_nat A13) A4) (=> (@ (@ tptp.member_nat A24) A4) (=> (@ (@ tptp.member_nat B3) B5) (=> (@ (@ R2 A13) B3) (=> (@ (@ R2 A24) B3) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5)))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_int) (R2 (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (exists ((B11 tptp.nat)) (and (@ (@ tptp.member_nat B11) B5) (@ (@ R2 A3) B11))))) (=> (forall ((A13 tptp.int) (A24 tptp.int) (B3 tptp.nat)) (=> (@ (@ tptp.member_int A13) A4) (=> (@ (@ tptp.member_int A24) A4) (=> (@ (@ tptp.member_nat B3) B5) (=> (@ (@ R2 A13) B3) (=> (@ (@ R2 A24) B3) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_nat B5)))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_o) (R2 (-> Bool tptp.int Bool))) (=> (@ tptp.finite_finite_int B5) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) A4) (exists ((B11 tptp.int)) (and (@ (@ tptp.member_int B11) B5) (@ (@ R2 A3) B11))))) (=> (forall ((A13 Bool) (A24 Bool) (B3 tptp.int)) (=> (@ (@ tptp.member_o A13) A4) (=> (@ (@ tptp.member_o A24) A4) (=> (@ (@ tptp.member_int B3) B5) (=> (@ (@ R2 A13) B3) (=> (@ (@ R2 A24) B3) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A4)) (@ tptp.finite_card_int B5)))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_nat) (R2 (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_int B5) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A4) (exists ((B11 tptp.int)) (and (@ (@ tptp.member_int B11) B5) (@ (@ R2 A3) B11))))) (=> (forall ((A13 tptp.nat) (A24 tptp.nat) (B3 tptp.int)) (=> (@ (@ tptp.member_nat A13) A4) (=> (@ (@ tptp.member_nat A24) A4) (=> (@ (@ tptp.member_int B3) B5) (=> (@ (@ R2 A13) B3) (=> (@ (@ R2 A24) B3) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_int B5)))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int) (R2 (-> tptp.int tptp.int Bool))) (=> (@ tptp.finite_finite_int B5) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) A4) (exists ((B11 tptp.int)) (and (@ (@ tptp.member_int B11) B5) (@ (@ R2 A3) B11))))) (=> (forall ((A13 tptp.int) (A24 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.member_int A13) A4) (=> (@ (@ tptp.member_int A24) A4) (=> (@ (@ tptp.member_int B3) B5) (=> (@ (@ R2 A13) B3) (=> (@ (@ R2 A24) B3) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int B5)))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_o) (R2 (-> Bool tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (forall ((A3 Bool)) (=> (@ (@ tptp.member_o A3) A4) (exists ((B11 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer B11) B5) (@ (@ R2 A3) B11))))) (=> (forall ((A13 Bool) (A24 Bool) (B3 tptp.code_integer)) (=> (@ (@ tptp.member_o A13) A4) (=> (@ (@ tptp.member_o A24) A4) (=> (@ (@ tptp.member_Code_integer B3) B5) (=> (@ (@ R2 A13) B3) (=> (@ (@ R2 A24) B3) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A4)) (@ tptp.finite4902975817058060853nteger B5)))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (X tptp.produc3843707927480180839at_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite3771342082235030671at_nat A4)) (@ tptp.finite3771342082235030671at_nat (@ (@ tptp.insert9069300056098147895at_nat X) A4)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat A4)) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.insert8211810215607154385at_nat X) A4)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_o) (X Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A4)) (@ tptp.finite_card_o (@ (@ tptp.insert_o X) A4)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) A4)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int (@ (@ tptp.insert_int X) A4)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_list_nat) (X tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat (@ (@ tptp.insert_list_nat X) A4)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat (@ (@ tptp.insert_set_nat X) A4)))))
% 8.20/8.65 (assert (forall ((S2 tptp.set_o) (T6 tptp.set_o) (R3 (-> Bool Bool Bool)) (K2 (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o S2) (=> (@ tptp.finite_finite_o T6) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) T6) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) S2) (@ (@ R3 I) X3))))) (@ K2 X3)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I Bool)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J Bool)) (and (@ (@ tptp.member_o J) T6) (@ (@ R3 I) J))))))) S2) (@ (@ tptp.groups8507830703676809646_o_nat K2) T6)))))))
% 8.20/8.65 (assert (forall ((S2 tptp.set_o) (T6 tptp.set_int) (R3 (-> Bool tptp.int Bool)) (K2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_o S2) (=> (@ tptp.finite_finite_int T6) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T6) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) S2) (@ (@ R3 I) X3))))) (@ K2 X3)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I Bool)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J tptp.int)) (and (@ (@ tptp.member_int J) T6) (@ (@ R3 I) J))))))) S2) (@ (@ tptp.groups4541462559716669496nt_nat K2) T6)))))))
% 8.20/8.65 (assert (forall ((S2 tptp.set_o) (T6 tptp.set_Code_integer) (R3 (-> Bool tptp.code_integer Bool)) (K2 (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite_finite_o S2) (=> (@ tptp.finite6017078050557962740nteger T6) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T6) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) S2) (@ (@ R3 I) X3))))) (@ K2 X3)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I Bool)) (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((J tptp.code_integer)) (and (@ (@ tptp.member_Code_integer J) T6) (@ (@ R3 I) J))))))) S2) (@ (@ tptp.groups7237345082560585321er_nat K2) T6)))))))
% 8.20/8.65 (assert (forall ((S2 tptp.set_int) (T6 tptp.set_o) (R3 (-> tptp.int Bool Bool)) (K2 (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_o T6) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) T6) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) S2) (@ (@ R3 I) X3))))) (@ K2 X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I tptp.int)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J Bool)) (and (@ (@ tptp.member_o J) T6) (@ (@ R3 I) J))))))) S2) (@ (@ tptp.groups8507830703676809646_o_nat K2) T6)))))))
% 8.20/8.65 (assert (forall ((S2 tptp.set_int) (T6 tptp.set_int) (R3 (-> tptp.int tptp.int Bool)) (K2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_int T6) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T6) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) S2) (@ (@ R3 I) X3))))) (@ K2 X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I tptp.int)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J tptp.int)) (and (@ (@ tptp.member_int J) T6) (@ (@ R3 I) J))))))) S2) (@ (@ tptp.groups4541462559716669496nt_nat K2) T6)))))))
% 8.20/8.65 (assert (forall ((S2 tptp.set_int) (T6 tptp.set_Code_integer) (R3 (-> tptp.int tptp.code_integer Bool)) (K2 (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite6017078050557962740nteger T6) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T6) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) S2) (@ (@ R3 I) X3))))) (@ K2 X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I tptp.int)) (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((J tptp.code_integer)) (and (@ (@ tptp.member_Code_integer J) T6) (@ (@ R3 I) J))))))) S2) (@ (@ tptp.groups7237345082560585321er_nat K2) T6)))))))
% 8.20/8.65 (assert (forall ((S2 tptp.set_Code_integer) (T6 tptp.set_o) (R3 (-> tptp.code_integer Bool Bool)) (K2 (-> Bool tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (@ tptp.finite_finite_o T6) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) T6) (= (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) S2) (@ (@ R3 I) X3))))) (@ K2 X3)))) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((I tptp.code_integer)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J Bool)) (and (@ (@ tptp.member_o J) T6) (@ (@ R3 I) J))))))) S2) (@ (@ tptp.groups8507830703676809646_o_nat K2) T6)))))))
% 8.20/8.65 (assert (forall ((S2 tptp.set_Code_integer) (T6 tptp.set_int) (R3 (-> tptp.code_integer tptp.int Bool)) (K2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (@ tptp.finite_finite_int T6) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T6) (= (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) S2) (@ (@ R3 I) X3))))) (@ K2 X3)))) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((I tptp.code_integer)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J tptp.int)) (and (@ (@ tptp.member_int J) T6) (@ (@ R3 I) J))))))) S2) (@ (@ tptp.groups4541462559716669496nt_nat K2) T6)))))))
% 8.20/8.65 (assert (forall ((S2 tptp.set_Code_integer) (T6 tptp.set_Code_integer) (R3 (-> tptp.code_integer tptp.code_integer Bool)) (K2 (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (@ tptp.finite6017078050557962740nteger T6) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T6) (= (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) S2) (@ (@ R3 I) X3))))) (@ K2 X3)))) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((I tptp.code_integer)) (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((J tptp.code_integer)) (and (@ (@ tptp.member_Code_integer J) T6) (@ (@ R3 I) J))))))) S2) (@ (@ tptp.groups7237345082560585321er_nat K2) T6)))))))
% 8.20/8.65 (assert (forall ((S2 tptp.set_o) (T6 tptp.set_nat) (R3 (-> Bool tptp.nat Bool)) (K2 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_o S2) (=> (@ tptp.finite_finite_nat T6) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T6) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) S2) (@ (@ R3 I) X3))))) (@ K2 X3)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I Bool)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J tptp.nat)) (and (@ (@ tptp.member_nat J) T6) (@ (@ R3 I) J))))))) S2) (@ (@ tptp.groups3542108847815614940at_nat K2) T6)))))))
% 8.20/8.65 (assert (= tptp.finite_card_int (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) tptp.one_one_nat))))
% 8.20/8.65 (assert (= tptp.finite_card_list_nat (@ tptp.groups4396056296759096172at_nat (lambda ((X4 tptp.list_nat)) tptp.one_one_nat))))
% 8.20/8.65 (assert (= tptp.finite_card_set_nat (@ tptp.groups8294997508430121362at_nat (lambda ((X4 tptp.set_nat)) tptp.one_one_nat))))
% 8.20/8.65 (assert (= tptp.finite_card_nat (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) tptp.one_one_nat))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (H (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I5) (= (@ (@ tptp.groups1351286907653491341at_rat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_rat (@ G I)) (@ H I)))) I5) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups1351286907653491341at_rat G) I5)) (@ (@ tptp.groups1351286907653491341at_rat H) I5))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_int) (G (-> tptp.int tptp.rat)) (H (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int I5) (= (@ (@ tptp.groups2350640619554545897nt_rat (lambda ((I tptp.int)) (@ (@ tptp.plus_plus_rat (@ G I)) (@ H I)))) I5) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2350640619554545897nt_rat G) I5)) (@ (@ tptp.groups2350640619554545897nt_rat H) I5))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (H (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger I5) (= (@ (@ tptp.groups8878813951405302554er_rat (lambda ((I tptp.code_integer)) (@ (@ tptp.plus_plus_rat (@ G I)) (@ H I)))) I5) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups8878813951405302554er_rat G) I5)) (@ (@ tptp.groups8878813951405302554er_rat H) I5))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat I5) (= (@ (@ tptp.groups1986416967739987077at_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G I)) (@ H I)))) I5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups1986416967739987077at_nat G) I5)) (@ (@ tptp.groups1986416967739987077at_nat H) I5))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_int) (G (-> tptp.int tptp.nat)) (H (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int I5) (= (@ (@ tptp.groups2985770679641041633nt_nat (lambda ((I tptp.int)) (@ (@ tptp.plus_plus_nat (@ G I)) (@ H I)))) I5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups2985770679641041633nt_nat G) I5)) (@ (@ tptp.groups2985770679641041633nt_nat H) I5))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (H (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger I5) (= (@ (@ tptp.groups290571974637022482er_nat (lambda ((I tptp.code_integer)) (@ (@ tptp.plus_plus_nat (@ G I)) (@ H I)))) I5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups290571974637022482er_nat G) I5)) (@ (@ tptp.groups290571974637022482er_nat H) I5))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_nat) (G (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat I5) (= (@ (@ tptp.groups1983926497230936801at_int (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_int (@ G I)) (@ H I)))) I5) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups1983926497230936801at_int G) I5)) (@ (@ tptp.groups1983926497230936801at_int H) I5))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_int) (G (-> tptp.int tptp.int)) (H (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int I5) (= (@ (@ tptp.groups2983280209131991357nt_int (lambda ((I tptp.int)) (@ (@ tptp.plus_plus_int (@ G I)) (@ H I)))) I5) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups2983280209131991357nt_int G) I5)) (@ (@ tptp.groups2983280209131991357nt_int H) I5))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int)) (H (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger I5) (= (@ (@ tptp.groups288081504127972206er_int (lambda ((I tptp.code_integer)) (@ (@ tptp.plus_plus_int (@ G I)) (@ H I)))) I5) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups288081504127972206er_int G) I5)) (@ (@ tptp.groups288081504127972206er_int H) I5))))))
% 8.20/8.65 (assert (forall ((I5 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.rat)) (H (-> tptp.product_prod_nat_nat tptp.rat))) (=> (@ tptp.finite6177210948735845034at_nat I5) (= (@ (@ tptp.groups3328076802468863542at_rat (lambda ((I tptp.product_prod_nat_nat)) (@ (@ tptp.plus_plus_rat (@ G I)) (@ H I)))) I5) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups3328076802468863542at_rat G) I5)) (@ (@ tptp.groups3328076802468863542at_rat H) I5))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_list_nat A4)) (@ tptp.finite8100373058378681591st_nat A4))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_set_nat A4)) (@ tptp.finite1152437895449049373et_nat A4))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat A4)) (@ tptp.finite_finite_nat A4))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_int A4)) (@ tptp.finite_finite_int A4))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite4902975817058060853nteger A4)) (@ tptp.finite6017078050557962740nteger A4))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite711546835091564841at_nat A4)) (@ tptp.finite6177210948735845034at_nat A4))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_list_nat) (C4 tptp.nat)) (=> (forall ((G5 tptp.set_list_nat)) (=> (@ (@ tptp.ord_le6045566169113846134st_nat G5) F5) (=> (@ tptp.finite8100373058378681591st_nat G5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat G5)) C4)))) (and (@ tptp.finite8100373058378681591st_nat F5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat F5)) C4)))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_set_nat) (C4 tptp.nat)) (=> (forall ((G5 tptp.set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat G5) F5) (=> (@ tptp.finite1152437895449049373et_nat G5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat G5)) C4)))) (and (@ tptp.finite1152437895449049373et_nat F5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat F5)) C4)))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_nat) (C4 tptp.nat)) (=> (forall ((G5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat G5) F5) (=> (@ tptp.finite_finite_nat G5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat G5)) C4)))) (and (@ tptp.finite_finite_nat F5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat F5)) C4)))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Code_integer) (C4 tptp.nat)) (=> (forall ((G5 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger G5) F5) (=> (@ tptp.finite6017078050557962740nteger G5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite4902975817058060853nteger G5)) C4)))) (and (@ tptp.finite6017078050557962740nteger F5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite4902975817058060853nteger F5)) C4)))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_Pr1261947904930325089at_nat) (C4 tptp.nat)) (=> (forall ((G5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat G5) F5) (=> (@ tptp.finite6177210948735845034at_nat G5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat G5)) C4)))) (and (@ tptp.finite6177210948735845034at_nat F5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat F5)) C4)))))
% 8.20/8.65 (assert (forall ((F5 tptp.set_int) (C4 tptp.nat)) (=> (forall ((G5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int G5) F5) (=> (@ tptp.finite_finite_int G5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int G5)) C4)))) (and (@ tptp.finite_finite_int F5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int F5)) C4)))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_list_nat) (A4 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B5) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat B5)) (@ tptp.finite_card_list_nat A4)) (= A4 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_set_nat) (A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B5) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat B5)) (@ tptp.finite_card_set_nat A4)) (= A4 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat B5)) (@ tptp.finite_card_nat A4)) (= A4 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite4902975817058060853nteger B5)) (@ tptp.finite4902975817058060853nteger A4)) (= A4 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat B5)) (@ tptp.finite711546835091564841at_nat A4)) (= A4 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int)) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int B5)) (@ tptp.finite_card_int A4)) (= A4 B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_list_nat) (A4 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B5) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_set_nat) (A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B5) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite4902975817058060853nteger A4)) (@ tptp.finite4902975817058060853nteger B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat A4)) (@ tptp.finite711546835091564841at_nat B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int)) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_set_int A4) B5) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int B5))))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat) (S tptp.set_list_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite_card_list_nat S)) (not (forall ((T8 tptp.set_list_nat)) (=> (@ (@ tptp.ord_le6045566169113846134st_nat T8) S) (=> (= (@ tptp.finite_card_list_nat T8) N2) (not (@ tptp.finite8100373058378681591st_nat T8)))))))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat) (S tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite_card_set_nat S)) (not (forall ((T8 tptp.set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat T8) S) (=> (= (@ tptp.finite_card_set_nat T8) N2) (not (@ tptp.finite1152437895449049373et_nat T8)))))))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat) (S tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite_card_nat S)) (not (forall ((T8 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat T8) S) (=> (= (@ tptp.finite_card_nat T8) N2) (not (@ tptp.finite_finite_nat T8)))))))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat) (S tptp.set_Code_integer)) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite4902975817058060853nteger S)) (not (forall ((T8 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger T8) S) (=> (= (@ tptp.finite4902975817058060853nteger T8) N2) (not (@ tptp.finite6017078050557962740nteger T8)))))))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat) (S tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite711546835091564841at_nat S)) (not (forall ((T8 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat T8) S) (=> (= (@ tptp.finite711546835091564841at_nat T8) N2) (not (@ tptp.finite6177210948735845034at_nat T8)))))))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat) (S tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite_card_int S)) (not (forall ((T8 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int T8) S) (=> (= (@ tptp.finite_card_int T8) N2) (not (@ tptp.finite_finite_int T8)))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_list_nat) (B5 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (=> (@ tptp.finite8100373058378681591st_nat B5) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat B5)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A4) B5))) (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat B5) A4))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ tptp.finite1152437895449049373et_nat B5) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat B5)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) B5))) (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat B5) A4))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat B5) A4))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int B5)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A4) B5))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int B5) A4))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite4902975817058060853nteger A4)) (@ tptp.finite4902975817058060853nteger B5)) (@ (@ tptp.ord_less_nat (@ tptp.finite4902975817058060853nteger (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ tptp.finite4902975817058060853nteger (@ (@ tptp.minus_2355218937544613996nteger B5) A4))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat A4)) (@ tptp.finite711546835091564841at_nat B5)) (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) B5))) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat B5) A4))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_list_nat) (B5 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A4) (=> (@ tptp.finite8100373058378681591st_nat B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A4) B5))) (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat B5) A4))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ tptp.finite1152437895449049373et_nat B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A4) B5))) (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat B5) A4))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A4) B5))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat B5) A4))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A4) B5))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int B5) A4))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Code_integer) (B5 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A4) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite4902975817058060853nteger A4)) (@ tptp.finite4902975817058060853nteger B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite4902975817058060853nteger (@ (@ tptp.minus_2355218937544613996nteger A4) B5))) (@ tptp.finite4902975817058060853nteger (@ (@ tptp.minus_2355218937544613996nteger B5) A4))))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A4) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat A4)) (@ tptp.finite711546835091564841at_nat B5)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) B5))) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat B5) A4))))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_list_nat) (A4 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B5) (=> (@ (@ tptp.ord_le1190675801316882794st_nat A4) B5) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_set_nat) (A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B5) (=> (@ (@ tptp.ord_less_set_set_nat A4) B5) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_nat) (A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B5) (=> (@ (@ tptp.ord_less_set_nat A4) B5) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_int) (A4 tptp.set_int)) (=> (@ tptp.finite_finite_int B5) (=> (@ (@ tptp.ord_less_set_int A4) B5) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Code_integer) (A4 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger B5) (=> (@ (@ tptp.ord_le1307284697595431911nteger A4) B5) (@ (@ tptp.ord_less_nat (@ tptp.finite4902975817058060853nteger A4)) (@ tptp.finite4902975817058060853nteger B5))))))
% 8.20/8.65 (assert (forall ((B5 tptp.set_Pr1261947904930325089at_nat) (A4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B5) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A4) B5) (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat A4)) (@ tptp.finite711546835091564841at_nat B5))))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_int) (B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.sup_sup_set_int A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_int A4)) (@ tptp.finite_card_int B5)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_list_nat) (B5 tptp.set_list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.sup_sup_set_list_nat A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat A4)) (@ tptp.finite_card_list_nat B5)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_set_nat) (B5 tptp.set_set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.sup_sup_set_set_nat A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_set_nat A4)) (@ tptp.finite_card_set_nat B5)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite7007076676225009423at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite7007076676225009423at_nat A4)) (@ tptp.finite7007076676225009423at_nat B5)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite3771342082235030671at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite3771342082235030671at_nat A4)) (@ tptp.finite3771342082235030671at_nat B5)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.sup_sup_set_nat A4) B5))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_nat A4)) (@ tptp.finite_card_nat B5)))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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))))))))))
% 8.20/8.65 (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))))))))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K2) (@ (@ tptp.plus_plus_nat K2) (@ tptp.finite_card_nat A4))))) (=> (@ (@ tptp.ord_less_eq_set_nat A4) _let_1) (= A4 _let_1)))))
% 8.20/8.65 (assert (@ (@ (@ tptp.lattic5374021519246970238et_rat tptp.ord_max_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))))
% 8.20/8.65 (assert (@ (@ (@ tptp.lattic2566483365489244608et_num tptp.ord_max_num) (lambda ((X4 tptp.num) (Y4 tptp.num)) (@ (@ tptp.ord_less_eq_num Y4) X4))) (lambda ((X4 tptp.num) (Y4 tptp.num)) (@ (@ tptp.ord_less_num Y4) X4))))
% 8.20/8.65 (assert (@ (@ (@ tptp.lattic6009151579333465974et_nat tptp.ord_max_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))))
% 8.20/8.65 (assert (@ (@ (@ tptp.lattic6006661108824415698et_int tptp.ord_max_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))))
% 8.20/8.65 (assert (forall ((F (-> tptp.int tptp.nat)) (A4 tptp.set_int)) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ tptp.suc (@ F X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A4)) (@ tptp.finite_card_int A4)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.list_nat tptp.nat)) (A4 tptp.set_list_nat)) (= (@ (@ tptp.groups4396056296759096172at_nat (lambda ((X4 tptp.list_nat)) (@ tptp.suc (@ F X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups4396056296759096172at_nat F) A4)) (@ tptp.finite_card_list_nat A4)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.set_nat tptp.nat)) (A4 tptp.set_set_nat)) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X4 tptp.set_nat)) (@ tptp.suc (@ F X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups8294997508430121362at_nat F) A4)) (@ tptp.finite_card_set_nat A4)))))
% 8.20/8.65 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ tptp.suc (@ F X4)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ tptp.finite_card_nat A4)))))
% 8.20/8.65 (assert (forall ((S tptp.set_o) (T7 tptp.set_o) (R3 (-> Bool Bool Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite_finite_o T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) T7) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) S) (@ (@ R3 I) X3))))) K2))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I Bool)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J Bool)) (and (@ (@ tptp.member_o J) T7) (@ (@ R3 I) J))))))) S) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_o T7))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_o) (T7 tptp.set_nat) (R3 (-> Bool tptp.nat Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite_finite_nat T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T7) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) S) (@ (@ R3 I) X3))))) K2))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I Bool)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J tptp.nat)) (and (@ (@ tptp.member_nat J) T7) (@ (@ R3 I) J))))))) S) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_nat T7))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_o) (T7 tptp.set_int) (R3 (-> Bool tptp.int Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite_finite_int T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T7) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) S) (@ (@ R3 I) X3))))) K2))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I Bool)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J tptp.int)) (and (@ (@ tptp.member_int J) T7) (@ (@ R3 I) J))))))) S) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_int T7))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_o) (T7 tptp.set_Code_integer) (R3 (-> Bool tptp.code_integer Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T7) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I Bool)) (and (@ (@ tptp.member_o I) S) (@ (@ R3 I) X3))))) K2))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I Bool)) (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((J tptp.code_integer)) (and (@ (@ tptp.member_Code_integer J) T7) (@ (@ R3 I) J))))))) S) (@ (@ tptp.times_times_nat K2) (@ tptp.finite4902975817058060853nteger T7))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_o) (R3 (-> tptp.int Bool Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_o T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) T7) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) S) (@ (@ R3 I) X3))))) K2))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I tptp.int)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J Bool)) (and (@ (@ tptp.member_o J) T7) (@ (@ R3 I) J))))))) S) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_o T7))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_nat) (R3 (-> tptp.int tptp.nat Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_nat T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T7) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) S) (@ (@ R3 I) X3))))) K2))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I tptp.int)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J tptp.nat)) (and (@ (@ tptp.member_nat J) T7) (@ (@ R3 I) J))))))) S) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_nat T7))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (R3 (-> tptp.int tptp.int Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_int T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T7) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) S) (@ (@ R3 I) X3))))) K2))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I tptp.int)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J tptp.int)) (and (@ (@ tptp.member_int J) T7) (@ (@ R3 I) J))))))) S) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_int T7))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_Code_integer) (R3 (-> tptp.int tptp.code_integer Bool)) (K2 tptp.nat)) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite6017078050557962740nteger T7) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T7) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I tptp.int)) (and (@ (@ tptp.member_int I) S) (@ (@ R3 I) X3))))) K2))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I tptp.int)) (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((J tptp.code_integer)) (and (@ (@ tptp.member_Code_integer J) T7) (@ (@ R3 I) J))))))) S) (@ (@ tptp.times_times_nat K2) (@ tptp.finite4902975817058060853nteger T7))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Code_integer) (T7 tptp.set_o) (R3 (-> tptp.code_integer Bool Bool)) (K2 tptp.nat)) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ tptp.finite_finite_o T7) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) T7) (= (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) S) (@ (@ R3 I) X3))))) K2))) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((I tptp.code_integer)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J Bool)) (and (@ (@ tptp.member_o J) T7) (@ (@ R3 I) J))))))) S) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_o T7))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Code_integer) (T7 tptp.set_nat) (R3 (-> tptp.code_integer tptp.nat Bool)) (K2 tptp.nat)) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ tptp.finite_finite_nat T7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T7) (= (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((I tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I) S) (@ (@ R3 I) X3))))) K2))) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((I tptp.code_integer)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J tptp.nat)) (and (@ (@ tptp.member_nat J) T7) (@ (@ R3 I) J))))))) S) (@ (@ tptp.times_times_nat K2) (@ tptp.finite_card_nat T7))))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3803682039294397627nteger G))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) T7) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ (@ tptp.minus_1356011639430497352at_nat T7) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 S) (@ _let_1 T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.multis2468970476368604999at_nat))) (let ((_let_1 (@ tptp.groups8361914993108267113at_nat G))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) T7) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ (@ tptp.minus_1356011639430497352at_nat T7) S)) (= (@ G X3) tptp.zero_z1048942125864253310at_nat))) (= (@ _let_1 S) (@ _let_1 T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups3328076802468863542at_rat G))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) T7) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ (@ tptp.minus_1356011639430497352at_nat T7) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S) (@ _let_1 T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.nat))) (let ((_let_1 (@ tptp.groups3963206862555359278at_nat G))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) T7) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ (@ tptp.minus_1356011639430497352at_nat T7) S)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 S) (@ _let_1 T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.int))) (let ((_let_1 (@ tptp.groups3960716392046309002at_int G))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) T7) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ (@ tptp.minus_1356011639430497352at_nat T7) S)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 S) (@ _let_1 T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups926780983652909934nteger G))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 S) (@ _let_1 T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (G (-> tptp.int tptp.multis2468970476368604999at_nat))) (let ((_let_1 (@ tptp.groups6906599089918680438at_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_z1048942125864253310at_nat))) (= (@ _let_1 S) (@ _let_1 T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups2350640619554545897nt_rat G))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S) (@ _let_1 T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups2985770679641041633nt_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 S) (@ _let_1 T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups2983280209131991357nt_int G))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 S) (@ _let_1 T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3803682039294397627nteger G))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) T7) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ (@ tptp.minus_1356011639430497352at_nat T7) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 T7) (@ _let_1 S)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.multis2468970476368604999at_nat))) (let ((_let_1 (@ tptp.groups8361914993108267113at_nat G))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) T7) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ (@ tptp.minus_1356011639430497352at_nat T7) S)) (= (@ G X3) tptp.zero_z1048942125864253310at_nat))) (= (@ _let_1 T7) (@ _let_1 S)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups3328076802468863542at_rat G))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) T7) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ (@ tptp.minus_1356011639430497352at_nat T7) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T7) (@ _let_1 S)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.nat))) (let ((_let_1 (@ tptp.groups3963206862555359278at_nat G))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) T7) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ (@ tptp.minus_1356011639430497352at_nat T7) S)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 T7) (@ _let_1 S)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T7 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.int))) (let ((_let_1 (@ tptp.groups3960716392046309002at_int G))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) T7) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ (@ tptp.minus_1356011639430497352at_nat T7) S)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 T7) (@ _let_1 S)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups926780983652909934nteger G))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 T7) (@ _let_1 S)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (G (-> tptp.int tptp.multis2468970476368604999at_nat))) (let ((_let_1 (@ tptp.groups6906599089918680438at_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_z1048942125864253310at_nat))) (= (@ _let_1 T7) (@ _let_1 S)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups2350640619554545897nt_rat G))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T7) (@ _let_1 S)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups2985770679641041633nt_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 T7) (@ _let_1 S)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups2983280209131991357nt_int G))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 T7) (@ _let_1 S)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_o) (T7 tptp.set_o) (H (-> Bool tptp.code_integer)) (G (-> Bool tptp.code_integer))) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o T7) S)) (= (@ H I3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups1402912129352969042nteger G) S) (@ (@ tptp.groups1402912129352969042nteger H) T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_nat) (T7 tptp.set_nat) (H (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ H I3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups555127423416065298nteger G) S) (@ (@ tptp.groups555127423416065298nteger H) T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_o) (T7 tptp.set_o) (H (-> Bool tptp.rat)) (G (-> Bool tptp.rat))) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o T7) S)) (= (@ H I3) tptp.zero_zero_rat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3921277224699582669_o_rat G) S) (@ (@ tptp.groups3921277224699582669_o_rat H) T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_nat) (T7 tptp.set_nat) (H (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ H I3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups1351286907653491341at_rat G) S) (@ (@ tptp.groups1351286907653491341at_rat H) T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_o) (T7 tptp.set_o) (H (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o T7) S)) (= (@ H I3) tptp.zero_zero_nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups4556407284786078405_o_nat G) S) (@ (@ tptp.groups4556407284786078405_o_nat H) T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_nat) (T7 tptp.set_nat) (H (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ H I3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups1986416967739987077at_nat G) S) (@ (@ tptp.groups1986416967739987077at_nat H) T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_o) (T7 tptp.set_o) (H (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (@ (@ tptp.ord_less_eq_set_o S) T7) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o T7) S)) (= (@ H I3) tptp.zero_zero_int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups4553916814277028129_o_int G) S) (@ (@ tptp.groups4553916814277028129_o_int H) T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_nat) (T7 tptp.set_nat) (H (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_set_nat S) T7) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) (@ (@ tptp.minus_minus_set_nat T7) S)) (= (@ H I3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups1983926497230936801at_int G) S) (@ (@ tptp.groups1983926497230936801at_int H) T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (H (-> tptp.int tptp.code_integer)) (G (-> tptp.int tptp.code_integer))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ H I3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups926780983652909934nteger G) S) (@ (@ tptp.groups926780983652909934nteger H) T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (H (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ H I3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups2350640619554545897nt_rat G) S) (@ (@ tptp.groups2350640619554545897nt_rat H) T7)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (G (-> tptp.int tptp.code_integer)) (H (-> tptp.int tptp.code_integer))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups926780983652909934nteger G) T7) (@ (@ tptp.groups926780983652909934nteger H) S)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (G (-> tptp.int tptp.multis2468970476368604999at_nat)) (H (-> tptp.int tptp.multis2468970476368604999at_nat))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_z1048942125864253310at_nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups6906599089918680438at_nat G) T7) (@ (@ tptp.groups6906599089918680438at_nat H) S)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (G (-> tptp.int tptp.rat)) (H (-> tptp.int tptp.rat))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups2350640619554545897nt_rat G) T7) (@ (@ tptp.groups2350640619554545897nt_rat H) S)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (G (-> tptp.int tptp.nat)) (H (-> tptp.int tptp.nat))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups2985770679641041633nt_nat G) T7) (@ (@ tptp.groups2985770679641041633nt_nat H) S)))))))
% 8.20/8.65 (assert (forall ((S tptp.set_int) (T7 tptp.set_int) (G (-> tptp.int tptp.int)) (H (-> tptp.int tptp.int))) (=> (@ (@ tptp.ord_less_eq_set_int S) T7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T7) S)) (= (@ G X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups2983280209131991357nt_int G) T7) (@ (@ tptp.groups2983280209131991357nt_int H) S)))))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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 ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ 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))))))))))))))))))))))))
% 8.20/8.65 (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 ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N5)))))))))))))))))))))))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.compow_nat_nat N2) tptp.suc) (@ tptp.plus_plus_nat N2))))
% 8.20/8.65 (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 ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))))
% 8.20/8.65 (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 ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ 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))))))))))))))))))))))))
% 8.20/8.65 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or5832277885323065728an_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) (@ (@ tptp.plus_plus_int L) tptp.one_one_int))))))
% 8.20/8.65 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (exists ((R4 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R4) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S))) (forall ((N10 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N10) (@ tptp.finite_card_nat S)) (@ (@ tptp.member_nat (@ R4 N10)) S))))))))
% 8.20/8.65 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or5832277885323065728an_int L) U))))
% 8.20/8.65 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or4266950643985792945nteger L) U))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_nat _let_1) J2) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J2)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J2))))))))
% 8.20/8.65 (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))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J2) (@ tptp.suc I2))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J2))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N2))))))
% 8.20/8.65 (assert (= tptp.split_seed (lambda ((S5 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc8282080750456430313atural (lambda ((V2 tptp.code_natural) (W3 tptp.code_natural)) (@ (@ tptp.produc8282080750456430313atural (lambda ((V4 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 V4) (@ (@ 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 S5))))) S5))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat) (J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J2) I2)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J2))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N2))))))
% 8.20/8.65 (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 ((U3 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 U3)) (@ _let_1 V2))) (@ (@ tptp.plus_plus_nat (@ _let_2 V2)) (@ _let_1 U3))))))) __flatten_var_0))) Xa) X)))))
% 8.20/8.65 (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))))
% 8.20/8.65 (assert (forall ((H tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn tptp.one_one_assn) H) (= (@ tptp.produc8586169260539613262et_nat H) tptp.bot_bot_set_nat))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J2) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J2)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J2))))))))
% 8.20/8.65 (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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U3) Y4)))) __flatten_var_0))) Xa) X))))
% 8.20/8.65 (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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U3) Y4)))) __flatten_var_0))) Xa) X))))
% 8.20/8.65 (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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U3)) (@ (@ tptp.plus_plus_nat Y4) V2)))) __flatten_var_0))) Xa) X)))))
% 8.20/8.65 (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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat Y4) U3)))) __flatten_var_0))) Xa) X)))))
% 8.20/8.65 (assert (forall ((P3 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P3) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B4 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 B4) C3))) (@ (@ tptp.times_times_int C3) D5))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P3)))))
% 8.20/8.65 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or2715278749043346189nteger L) U))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N2) K2)) (@ _let_1 K2)))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N2) K2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int))))
% 8.20/8.65 (assert (= tptp.minus_minus_rat (lambda ((Q8 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.plus_plus_rat Q8) (@ tptp.uminus_uminus_rat R5)))))
% 8.20/8.65 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.product_snd_int_int (@ tptp.quotient_of R2)))))
% 8.20/8.65 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or6656581121297822940st_int L) U))))
% 8.20/8.65 (assert (forall ((R2 tptp.rat) (P3 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int P3) Q6)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q6))))
% 8.20/8.65 (assert (= tptp.archim3151403230148437115or_rat (lambda ((P7 tptp.rat)) (@ (@ tptp.produc8211389475949308722nt_int tptp.divide_divide_int) (@ tptp.quotient_of P7)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (= tptp.ord_less_eq_rat (lambda ((P7 tptp.rat) (Q8 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A5 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B4 tptp.int) (D5 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A5) D5)) (@ (@ tptp.times_times_int C3) B4)))) (@ tptp.quotient_of Q8)))) (@ tptp.quotient_of P7)))))
% 8.20/8.65 (assert (= tptp.ord_less_rat (lambda ((P7 tptp.rat) (Q8 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A5 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B4 tptp.int) (D5 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A5) D5)) (@ (@ tptp.times_times_int C3) B4)))) (@ tptp.quotient_of Q8)))) (@ tptp.quotient_of P7)))))
% 8.20/8.65 (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))))
% 8.20/8.65 (assert (forall ((P3 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P3) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B4 tptp.int) (D5 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A5) D5)) (@ (@ tptp.times_times_int C3) B4))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P3)))))
% 8.20/8.65 (assert (forall ((P3 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P3) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B4 tptp.int) (D5 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A5) B4)) (@ (@ tptp.times_times_int C3) D5))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P3)))))
% 8.20/8.65 (assert (forall ((P3 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P3) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B4 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 B4) C3))) (@ (@ tptp.times_times_int C3) D5))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P3)))))
% 8.20/8.65 (assert (forall ((P3 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A5 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A5)) B4)) (@ tptp.abs_abs_int A5))))) (@ tptp.quotient_of P3)))))
% 8.20/8.65 (assert (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Xa2 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y4 tptp.nat) (Z tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat Y4) V2)) (@ (@ tptp.plus_plus_nat U3) Z)))) __flatten_var_0))) (@ tptp.rep_Integ X4)) (@ tptp.rep_Integ Xa2)))))
% 8.20/8.65 (assert (= tptp.ord_less_int (lambda ((X4 tptp.int) (Xa2 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y4 tptp.nat) (Z tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat Y4) V2)) (@ (@ tptp.plus_plus_nat U3) Z)))) __flatten_var_0))) (@ tptp.rep_Integ X4)) (@ tptp.rep_Integ Xa2)))))
% 8.20/8.65 (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))))
% 8.20/8.65 (assert (= tptp.ord_less_eq_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_rat X4) Y4) (= X4 Y4)))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X4 tptp.rat)) (@ tptp.the_int (lambda ((Z tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) X4) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)))))))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (assert (forall ((K2 tptp.code_natural) (S2 tptp.produc7822875418678951345atural)) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) K2) (@ (@ tptp.ord_le5570908160329646204atural (@ tptp.produc497848011034438852atural (@ (@ tptp.range K2) S2))) K2))))
% 8.20/8.65 (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)))))))))))
% 8.20/8.65 (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 ((U3 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 U3)) (@ _let_1 V2))) (@ (@ tptp.plus_plus_nat (@ _let_2 V2)) (@ _let_1 U3))))))) __flatten_var_0))))))
% 8.20/8.65 (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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U3)) (@ (@ tptp.plus_plus_nat Y4) V2)))) __flatten_var_0))))))
% 8.20/8.65 (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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat Y4) U3)))) __flatten_var_0))))))
% 8.20/8.65 (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)))))))))))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X) Y))))
% 8.20/8.65 (assert (forall ((X tptp.int) (Y tptp.int)) (exists ((U4 tptp.int) (V5 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U4) X)) (@ (@ tptp.times_times_int V5) Y)) (@ (@ tptp.gcd_gcd_int X) Y)))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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))))
% 8.20/8.65 (assert (forall ((X tptp.int) (Y tptp.int) (P2 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X))) (let ((_let_2 (@ P2 (@ _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 (@ P2 (@ _let_1 _let_3)))) (=> (=> _let_6 (=> _let_8 (@ P2 (@ _let_4 Y)))) (=> (=> _let_6 (=> _let_5 (@ P2 (@ _let_4 _let_3)))) _let_2)))))))))))))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 8.20/8.65 (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)))))))))))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X) Y))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X) Y)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int X))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int Y)))))))
% 8.20/8.65 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I2) J2))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I2) J2)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J2)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 8.20/8.65 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (= (= (@ (@ tptp.upto I2) J2) tptp.nil_int) (@ (@ tptp.ord_less_int J2) I2))))
% 8.20/8.65 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I2) J2)) (@ (@ tptp.ord_less_int J2) I2))))
% 8.20/8.65 (assert (forall ((J2 tptp.int) (I2 tptp.int)) (=> (@ (@ tptp.ord_less_int J2) I2) (= (@ (@ tptp.upto I2) J2) tptp.nil_int))))
% 8.20/8.65 (assert (forall ((I2 tptp.int) (K2 tptp.nat) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I2) (@ tptp.semiri1314217659103216013at_int K2)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J2) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I2) J2)) K2) _let_1)))))
% 8.20/8.65 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I2) J2)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J2) I2)) tptp.one_one_int)))))
% 8.20/8.65 (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)))))))))
% 8.20/8.65 (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)))))))))
% 8.20/8.65 (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)))))))))
% 8.20/8.65 (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)))))))))
% 8.20/8.65 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I2) J2))))
% 8.20/8.65 (assert (forall ((M tptp.int) (N2 tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M) N2))))
% 8.20/8.65 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I tptp.int) (J tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J)))))
% 8.20/8.65 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) J2) (= (@ (@ tptp.upto I2) J2) (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J2))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (assert (= tptp.upto (lambda ((I tptp.int) (J tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I) J)) (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J))) tptp.nil_int))))
% 8.20/8.65 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I tptp.int) (J tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J) tptp.one_one_int))))))
% 8.20/8.65 (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)))))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N2)) N2))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) tptp.one_one_nat) (= (@ tptp.num_of_nat N2) tptp.one))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (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))))))))
% 8.20/8.65 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M3 tptp.nat) (N tptp.nat)) (= N (@ tptp.suc M3)))))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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))))))))
% 8.20/8.65 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J2) (= (@ _let_1 J2) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))) (@ (@ tptp.cons_int J2) tptp.nil_int)))))))
% 8.20/8.65 (assert (forall ((B tptp.int) (D2 tptp.int) (A tptp.int) (C2 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 C2) 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 C2) B)) _let_1))))))))
% 8.20/8.65 (assert (forall ((B tptp.int) (D2 tptp.int) (A tptp.int) (C2 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 C2) 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 C2) B)) _let_1))))))))
% 8.20/8.65 (assert (forall ((B tptp.int) (D2 tptp.int) (A tptp.int) (C2 tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D2 tptp.zero_zero_int)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C2) D2)) (@ (@ tptp.fract (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) D2)) (@ (@ tptp.times_times_int C2) B))) (@ (@ tptp.times_times_int B) D2)))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.rat Bool)) (Q6 tptp.rat)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (@ P2 (@ (@ tptp.fract A3) B3)))) (@ P2 Q6))))
% 8.20/8.65 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J2) (=> (@ (@ tptp.ord_less_eq_int J2) K2) (= (@ _let_1 K2) (@ (@ tptp.append_int (@ _let_1 J2)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J2) tptp.one_one_int)) K2))))))))
% 8.20/8.65 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J2) (=> (@ (@ tptp.ord_less_eq_int J2) K2) (= (@ _let_1 K2) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))) (@ (@ tptp.upto J2) K2))))))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (forall ((N2 tptp.int) (M tptp.int)) (=> (not (= N2 tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ (@ tptp.plus_plus_int M) N2)) N2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract M) N2)) tptp.one_one_rat)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (forall ((I2 tptp.int) (J2 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J2) (=> (@ (@ tptp.ord_less_eq_int J2) K2) (= (@ _let_1 K2) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))) (@ (@ tptp.cons_int J2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J2) tptp.one_one_int)) K2)))))))))
% 8.20/8.65 (assert (forall ((I2 tptp.int) (J2 tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J2))) (= (@ (@ tptp.linord1735203802627413978nt_int (lambda ((X4 tptp.int)) X4)) _let_1) _let_1))))
% 8.20/8.65 (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))))
% 8.20/8.65 (assert (forall ((J2 tptp.nat)) (= (= (@ (@ tptp.upt tptp.zero_zero_nat) J2) tptp.nil_nat) (= J2 tptp.zero_zero_nat))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J2) (@ (@ tptp.ord_less_eq_nat J2) K2)) (= (@ (@ tptp.append_nat (@ _let_1 J2)) (@ (@ tptp.upt J2) K2)) (@ _let_1 K2))))))
% 8.20/8.65 (assert (forall ((J2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J2) I2) (= (@ (@ tptp.upt I2) J2) tptp.nil_nat))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (= (= (@ (@ tptp.upt I2) J2) tptp.nil_nat) (or (= J2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J2) I2)))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (K2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) K2))) (=> (@ (@ tptp.ord_less_nat _let_1) J2) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I2) J2)) K2) _let_1)))))
% 8.20/8.65 (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)))))))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (Xs tptp.list_nat) (Ys3 tptp.list_nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (= (@ (@ tptp.upt I2) J2) (@ (@ tptp.append_nat Xs) Ys3)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I2) K3) (@ (@ tptp.ord_less_eq_nat K3) J2) (= (@ (@ tptp.upt I2) K3) Xs) (= (@ (@ tptp.upt K3) J2) Ys3)))))))
% 8.20/8.65 (assert (forall ((Ofs tptp.nat) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat I) Ofs))) (@ (@ tptp.upt A) B)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat A) Ofs)) (@ (@ tptp.plus_plus_nat B) Ofs)))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.upt tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat I2) J2) (= (@ (@ tptp.append_nat (@ _let_1 I2)) (@ (@ tptp.upt I2) J2)) (@ _let_1 J2))))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J2) K2))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J2)) (@ (@ tptp.upt J2) _let_1))))))))
% 8.20/8.65 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N2))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat I) N2))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N2) (@ (@ tptp.plus_plus_nat M) N2)))))
% 8.20/8.65 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N2))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (= (@ (@ tptp.upt I2) J2) (@ (@ tptp.cons_nat I2) (@ (@ tptp.upt (@ tptp.suc I2)) J2))))))
% 8.20/8.65 (assert (= tptp.upt (lambda ((I tptp.nat) (J tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I) J)) (@ (@ tptp.cons_nat I) (@ (@ tptp.upt (@ tptp.suc I)) J))) tptp.nil_nat))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (let ((_let_2 (@ _let_1 (@ tptp.suc J2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I2) J2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J2)) (@ (@ tptp.cons_nat J2) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (= (@ _let_1 (@ tptp.suc J2)) (@ (@ tptp.append_nat (@ _let_1 J2)) (@ (@ tptp.cons_nat J2) tptp.nil_nat)))))))
% 8.20/8.65 (assert (forall ((U tptp.nat) (U5 tptp.nat) (P2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.upt tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.filter_nat2 P2))) (=> (@ (@ tptp.ord_less_eq_nat U) U5) (=> (forall ((I3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat U) I3) (@ (@ tptp.ord_less_nat I3) U5)) (not (@ P2 I3)))) (= (@ _let_2 (@ _let_1 U)) (@ _let_2 (@ _let_1 U5)))))))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (J2 tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I2) J2) (@ (@ tptp.cons_nat X) Xs)) (and (@ (@ tptp.ord_less_nat I2) J2) (= I2 X) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) tptp.one_one_nat)) J2) Xs)))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (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))))))))))
% 8.20/8.65 (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))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (= (@ tptp.hd_nat (@ (@ tptp.upt I2) J2)) I2))))
% 8.20/8.65 (assert (= tptp.finite_finite_int (lambda ((S4 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S4)) (@ tptp.set_ord_atMost_int K3))))))
% 8.20/8.65 (assert (= tptp.finite_finite_int (lambda ((S4 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S4)) (@ tptp.set_ord_lessThan_int K3))))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (assert (forall ((C2 tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C2) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_nat I) C2))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C2)) (@ (@ tptp.minus_minus_nat Y) C2)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_nat I) C2))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_nat I) C2))) _let_1) tptp.bot_bot_set_nat))))))))))
% 8.20/8.65 (assert (= (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 8.20/8.65 (assert (= tptp.comple4687483117567863418t_unit (lambda ((Uu3 tptp.set_Product_unit)) tptp.product_Unity)))
% 8.20/8.65 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atMost_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 8.20/8.65 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 8.20/8.65 (assert (= tptp.comple2584293577114468500t_unit (lambda ((Uu3 tptp.set_Product_unit)) tptp.product_Unity)))
% 8.20/8.65 (assert (forall ((K5 tptp.set_nat)) (=> (not (= K5 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.complete_Inf_Inf_nat K5)) K5))))
% 8.20/8.65 (assert (= tptp.complete_Inf_Inf_int (lambda ((X11 tptp.set_int)) (@ tptp.uminus_uminus_int (@ tptp.complete_Sup_Sup_int (@ (@ tptp.image_int_int tptp.uminus_uminus_int) X11))))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (= (@ (@ tptp.times_times_assn tptp.top_top_assn) tptp.top_top_assn) tptp.top_top_assn))
% 8.20/8.65 (assert (not (= tptp.top_top_assn tptp.one_one_assn)))
% 8.20/8.65 (assert (not (= tptp.top_top_assn tptp.bot_bot_assn)))
% 8.20/8.65 (assert (forall ((H tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn tptp.top_top_assn) H) (@ tptp.in_range H))))
% 8.20/8.65 (assert (= tptp.top_to1996260823553986621t_unit (@ (@ tptp.insert_Product_unit tptp.product_Unity) tptp.bot_bo3957492148770167129t_unit)))
% 8.20/8.65 (assert (forall ((P2 tptp.assn)) (@ (@ tptp.entails P2) tptp.top_top_assn)))
% 8.20/8.65 (assert (= tptp.top_top_Product_unit tptp.product_Unity))
% 8.20/8.65 (assert (forall ((P2 tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P2) tptp.top_top_assn)) H))))
% 8.20/8.65 (assert (forall ((P2 tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P2) tptp.top_top_assn)) H) (not (forall ((H4 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn P2) H4)))))))
% 8.20/8.65 (assert (= tptp.top_top_assn (@ tptp.abs_assn tptp.in_range)))
% 8.20/8.65 (assert (forall ((H tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.rep_assn tptp.top_top_assn) (@ (@ tptp.produc7507926704131184380et_nat H) tptp.bot_bot_set_nat))))
% 8.20/8.65 (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))))))))
% 8.20/8.65 (assert (forall ((P2 tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P2) tptp.top_top_assn)) H) (not (forall ((H4 tptp.produc3658429121746597890et_nat)) (=> (= (@ tptp.produc1824681642469235216et_nat H4) (@ tptp.produc1824681642469235216et_nat H)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.produc8586169260539613262et_nat H4)) (@ tptp.produc8586169260539613262et_nat H)) (not (@ (@ tptp.rep_assn P2) H4)))))))))
% 8.20/8.65 (assert (= tptp.top_top_set_o (@ (@ tptp.insert_o false) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))))
% 8.20/8.65 (assert (forall ((M tptp.nat) (I2 tptp.nat) (J2 tptp.nat)) (= (@ (@ tptp.drop_nat M) (@ (@ tptp.upt I2) J2)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) M)) J2))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (assert (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (= (@ tptp.last_nat (@ (@ tptp.upt I2) J2)) (@ (@ tptp.minus_minus_nat J2) tptp.one_one_nat)))))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) tptp.ord_less_nat) tptp.ord_less_nat))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re3403563459893282935_int_o (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (@ (@ tptp.bNF_re5089333283451836215nt_o_o (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) tptp.ord_less_int) tptp.ord_less_int))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)))) tptp.plus_plus_int) tptp.plus_plus_int))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)))) tptp.plus_plus_nat) tptp.plus_plus_nat))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re8402795839162346335um_int (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4))) (@ (@ tptp.bNF_re1822329894187522285nt_int (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4))) (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)))) (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)))))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) K3))) (lambda ((K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) K3))))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) tptp.ord_less_eq_nat) tptp.ord_less_eq_nat))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re3403563459893282935_int_o (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (@ (@ tptp.bNF_re5089333283451836215nt_o_o (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) tptp.ord_less_eq_int) tptp.ord_less_eq_int))
% 8.20/8.65 (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))))))
% 8.20/8.65 (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))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re3461391660133120880nt_rat (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (@ (@ tptp.bNF_re2214769303045360666nt_rat (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) tptp.pcr_rat)) (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B4 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A5) B4)))) tptp.fract))
% 8.20/8.65 (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))
% 8.20/8.65 (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))
% 8.20/8.65 (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))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re1494630372529172596at_o_o tptp.pcr_rat) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4))) (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))
% 8.20/8.65 (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 ((U3 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 U3)) (@ _let_1 V2))) (@ (@ tptp.plus_plus_nat (@ _let_2 V2)) (@ _let_1 U3))))))) __flatten_var_0)))) tptp.times_times_int))
% 8.20/8.65 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ tptp.positive X) (=> (@ tptp.positive Y) (@ tptp.positive (@ (@ tptp.plus_plus_rat X) Y))))))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re4555766996558763186at_nat tptp.pcr_int) (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat)) tptp.nat2))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re6830278522597306478at_int (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) tptp.pcr_int) (lambda ((N tptp.nat)) (@ (@ tptp.product_Pair_nat_nat N) tptp.zero_zero_nat))) tptp.semiri1314217659103216013at_int))
% 8.20/8.65 (assert (= tptp.ord_less_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (@ tptp.positive (@ (@ tptp.minus_minus_rat Y4) X4)))))
% 8.20/8.65 (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))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U3) Y4)))) __flatten_var_0)))) tptp.ord_less_int))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U3) Y4)))) __flatten_var_0)))) tptp.ord_less_eq_int))
% 8.20/8.65 (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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U3)) (@ (@ tptp.plus_plus_nat Y4) V2)))) __flatten_var_0)))) tptp.plus_plus_int))
% 8.20/8.65 (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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat Y4) U3)))) __flatten_var_0)))) tptp.minus_minus_int))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (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))))
% 8.20/8.65 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M3) N))) M3)))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 8.20/8.65 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 8.20/8.65 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 8.20/8.65 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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))))
% 8.20/8.65 (assert (forall ((K2 tptp.nat) (M tptp.nat)) (= (@ tptp.nat_prod_encode (@ (@ tptp.nat_prod_decode_aux K2) M)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K2)) M))))
% 8.20/8.65 (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 ((U3 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 U3)) (@ _let_1 V2))) (@ (@ tptp.plus_plus_nat (@ _let_2 V2)) (@ _let_1 U3))))))) __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 ((U3 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 U3)) (@ _let_1 V2))) (@ (@ tptp.plus_plus_nat (@ _let_2 V2)) (@ _let_1 U3))))))) __flatten_var_0)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (let ((_let_1 (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))) (@ (@ (@ (@ tptp.bNF_re8246922863344978751at_nat tptp.intrel) (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) _let_1) _let_1)))
% 8.20/8.65 (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 ((U3 tptp.nat) (V2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat X4) V2) (@ (@ tptp.plus_plus_nat U3) Y4)))) __flatten_var_0)))))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U3) 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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U3) Y4)))) __flatten_var_0)))))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U3) 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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U3) Y4)))) __flatten_var_0)))))
% 8.20/8.65 (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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U3)) (@ (@ 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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U3)) (@ (@ tptp.plus_plus_nat Y4) V2)))) __flatten_var_0)))))
% 8.20/8.65 (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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat Y4) U3)))) __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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat Y4) U3)))) __flatten_var_0)))))
% 8.20/8.65 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 8.20/8.65 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N2)))))
% 8.20/8.65 (assert (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2) (@ tptp.order_mono_nat_nat (lambda ((M3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K2) M3)) M3))))))
% 8.20/8.65 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 8.20/8.65 (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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U3) Y4)))) __flatten_var_0))))))
% 8.20/8.65 (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 ((U3 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U3) Y4)))) __flatten_var_0))))))
% 8.20/8.65 (assert (= tptp.nat2 (@ (@ (@ tptp.map_fu2345160673673942751at_nat tptp.rep_Integ) tptp.id_nat) (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (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)))
% 8.20/8.65 (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)))
% 8.20/8.65 (assert (= tptp.plus_p5714425477246183910nteger (@ (@ (@ tptp.map_fu8272188784021352819nteger tptp.code_int_of_integer) (@ (@ tptp.map_fu2599414010547811884nteger tptp.code_int_of_integer) tptp.code_integer_of_int)) tptp.plus_plus_int)))
% 8.20/8.65 (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))))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (assert (= tptp.fract (@ (@ (@ tptp.map_fu7831380289885515383nt_rat tptp.id_int) (@ (@ tptp.map_fu3424225382358772769nt_rat tptp.id_int) tptp.abs_Rat)) (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B4 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A5) B4))))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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))))))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re157797125943740599nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (@ (@ tptp.bNF_re6250860962936578807nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) tptp.ratrel)) (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B4 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A5) B4)))) (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B4 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A5) B4)))))
% 8.20/8.65 (assert (forall ((X tptp.code_integer)) (let ((_let_1 (@ tptp.code_int_of_integer X))) (= (@ tptp.code_int_of_integer (@ tptp.code_dup X)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 8.20/8.65 (assert (forall ((X tptp.int)) (= (@ tptp.code_dup (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.plus_plus_int X) X)))))
% 8.20/8.65 (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))))))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re8699439704749558557nt_o_o tptp.ratrel) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4))) (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))))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.code_sub (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_dup (@ (@ tptp.code_sub M) N2))) tptp.one_one_Code_integer))))
% 8.20/8.65 (assert (= tptp.cr_rat (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.rat)) (and (@ (@ tptp.ratrel X4) X4) (= (@ tptp.abs_Rat X4) Y4)))))
% 8.20/8.65 (assert (= tptp.code_sub (@ (@ (@ tptp.map_fu6891787308814931657nteger tptp.id_num) (@ (@ tptp.map_fu8638147718074629079nteger tptp.id_num) tptp.code_integer_of_int)) (lambda ((M3 tptp.num) (N tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M3)) (@ tptp.numeral_numeral_int N))))))
% 8.20/8.65 (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))))
% 8.20/8.65 (assert (forall ((Xa tptp.nat) (X tptp.nat)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ tptp.code_natural_of_nat Xa)) (@ tptp.code_natural_of_nat X)) (@ tptp.code_natural_of_nat (@ (@ tptp.plus_plus_nat Xa) X)))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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))))))))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (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))))))))
% 8.20/8.65 (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))))))))))
% 8.20/8.65 (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)))))))))
% 8.20/8.65 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 8.20/8.65 (assert (forall ((K5 tptp.set_int)) (= (@ tptp.gcd_Gcd_int (@ (@ tptp.image_int_int tptp.abs_abs_int) K5)) (@ tptp.gcd_Gcd_int K5))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (forall ((K5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K5))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (assert (forall ((N7 tptp.set_nat) (K2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.member_nat N5) N7) (@ (@ tptp.ord_less_eq_nat K2) N5))) (@ (@ tptp.inj_on_nat_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) K2))) N7))))
% 8.20/8.65 (assert (forall ((N7 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N7)))
% 8.20/8.65 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atLeast_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 8.20/8.65 (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)))))))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (assert (forall ((Q6 tptp.rat)) (not (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= Q6 (@ (@ tptp.fract A3) B3)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (not (@ (@ tptp.algebr932160517623751201me_int A3) B3))))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.rat Bool)) (Q6 tptp.rat)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (@ (@ tptp.algebr932160517623751201me_int A3) B3) (@ P2 (@ (@ tptp.fract A3) B3))))) (@ P2 Q6))))
% 8.20/8.65 (assert (forall ((Q6 tptp.rat)) (=> (forall ((A3 tptp.int) (B3 tptp.int)) (=> (= Q6 (@ (@ tptp.fract A3) B3)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (not (= A3 tptp.zero_zero_int)) (not (@ (@ tptp.algebr932160517623751201me_int A3) B3)))))) (= Q6 tptp.zero_zero_rat))))
% 8.20/8.65 (assert (forall ((R2 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 (= R2 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1) (forall ((Y5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y5))) (let ((_let_2 (@ tptp.product_fst_int_int Y5))) (=> (and (= R2 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)) (= Y5 X3)))))))))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (assert (@ tptp.wf_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 8.20/8.65 (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))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.nat Bool))) (=> (@ P2 tptp.zero_zero_nat) (= (@ tptp.ord_Least_nat P2) tptp.zero_zero_nat))))
% 8.20/8.65 (assert (= tptp.complete_Inf_Inf_nat (lambda ((X11 tptp.set_nat)) (@ tptp.ord_Least_nat (lambda ((N tptp.nat)) (@ (@ tptp.member_nat N) X11))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.nat Bool)) (N2 tptp.nat) (Q2 (-> tptp.nat Bool)) (M tptp.nat)) (=> (@ P2 N2) (=> (@ Q2 M) (=> (not (@ P2 tptp.zero_zero_nat)) (=> (forall ((K tptp.nat)) (= (@ P2 (@ tptp.suc K)) (@ Q2 K))) (= (@ tptp.ord_Least_nat P2) (@ tptp.suc (@ tptp.ord_Least_nat Q2)))))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P2 N2) (=> (not (@ P2 tptp.zero_zero_nat)) (= (@ tptp.ord_Least_nat P2) (@ tptp.suc (@ tptp.ord_Least_nat (lambda ((M3 tptp.nat)) (@ P2 (@ tptp.suc M3))))))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.nat Bool)) (K2 tptp.nat) (B tptp.nat)) (=> (@ P2 K2) (=> (forall ((Y3 tptp.nat)) (=> (@ P2 Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P2 (@ tptp.order_Greatest_nat P2))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.nat Bool)) (K2 tptp.nat) (B tptp.nat)) (=> (@ P2 K2) (=> (forall ((Y3 tptp.nat)) (=> (@ P2 Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ (@ tptp.ord_less_eq_nat K2) (@ tptp.order_Greatest_nat P2))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_12 tptp.nat)) (@ P2 X_12)) (=> (forall ((Y3 tptp.nat)) (=> (@ P2 Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P2 (@ tptp.order_Greatest_nat P2))))))
% 8.20/8.65 (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)))))))))
% 8.20/8.65 (assert (@ (@ (@ tptp.filter3212408913953519116et_nat tptp.set_ord_lessThan_nat) (@ tptp.finite3254316476582989077op_nat tptp.top_top_set_nat)) tptp.at_top_nat))
% 8.20/8.65 (assert (@ (@ (@ tptp.filter3212408913953519116et_nat tptp.set_ord_atMost_nat) (@ tptp.finite3254316476582989077op_nat tptp.top_top_set_nat)) tptp.at_top_nat))
% 8.20/8.65 (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))))
% 8.20/8.65 (assert (forall ((N2 tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N2)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N2)) N2))))))
% 8.20/8.65 (assert (forall ((X tptp.product_unit)) (@ (@ tptp.member_o (@ tptp.product_Rep_unit X)) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))))
% 8.20/8.65 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (= (@ tptp.product_Rep_unit X) (@ tptp.product_Rep_unit Y)) (= X Y))))
% 8.20/8.65 (assert (forall ((Y Bool) (P2 (-> Bool Bool))) (=> (@ (@ tptp.member_o Y) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (=> (forall ((X3 tptp.product_unit)) (@ P2 (@ tptp.product_Rep_unit X3))) (@ P2 Y)))))
% 8.20/8.65 (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))))))))
% 8.20/8.65 (assert (@ (@ (@ tptp.type_d6188575255521822967unit_o tptp.product_Rep_unit) tptp.product_Abs_unit) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)))
% 8.20/8.65 (assert (= tptp.product_Unity (@ tptp.product_Abs_unit true)))
% 8.20/8.65 (assert (forall ((X tptp.product_unit)) (= (@ tptp.product_Abs_unit (@ tptp.product_Rep_unit X)) X)))
% 8.20/8.65 (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))))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.product_unit Bool)) (X tptp.product_unit)) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (@ P2 (@ tptp.product_Abs_unit Y3)))) (@ P2 X))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (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))))
% 8.20/8.65 (assert (forall ((X tptp.code_natural) (Xa tptp.code_natural)) (= (@ tptp.code_nat_of_natural (@ (@ tptp.plus_p4538020629002901425atural X) Xa)) (@ (@ tptp.plus_plus_nat (@ tptp.code_nat_of_natural X)) (@ tptp.code_nat_of_natural Xa)))))
% 8.20/8.65 (assert (= tptp.ord_le5570908160329646204atural (lambda ((X4 tptp.code_natural) (Xa2 tptp.code_natural)) (@ (@ tptp.ord_less_nat (@ tptp.code_nat_of_natural X4)) (@ tptp.code_nat_of_natural Xa2)))))
% 8.20/8.65 (assert (= tptp.ord_le1926595141338095240atural (lambda ((X4 tptp.code_natural) (Xa2 tptp.code_natural)) (@ (@ tptp.ord_less_eq_nat (@ tptp.code_nat_of_natural X4)) (@ tptp.code_nat_of_natural Xa2)))))
% 8.20/8.65 (assert (= tptp.plus_p4538020629002901425atural (@ (@ (@ tptp.map_fu6549440983881763648atural tptp.code_nat_of_natural) (@ (@ tptp.map_fu1239815594074539274atural tptp.code_nat_of_natural) tptp.code_natural_of_nat)) tptp.plus_plus_nat)))
% 8.20/8.65 (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)))
% 8.20/8.65 (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)))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I tptp.nat)) (@ P2 (@ tptp.suc I)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P2) tptp.at_top_nat))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.nat Bool)) (K2 tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N tptp.nat)) (@ P2 (@ (@ tptp.plus_plus_nat N) K2)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P2) tptp.at_top_nat))))
% 8.20/8.65 (assert (not (@ (@ tptp.eventually_nat (lambda ((N tptp.nat)) false)) tptp.at_top_nat)))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P2) tptp.at_top_nat) (exists ((N8 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N) (@ P2 N)))))))
% 8.20/8.65 (assert (forall ((C2 tptp.nat) (P2 (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C2) X3) (@ P2 X3))) (@ (@ tptp.eventually_nat P2) tptp.at_top_nat))))
% 8.20/8.65 (assert (forall ((F5 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F5) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N8)) F5)))))
% 8.20/8.65 (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))))))))
% 8.20/8.65 (assert (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat S2) T6) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S2)) (@ (@ tptp.product_Pair_nat_nat B) T6))) tptp.fun_pair_less)))))
% 8.20/8.65 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.total_3592101749530773125at_nat A4) tptp.fun_pair_less)))
% 8.20/8.65 (assert (@ tptp.trans_4347625901269045472at_nat tptp.fun_pair_less))
% 8.20/8.65 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X))) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ _let_1 Y)) (@ _let_1 Z3))) tptp.fun_pair_less) (@ (@ tptp.ord_less_nat Y) Z3)))))
% 8.20/8.65 (assert (@ tptp.wf_Pro7803398752247294826at_nat tptp.fun_pair_less))
% 8.20/8.65 (assert (= tptp.fun_pair_less (@ (@ tptp.lex_prod_nat_nat tptp.less_than) tptp.less_than)))
% 8.20/8.65 (assert (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T6 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) T6))) tptp.fun_pair_less))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (assert (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat S2) T6) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S2)) (@ (@ tptp.product_Pair_nat_nat B) T6))) tptp.fun_pair_leq)))))
% 8.20/8.65 (assert (= tptp.fun_pair_leq (@ (@ tptp.sup_su718114333110466843at_nat tptp.fun_pair_less) tptp.id_Pro2258643101195443293at_nat)))
% 8.20/8.65 (assert (forall ((X7 tptp.set_Pr1261947904930325089at_nat)) (=> (not (= X7 tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X7) tptp.bot_bo2099793752762293965at_nat)) tptp.fun_min_strict))))
% 8.20/8.65 (assert (= tptp.fun_min_strict (@ tptp.min_ex6901939911449802026at_nat tptp.fun_pair_less)))
% 8.20/8.65 (assert (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T6 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) T6))) tptp.fun_pair_leq))))
% 8.20/8.65 (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))))))
% 8.20/8.65 (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)))))))
% 8.20/8.65 (assert (forall ((X7 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X7) tptp.bot_bo2099793752762293965at_nat)) tptp.fun_min_weak)))
% 8.20/8.65 (assert (forall ((X7 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat X7) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) X7)) tptp.fun_max_weak))))
% 8.20/8.65 (assert (@ tptp.fun_re2478310338295953701at_nat (@ (@ tptp.produc9060074326276436823at_nat tptp.fun_min_strict) tptp.fun_min_weak)))
% 8.20/8.65 (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))))
% 8.20/8.65 (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))))
% 8.20/8.65 (assert (forall ((Y tptp.product_prod_nat_nat) (Y7 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (X7 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 X7) Y7)) tptp.fun_max_strict) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ (@ tptp.insert8211810215607154385at_nat X) X7)) Y7)) tptp.fun_max_strict))))))
% 8.20/8.65 (assert (= tptp.fun_max_strict (@ tptp.max_ex8135407076693332796at_nat tptp.fun_pair_less)))
% 8.20/8.65 (assert (@ tptp.fun_re2478310338295953701at_nat (@ (@ tptp.produc9060074326276436823at_nat tptp.fun_max_strict) tptp.fun_max_weak)))
% 8.20/8.65 (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)))))
% 8.20/8.65 (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)))))
% 8.20/8.65 (assert (forall ((A4 tptp.multis2468970476368604999at_nat) (B5 tptp.multis2468970476368604999at_nat) (Z5 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat Z5))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A4)) (@ tptp.set_ms8126754132646256062at_nat B5))) tptp.fun_max_strict) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ _let_1 A4)) (@ _let_1 B5))) tptp.ms_strict)))))
% 8.20/8.65 (assert (forall ((A4 tptp.multis2468970476368604999at_nat) (B5 tptp.multis2468970476368604999at_nat) (Z5 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat Z5))) (=> (or (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A4)) (@ tptp.set_ms8126754132646256062at_nat B5))) tptp.fun_max_strict) (and (= A4 tptp.zero_z1048942125864253310at_nat) (= B5 tptp.zero_z1048942125864253310at_nat))) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ _let_1 A4)) (@ _let_1 B5))) tptp.ms_weak)))))
% 8.20/8.65 (assert (= tptp.ms_weak (@ (@ tptp.sup_su3035147773818789531at_nat tptp.ms_strict) tptp.id_mul2649389997224486051at_nat)))
% 8.20/8.65 (assert (forall ((Z5 tptp.multis2468970476368604999at_nat) (Z9 tptp.multis2468970476368604999at_nat) (A4 tptp.multis2468970476368604999at_nat) (B5 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq Z5) Z9) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A4)) (@ tptp.set_ms8126754132646256062at_nat B5))) tptp.fun_max_strict) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ (@ tptp.plus_p7104986032573967614at_nat Z5) A4)) (@ (@ tptp.plus_p7104986032573967614at_nat Z9) B5))) tptp.ms_weak)))))
% 8.20/8.65 (assert (forall ((Z5 tptp.multis2468970476368604999at_nat) (Z9 tptp.multis2468970476368604999at_nat) (A4 tptp.multis2468970476368604999at_nat) (B5 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq Z5) Z9) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A4)) (@ tptp.set_ms8126754132646256062at_nat B5))) tptp.fun_max_strict) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ (@ tptp.plus_p7104986032573967614at_nat Z5) A4)) (@ (@ tptp.plus_p7104986032573967614at_nat Z9) B5))) tptp.ms_strict)))))
% 8.20/8.65 (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 ((Y10 tptp.multis2468970476368604999at_nat)) (=> (= A23 (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat Y3) tptp.zero_z1048942125864253310at_nat)) Y10)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X3) Y3)) tptp.fun_pair_leq) (not (@ (@ tptp.pw_leq X14) Y10))))))))))))
% 8.20/8.65 (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) (Y11 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)) Y11)) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X4) Y4)) tptp.fun_pair_leq) (@ (@ tptp.pw_leq X11) Y11)))))))
% 8.20/8.65 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (X7 tptp.multis2468970476368604999at_nat) (Y7 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_leq) (=> (@ (@ tptp.pw_leq X7) Y7) (@ (@ tptp.pw_leq (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat X) tptp.zero_z1048942125864253310at_nat)) X7)) (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat Y) tptp.zero_z1048942125864253310at_nat)) Y7))))))
% 8.20/8.65 (assert (forall ((Z5 tptp.multis2468970476368604999at_nat) (Z9 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq Z5) Z9) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ (@ tptp.plus_p7104986032573967614at_nat Z5) tptp.zero_z1048942125864253310at_nat)) (@ (@ tptp.plus_p7104986032573967614at_nat Z9) tptp.zero_z1048942125864253310at_nat))) tptp.ms_weak))))
% 8.20/8.65 (assert (forall ((X7 tptp.multis2468970476368604999at_nat) (Y7 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq X7) Y7) (exists ((A9 tptp.multis2468970476368604999at_nat) (B9 tptp.multis2468970476368604999at_nat) (Z10 tptp.multis2468970476368604999at_nat)) (and (= X7 (@ (@ tptp.plus_p7104986032573967614at_nat A9) Z10)) (= Y7 (@ (@ tptp.plus_p7104986032573967614at_nat B9) Z10)) (or (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A9)) (@ tptp.set_ms8126754132646256062at_nat B9))) tptp.fun_max_strict) (and (= B9 tptp.zero_z1048942125864253310at_nat) (= A9 tptp.zero_z1048942125864253310at_nat))))))))
% 8.20/8.65 (assert (= tptp.condit2214826472909112428ve_nat tptp.finite_finite_nat))
% 8.20/8.65 (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))))))))
% 8.20/8.65 (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))))))))
% 8.20/8.65 (assert (@ (@ tptp.bNF_Ca1281551314933786834on_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_Ca8665028551170535155natLeq))
% 8.20/8.65 (assert (@ tptp.antisym_nat tptp.bNF_Ca8665028551170535155natLeq))
% 8.20/8.65 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ (@ tptp.minus_1356011639430497352at_nat tptp.bNF_Ca8665028551170535155natLeq) tptp.id_nat2)))
% 8.20/8.65 (assert (@ tptp.trans_nat tptp.bNF_Ca8665028551170535155natLeq))
% 8.20/8.65 (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))))))
% 8.20/8.65 (assert (@ (@ tptp.total_on_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_Ca8665028551170535155natLeq))
% 8.20/8.65 (assert (@ (@ tptp.order_4473980167227706203on_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_Ca8665028551170535155natLeq))
% 8.20/8.65 (assert (@ (@ tptp.order_4861654808422542329on_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_Ca8665028551170535155natLeq))
% 8.20/8.65 (assert (@ (@ tptp.refl_on_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_Ca8665028551170535155natLeq))
% 8.20/8.65 (assert (= (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq) tptp.top_top_set_nat))
% 8.20/8.65 (assert (= tptp.bNF_Ca8665028551170535155natLeq (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_eq_nat))))
% 8.20/8.65 (assert (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_Ca8665028551170535155natLeq))
% 8.20/8.65 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N2)) (lambda ((Uu2 tptp.nat)) (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) 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))))))))
% 8.20/8.65 (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))))))))
% 8.20/8.65 (assert (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.bNF_Ca3793111618940312692of_nat tptp.top_top_set_nat)) tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_We5258908940166488438at_nat))
% 8.20/8.65 (assert (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.bNF_Ca3793111618940312692of_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq))) tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_We5258908940166488438at_nat))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.eventu1038000079068216329at_nat P2) (@ (@ tptp.prod_filter_nat_nat tptp.at_top_nat) tptp.at_top_nat)) (exists ((N8 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M3) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N) (@ P2 (@ (@ tptp.product_Pair_nat_nat N) M3))))))))))
% 8.20/8.65 (assert (forall ((K2 tptp.nat) (M tptp.nat)) (= (@ tptp.nat_prod_decode (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K2)) M)) (@ (@ tptp.nat_prod_decode_aux K2) M))))
% 8.20/8.65 (assert (forall ((X tptp.nat) (Y tptp.list_nat)) (=> (= (@ tptp.nat_list_decode X) Y) (=> (=> (= X tptp.zero_zero_nat) (not (= Y tptp.nil_nat))) (not (forall ((N5 tptp.nat)) (=> (= X (@ tptp.suc N5)) (not (= Y (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y4)))) (@ tptp.nat_prod_decode N5)))))))))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat)) (= (@ tptp.nat_list_decode (@ tptp.suc N2)) (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y4)))) (@ tptp.nat_prod_decode N2)))))
% 8.20/8.65 (assert (forall ((X tptp.nat) (Y tptp.list_nat)) (let ((_let_1 (@ tptp.accp_nat tptp.nat_list_decode_rel))) (=> (= (@ tptp.nat_list_decode X) Y) (=> (@ _let_1 X) (=> (=> (= X tptp.zero_zero_nat) (=> (= Y tptp.nil_nat) (not (@ _let_1 tptp.zero_zero_nat)))) (not (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.suc N5))) (=> (= X _let_1) (=> (= Y (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y4)))) (@ tptp.nat_prod_decode N5))) (not (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1)))))))))))))
% 8.20/8.65 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1) (= (@ tptp.nat_list_decode _let_1) (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.cons_nat X4) (@ tptp.nat_list_decode Y4)))) (@ tptp.nat_prod_decode N2)))))))
% 8.20/8.65 (assert (= (@ tptp.domain9213661015745956397nt_rat tptp.pcr_rat) (lambda ((X4 tptp.product_prod_int_int)) (exists ((Y4 tptp.product_prod_int_int)) (and (@ (@ (@ (@ tptp.basic_4387203522000727145nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) X4) Y4) (@ (@ tptp.ratrel Y4) Y4))))))
% 8.20/8.65 (assert (@ (@ (@ (@ tptp.bNF_re7934895593101944656at_int (@ (@ tptp.basic_5328504652464829177at_nat (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)))) tptp.pcr_int) (lambda ((X4 tptp.product_prod_nat_nat)) X4)) tptp.abs_Integ))
% 8.20/8.65 (assert (forall ((P6 (-> tptp.product_prod_int_int Bool))) (=> (@ tptp.left_t3131394472396969446nt_int (@ (@ tptp.basic_4387203522000727145nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)))) (=> (@ (@ (@ (@ tptp.bNF_re8699439704749558557nt_o_o (@ (@ tptp.basic_4387203522000727145nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)))) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4))) P6) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.ratrel X4) X4))) (= (@ tptp.domain9213661015745956397nt_rat tptp.pcr_rat) P6)))))
% 8.20/8.65 (assert (forall ((DR1 (-> tptp.int Bool)) (DR2 (-> tptp.int Bool)) (P22 (-> tptp.product_prod_int_int Bool))) (=> (= (@ tptp.domainp_int_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) DR1) (=> (= (@ tptp.domainp_int_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) DR2) (=> (@ (@ (@ (@ tptp.bNF_re8699439704749558557nt_o_o (@ (@ tptp.basic_4387203522000727145nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)))) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4))) P22) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.ratrel X4) X4))) (= (@ tptp.domain9213661015745956397nt_rat tptp.pcr_rat) (@ (@ tptp.inf_in3604695632404883862_int_o (@ (@ tptp.basic_1567116559311922317nt_int DR1) DR2)) P22)))))))
% 8.20/8.65 (assert (forall ((X tptp.rat)) (not (forall ((Y3 tptp.set_Pr958786334691620121nt_int)) (=> (= X (@ tptp.abs_rat Y3)) (not (@ (@ tptp.member2340774599025711042nt_int Y3) (@ tptp.collec5210948495886036740nt_int (lambda ((C3 tptp.set_Pr958786334691620121nt_int)) (exists ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.ratrel X4))) (and (@ _let_1 X4) (= C3 (@ tptp.collec213857154873943460nt_int _let_1))))))))))))))
% 8.20/8.65 (assert (forall ((P2 (-> tptp.rat Bool)) (X tptp.rat)) (=> (forall ((Y3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int Y3) (@ tptp.collec5210948495886036740nt_int (lambda ((C3 tptp.set_Pr958786334691620121nt_int)) (exists ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.ratrel X4))) (and (@ _let_1 X4) (= C3 (@ tptp.collec213857154873943460nt_int _let_1)))))))) (@ P2 (@ tptp.abs_rat Y3)))) (@ P2 X))))
% 8.20/8.65 (assert (forall ((X tptp.set_Pr958786334691620121nt_int) (Y tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X) (@ tptp.collec5210948495886036740nt_int (lambda ((C3 tptp.set_Pr958786334691620121nt_int)) (exists ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.ratrel X4))) (and (@ _let_1 X4) (= C3 (@ tptp.collec213857154873943460nt_int _let_1)))))))) (=> (@ (@ tptp.member2340774599025711042nt_int Y) (@ tptp.collec5210948495886036740nt_int (lambda ((C3 tptp.set_Pr958786334691620121nt_int)) (exists ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.ratrel X4))) (and (@ _let_1 X4) (= C3 (@ tptp.collec213857154873943460nt_int _let_1)))))))) (= (= (@ tptp.abs_rat X) (@ tptp.abs_rat Y)) (= X Y))))))
% 8.20/8.65 (assert (forall ((Y tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int Y) (@ tptp.collec5210948495886036740nt_int (lambda ((C3 tptp.set_Pr958786334691620121nt_int)) (exists ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.ratrel X4))) (and (@ _let_1 X4) (= C3 (@ tptp.collec213857154873943460nt_int _let_1)))))))) (= (@ tptp.rep_rat (@ tptp.abs_rat Y)) Y))))
% 8.20/8.65 (assert (@ (@ (@ tptp.type_d8554052265237484179nt_int tptp.rep_rat) tptp.abs_rat) (@ tptp.collec5210948495886036740nt_int (lambda ((C3 tptp.set_Pr958786334691620121nt_int)) (exists ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.ratrel X4))) (and (@ _let_1 X4) (= C3 (@ tptp.collec213857154873943460nt_int _let_1)))))))))
% 8.20/8.65 (assert (forall ((X tptp.rat)) (@ (@ tptp.member2340774599025711042nt_int (@ tptp.rep_rat X)) (@ tptp.collec5210948495886036740nt_int (lambda ((C3 tptp.set_Pr958786334691620121nt_int)) (exists ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.ratrel X4))) (and (@ _let_1 X4) (= C3 (@ tptp.collec213857154873943460nt_int _let_1))))))))))
% 8.20/8.65 (assert (forall ((Y tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int Y) (@ tptp.collec5210948495886036740nt_int (lambda ((C3 tptp.set_Pr958786334691620121nt_int)) (exists ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.ratrel X4))) (and (@ _let_1 X4) (= C3 (@ tptp.collec213857154873943460nt_int _let_1)))))))) (not (forall ((X3 tptp.rat)) (not (= Y (@ tptp.rep_rat X3))))))))
% 8.20/8.65 (assert (forall ((Y tptp.set_Pr958786334691620121nt_int) (P2 (-> tptp.set_Pr958786334691620121nt_int Bool))) (=> (@ (@ tptp.member2340774599025711042nt_int Y) (@ tptp.collec5210948495886036740nt_int (lambda ((C3 tptp.set_Pr958786334691620121nt_int)) (exists ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.ratrel X4))) (and (@ _let_1 X4) (= C3 (@ tptp.collec213857154873943460nt_int _let_1)))))))) (=> (forall ((X3 tptp.rat)) (@ P2 (@ tptp.rep_rat X3))) (@ P2 Y)))))
% 8.20/8.65 (assert (= tptp.one_one_assn (@ tptp.abs_assn tptp.one_assn_raw)))
% 8.20/8.65 (assert (@ (@ tptp.order_5251275573222108571on_nat (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_Ca8665028551170535155natLeq))
% 8.20/8.65 (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))))
% 8.20/8.65 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.one_assn_raw X) Y) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (= Y (not (= As2 tptp.bot_bot_set_nat)))))))))
% 8.20/8.65 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.one_assn_raw X) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (not (= As2 tptp.bot_bot_set_nat))))))))
% 8.20/8.65 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.one_assn_raw X)) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (= As2 tptp.bot_bot_set_nat)))))))
% 8.20/8.65 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.one_assn_raw X)) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) X) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) _let_1) (= As2 tptp.bot_bot_set_nat))))))))))
% 8.20/8.65 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.one_assn_raw X) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) X) (not (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) _let_1) (not (= As2 tptp.bot_bot_set_nat)))))))))))
% 8.20/8.65 (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 ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (= X _let_1) (=> (= Y (= As2 tptp.bot_bot_set_nat)) (not (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) _let_1)))))))))))
% 8.20/8.65 (assert (forall ((B0 Bool) (B1 Bool) (B22 Bool) (B32 Bool) (B42 Bool) (B52 Bool) (B62 Bool) (B72 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.integer_of_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 B0) B1) B22) B32) B42) B52) B62) B72)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger B72)) _let_1)) (@ tptp.zero_n356916108424825756nteger B62))) _let_1)) (@ tptp.zero_n356916108424825756nteger B52))) _let_1)) (@ tptp.zero_n356916108424825756nteger B42))) _let_1)) (@ tptp.zero_n356916108424825756nteger B32))) _let_1)) (@ tptp.zero_n356916108424825756nteger B22))) _let_1)) (@ tptp.zero_n356916108424825756nteger B1))) _let_1)) (@ tptp.zero_n356916108424825756nteger B0))))))
% 8.20/8.65 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ (@ tptp.if_assn false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ (@ tptp.if_assn true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural)) (= (@ (@ (@ tptp.if_Code_natural false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural)) (= (@ (@ (@ tptp.if_Code_natural true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.option_set_o) (Y tptp.option_set_o)) (= (@ (@ (@ tptp.if_option_set_o false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.option_set_o) (Y tptp.option_set_o)) (= (@ (@ (@ tptp.if_option_set_o true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.option_set_int) (Y tptp.option_set_int)) (= (@ (@ (@ tptp.if_option_set_int false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.option_set_int) (Y tptp.option_set_int)) (= (@ (@ (@ tptp.if_option_set_int true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.option_set_nat) (Y tptp.option_set_nat)) (= (@ (@ (@ tptp.if_option_set_nat false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.option_set_nat) (Y tptp.option_set_nat)) (= (@ (@ (@ tptp.if_option_set_nat true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X (-> tptp.int tptp.product_prod_int_int)) (Y (-> tptp.int tptp.product_prod_int_int))) (= (@ (@ (@ tptp.if_int2409958687428134794nt_int false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X (-> tptp.int tptp.product_prod_int_int)) (Y (-> tptp.int tptp.product_prod_int_int))) (= (@ (@ (@ tptp.if_int2409958687428134794nt_int true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.multis2468970476368604999at_nat) (Y tptp.multis2468970476368604999at_nat)) (= (@ (@ (@ tptp.if_mul8430962117462786573at_nat false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.multis2468970476368604999at_nat) (Y tptp.multis2468970476368604999at_nat)) (= (@ (@ (@ tptp.if_mul8430962117462786573at_nat true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.option8963830502488799655at_nat) (Y tptp.option8963830502488799655at_nat)) (= (@ (@ (@ tptp.if_opt7704869406773131885at_nat false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.option8963830502488799655at_nat) (Y tptp.option8963830502488799655at_nat)) (= (@ (@ (@ tptp.if_opt7704869406773131885at_nat true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.option3562590408128118217it_nat) (Y tptp.option3562590408128118217it_nat)) (= (@ (@ (@ tptp.if_opt6883606601682554499it_nat false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.option3562590408128118217it_nat) (Y tptp.option3562590408128118217it_nat)) (= (@ (@ (@ tptp.if_opt6883606601682554499it_nat true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.option4065278094766928714it_nat) (Y tptp.option4065278094766928714it_nat)) (= (@ (@ (@ tptp.if_opt7386294288321364996it_nat false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.option4065278094766928714it_nat) (Y tptp.option4065278094766928714it_nat)) (= (@ (@ (@ tptp.if_opt7386294288321364996it_nat true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X tptp.option8956607266484857688it_nat) (Y tptp.option8956607266484857688it_nat)) (= (@ (@ (@ tptp.if_opt1729522071442692626it_nat false) X) Y) Y)))
% 8.20/8.65 (assert (forall ((X tptp.option8956607266484857688it_nat) (Y tptp.option8956607266484857688it_nat)) (= (@ (@ (@ tptp.if_opt1729522071442692626it_nat true) X) Y) X)))
% 8.20/8.65 (assert (forall ((X (-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)) (Y (-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural))) (= (@ (@ (@ tptp.if_Pro2760142802149639654atural false) X) Y) Y)))
% 112.47/112.91 (assert (forall ((X (-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)) (Y (-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural))) (= (@ (@ (@ tptp.if_Pro2760142802149639654atural true) X) Y) X)))
% 112.47/112.91 (assert (forall ((X (-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)) (Y (-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat))) (= (@ (@ (@ tptp.if_Pro3578090444564244254it_nat false) X) Y) Y)))
% 112.47/112.91 (assert (forall ((X (-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)) (Y (-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat))) (= (@ (@ (@ tptp.if_Pro3578090444564244254it_nat true) X) Y) X)))
% 112.47/112.91 (assert (forall ((X (-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)) (Y (-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat))) (= (@ (@ (@ tptp.if_Pro4080778131203054751it_nat false) X) Y) Y)))
% 112.47/112.91 (assert (forall ((X (-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)) (Y (-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat))) (= (@ (@ (@ tptp.if_Pro4080778131203054751it_nat true) X) Y) X)))
% 112.47/112.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)) (Y (-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat))) (= (@ (@ (@ tptp.if_Pro6440128116348121305et_nat false) X) Y) Y)))
% 112.47/112.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)) (Y (-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat))) (= (@ (@ (@ tptp.if_Pro6440128116348121305et_nat true) X) Y) X)))
% 112.47/112.91 (assert (forall ((P2 Bool)) (or (= P2 true) (= P2 false))))
% 112.47/112.91 (assert (forall ((X (-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)) (Y (-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat))) (= (@ (@ (@ tptp.if_Pro5796790085669187537et_nat false) X) Y) Y)))
% 112.47/112.91 (assert (forall ((X (-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)) (Y (-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat))) (= (@ (@ (@ tptp.if_Pro5796790085669187537et_nat true) X) Y) X)))
% 112.47/112.91 (assert (not (@ (@ tptp.rep_assn (@ tptp.q tptp.rg)) (@ (@ tptp.produc7507926704131184380et_nat tptp.h) (@ (@ (@ tptp.hoare_new_addrs tptp.h3) tptp.as) tptp.h)))))
% 112.47/112.91 (set-info :filename cvc5---1.0.5_798)
% 112.47/112.91 (check-sat-assuming ( true ))
% 112.47/112.91 ------- get file name : TPTP file name is ITP214^1
% 112.47/112.91 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_798.smt2...
% 112.47/112.91 --- Run --ho-elim --full-saturate-quant at 10...
% 112.47/112.91 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 112.47/112.91 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 112.47/112.91 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 112.47/112.91 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 112.47/112.91 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 112.47/112.91 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 112.47/112.91 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 112.47/112.91 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 112.47/112.91 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 112.47/112.91 % SZS status Theorem for ITP214^1
% 112.47/112.91 % SZS output start Proof for ITP214^1
% 112.47/112.91 (
% 112.47/112.91 (let ((_let_1 (@ (@ tptp.hoare_new_addrs tptp.h3) tptp.as))) (let ((_let_2 (@ _let_1 tptp.h))) (let ((_let_3 (@ tptp.produc7507926704131184380et_nat tptp.h))) (let ((_let_4 (@ tptp.rep_assn (@ tptp.q tptp.rg)))) (let ((_let_5 (not (@ _let_4 (@ _let_3 _let_2))))) (let ((_let_6 (@ tptp.field_nat tptp.bNF_Ca8665028551170535155natLeq))) (let ((_let_7 (= tptp.bNF_Ca8665028551170535155natLeq (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_eq_nat))))) (let ((_let_8 (= _let_6 tptp.top_top_set_nat))) (let ((_let_9 (= tptp.condit2214826472909112428ve_nat tptp.finite_finite_nat))) (let ((_let_10 (= tptp.ms_weak (@ (@ tptp.sup_su3035147773818789531at_nat tptp.ms_strict) tptp.id_mul2649389997224486051at_nat)))) (let ((_let_11 (= 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)))))) (let ((_let_12 (= tptp.fun_max_strict (@ tptp.max_ex8135407076693332796at_nat tptp.fun_pair_less)))) (let ((_let_13 (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)) tptp.bot_bo228742789529271731at_nat))) (let ((_let_14 (= tptp.fun_max_weak (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.max_ex8135407076693332796at_nat tptp.fun_pair_leq)) _let_13)))) (let ((_let_15 (= tptp.fun_min_weak (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.min_ex6901939911449802026at_nat tptp.fun_pair_leq)) _let_13)))) (let ((_let_16 (= tptp.fun_min_strict (@ tptp.min_ex6901939911449802026at_nat tptp.fun_pair_less)))) (let ((_let_17 (= tptp.fun_pair_leq (@ (@ tptp.sup_su718114333110466843at_nat tptp.fun_pair_less) tptp.id_Pro2258643101195443293at_nat)))) (let ((_let_18 (= tptp.fun_pair_less (@ (@ tptp.lex_prod_nat_nat tptp.less_than) tptp.less_than)))) (let ((_let_19 (@ (@ tptp.map_fu6256889081107267320ural_o tptp.code_nat_of_natural) (@ (@ tptp.map_fu4892316939951275536at_o_o tptp.code_nat_of_natural) tptp.id_o)))) (let ((_let_20 (= tptp.plus_p4538020629002901425atural (@ (@ (@ tptp.map_fu6549440983881763648atural tptp.code_nat_of_natural) (@ (@ tptp.map_fu1239815594074539274atural tptp.code_nat_of_natural) tptp.code_natural_of_nat)) tptp.plus_plus_nat)))) (let ((_let_21 (= tptp.ord_le1926595141338095240atural (lambda ((X4 tptp.code_natural) (Xa2 tptp.code_natural)) (@ (@ tptp.ord_less_eq_nat (@ tptp.code_nat_of_natural X4)) (@ tptp.code_nat_of_natural Xa2)))))) (let ((_let_22 (= tptp.ord_le5570908160329646204atural (lambda ((X4 tptp.code_natural) (Xa2 tptp.code_natural)) (@ (@ tptp.ord_less_nat (@ tptp.code_nat_of_natural X4)) (@ tptp.code_nat_of_natural Xa2)))))) (let ((_let_23 (= tptp.product_Unity (@ tptp.product_Abs_unit true)))) (let ((_let_24 (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))) (let ((_let_25 (@ tptp.finite3254316476582989077op_nat tptp.top_top_set_nat))) (let ((_let_26 (= 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)))))))))) (let ((_let_27 (= tptp.complete_Inf_Inf_nat (lambda ((X11 tptp.set_nat)) (@ tptp.ord_Least_nat (lambda ((N tptp.nat)) (@ (@ tptp.member_nat N) X11))))))) (let ((_let_28 (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat)))) (let ((_let_29 (= 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)))))))))) (let ((_let_30 (= 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))))))) (let ((_let_31 (= tptp.code_sub (@ (@ (@ tptp.map_fu6891787308814931657nteger tptp.id_num) (@ (@ tptp.map_fu8638147718074629079nteger tptp.id_num) tptp.code_integer_of_int)) (lambda ((M3 tptp.num) (N tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M3)) (@ tptp.numeral_numeral_int N))))))) (let ((_let_32 (= tptp.cr_rat (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.rat)) (and (@ (@ tptp.ratrel X4) X4) (= (@ tptp.abs_Rat X4) Y4)))))) (let ((_let_33 (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel))) (let ((_let_34 (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) _let_33))) (let ((_let_35 (= tptp.ratrel (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X4))) (let ((_let_2 (@ tptp.product_snd_int_int Y4))) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y4)) _let_1))))))))) (let ((_let_36 (@ (@ tptp.map_fu2599414010547811884nteger tptp.code_int_of_integer) tptp.code_integer_of_int))) (let ((_let_37 (= tptp.code_dup (@ _let_36 (lambda ((K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) K3)))))) (let ((_let_38 (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat))) (let ((_let_39 (= tptp.uminus_uminus_rat (@ _let_38 (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))))))) (let ((_let_40 (@ (@ tptp.map_fu7831380289885515383nt_rat tptp.id_int) (@ (@ tptp.map_fu3424225382358772769nt_rat tptp.id_int) tptp.abs_Rat)))) (let ((_let_41 (= tptp.fract (@ _let_40 (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B4 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A5) B4))))))) (let ((_let_42 (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) _let_38))) (let ((_let_43 (= tptp.times_times_rat (@ _let_42 (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) (@ tptp.product_fst_int_int Y4))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X4)) (@ tptp.product_snd_int_int Y4)))))))) (let ((_let_44 (= tptp.inverse_inverse_rat (@ _let_38 (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)))))))) (let ((_let_45 (= tptp.plus_plus_rat (@ _let_42 (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y4))) (let ((_let_2 (@ tptp.product_snd_int_int X4))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y4)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))) (let ((_let_46 (= tptp.plus_p5714425477246183910nteger (@ (@ (@ tptp.map_fu8272188784021352819nteger tptp.code_int_of_integer) _let_36) tptp.plus_plus_int)))) (let ((_let_47 (@ (@ tptp.map_fu2496120808607739376eger_o tptp.code_int_of_integer) (@ (@ tptp.map_fu6957801986076833569nt_o_o tptp.code_int_of_integer) tptp.id_o)))) (let ((_let_48 (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))) (let ((_let_49 (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)))) (let ((_let_50 (= tptp.semiri1316708129612266289at_nat tptp.id_nat))) (let ((_let_51 (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel))) (let ((_let_52 (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) _let_51))) (let ((_let_53 (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel))) (let ((_let_54 (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel))) (let ((_let_55 (= 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 ((U3 tptp.nat) (V2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat X4) V2) (@ (@ tptp.plus_plus_nat U3) Y4)))) __flatten_var_0)))))) (let ((_let_56 (= tptp.inf_inf_nat tptp.ord_min_nat))) (let ((_let_57 (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M3) N))) M3)))))) (let ((_let_58 (= tptp.positive (lambda ((X4 tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X4))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.product_snd_int_int _let_1)))))))) (let ((_let_59 (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int))) (let ((_let_60 (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) _let_59))) (let ((_let_61 (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int))) (let ((_let_62 (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int))) (let ((_let_63 (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat))) (let ((_let_64 (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) _let_63))) (let ((_let_65 (= tptp.top_top_set_o (@ (@ tptp.insert_o false) _let_24)))) (let ((_let_66 (= 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))))))))) (let ((_let_67 (= tptp.top_top_assn (@ tptp.abs_assn tptp.in_range)))) (let ((_let_68 (= tptp.top_top_Product_unit tptp.product_Unity))) (let ((_let_69 (= tptp.top_to1996260823553986621t_unit (@ (@ tptp.insert_Product_unit tptp.product_Unity) tptp.bot_bo3957492148770167129t_unit)))) (let ((_let_70 (= tptp.complete_Inf_Inf_int (lambda ((X11 tptp.set_int)) (@ tptp.uminus_uminus_int (@ tptp.complete_Sup_Sup_int (@ (@ tptp.image_int_int tptp.uminus_uminus_int) X11))))))) (let ((_let_71 (= tptp.comple2584293577114468500t_unit (lambda ((Uu3 tptp.set_Product_unit)) tptp.product_Unity)))) (let ((_let_72 (= tptp.comple4687483117567863418t_unit (lambda ((Uu3 tptp.set_Product_unit)) tptp.product_Unity)))) (let ((_let_73 (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat))) (let ((_let_74 (= _let_73 tptp.zero_zero_nat))) (let ((_let_75 (= tptp.finite_finite_int (lambda ((S4 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S4)) (@ tptp.set_ord_atMost_int K3))))))) (let ((_let_76 (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M3 tptp.nat) (N tptp.nat)) (= N (@ tptp.suc M3)))))))) (let ((_let_77 (= tptp.set_or5832277885323065728an_int (lambda ((I tptp.int) (J tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J) tptp.one_one_int))))))) (let ((_let_78 (= tptp.set_or6656581121297822940st_int (lambda ((I tptp.int) (J tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J)))))) (let ((_let_79 (= 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)))))))))))))) (let ((_let_80 (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ))) (let ((_let_81 (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) _let_80))) (let ((_let_82 (= tptp.archim3151403230148437115or_rat (lambda ((P7 tptp.rat)) (@ (@ tptp.produc8211389475949308722nt_int tptp.divide_divide_int) (@ tptp.quotient_of P7)))))) (let ((_let_83 (= tptp.split_seed (lambda ((S5 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc8282080750456430313atural (lambda ((V2 tptp.code_natural) (W3 tptp.code_natural)) (@ (@ tptp.produc8282080750456430313atural (lambda ((V4 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 V4) (@ (@ 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 S5))))) S5))))) (let ((_let_84 (= tptp.finite_card_nat (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) tptp.one_one_nat))))) (let ((_let_85 (= tptp.finite_card_set_nat (@ tptp.groups8294997508430121362at_nat (lambda ((X4 tptp.set_nat)) tptp.one_one_nat))))) (let ((_let_86 (= tptp.finite_card_list_nat (@ tptp.groups4396056296759096172at_nat (lambda ((X4 tptp.list_nat)) tptp.one_one_nat))))) (let ((_let_87 (= tptp.finite_card_int (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) tptp.one_one_nat))))) (let ((_let_88 (= tptp.ord_max_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A5) B4)) B4) A5))))) (let ((_let_89 (= tptp.ord_max_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A5) B4)) B4) A5))))) (let ((_let_90 (= tptp.ord_max_set_int (lambda ((A5 tptp.set_int) (B4 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A5) B4)) B4) A5))))) (let ((_let_91 (= tptp.ord_less_eq_num (lambda ((A5 tptp.num) (B4 tptp.num)) (= (@ (@ tptp.ord_max_num A5) B4) B4))))) (let ((_let_92 (= tptp.sup_sup_nat tptp.ord_max_nat))) (let ((_let_93 (= tptp.sup_sup_int tptp.ord_max_int))) (let ((_let_94 (= 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)))))))) (let ((_let_95 (= 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)))))))) (let ((_let_96 (= 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)))))))) (let ((_let_97 (= 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)))))))) (let ((_let_98 (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (A5 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.bit_se547839408752420682it_nat K3) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.bit_se1148574629649215175it_nat A5) K3))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))) (let ((_let_99 (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (A5 tptp.int)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.bit_se545348938243370406it_int K3) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int A5) K3))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))) (let ((_let_100 (= tptp.bit_se1745604003318907178nteger (lambda ((N tptp.nat) (A5 tptp.code_integer)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ tptp.bit_se7788150548672797655nteger K3) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.bit_se9216721137139052372nteger A5) K3))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))) (let ((_let_101 (= tptp.bit_concat_bit (lambda ((N tptp.nat) (K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N) K3)) (@ (@ tptp.bit_se545348938243370406it_int N) L2)))))) (let ((_let_102 (= 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)))))))) (let ((_let_103 (= tptp.bit_ri6519982836138164636nteger (lambda ((N tptp.nat) (A5 tptp.code_integer)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger _let_1) A5))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.bit_se7788150548672797655nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) _let_2))))))) (let ((_let_104 (= tptp.set_ord_lessThan_int (lambda ((U3 tptp.int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_int X4) U3))))))) (let ((_let_105 (= tptp.set_ord_lessThan_nat (lambda ((U3 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) U3))))))) (let ((_let_106 (= tptp.set_ord_lessThan_num (lambda ((U3 tptp.num)) (@ tptp.collect_num (lambda ((X4 tptp.num)) (@ (@ tptp.ord_less_num X4) U3))))))) (let ((_let_107 (= tptp.set_ord_lessThan_rat (lambda ((U3 tptp.rat)) (@ tptp.collect_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.ord_less_rat X4) U3))))))) (let ((_let_108 (= tptp.set_or7637083652282234053n_assn (lambda ((U3 tptp.assn)) (@ tptp.collect_assn (lambda ((X4 tptp.assn)) (@ (@ tptp.ord_less_assn X4) U3))))))) (let ((_let_109 (= tptp.set_or890127255671739683et_nat (lambda ((U3 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_set_nat X4) U3))))))) (let ((_let_110 (= tptp.set_or4940836740269066044nt_int (lambda ((U3 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.ord_le7563427860532173253nt_int X4) U3))))))) (let ((_let_111 (= tptp.bNF_Ca8459412986667044542atLess _let_28))) (let ((_let_112 (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K3 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R5 tptp.code_integer) (S5 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K3)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S5))) (= S5 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))) (let ((_let_113 (= tptp.groups9116527308978886569_o_int (lambda ((F3 (-> Bool tptp.int)) (A5 tptp.int) (Xs3 tptp.list_o)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ F3 (@ (@ tptp.nth_o Xs3) N))) (@ (@ tptp.power_power_int A5) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs3))))))) (let ((_let_114 (= 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))))))) (let ((_let_115 (= tptp.groups9119017779487936845_o_nat (lambda ((F3 (-> Bool tptp.nat)) (A5 tptp.nat) (Xs3 tptp.list_o)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_nat (@ F3 (@ (@ tptp.nth_o Xs3) N))) (@ (@ tptp.power_power_nat A5) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs3))))))) (let ((_let_116 (= 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))))))) (let ((_let_117 (= 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))))))) (let ((_let_118 (= 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))))))) (let ((_let_119 (= 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))))))) (let ((_let_120 (= 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))))))) (let ((_let_121 (= 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))))))) (let ((_let_122 (= tptp.gbinomial_int (lambda ((A5 tptp.int) (K3 tptp.nat)) (@ (@ tptp.divide_divide_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_int A5) (@ tptp.semiri1314217659103216013at_int I)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3))) (@ tptp.semiri1406184849735516958ct_int K3)))))) (let ((_let_123 (= tptp.gbinomial_nat (lambda ((A5 tptp.nat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I tptp.nat)) (@ (@ tptp.minus_minus_nat A5) (@ tptp.semiri1316708129612266289at_nat I)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3))) (@ tptp.semiri1408675320244567234ct_nat K3)))))) (let ((_let_124 (= tptp.gbinom8545251970709558553nteger (lambda ((A5 tptp.code_integer) (K3 tptp.nat)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.groups3455450783089532116nteger (lambda ((I tptp.nat)) (@ (@ tptp.minus_8373710615458151222nteger A5) (@ tptp.semiri4939895301339042750nteger I)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3))) (@ tptp.semiri3624122377584611663nteger K3)))))) (let ((_let_125 (= tptp.gbinom7368847122466276068atural (lambda ((A5 tptp.code_natural) (K3 tptp.nat)) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.groups2279045934846249631atural (lambda ((I tptp.nat)) (@ (@ tptp.minus_7197305767214868737atural A5) (@ tptp.semiri3763490453095760265atural I)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3))) (@ tptp.semiri2447717529341329178atural K3)))))) (let ((_let_126 (= 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))))))) (let ((_let_127 (= 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))))))) (let ((_let_128 (= 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))))))) (let ((_let_129 (= 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 ((R5 tptp.code_integer) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 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)) S5)))))) _let_1))))))))))) (let ((_let_130 (= tptp.set_ord_atMost_int (lambda ((U3 tptp.int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_eq_int X4) U3))))))) (let ((_let_131 (= tptp.set_ord_atMost_nat (lambda ((U3 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X4) U3))))))) (let ((_let_132 (= tptp.set_ord_atMost_num (lambda ((U3 tptp.num)) (@ tptp.collect_num (lambda ((X4 tptp.num)) (@ (@ tptp.ord_less_eq_num X4) U3))))))) (let ((_let_133 (= tptp.set_ord_atMost_rat (lambda ((U3 tptp.rat)) (@ tptp.collect_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X4) U3))))))) (let ((_let_134 (= tptp.set_or58775011639299419et_int (lambda ((U3 tptp.set_int)) (@ tptp.collect_set_int (lambda ((X4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X4) U3))))))) (let ((_let_135 (= tptp.set_or4236626031148496127et_nat (lambda ((U3 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X4) U3))))))) (let ((_let_136 (= tptp.set_or2459421552957432928nt_int (lambda ((U3 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.ord_le2843351958646193337nt_int X4) U3))))))) (let ((_let_137 (= 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)))))) (let ((_let_138 (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X23 tptp.nat)) X23))))) (let ((_let_139 (= tptp.uminus_uminus_int (lambda ((A5 tptp.int)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A5)) tptp.one_one_int))))) (let ((_let_140 (= tptp.uminus1351360451143612070nteger (lambda ((A5 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.bit_ri7632146776885996613nteger A5)) tptp.one_one_Code_integer))))) (let ((_let_141 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_142 (not (@ _let_141 tptp.zero_z3403309356797280102nteger)))) (let ((_let_143 (= tptp.is_singleton_int (lambda ((A6 tptp.set_int)) (= A6 (@ (@ tptp.insert_int (@ tptp.the_elem_int A6)) tptp.bot_bot_set_int)))))) (let ((_let_144 (= tptp.is_singleton_nat (lambda ((A6 tptp.set_nat)) (= A6 (@ (@ tptp.insert_nat (@ tptp.the_elem_nat A6)) tptp.bot_bot_set_nat)))))) (let ((_let_145 (= tptp.is_singleton_o (lambda ((A6 tptp.set_o)) (= A6 (@ (@ tptp.insert_o (@ tptp.the_elem_o A6)) tptp.bot_bot_set_o)))))) (let ((_let_146 (= tptp.is_sin2850979758926227957at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat)) (= A6 (@ (@ tptp.insert8211810215607154385at_nat (@ tptp.the_el2281957884133575798at_nat A6)) tptp.bot_bo2099793752762293965at_nat)))))) (let ((_let_147 (= tptp.is_sin2937591304547752795at_nat (lambda ((A6 tptp.set_Pr4329608150637261639at_nat)) (= A6 (@ (@ tptp.insert9069300056098147895at_nat (@ tptp.the_el221668144340439132at_nat A6)) tptp.bot_bo228742789529271731at_nat)))))) (let ((_let_148 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_149 (@ _let_148 tptp.zero_z3403309356797280102nteger))) (let ((_let_150 (= tptp.inc_shift (lambda ((V2 tptp.code_natural) (K3 tptp.code_natural)) (@ (@ (@ tptp.if_Code_natural (= V2 K3)) tptp.one_one_Code_natural) (@ (@ tptp.plus_p4538020629002901425atural K3) tptp.one_one_Code_natural)))))) (let ((_let_151 (= tptp.bit_se7879613467334960850it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))) (let ((_let_152 (= tptp.produc5538323210962509403atural (lambda ((F3 (-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)) (G3 (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)) (X4 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc8638916746724166107atural G3) (@ F3 X4)))))) (let ((_let_153 (= 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))))) (let ((_let_154 (= 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))))))))))) (let ((_let_155 (= tptp.minus_shift (lambda ((R5 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 R5) K3)) L2)) (@ (@ tptp.minus_7197305767214868737atural K3) L2)))))) (let ((_let_156 (= tptp.int_ge_less_than (lambda ((D5 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z8 tptp.int) (Z tptp.int)) (and (@ (@ tptp.ord_less_eq_int D5) Z8) (@ (@ tptp.ord_less_int Z8) Z))))))))) (let ((_let_157 (= tptp.int_ge_less_than2 (lambda ((D5 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z8 tptp.int) (Z tptp.int)) (and (@ (@ tptp.ord_less_eq_int D5) Z) (@ (@ tptp.ord_less_int Z8) Z))))))))) (let ((_let_158 (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q8 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q8) (@ tptp.zero_n2684676970156552555ol_int (not (= R5 tptp.zero_zero_int))))))))) (let ((_let_159 (= tptp.insert6337962749363155127at_nat (lambda ((A5 tptp.produc4166570645942440679at_nat) (__flatten_var_0 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ tptp.collec5204685387357076818at_nat (lambda ((X4 tptp.produc4166570645942440679at_nat)) (= X4 A5)))) __flatten_var_0))))) (let ((_let_160 (= tptp.insert_int (lambda ((A5 tptp.int) (B6 tptp.set_int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (or (= X4 A5) (@ (@ tptp.member_int X4) B6)))))))) (let ((_let_161 (= tptp.insert_nat (lambda ((A5 tptp.nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (or (= X4 A5) (@ (@ tptp.member_nat X4) B6)))))))) (let ((_let_162 (= tptp.insert_set_nat (lambda ((A5 tptp.set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (or (= X4 A5) (@ (@ tptp.member_set_nat X4) B6)))))))) (let ((_let_163 (= tptp.insert8897473484851387113nt_int (lambda ((A5 tptp.set_Pr958786334691620121nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (or (= X4 A5) (@ (@ tptp.member2340774599025711042nt_int X4) B6)))))))) (let ((_let_164 (= tptp.insert_list_nat (lambda ((A5 tptp.list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (or (= X4 A5) (@ (@ tptp.member_list_nat X4) B6)))))))) (let ((_let_165 (= tptp.insert_o (lambda ((A5 Bool) (B6 tptp.set_o)) (@ tptp.collect_o (lambda ((X4 Bool)) (or (= X4 A5) (@ (@ tptp.member_o X4) B6)))))))) (let ((_let_166 (= tptp.insert8211810215607154385at_nat (lambda ((A5 tptp.product_prod_nat_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (or (= X4 A5) (@ (@ tptp.member8440522571783428010at_nat X4) B6)))))))) (let ((_let_167 (= tptp.insert9069300056098147895at_nat (lambda ((A5 tptp.produc3843707927480180839at_nat) (B6 tptp.set_Pr4329608150637261639at_nat)) (@ tptp.collec6321179662152712658at_nat (lambda ((X4 tptp.produc3843707927480180839at_nat)) (or (= X4 A5) (@ (@ tptp.member8757157785044589968at_nat X4) B6)))))))) (let ((_let_168 (= tptp.mlex_prod_int (lambda ((F3 (-> tptp.int tptp.nat)) (R 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)) R)))))))))))) (let ((_let_169 (= tptp.rel_of_int_int (lambda ((M3 (-> tptp.int tptp.option_int)) (P5 (-> 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)) (@ P5 (@ (@ tptp.product_Pair_int_int K3) V2)))))))))) (let ((_let_170 (= tptp.rel_of2761222537318653906it_nat (lambda ((M3 (-> tptp.a tptp.option233860712434008220it_nat)) (P5 (-> 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)) (@ P5 (@ (@ tptp.produc9178034014595674355it_nat K3) V2)))))))))) (let ((_let_171 (= tptp.rel_of6889123638293104083it_nat (lambda ((M3 (-> tptp.b tptp.option233860712434008220it_nat)) (P5 (-> tptp.produc7388388658123137530it_nat Bool))) (@ tptp.collec8276579174399660751it_nat (@ tptp.produc3971132677695353399_nat_o (lambda ((K3 tptp.b) (V2 tptp.produc6653097349344004940it_nat)) (and (= (@ M3 K3) (@ tptp.some_P1054239925786823975it_nat V2)) (@ P5 (@ (@ tptp.produc4082563078715348724it_nat K3) V2)))))))))) (let ((_let_172 (= tptp.rel_of7774016450764239315et_nat (lambda ((M3 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.option5190343406534369742et_nat)) (P5 (-> 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)) (@ P5 (@ (@ tptp.produc2245416461498447860et_nat K3) V2)))))))))) (let ((_let_173 (= tptp.rel_of4838799251197538391et_nat (lambda ((M3 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.option936205604648967762et_nat)) (P5 (-> 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)) (@ P5 (@ (@ tptp.produc5001842942810119800et_nat K3) V2)))))))))) (let ((_let_174 (= 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 ((R5 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 R5)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_a F3) H6)))))))) (let ((_let_175 (= tptp.heap_T3413130826733729493t_unit (lambda ((F3 tptp.heap_Time_Heap_b) (G3 (-> tptp.b tptp.heap_T5738788834812785303t_unit))) (@ tptp.heap_T6183433275982383450t_unit (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ (@ tptp.case_o2632329678403290591it_nat tptp.none_P9117596204409417319it_nat) (@ tptp.produc450363836004716793it_nat (lambda ((R5 tptp.b) (__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 R5)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_b F3) H6)))))))) (let ((_let_176 (= 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 ((R5 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 R5)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_a F3) H6)))))))) (let ((_let_177 (= tptp.heap_Time_bind_b_a (lambda ((F3 tptp.heap_Time_Heap_b) (G3 (-> tptp.b tptp.heap_Time_Heap_a))) (@ tptp.heap_Time_Heap_a2 (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ (@ tptp.case_o965627003169710416it_nat tptp.none_P2651198173097904984it_nat) (@ tptp.produc3428986626803312746it_nat (lambda ((R5 tptp.b) (__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 R5)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_b F3) H6)))))))) (let ((_let_178 (= tptp.heap_Time_bind_a_b (lambda ((F3 tptp.heap_Time_Heap_a) (G3 (-> tptp.a tptp.heap_Time_Heap_b))) (@ tptp.heap_Time_Heap_b2 (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ (@ tptp.case_o1773283271472524752it_nat tptp.none_P6779099274072355161it_nat) (@ tptp.produc8352694711413002346it_nat (lambda ((R5 tptp.a) (__flatten_var_0 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.produc6148253707941125437it_nat (lambda ((H7 tptp.heap_e7401611519738050253t_unit) (N tptp.nat)) (@ (@ tptp.heap_T7616092557645711336rame_b N) (@ (@ tptp.heap_Time_execute_b (@ G3 R5)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_a F3) H6)))))))) (let ((_let_179 (= tptp.heap_Time_bind_b_b (lambda ((F3 tptp.heap_Time_Heap_b) (G3 (-> tptp.b tptp.heap_Time_Heap_b))) (@ tptp.heap_Time_Heap_b2 (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ (@ tptp.case_o5901184372446974929it_nat tptp.none_P6779099274072355161it_nat) (@ tptp.produc3931674313442123243it_nat (lambda ((R5 tptp.b) (__flatten_var_0 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.produc6148253707941125437it_nat (lambda ((H7 tptp.heap_e7401611519738050253t_unit) (N tptp.nat)) (@ (@ tptp.heap_T7616092557645711336rame_b N) (@ (@ tptp.heap_Time_execute_b (@ G3 R5)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_b F3) H6)))))))) (let ((_let_180 (= 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))))))))) (let ((_let_181 (= tptp.lex_prod_nat_nat (lambda ((Ra tptp.set_Pr1261947904930325089at_nat) (Rb tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec7088162979684241874at_nat (@ tptp.produc6590410687421337004_nat_o (@ tptp.produc8739625826339149834_nat_o (lambda ((A5 tptp.nat) (B4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((A8 tptp.nat) (B8 tptp.nat)) (or (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A5) A8)) Ra) (and (= A5 A8) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B4) B8)) Rb))))) __flatten_var_0))))))))) (let ((_let_182 (= tptp.lex_prod_int_int (lambda ((Ra tptp.set_Pr958786334691620121nt_int) (Rb tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec7447955092554649554nt_int (@ tptp.produc1676490119946744748_int_o (@ tptp.produc1459180154077124618_int_o (lambda ((A5 tptp.int) (B4 tptp.int) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A8 tptp.int) (B8 tptp.int)) (or (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A5) A8)) Ra) (and (= A5 A8) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B4) B8)) Rb))))) __flatten_var_0))))))))) (let ((_let_183 (= tptp.same_fst_nat_nat (lambda ((P5 (-> tptp.nat Bool)) (R (-> tptp.nat tptp.set_Pr1261947904930325089at_nat))) (@ tptp.collec7088162979684241874at_nat (@ tptp.produc6590410687421337004_nat_o (@ tptp.produc8739625826339149834_nat_o (lambda ((X8 tptp.nat) (Y9 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (= X8 X4) (@ P5 X4) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y9) Y4)) (@ R X4))))) __flatten_var_0))))))))) (let ((_let_184 (= tptp.same_fst_int_int (lambda ((P5 (-> tptp.int Bool)) (R (-> tptp.int tptp.set_Pr958786334691620121nt_int))) (@ tptp.collec7447955092554649554nt_int (@ tptp.produc1676490119946744748_int_o (@ tptp.produc1459180154077124618_int_o (lambda ((X8 tptp.int) (Y9 tptp.int) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((X4 tptp.int) (Y4 tptp.int)) (and (= X8 X4) (@ P5 X4) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y9) Y4)) (@ R X4))))) __flatten_var_0))))))))) (let ((_let_185 (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q8 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q8))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))) (let ((_let_186 (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q8 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q8))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))) (let ((_let_187 (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))) (let ((_let_188 (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q8 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q8))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))) (let ((_let_189 (= tptp.produc7926200574084438792nt_int tptp.produc8211389475949308722nt_int))) (let ((_let_190 (= tptp.produc8005341501107743676_int_o tptp.produc4947309494688390418_int_o))) (let ((_let_191 (= tptp.produc297006045350968285nt_int tptp.produc4245557441103728435nt_int))) (let ((_let_192 (= tptp.produc4780622933104268256_nat_o tptp.produc8739625826339149834_nat_o))) (let ((_let_193 (= tptp.produc1854806715440696265at_nat tptp.produc27273713700761075at_nat))) (let ((_let_194 (= tptp.uncurry_int_int_int tptp.produc8211389475949308722nt_int))) (let ((_let_195 (= tptp.uncurry_int_int_o tptp.produc4947309494688390418_int_o))) (let ((_let_196 (= tptp.uncurr7650761721940715016nt_int tptp.produc4245557441103728435nt_int))) (let ((_let_197 (= tptp.uncurr7511940902602773877_nat_o tptp.produc8739625826339149834_nat_o))) (let ((_let_198 (= tptp.uncurr8011562610307062878at_nat tptp.produc27273713700761075at_nat))) (let ((_let_199 (= 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) (R5 tptp.nat)) (@ (@ (@ F3 L2) R5) Y4))) X4))))) (let ((_let_200 (= 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) (R5 tptp.nat)) (@ (@ (@ F3 L2) R5) Y4))) X4))))) (let ((_let_201 (= 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)))))))) (let ((_let_202 (= 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)))))))) (let ((_let_203 (= 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)))))))) (let ((_let_204 (= tptp.archim7778729529865785530nd_rat (lambda ((X4 tptp.rat)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))) (let ((_let_205 (@ tptp.bit0 tptp.one))) (let ((_let_206 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_207 (@ _let_206 tptp.one_one_nat))) (let ((_let_208 (= _let_207 (@ tptp.numeral_numeral_nat _let_205)))) (let ((_let_209 (@ tptp.numeral_numeral_rat _let_205))) (let ((_let_210 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_211 (@ tptp.plus_plus_rat _let_210))) (let ((_let_212 (@ tptp.numera6620942414471956472nteger _let_205))) (let ((_let_213 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_214 (@ tptp.plus_p5714425477246183910nteger _let_213))) (let ((_let_215 (@ tptp.numeral_numeral_int _let_205))) (let ((_let_216 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_217 (@ tptp.plus_plus_int _let_216))) (let ((_let_218 (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (let ((_let_219 (@ _let_218 tptp.one_one_Code_integer))) (let ((_let_220 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_221 (@ _let_220 tptp.one_one_int))) (let ((_let_222 (@ tptp.plus_plus_rat tptp.one_one_rat))) (let ((_let_223 (@ _let_222 tptp.one_one_rat))) (let ((_let_224 (= tptp.archim2889992004027027881ng_rat (lambda ((X4 tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X4))) (@ (@ (@ tptp.if_int (= X4 (@ tptp.ring_1_of_int_rat _let_1))) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))) (let ((_let_225 (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 K3))))))) (let ((_let_226 (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 K3))))))) (let ((_let_227 (= tptp.ring_1_of_int_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 K3))))))) (let ((_let_228 (= tptp.numeral_numeral_nat (lambda ((I tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I)))))) (let ((_let_229 (= tptp.sorted_wrt_int (lambda ((P5 (-> tptp.int tptp.int Bool)) (Xs3 tptp.list_int)) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs3))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int Xs3)) (@ (@ P5 (@ _let_1 I)) (@ _let_1 J)))))))))) (let ((_let_230 (= tptp.sorted_wrt_o (lambda ((P5 (-> Bool Bool Bool)) (Xs3 tptp.list_o)) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs3))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_o Xs3)) (@ (@ P5 (@ _let_1 I)) (@ _let_1 J)))))))))) (let ((_let_231 (= tptp.sorted_wrt_nat (lambda ((P5 (-> tptp.nat tptp.nat Bool)) (Xs3 tptp.list_nat)) (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs3))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs3)) (@ (@ P5 (@ _let_1 I)) (@ _let_1 J)))))))))) (let ((_let_232 (= tptp.array_of_list_int (lambda ((Xs3 tptp.list_int)) (@ (@ tptp.array_make_int (@ tptp.size_size_list_int Xs3)) (@ tptp.nth_int Xs3)))))) (let ((_let_233 (= tptp.array_of_list_o (lambda ((Xs3 tptp.list_o)) (@ (@ tptp.array_make_o (@ tptp.size_size_list_o Xs3)) (@ tptp.nth_o Xs3)))))) (let ((_let_234 (= tptp.array_of_list_nat (lambda ((Xs3 tptp.list_nat)) (@ (@ tptp.array_make_nat (@ tptp.size_size_list_nat Xs3)) (@ tptp.nth_nat Xs3)))))) (let ((_let_235 (= 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))))))) (let ((_let_236 (= 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))))))) (let ((_let_237 (= tptp.sgn_sgn_int (lambda ((I tptp.int)) (@ (@ (@ tptp.if_int (= I tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))) (let ((_let_238 (= tptp.neg_nu3811975205180677377ec_int (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X4) X4)) tptp.one_one_int))))) (let ((_let_239 (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X4) X4)) tptp.one_one_rat))))) (let ((_let_240 (= tptp.neg_nu7757733837767384882nteger (lambda ((X4 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger X4) X4)) tptp.one_one_Code_integer))))) (let ((_let_241 (= 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) (Q8 tptp.int)) (and (= A12 K3) (= A22 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q8) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q8) L2)))) (exists ((R5 tptp.int) (L2 tptp.int) (K3 tptp.int) (Q8 tptp.int)) (and (= A12 K3) (= A22 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q8) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L2)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L2)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q8) L2)) R5))))))))) (let ((_let_242 (= tptp.abs_abs_rat (lambda ((A5 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A5) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A5)) A5))))) (let ((_let_243 (= tptp.abs_abs_Code_integer (lambda ((A5 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A5) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A5)) A5))))) (let ((_let_244 (= tptp.abs_abs_int (lambda ((A5 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A5) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A5)) A5))))) (let ((_let_245 (= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A5) (@ tptp.semiri681578069525770553at_rat K3))) tptp.one_one_rat)) K3)) (@ tptp.semiri773545260158071498ct_rat K3)))))) (let ((_let_246 (= 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)))))))) (let ((_let_247 (= 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)))))))) (let ((_let_248 (= 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)))))))) (let ((_let_249 (= 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)))))))) (let ((_let_250 (= tptp.minus_2612819937483484256nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (@ tptp.collec5210948495886036740nt_int (@ (@ tptp.minus_357216186751819389_int_o (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) A6))) (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) B6)))))))) (let ((_let_251 (= 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)))))))) (let ((_let_252 (= 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)))))))) (let ((_let_253 (= 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)))))))) (let ((_let_254 (= 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)))))))) (let ((_let_255 (= 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)))))))) (let ((_let_256 (= tptp.uminus6423885277529793776nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int)) (@ tptp.collec5210948495886036740nt_int (@ tptp.uminus8147837162492574189_int_o (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) A6)))))))) (let ((_let_257 (= 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)))))))) (let ((_let_258 (= 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)))))))) (let ((_let_259 (= tptp.uminus_uminus_assn (lambda ((P5 tptp.assn)) (@ tptp.abs_assn (lambda ((H6 tptp.produc3658429121746597890et_nat)) (and (@ tptp.in_range H6) (not (@ (@ tptp.rep_assn P5) H6))))))))) (let ((_let_260 (= tptp.uminus2952777764628376836t_unit (lambda ((Uu3 tptp.product_unit)) tptp.product_Unity)))) (let ((_let_261 (= tptp.minus_minus_assn (lambda ((A5 tptp.assn) (B4 tptp.assn)) (@ (@ tptp.inf_inf_assn A5) (@ tptp.uminus_uminus_assn B4)))))) (let ((_let_262 (= 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)))))) (let ((_let_263 (= 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)))))) (let ((_let_264 (= 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)))))) (let ((_let_265 (= 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)))))) (let ((_let_266 (= tptp.modulo_modulo_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4))))))) (let ((_let_267 (= tptp.divide_divide_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4))))))) (let ((_let_268 (= tptp.times_times_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4))))))) (let ((_let_269 (= tptp.plus_plus_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4))))))) (let ((_let_270 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_271 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_272 (@ tptp.ord_less_rat _let_210))) (let ((_let_273 (@ tptp.ord_le6747313008572928689nteger _let_213))) (let ((_let_274 (@ tptp.ord_less_int _let_216))) (let ((_let_275 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_276 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_277 (@ tptp.ord_less_eq_int _let_216))) (let ((_let_278 (@ tptp.ord_less_eq_rat _let_210))) (let ((_let_279 (@ tptp.ord_le3102999989581377725nteger _let_213))) (let ((_let_280 (@ tptp.ord_less_rat tptp.one_one_rat))) (let ((_let_281 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (let ((_let_282 (@ tptp.ord_less_int tptp.one_one_int))) (let ((_let_283 (@ tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_284 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (let ((_let_285 (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer))) (let ((_let_286 (= tptp.minus_minus_nat (lambda ((A5 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B4))))))) (let ((_let_287 (= tptp.minus_minus_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.uminus_uminus_rat B4)))))) (let ((_let_288 (= tptp.minus_8373710615458151222nteger (lambda ((A5 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.uminus1351360451143612070nteger B4)))))) (let ((_let_289 (= tptp.minus_minus_int (lambda ((A5 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A5) (@ tptp.uminus_uminus_int B4)))))) (let ((_let_290 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_291 (= tptp.one_one_nat _let_290))) (let ((_let_292 (@ _let_275 tptp.zero_zero_int))) (let ((_let_293 (not (@ _let_271 tptp.zero_zero_int)))) (let ((_let_294 (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I tptp.nat)) (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat))) N) tptp.zero_zero_nat))))) (let ((_let_295 (= tptp.times_times_assn (lambda ((P5 tptp.assn) (Q3 tptp.assn)) (@ tptp.abs_assn (@ (@ tptp.times_assn_raw (@ tptp.rep_assn P5)) (@ tptp.rep_assn Q3))))))) (let ((_let_296 (= tptp.inf_inf_assn (lambda ((P5 tptp.assn) (Q3 tptp.assn)) (@ tptp.abs_assn (lambda ((H6 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.rep_assn P5) H6) (@ (@ tptp.rep_assn Q3) H6)))))))) (let ((_let_297 (= tptp.sup_sup_assn (lambda ((P5 tptp.assn) (Q3 tptp.assn)) (@ tptp.abs_assn (lambda ((H6 tptp.produc3658429121746597890et_nat)) (or (@ (@ tptp.rep_assn P5) H6) (@ (@ tptp.rep_assn Q3) H6)))))))) (let ((_let_298 (= tptp.pure_assn (lambda ((B4 Bool)) (@ tptp.abs_assn (@ tptp.pure_a825153325127701367it_nat B4)))))) (let ((_let_299 (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))) (let ((_let_300 (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat))) (let ((_let_301 (= _let_300 tptp.zero_zero_int))) (let ((_let_302 (= (@ tptp.semiri4939895301339042750nteger tptp.one_one_nat) tptp.one_one_Code_integer))) (let ((_let_303 (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))) (let ((_let_304 (@ tptp.semiri4939895301339042750nteger tptp.zero_zero_nat))) (let ((_let_305 (= _let_304 tptp.zero_z3403309356797280102nteger))) (let ((_let_306 (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat))) (let ((_let_307 (= _let_306 tptp.zero_zero_rat))) (let ((_let_308 (= tptp.wand_assn (lambda ((P5 tptp.assn) (Q3 tptp.assn)) (@ tptp.abs_assn (@ (@ tptp.wand_raw (@ tptp.rep_assn P5)) (@ tptp.rep_assn Q3))))))) (let ((_let_309 (= tptp.defaul566961228789861419t_unit tptp.product_Unity))) (let ((_let_310 (= 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))))))))) (let ((_let_311 (= tptp.bot_bot_Product_unit tptp.product_Unity))) (let ((_let_312 (= tptp.sup_sup_Product_unit (lambda ((Uu3 tptp.product_unit) (Uv tptp.product_unit)) tptp.product_Unity)))) (let ((_let_313 (= tptp.inf_inf_Product_unit (lambda ((Uu3 tptp.product_unit) (Uv tptp.product_unit)) tptp.product_Unity)))) (let ((_let_314 (= 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)))))))) (let ((_let_315 (= tptp.inf_in7104746047340619750_int_o (lambda ((X4 tptp.option1893999432384633940_int_o) (Y4 tptp.option1893999432384633940_int_o)) (@ (@ (@ tptp.case_o670596351732880613_int_o tptp.none_P2320557853698873699_int_o) (lambda ((Z (-> tptp.product_prod_int_int Bool))) (@ (@ (@ tptp.case_o670596351732880613_int_o tptp.none_P2320557853698873699_int_o) (lambda ((Aa (-> tptp.product_prod_int_int Bool))) (@ tptp.some_P180497116919641311_int_o (@ (@ tptp.inf_in3604695632404883862_int_o Z) Aa)))) Y4))) X4))))) (let ((_let_316 (= tptp.inf_inf_option_nat (lambda ((X4 tptp.option_nat) (Y4 tptp.option_nat)) (@ (@ (@ tptp.case_o7429725398727453821at_nat tptp.none_nat) (lambda ((Z tptp.nat)) (@ (@ (@ tptp.case_o7429725398727453821at_nat tptp.none_nat) (lambda ((Aa tptp.nat)) (@ tptp.some_nat (@ (@ tptp.inf_inf_nat Z) Aa)))) Y4))) X4))))) (let ((_let_317 (= tptp.inf_in7812914138253463912et_nat (lambda ((X4 tptp.option_set_nat) (Y4 tptp.option_set_nat)) (@ (@ (@ tptp.case_o4054078431260844265et_nat tptp.none_set_nat) (lambda ((Z 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 Z) Aa)))) Y4))) X4))))) (let ((_let_318 (= tptp.inf_in777885744494410645at_nat (lambda ((X4 tptp.option8963830502488799655at_nat) (Y4 tptp.option8963830502488799655at_nat)) (@ (@ (@ tptp.case_o311359030874850053at_nat tptp.none_s625347054029921090at_nat) (lambda ((Z 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 Z) Aa)))) Y4))) X4))))) (let ((_let_319 (= tptp.inf_inf_option_assn (lambda ((X4 tptp.option_assn) (Y4 tptp.option_assn)) (@ (@ (@ tptp.case_o4484465799723439917n_assn tptp.none_assn) (lambda ((Z tptp.assn)) (@ (@ (@ tptp.case_o4484465799723439917n_assn tptp.none_assn) (lambda ((Aa tptp.assn)) (@ tptp.some_assn (@ (@ tptp.inf_inf_assn Z) Aa)))) Y4))) X4))))) (let ((_let_320 (= tptp.ord_le8213806771718485336_int_o (lambda ((A5 (-> tptp.product_prod_int_int Bool)) (B4 (-> tptp.product_prod_int_int Bool))) (and (= A5 (@ (@ tptp.inf_in3604695632404883862_int_o A5) B4)) (not (= A5 B4))))))) (let ((_let_321 (= tptp.ord_le7866589430770878221at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (and (= A5 (@ (@ tptp.inf_in2572325071724192079at_nat A5) B4)) (not (= A5 B4))))))) (let ((_let_322 (= tptp.ord_le8369615600986905444_int_o (lambda ((X4 (-> tptp.product_prod_int_int Bool)) (Y4 (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o X4) Y4) X4))))) (let ((_let_323 (= tptp.ord_le3146513528884898305at_nat (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X4) Y4) X4))))) (let ((_let_324 (= tptp.ord_less_eq_assn (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (= (@ (@ tptp.inf_inf_assn X4) Y4) X4))))) (let ((_let_325 (= 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))))))))) (let ((_let_326 (= 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))))))))) (let ((_let_327 (= 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))))))))) (let ((_let_328 (= 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))))))))) (let ((_let_329 (= tptp.inf_in8396524679539076455nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int X4))) (and (@ _let_1 A6) (@ _let_1 B6))))))))) (let ((_let_330 (= 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))))))))) (let ((_let_331 (= 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))))))))) (let ((_let_332 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_333 (= tptp.heap_Time_ureturn_a (lambda ((X4 tptp.a)) (@ tptp.heap_Time_heap_a (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc9178034014595674355it_nat X4) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.zero_zero_nat)))))))) (let ((_let_334 (= tptp.heap_Time_ureturn_b (lambda ((X4 tptp.b)) (@ tptp.heap_Time_heap_b (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc4082563078715348724it_nat X4) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.zero_zero_nat)))))))) (let ((_let_335 (@ _let_271 tptp.one_one_int))) (let ((_let_336 (@ _let_332 tptp.one_one_nat))) (let ((_let_337 (@ _let_270 tptp.one_one_rat))) (let ((_let_338 (@ _let_141 tptp.one_one_Code_integer))) (let ((_let_339 (@ tptp.ord_less_nat tptp.one_one_nat))) (let ((_let_340 (@ _let_275 tptp.one_one_int))) (let ((_let_341 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_342 (@ _let_341 tptp.one_one_nat))) (let ((_let_343 (@ _let_276 tptp.one_one_rat))) (let ((_let_344 (@ _let_148 tptp.one_one_Code_integer))) (let ((_let_345 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (let ((_let_346 (= tptp.entails (lambda ((P5 tptp.assn) (Q3 tptp.assn)) (forall ((H6 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P5) H6) (@ (@ tptp.rep_assn Q3) H6))))))) (let ((_let_347 (= tptp.bot_bot_nat tptp.zero_zero_nat))) (let ((_let_348 (= (@ tptp.pure_assn false) tptp.bot_bot_assn))) (let ((_let_349 (= (@ tptp.pure_assn true) tptp.one_one_assn))) (let ((_let_350 (= tptp.is_empty_int (lambda ((A6 tptp.set_int)) (= A6 tptp.bot_bot_set_int))))) (let ((_let_351 (= tptp.is_empty_nat (lambda ((A6 tptp.set_nat)) (= A6 tptp.bot_bot_set_nat))))) (let ((_let_352 (= tptp.is_empty_o (lambda ((A6 tptp.set_o)) (= A6 tptp.bot_bot_set_o))))) (let ((_let_353 (= tptp.is_emp1662574758705540307at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat)) (= A6 tptp.bot_bo2099793752762293965at_nat))))) (let ((_let_354 (= tptp.heap_T6927113302350381334t_unit (lambda ((F3 (-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat))) (@ tptp.heap_T6183433275982383450t_unit (@ (@ tptp.comp_P3118722334806803912t_unit tptp.some_P1914260805536162275it_nat) F3)))))) (let ((_let_355 (= tptp.heap_Time_heap_a (lambda ((F3 (-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat))) (@ tptp.heap_Time_Heap_a2 (@ (@ tptp.comp_P8552900652980440422t_unit tptp.some_P7913643980934408916it_nat) F3)))))) (let ((_let_356 (= tptp.heap_Time_heap_b (lambda ((F3 (-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat))) (@ tptp.heap_Time_Heap_b2 (@ (@ tptp.comp_P6401406225962756324t_unit tptp.some_P2818173045054083285it_nat) F3)))))) (let ((_let_357 (= tptp.heap_Time_return_a (lambda ((X4 tptp.a)) (@ tptp.heap_Time_heap_a (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc9178034014595674355it_nat X4) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.one_one_nat)))))))) (let ((_let_358 (= tptp.heap_Time_return_b (lambda ((X4 tptp.b)) (@ tptp.heap_Time_heap_b (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.produc4082563078715348724it_nat X4) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.one_one_nat)))))))) (let ((_let_359 (= 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))))))))) (let ((_let_360 (= 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))))))))) (let ((_let_361 (= tptp.heap_Time_tap_b (lambda ((F3 (-> tptp.heap_e7401611519738050253t_unit tptp.b))) (@ tptp.heap_Time_Heap_b2 (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat (@ F3 H6)) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.one_one_nat))))))))) (let ((_let_362 (= tptp.ord_le6747313008572928689nteger (lambda ((A5 tptp.code_integer) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A5) tptp.one_one_Code_integer)) __flatten_var_0))))) (let ((_let_363 (= tptp.bot_bot_option_num tptp.none_num))) (let ((_let_364 (= 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))))) (let ((_let_365 (= 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))))) (let ((_let_366 (= tptp.bot_bo5216386038637673661_nat_o (lambda ((X4 tptp.b) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat X4) Y4)) tptp.bot_bo8983147464310796868it_nat))))) (let ((_let_367 (= 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))))) (let ((_let_368 (= 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))))) (let ((_let_369 (= tptp.bot_bot_int_int_o (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y4)) tptp.bot_bo1796632182523588997nt_int))))) (let ((_let_370 (@ tptp.dflt_None_set_int tptp.bot_bot_set_int))) (let ((_let_371 (= _let_370 tptp.none_set_int))) (let ((_let_372 (@ tptp.dflt_None_set_nat tptp.bot_bot_set_nat))) (let ((_let_373 (= _let_372 tptp.none_set_nat))) (let ((_let_374 (@ tptp.dflt_None_set_o tptp.bot_bot_set_o))) (let ((_let_375 (= _let_374 tptp.none_set_o))) (let ((_let_376 (@ tptp.dflt_N6592383573632408824at_nat tptp.bot_bo2099793752762293965at_nat))) (let ((_let_377 (= _let_376 tptp.none_s625347054029921090at_nat))) (let ((_let_378 (= tptp.bot_bot_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) false))))) (let ((_let_379 (= tptp.bot_bot_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) false))))) (let ((_let_380 (= tptp.bot_bot_set_o (@ tptp.collect_o (lambda ((X4 Bool)) false))))) (let ((_let_381 (= tptp.bot_bo2099793752762293965at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) false))))) (let ((_let_382 (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) false))))) (let ((_let_383 (= tptp.bot_bo1488462491386950373nt_int (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) false))))) (let ((_let_384 (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) false))))) (let ((_let_385 (= 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 ((Z tptp.num)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num Z)) (lambda ((Aa tptp.num)) (@ tptp.some_num (@ (@ F3 Z) Aa)))) Y4))) X4))))) (let ((_let_386 (= 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 ((Z tptp.produc8664842809031399944it_nat)) (@ (@ (@ tptp.case_o2963978774867076333it_nat (@ tptp.some_P1914260805536162275it_nat Z)) (lambda ((Aa tptp.produc8664842809031399944it_nat)) (@ tptp.some_P1914260805536162275it_nat (@ (@ F3 Z) Aa)))) Y4))) X4))))) (let ((_let_387 (= 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 ((Z tptp.produc3260487557148687353it_nat)) (@ (@ (@ tptp.case_o6061097939050036047it_nat (@ tptp.some_P7913643980934408916it_nat Z)) (lambda ((Aa tptp.produc3260487557148687353it_nat)) (@ tptp.some_P7913643980934408916it_nat (@ (@ F3 Z) Aa)))) Y4))) X4))))) (let ((_let_388 (= tptp.combin724284867043296059it_nat (lambda ((F3 (-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)) (X4 tptp.option4065278094766928714it_nat) (Y4 tptp.option4065278094766928714it_nat)) (@ (@ (@ tptp.case_o5901184372446974929it_nat Y4) (lambda ((Z tptp.produc7388388658123137530it_nat)) (@ (@ (@ tptp.case_o5901184372446974929it_nat (@ tptp.some_P2818173045054083285it_nat Z)) (lambda ((Aa tptp.produc7388388658123137530it_nat)) (@ tptp.some_P2818173045054083285it_nat (@ (@ F3 Z) Aa)))) Y4))) X4))))) (let ((_let_389 (= tptp.heap_T2927564422264180874t_unit (lambda ((S5 tptp.list_char)) (@ tptp.heap_T6183433275982383450t_unit (lambda ((Uu2 tptp.heap_e7401611519738050253t_unit)) tptp.none_P9117596204409417319it_nat)))))) (let ((_let_390 (= 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 ((Z tptp.int)) (@ (@ tptp.ord_less_int Z) Y4))) X4))) __flatten_var_0))))) (let ((_let_391 (= 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 ((Z tptp.nat)) (@ (@ tptp.ord_less_nat Z) Y4))) X4))) __flatten_var_0))))) (let ((_let_392 (= 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 ((Z tptp.num)) (@ (@ tptp.ord_less_num Z) Y4))) X4))) __flatten_var_0))))) (let ((_let_393 (= 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 ((Z tptp.rat)) (@ (@ tptp.ord_less_rat Z) Y4))) X4))) __flatten_var_0))))) (let ((_let_394 (= 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 ((Z tptp.assn)) (@ (@ tptp.ord_less_assn Z) Y4))) X4))) __flatten_var_0))))) (let ((_let_395 (= tptp.ord_le1736525451366464988on_int (lambda ((X4 tptp.option_int) (Y4 tptp.option_int)) (@ (@ (@ tptp.case_option_o_int true) (lambda ((Z tptp.int)) (@ (@ (@ tptp.case_option_o_int false) (@ tptp.ord_less_eq_int Z)) Y4))) X4))))) (let ((_let_396 (= tptp.ord_le5914376470875661696on_nat (lambda ((X4 tptp.option_nat) (Y4 tptp.option_nat)) (@ (@ (@ tptp.case_option_o_nat true) (lambda ((Z tptp.nat)) (@ (@ (@ tptp.case_option_o_nat false) (@ tptp.ord_less_eq_nat Z)) Y4))) X4))))) (let ((_let_397 (= tptp.ord_le6622620407824499402on_num (lambda ((X4 tptp.option_num) (Y4 tptp.option_num)) (@ (@ (@ tptp.case_option_o_num true) (lambda ((Z tptp.num)) (@ (@ (@ tptp.case_option_o_num false) (@ tptp.ord_less_eq_num Z)) Y4))) X4))))) (let ((_let_398 (= tptp.ord_le2406147912482264968on_rat (lambda ((X4 tptp.option_rat) (Y4 tptp.option_rat)) (@ (@ (@ tptp.case_option_o_rat true) (lambda ((Z tptp.rat)) (@ (@ (@ tptp.case_option_o_rat false) (@ tptp.ord_less_eq_rat Z)) Y4))) X4))))) (let ((_let_399 (= tptp.ord_le353528952715127954et_int (lambda ((X4 tptp.option_set_int) (Y4 tptp.option_set_int)) (@ (@ (@ tptp.case_o223999843215110191et_int true) (lambda ((Z tptp.set_int)) (@ (@ (@ tptp.case_o223999843215110191et_int false) (@ tptp.ord_less_eq_set_int Z)) Y4))) X4))))) (let ((_let_400 (= tptp.heap_T8440541562793052209t_unit (lambda ((P5 (-> 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 (@ P5 H6)) (@ tptp.some_P1914260805536162275it_nat (@ F3 H6))) tptp.none_P9117596204409417319it_nat))))))) (let ((_let_401 (= tptp.heap_Time_guard_a (lambda ((P5 (-> 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 (@ P5 H6)) (@ tptp.some_P7913643980934408916it_nat (@ F3 H6))) tptp.none_P2651198173097904984it_nat))))))) (let ((_let_402 (= tptp.heap_Time_guard_b (lambda ((P5 (-> tptp.heap_e7401611519738050253t_unit Bool)) (F3 (-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat))) (@ tptp.heap_Time_Heap_b2 (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ (@ tptp.if_opt7386294288321364996it_nat (@ P5 H6)) (@ tptp.some_P2818173045054083285it_nat (@ F3 H6))) tptp.none_P6779099274072355161it_nat))))))) (let ((_let_403 (= tptp.set_to2008915276733485075it_nat (lambda ((S4 tptp.set_Pr7098220151150636591it_nat) (K3 tptp.a)) (@ tptp.eps_Op8301357815426737072it_nat (lambda ((V2 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat K3) V2)) S4))))))) (let ((_let_404 (= tptp.set_to6136816377707935252it_nat (lambda ((S4 tptp.set_Pr7600907837789447088it_nat) (K3 tptp.b)) (@ tptp.eps_Op8301357815426737072it_nat (lambda ((V2 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat K3) V2)) S4))))))) (let ((_let_405 (= tptp.set_to2047380710992656148et_nat (lambda ((S4 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)) S4))))))) (let ((_let_406 (= tptp.set_to6040779677306527128et_nat (lambda ((S4 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)) S4))))))) (let ((_let_407 (= tptp.set_to_map_int_int (lambda ((S4 tptp.set_Pr958786334691620121nt_int) (K3 tptp.int)) (@ tptp.eps_Opt_int (lambda ((V2 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int K3) V2)) S4))))))) (let ((_let_408 (= 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)))))) (let ((_let_409 (= tptp.heap_Time_success_b (lambda ((F3 tptp.heap_Time_Heap_b) (H6 tptp.heap_e7401611519738050253t_unit)) (not (= (@ (@ tptp.heap_Time_execute_b F3) H6) tptp.none_P6779099274072355161it_nat)))))) (let ((_let_410 (= (@ tptp.eps_Opt_num (lambda ((Uu2 tptp.num)) false)) tptp.none_num))) (let ((_let_411 (= tptp.sup_sup_option_int (lambda ((X4 tptp.option_int) (Y4 tptp.option_int)) (@ (@ (@ tptp.case_o390784466056649525nt_int Y4) (lambda ((X8 tptp.int)) (@ (@ (@ tptp.case_o390784466056649525nt_int X4) (lambda ((Z tptp.int)) (@ tptp.some_int (@ (@ tptp.sup_sup_int X8) Z)))) Y4))) X4))))) (let ((_let_412 (= 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 ((Z tptp.nat)) (@ tptp.some_nat (@ (@ tptp.sup_sup_nat X8) Z)))) Y4))) X4))))) (let ((_let_413 (= 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 ((Z tptp.set_nat)) (@ tptp.some_set_nat (@ (@ tptp.sup_sup_set_nat X8) Z)))) Y4))) X4))))) (let ((_let_414 (= 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 ((Z tptp.set_Pr4329608150637261639at_nat)) (@ tptp.some_s5890477192898017836at_nat (@ (@ tptp.sup_su5525570899277871387at_nat X8) Z)))) Y4))) X4))))) (let ((_let_415 (= 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 ((Z tptp.set_Pr8551490117392284871at_nat)) (@ tptp.some_s287724117700012716at_nat (@ (@ tptp.sup_su3035147773818789531at_nat X8) Z)))) Y4))) X4))))) (let ((_let_416 (= tptp.ord_le2604355607129572851at_nat (lambda ((B4 tptp.set_Pr4329608150637261639at_nat) (A5 tptp.set_Pr4329608150637261639at_nat)) (and (= A5 (@ (@ tptp.sup_su5525570899277871387at_nat A5) B4)) (not (= A5 B4))))))) (let ((_let_417 (= tptp.ord_le7642048601412989811at_nat (lambda ((B4 tptp.set_Pr8551490117392284871at_nat) (A5 tptp.set_Pr8551490117392284871at_nat)) (and (= A5 (@ (@ tptp.sup_su3035147773818789531at_nat A5) B4)) (not (= A5 B4))))))) (let ((_let_418 (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.sup_sup_int A5) B4) B4))))) (let ((_let_419 (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.sup_sup_rat A5) B4) B4))))) (let ((_let_420 (= 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)))))))) (let ((_let_421 (= tptp.ord_le483042692224249369nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (forall ((X4 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int X4))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))) (let ((_let_422 (= 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)))))))) (let ((_let_423 (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (exists ((K3 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M3) K3))))))) (let ((_let_424 (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A6) B6) B6))))) (let ((_let_425 (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A6) B6) B6))))) (let ((_let_426 (= tptp.ord_le1268244103169919719at_nat (lambda ((A6 tptp.set_Pr4329608150637261639at_nat) (B6 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A6) B6) B6))))) (let ((_let_427 (= tptp.ord_le8081472938463900775at_nat (lambda ((A6 tptp.set_Pr8551490117392284871at_nat) (B6 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A6) B6) B6))))) (let ((_let_428 (= 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))))))))) (let ((_let_429 (= 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))))))))) (let ((_let_430 (= 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))))))))) (let ((_let_431 (= 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))))))))) (let ((_let_432 (= 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))))))))) (let ((_let_433 (= tptp.sup_su2047564715030645325nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (@ tptp.collec5210948495886036740nt_int (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member2340774599025711042nt_int X4))) (or (@ _let_1 A6) (@ _let_1 B6))))))))) (let ((_let_434 (= 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))))))))) (let ((_let_435 (= 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))))))))) (let ((_let_436 (= 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))))))) (let ((_let_437 (= 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))))))) (let ((_let_438 (= tptp.ord_le1924305788584680229nt_int (lambda ((A6 tptp.set_se6260736226359567993nt_int) (B6 tptp.set_se6260736226359567993nt_int)) (@ (@ tptp.ord_le2688692977766382584_int_o (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) A6))) (lambda ((X4 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member2340774599025711042nt_int X4) B6))))))) (let ((_let_439 (= 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))))))) (let ((_let_440 (= tptp.hoare_new_addrs (lambda ((H6 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat) (H7 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.sup_sup_set_nat As4) (@ 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)))))))))) (let ((_let_441 (= tptp.heap_Time_effect_a (lambda ((C3 tptp.heap_Time_Heap_a) (H6 tptp.heap_e7401611519738050253t_unit) (H7 tptp.heap_e7401611519738050253t_unit) (R5 tptp.a) (N tptp.nat)) (= (@ (@ tptp.heap_Time_execute_a C3) H6) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) N)))))))) (let ((_let_442 (= tptp.heap_Time_effect_b (lambda ((C3 tptp.heap_Time_Heap_b) (H6 tptp.heap_e7401611519738050253t_unit) (H7 tptp.heap_e7401611519738050253t_unit) (R5 tptp.b) (N tptp.nat)) (= (@ (@ tptp.heap_Time_execute_b C3) H6) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) N)))))))) (let ((_let_443 (= tptp.heap_T6553295506729943825t_unit (lambda ((C3 tptp.heap_T5738788834812785303t_unit) (H6 tptp.heap_e7401611519738050253t_unit) (H7 tptp.heap_e7401611519738050253t_unit) (R5 tptp.product_unit) (N tptp.nat)) (= (@ (@ tptp.heap_T875086893843062177t_unit C3) H6) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) N)))))))) (let ((_let_444 (= tptp.hoare_8945653483474564448t_unit (lambda ((P5 tptp.assn) (C3 tptp.heap_T5738788834812785303t_unit) (Q3 (-> tptp.product_unit tptp.assn))) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P5) (@ (@ tptp.produc7507926704131184380et_nat H6) As4)) (exists ((R5 tptp.product_unit) (H7 tptp.heap_e7401611519738050253t_unit)) (and (exists ((T4 tptp.nat)) (= (@ (@ tptp.heap_T875086893843062177t_unit C3) H6) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) T4))))) (@ (@ tptp.rep_assn (@ Q3 R5)) (@ (@ tptp.produc7507926704131184380et_nat H7) (@ (@ (@ tptp.hoare_new_addrs H6) As4) 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) As4)))))) H6) H7) (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H6)) (@ tptp.lim_Product_unit H7)))))))))) (let ((_let_445 (= tptp.hoare_hoare_triple_b (lambda ((P5 tptp.assn) (C3 tptp.heap_Time_Heap_b) (Q3 (-> tptp.b tptp.assn))) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P5) (@ (@ tptp.produc7507926704131184380et_nat H6) As4)) (exists ((R5 tptp.b) (H7 tptp.heap_e7401611519738050253t_unit)) (and (exists ((T4 tptp.nat)) (= (@ (@ tptp.heap_Time_execute_b C3) H6) (@ tptp.some_P2818173045054083285it_nat (@ (@ tptp.produc4082563078715348724it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) T4))))) (@ (@ tptp.rep_assn (@ Q3 R5)) (@ (@ tptp.produc7507926704131184380et_nat H7) (@ (@ (@ tptp.hoare_new_addrs H6) As4) 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) As4)))))) H6) H7) (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H6)) (@ tptp.lim_Product_unit H7)))))))))) (let ((_let_446 (= tptp.hoare_hoare_triple_a (lambda ((P5 tptp.assn) (C3 tptp.heap_Time_Heap_a) (Q3 (-> tptp.a tptp.assn))) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P5) (@ (@ tptp.produc7507926704131184380et_nat H6) As4)) (exists ((R5 tptp.a) (H7 tptp.heap_e7401611519738050253t_unit)) (and (exists ((T4 tptp.nat)) (= (@ (@ tptp.heap_Time_execute_a C3) H6) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H7) T4))))) (@ (@ tptp.rep_assn (@ Q3 R5)) (@ (@ tptp.produc7507926704131184380et_nat H7) (@ (@ (@ tptp.hoare_new_addrs H6) As4) 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) As4)))))) H6) H7) (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H6)) (@ tptp.lim_Product_unit H7)))))))))) (let ((_let_447 (= 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))))))) (let ((_let_448 (= 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))))))) (let ((_let_449 (= 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))))))) (let ((_let_450 (= 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))))))) (let ((_let_451 (= 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))))))) (let ((_let_452 (= 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))))))) (let ((_let_453 (= tptp.bNF_Ca1965613569405424510nt_int (lambda ((R5 tptp.set_Pr958786334691620121nt_int) (As3 (-> tptp.int tptp.int))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R5) (@ (@ tptp.ord_less_eq_int (@ As3 I)) (@ As3 J)))))))) (let ((_let_454 (= tptp.bNF_Ca1968104039914474786nt_nat (lambda ((R5 tptp.set_Pr958786334691620121nt_int) (As3 (-> tptp.int tptp.nat))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R5) (@ (@ tptp.ord_less_eq_nat (@ As3 I)) (@ As3 J)))))))) (let ((_let_455 (= tptp.bNF_Ca7748807862925029228nt_num (lambda ((R5 tptp.set_Pr958786334691620121nt_int) (As3 (-> tptp.int tptp.num))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R5) (@ (@ tptp.ord_less_eq_num (@ As3 I)) (@ As3 J)))))))) (let ((_let_456 (= tptp.bNF_Ca1332973979827979050nt_rat (lambda ((R5 tptp.set_Pr958786334691620121nt_int) (As3 (-> tptp.int tptp.rat))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R5) (@ (@ tptp.ord_less_eq_rat (@ As3 I)) (@ As3 J)))))))) (let ((_let_457 (= tptp.bNF_Ca583493526879471924et_int (lambda ((R5 tptp.set_Pr958786334691620121nt_int) (As3 (-> tptp.int tptp.set_int))) (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I) J)) R5) (@ (@ tptp.ord_less_eq_set_int (@ As3 I)) (@ As3 J)))))))) (let ((_let_458 (= tptp.biject8592306251674886141it_nat (lambda ((R tptp.set_Pr7098220151150636591it_nat)) (and (forall ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat) (Z tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.produc9178034014595674355it_nat X4))) (=> (and (@ (@ tptp.member4554412811331277712it_nat (@ _let_1 Y4)) R) (@ (@ tptp.member4554412811331277712it_nat (@ _let_1 Z)) R)) (= Y4 Z)))) (forall ((X4 tptp.a) (Y4 tptp.a) (Z tptp.produc6653097349344004940it_nat)) (=> (and (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Z)) R) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat Y4) Z)) R)) (= X4 Y4)))))))) (let ((_let_459 (= tptp.biject3496835315794560510it_nat (lambda ((R tptp.set_Pr7600907837789447088it_nat)) (and (forall ((X4 tptp.b) (Y4 tptp.produc6653097349344004940it_nat) (Z tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.produc4082563078715348724it_nat X4))) (=> (and (@ (@ tptp.member8682313912305727889it_nat (@ _let_1 Y4)) R) (@ (@ tptp.member8682313912305727889it_nat (@ _let_1 Z)) R)) (= Y4 Z)))) (forall ((X4 tptp.b) (Y4 tptp.b) (Z tptp.produc6653097349344004940it_nat)) (=> (and (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat X4) Z)) R) (@ (@ tptp.member8682313912305727889it_nat (@ (@ tptp.produc4082563078715348724it_nat Y4) Z)) R)) (= X4 Y4)))))))) (let ((_let_460 (= tptp.biject1468766312547416318et_nat (lambda ((R tptp.set_Pr8536935166611901872et_nat)) (and (forall ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat) (Z tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat X4))) (=> (and (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Y4)) R) (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Z)) R)) (= Y4 Z)))) (forall ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 (-> tptp.produc3658429121746597890et_nat Bool)) (Z tptp.produc3925858234332021118et_nat)) (=> (and (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Z)) R) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat Y4) Z)) R)) (= X4 Y4)))))))) (let ((_let_461 (= tptp.biject2615096655818420098et_nat (lambda ((R tptp.set_Pr3286484037609594932et_nat)) (and (forall ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat) (Z tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat X4))) (=> (and (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Y4)) R) (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Z)) R)) (= Y4 Z)))) (forall ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 (-> tptp.produc3658429121746597890et_nat Bool)) (Z tptp.produc3658429121746597890et_nat)) (=> (and (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Z)) R) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat Y4) Z)) R)) (= X4 Y4)))))))) (let ((_let_462 (= tptp.bijective_int_int (lambda ((R tptp.set_Pr958786334691620121nt_int)) (and (forall ((X4 tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int X4))) (=> (and (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Y4)) R) (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Z)) R)) (= Y4 Z)))) (forall ((X4 tptp.int) (Y4 tptp.int) (Z tptp.int)) (=> (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Z)) R) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y4) Z)) R)) (= X4 Y4)))))))) (let ((_let_463 (@ tptp.lim_Product_unit tptp.h2))) (let ((_let_464 (@ _let_1 tptp.h2))) (let ((_let_465 (@ (@ (@ tptp.hoare_new_addrs tptp.h2) _let_464) tptp.h))) (let ((_let_466 (@ _let_4 (@ _let_3 _let_465)))) (let ((_let_467 (= _let_465 _let_2))) (let ((_let_468 (ho_11107 k_11106 k_24257))) (let ((_let_469 (ho_11107 k_11106 k_24256))) (let ((_let_470 (= _let_469 _let_468))) (let ((_let_471 (ho_24259 k_24258 tptp.h))) (let ((_let_472 (ho_11327 k_11329 (ho_24262 k_24261 tptp.rg)))) (let ((_let_473 (ho_11328 _let_472 (ho_24260 _let_471 _let_468)))) (let ((_let_474 (ho_11328 _let_472 (ho_24260 _let_471 _let_469)))) (let ((_let_475 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.produc5728234346263159722nt_int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.produc5728234346263159722nt_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (= (ho_25212 x z) (ho_25212 y z)))) (= x y))))) (let ((_let_476 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_17201 x z) (ho_17201 y z)))) (= x y))))) (let ((_let_477 (forall ((x |u_(-> _u_(-> Bool tptp.code_integer)_ tptp.code_integer tptp.list_o tptp.code_integer)|) (y |u_(-> _u_(-> Bool tptp.code_integer)_ tptp.code_integer tptp.list_o tptp.code_integer)|)) (or (not (forall ((z |u_(-> Bool tptp.code_integer)|)) (= (ho_25207 x z) (ho_25207 y z)))) (= x y))))) (let ((_let_478 (forall ((x |u_(-> tptp.code_integer tptp.list_o tptp.code_integer)|) (y |u_(-> tptp.code_integer tptp.list_o tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_25208 x z) (ho_25208 y z)))) (= x y))))) (let ((_let_479 (forall ((x |u_(-> tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_11191 x z) (ho_11191 y z)))) (= x y))))) (let ((_let_480 (forall ((x |u_(-> _u_(-> Bool tptp.code_natural)_ tptp.code_natural tptp.list_o tptp.code_natural)|) (y |u_(-> _u_(-> Bool tptp.code_natural)_ tptp.code_natural tptp.list_o tptp.code_natural)|)) (or (not (forall ((z |u_(-> Bool tptp.code_natural)|)) (= (ho_25202 x z) (ho_25202 y z)))) (= x y))))) (let ((_let_481 (forall ((x |u_(-> tptp.nat tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_11323 x z) (ho_11323 y z)))) (= x y))))) (let ((_let_482 (forall ((x |u_(-> tptp.code_natural tptp.list_o tptp.code_natural)|) (y |u_(-> tptp.code_natural tptp.list_o tptp.code_natural)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_25203 x z) (ho_25203 y z)))) (= x y))))) (let ((_let_483 (forall ((x |u_(-> tptp.list_o tptp.code_natural)|) (y |u_(-> tptp.list_o tptp.code_natural)|)) (or (not (forall ((z tptp.list_o)) (= (ho_25204 x z) (ho_25204 y z)))) (= x y))))) (let ((_let_484 (forall ((x |u_(-> tptp.code_integer tptp.num)|) (y |u_(-> tptp.code_integer tptp.num)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12552 x z) (ho_12552 y z)))) (= x y))))) (let ((_let_485 (forall ((x |u_(-> tptp.rat tptp.set_nat tptp.rat)|) (y |u_(-> tptp.rat tptp.set_nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_15293 x z) (ho_15293 y z)))) (= x y))))) (let ((_let_486 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int tptp.nat)_ tptp.set_nat _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.int tptp.nat)_ tptp.set_nat _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int tptp.nat)|)) (= (ho_17276 x z) (ho_17276 y z)))) (= x y))))) (let ((_let_487 (forall ((x |u_(-> tptp.produc7822875418678951345atural Bool)|) (y |u_(-> tptp.produc7822875418678951345atural Bool)|)) (or (not (forall ((z tptp.produc7822875418678951345atural)) (= (ho_25198 x z) (ho_25198 y z)))) (= x y))))) (let ((_let_488 (forall ((x |u_(-> tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int)|) (y |u_(-> tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_25190 x z) (ho_25190 y z)))) (= x y))))) (let ((_let_489 (forall ((x |u_(-> tptp.code_integer _u_(-> tptp.num tptp.code_integer)_ tptp.option_num tptp.code_integer)|) (y |u_(-> tptp.code_integer _u_(-> tptp.num tptp.code_integer)_ tptp.option_num tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_25179 x z) (ho_25179 y z)))) (= x y))))) (let ((_let_490 (forall ((x |u_(-> tptp.code_natural _u_(-> tptp.num tptp.code_natural)_ tptp.option_num tptp.code_natural)|) (y |u_(-> tptp.code_natural _u_(-> tptp.num tptp.code_natural)_ tptp.option_num tptp.code_natural)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_25175 x z) (ho_25175 y z)))) (= x y))))) (let ((_let_491 (forall ((x |u_(-> _u_(-> tptp.num tptp.code_natural)_ tptp.option_num tptp.code_natural)|) (y |u_(-> _u_(-> tptp.num tptp.code_natural)_ tptp.option_num tptp.code_natural)|)) (or (not (forall ((z |u_(-> tptp.num tptp.code_natural)|)) (= (ho_25176 x z) (ho_25176 y z)))) (= x y))))) (let ((_let_492 (forall ((x |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_nat)|) (y |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_nat)|)) (or (not (forall ((z tptp.a)) (= (ho_25170 x z) (ho_25170 y z)))) (= x y))))) (let ((_let_493 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.set_o)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.set_o)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_25169 x z) (ho_25169 y z)))) (= x y))))) (let ((_let_494 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.set_int)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.set_int)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_25165 x z) (ho_25165 y z)))) (= x y))))) (let ((_let_495 (forall ((x |u_(-> tptp.code_natural tptp.nat tptp.code_natural)|) (y |u_(-> tptp.code_natural tptp.nat tptp.code_natural)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_15838 x z) (ho_15838 y z)))) (= x y))))) (let ((_let_496 (forall ((x |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_int)_ tptp.produc7388388658123137530it_nat tptp.set_int)|) (y |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_int)_ tptp.produc7388388658123137530it_nat tptp.set_int)|)) (or (not (forall ((z |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_int)|)) (= (ho_25163 x z) (ho_25163 y z)))) (= x y))))) (let ((_let_497 (forall ((x |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_nat)_ tptp.produc7388388658123137530it_nat tptp.set_nat)|) (y |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_nat)_ tptp.produc7388388658123137530it_nat tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_nat)|)) (= (ho_25158 x z) (ho_25158 y z)))) (= x y))))) (let ((_let_498 (forall ((x |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_o)_ tptp.produc7388388658123137530it_nat tptp.set_o)|) (y |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_o)_ tptp.produc7388388658123137530it_nat tptp.set_o)|)) (or (not (forall ((z |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_o)|)) (= (ho_25153 x z) (ho_25153 y z)))) (= x y))))) (let ((_let_499 (forall ((x |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_o)|) (y |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_o)|)) (or (not (forall ((z tptp.b)) (= (ho_25151 x z) (ho_25151 y z)))) (= x y))))) (let ((_let_500 (forall ((x |u_(-> tptp.filter_nat tptp.filter1242075044329608583at_nat)|) (y |u_(-> tptp.filter_nat tptp.filter1242075044329608583at_nat)|)) (or (not (forall ((z tptp.filter_nat)) (= (ho_26084 x z) (ho_26084 y z)))) (= x y))))) (let ((_let_501 (forall ((x |u_(-> tptp.int tptp.set_set_nat)|) (y |u_(-> tptp.int tptp.set_set_nat)|)) (or (not (forall ((z tptp.int)) (= (ho_25145 x z) (ho_25145 y z)))) (= x y))))) (let ((_let_502 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_25992 x z) (ho_25992 y z)))) (= x y))))) (let ((_let_503 (forall ((x |u_(-> tptp.int tptp.int tptp.set_set_nat)|) (y |u_(-> tptp.int tptp.int tptp.set_set_nat)|)) (or (not (forall ((z tptp.int)) (= (ho_25141 x z) (ho_25141 y z)))) (= x y))))) (let ((_let_504 (forall ((x |u_(-> tptp.int tptp.set_nat)|) (y |u_(-> tptp.int tptp.set_nat)|)) (or (not (forall ((z tptp.int)) (= (ho_25137 x z) (ho_25137 y z)))) (= x y))))) (let ((_let_505 (forall ((x |u_(-> Bool tptp.product_prod_int_o)|) (y |u_(-> Bool tptp.product_prod_int_o)|)) (or (not (forall ((z Bool)) (= (ho_24801 x z) (ho_24801 y z)))) (= x y))))) (let ((_let_506 (forall ((x |u_(-> tptp.set_nat tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.set_nat tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_26081 x z) (ho_26081 y z)))) (= x y))))) (let ((_let_507 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.set_nat)_ tptp.product_prod_int_int tptp.set_nat)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.set_nat)_ tptp.product_prod_int_int tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.set_nat)|)) (= (ho_25135 x z) (ho_25135 y z)))) (= x y))))) (let ((_let_508 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.set_o)_ tptp.product_prod_int_int tptp.set_o)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.set_o)_ tptp.product_prod_int_int tptp.set_o)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.set_o)|)) (= (ho_25130 x z) (ho_25130 y z)))) (= x y))))) (let ((_let_509 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit Bool)_ _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit Bool)_ _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit Bool)|)) (= (ho_22730 x z) (ho_22730 y z)))) (= x y))))) (let ((_let_510 (forall ((x |u_(-> Bool _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|) (y |u_(-> Bool _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|)) (or (not (forall ((z Bool)) (= (ho_25117 x z) (ho_25117 y z)))) (= x y))))) (let ((_let_511 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_25115 x z) (ho_25115 y z)))) (= x y))))) (let ((_let_512 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (= (ho_25109 x z) (ho_25109 y z)))) (= x y))))) (let ((_let_513 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (= (ho_25106 x z) (ho_25106 y z)))) (= x y))))) (let ((_let_514 (forall ((x |u_(-> tptp.int tptp.code_integer tptp.int)|) (y |u_(-> tptp.int tptp.code_integer tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_12208 x z) (ho_12208 y z)))) (= x y))))) (let ((_let_515 (forall ((x |u_(-> tptp.produc4166570645942440679at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.produc4166570645942440679at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.produc4166570645942440679at_nat)) (= (ho_11050 x z) (ho_11050 y z)))) (= x y))))) (let ((_let_516 (forall ((x |u_(-> tptp.product_unit tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)|) (y |u_(-> tptp.product_unit tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_25088 x z) (ho_25088 y z)))) (= x y))))) (let ((_let_517 (forall ((x |u_(-> tptp.int tptp.nat)|) (y |u_(-> tptp.int tptp.nat)|)) (or (not (forall ((z tptp.int)) (= (ho_11061 x z) (ho_11061 y z)))) (= x y))))) (let ((_let_518 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_25089 x z) (ho_25089 y z)))) (= x y))))) (let ((_let_519 (forall ((x |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|) (y |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_25079 x z) (ho_25079 y z)))) (= x y))))) (let ((_let_520 (forall ((x |u_(-> tptp.product_prod_nat_nat _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_19169 x z) (ho_19169 y z)))) (= x y))))) (let ((_let_521 (forall ((x |u_(-> tptp.b tptp.b tptp.product_prod_b_b)|) (y |u_(-> tptp.b tptp.b tptp.product_prod_b_b)|)) (or (not (forall ((z tptp.b)) (= (ho_25067 x z) (ho_25067 y z)))) (= x y))))) (let ((_let_522 (forall ((x |u_(-> tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr7928877670098842301et_nat tptp.set_Pr3444600963470892981et_nat)|) (y |u_(-> tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr7928877670098842301et_nat tptp.set_Pr3444600963470892981et_nat)|)) (or (not (forall ((z tptp.set_Pr2161125870931222855_nat_o)) (= (ho_25064 x z) (ho_25064 y z)))) (= x y))))) (let ((_let_523 (forall ((x |u_(-> tptp.nat tptp.rat tptp.nat tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.nat tptp.rat tptp.nat tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_12482 x z) (ho_12482 y z)))) (= x y))))) (let ((_let_524 (forall ((x |u_(-> tptp.set_Pr7928877670098842301et_nat tptp.set_Pr3444600963470892981et_nat)|) (y |u_(-> tptp.set_Pr7928877670098842301et_nat tptp.set_Pr3444600963470892981et_nat)|)) (or (not (forall ((z tptp.set_Pr7928877670098842301et_nat)) (= (ho_25065 x z) (ho_25065 y z)))) (= x y))))) (let ((_let_525 (forall ((x |u_(-> tptp.heap_T5738788834812785303t_unit tptp.product_unit tptp.heap_T5738788834812785303t_unit)|) (y |u_(-> tptp.heap_T5738788834812785303t_unit tptp.product_unit tptp.heap_T5738788834812785303t_unit)|)) (or (not (forall ((z tptp.heap_T5738788834812785303t_unit)) (= (ho_22585 x z) (ho_22585 y z)))) (= x y))))) (let ((_let_526 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ tptp.produc1219242969750017639nt_int Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ tptp.produc1219242969750017639nt_int Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_25051 x z) (ho_25051 y z)))) (= x y))))) (let ((_let_527 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.list_nat tptp.rat tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.list_nat tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_18676 x z) (ho_18676 y z)))) (= x y))))) (let ((_let_528 (forall ((x |u_(-> tptp.set_int tptp.code_natural _u_(-> tptp.int tptp.code_natural)_ tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.code_natural _u_(-> tptp.int tptp.code_natural)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15855 x z) (ho_15855 y z)))) (= x y))))) (let ((_let_529 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.product_prod_int_int Bool)|)) (= (ho_25049 x z) (ho_25049 y z)))) (= x y))))) (let ((_let_530 (forall ((x |u_(-> tptp.num tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.num tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.num)) (= (ho_12591 x z) (ho_12591 y z)))) (= x y))))) (let ((_let_531 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a tptp.set_Pr4389693562480114009it_nat)_ tptp.set_Pr2819221443900773171it_nat)|) (y |u_(-> _u_(-> tptp.a Bool)_ _u_(-> tptp.a tptp.set_Pr4389693562480114009it_nat)_ tptp.set_Pr2819221443900773171it_nat)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_25046 x z) (ho_25046 y z)))) (= x y))))) (let ((_let_532 (forall ((x |u_(-> tptp.produc8961450480463052793it_nat tptp.set_Pr4389693562480114009it_nat Bool)|) (y |u_(-> tptp.produc8961450480463052793it_nat tptp.set_Pr4389693562480114009it_nat Bool)|)) (or (not (forall ((z tptp.produc8961450480463052793it_nat)) (= (ho_25042 x z) (ho_25042 y z)))) (= x y))))) (let ((_let_533 (forall ((x |u_(-> _u_(-> tptp.b Bool)_ _u_(-> tptp.b tptp.set_Pr4389693562480114009it_nat)_ tptp.set_Pr5508209795250834101it_nat)|) (y |u_(-> _u_(-> tptp.b Bool)_ _u_(-> tptp.b tptp.set_Pr4389693562480114009it_nat)_ tptp.set_Pr5508209795250834101it_nat)|)) (or (not (forall ((z |u_(-> tptp.b Bool)|)) (= (ho_25036 x z) (ho_25036 y z)))) (= x y))))) (let ((_let_534 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.set_Pr7928877670098842301et_nat)_ tptp.set_Pr3444600963470892981et_nat)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.set_Pr7928877670098842301et_nat)_ tptp.set_Pr3444600963470892981et_nat)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.set_Pr7928877670098842301et_nat)|)) (= (ho_25033 x z) (ho_25033 y z)))) (= x y))))) (let ((_let_535 (forall ((x |u_(-> Bool _u_(-> tptp.produc7388388658123137530it_nat Bool)_ tptp.option4065278094766928714it_nat Bool)|) (y |u_(-> Bool _u_(-> tptp.produc7388388658123137530it_nat Bool)_ tptp.option4065278094766928714it_nat Bool)|)) (or (not (forall ((z Bool)) (= (ho_24444 x z) (ho_24444 y z)))) (= x y))))) (let ((_let_536 (forall ((x |u_(-> tptp.produc8111630337999740517et_nat tptp.set_Pr719794911490849221et_nat Bool)|) (y |u_(-> tptp.produc8111630337999740517et_nat tptp.set_Pr719794911490849221et_nat Bool)|)) (or (not (forall ((z tptp.produc8111630337999740517et_nat)) (= (ho_25028 x z) (ho_25028 y z)))) (= x y))))) (let ((_let_537 (forall ((x |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat tptp.produc8111630337999740517et_nat)|) (y |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat tptp.produc8111630337999740517et_nat)|)) (or (not (forall ((z tptp.produc3658429121746597890et_nat)) (= (ho_25025 x z) (ho_25025 y z)))) (= x y))))) (let ((_let_538 (forall ((x |u_(-> tptp.num tptp.nat tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.num tptp.nat tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.num)) (= (ho_13131 x z) (ho_13131 y z)))) (= x y))))) (let ((_let_539 (forall ((x |u_(-> tptp.rat tptp.list_rat tptp.list_rat)|) (y |u_(-> tptp.rat tptp.list_rat tptp.list_rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_25017 x z) (ho_25017 y z)))) (= x y))))) (let ((_let_540 (forall ((x |u_(-> tptp.list_P5707943133018811711nt_int tptp.nat)|) (y |u_(-> tptp.list_P5707943133018811711nt_int tptp.nat)|)) (or (not (forall ((z tptp.list_P5707943133018811711nt_int)) (= (ho_25015 x z) (ho_25015 y z)))) (= x y))))) (let ((_let_541 (forall ((x |u_(-> tptp.set_Pr2819221443900773171it_nat Bool)|) (y |u_(-> tptp.set_Pr2819221443900773171it_nat Bool)|)) (or (not (forall ((z tptp.set_Pr2819221443900773171it_nat)) (= (ho_24896 x z) (ho_24896 y z)))) (= x y))))) (let ((_let_542 (forall ((x |u_(-> tptp.list_P5087981734274514673_int_o tptp.nat)|) (y |u_(-> tptp.list_P5087981734274514673_int_o tptp.nat)|)) (or (not (forall ((z tptp.list_P5087981734274514673_int_o)) (= (ho_25013 x z) (ho_25013 y z)))) (= x y))))) (let ((_let_543 (forall ((x |u_(-> tptp.list_P8198026277950538467nt_nat tptp.nat)|) (y |u_(-> tptp.list_P8198026277950538467nt_nat tptp.nat)|)) (or (not (forall ((z tptp.list_P8198026277950538467nt_nat)) (= (ho_25011 x z) (ho_25011 y z)))) (= x y))))) (let ((_let_544 (forall ((x |u_(-> tptp.list_P4002435161011370285od_o_o tptp.nat)|) (y |u_(-> tptp.list_P4002435161011370285od_o_o tptp.nat)|)) (or (not (forall ((z tptp.list_P4002435161011370285od_o_o)) (= (ho_25007 x z) (ho_25007 y z)))) (= x y))))) (let ((_let_545 (forall ((x |u_(-> tptp.list_P6285523579766656935_o_nat tptp.nat)|) (y |u_(-> tptp.list_P6285523579766656935_o_nat tptp.nat)|)) (or (not (forall ((z tptp.list_P6285523579766656935_o_nat)) (= (ho_25005 x z) (ho_25005 y z)))) (= x y))))) (let ((_let_546 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_15145 x z) (ho_15145 y z)))) (= x y))))) (let ((_let_547 (forall ((x |u_(-> tptp.list_P3521021558325789923at_int tptp.nat)|) (y |u_(-> tptp.list_P3521021558325789923at_int tptp.nat)|)) (or (not (forall ((z tptp.list_P3521021558325789923at_int)) (= (ho_25003 x z) (ho_25003 y z)))) (= x y))))) (let ((_let_548 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.code_integer)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.code_integer)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_17181 x z) (ho_17181 y z)))) (= x y))))) (let ((_let_549 (forall ((x |u_(-> tptp.num tptp.list_num tptp.list_num)|) (y |u_(-> tptp.num tptp.list_num tptp.list_num)|)) (or (not (forall ((z tptp.num)) (= (ho_24996 x z) (ho_24996 y z)))) (= x y))))) (let ((_let_550 (forall ((x |u_(-> tptp.a tptp.list_a tptp.list_a)|) (y |u_(-> tptp.a tptp.list_a tptp.list_a)|)) (or (not (forall ((z tptp.a)) (= (ho_24990 x z) (ho_24990 y z)))) (= x y))))) (let ((_let_551 (forall ((x |u_(-> tptp.list_P6935614879863011209it_nat tptp.list_P6935614879863011209it_nat)|) (y |u_(-> tptp.list_P6935614879863011209it_nat tptp.list_P6935614879863011209it_nat)|)) (or (not (forall ((z tptp.list_P6935614879863011209it_nat)) (= (ho_24988 x z) (ho_24988 y z)))) (= x y))))) (let ((_let_552 (forall ((x |u_(-> tptp.list_a tptp.list_P131111800688179804it_nat tptp.list_P6935614879863011209it_nat)|) (y |u_(-> tptp.list_a tptp.list_P131111800688179804it_nat tptp.list_P6935614879863011209it_nat)|)) (or (not (forall ((z tptp.list_a)) (= (ho_24984 x z) (ho_24984 y z)))) (= x y))))) (let ((_let_553 (forall ((x |u_(-> tptp.b tptp.list_b tptp.list_b)|) (y |u_(-> tptp.b tptp.list_b tptp.list_b)|)) (or (not (forall ((z tptp.b)) (= (ho_24981 x z) (ho_24981 y z)))) (= x y))))) (let ((_let_554 (forall ((x |u_(-> tptp.produc2732055786443039994et_nat tptp.list_P362550909693114634et_nat tptp.list_P362550909693114634et_nat)|) (y |u_(-> tptp.produc2732055786443039994et_nat tptp.list_P362550909693114634et_nat tptp.list_P362550909693114634et_nat)|)) (or (not (forall ((z tptp.produc2732055786443039994et_nat)) (= (ho_24972 x z) (ho_24972 y z)))) (= x y))))) (let ((_let_555 (forall ((x |u_(-> tptp.list_P7985473006766602707_nat_o tptp.list_P2321686559999237006et_nat tptp.list_P362550909693114634et_nat)|) (y |u_(-> tptp.list_P7985473006766602707_nat_o tptp.list_P2321686559999237006et_nat tptp.list_P362550909693114634et_nat)|)) (or (not (forall ((z tptp.list_P7985473006766602707_nat_o)) (= (ho_24969 x z) (ho_24969 y z)))) (= x y))))) (let ((_let_556 (forall ((x |u_(-> tptp.produc3658429121746597890et_nat tptp.list_P9062070895058802706et_nat tptp.list_P9062070895058802706et_nat)|) (y |u_(-> tptp.produc3658429121746597890et_nat tptp.list_P9062070895058802706et_nat tptp.list_P9062070895058802706et_nat)|)) (or (not (forall ((z tptp.produc3658429121746597890et_nat)) (= (ho_24963 x z) (ho_24963 y z)))) (= x y))))) (let ((_let_557 (forall ((x |u_(-> _u_(-> tptp.set_o tptp.set_o Bool)_ _u_(-> tptp.set_o tptp.set_o Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_o tptp.set_o Bool)_ _u_(-> tptp.set_o tptp.set_o Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_o tptp.set_o Bool)|)) (= (ho_24516 x z) (ho_24516 y z)))) (= x y))))) (let ((_let_558 (forall ((x |u_(-> tptp.product_prod_int_int tptp.list_P5707943133018811711nt_int tptp.list_P5707943133018811711nt_int)|) (y |u_(-> tptp.product_prod_int_int tptp.list_P5707943133018811711nt_int tptp.list_P5707943133018811711nt_int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_24954 x z) (ho_24954 y z)))) (= x y))))) (let ((_let_559 (forall ((x |u_(-> tptp.list_P6011104703257516679at_nat tptp.list_P6011104703257516679at_nat)|) (y |u_(-> tptp.list_P6011104703257516679at_nat tptp.list_P6011104703257516679at_nat)|)) (or (not (forall ((z tptp.list_P6011104703257516679at_nat)) (= (ho_24952 x z) (ho_24952 y z)))) (= x y))))) (let ((_let_560 (forall ((x |u_(-> tptp.product_prod_int_nat tptp.list_P8198026277950538467nt_nat tptp.list_P8198026277950538467nt_nat)|) (y |u_(-> tptp.product_prod_int_nat tptp.list_P8198026277950538467nt_nat tptp.list_P8198026277950538467nt_nat)|)) (or (not (forall ((z tptp.product_prod_int_nat)) (= (ho_24945 x z) (ho_24945 y z)))) (= x y))))) (let ((_let_561 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.list_int tptp.option_int)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.list_int tptp.option_int)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_24942 x z) (ho_24942 y z)))) (= x y))))) (let ((_let_562 (forall ((x |u_(-> _u_(-> Bool Bool)_ tptp.list_o tptp.option_o)|) (y |u_(-> _u_(-> Bool Bool)_ tptp.list_o tptp.option_o)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_24939 x z) (ho_24939 y z)))) (= x y))))) (let ((_let_563 (forall ((x |u_(-> tptp.b tptp.produc8449588929630179473_nat_b)|) (y |u_(-> tptp.b tptp.produc8449588929630179473_nat_b)|)) (or (not (forall ((z tptp.b)) (= (ho_25246 x z) (ho_25246 y z)))) (= x y))))) (let ((_let_564 (forall ((x |u_(-> Bool tptp.option_o)|) (y |u_(-> Bool tptp.option_o)|)) (or (not (forall ((z Bool)) (= (ho_24937 x z) (ho_24937 y z)))) (= x y))))) (let ((_let_565 (forall ((x |u_(-> tptp.list_nat tptp.option_nat)|) (y |u_(-> tptp.list_nat tptp.option_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_24935 x z) (ho_24935 y z)))) (= x y))))) (let ((_let_566 (forall ((x |u_(-> _u_(-> tptp.num Bool)_ tptp.list_num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num Bool)_ tptp.list_num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num Bool)|)) (= (ho_24931 x z) (ho_24931 y z)))) (= x y))))) (let ((_let_567 (forall ((x |u_(-> tptp.list_num tptp.option_num)|) (y |u_(-> tptp.list_num tptp.option_num)|)) (or (not (forall ((z tptp.list_num)) (= (ho_24932 x z) (ho_24932 y z)))) (= x y))))) (let ((_let_568 (forall ((x |u_(-> tptp.num tptp.nat tptp.nat tptp.int)|) (y |u_(-> tptp.num tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z tptp.num)) (= (ho_20229 x z) (ho_20229 y z)))) (= x y))))) (let ((_let_569 (forall ((x |u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat)|) (y |u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat)|)) (or (not (forall ((z tptp.produc2732055786443039994et_nat)) (= (ho_25110 x z) (ho_25110 y z)))) (= x y))))) (let ((_let_570 (forall ((x |u_(-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat tptp.produc8664842809031399944it_nat)|) (y |u_(-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat tptp.produc8664842809031399944it_nat)|)) (or (not (forall ((z tptp.produc8664842809031399944it_nat)) (= (ho_24287 x z) (ho_24287 y z)))) (= x y))))) (let ((_let_571 (forall ((x |u_(-> tptp.list_P626663023886443800it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.list_P626663023886443800it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.list_P626663023886443800it_nat)) (= (ho_24929 x z) (ho_24929 y z)))) (= x y))))) (let ((_let_572 (forall ((x |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)_ tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)_ tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)|)) (= (ho_23093 x z) (ho_23093 y z)))) (= x y))))) (let ((_let_573 (forall ((x |u_(-> tptp.assn tptp.assn tptp.set_assn)|) (y |u_(-> tptp.assn tptp.assn tptp.set_assn)|)) (or (not (forall ((z tptp.assn)) (= (ho_25368 x z) (ho_25368 y z)))) (= x y))))) (let ((_let_574 (forall ((x |u_(-> tptp.list_P626663023886443800it_nat tptp.nat)|) (y |u_(-> tptp.list_P626663023886443800it_nat tptp.nat)|)) (or (not (forall ((z tptp.list_P626663023886443800it_nat)) (= (ho_24926 x z) (ho_24926 y z)))) (= x y))))) (let ((_let_575 (forall ((x |u_(-> tptp.list_P626663023886443800it_nat tptp.nat tptp.produc8664842809031399944it_nat)|) (y |u_(-> tptp.list_P626663023886443800it_nat tptp.nat tptp.produc8664842809031399944it_nat)|)) (or (not (forall ((z tptp.list_P626663023886443800it_nat)) (= (ho_24923 x z) (ho_24923 y z)))) (= x y))))) (let ((_let_576 (forall ((x |u_(-> _u_(-> tptp.produc3260487557148687353it_nat Bool)_ tptp.list_P6935614879863011209it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.produc3260487557148687353it_nat Bool)_ tptp.list_P6935614879863011209it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3260487557148687353it_nat Bool)|)) (= (ho_24920 x z) (ho_24920 y z)))) (= x y))))) (let ((_let_577 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.int tptp.int)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.int tptp.int)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_20088 x z) (ho_20088 y z)))) (= x y))))) (let ((_let_578 (forall ((x |u_(-> tptp.list_P6935614879863011209it_nat tptp.nat)|) (y |u_(-> tptp.list_P6935614879863011209it_nat tptp.nat)|)) (or (not (forall ((z tptp.list_P6935614879863011209it_nat)) (= (ho_24918 x z) (ho_24918 y z)))) (= x y))))) (let ((_let_579 (forall ((x |u_(-> _u_(-> tptp.produc7388388658123137530it_nat Bool)_ tptp.list_P7438302566501821706it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.produc7388388658123137530it_nat Bool)_ tptp.list_P7438302566501821706it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc7388388658123137530it_nat Bool)|)) (= (ho_24912 x z) (ho_24912 y z)))) (= x y))))) (let ((_let_580 (forall ((x |u_(-> tptp.list_P7438302566501821706it_nat tptp.nat)|) (y |u_(-> tptp.list_P7438302566501821706it_nat tptp.nat)|)) (or (not (forall ((z tptp.list_P7438302566501821706it_nat)) (= (ho_24910 x z) (ho_24910 y z)))) (= x y))))) (let ((_let_581 (forall ((x |u_(-> tptp.set_Pr2819221443900773171it_nat tptp.set_Pr2819221443900773171it_nat)|) (y |u_(-> tptp.set_Pr2819221443900773171it_nat tptp.set_Pr2819221443900773171it_nat)|)) (or (not (forall ((z tptp.set_Pr2819221443900773171it_nat)) (= (ho_24898 x z) (ho_24898 y z)))) (= x y))))) (let ((_let_582 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int tptp.int tptp.int tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int tptp.int tptp.int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_20320 x z) (ho_20320 y z)))) (= x y))))) (let ((_let_583 (forall ((x |u_(-> tptp.produc9011797661310329043it_nat tptp.set_Pr2819221443900773171it_nat Bool)|) (y |u_(-> tptp.produc9011797661310329043it_nat tptp.set_Pr2819221443900773171it_nat Bool)|)) (or (not (forall ((z tptp.produc9011797661310329043it_nat)) (= (ho_24895 x z) (ho_24895 y z)))) (= x y))))) (let ((_let_584 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat tptp.produc9011797661310329043it_nat)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat tptp.produc9011797661310329043it_nat)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_24892 x z) (ho_24892 y z)))) (= x y))))) (let ((_let_585 (forall ((x |u_(-> tptp.set_Pr5508209795250834101it_nat tptp.set_Pr5508209795250834101it_nat)|) (y |u_(-> tptp.set_Pr5508209795250834101it_nat tptp.set_Pr5508209795250834101it_nat)|)) (or (not (forall ((z tptp.set_Pr5508209795250834101it_nat)) (= (ho_24890 x z) (ho_24890 y z)))) (= x y))))) (let ((_let_586 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat tptp.produc1273031398460193109it_nat)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat tptp.produc1273031398460193109it_nat)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_24884 x z) (ho_24884 y z)))) (= x y))))) (let ((_let_587 (forall ((x |u_(-> tptp.set_Pr3444600963470892981et_nat tptp.set_Pr3444600963470892981et_nat)|) (y |u_(-> tptp.set_Pr3444600963470892981et_nat tptp.set_Pr3444600963470892981et_nat)|)) (or (not (forall ((z tptp.set_Pr3444600963470892981et_nat)) (= (ho_24882 x z) (ho_24882 y z)))) (= x y))))) (let ((_let_588 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.assn)_ _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.assn)_ _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.assn)|)) (= (ho_17155 x z) (ho_17155 y z)))) (= x y))))) (let ((_let_589 (forall ((x |u_(-> tptp.produc5657529347773406293et_nat tptp.set_Pr3444600963470892981et_nat Bool)|) (y |u_(-> tptp.produc5657529347773406293et_nat tptp.set_Pr3444600963470892981et_nat Bool)|)) (or (not (forall ((z tptp.produc5657529347773406293et_nat)) (= (ho_24879 x z) (ho_24879 y z)))) (= x y))))) (let ((_let_590 (forall ((x |u_(-> tptp.produc6830853553727218525et_nat tptp.set_Pr7928877670098842301et_nat Bool)|) (y |u_(-> tptp.produc6830853553727218525et_nat tptp.set_Pr7928877670098842301et_nat Bool)|)) (or (not (forall ((z tptp.produc6830853553727218525et_nat)) (= (ho_24871 x z) (ho_24871 y z)))) (= x y))))) (let ((_let_591 (forall ((x |u_(-> tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat tptp.produc6830853553727218525et_nat)|) (y |u_(-> tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat tptp.produc6830853553727218525et_nat)|)) (or (not (forall ((z tptp.produc3925858234332021118et_nat)) (= (ho_24868 x z) (ho_24868 y z)))) (= x y))))) (let ((_let_592 (forall ((x |u_(-> tptp.option_rat tptp.rat Bool)|) (y |u_(-> tptp.option_rat tptp.rat Bool)|)) (or (not (forall ((z tptp.option_rat)) (= (ho_24241 x z) (ho_24241 y z)))) (= x y))))) (let ((_let_593 (forall ((x |u_(-> tptp.produc1219242969750017639nt_int tptp.set_Pr2560585780119916871nt_int Bool)|) (y |u_(-> tptp.produc1219242969750017639nt_int tptp.set_Pr2560585780119916871nt_int Bool)|)) (or (not (forall ((z tptp.produc1219242969750017639nt_int)) (= (ho_24863 x z) (ho_24863 y z)))) (= x y))))) (let ((_let_594 (forall ((x |u_(-> tptp.int tptp.nat tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_12402 x z) (ho_12402 y z)))) (= x y))))) (let ((_let_595 (forall ((x |u_(-> tptp.list_o tptp.option_o)|) (y |u_(-> tptp.list_o tptp.option_o)|)) (or (not (forall ((z tptp.list_o)) (= (ho_24940 x z) (ho_24940 y z)))) (= x y))))) (let ((_let_596 (forall ((x |u_(-> _u_(-> tptp.produc6197004810343482825et_nat tptp.produc6197004810343482825et_nat Bool)_ tptp.produc6197004810343482825et_nat Bool)|) (y |u_(-> _u_(-> tptp.produc6197004810343482825et_nat tptp.produc6197004810343482825et_nat Bool)_ tptp.produc6197004810343482825et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc6197004810343482825et_nat tptp.produc6197004810343482825et_nat Bool)|)) (= (ho_24620 x z) (ho_24620 y z)))) (= x y))))) (let ((_let_597 (forall ((x |u_(-> tptp.nat tptp.list_int tptp.list_P3521021558325789923at_int)|) (y |u_(-> tptp.nat tptp.list_int tptp.list_P3521021558325789923at_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_24850 x z) (ho_24850 y z)))) (= x y))))) (let ((_let_598 (forall ((x |u_(-> tptp.nat tptp.list_o tptp.list_P7333126701944960589_nat_o)|) (y |u_(-> tptp.nat tptp.list_o tptp.list_P7333126701944960589_nat_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_24848 x z) (ho_24848 y z)))) (= x y))))) (let ((_let_599 (forall ((x |u_(-> _u_(-> tptp.num tptp.num Bool)_ tptp.list_num Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num Bool)_ tptp.list_num Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num Bool)|)) (= (ho_24841 x z) (ho_24841 y z)))) (= x y))))) (let ((_let_600 (forall ((x |u_(-> tptp.filter_nat Bool)|) (y |u_(-> tptp.filter_nat Bool)|)) (or (not (forall ((z tptp.filter_nat)) (= (ho_26040 x z) (ho_26040 y z)))) (= x y))))) (let ((_let_601 (forall ((x |u_(-> tptp.list_rat Bool)|) (y |u_(-> tptp.list_rat Bool)|)) (or (not (forall ((z tptp.list_rat)) (= (ho_24835 x z) (ho_24835 y z)))) (= x y))))) (let ((_let_602 (forall ((x |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn tptp.assn)|) (y |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.assn)|)) (= (ho_17988 x z) (ho_17988 y z)))) (= x y))))) (let ((_let_603 (forall ((x |u_(-> tptp.list_rat tptp.nat tptp.rat)|) (y |u_(-> tptp.list_rat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.list_rat)) (= (ho_24832 x z) (ho_24832 y z)))) (= x y))))) (let ((_let_604 (forall ((x |u_(-> tptp.nat tptp.nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_18804 x z) (ho_18804 y z)))) (= x y))))) (let ((_let_605 (forall ((x |u_(-> tptp.nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> tptp.nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_24826 x z) (ho_24826 y z)))) (= x y))))) (let ((_let_606 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_25858 x z) (ho_25858 y z)))) (= x y))))) (let ((_let_607 (forall ((x |u_(-> tptp.list_P131111800688179804it_nat tptp.nat)|) (y |u_(-> tptp.list_P131111800688179804it_nat tptp.nat)|)) (or (not (forall ((z tptp.list_P131111800688179804it_nat)) (= (ho_24815 x z) (ho_24815 y z)))) (= x y))))) (let ((_let_608 (forall ((x |u_(-> tptp.list_P5707943133018811711nt_int tptp.nat tptp.product_prod_int_int)|) (y |u_(-> tptp.list_P5707943133018811711nt_int tptp.nat tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.list_P5707943133018811711nt_int)) (= (ho_24812 x z) (ho_24812 y z)))) (= x y))))) (let ((_let_609 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.code_integer)_ Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.code_integer)_ Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_15133 x z) (ho_15133 y z)))) (= x y))))) (let ((_let_610 (forall ((x |u_(-> tptp.list_int tptp.list_P5707943133018811711nt_int)|) (y |u_(-> tptp.list_int tptp.list_P5707943133018811711nt_int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_24810 x z) (ho_24810 y z)))) (= x y))))) (let ((_let_611 (forall ((x |u_(-> tptp.nat tptp.product_prod_int_int)|) (y |u_(-> tptp.nat tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_24813 x z) (ho_24813 y z)))) (= x y))))) (let ((_let_612 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_23347 x z) (ho_23347 y z)))) (= x y))))) (let ((_let_613 (forall ((x |u_(-> tptp.list_P8198026277950538467nt_nat tptp.nat tptp.product_prod_int_nat)|) (y |u_(-> tptp.list_P8198026277950538467nt_nat tptp.nat tptp.product_prod_int_nat)|)) (or (not (forall ((z tptp.list_P8198026277950538467nt_nat)) (= (ho_24798 x z) (ho_24798 y z)))) (= x y))))) (let ((_let_614 (forall ((x |u_(-> tptp.list_int tptp.list_nat tptp.list_P8198026277950538467nt_nat)|) (y |u_(-> tptp.list_int tptp.list_nat tptp.list_P8198026277950538467nt_nat)|)) (or (not (forall ((z tptp.list_int)) (= (ho_24795 x z) (ho_24795 y z)))) (= x y))))) (let ((_let_615 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_15186 x z) (ho_15186 y z)))) (= x y))))) (let ((_let_616 (forall ((x |u_(-> tptp.nat tptp.product_prod_o_int)|) (y |u_(-> tptp.nat tptp.product_prod_o_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_24790 x z) (ho_24790 y z)))) (= x y))))) (let ((_let_617 (forall ((x |u_(-> tptp.option8956607266484857688it_nat tptp.produc8664842809031399944it_nat)|) (y |u_(-> tptp.option8956607266484857688it_nat tptp.produc8664842809031399944it_nat)|)) (or (not (forall ((z tptp.option8956607266484857688it_nat)) (= (ho_24288 x z) (ho_24288 y z)))) (= x y))))) (let ((_let_618 (forall ((x |u_(-> tptp.int tptp.product_prod_o_int)|) (y |u_(-> tptp.int tptp.product_prod_o_int)|)) (or (not (forall ((z tptp.int)) (= (ho_24784 x z) (ho_24784 y z)))) (= x y))))) (let ((_let_619 (forall ((x |u_(-> tptp.list_o tptp.list_P4002435161011370285od_o_o)|) (y |u_(-> tptp.list_o tptp.list_P4002435161011370285od_o_o)|)) (or (not (forall ((z tptp.list_o)) (= (ho_24778 x z) (ho_24778 y z)))) (= x y))))) (let ((_let_620 (forall ((x |u_(-> tptp.nat tptp.product_prod_o_o)|) (y |u_(-> tptp.nat tptp.product_prod_o_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_24781 x z) (ho_24781 y z)))) (= x y))))) (let ((_let_621 (forall ((x |u_(-> Bool tptp.product_prod_o_o)|) (y |u_(-> Bool tptp.product_prod_o_o)|)) (or (not (forall ((z Bool)) (= (ho_24775 x z) (ho_24775 y z)))) (= x y))))) (let ((_let_622 (forall ((x |u_(-> tptp.list_P6285523579766656935_o_nat tptp.nat tptp.product_prod_o_nat)|) (y |u_(-> tptp.list_P6285523579766656935_o_nat tptp.nat tptp.product_prod_o_nat)|)) (or (not (forall ((z tptp.list_P6285523579766656935_o_nat)) (= (ho_24772 x z) (ho_24772 y z)))) (= x y))))) (let ((_let_623 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_18807 x z) (ho_18807 y z)))) (= x y))))) (let ((_let_624 (forall ((x |u_(-> tptp.list_o tptp.list_nat tptp.list_P6285523579766656935_o_nat)|) (y |u_(-> tptp.list_o tptp.list_nat tptp.list_P6285523579766656935_o_nat)|)) (or (not (forall ((z tptp.list_o)) (= (ho_24769 x z) (ho_24769 y z)))) (= x y))))) (let ((_let_625 (forall ((x |u_(-> tptp.list_nat tptp.list_P6285523579766656935_o_nat)|) (y |u_(-> tptp.list_nat tptp.list_P6285523579766656935_o_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_24770 x z) (ho_24770 y z)))) (= x y))))) (let ((_let_626 (forall ((x |u_(-> Bool tptp.nat tptp.product_prod_o_nat)|) (y |u_(-> Bool tptp.nat tptp.product_prod_o_nat)|)) (or (not (forall ((z Bool)) (= (ho_24766 x z) (ho_24766 y z)))) (= x y))))) (let ((_let_627 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_int)|) (y |u_(-> tptp.nat tptp.product_prod_nat_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_24764 x z) (ho_24764 y z)))) (= x y))))) (let ((_let_628 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat Bool)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat Bool)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat Bool)|)) (= (ho_14880 x z) (ho_14880 y z)))) (= x y))))) (let ((_let_629 (forall ((x |u_(-> tptp.nat tptp.int tptp.product_prod_nat_int)|) (y |u_(-> tptp.nat tptp.int tptp.product_prod_nat_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_24757 x z) (ho_24757 y z)))) (= x y))))) (let ((_let_630 (forall ((x |u_(-> tptp.int tptp.product_prod_nat_int)|) (y |u_(-> tptp.int tptp.product_prod_nat_int)|)) (or (not (forall ((z tptp.int)) (= (ho_24758 x z) (ho_24758 y z)))) (= x y))))) (let ((_let_631 (forall ((x |u_(-> tptp.list_P7333126701944960589_nat_o tptp.nat tptp.product_prod_nat_o)|) (y |u_(-> tptp.list_P7333126701944960589_nat_o tptp.nat tptp.product_prod_nat_o)|)) (or (not (forall ((z tptp.list_P7333126701944960589_nat_o)) (= (ho_24754 x z) (ho_24754 y z)))) (= x y))))) (let ((_let_632 (forall ((x |u_(-> tptp.set_Pr2560585780119916871nt_int Bool)|) (y |u_(-> tptp.set_Pr2560585780119916871nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr2560585780119916871nt_int)) (= (ho_24864 x z) (ho_24864 y z)))) (= x y))))) (let ((_let_633 (forall ((x |u_(-> tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.list_P6011104703257516679at_nat)) (= (ho_24746 x z) (ho_24746 y z)))) (= x y))))) (let ((_let_634 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.int)_ tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.int)_ tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_int_int)|)) (= (ho_20073 x z) (ho_20073 y z)))) (= x y))))) (let ((_let_635 (forall ((x |u_(-> tptp.list_nat tptp.list_nat tptp.list_P6011104703257516679at_nat)|) (y |u_(-> tptp.list_nat tptp.list_nat tptp.list_P6011104703257516679at_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_24743 x z) (ho_24743 y z)))) (= x y))))) (let ((_let_636 (forall ((x |u_(-> tptp.list_nat tptp.list_P6011104703257516679at_nat)|) (y |u_(-> tptp.list_nat tptp.list_P6011104703257516679at_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_24744 x z) (ho_24744 y z)))) (= x y))))) (let ((_let_637 (forall ((x |u_(-> tptp.list_Product_unit tptp.nat)|) (y |u_(-> tptp.list_Product_unit tptp.nat)|)) (or (not (forall ((z tptp.list_Product_unit)) (= (ho_24741 x z) (ho_24741 y z)))) (= x y))))) (let ((_let_638 (forall ((x |u_(-> tptp.nat tptp.heap_T5738788834812785303t_unit)|) (y |u_(-> tptp.nat tptp.heap_T5738788834812785303t_unit)|)) (or (not (forall ((z tptp.nat)) (= (ho_24739 x z) (ho_24739 y z)))) (= x y))))) (let ((_let_639 (forall ((x |u_(-> tptp.list_Product_unit tptp.assn)|) (y |u_(-> tptp.list_Product_unit tptp.assn)|)) (or (not (forall ((z tptp.list_Product_unit)) (= (ho_24736 x z) (ho_24736 y z)))) (= x y))))) (let ((_let_640 (forall ((x |u_(-> tptp.list_Product_unit tptp.nat tptp.product_unit)|) (y |u_(-> tptp.list_Product_unit tptp.nat tptp.product_unit)|)) (or (not (forall ((z tptp.list_Product_unit)) (= (ho_24732 x z) (ho_24732 y z)))) (= x y))))) (let ((_let_641 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.int)|)) (= (ho_20074 x z) (ho_20074 y z)))) (= x y))))) (let ((_let_642 (forall ((x |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)|)) (= (ho_24382 x z) (ho_24382 y z)))) (= x y))))) (let ((_let_643 (forall ((x |u_(-> tptp.assn tptp.heap_Time_Heap_int _u_(-> tptp.int tptp.assn)_ Bool)|) (y |u_(-> tptp.assn tptp.heap_Time_Heap_int _u_(-> tptp.int tptp.assn)_ Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_24728 x z) (ho_24728 y z)))) (= x y))))) (let ((_let_644 (forall ((x |u_(-> tptp.array_int tptp.nat tptp.heap_Time_Heap_int)|) (y |u_(-> tptp.array_int tptp.nat tptp.heap_Time_Heap_int)|)) (or (not (forall ((z tptp.array_int)) (= (ho_24725 x z) (ho_24725 y z)))) (= x y))))) (let ((_let_645 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_25331 x z) (ho_25331 y z)))) (= x y))))) (let ((_let_646 (forall ((x |u_(-> _u_(-> tptp.int tptp.assn)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.assn)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.assn)|)) (= (ho_24730 x z) (ho_24730 y z)))) (= x y))))) (let ((_let_647 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat tptp.int)_ tptp.nat tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.nat tptp.int)_ tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat tptp.int)|)) (= (ho_12452 x z) (ho_12452 y z)))) (= x y))))) (let ((_let_648 (forall ((x |u_(-> tptp.heap_Time_Heap_o _u_(-> Bool tptp.assn)_ Bool)|) (y |u_(-> tptp.heap_Time_Heap_o _u_(-> Bool tptp.assn)_ Bool)|)) (or (not (forall ((z tptp.heap_Time_Heap_o)) (= (ho_24722 x z) (ho_24722 y z)))) (= x y))))) (let ((_let_649 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_25931 x z) (ho_25931 y z)))) (= x y))))) (let ((_let_650 (forall ((x |u_(-> _u_(-> Bool tptp.assn)_ Bool)|) (y |u_(-> _u_(-> Bool tptp.assn)_ Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.assn)|)) (= (ho_24723 x z) (ho_24723 y z)))) (= x y))))) (let ((_let_651 (forall ((x |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.assn)|)) (= (ho_21233 x z) (ho_21233 y z)))) (= x y))))) (let ((_let_652 (forall ((x |u_(-> tptp.array_nat tptp.nat tptp.heap_Time_Heap_nat)|) (y |u_(-> tptp.array_nat tptp.nat tptp.heap_Time_Heap_nat)|)) (or (not (forall ((z tptp.array_nat)) (= (ho_24715 x z) (ho_24715 y z)))) (= x y))))) (let ((_let_653 (forall ((x |u_(-> tptp.nat tptp.nat tptp.list_int tptp.list_int)|) (y |u_(-> tptp.nat tptp.nat tptp.list_int tptp.list_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_24708 x z) (ho_24708 y z)))) (= x y))))) (let ((_let_654 (forall ((x |u_(-> tptp.nat tptp.list_o tptp.list_o)|) (y |u_(-> tptp.nat tptp.list_o tptp.list_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_24706 x z) (ho_24706 y z)))) (= x y))))) (let ((_let_655 (forall ((x |u_(-> tptp.nat tptp.nat tptp.list_nat tptp.list_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_24703 x z) (ho_24703 y z)))) (= x y))))) (let ((_let_656 (forall ((x |u_(-> tptp.set_Pr7928877670098842301et_nat Bool)|) (y |u_(-> tptp.set_Pr7928877670098842301et_nat Bool)|)) (or (not (forall ((z tptp.set_Pr7928877670098842301et_nat)) (= (ho_24872 x z) (ho_24872 y z)))) (= x y))))) (let ((_let_657 (forall ((x |u_(-> tptp.array_int tptp.heap_Time_Heap_nat)|) (y |u_(-> tptp.array_int tptp.heap_Time_Heap_nat)|)) (or (not (forall ((z tptp.array_int)) (= (ho_24701 x z) (ho_24701 y z)))) (= x y))))) (let ((_let_658 (forall ((x |u_(-> _u_(-> tptp.nat tptp.assn)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.assn)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.assn)|)) (= (ho_24697 x z) (ho_24697 y z)))) (= x y))))) (let ((_let_659 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_19177 x z) (ho_19177 y z)))) (= x y))))) (let ((_let_660 (forall ((x |u_(-> tptp.multis2468970476368604999at_nat tptp.nat)|) (y |u_(-> tptp.multis2468970476368604999at_nat tptp.nat)|)) (or (not (forall ((z tptp.multis2468970476368604999at_nat)) (= (ho_24691 x z) (ho_24691 y z)))) (= x y))))) (let ((_let_661 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_15281 x z) (ho_15281 y z)))) (= x y))))) (let ((_let_662 (forall ((x |u_(-> tptp.product_unit tptp.nat)|) (y |u_(-> tptp.product_unit tptp.nat)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_24673 x z) (ho_24673 y z)))) (= x y))))) (let ((_let_663 (forall ((x |u_(-> _u_(-> tptp.num tptp.nat)_ tptp.option_num tptp.nat)|) (y |u_(-> _u_(-> tptp.num tptp.nat)_ tptp.option_num tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.num tptp.nat)|)) (= (ho_24672 x z) (ho_24672 y z)))) (= x y))))) (let ((_let_664 (forall ((x |u_(-> _u_(-> tptp.produc8664842809031399944it_nat tptp.nat)_ tptp.option8956607266484857688it_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.produc8664842809031399944it_nat tptp.nat)_ tptp.option8956607266484857688it_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.produc8664842809031399944it_nat tptp.nat)|)) (= (ho_24669 x z) (ho_24669 y z)))) (= x y))))) (let ((_let_665 (forall ((x |u_(-> tptp.option8956607266484857688it_nat tptp.nat)|) (y |u_(-> tptp.option8956607266484857688it_nat tptp.nat)|)) (or (not (forall ((z tptp.option8956607266484857688it_nat)) (= (ho_24670 x z) (ho_24670 y z)))) (= x y))))) (let ((_let_666 (forall ((x |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.nat)_ tptp.option3562590408128118217it_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.nat)_ tptp.option3562590408128118217it_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.produc3260487557148687353it_nat tptp.nat)|)) (= (ho_24665 x z) (ho_24665 y z)))) (= x y))))) (let ((_let_667 (forall ((x |u_(-> tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat)|) (y |u_(-> tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat)|)) (or (not (forall ((z tptp.option8963830502488799655at_nat)) (= (ho_22214 x z) (ho_22214 y z)))) (= x y))))) (let ((_let_668 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.nat)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.nat)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_24663 x z) (ho_24663 y z)))) (= x y))))) (let ((_let_669 (forall ((x |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.nat)_ tptp.option4065278094766928714it_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.nat)_ tptp.option4065278094766928714it_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.produc7388388658123137530it_nat tptp.nat)|)) (= (ho_24661 x z) (ho_24661 y z)))) (= x y))))) (let ((_let_670 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_19219 x z) (ho_19219 y z)))) (= x y))))) (let ((_let_671 (forall ((x |u_(-> tptp.int tptp.rat Bool)|) (y |u_(-> tptp.int tptp.rat Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_24649 x z) (ho_24649 y z)))) (= x y))))) (let ((_let_672 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_24643 x z) (ho_24643 y z)))) (= x y))))) (let ((_let_673 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int Bool)_ _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)_ _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int Bool)_ _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)_ _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int Bool)|)) (= (ho_24629 x z) (ho_24629 y z)))) (= x y))))) (let ((_let_674 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)|)) (= (ho_24631 x z) (ho_24631 y z)))) (= x y))))) (let ((_let_675 (forall ((x |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)_ _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)_ _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)|)) (= (ho_24627 x z) (ho_24627 y z)))) (= x y))))) (let ((_let_676 (forall ((x |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_20094 x z) (ho_20094 y z)))) (= x y))))) (let ((_let_677 (forall ((x |u_(-> tptp.produc6197004810343482825et_nat tptp.produc6197004810343482825et_nat Bool)|) (y |u_(-> tptp.produc6197004810343482825et_nat tptp.produc6197004810343482825et_nat Bool)|)) (or (not (forall ((z tptp.produc6197004810343482825et_nat)) (= (ho_24618 x z) (ho_24618 y z)))) (= x y))))) (let ((_let_678 (forall ((x |u_(-> tptp.produc6197004810343482825et_nat Bool)|) (y |u_(-> tptp.produc6197004810343482825et_nat Bool)|)) (or (not (forall ((z tptp.produc6197004810343482825et_nat)) (= (ho_24621 x z) (ho_24621 y z)))) (= x y))))) (let ((_let_679 (forall ((x |u_(-> Bool tptp.produc3658429121746597890et_nat tptp.produc6197004810343482825et_nat)|) (y |u_(-> Bool tptp.produc3658429121746597890et_nat tptp.produc6197004810343482825et_nat)|)) (or (not (forall ((z Bool)) (= (ho_24615 x z) (ho_24615 y z)))) (= x y))))) (let ((_let_680 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_16862 x z) (ho_16862 y z)))) (= x y))))) (let ((_let_681 (forall ((x |u_(-> tptp.produc8923325533196201883nteger Bool)|) (y |u_(-> tptp.produc8923325533196201883nteger Bool)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_24611 x z) (ho_24611 y z)))) (= x y))))) (let ((_let_682 (forall ((x |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)_ tptp.produc7388388658123137530it_nat Bool)|) (y |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)_ tptp.produc7388388658123137530it_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)|)) (= (ho_25125 x z) (ho_25125 y z)))) (= x y))))) (let ((_let_683 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.list_int tptp.nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.list_int tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_18674 x z) (ho_18674 y z)))) (= x y))))) (let ((_let_684 (forall ((x |u_(-> tptp.int tptp.nat tptp.nat tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.nat tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_20006 x z) (ho_20006 y z)))) (= x y))))) (let ((_let_685 (forall ((x |u_(-> tptp.produc2732055786443039994et_nat tptp.produc5657529347773406293et_nat)|) (y |u_(-> tptp.produc2732055786443039994et_nat tptp.produc5657529347773406293et_nat)|)) (or (not (forall ((z tptp.produc2732055786443039994et_nat)) (= (ho_24877 x z) (ho_24877 y z)))) (= x y))))) (let ((_let_686 (forall ((x |u_(-> tptp.set_int tptp.option_set_int)|) (y |u_(-> tptp.set_int tptp.option_set_int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_22410 x z) (ho_22410 y z)))) (= x y))))) (let ((_let_687 (forall ((x |u_(-> tptp.ref_Product_unit tptp.product_unit tptp.assn)|) (y |u_(-> tptp.ref_Product_unit tptp.product_unit tptp.assn)|)) (or (not (forall ((z tptp.ref_Product_unit)) (= (ho_24608 x z) (ho_24608 y z)))) (= x y))))) (let ((_let_688 (forall ((x |u_(-> tptp.list_o tptp.list_P5087981734274514673_int_o)|) (y |u_(-> tptp.list_o tptp.list_P5087981734274514673_int_o)|)) (or (not (forall ((z tptp.list_o)) (= (ho_24804 x z) (ho_24804 y z)))) (= x y))))) (let ((_let_689 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.produc7248412053542808358at_nat tptp.produc4471711990508489141at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.produc7248412053542808358at_nat tptp.produc4471711990508489141at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_24598 x z) (ho_24598 y z)))) (= x y))))) (let ((_let_690 (forall ((x |u_(-> tptp.produc7248412053542808358at_nat tptp.produc4471711990508489141at_nat)|) (y |u_(-> tptp.produc7248412053542808358at_nat tptp.produc4471711990508489141at_nat)|)) (or (not (forall ((z tptp.produc7248412053542808358at_nat)) (= (ho_24599 x z) (ho_24599 y z)))) (= x y))))) (let ((_let_691 (forall ((x |u_(-> _u_(-> tptp.nat tptp.option_nat)_ tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.option_nat)_ tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.option_nat)|)) (= (ho_24583 x z) (ho_24583 y z)))) (= x y))))) (let ((_let_692 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ Bool)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.set_Pr7928877670098842301et_nat)_ tptp.set_Pr3444600963470892981et_nat)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ Bool)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.set_Pr7928877670098842301et_nat)_ tptp.set_Pr3444600963470892981et_nat)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ Bool)|)) (= (ho_25032 x z) (ho_25032 y z)))) (= x y))))) (let ((_let_693 (forall ((x |u_(-> _u_(-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat)_ _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat)_ _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat)|)) (= (ho_24581 x z) (ho_24581 y z)))) (= x y))))) (let ((_let_694 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.ref_Product_unit tptp.product_unit)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.ref_Product_unit tptp.product_unit)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_24576 x z) (ho_24576 y z)))) (= x y))))) (let ((_let_695 (forall ((x |u_(-> _u_(-> Bool tptp.assn)_ _u_(-> Bool tptp.assn)_ Bool Bool)|) (y |u_(-> _u_(-> Bool tptp.assn)_ _u_(-> Bool tptp.assn)_ Bool Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.assn)|)) (= (ho_17177 x z) (ho_17177 y z)))) (= x y))))) (let ((_let_696 (forall ((x |u_(-> tptp.code_natural tptp.code_integer tptp.code_natural)|) (y |u_(-> tptp.code_natural tptp.code_integer tptp.code_natural)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_15845 x z) (ho_15845 y z)))) (= x y))))) (let ((_let_697 (forall ((x |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)_ _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)_ _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)|)) (= (ho_24571 x z) (ho_24571 y z)))) (= x y))))) (let ((_let_698 (forall ((x |u_(-> _u_(-> tptp.nat tptp.option_nat)_ _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.option_nat)_ _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.option_nat)|)) (= (ho_24569 x z) (ho_24569 y z)))) (= x y))))) (let ((_let_699 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.option_nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.option_nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_24560 x z) (ho_24560 y z)))) (= x y))))) (let ((_let_700 (forall ((x |u_(-> tptp.assn tptp.rat)|) (y |u_(-> tptp.assn tptp.rat)|)) (or (not (forall ((z tptp.assn)) (= (ho_24293 x z) (ho_24293 y z)))) (= x y))))) (let ((_let_701 (forall ((x |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (= (ho_24544 x z) (ho_24544 y z)))) (= x y))))) (let ((_let_702 (forall ((x |u_(-> tptp.set_Code_integer tptp.assn)|) (y |u_(-> tptp.set_Code_integer tptp.assn)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_25504 x z) (ho_25504 y z)))) (= x y))))) (let ((_let_703 (forall ((x |u_(-> _u_(-> tptp.set_int tptp.set_int Bool)_ _u_(-> tptp.set_int tptp.set_int Bool)_ tptp.set_int Bool)|) (y |u_(-> _u_(-> tptp.set_int tptp.set_int Bool)_ _u_(-> tptp.set_int tptp.set_int Bool)_ tptp.set_int Bool)|)) (or (not (forall ((z |u_(-> tptp.set_int tptp.set_int Bool)|)) (= (ho_24555 x z) (ho_24555 y z)))) (= x y))))) (let ((_let_704 (forall ((x |u_(-> _u_(-> tptp.assn tptp.assn Bool)_ _u_(-> tptp.assn tptp.assn Bool)_ tptp.assn Bool)|) (y |u_(-> _u_(-> tptp.assn tptp.assn Bool)_ _u_(-> tptp.assn tptp.assn Bool)_ tptp.assn Bool)|)) (or (not (forall ((z |u_(-> tptp.assn tptp.assn Bool)|)) (= (ho_24552 x z) (ho_24552 y z)))) (= x y))))) (let ((_let_705 (forall ((x |u_(-> tptp.int tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.int tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_11518 x z) (ho_11518 y z)))) (= x y))))) (let ((_let_706 (forall ((x |u_(-> _u_(-> tptp.assn tptp.assn Bool)_ tptp.assn Bool)|) (y |u_(-> _u_(-> tptp.assn tptp.assn Bool)_ tptp.assn Bool)|)) (or (not (forall ((z |u_(-> tptp.assn tptp.assn Bool)|)) (= (ho_24553 x z) (ho_24553 y z)))) (= x y))))) (let ((_let_707 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_12543 x z) (ho_12543 y z)))) (= x y))))) (let ((_let_708 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.set_nat Bool)_ _u_(-> tptp.set_nat tptp.set_nat Bool)_ tptp.set_nat Bool)|) (y |u_(-> _u_(-> tptp.set_nat tptp.set_nat Bool)_ _u_(-> tptp.set_nat tptp.set_nat Bool)_ tptp.set_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.set_nat Bool)|)) (= (ho_24549 x z) (ho_24549 y z)))) (= x y))))) (let ((_let_709 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.set_nat Bool)_ tptp.set_nat Bool)|) (y |u_(-> _u_(-> tptp.set_nat tptp.set_nat Bool)_ tptp.set_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.set_nat Bool)|)) (= (ho_24550 x z) (ho_24550 y z)))) (= x y))))) (let ((_let_710 (forall ((x |u_(-> tptp.nat tptp.nat tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_19510 x z) (ho_19510 y z)))) (= x y))))) (let ((_let_711 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.product_prod_int_int tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.product_prod_int_int tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (= (ho_14700 x z) (ho_14700 y z)))) (= x y))))) (let ((_let_712 (forall ((x |u_(-> _u_(-> tptp.set_o tptp.set_o Bool)_ _u_(-> tptp.set_o tptp.set_o Bool)_ tptp.set_o Bool)|) (y |u_(-> _u_(-> tptp.set_o tptp.set_o Bool)_ _u_(-> tptp.set_o tptp.set_o Bool)_ tptp.set_o Bool)|)) (or (not (forall ((z |u_(-> tptp.set_o tptp.set_o Bool)|)) (= (ho_24546 x z) (ho_24546 y z)))) (= x y))))) (let ((_let_713 (forall ((x |u_(-> _u_(-> tptp.set_o tptp.set_o Bool)_ tptp.set_o Bool)|) (y |u_(-> _u_(-> tptp.set_o tptp.set_o Bool)_ tptp.set_o Bool)|)) (or (not (forall ((z |u_(-> tptp.set_o tptp.set_o Bool)|)) (= (ho_24547 x z) (ho_24547 y z)))) (= x y))))) (let ((_let_714 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_24284 x z) (ho_24284 y z)))) (= x y))))) (let ((_let_715 (forall ((x |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (= (ho_24543 x z) (ho_24543 y z)))) (= x y))))) (let ((_let_716 (forall ((x |u_(-> tptp.set_int tptp.option_set_int tptp.set_int)|) (y |u_(-> tptp.set_int tptp.option_set_int tptp.set_int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_24540 x z) (ho_24540 y z)))) (= x y))))) (let ((_let_717 (forall ((x |u_(-> tptp.list_o tptp.list_o tptp.list_P4002435161011370285od_o_o)|) (y |u_(-> tptp.list_o tptp.list_o tptp.list_P4002435161011370285od_o_o)|)) (or (not (forall ((z tptp.list_o)) (= (ho_24777 x z) (ho_24777 y z)))) (= x y))))) (let ((_let_718 (forall ((x |u_(-> tptp.option_set_int tptp.set_int)|) (y |u_(-> tptp.option_set_int tptp.set_int)|)) (or (not (forall ((z tptp.option_set_int)) (= (ho_24541 x z) (ho_24541 y z)))) (= x y))))) (let ((_let_719 (forall ((x |u_(-> tptp.set_nat tptp.option_set_nat tptp.set_nat)|) (y |u_(-> tptp.set_nat tptp.option_set_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_24537 x z) (ho_24537 y z)))) (= x y))))) (let ((_let_720 (forall ((x |u_(-> tptp.list_P7438302566501821706it_nat tptp.nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> tptp.list_P7438302566501821706it_nat tptp.nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z tptp.list_P7438302566501821706it_nat)) (= (ho_24825 x z) (ho_24825 y z)))) (= x y))))) (let ((_let_721 (forall ((x |u_(-> tptp.int tptp.set_int tptp.int Bool)|) (y |u_(-> tptp.int tptp.set_int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_11233 x z) (ho_11233 y z)))) (= x y))))) (let ((_let_722 (forall ((x |u_(-> tptp.option_set_nat tptp.set_nat)|) (y |u_(-> tptp.option_set_nat tptp.set_nat)|)) (or (not (forall ((z tptp.option_set_nat)) (= (ho_24538 x z) (ho_24538 y z)))) (= x y))))) (let ((_let_723 (forall ((x |u_(-> tptp.set_o tptp.option_set_o tptp.set_o)|) (y |u_(-> tptp.set_o tptp.option_set_o tptp.set_o)|)) (or (not (forall ((z tptp.set_o)) (= (ho_24534 x z) (ho_24534 y z)))) (= x y))))) (let ((_let_724 (forall ((x |u_(-> tptp.product_unit Bool)|) (y |u_(-> tptp.product_unit Bool)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_24527 x z) (ho_24527 y z)))) (= x y))))) (let ((_let_725 (forall ((x |u_(-> _u_(-> tptp.set_int tptp.set_int tptp.set_int)_ tptp.set_int _u_(-> tptp.set_int tptp.set_int Bool)_ _u_(-> tptp.set_int tptp.set_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_int tptp.set_int tptp.set_int)_ tptp.set_int _u_(-> tptp.set_int tptp.set_int Bool)_ _u_(-> tptp.set_int tptp.set_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_int tptp.set_int tptp.set_int)|)) (= (ho_24525 x z) (ho_24525 y z)))) (= x y))))) (let ((_let_726 (forall ((x |u_(-> tptp.assn _u_(-> tptp.assn tptp.assn Bool)_ _u_(-> tptp.assn tptp.assn Bool)_ Bool)|) (y |u_(-> tptp.assn _u_(-> tptp.assn tptp.assn Bool)_ _u_(-> tptp.assn tptp.assn Bool)_ Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_24523 x z) (ho_24523 y z)))) (= x y))))) (let ((_let_727 (forall ((x |u_(-> tptp.list_num tptp.nat tptp.num)|) (y |u_(-> tptp.list_num tptp.nat tptp.num)|)) (or (not (forall ((z tptp.list_num)) (= (ho_24839 x z) (ho_24839 y z)))) (= x y))))) (let ((_let_728 (forall ((x |u_(-> tptp.produc7250841696378415494atural tptp.produc1399344845416535567atural)|) (y |u_(-> tptp.produc7250841696378415494atural tptp.produc1399344845416535567atural)|)) (or (not (forall ((z tptp.produc7250841696378415494atural)) (= (ho_25271 x z) (ho_25271 y z)))) (= x y))))) (let ((_let_729 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)_ tptp.set_nat _u_(-> tptp.set_nat tptp.set_nat Bool)_ _u_(-> tptp.set_nat tptp.set_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)_ tptp.set_nat _u_(-> tptp.set_nat tptp.set_nat Bool)_ _u_(-> tptp.set_nat tptp.set_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)|)) (= (ho_24519 x z) (ho_24519 y z)))) (= x y))))) (let ((_let_730 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.set_nat tptp.set_nat Bool)_ _u_(-> tptp.set_nat tptp.set_nat Bool)_ Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.set_nat tptp.set_nat Bool)_ _u_(-> tptp.set_nat tptp.set_nat Bool)_ Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_24520 x z) (ho_24520 y z)))) (= x y))))) (let ((_let_731 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_24507 x z) (ho_24507 y z)))) (= x y))))) (let ((_let_732 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_20092 x z) (ho_20092 y z)))) (= x y))))) (let ((_let_733 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.list_nat tptp.option_nat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.list_nat tptp.option_nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_24934 x z) (ho_24934 y z)))) (= x y))))) (let ((_let_734 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_24496 x z) (ho_24496 y z)))) (= x y))))) (let ((_let_735 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ tptp.a tptp.heap_Time_Heap_a)|) (y |u_(-> _u_(-> tptp.a Bool)_ tptp.a tptp.heap_Time_Heap_a)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_24492 x z) (ho_24492 y z)))) (= x y))))) (let ((_let_736 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_24490 x z) (ho_24490 y z)))) (= x y))))) (let ((_let_737 (forall ((x |u_(-> tptp.b Bool)|) (y |u_(-> tptp.b Bool)|)) (or (not (forall ((z tptp.b)) (= (ho_24487 x z) (ho_24487 y z)))) (= x y))))) (let ((_let_738 (forall ((x |u_(-> _u_(-> tptp.produc2732055786443039994et_nat Bool)_ _u_(-> tptp.produc2732055786443039994et_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.produc2732055786443039994et_nat Bool)_ _u_(-> tptp.produc2732055786443039994et_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.produc2732055786443039994et_nat Bool)|)) (= (ho_24478 x z) (ho_24478 y z)))) (= x y))))) (let ((_let_739 (forall ((x |u_(-> tptp.set_Pr7600907837789447088it_nat tptp.b tptp.produc6653097349344004940it_nat Bool)|) (y |u_(-> tptp.set_Pr7600907837789447088it_nat tptp.b tptp.produc6653097349344004940it_nat Bool)|)) (or (not (forall ((z tptp.set_Pr7600907837789447088it_nat)) (= (ho_21358 x z) (ho_21358 y z)))) (= x y))))) (let ((_let_740 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.int tptp.nat Bool)_ tptp.int tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.int tptp.nat Bool)_ tptp.int tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_11576 x z) (ho_11576 y z)))) (= x y))))) (let ((_let_741 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (= (ho_24586 x z) (ho_24586 y z)))) (= x y))))) (let ((_let_742 (forall ((x |u_(-> _u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)_ tptp.produc2732055786443039994et_nat Bool)|) (y |u_(-> _u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)_ tptp.produc2732055786443039994et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)|)) (= (ho_24476 x z) (ho_24476 y z)))) (= x y))))) (let ((_let_743 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.nat)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.nat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_14873 x z) (ho_14873 y z)))) (= x y))))) (let ((_let_744 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_24472 x z) (ho_24472 y z)))) (= x y))))) (let ((_let_745 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.nat)_ _u_(-> Bool tptp.nat)_ Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.nat)_ _u_(-> Bool tptp.nat)_ Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_17207 x z) (ho_17207 y z)))) (= x y))))) (let ((_let_746 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.nat)_ Bool tptp.nat)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.nat)_ Bool tptp.nat)|)) (or (not (forall ((z tptp.set_o)) (= (ho_16814 x z) (ho_16814 y z)))) (= x y))))) (let ((_let_747 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_24473 x z) (ho_24473 y z)))) (= x y))))) (let ((_let_748 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_24467 x z) (ho_24467 y z)))) (= x y))))) (let ((_let_749 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_24468 x z) (ho_24468 y z)))) (= x y))))) (let ((_let_750 (forall ((x |u_(-> _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)|)) (= (ho_24459 x z) (ho_24459 y z)))) (= x y))))) (let ((_let_751 (forall ((x |u_(-> _u_(-> tptp.product_prod_num_num Bool)_ _u_(-> tptp.product_prod_num_num Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_num_num Bool)_ _u_(-> tptp.product_prod_num_num Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_num_num Bool)|)) (= (ho_24456 x z) (ho_24456 y z)))) (= x y))))) (let ((_let_752 (forall ((x |u_(-> Bool _u_(-> tptp.produc8664842809031399944it_nat Bool)_ tptp.option8956607266484857688it_nat Bool)|) (y |u_(-> Bool _u_(-> tptp.produc8664842809031399944it_nat Bool)_ tptp.option8956607266484857688it_nat Bool)|)) (or (not (forall ((z Bool)) (= (ho_24450 x z) (ho_24450 y z)))) (= x y))))) (let ((_let_753 (forall ((x |u_(-> Bool _u_(-> tptp.produc3260487557148687353it_nat Bool)_ tptp.option3562590408128118217it_nat Bool)|) (y |u_(-> Bool _u_(-> tptp.produc3260487557148687353it_nat Bool)_ tptp.option3562590408128118217it_nat Bool)|)) (or (not (forall ((z Bool)) (= (ho_24447 x z) (ho_24447 y z)))) (= x y))))) (let ((_let_754 (forall ((x |u_(-> _u_(-> tptp.produc3260487557148687353it_nat Bool)_ tptp.option3562590408128118217it_nat Bool)|) (y |u_(-> _u_(-> tptp.produc3260487557148687353it_nat Bool)_ tptp.option3562590408128118217it_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc3260487557148687353it_nat Bool)|)) (= (ho_24448 x z) (ho_24448 y z)))) (= x y))))) (let ((_let_755 (forall ((x |u_(-> tptp.produc3911288613690379145it_nat tptp.produc3911288613690379145it_nat Bool)|) (y |u_(-> tptp.produc3911288613690379145it_nat tptp.produc3911288613690379145it_nat Bool)|)) (or (not (forall ((z tptp.produc3911288613690379145it_nat)) (= (ho_24439 x z) (ho_24439 y z)))) (= x y))))) (let ((_let_756 (forall ((x |u_(-> tptp.set_Pr7928877670098842301et_nat tptp.set_Pr7928877670098842301et_nat)|) (y |u_(-> tptp.set_Pr7928877670098842301et_nat tptp.set_Pr7928877670098842301et_nat)|)) (or (not (forall ((z tptp.set_Pr7928877670098842301et_nat)) (= (ho_24874 x z) (ho_24874 y z)))) (= x y))))) (let ((_let_757 (forall ((x |u_(-> _u_(-> tptp.int Bool Bool)_ Bool tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool Bool)_ Bool tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool Bool)|)) (= (ho_14885 x z) (ho_14885 y z)))) (= x y))))) (let ((_let_758 (forall ((x |u_(-> tptp.produc3911288613690379145it_nat Bool)|) (y |u_(-> tptp.produc3911288613690379145it_nat Bool)|)) (or (not (forall ((z tptp.produc3911288613690379145it_nat)) (= (ho_24442 x z) (ho_24442 y z)))) (= x y))))) (let ((_let_759 (forall ((x |u_(-> _u_(-> tptp.produc4453839368661128058it_nat tptp.produc4453839368661128058it_nat Bool)_ tptp.produc4453839368661128058it_nat Bool)|) (y |u_(-> _u_(-> tptp.produc4453839368661128058it_nat tptp.produc4453839368661128058it_nat Bool)_ tptp.produc4453839368661128058it_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc4453839368661128058it_nat tptp.produc4453839368661128058it_nat Bool)|)) (= (ho_24436 x z) (ho_24436 y z)))) (= x y))))) (let ((_let_760 (forall ((x |u_(-> _u_(-> Bool tptp.assn)_ Bool tptp.assn)|) (y |u_(-> _u_(-> Bool tptp.assn)_ Bool tptp.assn)|)) (or (not (forall ((z |u_(-> Bool tptp.assn)|)) (= (ho_15810 x z) (ho_15810 y z)))) (= x y))))) (let ((_let_761 (forall ((x |u_(-> tptp.produc4453839368661128058it_nat tptp.produc4453839368661128058it_nat Bool)|) (y |u_(-> tptp.produc4453839368661128058it_nat tptp.produc4453839368661128058it_nat Bool)|)) (or (not (forall ((z tptp.produc4453839368661128058it_nat)) (= (ho_24434 x z) (ho_24434 y z)))) (= x y))))) (let ((_let_762 (forall ((x |u_(-> tptp.produc4453839368661128058it_nat Bool)|) (y |u_(-> tptp.produc4453839368661128058it_nat Bool)|)) (or (not (forall ((z tptp.produc4453839368661128058it_nat)) (= (ho_24437 x z) (ho_24437 y z)))) (= x y))))) (let ((_let_763 (forall ((x |u_(-> tptp.produc2207270350733924475it_nat tptp.produc2207270350733924475it_nat Bool)|) (y |u_(-> tptp.produc2207270350733924475it_nat tptp.produc2207270350733924475it_nat Bool)|)) (or (not (forall ((z tptp.produc2207270350733924475it_nat)) (= (ho_24429 x z) (ho_24429 y z)))) (= x y))))) (let ((_let_764 (forall ((x |u_(-> tptp.b tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat)|) (y |u_(-> tptp.b tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z tptp.b)) (= (ho_22289 x z) (ho_22289 y z)))) (= x y))))) (let ((_let_765 (forall ((x |u_(-> tptp.nat tptp.option8956607266484857688it_nat tptp.produc3911288613690379145it_nat)|) (y |u_(-> tptp.nat tptp.option8956607266484857688it_nat tptp.produc3911288613690379145it_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_24426 x z) (ho_24426 y z)))) (= x y))))) (let ((_let_766 (forall ((x |u_(-> tptp.nat tptp.option3562590408128118217it_nat tptp.produc4453839368661128058it_nat)|) (y |u_(-> tptp.nat tptp.option3562590408128118217it_nat tptp.produc4453839368661128058it_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_24423 x z) (ho_24423 y z)))) (= x y))))) (let ((_let_767 (forall ((x |u_(-> tptp.option3562590408128118217it_nat tptp.produc4453839368661128058it_nat)|) (y |u_(-> tptp.option3562590408128118217it_nat tptp.produc4453839368661128058it_nat)|)) (or (not (forall ((z tptp.option3562590408128118217it_nat)) (= (ho_24424 x z) (ho_24424 y z)))) (= x y))))) (let ((_let_768 (forall ((x |u_(-> tptp.nat tptp.option4065278094766928714it_nat tptp.produc2207270350733924475it_nat)|) (y |u_(-> tptp.nat tptp.option4065278094766928714it_nat tptp.produc2207270350733924475it_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_24420 x z) (ho_24420 y z)))) (= x y))))) (let ((_let_769 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.set_int)_ tptp.nat tptp.int Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.set_int)_ tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_21231 x z) (ho_21231 y z)))) (= x y))))) (let ((_let_770 (forall ((x |u_(-> tptp.nat _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_15870 x z) (ho_15870 y z)))) (= x y))))) (let ((_let_771 (forall ((x |u_(-> tptp.option4065278094766928714it_nat tptp.option8956607266484857688it_nat Bool)|) (y |u_(-> tptp.option4065278094766928714it_nat tptp.option8956607266484857688it_nat Bool)|)) (or (not (forall ((z tptp.option4065278094766928714it_nat)) (= (ho_24418 x z) (ho_24418 y z)))) (= x y))))) (let ((_let_772 (forall ((x |u_(-> tptp.set_nat tptp.set_set_nat tptp.set_set_nat)|) (y |u_(-> tptp.set_nat tptp.set_set_nat tptp.set_set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_19141 x z) (ho_19141 y z)))) (= x y))))) (let ((_let_773 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc4928098042776334183_nat_o)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc4928098042776334183_nat_o)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_25055 x z) (ho_25055 y z)))) (= x y))))) (let ((_let_774 (forall ((x |u_(-> tptp.option4065278094766928714it_nat tptp.option3562590408128118217it_nat Bool)|) (y |u_(-> tptp.option4065278094766928714it_nat tptp.option3562590408128118217it_nat Bool)|)) (or (not (forall ((z tptp.option4065278094766928714it_nat)) (= (ho_24417 x z) (ho_24417 y z)))) (= x y))))) (let ((_let_775 (forall ((x |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)_ tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)_ tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)|)) (= (ho_23100 x z) (ho_23100 y z)))) (= x y))))) (let ((_let_776 (forall ((x |u_(-> tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat Bool)|) (y |u_(-> tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat Bool)|)) (or (not (forall ((z tptp.option4065278094766928714it_nat)) (= (ho_24416 x z) (ho_24416 y z)))) (= x y))))) (let ((_let_777 (forall ((x |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)_ tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)_ tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)|)) (= (ho_23106 x z) (ho_23106 y z)))) (= x y))))) (let ((_let_778 (forall ((x |u_(-> _u_(-> tptp.set_nat Bool)_ tptp.set_set_nat)|) (y |u_(-> _u_(-> tptp.set_nat Bool)_ tptp.set_set_nat)|)) (or (not (forall ((z |u_(-> tptp.set_nat Bool)|)) (= (ho_11204 x z) (ho_11204 y z)))) (= x y))))) (let ((_let_779 (forall ((x |u_(-> tptp.option_num tptp.option8956607266484857688it_nat Bool)|) (y |u_(-> tptp.option_num tptp.option8956607266484857688it_nat Bool)|)) (or (not (forall ((z tptp.option_num)) (= (ho_24415 x z) (ho_24415 y z)))) (= x y))))) (let ((_let_780 (forall ((x |u_(-> _u_(-> tptp.produc859450856879609959at_nat Bool)_ tptp.set_Pr8693737435421807431at_nat)|) (y |u_(-> _u_(-> tptp.produc859450856879609959at_nat Bool)_ tptp.set_Pr8693737435421807431at_nat)|)) (or (not (forall ((z |u_(-> tptp.produc859450856879609959at_nat Bool)|)) (= (ho_14473 x z) (ho_14473 y z)))) (= x y))))) (let ((_let_781 (forall ((x |u_(-> tptp.option_num tptp.option3562590408128118217it_nat Bool)|) (y |u_(-> tptp.option_num tptp.option3562590408128118217it_nat Bool)|)) (or (not (forall ((z tptp.option_num)) (= (ho_24414 x z) (ho_24414 y z)))) (= x y))))) (let ((_let_782 (forall ((x |u_(-> tptp.code_integer Bool)|) (y |u_(-> tptp.code_integer Bool)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_11564 x z) (ho_11564 y z)))) (= x y))))) (let ((_let_783 (forall ((x |u_(-> tptp.product_prod_num_num Bool)|) (y |u_(-> tptp.product_prod_num_num Bool)|)) (or (not (forall ((z tptp.product_prod_num_num)) (= (ho_24486 x z) (ho_24486 y z)))) (= x y))))) (let ((_let_784 (forall ((x |u_(-> tptp.option_num tptp.option4065278094766928714it_nat Bool)|) (y |u_(-> tptp.option_num tptp.option4065278094766928714it_nat Bool)|)) (or (not (forall ((z tptp.option_num)) (= (ho_24413 x z) (ho_24413 y z)))) (= x y))))) (let ((_let_785 (forall ((x |u_(-> tptp.product_unit tptp.product_unit Bool)|) (y |u_(-> tptp.product_unit tptp.product_unit Bool)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_24684 x z) (ho_24684 y z)))) (= x y))))) (let ((_let_786 (forall ((x |u_(-> tptp.option3562590408128118217it_nat tptp.option_num Bool)|) (y |u_(-> tptp.option3562590408128118217it_nat tptp.option_num Bool)|)) (or (not (forall ((z tptp.option3562590408128118217it_nat)) (= (ho_24411 x z) (ho_24411 y z)))) (= x y))))) (let ((_let_787 (forall ((x |u_(-> tptp.list_nat tptp.set_list_nat tptp.list_nat Bool)|) (y |u_(-> tptp.list_nat tptp.set_list_nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_12841 x z) (ho_12841 y z)))) (= x y))))) (let ((_let_788 (forall ((x |u_(-> tptp.assn tptp.assn tptp.option_assn)|) (y |u_(-> tptp.assn tptp.assn tptp.option_assn)|)) (or (not (forall ((z tptp.assn)) (= (ho_13866 x z) (ho_13866 y z)))) (= x y))))) (let ((_let_789 (forall ((x |u_(-> tptp.produc7538756082594784606_nat_b tptp.produc7538756082594784606_nat_b Bool)|) (y |u_(-> tptp.produc7538756082594784606_nat_b tptp.produc7538756082594784606_nat_b Bool)|)) (or (not (forall ((z tptp.produc7538756082594784606_nat_b)) (= (ho_25251 x z) (ho_25251 y z)))) (= x y))))) (let ((_let_790 (forall ((x |u_(-> tptp.produc5728234346263159722nt_int tptp.produc3500511559948749619nt_int)|) (y |u_(-> tptp.produc5728234346263159722nt_int tptp.produc3500511559948749619nt_int)|)) (or (not (forall ((z tptp.produc5728234346263159722nt_int)) (= (ho_25216 x z) (ho_25216 y z)))) (= x y))))) (let ((_let_791 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_25768 x z) (ho_25768 y z)))) (= x y))))) (let ((_let_792 (forall ((x |u_(-> tptp.option4065278094766928714it_nat tptp.option_num Bool)|) (y |u_(-> tptp.option4065278094766928714it_nat tptp.option_num Bool)|)) (or (not (forall ((z tptp.option4065278094766928714it_nat)) (= (ho_24410 x z) (ho_24410 y z)))) (= x y))))) (let ((_let_793 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_natural)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.code_natural)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_natural)|)) (= (ho_11870 x z) (ho_11870 y z)))) (= x y))))) (let ((_let_794 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int)|)) (= (ho_15343 x z) (ho_15343 y z)))) (= x y))))) (let ((_let_795 (forall ((x |u_(-> tptp.option_num tptp.option_num Bool)|) (y |u_(-> tptp.option_num tptp.option_num Bool)|)) (or (not (forall ((z tptp.option_num)) (= (ho_24409 x z) (ho_24409 y z)))) (= x y))))) (let ((_let_796 (forall ((x |u_(-> tptp.list_char tptp.heap_Time_Heap_a)|) (y |u_(-> tptp.list_char tptp.heap_Time_Heap_a)|)) (or (not (forall ((z tptp.list_char)) (= (ho_24408 x z) (ho_24408 y z)))) (= x y))))) (let ((_let_797 (forall ((x |u_(-> tptp.list_char tptp.heap_Time_Heap_b)|) (y |u_(-> tptp.list_char tptp.heap_Time_Heap_b)|)) (or (not (forall ((z tptp.list_char)) (= (ho_24406 x z) (ho_24406 y z)))) (= x y))))) (let ((_let_798 (forall ((x |u_(-> tptp.list_P626663023886443800it_nat tptp.list_P626663023886443800it_nat)|) (y |u_(-> tptp.list_P626663023886443800it_nat tptp.list_P626663023886443800it_nat)|)) (or (not (forall ((z tptp.list_P626663023886443800it_nat)) (= (ho_24994 x z) (ho_24994 y z)))) (= x y))))) (let ((_let_799 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_24464 x z) (ho_24464 y z)))) (= x y))))) (let ((_let_800 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int tptp.int)_ tptp.set_int _u_(-> tptp.code_integer tptp.int Bool)_ tptp.code_integer tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int tptp.int)_ tptp.set_int _u_(-> tptp.code_integer tptp.int Bool)_ tptp.code_integer tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int tptp.int)|)) (= (ho_17294 x z) (ho_17294 y z)))) (= x y))))) (let ((_let_801 (forall ((x |u_(-> _u_(-> tptp.num tptp.int)_ tptp.option_num tptp.int)|) (y |u_(-> _u_(-> tptp.num tptp.int)_ tptp.option_num tptp.int)|)) (or (not (forall ((z |u_(-> tptp.num tptp.int)|)) (= (ho_24404 x z) (ho_24404 y z)))) (= x y))))) (let ((_let_802 (forall ((x |u_(-> tptp.option_set_o tptp.option_set_o)|) (y |u_(-> tptp.option_set_o tptp.option_set_o)|)) (or (not (forall ((z tptp.option_set_o)) (= (ho_22427 x z) (ho_22427 y z)))) (= x y))))) (let ((_let_803 (forall ((x |u_(-> tptp.produc2732055786443039994et_nat tptp.option2860828798490689354et_nat)|) (y |u_(-> tptp.produc2732055786443039994et_nat tptp.option2860828798490689354et_nat)|)) (or (not (forall ((z tptp.produc2732055786443039994et_nat)) (= (ho_24401 x z) (ho_24401 y z)))) (= x y))))) (let ((_let_804 (forall ((x |u_(-> tptp.option4065278094766928714it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.option4065278094766928714it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.option4065278094766928714it_nat)) (= (ho_19864 x z) (ho_19864 y z)))) (= x y))))) (let ((_let_805 (forall ((x |u_(-> _u_(-> tptp.set_int tptp.set_int Bool)_ tptp.set_int Bool)|) (y |u_(-> _u_(-> tptp.set_int tptp.set_int Bool)_ tptp.set_int Bool)|)) (or (not (forall ((z |u_(-> tptp.set_int tptp.set_int Bool)|)) (= (ho_24556 x z) (ho_24556 y z)))) (= x y))))) (let ((_let_806 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.nat tptp.code_integer tptp.code_integer)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.nat tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer)|)) (= (ho_21250 x z) (ho_21250 y z)))) (= x y))))) (let ((_let_807 (forall ((x |u_(-> _u_(-> tptp.produc8664842809031399944it_nat Bool)_ tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.produc8664842809031399944it_nat Bool)_ tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc8664842809031399944it_nat Bool)|)) (= (ho_24395 x z) (ho_24395 y z)))) (= x y))))) (let ((_let_808 (forall ((x |u_(-> _u_(-> tptp.produc3260487557148687353it_nat Bool)_ tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.produc3260487557148687353it_nat Bool)_ tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3260487557148687353it_nat Bool)|)) (= (ho_24393 x z) (ho_24393 y z)))) (= x y))))) (let ((_let_809 (forall ((x |u_(-> tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat Bool)|) (y |u_(-> tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat Bool)|)) (or (not (forall ((z tptp.set_Pr7098220151150636591it_nat)) (= (ho_24389 x z) (ho_24389 y z)))) (= x y))))) (let ((_let_810 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)_ _u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)_ _u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)|)) (= (ho_24386 x z) (ho_24386 y z)))) (= x y))))) (let ((_let_811 (forall ((x |u_(-> tptp.set_Pr7600907837789447088it_nat tptp.set_Pr7600907837789447088it_nat Bool)|) (y |u_(-> tptp.set_Pr7600907837789447088it_nat tptp.set_Pr7600907837789447088it_nat Bool)|)) (or (not (forall ((z tptp.set_Pr7600907837789447088it_nat)) (= (ho_24384 x z) (ho_24384 y z)))) (= x y))))) (let ((_let_812 (forall ((x |u_(-> tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat Bool)|) (y |u_(-> tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8536935166611901872et_nat)) (= (ho_24379 x z) (ho_24379 y z)))) (= x y))))) (let ((_let_813 (forall ((x |u_(-> _u_(-> Bool tptp.nat)_ Bool Bool)|) (y |u_(-> _u_(-> Bool tptp.nat)_ Bool Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.nat)|)) (= (ho_15123 x z) (ho_15123 y z)))) (= x y))))) (let ((_let_814 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|)) (= (ho_24376 x z) (ho_24376 y z)))) (= x y))))) (let ((_let_815 (forall ((x |u_(-> tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat Bool)|) (y |u_(-> tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat Bool)|)) (or (not (forall ((z tptp.set_Pr3286484037609594932et_nat)) (= (ho_24374 x z) (ho_24374 y z)))) (= x y))))) (let ((_let_816 (forall ((x |u_(-> tptp.code_natural tptp.rat Bool)|) (y |u_(-> tptp.code_natural tptp.rat Bool)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_24653 x z) (ho_24653 y z)))) (= x y))))) (let ((_let_817 (forall ((x |u_(-> _u_(-> tptp.a tptp.heap_Time_Heap_b)_ tptp.a tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.heap_Time_Heap_b)_ tptp.a tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.heap_Time_Heap_b)|)) (= (ho_13113 x z) (ho_13113 y z)))) (= x y))))) (let ((_let_818 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.num tptp.int)_ tptp.num tptp.code_integer)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.num tptp.int)_ tptp.num tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer)|)) (= (ho_26016 x z) (ho_26016 y z)))) (= x y))))) (let ((_let_819 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_24372 x z) (ho_24372 y z)))) (= x y))))) (let ((_let_820 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.list_P6935614879863011209it_nat tptp.list_P6935614879863011209it_nat)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.list_P6935614879863011209it_nat tptp.list_P6935614879863011209it_nat)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_24987 x z) (ho_24987 y z)))) (= x y))))) (let ((_let_821 (forall ((x |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (= (ho_24368 x z) (ho_24368 y z)))) (= x y))))) (let ((_let_822 (forall ((x |u_(-> _u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)_ _u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)_ tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|) (y |u_(-> _u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)_ _u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)_ tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|)) (= (ho_24364 x z) (ho_24364 y z)))) (= x y))))) (let ((_let_823 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)_ tptp.a tptp.produc6653097349344004940it_nat Bool)|) (y |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)_ tptp.a tptp.produc6653097349344004940it_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)|)) (= (ho_24362 x z) (ho_24362 y z)))) (= x y))))) (let ((_let_824 (forall ((x |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)_ _u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)_ tptp.b tptp.produc6653097349344004940it_nat Bool)|) (y |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)_ _u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)_ tptp.b tptp.produc6653097349344004940it_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)|)) (= (ho_24358 x z) (ho_24358 y z)))) (= x y))))) (let ((_let_825 (forall ((x |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)_ tptp.b tptp.produc6653097349344004940it_nat Bool)|) (y |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)_ tptp.b tptp.produc6653097349344004940it_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)|)) (= (ho_24359 x z) (ho_24359 y z)))) (= x y))))) (let ((_let_826 (forall ((x |u_(-> tptp.set_nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_11209 x z) (ho_11209 y z)))) (= x y))))) (let ((_let_827 (forall ((x |u_(-> tptp.produc3658429121746597890et_nat tptp.produc6197004810343482825et_nat)|) (y |u_(-> tptp.produc3658429121746597890et_nat tptp.produc6197004810343482825et_nat)|)) (or (not (forall ((z tptp.produc3658429121746597890et_nat)) (= (ho_24616 x z) (ho_24616 y z)))) (= x y))))) (let ((_let_828 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|)) (= (ho_24355 x z) (ho_24355 y z)))) (= x y))))) (let ((_let_829 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_24352 x z) (ho_24352 y z)))) (= x y))))) (let ((_let_830 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_24353 x z) (ho_24353 y z)))) (= x y))))) (let ((_let_831 (forall ((x |u_(-> _u_(-> tptp.assn tptp.assn tptp.assn)_ tptp.assn tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.assn tptp.assn tptp.assn)_ tptp.assn tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.assn tptp.assn tptp.assn)|)) (= (ho_22000 x z) (ho_22000 y z)))) (= x y))))) (let ((_let_832 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_24350 x z) (ho_24350 y z)))) (= x y))))) (let ((_let_833 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat Bool)|)) (= (ho_15572 x z) (ho_15572 y z)))) (= x y))))) (let ((_let_834 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.int)|)) (= (ho_24346 x z) (ho_24346 y z)))) (= x y))))) (let ((_let_835 (forall ((x |u_(-> tptp.nat tptp.nat tptp.option_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.option_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_13851 x z) (ho_13851 y z)))) (= x y))))) (let ((_let_836 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_24344 x z) (ho_24344 y z)))) (= x y))))) (let ((_let_837 (forall ((x |u_(-> tptp.int tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_20278 x z) (ho_20278 y z)))) (= x y))))) (let ((_let_838 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.set_int tptp.set_int Bool)_ _u_(-> tptp.set_int tptp.set_int Bool)_ Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.set_int tptp.set_int Bool)_ _u_(-> tptp.set_int tptp.set_int Bool)_ Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_24526 x z) (ho_24526 y z)))) (= x y))))) (let ((_let_839 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_18808 x z) (ho_18808 y z)))) (= x y))))) (let ((_let_840 (forall ((x |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.rat)_ _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer tptp.rat)|) (y |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.rat)_ _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer tptp.rat)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_15784 x z) (ho_15784 y z)))) (= x y))))) (let ((_let_841 (forall ((x |u_(-> _u_(-> tptp.set_int tptp.set_int tptp.set_int)_ _u_(-> tptp.set_int tptp.set_int Bool)_ _u_(-> tptp.set_int tptp.set_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_int tptp.set_int tptp.set_int)_ _u_(-> tptp.set_int tptp.set_int Bool)_ _u_(-> tptp.set_int tptp.set_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_int tptp.set_int tptp.set_int)|)) (= (ho_24334 x z) (ho_24334 y z)))) (= x y))))) (let ((_let_842 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_11063 x z) (ho_11063 y z)))) (= x y))))) (let ((_let_843 (forall ((x |u_(-> _u_(-> tptp.assn tptp.assn tptp.assn)_ _u_(-> tptp.assn tptp.assn Bool)_ _u_(-> tptp.assn tptp.assn Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.assn tptp.assn tptp.assn)_ _u_(-> tptp.assn tptp.assn Bool)_ _u_(-> tptp.assn tptp.assn Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.assn tptp.assn tptp.assn)|)) (= (ho_24330 x z) (ho_24330 y z)))) (= x y))))) (let ((_let_844 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_18030 x z) (ho_18030 y z)))) (= x y))))) (let ((_let_845 (forall ((x |u_(-> _u_(-> tptp.assn tptp.assn Bool)_ _u_(-> tptp.assn tptp.assn Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.assn tptp.assn Bool)_ _u_(-> tptp.assn tptp.assn Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.assn tptp.assn Bool)|)) (= (ho_24331 x z) (ho_24331 y z)))) (= x y))))) (let ((_let_846 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.set_int tptp.rat)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.set_int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_25291 x z) (ho_25291 y z)))) (= x y))))) (let ((_let_847 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)_ _u_(-> tptp.set_nat tptp.set_nat Bool)_ _u_(-> tptp.set_nat tptp.set_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)_ _u_(-> tptp.set_nat tptp.set_nat Bool)_ _u_(-> tptp.set_nat tptp.set_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)|)) (= (ho_24326 x z) (ho_24326 y z)))) (= x y))))) (let ((_let_848 (forall ((x |u_(-> tptp.num tptp.product_prod_num_num)|) (y |u_(-> tptp.num tptp.product_prod_num_num)|)) (or (not (forall ((z tptp.num)) (= (ho_25790 x z) (ho_25790 y z)))) (= x y))))) (let ((_let_849 (forall ((x |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)_ _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)_ _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)|)) (= (ho_24322 x z) (ho_24322 y z)))) (= x y))))) (let ((_let_850 (forall ((x |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)|)) (= (ho_24323 x z) (ho_24323 y z)))) (= x y))))) (let ((_let_851 (forall ((x |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)|)) (= (ho_24319 x z) (ho_24319 y z)))) (= x y))))) (let ((_let_852 (forall ((x |u_(-> _u_(-> Bool tptp.nat Bool)_ Bool tptp.int)|) (y |u_(-> _u_(-> Bool tptp.nat Bool)_ Bool tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.nat Bool)|)) (= (ho_17330 x z) (ho_17330 y z)))) (= x y))))) (let ((_let_853 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)_ tptp.heap_Time_Heap_a)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)_ tptp.heap_Time_Heap_a)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|)) (= (ho_24309 x z) (ho_24309 y z)))) (= x y))))) (let ((_let_854 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)_ tptp.heap_Time_Heap_b)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)_ tptp.heap_Time_Heap_b)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|)) (= (ho_24307 x z) (ho_24307 y z)))) (= x y))))) (let ((_let_855 (forall ((x |u_(-> _u_(-> tptp.product_unit tptp.heap_Time_Heap_a)_ tptp.heap_Time_Heap_a)|) (y |u_(-> _u_(-> tptp.product_unit tptp.heap_Time_Heap_a)_ tptp.heap_Time_Heap_a)|)) (or (not (forall ((z |u_(-> tptp.product_unit tptp.heap_Time_Heap_a)|)) (= (ho_24305 x z) (ho_24305 y z)))) (= x y))))) (let ((_let_856 (forall ((x |u_(-> _u_(-> tptp.list_nat tptp.int)_ tptp.set_list_nat tptp.int)|) (y |u_(-> _u_(-> tptp.list_nat tptp.int)_ tptp.set_list_nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.list_nat tptp.int)|)) (= (ho_25703 x z) (ho_25703 y z)))) (= x y))))) (let ((_let_857 (forall ((x |u_(-> tptp.heap_T5738788834812785303t_unit _u_(-> tptp.product_unit tptp.heap_Time_Heap_b)_ tptp.heap_Time_Heap_b)|) (y |u_(-> tptp.heap_T5738788834812785303t_unit _u_(-> tptp.product_unit tptp.heap_Time_Heap_b)_ tptp.heap_Time_Heap_b)|)) (or (not (forall ((z tptp.heap_T5738788834812785303t_unit)) (= (ho_24301 x z) (ho_24301 y z)))) (= x y))))) (let ((_let_858 (forall ((x |u_(-> tptp.nat tptp.num)|) (y |u_(-> tptp.nat tptp.num)|)) (or (not (forall ((z tptp.nat)) (= (ho_24299 x z) (ho_24299 y z)))) (= x y))))) (let ((_let_859 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_24558 x z) (ho_24558 y z)))) (= x y))))) (let ((_let_860 (forall ((x |u_(-> tptp.rat tptp.num)|) (y |u_(-> tptp.rat tptp.num)|)) (or (not (forall ((z tptp.rat)) (= (ho_24297 x z) (ho_24297 y z)))) (= x y))))) (let ((_let_861 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_24347 x z) (ho_24347 y z)))) (= x y))))) (let ((_let_862 (forall ((x |u_(-> tptp.set_Pr7600907837789447088it_nat tptp.set_Pr7600907837789447088it_nat tptp.b tptp.produc6653097349344004940it_nat Bool)|) (y |u_(-> tptp.set_Pr7600907837789447088it_nat tptp.set_Pr7600907837789447088it_nat tptp.b tptp.produc6653097349344004940it_nat Bool)|)) (or (not (forall ((z tptp.set_Pr7600907837789447088it_nat)) (= (ho_21365 x z) (ho_21365 y z)))) (= x y))))) (let ((_let_863 (forall ((x |u_(-> tptp.assn tptp.int)|) (y |u_(-> tptp.assn tptp.int)|)) (or (not (forall ((z tptp.assn)) (= (ho_24296 x z) (ho_24296 y z)))) (= x y))))) (let ((_let_864 (forall ((x |u_(-> tptp.assn tptp.nat)|) (y |u_(-> tptp.assn tptp.nat)|)) (or (not (forall ((z tptp.assn)) (= (ho_24295 x z) (ho_24295 y z)))) (= x y))))) (let ((_let_865 (forall ((x |u_(-> tptp.option_num _u_(-> tptp.nat tptp.option_num)_ tptp.nat tptp.option_num)|) (y |u_(-> tptp.option_num _u_(-> tptp.nat tptp.option_num)_ tptp.nat tptp.option_num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_12587 x z) (ho_12587 y z)))) (= x y))))) (let ((_let_866 (forall ((x |u_(-> tptp.assn tptp.num)|) (y |u_(-> tptp.assn tptp.num)|)) (or (not (forall ((z tptp.assn)) (= (ho_24294 x z) (ho_24294 y z)))) (= x y))))) (let ((_let_867 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_11538 x z) (ho_11538 y z)))) (= x y))))) (let ((_let_868 (forall ((x |u_(-> tptp.num tptp.option_num tptp.num)|) (y |u_(-> tptp.num tptp.option_num tptp.num)|)) (or (not (forall ((z tptp.num)) (= (ho_24290 x z) (ho_24290 y z)))) (= x y))))) (let ((_let_869 (forall ((x |u_(-> tptp.option3562590408128118217it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> tptp.option3562590408128118217it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z tptp.option3562590408128118217it_nat)) (= (ho_24285 x z) (ho_24285 y z)))) (= x y))))) (let ((_let_870 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_24281 x z) (ho_24281 y z)))) (= x y))))) (let ((_let_871 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15285 x z) (ho_15285 y z)))) (= x y))))) (let ((_let_872 (forall ((x |u_(-> tptp.product_unit tptp.assn)|) (y |u_(-> tptp.product_unit tptp.assn)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_24279 x z) (ho_24279 y z)))) (= x y))))) (let ((_let_873 (forall ((x |u_(-> _u_(-> tptp.produc3260487557148687353it_nat Bool)_ tptp.a tptp.produc6653097349344004940it_nat Bool)|) (y |u_(-> _u_(-> tptp.produc3260487557148687353it_nat Bool)_ tptp.a tptp.produc6653097349344004940it_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc3260487557148687353it_nat Bool)|)) (= (ho_24278 x z) (ho_24278 y z)))) (= x y))))) (let ((_let_874 (forall ((x |u_(-> _u_(-> tptp.option4065278094766928714it_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.option4065278094766928714it_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.option4065278094766928714it_nat Bool)|)) (= (ho_22656 x z) (ho_22656 y z)))) (= x y))))) (let ((_let_875 (forall ((x |u_(-> tptp.product_prod_int_int tptp.produc1219242969750017639nt_int)|) (y |u_(-> tptp.product_prod_int_int tptp.produc1219242969750017639nt_int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_24861 x z) (ho_24861 y z)))) (= x y))))) (let ((_let_876 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_20078 x z) (ho_20078 y z)))) (= x y))))) (let ((_let_877 (forall ((x |u_(-> _u_(-> tptp.produc7388388658123137530it_nat Bool)_ tptp.b tptp.produc6653097349344004940it_nat Bool)|) (y |u_(-> _u_(-> tptp.produc7388388658123137530it_nat Bool)_ tptp.b tptp.produc6653097349344004940it_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc7388388658123137530it_nat Bool)|)) (= (ho_24276 x z) (ho_24276 y z)))) (= x y))))) (let ((_let_878 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat)|)) (= (ho_22731 x z) (ho_22731 y z)))) (= x y))))) (let ((_let_879 (forall ((x |u_(-> tptp.produc2732055786443039994et_nat Bool)|) (y |u_(-> tptp.produc2732055786443039994et_nat Bool)|)) (or (not (forall ((z tptp.produc2732055786443039994et_nat)) (= (ho_24265 x z) (ho_24265 y z)))) (= x y))))) (let ((_let_880 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_17188 x z) (ho_17188 y z)))) (= x y))))) (let ((_let_881 (forall ((x |u_(-> tptp.b tptp.assn)|) (y |u_(-> tptp.b tptp.assn)|)) (or (not (forall ((z tptp.b)) (= (ho_24262 x z) (ho_24262 y z)))) (= x y))))) (let ((_let_882 (forall ((x |u_(-> tptp.set_nat tptp.produc3658429121746597890et_nat)|) (y |u_(-> tptp.set_nat tptp.produc3658429121746597890et_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_24260 x z) (ho_24260 y z)))) (= x y))))) (let ((_let_883 (forall ((x |u_(-> tptp.option_set_int tptp.set_int Bool)|) (y |u_(-> tptp.option_set_int tptp.set_int Bool)|)) (or (not (forall ((z tptp.option_set_int)) (= (ho_24243 x z) (ho_24243 y z)))) (= x y))))) (let ((_let_884 (forall ((x |u_(-> tptp.option_nat tptp.nat Bool)|) (y |u_(-> tptp.option_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_24238 x z) (ho_24238 y z)))) (= x y))))) (let ((_let_885 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat)_ tptp.nat tptp.code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat)_ tptp.nat tptp.code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat)|)) (= (ho_15868 x z) (ho_15868 y z)))) (= x y))))) (let ((_let_886 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc1319942482725812455at_nat)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc1319942482725812455at_nat)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_26065 x z) (ho_26065 y z)))) (= x y))))) (let ((_let_887 (forall ((x |u_(-> _u_(-> tptp.b Bool)_ tptp.b tptp.heap_Time_Heap_b)|) (y |u_(-> _u_(-> tptp.b Bool)_ tptp.b tptp.heap_Time_Heap_b)|)) (or (not (forall ((z |u_(-> tptp.b Bool)|)) (= (ho_24489 x z) (ho_24489 y z)))) (= x y))))) (let ((_let_888 (forall ((x |u_(-> tptp.option_int tptp.int Bool)|) (y |u_(-> tptp.option_int tptp.int Bool)|)) (or (not (forall ((z tptp.option_int)) (= (ho_24236 x z) (ho_24236 y z)))) (= x y))))) (let ((_let_889 (forall ((x |u_(-> Bool _u_(-> tptp.set_int Bool)_ tptp.option_set_int Bool)|) (y |u_(-> Bool _u_(-> tptp.set_int Bool)_ tptp.option_set_int Bool)|)) (or (not (forall ((z Bool)) (= (ho_24223 x z) (ho_24223 y z)))) (= x y))))) (let ((_let_890 (forall ((x |u_(-> tptp.option_set_int Bool)|) (y |u_(-> tptp.option_set_int Bool)|)) (or (not (forall ((z tptp.option_set_int)) (= (ho_24225 x z) (ho_24225 y z)))) (= x y))))) (let ((_let_891 (forall ((x |u_(-> Bool _u_(-> tptp.assn Bool)_ tptp.option_assn Bool)|) (y |u_(-> Bool _u_(-> tptp.assn Bool)_ tptp.option_assn Bool)|)) (or (not (forall ((z Bool)) (= (ho_24201 x z) (ho_24201 y z)))) (= x y))))) (let ((_let_892 (forall ((x |u_(-> _u_(-> tptp.assn Bool)_ tptp.option_assn Bool)|) (y |u_(-> _u_(-> tptp.assn Bool)_ tptp.option_assn Bool)|)) (or (not (forall ((z |u_(-> tptp.assn Bool)|)) (= (ho_24202 x z) (ho_24202 y z)))) (= x y))))) (let ((_let_893 (forall ((x |u_(-> Bool _u_(-> tptp.rat Bool)_ tptp.option_rat Bool)|) (y |u_(-> Bool _u_(-> tptp.rat Bool)_ tptp.option_rat Bool)|)) (or (not (forall ((z Bool)) (= (ho_24194 x z) (ho_24194 y z)))) (= x y))))) (let ((_let_894 (forall ((x |u_(-> tptp.rat tptp.option_rat)|) (y |u_(-> tptp.rat tptp.option_rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_24192 x z) (ho_24192 y z)))) (= x y))))) (let ((_let_895 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat Bool)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat Bool)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_22718 x z) (ho_22718 y z)))) (= x y))))) (let ((_let_896 (forall ((x |u_(-> Bool _u_(-> tptp.nat Bool)_ tptp.option_nat Bool)|) (y |u_(-> Bool _u_(-> tptp.nat Bool)_ tptp.option_nat Bool)|)) (or (not (forall ((z Bool)) (= (ho_24186 x z) (ho_24186 y z)))) (= x y))))) (let ((_let_897 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_nat tptp.produc7248412053542808358at_nat)|) (y |u_(-> tptp.nat tptp.product_prod_nat_nat tptp.produc7248412053542808358at_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_24595 x z) (ho_24595 y z)))) (= x y))))) (let ((_let_898 (forall ((x |u_(-> tptp.option_nat Bool)|) (y |u_(-> tptp.option_nat Bool)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_24188 x z) (ho_24188 y z)))) (= x y))))) (let ((_let_899 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.option_int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.option_int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_24182 x z) (ho_24182 y z)))) (= x y))))) (let ((_let_900 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_24371 x z) (ho_24371 y z)))) (= x y))))) (let ((_let_901 (forall ((x |u_(-> tptp.nat tptp.set_nat tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.set_nat tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_19232 x z) (ho_19232 y z)))) (= x y))))) (let ((_let_902 (forall ((x |u_(-> tptp.assn _u_(-> tptp.assn tptp.assn)_ tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.assn _u_(-> tptp.assn tptp.assn)_ tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_23835 x z) (ho_23835 y z)))) (= x y))))) (let ((_let_903 (forall ((x |u_(-> _u_(-> tptp.assn tptp.assn)_ tptp.assn tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.assn tptp.assn)_ tptp.assn tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.assn tptp.assn)|)) (= (ho_23831 x z) (ho_23831 y z)))) (= x y))))) (let ((_let_904 (forall ((x |u_(-> tptp.list_a tptp.list_a)|) (y |u_(-> tptp.list_a tptp.list_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_24991 x z) (ho_24991 y z)))) (= x y))))) (let ((_let_905 (forall ((x |u_(-> tptp.assn _u_(-> tptp.rat tptp.assn)_ tptp.rat tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.assn _u_(-> tptp.rat tptp.assn)_ tptp.rat tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_23827 x z) (ho_23827 y z)))) (= x y))))) (let ((_let_906 (forall ((x |u_(-> _u_(-> tptp.rat tptp.assn)_ tptp.rat tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.rat tptp.assn)_ tptp.rat tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.assn)|)) (= (ho_23822 x z) (ho_23822 y z)))) (= x y))))) (let ((_let_907 (forall ((x |u_(-> Bool tptp.nat tptp.int)|) (y |u_(-> Bool tptp.nat tptp.int)|)) (or (not (forall ((z Bool)) (= (ho_12231 x z) (ho_12231 y z)))) (= x y))))) (let ((_let_908 (forall ((x |u_(-> _u_(-> tptp.product_unit tptp.nat)_ tptp.heap_T5738788834812785303t_unit tptp.nat)|) (y |u_(-> _u_(-> tptp.product_unit tptp.nat)_ tptp.heap_T5738788834812785303t_unit tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.product_unit tptp.nat)|)) (= (ho_24675 x z) (ho_24675 y z)))) (= x y))))) (let ((_let_909 (forall ((x |u_(-> _u_(-> tptp.num tptp.assn)_ tptp.num tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.num tptp.assn)_ tptp.num tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.assn)|)) (= (ho_23806 x z) (ho_23806 y z)))) (= x y))))) (let ((_let_910 (forall ((x |u_(-> tptp.num tptp.assn)|) (y |u_(-> tptp.num tptp.assn)|)) (or (not (forall ((z tptp.num)) (= (ho_23804 x z) (ho_23804 y z)))) (= x y))))) (let ((_let_911 (forall ((x |u_(-> tptp.nat tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.nat tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_23797 x z) (ho_23797 y z)))) (= x y))))) (let ((_let_912 (forall ((x |u_(-> _u_(-> tptp.int tptp.assn)_ tptp.int tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.int tptp.assn)_ tptp.int tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.assn)|)) (= (ho_23788 x z) (ho_23788 y z)))) (= x y))))) (let ((_let_913 (forall ((x |u_(-> tptp.int tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.int tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_23789 x z) (ho_23789 y z)))) (= x y))))) (let ((_let_914 (forall ((x |u_(-> tptp.int tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.int tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_23785 x z) (ho_23785 y z)))) (= x y))))) (let ((_let_915 (forall ((x |u_(-> _u_(-> tptp.b tptp.heap_T5738788834812785303t_unit)_ tptp.heap_Time_Heap_b tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.heap_T5738788834812785303t_unit)_ tptp.heap_Time_Heap_b tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.heap_T5738788834812785303t_unit)|)) (= (ho_23679 x z) (ho_23679 y z)))) (= x y))))) (let ((_let_916 (forall ((x |u_(-> tptp.heap_Time_Heap_b tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.heap_Time_Heap_b tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.heap_Time_Heap_b)) (= (ho_23680 x z) (ho_23680 y z)))) (= x y))))) (let ((_let_917 (forall ((x |u_(-> tptp.array_o tptp.nat tptp.heap_Time_Heap_o)|) (y |u_(-> tptp.array_o tptp.nat tptp.heap_Time_Heap_o)|)) (or (not (forall ((z tptp.array_o)) (= (ho_24718 x z) (ho_24718 y z)))) (= x y))))) (let ((_let_918 (forall ((x |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.option8956607266484857688it_nat)_ tptp.option4065278094766928714it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.option8956607266484857688it_nat)_ tptp.option4065278094766928714it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc7388388658123137530it_nat tptp.option8956607266484857688it_nat)|)) (= (ho_23676 x z) (ho_23676 y z)))) (= x y))))) (let ((_let_919 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_26153 x z) (ho_26153 y z)))) (= x y))))) (let ((_let_920 (forall ((x |u_(-> tptp.option4065278094766928714it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.option4065278094766928714it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.option4065278094766928714it_nat)) (= (ho_23677 x z) (ho_23677 y z)))) (= x y))))) (let ((_let_921 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_11218 x z) (ho_11218 y z)))) (= x y))))) (let ((_let_922 (forall ((x |u_(-> _u_(-> tptp.a tptp.heap_T5738788834812785303t_unit)_ tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.heap_T5738788834812785303t_unit)_ tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.heap_T5738788834812785303t_unit)|)) (= (ho_23668 x z) (ho_23668 y z)))) (= x y))))) (let ((_let_923 (forall ((x |u_(-> tptp.int tptp.product_prod_int_int)|) (y |u_(-> tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.int)) (= (ho_11521 x z) (ho_11521 y z)))) (= x y))))) (let ((_let_924 (forall ((x |u_(-> tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.heap_Time_Heap_a)) (= (ho_23669 x z) (ho_23669 y z)))) (= x y))))) (let ((_let_925 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_25861 x z) (ho_25861 y z)))) (= x y))))) (let ((_let_926 (forall ((x |u_(-> tptp.option8956607266484857688it_nat _u_(-> tptp.produc3260487557148687353it_nat tptp.option8956607266484857688it_nat)_ tptp.option3562590408128118217it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.option8956607266484857688it_nat _u_(-> tptp.produc3260487557148687353it_nat tptp.option8956607266484857688it_nat)_ tptp.option3562590408128118217it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.option8956607266484857688it_nat)) (= (ho_23664 x z) (ho_23664 y z)))) (= x y))))) (let ((_let_927 (forall ((x |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.option8956607266484857688it_nat)_ tptp.option3562590408128118217it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.option8956607266484857688it_nat)_ tptp.option3562590408128118217it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3260487557148687353it_nat tptp.option8956607266484857688it_nat)|)) (= (ho_23665 x z) (ho_23665 y z)))) (= x y))))) (let ((_let_928 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_26152 x z) (ho_26152 y z)))) (= x y))))) (let ((_let_929 (forall ((x |u_(-> tptp.option3562590408128118217it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.option3562590408128118217it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.option3562590408128118217it_nat)) (= (ho_23666 x z) (ho_23666 y z)))) (= x y))))) (let ((_let_930 (forall ((x |u_(-> tptp.set_nat tptp.set_nat _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_nat _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_23654 x z) (ho_23654 y z)))) (= x y))))) (let ((_let_931 (forall ((x |u_(-> tptp.set_int tptp.set_int _u_(-> tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.set_int _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_23650 x z) (ho_23650 y z)))) (= x y))))) (let ((_let_932 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_o)_ tptp.produc3260487557148687353it_nat tptp.set_o)|) (y |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_o)_ tptp.produc3260487557148687353it_nat tptp.set_o)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_o)|)) (= (ho_25168 x z) (ho_25168 y z)))) (= x y))))) (let ((_let_933 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_23629 x z) (ho_23629 y z)))) (= x y))))) (let ((_let_934 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.option1583680563626158861at_nat)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.option1583680563626158861at_nat)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_23585 x z) (ho_23585 y z)))) (= x y))))) (let ((_let_935 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_18828 x z) (ho_18828 y z)))) (= x y))))) (let ((_let_936 (forall ((x |u_(-> tptp.option1583680563626158861at_nat _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.option1583680563626158861at_nat)_ tptp.option1583680563626158861at_nat tptp.option1583680563626158861at_nat)|) (y |u_(-> tptp.option1583680563626158861at_nat _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.option1583680563626158861at_nat)_ tptp.option1583680563626158861at_nat tptp.option1583680563626158861at_nat)|)) (or (not (forall ((z tptp.option1583680563626158861at_nat)) (= (ho_23581 x z) (ho_23581 y z)))) (= x y))))) (let ((_let_937 (forall ((x |u_(-> _u_(-> tptp.a tptp.set_Pr4389693562480114009it_nat)_ tptp.set_Pr2819221443900773171it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.set_Pr4389693562480114009it_nat)_ tptp.set_Pr2819221443900773171it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.set_Pr4389693562480114009it_nat)|)) (= (ho_25047 x z) (ho_25047 y z)))) (= x y))))) (let ((_let_938 (forall ((x |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.option1583680563626158861at_nat)_ tptp.option1583680563626158861at_nat tptp.option1583680563626158861at_nat)|) (y |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.option1583680563626158861at_nat)_ tptp.option1583680563626158861at_nat tptp.option1583680563626158861at_nat)|)) (or (not (forall ((z |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.option1583680563626158861at_nat)|)) (= (ho_23582 x z) (ho_23582 y z)))) (= x y))))) (let ((_let_939 (forall ((x |u_(-> tptp.option_int _u_(-> tptp.int tptp.option_int)_ tptp.option_int tptp.option_int)|) (y |u_(-> tptp.option_int _u_(-> tptp.int tptp.option_int)_ tptp.option_int tptp.option_int)|)) (or (not (forall ((z tptp.option_int)) (= (ho_23570 x z) (ho_23570 y z)))) (= x y))))) (let ((_let_940 (forall ((x |u_(-> tptp.set_Pr2560585780119916871nt_int tptp.set_Pr2560585780119916871nt_int)|) (y |u_(-> tptp.set_Pr2560585780119916871nt_int tptp.set_Pr2560585780119916871nt_int)|)) (or (not (forall ((z tptp.set_Pr2560585780119916871nt_int)) (= (ho_24866 x z) (ho_24866 y z)))) (= x y))))) (let ((_let_941 (forall ((x |u_(-> tptp.rat tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> tptp.rat tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.rat)) (= (ho_14702 x z) (ho_14702 y z)))) (= x y))))) (let ((_let_942 (forall ((x |u_(-> _u_(-> tptp.int tptp.option_int)_ tptp.option_int tptp.option_int)|) (y |u_(-> _u_(-> tptp.int tptp.option_int)_ tptp.option_int tptp.option_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.option_int)|)) (= (ho_23571 x z) (ho_23571 y z)))) (= x y))))) (let ((_let_943 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_11312 x z) (ho_11312 y z)))) (= x y))))) (let ((_let_944 (forall ((x |u_(-> tptp.set_Product_prod_b_b tptp.set_Pr4389693562480114009it_nat tptp.set_Pr5508209795250834101it_nat)|) (y |u_(-> tptp.set_Product_prod_b_b tptp.set_Pr4389693562480114009it_nat tptp.set_Pr5508209795250834101it_nat)|)) (or (not (forall ((z tptp.set_Product_prod_b_b)) (= (ho_25073 x z) (ho_25073 y z)))) (= x y))))) (let ((_let_945 (forall ((x |u_(-> tptp.option_int tptp.option_int)|) (y |u_(-> tptp.option_int tptp.option_int)|)) (or (not (forall ((z tptp.option_int)) (= (ho_23572 x z) (ho_23572 y z)))) (= x y))))) (let ((_let_946 (forall ((x |u_(-> _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (y |u_(-> _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (or (not (forall ((z |u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (= (ho_18695 x z) (ho_18695 y z)))) (= x y))))) (let ((_let_947 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int Bool)_ tptp.code_integer Bool)_ _u_(-> tptp.int tptp.int Bool)_ tptp.code_integer tptp.code_integer Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.int Bool)_ tptp.code_integer Bool)_ _u_(-> tptp.int tptp.int Bool)_ tptp.code_integer tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int Bool)_ tptp.code_integer Bool)|)) (= (ho_25989 x z) (ho_25989 y z)))) (= x y))))) (let ((_let_948 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.set_int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.set_int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_23365 x z) (ho_23365 y z)))) (= x y))))) (let ((_let_949 (forall ((x |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr958786334691620121nt_int Bool)|)) (= (ho_23359 x z) (ho_23359 y z)))) (= x y))))) (let ((_let_950 (forall ((x |u_(-> tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural Bool)|) (y |u_(-> tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural Bool)|)) (or (not (forall ((z tptp.produc7822875418678951345atural)) (= (ho_25195 x z) (ho_25195 y z)))) (= x y))))) (let ((_let_951 (forall ((x |u_(-> tptp.set_set_nat tptp.set_set_nat Bool)|) (y |u_(-> tptp.set_set_nat tptp.set_set_nat Bool)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_23356 x z) (ho_23356 y z)))) (= x y))))) (let ((_let_952 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.rat)_ _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.rat)_ _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.rat)|)) (= (ho_17213 x z) (ho_17213 y z)))) (= x y))))) (let ((_let_953 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer tptp.rat)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer tptp.rat)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_16816 x z) (ho_16816 y z)))) (= x y))))) (let ((_let_954 (forall ((x |u_(-> tptp.int tptp.produc5728234346263159722nt_int)|) (y |u_(-> tptp.int tptp.produc5728234346263159722nt_int)|)) (or (not (forall ((z tptp.int)) (= (ho_25213 x z) (ho_25213 y z)))) (= x y))))) (let ((_let_955 (forall ((x |u_(-> tptp.set_o tptp.set_o Bool)|) (y |u_(-> tptp.set_o tptp.set_o Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_22447 x z) (ho_22447 y z)))) (= x y))))) (let ((_let_956 (forall ((x |u_(-> _u_(-> tptp.set_nat Bool)_ _u_(-> tptp.set_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_nat Bool)_ _u_(-> tptp.set_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat Bool)|)) (= (ho_23353 x z) (ho_23353 y z)))) (= x y))))) (let ((_let_957 (forall ((x |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)_ _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)_ _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)|)) (= (ho_24318 x z) (ho_24318 y z)))) (= x y))))) (let ((_let_958 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_23348 x z) (ho_23348 y z)))) (= x y))))) (let ((_let_959 (forall ((x |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)_ tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)_ tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)|)) (= (ho_23110 x z) (ho_23110 y z)))) (= x y))))) (let ((_let_960 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)_ tptp.set_nat tptp.set_nat tptp.set_nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)_ tptp.set_nat tptp.set_nat tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)|)) (= (ho_23090 x z) (ho_23090 y z)))) (= x y))))) (let ((_let_961 (forall ((x |u_(-> tptp.rat tptp.set_rat)|) (y |u_(-> tptp.rat tptp.set_rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_25341 x z) (ho_25341 y z)))) (= x y))))) (let ((_let_962 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_23026 x z) (ho_23026 y z)))) (= x y))))) (let ((_let_963 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.code_integer tptp.int Bool)_ tptp.code_integer tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.code_integer tptp.int Bool)_ tptp.code_integer tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_11621 x z) (ho_11621 y z)))) (= x y))))) (let ((_let_964 (forall ((x |u_(-> tptp.produc50402934264563236_nat_o tptp.produc50402934264563236_nat_o Bool)|) (y |u_(-> tptp.produc50402934264563236_nat_o tptp.produc50402934264563236_nat_o Bool)|)) (or (not (forall ((z tptp.produc50402934264563236_nat_o)) (= (ho_25229 x z) (ho_25229 y z)))) (= x y))))) (let ((_let_965 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_23021 x z) (ho_23021 y z)))) (= x y))))) (let ((_let_966 (forall ((x |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|) (y |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_25076 x z) (ho_25076 y z)))) (= x y))))) (let ((_let_967 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_22762 x z) (ho_22762 y z)))) (= x y))))) (let ((_let_968 (forall ((x |u_(-> tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.option8956607266484857688it_nat)) (= (ho_22734 x z) (ho_22734 y z)))) (= x y))))) (let ((_let_969 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat Bool)|) (y |u_(-> tptp.produc7388388658123137530it_nat Bool)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_22722 x z) (ho_22722 y z)))) (= x y))))) (let ((_let_970 (forall ((x |u_(-> tptp.produc8664842809031399944it_nat Bool)|) (y |u_(-> tptp.produc8664842809031399944it_nat Bool)|)) (or (not (forall ((z tptp.produc8664842809031399944it_nat)) (= (ho_22716 x z) (ho_22716 y z)))) (= x y))))) (let ((_let_971 (forall ((x |u_(-> Bool tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> Bool tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z Bool)) (= (ho_22707 x z) (ho_22707 y z)))) (= x y))))) (let ((_let_972 (forall ((x |u_(-> tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.option4065278094766928714it_nat)) (= (ho_22708 x z) (ho_22708 y z)))) (= x y))))) (let ((_let_973 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit Bool)_ _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit Bool)_ _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit Bool)|)) (= (ho_22704 x z) (ho_22704 y z)))) (= x y))))) (let ((_let_974 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.int)_ tptp.product_prod_nat_nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.int)_ tptp.product_prod_nat_nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.int)|)) (= (ho_25460 x z) (ho_25460 y z)))) (= x y))))) (let ((_let_975 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat)|)) (= (ho_22705 x z) (ho_22705 y z)))) (= x y))))) (let ((_let_976 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.int)_ tptp.produc8923325533196201883nteger tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.int)_ tptp.produc8923325533196201883nteger tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer tptp.int)|)) (= (ho_18547 x z) (ho_18547 y z)))) (= x y))))) (let ((_let_977 (forall ((x |u_(-> Bool tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> Bool tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z Bool)) (= (ho_22701 x z) (ho_22701 y z)))) (= x y))))) (let ((_let_978 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit Bool)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit Bool)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_22696 x z) (ho_22696 y z)))) (= x y))))) (let ((_let_979 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat)|)) (= (ho_22699 x z) (ho_22699 y z)))) (= x y))))) (let ((_let_980 (forall ((x |u_(-> _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc5835291356934675326atural tptp.produc5835291356934675326atural)|) (y |u_(-> _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc5835291356934675326atural tptp.produc5835291356934675326atural)|)) (or (not (forall ((z |u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (= (ho_12599 x z) (ho_12599 y z)))) (= x y))))) (let ((_let_981 (forall ((x |u_(-> tptp.int tptp.option_num)|) (y |u_(-> tptp.int tptp.option_num)|)) (or (not (forall ((z tptp.int)) (= (ho_22687 x z) (ho_22687 y z)))) (= x y))))) (let ((_let_982 (forall ((x |u_(-> tptp.set_rat tptp.set_rat Bool)|) (y |u_(-> tptp.set_rat tptp.set_rat Bool)|)) (or (not (forall ((z tptp.set_rat)) (= (ho_25373 x z) (ho_25373 y z)))) (= x y))))) (let ((_let_983 (forall ((x |u_(-> tptp.int tptp.num)|) (y |u_(-> tptp.int tptp.num)|)) (or (not (forall ((z tptp.int)) (= (ho_22683 x z) (ho_22683 y z)))) (= x y))))) (let ((_let_984 (forall ((x |u_(-> _u_(-> tptp.num tptp.int)_ tptp.num tptp.num)|) (y |u_(-> _u_(-> tptp.num tptp.int)_ tptp.num tptp.num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.int)|)) (= (ho_22686 x z) (ho_22686 y z)))) (= x y))))) (let ((_let_985 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_24462 x z) (ho_24462 y z)))) (= x y))))) (let ((_let_986 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_19008 x z) (ho_19008 y z)))) (= x y))))) (let ((_let_987 (forall ((x |u_(-> _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.int)|) (y |u_(-> _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.int)|)) (or (not (forall ((z |u_(-> tptp.num tptp.option_num)|)) (= (ho_22682 x z) (ho_22682 y z)))) (= x y))))) (let ((_let_988 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr4389693562480114009it_nat tptp.set_Pr2819221443900773171it_nat)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.set_Pr4389693562480114009it_nat tptp.set_Pr2819221443900773171it_nat)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_25082 x z) (ho_25082 y z)))) (= x y))))) (let ((_let_989 (forall ((x |u_(-> _u_(-> tptp.option_num tptp.num)_ _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.num)|) (y |u_(-> _u_(-> tptp.option_num tptp.num)_ _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.num)|)) (or (not (forall ((z |u_(-> tptp.option_num tptp.num)|)) (= (ho_22676 x z) (ho_22676 y z)))) (= x y))))) (let ((_let_990 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_12574 x z) (ho_12574 y z)))) (= x y))))) (let ((_let_991 (forall ((x |u_(-> _u_(-> tptp.num tptp.num)_ tptp.num tptp.int)|) (y |u_(-> _u_(-> tptp.num tptp.num)_ tptp.num tptp.int)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num)|)) (= (ho_22674 x z) (ho_22674 y z)))) (= x y))))) (let ((_let_992 (forall ((x |u_(-> _u_(-> tptp.num tptp.num)_ tptp.num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num tptp.num)_ tptp.num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num)|)) (= (ho_22671 x z) (ho_22671 y z)))) (= x y))))) (let ((_let_993 (forall ((x |u_(-> _u_(-> tptp.produc7388388658123137530it_nat Bool)_ tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.produc7388388658123137530it_nat Bool)_ tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc7388388658123137530it_nat Bool)|)) (= (ho_24391 x z) (ho_24391 y z)))) (= x y))))) (let ((_let_994 (forall ((x |u_(-> _u_(-> tptp.num tptp.num)_ tptp.num tptp.num)|) (y |u_(-> _u_(-> tptp.num tptp.num)_ tptp.num tptp.num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num)|)) (= (ho_22668 x z) (ho_22668 y z)))) (= x y))))) (let ((_let_995 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.nat)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.nat)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15118 x z) (ho_15118 y z)))) (= x y))))) (let ((_let_996 (forall ((x |u_(-> tptp.option4065278094766928714it_nat Bool)|) (y |u_(-> tptp.option4065278094766928714it_nat Bool)|)) (or (not (forall ((z tptp.option4065278094766928714it_nat)) (= (ho_22654 x z) (ho_22654 y z)))) (= x y))))) (let ((_let_997 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.int)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.int)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.int)|)) (= (ho_20032 x z) (ho_20032 y z)))) (= x y))))) (let ((_let_998 (forall ((x |u_(-> tptp.set_int tptp.int tptp.set_int tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.int tptp.set_int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_18835 x z) (ho_18835 y z)))) (= x y))))) (let ((_let_999 (forall ((x |u_(-> _u_(-> tptp.option3562590408128118217it_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.option3562590408128118217it_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.option3562590408128118217it_nat Bool)|)) (= (ho_22652 x z) (ho_22652 y z)))) (= x y))))) (let ((_let_1000 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.nat)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.nat)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12536 x z) (ho_12536 y z)))) (= x y))))) (let ((_let_1001 (forall ((x |u_(-> tptp.option3562590408128118217it_nat Bool)|) (y |u_(-> tptp.option3562590408128118217it_nat Bool)|)) (or (not (forall ((z tptp.option3562590408128118217it_nat)) (= (ho_22650 x z) (ho_22650 y z)))) (= x y))))) (let ((_let_1002 (forall ((x |u_(-> _u_(-> tptp.option8956607266484857688it_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.option8956607266484857688it_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.option8956607266484857688it_nat Bool)|)) (= (ho_22648 x z) (ho_22648 y z)))) (= x y))))) (let ((_let_1003 (forall ((x |u_(-> _u_(-> tptp.array_int tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat)_ tptp.produc3407818250607552075t_unit tptp.produc7196121022310644452it_nat)|) (y |u_(-> _u_(-> tptp.array_int tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat)_ tptp.produc3407818250607552075t_unit tptp.produc7196121022310644452it_nat)|)) (or (not (forall ((z |u_(-> tptp.array_int tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat)|)) (= (ho_11804 x z) (ho_11804 y z)))) (= x y))))) (let ((_let_1004 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_17966 x z) (ho_17966 y z)))) (= x y))))) (let ((_let_1005 (forall ((x |u_(-> tptp.option8956607266484857688it_nat Bool)|) (y |u_(-> tptp.option8956607266484857688it_nat Bool)|)) (or (not (forall ((z tptp.option8956607266484857688it_nat)) (= (ho_22646 x z) (ho_22646 y z)))) (= x y))))) (let ((_let_1006 (forall ((x |u_(-> _u_(-> tptp.num Bool)_ tptp.option_num Bool)|) (y |u_(-> _u_(-> tptp.num Bool)_ tptp.option_num Bool)|)) (or (not (forall ((z |u_(-> tptp.num Bool)|)) (= (ho_22640 x z) (ho_22640 y z)))) (= x y))))) (let ((_let_1007 (forall ((x |u_(-> tptp.code_integer Bool Bool)|) (y |u_(-> tptp.code_integer Bool Bool)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_11555 x z) (ho_11555 y z)))) (= x y))))) (let ((_let_1008 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_22602 x z) (ho_22602 y z)))) (= x y))))) (let ((_let_1009 (forall ((x |u_(-> Bool tptp.set_o tptp.set_o Bool Bool)|) (y |u_(-> Bool tptp.set_o tptp.set_o Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_19253 x z) (ho_19253 y z)))) (= x y))))) (let ((_let_1010 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_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)|) (y |u_(-> _u_(-> tptp.product_prod_nat_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)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_13158 x z) (ho_13158 y z)))) (= x y))))) (let ((_let_1011 (forall ((x |u_(-> tptp.heap_Time_Heap_a tptp.product_unit tptp.heap_Time_Heap_a)|) (y |u_(-> tptp.heap_Time_Heap_a tptp.product_unit tptp.heap_Time_Heap_a)|)) (or (not (forall ((z tptp.heap_Time_Heap_a)) (= (ho_22597 x z) (ho_22597 y z)))) (= x y))))) (let ((_let_1012 (forall ((x |u_(-> tptp.product_unit tptp.heap_Time_Heap_a)|) (y |u_(-> tptp.product_unit tptp.heap_Time_Heap_a)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_22598 x z) (ho_22598 y z)))) (= x y))))) (let ((_let_1013 (forall ((x |u_(-> _u_(-> Bool tptp.int Bool)_ tptp.int Bool Bool)|) (y |u_(-> _u_(-> Bool tptp.int Bool)_ tptp.int Bool Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.int Bool)|)) (= (ho_12221 x z) (ho_12221 y z)))) (= x y))))) (let ((_let_1014 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.list_P7985473006766602707_nat_o tptp.list_P7985473006766602707_nat_o)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.list_P7985473006766602707_nat_o tptp.list_P7985473006766602707_nat_o)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_24966 x z) (ho_24966 y z)))) (= x y))))) (let ((_let_1015 (forall ((x |u_(-> tptp.list_int tptp.option_int)|) (y |u_(-> tptp.list_int tptp.option_int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_24943 x z) (ho_24943 y z)))) (= x y))))) (let ((_let_1016 (forall ((x |u_(-> tptp.heap_Time_Heap_b tptp.product_unit tptp.heap_Time_Heap_b)|) (y |u_(-> tptp.heap_Time_Heap_b tptp.product_unit tptp.heap_Time_Heap_b)|)) (or (not (forall ((z tptp.heap_Time_Heap_b)) (= (ho_22591 x z) (ho_22591 y z)))) (= x y))))) (let ((_let_1017 (forall ((x |u_(-> tptp.assn _u_(-> tptp.num tptp.assn)_ tptp.num tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.assn _u_(-> tptp.num tptp.assn)_ tptp.num tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_23815 x z) (ho_23815 y z)))) (= x y))))) (let ((_let_1018 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.code_natural)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.code_natural)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_15336 x z) (ho_15336 y z)))) (= x y))))) (let ((_let_1019 (forall ((x |u_(-> tptp.set_o _u_(-> Bool Bool)_ Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> Bool Bool)_ Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_17054 x z) (ho_17054 y z)))) (= x y))))) (let ((_let_1020 (forall ((x |u_(-> tptp.product_unit tptp.heap_Time_Heap_b)|) (y |u_(-> tptp.product_unit tptp.heap_Time_Heap_b)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_22592 x z) (ho_22592 y z)))) (= x y))))) (let ((_let_1021 (forall ((x |u_(-> tptp.option8956607266484857688it_nat _u_(-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat)_ tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.option8956607266484857688it_nat _u_(-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat)_ tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.option8956607266484857688it_nat)) (= (ho_22527 x z) (ho_22527 y z)))) (= x y))))) (let ((_let_1022 (forall ((x |u_(-> _u_(-> tptp.num tptp.num tptp.num)_ tptp.option_num tptp.num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num tptp.num tptp.num)_ tptp.option_num tptp.num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num tptp.num)|)) (= (ho_22523 x z) (ho_22523 y z)))) (= x y))))) (let ((_let_1023 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.rat)|)) (= (ho_25910 x z) (ho_25910 y z)))) (= x y))))) (let ((_let_1024 (forall ((x |u_(-> tptp.option_num tptp.num tptp.option_num)|) (y |u_(-> tptp.option_num tptp.num tptp.option_num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_22524 x z) (ho_22524 y z)))) (= x y))))) (let ((_let_1025 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_22468 x z) (ho_22468 y z)))) (= x y))))) (let ((_let_1026 (forall ((x |u_(-> _u_(-> tptp.product_unit tptp.heap_T5738788834812785303t_unit)_ tptp.heap_T5738788834812785303t_unit)|) (y |u_(-> _u_(-> tptp.product_unit tptp.heap_T5738788834812785303t_unit)_ tptp.heap_T5738788834812785303t_unit)|)) (or (not (forall ((z |u_(-> tptp.product_unit tptp.heap_T5738788834812785303t_unit)|)) (= (ho_24312 x z) (ho_24312 y z)))) (= x y))))) (let ((_let_1027 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_22465 x z) (ho_22465 y z)))) (= x y))))) (let ((_let_1028 (forall ((x |u_(-> tptp.set_o tptp.option_set_o)|) (y |u_(-> tptp.set_o tptp.option_set_o)|)) (or (not (forall ((z tptp.set_o)) (= (ho_22422 x z) (ho_22422 y z)))) (= x y))))) (let ((_let_1029 (forall ((x |u_(-> tptp.option8963830502488799655at_nat tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.option8963830502488799655at_nat tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.option8963830502488799655at_nat)) (= (ho_24532 x z) (ho_24532 y z)))) (= x y))))) (let ((_let_1030 (forall ((x |u_(-> tptp.nat tptp.nat tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_23796 x z) (ho_23796 y z)))) (= x y))))) (let ((_let_1031 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.nat tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.nat tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (= (ho_25934 x z) (ho_25934 y z)))) (= x y))))) (let ((_let_1032 (forall ((x |u_(-> tptp.option_set_nat tptp.option_set_nat tptp.option_set_nat)|) (y |u_(-> tptp.option_set_nat tptp.option_set_nat tptp.option_set_nat)|)) (or (not (forall ((z tptp.option_set_nat)) (= (ho_22419 x z) (ho_22419 y z)))) (= x y))))) (let ((_let_1033 (forall ((x |u_(-> Bool tptp.option_set_int tptp.option_set_int tptp.option_set_int)|) (y |u_(-> Bool tptp.option_set_int tptp.option_set_int tptp.option_set_int)|)) (or (not (forall ((z Bool)) (= (ho_22413 x z) (ho_22413 y z)))) (= x y))))) (let ((_let_1034 (forall ((x |u_(-> tptp.option_set_int tptp.option_set_int)|) (y |u_(-> tptp.option_set_int tptp.option_set_int)|)) (or (not (forall ((z tptp.option_set_int)) (= (ho_22415 x z) (ho_22415 y z)))) (= x y))))) (let ((_let_1035 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.b)_ tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.b)_ tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit tptp.b)|)) (= (ho_22402 x z) (ho_22402 y z)))) (= x y))))) (let ((_let_1036 (forall ((x |u_(-> _u_(-> tptp.b tptp.heap_Time_Heap_b)_ tptp.b tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.heap_Time_Heap_b)_ tptp.b tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.heap_Time_Heap_b)|)) (= (ho_13117 x z) (ho_13117 y z)))) (= x y))))) (let ((_let_1037 (forall ((x |u_(-> tptp.num tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.num tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_23811 x z) (ho_23811 y z)))) (= x y))))) (let ((_let_1038 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.b)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.b)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_22400 x z) (ho_22400 y z)))) (= x y))))) (let ((_let_1039 (forall ((x |u_(-> _u_(-> tptp.set_o tptp.set_o Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_o tptp.set_o Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_o tptp.set_o Bool)|)) (= (ho_24517 x z) (ho_24517 y z)))) (= x y))))) (let ((_let_1040 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat tptp.list_P6011104703257516679at_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat tptp.list_P6011104703257516679at_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_24951 x z) (ho_24951 y z)))) (= x y))))) (let ((_let_1041 (forall ((x |u_(-> tptp.nat tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.nat tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_22392 x z) (ho_22392 y z)))) (= x y))))) (let ((_let_1042 (forall ((x |u_(-> _u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (= (ho_22369 x z) (ho_22369 y z)))) (= x y))))) (let ((_let_1043 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.set_Pr7928877670098842301et_nat)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.set_Pr7928877670098842301et_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_25030 x z) (ho_25030 y z)))) (= x y))))) (let ((_let_1044 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_12407 x z) (ho_12407 y z)))) (= x y))))) (let ((_let_1045 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_22365 x z) (ho_22365 y z)))) (= x y))))) (let ((_let_1046 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.int)_ tptp.code_integer tptp.code_integer)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.int)_ tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer)|)) (= (ho_12157 x z) (ho_12157 y z)))) (= x y))))) (let ((_let_1047 (forall ((x |u_(-> tptp.product_unit tptp.produc6653097349344004940it_nat tptp.produc8664842809031399944it_nat)|) (y |u_(-> tptp.product_unit tptp.produc6653097349344004940it_nat tptp.produc8664842809031399944it_nat)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_22361 x z) (ho_22361 y z)))) (= x y))))) (let ((_let_1048 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.set_Pr958786334691620121nt_int tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.set_Pr958786334691620121nt_int tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_22353 x z) (ho_22353 y z)))) (= x y))))) (let ((_let_1049 (forall ((x |u_(-> tptp.list_o tptp.nat tptp.int)|) (y |u_(-> tptp.list_o tptp.nat tptp.int)|)) (or (not (forall ((z tptp.list_o)) (= (ho_18766 x z) (ho_18766 y z)))) (= x y))))) (let ((_let_1050 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.set_nat tptp.heap_e7401611519738050253t_unit tptp.nat Bool)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.set_nat tptp.heap_e7401611519738050253t_unit tptp.nat Bool)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_22301 x z) (ho_22301 y z)))) (= x y))))) (let ((_let_1051 (forall ((x |u_(-> tptp.a tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat)|) (y |u_(-> tptp.a tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z tptp.a)) (= (ho_22292 x z) (ho_22292 y z)))) (= x y))))) (let ((_let_1052 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ Bool)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.set_Pr719794911490849221et_nat)_ tptp.set_Pr7928877670098842301et_nat)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ Bool)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.set_Pr719794911490849221et_nat)_ tptp.set_Pr7928877670098842301et_nat)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ Bool)|)) (= (ho_25022 x z) (ho_25022 y z)))) (= x y))))) (let ((_let_1053 (forall ((x |u_(-> tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.produc3843707927480180839at_nat)) (= (ho_19065 x z) (ho_19065 y z)))) (= x y))))) (let ((_let_1054 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_22293 x z) (ho_22293 y z)))) (= x y))))) (let ((_let_1055 (forall ((x |u_(-> tptp.option_assn tptp.option_assn)|) (y |u_(-> tptp.option_assn tptp.option_assn)|)) (or (not (forall ((z tptp.option_assn)) (= (ho_22220 x z) (ho_22220 y z)))) (= x y))))) (let ((_let_1056 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.num)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.num)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12558 x z) (ho_12558 y z)))) (= x y))))) (let ((_let_1057 (forall ((x |u_(-> tptp.option8963830502488799655at_nat _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.option8963830502488799655at_nat)_ tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat)|) (y |u_(-> tptp.option8963830502488799655at_nat _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.option8963830502488799655at_nat)_ tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat)|)) (or (not (forall ((z tptp.option8963830502488799655at_nat)) (= (ho_22212 x z) (ho_22212 y z)))) (= x y))))) (let ((_let_1058 (forall ((x |u_(-> Bool _u_(-> tptp.int Bool)_ tptp.option_int Bool)|) (y |u_(-> Bool _u_(-> tptp.int Bool)_ tptp.option_int Bool)|)) (or (not (forall ((z Bool)) (= (ho_24181 x z) (ho_24181 y z)))) (= x y))))) (let ((_let_1059 (forall ((x |u_(-> tptp.option_set_nat _u_(-> tptp.set_nat tptp.option_set_nat)_ tptp.option_set_nat tptp.option_set_nat)|) (y |u_(-> tptp.option_set_nat _u_(-> tptp.set_nat tptp.option_set_nat)_ tptp.option_set_nat tptp.option_set_nat)|)) (or (not (forall ((z tptp.option_set_nat)) (= (ho_22205 x z) (ho_22205 y z)))) (= x y))))) (let ((_let_1060 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> Bool tptp.code_integer Bool)_ Bool tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> Bool tptp.code_integer Bool)_ Bool tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_11585 x z) (ho_11585 y z)))) (= x y))))) (let ((_let_1061 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.produc8664842809031399944it_nat)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.produc8664842809031399944it_nat)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_22362 x z) (ho_22362 y z)))) (= x y))))) (let ((_let_1062 (forall ((x |u_(-> Bool tptp.code_integer tptp.code_integer tptp.code_integer)|) (y |u_(-> Bool tptp.code_integer tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z Bool)) (= (ho_12388 x z) (ho_12388 y z)))) (= x y))))) (let ((_let_1063 (forall ((x |u_(-> tptp.option_nat _u_(-> tptp.nat tptp.option_nat)_ tptp.option_nat tptp.option_nat)|) (y |u_(-> tptp.option_nat _u_(-> tptp.nat tptp.option_nat)_ tptp.option_nat tptp.option_nat)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_22199 x z) (ho_22199 y z)))) (= x y))))) (let ((_let_1064 (forall ((x |u_(-> _u_(-> tptp.nat tptp.option_nat)_ tptp.option_nat tptp.option_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.option_nat)_ tptp.option_nat tptp.option_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.option_nat)|)) (= (ho_22200 x z) (ho_22200 y z)))) (= x y))))) (let ((_let_1065 (forall ((x |u_(-> tptp.option1893999432384633940_int_o tptp.option1893999432384633940_int_o)|) (y |u_(-> tptp.option1893999432384633940_int_o tptp.option1893999432384633940_int_o)|)) (or (not (forall ((z tptp.option1893999432384633940_int_o)) (= (ho_22196 x z) (ho_22196 y z)))) (= x y))))) (let ((_let_1066 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.set_se6260736226359567993nt_int)_ tptp.product_prod_int_int tptp.set_se6260736226359567993nt_int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.set_se6260736226359567993nt_int)_ tptp.product_prod_int_int tptp.set_se6260736226359567993nt_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.set_se6260736226359567993nt_int)|)) (= (ho_25148 x z) (ho_25148 y z)))) (= x y))))) (let ((_let_1067 (forall ((x |u_(-> tptp.assn tptp.assn tptp.assn tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.assn tptp.assn tptp.assn tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_22053 x z) (ho_22053 y z)))) (= x y))))) (let ((_let_1068 (forall ((x |u_(-> tptp.code_natural tptp.produc7822875418678951345atural)|) (y |u_(-> tptp.code_natural tptp.produc7822875418678951345atural)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_25193 x z) (ho_25193 y z)))) (= x y))))) (let ((_let_1069 (forall ((x |u_(-> tptp.list_P9062070895058802706et_nat tptp.list_P2321686559999237006et_nat)|) (y |u_(-> tptp.list_P9062070895058802706et_nat tptp.list_P2321686559999237006et_nat)|)) (or (not (forall ((z tptp.list_P9062070895058802706et_nat)) (= (ho_24958 x z) (ho_24958 y z)))) (= x y))))) (let ((_let_1070 (forall ((x |u_(-> _u_(-> tptp.int tptp.option_num)_ _u_(-> tptp.num tptp.int)_ tptp.num tptp.option_num)|) (y |u_(-> _u_(-> tptp.int tptp.option_num)_ _u_(-> tptp.num tptp.int)_ tptp.num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.int tptp.option_num)|)) (= (ho_22689 x z) (ho_22689 y z)))) (= x y))))) (let ((_let_1071 (forall ((x |u_(-> tptp.assn _u_(-> tptp.assn tptp.assn tptp.assn)_ tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.assn _u_(-> tptp.assn tptp.assn tptp.assn)_ tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_22002 x z) (ho_22002 y z)))) (= x y))))) (let ((_let_1072 (forall ((x |u_(-> tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr719794911490849221et_nat tptp.set_Pr7928877670098842301et_nat)|) (y |u_(-> tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr719794911490849221et_nat tptp.set_Pr7928877670098842301et_nat)|)) (or (not (forall ((z tptp.set_Pr2161125870931222855_nat_o)) (= (ho_25061 x z) (ho_25061 y z)))) (= x y))))) (let ((_let_1073 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat)_ _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat)_ _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat)|)) (= (ho_16855 x z) (ho_16855 y z)))) (= x y))))) (let ((_let_1074 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)_ tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)_ tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_21997 x z) (ho_21997 y z)))) (= x y))))) (let ((_let_1075 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)_ tptp.set_nat tptp.set_nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)_ tptp.set_nat tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)|)) (= (ho_21980 x z) (ho_21980 y z)))) (= x y))))) (let ((_let_1076 (forall ((x |u_(-> _u_(-> tptp.produc1399344845416535567atural tptp.produc1399344845416535567atural Bool)_ tptp.produc1399344845416535567atural Bool)|) (y |u_(-> _u_(-> tptp.produc1399344845416535567atural tptp.produc1399344845416535567atural Bool)_ tptp.produc1399344845416535567atural Bool)|)) (or (not (forall ((z |u_(-> tptp.produc1399344845416535567atural tptp.produc1399344845416535567atural Bool)|)) (= (ho_25275 x z) (ho_25275 y z)))) (= x y))))) (let ((_let_1077 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.set_Pr719794911490849221et_nat)_ tptp.set_Pr7928877670098842301et_nat)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.set_Pr719794911490849221et_nat)_ tptp.set_Pr7928877670098842301et_nat)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.set_Pr719794911490849221et_nat)|)) (= (ho_25023 x z) (ho_25023 y z)))) (= x y))))) (let ((_let_1078 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_11671 x z) (ho_11671 y z)))) (= x y))))) (let ((_let_1079 (forall ((x |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat tptp.option_set_nat)|) (y |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat tptp.option_set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_23578 x z) (ho_23578 y z)))) (= x y))))) (let ((_let_1080 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.set_int tptp.set_int tptp.set_int)_ tptp.set_int tptp.set_int tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.set_int tptp.set_int tptp.set_int)_ tptp.set_int tptp.set_int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_21977 x z) (ho_21977 y z)))) (= x y))))) (let ((_let_1081 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.list_P7438302566501821706it_nat tptp.list_P7438302566501821706it_nat)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.list_P7438302566501821706it_nat tptp.list_P7438302566501821706it_nat)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_24975 x z) (ho_24975 y z)))) (= x y))))) (let ((_let_1082 (forall ((x |u_(-> _u_(-> tptp.set_int tptp.set_int tptp.set_int)_ tptp.set_int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.set_int tptp.set_int tptp.set_int)_ tptp.set_int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.set_int tptp.set_int tptp.set_int)|)) (= (ho_21973 x z) (ho_21973 y z)))) (= x y))))) (let ((_let_1083 (forall ((x |u_(-> tptp.produc1273031398460193109it_nat tptp.set_Pr5508209795250834101it_nat Bool)|) (y |u_(-> tptp.produc1273031398460193109it_nat tptp.set_Pr5508209795250834101it_nat Bool)|)) (or (not (forall ((z tptp.produc1273031398460193109it_nat)) (= (ho_24887 x z) (ho_24887 y z)))) (= x y))))) (let ((_let_1084 (forall ((x |u_(-> _u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)_ _u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)_ _u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)|)) (= (ho_24481 x z) (ho_24481 y z)))) (= x y))))) (let ((_let_1085 (forall ((x |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_21591 x z) (ho_21591 y z)))) (= x y))))) (let ((_let_1086 (forall ((x |u_(-> tptp.set_set_nat _u_(-> tptp.set_nat Bool)_ tptp.set_nat Bool)|) (y |u_(-> tptp.set_set_nat _u_(-> tptp.set_nat Bool)_ tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_21545 x z) (ho_21545 y z)))) (= x y))))) (let ((_let_1087 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat Bool)_ tptp.set_nat _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat Bool)_ tptp.set_nat _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_21537 x z) (ho_21537 y z)))) (= x y))))) (let ((_let_1088 (forall ((x |u_(-> tptp.option_Code_integer tptp.option7428179582072448501nteger)|) (y |u_(-> tptp.option_Code_integer tptp.option7428179582072448501nteger)|)) (or (not (forall ((z tptp.option_Code_integer)) (= (ho_25733 x z) (ho_25733 y z)))) (= x y))))) (let ((_let_1089 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int Bool)_ tptp.set_int _u_(-> tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int Bool)_ tptp.set_int _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_21532 x z) (ho_21532 y z)))) (= x y))))) (let ((_let_1090 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_21403 x z) (ho_21403 y z)))) (= x y))))) (let ((_let_1091 (forall ((x |u_(-> Bool Bool tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> Bool Bool tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z Bool)) (= (ho_21399 x z) (ho_21399 y z)))) (= x y))))) (let ((_let_1092 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc6999243976208994655_nat_o)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc6999243976208994655_nat_o)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_25235 x z) (ho_25235 y z)))) (= x y))))) (let ((_let_1093 (forall ((x |u_(-> tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat)|) (y |u_(-> tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat)|)) (or (not (forall ((z tptp.set_Pr3286484037609594932et_nat)) (= (ho_21391 x z) (ho_21391 y z)))) (= x y))))) (let ((_let_1094 (forall ((x |u_(-> tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat)|) (y |u_(-> tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat)|)) (or (not (forall ((z tptp.set_Pr3286484037609594932et_nat)) (= (ho_21392 x z) (ho_21392 y z)))) (= x y))))) (let ((_let_1095 (forall ((x |u_(-> tptp.assn tptp.nat tptp.assn)|) (y |u_(-> tptp.assn tptp.nat tptp.assn)|)) (or (not (forall ((z tptp.assn)) (= (ho_24625 x z) (ho_24625 y z)))) (= x y))))) (let ((_let_1096 (forall ((x |u_(-> tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.set_Pr3286484037609594932et_nat)) (= (ho_21389 x z) (ho_21389 y z)))) (= x y))))) (let ((_let_1097 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat Bool)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat Bool)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_13236 x z) (ho_13236 y z)))) (= x y))))) (let ((_let_1098 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_25848 x z) (ho_25848 y z)))) (= x y))))) (let ((_let_1099 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.produc1319942482725812455at_nat)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.produc1319942482725812455at_nat)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_26066 x z) (ho_26066 y z)))) (= x y))))) (let ((_let_1100 (forall ((x |u_(-> tptp.set_Pr3286484037609594932et_nat Bool)|) (y |u_(-> tptp.set_Pr3286484037609594932et_nat Bool)|)) (or (not (forall ((z tptp.set_Pr3286484037609594932et_nat)) (= (ho_21386 x z) (ho_21386 y z)))) (= x y))))) (let ((_let_1101 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer)|)) (= (ho_11691 x z) (ho_11691 y z)))) (= x y))))) (let ((_let_1102 (forall ((x |u_(-> tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat)|) (y |u_(-> tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat)|)) (or (not (forall ((z tptp.set_Pr8536935166611901872et_nat)) (= (ho_21381 x z) (ho_21381 y z)))) (= x y))))) (let ((_let_1103 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.option2498585697089621389at_nat)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.option2498585697089621389at_nat)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_23592 x z) (ho_23592 y z)))) (= x y))))) (let ((_let_1104 (forall ((x |u_(-> tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|) (y |u_(-> tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8536935166611901872et_nat)) (= (ho_21378 x z) (ho_21378 y z)))) (= x y))))) (let ((_let_1105 (forall ((x |u_(-> tptp.produc2732055786443039994et_nat tptp.set_Pr8536935166611901872et_nat Bool)|) (y |u_(-> tptp.produc2732055786443039994et_nat tptp.set_Pr8536935166611901872et_nat Bool)|)) (or (not (forall ((z tptp.produc2732055786443039994et_nat)) (= (ho_21374 x z) (ho_21374 y z)))) (= x y))))) (let ((_let_1106 (forall ((x |u_(-> tptp.set_Pr8536935166611901872et_nat Bool)|) (y |u_(-> tptp.set_Pr8536935166611901872et_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8536935166611901872et_nat)) (= (ho_21375 x z) (ho_21375 y z)))) (= x y))))) (let ((_let_1107 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_21371 x z) (ho_21371 y z)))) (= x y))))) (let ((_let_1108 (forall ((x |u_(-> tptp.produc3925858234332021118et_nat Bool)|) (y |u_(-> tptp.produc3925858234332021118et_nat Bool)|)) (or (not (forall ((z tptp.produc3925858234332021118et_nat)) (= (ho_21372 x z) (ho_21372 y z)))) (= x y))))) (let ((_let_1109 (forall ((x |u_(-> tptp.set_Pr7600907837789447088it_nat tptp.set_Pr7600907837789447088it_nat tptp.set_Pr7600907837789447088it_nat)|) (y |u_(-> tptp.set_Pr7600907837789447088it_nat tptp.set_Pr7600907837789447088it_nat tptp.set_Pr7600907837789447088it_nat)|)) (or (not (forall ((z tptp.set_Pr7600907837789447088it_nat)) (= (ho_21367 x z) (ho_21367 y z)))) (= x y))))) (let ((_let_1110 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.set_Pr7600907837789447088it_nat Bool)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.set_Pr7600907837789447088it_nat Bool)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_21361 x z) (ho_21361 y z)))) (= x y))))) (let ((_let_1111 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.set_nat tptp.produc3658429121746597890et_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.set_nat tptp.produc3658429121746597890et_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_24259 x z) (ho_24259 y z)))) (= x y))))) (let ((_let_1112 (forall ((x |u_(-> tptp.list_P7438302566501821706it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.list_P7438302566501821706it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.list_P7438302566501821706it_nat)) (= (ho_24913 x z) (ho_24913 y z)))) (= x y))))) (let ((_let_1113 (forall ((x |u_(-> tptp.code_integer tptp.set_Code_integer tptp.set_Code_integer)|) (y |u_(-> tptp.code_integer tptp.set_Code_integer tptp.set_Code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_25453 x z) (ho_25453 y z)))) (= x y))))) (let ((_let_1114 (forall ((x |u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)|) (y |u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)|)) (or (not (forall ((z tptp.b)) (= (ho_21359 x z) (ho_21359 y z)))) (= x y))))) (let ((_let_1115 (forall ((x |u_(-> tptp.option_num tptp.code_natural)|) (y |u_(-> tptp.option_num tptp.code_natural)|)) (or (not (forall ((z tptp.option_num)) (= (ho_25177 x z) (ho_25177 y z)))) (= x y))))) (let ((_let_1116 (forall ((x |u_(-> tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat)|) (y |u_(-> tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat)|)) (or (not (forall ((z tptp.set_Pr7098220151150636591it_nat)) (= (ho_21356 x z) (ho_21356 y z)))) (= x y))))) (let ((_let_1117 (forall ((x |u_(-> tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat tptp.a tptp.produc6653097349344004940it_nat Bool)|) (y |u_(-> tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat tptp.a tptp.produc6653097349344004940it_nat Bool)|)) (or (not (forall ((z tptp.set_Pr7098220151150636591it_nat)) (= (ho_21353 x z) (ho_21353 y z)))) (= x y))))) (let ((_let_1118 (forall ((x |u_(-> tptp.filter_nat tptp.filter_nat Bool)|) (y |u_(-> tptp.filter_nat tptp.filter_nat Bool)|)) (or (not (forall ((z tptp.filter_nat)) (= (ho_26058 x z) (ho_26058 y z)))) (= x y))))) (let ((_let_1119 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.set_Pr7098220151150636591it_nat Bool)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.set_Pr7098220151150636591it_nat Bool)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_21349 x z) (ho_21349 y z)))) (= x y))))) (let ((_let_1120 (forall ((x |u_(-> tptp.set_Pr7098220151150636591it_nat tptp.a tptp.produc6653097349344004940it_nat Bool)|) (y |u_(-> tptp.set_Pr7098220151150636591it_nat tptp.a tptp.produc6653097349344004940it_nat Bool)|)) (or (not (forall ((z tptp.set_Pr7098220151150636591it_nat)) (= (ho_21345 x z) (ho_21345 y z)))) (= x y))))) (let ((_let_1121 (forall ((x |u_(-> Bool _u_(-> Bool tptp.nat)_ Bool tptp.nat)|) (y |u_(-> Bool _u_(-> Bool tptp.nat)_ Bool tptp.nat)|)) (or (not (forall ((z Bool)) (= (ho_17564 x z) (ho_17564 y z)))) (= x y))))) (let ((_let_1122 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat Bool)|) (y |u_(-> tptp.produc6653097349344004940it_nat Bool)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_21347 x z) (ho_21347 y z)))) (= x y))))) (let ((_let_1123 (forall ((x |u_(-> _u_(-> tptp.set_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat Bool)|)) (= (ho_23354 x z) (ho_23354 y z)))) (= x y))))) (let ((_let_1124 (forall ((x |u_(-> tptp.rat tptp.set_Pr958786334691620121nt_int)|) (y |u_(-> tptp.rat tptp.set_Pr958786334691620121nt_int)|)) (or (not (forall ((z tptp.rat)) (= (ho_26112 x z) (ho_26112 y z)))) (= x y))))) (let ((_let_1125 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_21317 x z) (ho_21317 y z)))) (= x y))))) (let ((_let_1126 (forall ((x |u_(-> _u_(-> tptp.rat tptp.rat)_ tptp.nat tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.rat tptp.rat)_ tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.rat)|)) (= (ho_21255 x z) (ho_21255 y z)))) (= x y))))) (let ((_let_1127 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_natural)_ _u_(-> tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural)|) (y |u_(-> _u_(-> tptp.nat tptp.code_natural)_ _u_(-> tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_natural)|)) (= (ho_11486 x z) (ho_11486 y z)))) (= x y))))) (let ((_let_1128 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_24465 x z) (ho_24465 y z)))) (= x y))))) (let ((_let_1129 (forall ((x |u_(-> tptp.nat tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.nat tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_21234 x z) (ho_21234 y z)))) (= x y))))) (let ((_let_1130 (forall ((x |u_(-> tptp.array_nat tptp.list_nat tptp.nat tptp.assn)|) (y |u_(-> tptp.array_nat tptp.list_nat tptp.nat tptp.assn)|)) (or (not (forall ((z tptp.array_nat)) (= (ho_21057 x z) (ho_21057 y z)))) (= x y))))) (let ((_let_1131 (forall ((x |u_(-> tptp.list_nat tptp.nat tptp.assn)|) (y |u_(-> tptp.list_nat tptp.nat tptp.assn)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_21058 x z) (ho_21058 y z)))) (= x y))))) (let ((_let_1132 (forall ((x |u_(-> tptp.list_o tptp.nat tptp.assn)|) (y |u_(-> tptp.list_o tptp.nat tptp.assn)|)) (or (not (forall ((z tptp.list_o)) (= (ho_21055 x z) (ho_21055 y z)))) (= x y))))) (let ((_let_1133 (forall ((x |u_(-> tptp.list_int tptp.nat tptp.assn)|) (y |u_(-> tptp.list_int tptp.nat tptp.assn)|)) (or (not (forall ((z tptp.list_int)) (= (ho_21052 x z) (ho_21052 y z)))) (= x y))))) (let ((_let_1134 (forall ((x |u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)|) (y |u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_21346 x z) (ho_21346 y z)))) (= x y))))) (let ((_let_1135 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_20960 x z) (ho_20960 y z)))) (= x y))))) (let ((_let_1136 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (= (ho_18753 x z) (ho_18753 y z)))) (= x y))))) (let ((_let_1137 (forall ((x |u_(-> tptp.set_o Bool)|) (y |u_(-> tptp.set_o Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_11199 x z) (ho_11199 y z)))) (= x y))))) (let ((_let_1138 (forall ((x |u_(-> tptp.set_int tptp.set_int tptp.set_int tptp.set_int tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.set_int tptp.set_int tptp.set_int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_20954 x z) (ho_20954 y z)))) (= x y))))) (let ((_let_1139 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.nat tptp.nat tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.nat tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int tptp.int)|)) (= (ho_18075 x z) (ho_18075 y z)))) (= x y))))) (let ((_let_1140 (forall ((x |u_(-> _u_(-> tptp.produc4166570645942440679at_nat Bool)_ _u_(-> tptp.produc4166570645942440679at_nat Bool)_ tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> _u_(-> tptp.produc4166570645942440679at_nat Bool)_ _u_(-> tptp.produc4166570645942440679at_nat Bool)_ tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc4166570645942440679at_nat Bool)|)) (= (ho_20852 x z) (ho_20852 y z)))) (= x y))))) (let ((_let_1141 (forall ((x |u_(-> _u_(-> tptp.produc4166570645942440679at_nat Bool)_ tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> _u_(-> tptp.produc4166570645942440679at_nat Bool)_ tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc4166570645942440679at_nat Bool)|)) (= (ho_20853 x z) (ho_20853 y z)))) (= x y))))) (let ((_let_1142 (forall ((x |u_(-> _u_(-> tptp.produc4166570645942440679at_nat tptp.nat)_ tptp.set_Pr8551490117392284871at_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.produc4166570645942440679at_nat tptp.nat)_ tptp.set_Pr8551490117392284871at_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.produc4166570645942440679at_nat tptp.nat)|)) (= (ho_25550 x z) (ho_25550 y z)))) (= x y))))) (let ((_let_1143 (forall ((x |u_(-> _u_(-> tptp.produc3843707927480180839at_nat Bool)_ _u_(-> tptp.produc3843707927480180839at_nat Bool)_ tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> _u_(-> tptp.produc3843707927480180839at_nat Bool)_ _u_(-> tptp.produc3843707927480180839at_nat Bool)_ tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc3843707927480180839at_nat Bool)|)) (= (ho_20849 x z) (ho_20849 y z)))) (= x y))))) (let ((_let_1144 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.int tptp.int)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_20662 x z) (ho_20662 y z)))) (= x y))))) (let ((_let_1145 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.code_integer tptp.code_integer)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z tptp.nat)) (= (ho_20660 x z) (ho_20660 y z)))) (= x y))))) (let ((_let_1146 (forall ((x |u_(-> tptp.int tptp.nat tptp.nat tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.nat tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_20627 x z) (ho_20627 y z)))) (= x y))))) (let ((_let_1147 (forall ((x |u_(-> tptp.produc3925858234332021118et_nat tptp.list_P2321686559999237006et_nat tptp.list_P2321686559999237006et_nat)|) (y |u_(-> tptp.produc3925858234332021118et_nat tptp.list_P2321686559999237006et_nat tptp.list_P2321686559999237006et_nat)|)) (or (not (forall ((z tptp.produc3925858234332021118et_nat)) (= (ho_24960 x z) (ho_24960 y z)))) (= x y))))) (let ((_let_1148 (forall ((x |u_(-> tptp.multis2468970476368604999at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.multis2468970476368604999at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.multis2468970476368604999at_nat)) (= (ho_18817 x z) (ho_18817 y z)))) (= x y))))) (let ((_let_1149 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.int)|)) (= (ho_12450 x z) (ho_12450 y z)))) (= x y))))) (let ((_let_1150 (forall ((x |u_(-> Bool tptp.set_o Bool Bool)|) (y |u_(-> Bool tptp.set_o Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_12648 x z) (ho_12648 y z)))) (= x y))))) (let ((_let_1151 (forall ((x |u_(-> tptp.code_integer tptp.nat tptp.nat tptp.code_integer tptp.code_integer)|) (y |u_(-> tptp.code_integer tptp.nat tptp.nat tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_20624 x z) (ho_20624 y z)))) (= x y))))) (let ((_let_1152 (forall ((x |u_(-> tptp.array_nat tptp.heap_e7401611519738050253t_unit tptp.produc1730305018825802663t_unit)|) (y |u_(-> tptp.array_nat tptp.heap_e7401611519738050253t_unit tptp.produc1730305018825802663t_unit)|)) (or (not (forall ((z tptp.array_nat)) (= (ho_25568 x z) (ho_25568 y z)))) (= x y))))) (let ((_let_1153 (forall ((x |u_(-> tptp.set_list_nat tptp.set_list_nat tptp.set_list_nat)|) (y |u_(-> tptp.set_list_nat tptp.set_list_nat tptp.set_list_nat)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_20508 x z) (ho_20508 y z)))) (= x y))))) (let ((_let_1154 (forall ((x |u_(-> tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int)|) (y |u_(-> tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int)|)) (or (not (forall ((z tptp.set_se6260736226359567993nt_int)) (= (ho_20504 x z) (ho_20504 y z)))) (= x y))))) (let ((_let_1155 (forall ((x |u_(-> tptp.set_set_nat tptp.set_set_nat tptp.set_set_nat)|) (y |u_(-> tptp.set_set_nat tptp.set_set_nat tptp.set_set_nat)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_20501 x z) (ho_20501 y z)))) (= x y))))) (let ((_let_1156 (forall ((x |u_(-> tptp.rat tptp.nat tptp.nat tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.nat tptp.nat tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_20434 x z) (ho_20434 y z)))) (= x y))))) (let ((_let_1157 (forall ((x |u_(-> tptp.list_o Bool)|) (y |u_(-> tptp.list_o Bool)|)) (or (not (forall ((z tptp.list_o)) (= (ho_20415 x z) (ho_20415 y z)))) (= x y))))) (let ((_let_1158 (forall ((x |u_(-> tptp.array_nat tptp.list_nat tptp.assn)|) (y |u_(-> tptp.array_nat tptp.list_nat tptp.assn)|)) (or (not (forall ((z tptp.array_nat)) (= (ho_20405 x z) (ho_20405 y z)))) (= x y))))) (let ((_let_1159 (forall ((x |u_(-> _u_(-> Bool tptp.int Bool)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> Bool tptp.int Bool)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.int Bool)|)) (= (ho_17316 x z) (ho_17316 y z)))) (= x y))))) (let ((_let_1160 (forall ((x |u_(-> tptp.option_num tptp.code_integer)|) (y |u_(-> tptp.option_num tptp.code_integer)|)) (or (not (forall ((z tptp.option_num)) (= (ho_25181 x z) (ho_25181 y z)))) (= x y))))) (let ((_let_1161 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.rat)_ tptp.set_Pr1261947904930325089at_nat tptp.rat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.rat)_ tptp.set_Pr1261947904930325089at_nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.rat)|)) (= (ho_25525 x z) (ho_25525 y z)))) (= x y))))) (let ((_let_1162 (forall ((x |u_(-> tptp.list_nat tptp.assn)|) (y |u_(-> tptp.list_nat tptp.assn)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_20406 x z) (ho_20406 y z)))) (= x y))))) (let ((_let_1163 (forall ((x |u_(-> _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.multis2468970476368604999at_nat)|)) (= (ho_18339 x z) (ho_18339 y z)))) (= x y))))) (let ((_let_1164 (forall ((x |u_(-> tptp.set_Product_prod_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_25080 x z) (ho_25080 y z)))) (= x y))))) (let ((_let_1165 (forall ((x |u_(-> tptp.array_nat tptp.list_nat tptp.nat tptp.nat tptp.assn)|) (y |u_(-> tptp.array_nat tptp.list_nat tptp.nat tptp.nat tptp.assn)|)) (or (not (forall ((z tptp.array_nat)) (= (ho_20401 x z) (ho_20401 y z)))) (= x y))))) (let ((_let_1166 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_13220 x z) (ho_13220 y z)))) (= x y))))) (let ((_let_1167 (forall ((x |u_(-> _u_(-> tptp.set_int tptp.set_int Bool)_ _u_(-> tptp.set_int tptp.set_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_int tptp.set_int Bool)_ _u_(-> tptp.set_int tptp.set_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_int tptp.set_int Bool)|)) (= (ho_24335 x z) (ho_24335 y z)))) (= x y))))) (let ((_let_1168 (forall ((x |u_(-> tptp.list_nat tptp.nat tptp.nat tptp.assn)|) (y |u_(-> tptp.list_nat tptp.nat tptp.nat tptp.assn)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_20402 x z) (ho_20402 y z)))) (= x y))))) (let ((_let_1169 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (= (ho_25114 x z) (ho_25114 y z)))) (= x y))))) (let ((_let_1170 (forall ((x |u_(-> tptp.array_o tptp.list_o tptp.assn)|) (y |u_(-> tptp.array_o tptp.list_o tptp.assn)|)) (or (not (forall ((z tptp.array_o)) (= (ho_20398 x z) (ho_20398 y z)))) (= x y))))) (let ((_let_1171 (forall ((x |u_(-> tptp.set_int _u_(-> Bool tptp.int Bool)_ Bool tptp.int)|) (y |u_(-> tptp.set_int _u_(-> Bool tptp.int Bool)_ Bool tptp.int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_17308 x z) (ho_17308 y z)))) (= x y))))) (let ((_let_1172 (forall ((x |u_(-> tptp.list_o tptp.assn)|) (y |u_(-> tptp.list_o tptp.assn)|)) (or (not (forall ((z tptp.list_o)) (= (ho_20399 x z) (ho_20399 y z)))) (= x y))))) (let ((_let_1173 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.int Bool)_ tptp.int tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.int Bool)_ tptp.int tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_12210 x z) (ho_12210 y z)))) (= x y))))) (let ((_let_1174 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_21542 x z) (ho_21542 y z)))) (= x y))))) (let ((_let_1175 (forall ((x |u_(-> tptp.list_o tptp.nat Bool tptp.assn)|) (y |u_(-> tptp.list_o tptp.nat Bool tptp.assn)|)) (or (not (forall ((z tptp.list_o)) (= (ho_20395 x z) (ho_20395 y z)))) (= x y))))) (let ((_let_1176 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.nat)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.nat)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_25555 x z) (ho_25555 y z)))) (= x y))))) (let ((_let_1177 (forall ((x |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_o)|) (y |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_o)|)) (or (not (forall ((z tptp.a)) (= (ho_25166 x z) (ho_25166 y z)))) (= x y))))) (let ((_let_1178 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)|)) (= (ho_17913 x z) (ho_17913 y z)))) (= x y))))) (let ((_let_1179 (forall ((x |u_(-> tptp.array_int tptp.list_int tptp.assn)|) (y |u_(-> tptp.array_int tptp.list_int tptp.assn)|)) (or (not (forall ((z tptp.array_int)) (= (ho_20391 x z) (ho_20391 y z)))) (= x y))))) (let ((_let_1180 (forall ((x |u_(-> tptp.list_int tptp.assn)|) (y |u_(-> tptp.list_int tptp.assn)|)) (or (not (forall ((z tptp.list_int)) (= (ho_20392 x z) (ho_20392 y z)))) (= x y))))) (let ((_let_1181 (forall ((x |u_(-> tptp.list_int tptp.nat tptp.int tptp.assn)|) (y |u_(-> tptp.list_int tptp.nat tptp.int tptp.assn)|)) (or (not (forall ((z tptp.list_int)) (= (ho_20388 x z) (ho_20388 y z)))) (= x y))))) (let ((_let_1182 (forall ((x |u_(-> tptp.set_list_nat Bool)|) (y |u_(-> tptp.set_list_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_11660 x z) (ho_11660 y z)))) (= x y))))) (let ((_let_1183 (forall ((x |u_(-> tptp.code_natural tptp.nat Bool)|) (y |u_(-> tptp.code_natural tptp.nat Bool)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_24655 x z) (ho_24655 y z)))) (= x y))))) (let ((_let_1184 (forall ((x |u_(-> _u_(-> tptp.set_int tptp.set_int tptp.set_int)_ tptp.set_int tptp.set_int tptp.set_int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.set_int tptp.set_int tptp.set_int)_ tptp.set_int tptp.set_int tptp.set_int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.set_int tptp.set_int tptp.set_int)|)) (= (ho_23083 x z) (ho_23083 y z)))) (= x y))))) (let ((_let_1185 (forall ((x |u_(-> tptp.nat tptp.nat tptp.assn)|) (y |u_(-> tptp.nat tptp.nat tptp.assn)|)) (or (not (forall ((z tptp.nat)) (= (ho_20403 x z) (ho_20403 y z)))) (= x y))))) (let ((_let_1186 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)_ tptp.int tptp.int tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)_ tptp.int tptp.int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_20377 x z) (ho_20377 y z)))) (= x y))))) (let ((_let_1187 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_26108 x z) (ho_26108 y z)))) (= x y))))) (let ((_let_1188 (forall ((x |u_(-> _u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)_ tptp.int tptp.int tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)_ tptp.int tptp.int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)|)) (= (ho_20378 x z) (ho_20378 y z)))) (= x y))))) (let ((_let_1189 (forall ((x |u_(-> _u_(-> tptp.int tptp.assn)_ _u_(-> tptp.int tptp.assn)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.assn)_ _u_(-> tptp.int tptp.assn)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.assn)|)) (= (ho_17164 x z) (ho_17164 y z)))) (= x y))))) (let ((_let_1190 (forall ((x |u_(-> tptp.set_nat tptp.set_nat tptp.set_set_nat)|) (y |u_(-> tptp.set_nat tptp.set_nat tptp.set_set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_25353 x z) (ho_25353 y z)))) (= x y))))) (let ((_let_1191 (forall ((x |u_(-> tptp.int tptp.int tptp.list_int tptp.list_int)|) (y |u_(-> tptp.int tptp.int tptp.list_int tptp.list_int)|)) (or (not (forall ((z tptp.int)) (= (ho_20374 x z) (ho_20374 y z)))) (= x y))))) (let ((_let_1192 (forall ((x |u_(-> tptp.rat tptp.num tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.rat tptp.num tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_20358 x z) (ho_20358 y z)))) (= x y))))) (let ((_let_1193 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_12610 x z) (ho_12610 y z)))) (= x y))))) (let ((_let_1194 (forall ((x |u_(-> _u_(-> tptp.num tptp.num Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num Bool)|)) (= (ho_25773 x z) (ho_25773 y z)))) (= x y))))) (let ((_let_1195 (forall ((x |u_(-> _u_(-> tptp.b tptp.set_Pr4389693562480114009it_nat)_ tptp.set_Pr5508209795250834101it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.set_Pr4389693562480114009it_nat)_ tptp.set_Pr5508209795250834101it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.set_Pr4389693562480114009it_nat)|)) (= (ho_25037 x z) (ho_25037 y z)))) (= x y))))) (let ((_let_1196 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_11664 x z) (ho_11664 y z)))) (= x y))))) (let ((_let_1197 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.int tptp.int tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.int tptp.int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_20321 x z) (ho_20321 y z)))) (= x y))))) (let ((_let_1198 (forall ((x |u_(-> tptp.int tptp.int tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.int tptp.int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_20322 x z) (ho_20322 y z)))) (= x y))))) (let ((_let_1199 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_20318 x z) (ho_20318 y z)))) (= x y))))) (let ((_let_1200 (forall ((x |u_(-> tptp.assn tptp.heap_Time_Heap_o _u_(-> Bool tptp.assn)_ Bool)|) (y |u_(-> tptp.assn tptp.heap_Time_Heap_o _u_(-> Bool tptp.assn)_ Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_24721 x z) (ho_24721 y z)))) (= x y))))) (let ((_let_1201 (forall ((x |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.nat tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.nat tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.assn)|)) (= (ho_23795 x z) (ho_23795 y z)))) (= x y))))) (let ((_let_1202 (forall ((x |u_(-> tptp.produc2207270350733924475it_nat Bool)|) (y |u_(-> tptp.produc2207270350733924475it_nat Bool)|)) (or (not (forall ((z tptp.produc2207270350733924475it_nat)) (= (ho_24432 x z) (ho_24432 y z)))) (= x y))))) (let ((_let_1203 (forall ((x |u_(-> tptp.num tptp.num tptp.product_prod_nat_nat)|) (y |u_(-> tptp.num tptp.num tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.num)) (= (ho_20133 x z) (ho_20133 y z)))) (= x y))))) (let ((_let_1204 (forall ((x |u_(-> tptp.num tptp.product_prod_nat_nat)|) (y |u_(-> tptp.num tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.num)) (= (ho_20134 x z) (ho_20134 y z)))) (= x y))))) (let ((_let_1205 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.set_set_nat)_ tptp.product_prod_int_int tptp.set_set_nat)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.set_set_nat)_ tptp.product_prod_int_int tptp.set_set_nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.set_set_nat)|)) (= (ho_25143 x z) (ho_25143 y z)))) (= x y))))) (let ((_let_1206 (forall ((x |u_(-> tptp.option_nat tptp.option_nat)|) (y |u_(-> tptp.option_nat tptp.option_nat)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_22201 x z) (ho_22201 y z)))) (= x y))))) (let ((_let_1207 (forall ((x |u_(-> tptp.array_nat tptp.heap_Time_Heap_nat)|) (y |u_(-> tptp.array_nat tptp.heap_Time_Heap_nat)|)) (or (not (forall ((z tptp.array_nat)) (= (ho_24693 x z) (ho_24693 y z)))) (= x y))))) (let ((_let_1208 (forall ((x |u_(-> tptp.produc5835291356934675326atural tptp.produc5835291356934675326atural)|) (y |u_(-> tptp.produc5835291356934675326atural tptp.produc5835291356934675326atural)|)) (or (not (forall ((z tptp.produc5835291356934675326atural)) (= (ho_12600 x z) (ho_12600 y z)))) (= x y))))) (let ((_let_1209 (forall ((x |u_(-> tptp.produc2732055786443039994et_nat tptp.produc3925858234332021118et_nat)|) (y |u_(-> tptp.produc2732055786443039994et_nat tptp.produc3925858234332021118et_nat)|)) (or (not (forall ((z tptp.produc2732055786443039994et_nat)) (= (ho_25413 x z) (ho_25413 y z)))) (= x y))))) (let ((_let_1210 (forall ((x |u_(-> _u_(-> Bool tptp.int)_ _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> Bool tptp.int)_ _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.int)|)) (= (ho_20091 x z) (ho_20091 y z)))) (= x y))))) (let ((_let_1211 (forall ((x |u_(-> tptp.nat tptp.list_nat tptp.list_P6011104703257516679at_nat)|) (y |u_(-> tptp.nat tptp.list_nat tptp.list_P6011104703257516679at_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_24846 x z) (ho_24846 y z)))) (= x y))))) (let ((_let_1212 (forall ((x |u_(-> tptp.produc7538756082594784606_nat_b Bool)|) (y |u_(-> tptp.produc7538756082594784606_nat_b Bool)|)) (or (not (forall ((z tptp.produc7538756082594784606_nat_b)) (= (ho_25254 x z) (ho_25254 y z)))) (= x y))))) (let ((_let_1213 (forall ((x |u_(-> tptp.array_Product_unit tptp.nat tptp.heap_T5738788834812785303t_unit)|) (y |u_(-> tptp.array_Product_unit tptp.nat tptp.heap_T5738788834812785303t_unit)|)) (or (not (forall ((z tptp.array_Product_unit)) (= (ho_24738 x z) (ho_24738 y z)))) (= x y))))) (let ((_let_1214 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_nat)_ tptp.produc3260487557148687353it_nat tptp.set_nat)|) (y |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_nat)_ tptp.produc3260487557148687353it_nat tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_nat)|)) (= (ho_25172 x z) (ho_25172 y z)))) (= x y))))) (let ((_let_1215 (forall ((x |u_(-> tptp.array_Product_unit tptp.list_Product_unit tptp.assn)|) (y |u_(-> tptp.array_Product_unit tptp.list_Product_unit tptp.assn)|)) (or (not (forall ((z tptp.array_Product_unit)) (= (ho_24735 x z) (ho_24735 y z)))) (= x y))))) (let ((_let_1216 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_20083 x z) (ho_20083 y z)))) (= x y))))) (let ((_let_1217 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.int)|)) (= (ho_20080 x z) (ho_20080 y z)))) (= x y))))) (let ((_let_1218 (forall ((x |u_(-> tptp.rat tptp.int tptp.int Bool)|) (y |u_(-> tptp.rat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_11540 x z) (ho_11540 y z)))) (= x y))))) (let ((_let_1219 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (= (ho_20081 x z) (ho_20081 y z)))) (= x y))))) (let ((_let_1220 (forall ((x |u_(-> tptp.list_int tptp.nat tptp.int)|) (y |u_(-> tptp.list_int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_15659 x z) (ho_15659 y z)))) (= x y))))) (let ((_let_1221 (forall ((x |u_(-> tptp.option_assn Bool)|) (y |u_(-> tptp.option_assn Bool)|)) (or (not (forall ((z tptp.option_assn)) (= (ho_24203 x z) (ho_24203 y z)))) (= x y))))) (let ((_let_1222 (forall ((x |u_(-> tptp.num tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.num tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.num)) (= (ho_19915 x z) (ho_19915 y z)))) (= x y))))) (let ((_let_1223 (forall ((x |u_(-> Bool tptp.product_prod_int_int)|) (y |u_(-> Bool tptp.product_prod_int_int)|)) (or (not (forall ((z Bool)) (= (ho_20075 x z) (ho_20075 y z)))) (= x y))))) (let ((_let_1224 (forall ((x |u_(-> Bool _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.product_prod_int_int)|) (y |u_(-> Bool _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z Bool)) (= (ho_18762 x z) (ho_18762 y z)))) (= x y))))) (let ((_let_1225 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_20071 x z) (ho_20071 y z)))) (= x y))))) (let ((_let_1226 (forall ((x |u_(-> _u_(-> Bool tptp.code_integer)_ Bool Bool)|) (y |u_(-> _u_(-> Bool tptp.code_integer)_ Bool Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.code_integer)|)) (= (ho_15134 x z) (ho_15134 y z)))) (= x y))))) (let ((_let_1227 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|)) (= (ho_20069 x z) (ho_20069 y z)))) (= x y))))) (let ((_let_1228 (forall ((x |u_(-> _u_(-> tptp.nat tptp.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)|) (y |u_(-> _u_(-> tptp.nat tptp.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)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_20056 x z) (ho_20056 y z)))) (= x y))))) (let ((_let_1229 (forall ((x |u_(-> tptp.option4065278094766928714it_nat tptp.nat)|) (y |u_(-> tptp.option4065278094766928714it_nat tptp.nat)|)) (or (not (forall ((z tptp.option4065278094766928714it_nat)) (= (ho_24662 x z) (ho_24662 y z)))) (= x y))))) (let ((_let_1230 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)_ tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)_ tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|)) (= (ho_20054 x z) (ho_20054 y z)))) (= x y))))) (let ((_let_1231 (forall ((x |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer)|)) (= (ho_24587 x z) (ho_24587 y z)))) (= x y))))) (let ((_let_1232 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_20036 x z) (ho_20036 y z)))) (= x y))))) (let ((_let_1233 (forall ((x |u_(-> _u_(-> tptp.num tptp.num)_ tptp.num tptp.nat)|) (y |u_(-> _u_(-> tptp.num tptp.num)_ tptp.num tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num)|)) (= (ho_25758 x z) (ho_25758 y z)))) (= x y))))) (let ((_let_1234 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_20034 x z) (ho_20034 y z)))) (= x y))))) (let ((_let_1235 (forall ((x |u_(-> _u_(-> tptp.option_num tptp.option_num)_ tptp.option_num tptp.nat)|) (y |u_(-> _u_(-> tptp.option_num tptp.option_num)_ tptp.option_num tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.option_num tptp.option_num)|)) (= (ho_25761 x z) (ho_25761 y z)))) (= x y))))) (let ((_let_1236 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|)) (= (ho_20028 x z) (ho_20028 y z)))) (= x y))))) (let ((_let_1237 (forall ((x |u_(-> tptp.nat tptp.int tptp.nat tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.int tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_19992 x z) (ho_19992 y z)))) (= x y))))) (let ((_let_1238 (forall ((x |u_(-> tptp.nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> tptp.nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_24916 x z) (ho_24916 y z)))) (= x y))))) (let ((_let_1239 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.nat tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.nat tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_11443 x z) (ho_11443 y z)))) (= x y))))) (let ((_let_1240 (forall ((x |u_(-> tptp.nat tptp.nat tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.nat tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_19981 x z) (ho_19981 y z)))) (= x y))))) (let ((_let_1241 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_11186 x z) (ho_11186 y z)))) (= x y))))) (let ((_let_1242 (forall ((x |u_(-> tptp.int Bool Bool)|) (y |u_(-> tptp.int Bool Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_11579 x z) (ho_11579 y z)))) (= x y))))) (let ((_let_1243 (forall ((x |u_(-> tptp.heap_T5738788834812785303t_unit _u_(-> tptp.product_unit tptp.heap_T5738788834812785303t_unit)_ tptp.heap_T5738788834812785303t_unit)|) (y |u_(-> tptp.heap_T5738788834812785303t_unit _u_(-> tptp.product_unit tptp.heap_T5738788834812785303t_unit)_ tptp.heap_T5738788834812785303t_unit)|)) (or (not (forall ((z tptp.heap_T5738788834812785303t_unit)) (= (ho_24311 x z) (ho_24311 y z)))) (= x y))))) (let ((_let_1244 (forall ((x |u_(-> _u_(-> tptp.b tptp.heap_Time_Heap_a)_ tptp.b tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.heap_Time_Heap_a)_ tptp.b tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.heap_Time_Heap_a)|)) (= (ho_13106 x z) (ho_13106 y z)))) (= x y))))) (let ((_let_1245 (forall ((x |u_(-> tptp.num tptp.nat tptp.nat)|) (y |u_(-> tptp.num tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.num)) (= (ho_19895 x z) (ho_19895 y z)))) (= x y))))) (let ((_let_1246 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.code_natural)_ Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.code_natural)_ Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_15339 x z) (ho_15339 y z)))) (= x y))))) (let ((_let_1247 (forall ((x |u_(-> tptp.nat tptp.nat tptp.list_o tptp.list_o)|) (y |u_(-> tptp.nat tptp.nat tptp.list_o tptp.list_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_24705 x z) (ho_24705 y z)))) (= x y))))) (let ((_let_1248 (forall ((x |u_(-> _u_(-> tptp.b tptp.heap_Time_Heap_b)_ tptp.heap_Time_Heap_b tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.heap_Time_Heap_b)_ tptp.heap_Time_Heap_b tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.heap_Time_Heap_b)|)) (= (ho_19885 x z) (ho_19885 y z)))) (= x y))))) (let ((_let_1249 (forall ((x |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)_ tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)_ tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)|)) (= (ho_19883 x z) (ho_19883 y z)))) (= x y))))) (let ((_let_1250 (forall ((x |u_(-> tptp.product_prod_int_int tptp.set_o)|) (y |u_(-> tptp.product_prod_int_int tptp.set_o)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_25131 x z) (ho_25131 y z)))) (= x y))))) (let ((_let_1251 (forall ((x |u_(-> _u_(-> Bool tptp.int Bool)_ Bool tptp.int)|) (y |u_(-> _u_(-> Bool tptp.int Bool)_ Bool tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.int Bool)|)) (= (ho_17309 x z) (ho_17309 y z)))) (= x y))))) (let ((_let_1252 (forall ((x |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)_ tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)_ tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)|)) (= (ho_19880 x z) (ho_19880 y z)))) (= x y))))) (let ((_let_1253 (forall ((x |u_(-> _u_(-> tptp.a tptp.heap_Time_Heap_b)_ tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.heap_Time_Heap_b)_ tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.heap_Time_Heap_b)|)) (= (ho_19876 x z) (ho_19876 y z)))) (= x y))))) (let ((_let_1254 (forall ((x |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.option4065278094766928714it_nat)_ tptp.option3562590408128118217it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.option4065278094766928714it_nat)_ tptp.option3562590408128118217it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3260487557148687353it_nat tptp.option4065278094766928714it_nat)|)) (= (ho_19873 x z) (ho_19873 y z)))) (= x y))))) (let ((_let_1255 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer)|)) (= (ho_17182 x z) (ho_17182 y z)))) (= x y))))) (let ((_let_1256 (forall ((x |u_(-> tptp.set_nat tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit Bool)|) (y |u_(-> tptp.set_nat tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_24267 x z) (ho_24267 y z)))) (= x y))))) (let ((_let_1257 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_25334 x z) (ho_25334 y z)))) (= x y))))) (let ((_let_1258 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)_ tptp.produc3260487557148687353it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)_ tptp.produc3260487557148687353it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)|)) (= (ho_19870 x z) (ho_19870 y z)))) (= x y))))) (let ((_let_1259 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_26151 x z) (ho_26151 y z)))) (= x y))))) (let ((_let_1260 (forall ((x |u_(-> tptp.option3562590408128118217it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.option3562590408128118217it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.option3562590408128118217it_nat)) (= (ho_19874 x z) (ho_19874 y z)))) (= x y))))) (let ((_let_1261 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.assn)_ _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.assn)_ _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn)|)) (or (not (forall ((z tptp.nat)) (= (ho_15800 x z) (ho_15800 y z)))) (= x y))))) (let ((_let_1262 (forall ((x |u_(-> tptp.heap_Time_Heap_b tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.heap_Time_Heap_b tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.heap_Time_Heap_b)) (= (ho_19867 x z) (ho_19867 y z)))) (= x y))))) (let ((_let_1263 (forall ((x |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.option3562590408128118217it_nat)_ tptp.option4065278094766928714it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.option3562590408128118217it_nat)_ tptp.option4065278094766928714it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc7388388658123137530it_nat tptp.option3562590408128118217it_nat)|)) (= (ho_19863 x z) (ho_19863 y z)))) (= x y))))) (let ((_let_1264 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_26150 x z) (ho_26150 y z)))) (= x y))))) (let ((_let_1265 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_17142 x z) (ho_17142 y z)))) (= x y))))) (let ((_let_1266 (forall ((x |u_(-> tptp.option3562590408128118217it_nat _u_(-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)_ tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.option3562590408128118217it_nat _u_(-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)_ tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.option3562590408128118217it_nat)) (= (ho_19854 x z) (ho_19854 y z)))) (= x y))))) (let ((_let_1267 (forall ((x |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)_ tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)_ tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)|)) (= (ho_19855 x z) (ho_19855 y z)))) (= x y))))) (let ((_let_1268 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)_ tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)_ tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)|)) (= (ho_19852 x z) (ho_19852 y z)))) (= x y))))) (let ((_let_1269 (forall ((x |u_(-> _u_(-> tptp.produc2207270350733924475it_nat tptp.produc2207270350733924475it_nat Bool)_ tptp.produc2207270350733924475it_nat Bool)|) (y |u_(-> _u_(-> tptp.produc2207270350733924475it_nat tptp.produc2207270350733924475it_nat Bool)_ tptp.produc2207270350733924475it_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc2207270350733924475it_nat tptp.produc2207270350733924475it_nat Bool)|)) (= (ho_24431 x z) (ho_24431 y z)))) (= x y))))) (let ((_let_1270 (forall ((x |u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.num)_ tptp.num tptp.int)|) (y |u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.num)_ tptp.num tptp.int)|)) (or (not (forall ((z |u_(-> tptp.num tptp.int)|)) (= (ho_22673 x z) (ho_22673 y z)))) (= x y))))) (let ((_let_1271 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_17358 x z) (ho_17358 y z)))) (= x y))))) (let ((_let_1272 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_19704 x z) (ho_19704 y z)))) (= x y))))) (let ((_let_1273 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_19516 x z) (ho_19516 y z)))) (= x y))))) (let ((_let_1274 (forall ((x |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.int)_ _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer tptp.int)|) (y |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.int)_ _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer tptp.int)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_15917 x z) (ho_15917 y z)))) (= x y))))) (let ((_let_1275 (forall ((x |u_(-> tptp.set_o Bool tptp.set_o Bool Bool)|) (y |u_(-> tptp.set_o Bool tptp.set_o Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_19307 x z) (ho_19307 y z)))) (= x y))))) (let ((_let_1276 (forall ((x |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.b tptp.produc8449588929630179473_nat_b)|) (y |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.b tptp.produc8449588929630179473_nat_b)|)) (or (not (forall ((z |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (= (ho_25245 x z) (ho_25245 y z)))) (= x y))))) (let ((_let_1277 (forall ((x |u_(-> tptp.set_se6260736226359567993nt_int tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.set_se6260736226359567993nt_int tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.set_se6260736226359567993nt_int)) (= (ho_19302 x z) (ho_19302 y z)))) (= x y))))) (let ((_let_1278 (forall ((x |u_(-> tptp.set_set_nat tptp.set_nat tptp.set_set_nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_set_nat tptp.set_nat tptp.set_set_nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_19297 x z) (ho_19297 y z)))) (= x y))))) (let ((_let_1279 (forall ((x |u_(-> tptp.set_int tptp.set_int tptp.produc2115011035271226405et_int)|) (y |u_(-> tptp.set_int tptp.set_int tptp.produc2115011035271226405et_int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_25610 x z) (ho_25610 y z)))) (= x y))))) (let ((_let_1280 (forall ((x |u_(-> tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat)|) (y |u_(-> tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat)|)) (or (not (forall ((z tptp.set_Pr8536935166611901872et_nat)) (= (ho_21380 x z) (ho_21380 y z)))) (= x y))))) (let ((_let_1281 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_19246 x z) (ho_19246 y z)))) (= x y))))) (let ((_let_1282 (forall ((x |u_(-> tptp.produc3843707927480180839at_nat _u_(-> tptp.produc3843707927480180839at_nat Bool)_ tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.produc3843707927480180839at_nat _u_(-> tptp.produc3843707927480180839at_nat Bool)_ tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.produc3843707927480180839at_nat)) (= (ho_19185 x z) (ho_19185 y z)))) (= x y))))) (let ((_let_1283 (forall ((x |u_(-> tptp.produc4166570645942440679at_nat tptp.set_Pr8551490117392284871at_nat Bool)|) (y |u_(-> tptp.produc4166570645942440679at_nat tptp.set_Pr8551490117392284871at_nat Bool)|)) (or (not (forall ((z tptp.produc4166570645942440679at_nat)) (= (ho_11266 x z) (ho_11266 y z)))) (= x y))))) (let ((_let_1284 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer Bool)_ tptp.int tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer Bool)_ tptp.int tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer Bool)|)) (= (ho_11563 x z) (ho_11563 y z)))) (= x y))))) (let ((_let_1285 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_19161 x z) (ho_19161 y z)))) (= x y))))) (let ((_let_1286 (forall ((x |u_(-> _u_(-> Bool Bool)_ _u_(-> Bool tptp.rat)_ Bool tptp.rat)|) (y |u_(-> _u_(-> Bool Bool)_ _u_(-> Bool tptp.rat)_ Bool tptp.rat)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_17057 x z) (ho_17057 y z)))) (= x y))))) (let ((_let_1287 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.set_o)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.set_o)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_25154 x z) (ho_25154 y z)))) (= x y))))) (let ((_let_1288 (forall ((x |u_(-> tptp.int _u_(-> tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> tptp.int _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_19157 x z) (ho_19157 y z)))) (= x y))))) (let ((_let_1289 (forall ((x |u_(-> _u_(-> tptp.rat tptp.rat Bool)_ _u_(-> tptp.rat tptp.rat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.rat tptp.rat Bool)_ _u_(-> tptp.rat tptp.rat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.rat Bool)|)) (= (ho_24339 x z) (ho_24339 y z)))) (= x y))))) (let ((_let_1290 (forall ((x |u_(-> _u_(-> tptp.produc3843707927480180839at_nat tptp.nat)_ tptp.set_Pr4329608150637261639at_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.produc3843707927480180839at_nat tptp.nat)_ tptp.set_Pr4329608150637261639at_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.produc3843707927480180839at_nat tptp.nat)|)) (= (ho_25554 x z) (ho_25554 y z)))) (= x y))))) (let ((_let_1291 (forall ((x |u_(-> tptp.list_nat tptp.set_list_nat tptp.set_list_nat)|) (y |u_(-> tptp.list_nat tptp.set_list_nat tptp.set_list_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_19149 x z) (ho_19149 y z)))) (= x y))))) (let ((_let_1292 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|)) (= (ho_24356 x z) (ho_24356 y z)))) (= x y))))) (let ((_let_1293 (forall ((x |u_(-> tptp.set_list_nat tptp.set_list_nat)|) (y |u_(-> tptp.set_list_nat tptp.set_list_nat)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_19150 x z) (ho_19150 y z)))) (= x y))))) (let ((_let_1294 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_19145 x z) (ho_19145 y z)))) (= x y))))) (let ((_let_1295 (forall ((x |u_(-> tptp.set_Pr5488025237498180813et_nat Bool)|) (y |u_(-> tptp.set_Pr5488025237498180813et_nat Bool)|)) (or (not (forall ((z tptp.set_Pr5488025237498180813et_nat)) (= (ho_25604 x z) (ho_25604 y z)))) (= x y))))) (let ((_let_1296 (forall ((x |u_(-> tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int)|) (y |u_(-> tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int)|)) (or (not (forall ((z tptp.set_se6260736226359567993nt_int)) (= (ho_19146 x z) (ho_19146 y z)))) (= x y))))) (let ((_let_1297 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.option_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.option_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_23576 x z) (ho_23576 y z)))) (= x y))))) (let ((_let_1298 (forall ((x |u_(-> tptp.set_set_nat tptp.set_set_nat)|) (y |u_(-> tptp.set_set_nat tptp.set_set_nat)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_19142 x z) (ho_19142 y z)))) (= x y))))) (let ((_let_1299 (forall ((x |u_(-> _u_(-> tptp.rat tptp.rat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.rat tptp.rat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.rat Bool)|)) (= (ho_24340 x z) (ho_24340 y z)))) (= x y))))) (let ((_let_1300 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.nat)_ tptp.set_set_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.set_nat tptp.nat)_ tptp.set_set_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.nat)|)) (= (ho_15161 x z) (ho_15161 y z)))) (= x y))))) (let ((_let_1301 (forall ((x |u_(-> tptp.produc4166570645942440679at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)|) (y |u_(-> tptp.produc4166570645942440679at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)|)) (or (not (forall ((z tptp.produc4166570645942440679at_nat)) (= (ho_19114 x z) (ho_19114 y z)))) (= x y))))) (let ((_let_1302 (forall ((x |u_(-> tptp.set_o tptp.set_o)|) (y |u_(-> tptp.set_o tptp.set_o)|)) (or (not (forall ((z tptp.set_o)) (= (ho_19108 x z) (ho_19108 y z)))) (= x y))))) (let ((_let_1303 (forall ((x |u_(-> _u_(-> Bool tptp.nat tptp.int)_ tptp.set_nat _u_(-> Bool tptp.nat Bool)_ Bool tptp.int)|) (y |u_(-> _u_(-> Bool tptp.nat tptp.int)_ tptp.set_nat _u_(-> Bool tptp.nat Bool)_ Bool tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.nat tptp.int)|)) (= (ho_17328 x z) (ho_17328 y z)))) (= x y))))) (let ((_let_1304 (forall ((x |u_(-> tptp.set_nat tptp.set_nat)|) (y |u_(-> tptp.set_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_19105 x z) (ho_19105 y z)))) (= x y))))) (let ((_let_1305 (forall ((x |u_(-> tptp.int tptp.set_int tptp.set_int)|) (y |u_(-> tptp.int tptp.set_int tptp.set_int)|)) (or (not (forall ((z tptp.int)) (= (ho_19102 x z) (ho_19102 y z)))) (= x y))))) (let ((_let_1306 (forall ((x |u_(-> tptp.list_P7438302566501821706it_nat tptp.list_P7438302566501821706it_nat)|) (y |u_(-> tptp.list_P7438302566501821706it_nat tptp.list_P7438302566501821706it_nat)|)) (or (not (forall ((z tptp.list_P7438302566501821706it_nat)) (= (ho_24976 x z) (ho_24976 y z)))) (= x y))))) (let ((_let_1307 (forall ((x |u_(-> _u_(-> tptp.num tptp.num)_ _u_(-> tptp.num tptp.num)_ tptp.num tptp.num)|) (y |u_(-> _u_(-> tptp.num tptp.num)_ _u_(-> tptp.num tptp.num)_ tptp.num tptp.num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num)|)) (= (ho_22667 x z) (ho_22667 y z)))) (= x y))))) (let ((_let_1308 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (= (ho_18701 x z) (ho_18701 y z)))) (= x y))))) (let ((_let_1309 (forall ((x |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ tptp.rat Bool)|) (y |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ tptp.rat Bool)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_25982 x z) (ho_25982 y z)))) (= x y))))) (let ((_let_1310 (forall ((x |u_(-> tptp.int tptp.set_int tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.set_int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_19054 x z) (ho_19054 y z)))) (= x y))))) (let ((_let_1311 (forall ((x |u_(-> tptp.set_nat tptp.set_nat tptp.nat tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_nat tptp.nat tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_18975 x z) (ho_18975 y z)))) (= x y))))) (let ((_let_1312 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_18969 x z) (ho_18969 y z)))) (= x y))))) (let ((_let_1313 (forall ((x |u_(-> tptp.list_P131111800688179804it_nat tptp.list_P131111800688179804it_nat)|) (y |u_(-> tptp.list_P131111800688179804it_nat tptp.list_P131111800688179804it_nat)|)) (or (not (forall ((z tptp.list_P131111800688179804it_nat)) (= (ho_24979 x z) (ho_24979 y z)))) (= x y))))) (let ((_let_1314 (forall ((x |u_(-> tptp.a tptp.set_Pr4389693562480114009it_nat)|) (y |u_(-> tptp.a tptp.set_Pr4389693562480114009it_nat)|)) (or (not (forall ((z tptp.a)) (= (ho_25044 x z) (ho_25044 y z)))) (= x y))))) (let ((_let_1315 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.produc7248412053542808358at_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.produc7248412053542808358at_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_24596 x z) (ho_24596 y z)))) (= x y))))) (let ((_let_1316 (forall ((x |u_(-> tptp.rat tptp.nat)|) (y |u_(-> tptp.rat tptp.nat)|)) (or (not (forall ((z tptp.rat)) (= (ho_24298 x z) (ho_24298 y z)))) (= x y))))) (let ((_let_1317 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_18932 x z) (ho_18932 y z)))) (= x y))))) (let ((_let_1318 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_17125 x z) (ho_17125 y z)))) (= x y))))) (let ((_let_1319 (forall ((x |u_(-> tptp.set_nat tptp.nat tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.nat tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_18925 x z) (ho_18925 y z)))) (= x y))))) (let ((_let_1320 (forall ((x |u_(-> tptp.nat tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_12325 x z) (ho_12325 y z)))) (= x y))))) (let ((_let_1321 (forall ((x |u_(-> tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.produc3843707927480180839at_nat)) (= (ho_18883 x z) (ho_18883 y z)))) (= x y))))) (let ((_let_1322 (forall ((x |u_(-> tptp.num tptp.produc7388388658123137530it_nat)|) (y |u_(-> tptp.num tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z tptp.num)) (= (ho_25643 x z) (ho_25643 y z)))) (= x y))))) (let ((_let_1323 (forall ((x |u_(-> _u_(-> tptp.num tptp.code_integer)_ tptp.option_num tptp.code_integer)|) (y |u_(-> _u_(-> tptp.num tptp.code_integer)_ tptp.option_num tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.num tptp.code_integer)|)) (= (ho_25180 x z) (ho_25180 y z)))) (= x y))))) (let ((_let_1324 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_18878 x z) (ho_18878 y z)))) (= x y))))) (let ((_let_1325 (forall ((x |u_(-> tptp.set_Code_integer tptp.set_Code_integer tptp.set_Code_integer)|) (y |u_(-> tptp.set_Code_integer tptp.set_Code_integer tptp.set_Code_integer)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_17409 x z) (ho_17409 y z)))) (= x y))))) (let ((_let_1326 (forall ((x |u_(-> tptp.product_prod_nat_int tptp.list_P3521021558325789923at_int tptp.list_P3521021558325789923at_int)|) (y |u_(-> tptp.product_prod_nat_int tptp.list_P3521021558325789923at_int tptp.list_P3521021558325789923at_int)|)) (or (not (forall ((z tptp.product_prod_nat_int)) (= (ho_24948 x z) (ho_24948 y z)))) (= x y))))) (let ((_let_1327 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_18879 x z) (ho_18879 y z)))) (= x y))))) (let ((_let_1328 (forall ((x |u_(-> tptp.list_P362550909693114634et_nat tptp.list_P362550909693114634et_nat)|) (y |u_(-> tptp.list_P362550909693114634et_nat tptp.list_P362550909693114634et_nat)|)) (or (not (forall ((z tptp.list_P362550909693114634et_nat)) (= (ho_24973 x z) (ho_24973 y z)))) (= x y))))) (let ((_let_1329 (forall ((x |u_(-> tptp.set_o Bool Bool Bool)|) (y |u_(-> tptp.set_o Bool Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_18859 x z) (ho_18859 y z)))) (= x y))))) (let ((_let_1330 (forall ((x |u_(-> _u_(-> Bool Bool)_ _u_(-> Bool Bool)_ Bool Bool)|) (y |u_(-> _u_(-> Bool Bool)_ _u_(-> Bool Bool)_ Bool Bool)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_18857 x z) (ho_18857 y z)))) (= x y))))) (let ((_let_1331 (forall ((x |u_(-> _u_(-> tptp.option_Code_integer tptp.option_Code_integer)_ tptp.option_Code_integer tptp.option7428179582072448501nteger)|) (y |u_(-> _u_(-> tptp.option_Code_integer tptp.option_Code_integer)_ tptp.option_Code_integer tptp.option7428179582072448501nteger)|)) (or (not (forall ((z |u_(-> tptp.option_Code_integer tptp.option_Code_integer)|)) (= (ho_25719 x z) (ho_25719 y z)))) (= x y))))) (let ((_let_1332 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_18845 x z) (ho_18845 y z)))) (= x y))))) (let ((_let_1333 (forall ((x |u_(-> tptp.array_o tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat)|) (y |u_(-> tptp.array_o tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat)|)) (or (not (forall ((z tptp.array_o)) (= (ho_11157 x z) (ho_11157 y z)))) (= x y))))) (let ((_let_1334 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int tptp.list_int tptp.rat tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int tptp.list_int tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_18682 x z) (ho_18682 y z)))) (= x y))))) (let ((_let_1335 (forall ((x |u_(-> tptp.int tptp.set_int tptp.set_int tptp.int Bool)|) (y |u_(-> tptp.int tptp.set_int tptp.set_int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_18843 x z) (ho_18843 y z)))) (= x y))))) (let ((_let_1336 (forall ((x |u_(-> tptp.set_se6260736226359567993nt_int _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.set_se6260736226359567993nt_int _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.set_se6260736226359567993nt_int)) (= (ho_21548 x z) (ho_21548 y z)))) (= x y))))) (let ((_let_1337 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr1261947904930325089at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr1261947904930325089at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_18812 x z) (ho_18812 y z)))) (= x y))))) (let ((_let_1338 (forall ((x |u_(-> tptp.list_int tptp.set_int)|) (y |u_(-> tptp.list_int tptp.set_int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_25796 x z) (ho_25796 y z)))) (= x y))))) (let ((_let_1339 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.option8963830502488799655at_nat tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.option8963830502488799655at_nat tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_24531 x z) (ho_24531 y z)))) (= x y))))) (let ((_let_1340 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.produc1273031398460193109it_nat)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.produc1273031398460193109it_nat)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_24885 x z) (ho_24885 y z)))) (= x y))))) (let ((_let_1341 (forall ((x |u_(-> tptp.nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_18805 x z) (ho_18805 y z)))) (= x y))))) (let ((_let_1342 (forall ((x |u_(-> tptp.filter_set_nat tptp.filter_nat Bool)|) (y |u_(-> tptp.filter_set_nat tptp.filter_nat Bool)|)) (or (not (forall ((z tptp.filter_set_nat)) (= (ho_26039 x z) (ho_26039 y z)))) (= x y))))) (let ((_let_1343 (forall ((x |u_(-> tptp.list_P6011104703257516679at_nat tptp.nat)|) (y |u_(-> tptp.list_P6011104703257516679at_nat tptp.nat)|)) (or (not (forall ((z tptp.list_P6011104703257516679at_nat)) (= (ho_24999 x z) (ho_24999 y z)))) (= x y))))) (let ((_let_1344 (forall ((x |u_(-> tptp.int tptp.set_Pr958786334691620121nt_int tptp.int tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.set_Pr958786334691620121nt_int tptp.int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_18796 x z) (ho_18796 y z)))) (= x y))))) (let ((_let_1345 (forall ((x |u_(-> tptp.list_rat tptp.nat)|) (y |u_(-> tptp.list_rat tptp.nat)|)) (or (not (forall ((z tptp.list_rat)) (= (ho_24837 x z) (ho_24837 y z)))) (= x y))))) (let ((_let_1346 (forall ((x |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn)|) (y |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.assn)|)) (= (ho_17896 x z) (ho_17896 y z)))) (= x y))))) (let ((_let_1347 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.int tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_18797 x z) (ho_18797 y z)))) (= x y))))) (let ((_let_1348 (forall ((x |u_(-> _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (y |u_(-> _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (or (not (forall ((z |u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (= (ho_18779 x z) (ho_18779 y z)))) (= x y))))) (let ((_let_1349 (forall ((x |u_(-> _u_(-> tptp.product_unit tptp.heap_Time_Heap_b)_ tptp.heap_Time_Heap_b)|) (y |u_(-> _u_(-> tptp.product_unit tptp.heap_Time_Heap_b)_ tptp.heap_Time_Heap_b)|)) (or (not (forall ((z |u_(-> tptp.product_unit tptp.heap_Time_Heap_b)|)) (= (ho_24302 x z) (ho_24302 y z)))) (= x y))))) (let ((_let_1350 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.code_integer)_ tptp.set_Pr1261947904930325089at_nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.code_integer)_ tptp.set_Pr1261947904930325089at_nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.code_integer)|)) (= (ho_25776 x z) (ho_25776 y z)))) (= x y))))) (let ((_let_1351 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_int_int)|)) (= (ho_18763 x z) (ho_18763 y z)))) (= x y))))) (let ((_let_1352 (forall ((x |u_(-> tptp.set_int tptp.nat)|) (y |u_(-> tptp.set_int tptp.nat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_14871 x z) (ho_14871 y z)))) (= x y))))) (let ((_let_1353 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (= (ho_18760 x z) (ho_18760 y z)))) (= x y))))) (let ((_let_1354 (forall ((x |u_(-> Bool _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|) (y |u_(-> Bool _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (or (not (forall ((z Bool)) (= (ho_18751 x z) (ho_18751 y z)))) (= x y))))) (let ((_let_1355 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (= (ho_18752 x z) (ho_18752 y z)))) (= x y))))) (let ((_let_1356 (forall ((x |u_(-> _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)|)) (= (ho_24460 x z) (ho_24460 y z)))) (= x y))))) (let ((_let_1357 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (= (ho_18748 x z) (ho_18748 y z)))) (= x y))))) (let ((_let_1358 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.assn)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.assn)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_12113 x z) (ho_12113 y z)))) (= x y))))) (let ((_let_1359 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_15585 x z) (ho_15585 y z)))) (= x y))))) (let ((_let_1360 (forall ((x |u_(-> tptp.code_natural _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|) (y |u_(-> tptp.code_natural _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_18742 x z) (ho_18742 y z)))) (= x y))))) (let ((_let_1361 (forall ((x |u_(-> _u_(-> tptp.product_prod_num_num Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_num_num Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_num_num Bool)|)) (= (ho_24457 x z) (ho_24457 y z)))) (= x y))))) (let ((_let_1362 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (= (ho_18743 x z) (ho_18743 y z)))) (= x y))))) (let ((_let_1363 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_18740 x z) (ho_18740 y z)))) (= x y))))) (let ((_let_1364 (forall ((x |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|) (y |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (or (not (forall ((z tptp.produc3658429121746597890et_nat)) (= (ho_18744 x z) (ho_18744 y z)))) (= x y))))) (let ((_let_1365 (forall ((x |u_(-> tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat)|) (y |u_(-> tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat)|)) (or (not (forall ((z tptp.option8963830502488799655at_nat)) (= (ho_22431 x z) (ho_22431 y z)))) (= x y))))) (let ((_let_1366 (forall ((x |u_(-> _u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|) (y |u_(-> _u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (= (ho_18739 x z) (ho_18739 y z)))) (= x y))))) (let ((_let_1367 (forall ((x |u_(-> tptp.set_rat Bool)|) (y |u_(-> tptp.set_rat Bool)|)) (or (not (forall ((z tptp.set_rat)) (= (ho_16780 x z) (ho_16780 y z)))) (= x y))))) (let ((_let_1368 (forall ((x |u_(-> _u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|) (y |u_(-> _u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (= (ho_18733 x z) (ho_18733 y z)))) (= x y))))) (let ((_let_1369 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (= (ho_18734 x z) (ho_18734 y z)))) (= x y))))) (let ((_let_1370 (forall ((x |u_(-> tptp.code_natural _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|) (y |u_(-> tptp.code_natural _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_18728 x z) (ho_18728 y z)))) (= x y))))) (let ((_let_1371 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (= (ho_18729 x z) (ho_18729 y z)))) (= x y))))) (let ((_let_1372 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc1730305018825802663t_unit)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc1730305018825802663t_unit)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_11818 x z) (ho_11818 y z)))) (= x y))))) (let ((_let_1373 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_25975 x z) (ho_25975 y z)))) (= x y))))) (let ((_let_1374 (forall ((x |u_(-> tptp.list_o tptp.code_integer)|) (y |u_(-> tptp.list_o tptp.code_integer)|)) (or (not (forall ((z tptp.list_o)) (= (ho_25209 x z) (ho_25209 y z)))) (= x y))))) (let ((_let_1375 (forall ((x |u_(-> tptp.product_prod_int_int tptp.int)|) (y |u_(-> tptp.product_prod_int_int tptp.int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_11111 x z) (ho_11111 y z)))) (= x y))))) (let ((_let_1376 (forall ((x |u_(-> Bool _u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ _u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> Bool _u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ _u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z Bool)) (= (ho_18723 x z) (ho_18723 y z)))) (= x y))))) (let ((_let_1377 (forall ((x |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (= (ho_18725 x z) (ho_18725 y z)))) (= x y))))) (let ((_let_1378 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (= (ho_17915 x z) (ho_17915 y z)))) (= x y))))) (let ((_let_1379 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.produc8032495849646651230it_nat)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.produc8032495849646651230it_nat)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_11154 x z) (ho_11154 y z)))) (= x y))))) (let ((_let_1380 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.rat)_ _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer tptp.rat)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.rat)_ _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_16283 x z) (ho_16283 y z)))) (= x y))))) (let ((_let_1381 (forall ((x |u_(-> tptp.code_natural _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> tptp.code_natural _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_18714 x z) (ho_18714 y z)))) (= x y))))) (let ((_let_1382 (forall ((x |u_(-> tptp.assn _u_(-> tptp.int tptp.assn)_ tptp.int tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.assn _u_(-> tptp.int tptp.assn)_ tptp.int tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_23793 x z) (ho_23793 y z)))) (= x y))))) (let ((_let_1383 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_18177 x z) (ho_18177 y z)))) (= x y))))) (let ((_let_1384 (forall ((x |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (= (ho_18715 x z) (ho_18715 y z)))) (= x y))))) (let ((_let_1385 (forall ((x |u_(-> _u_(-> tptp.assn tptp.assn)_ tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.assn tptp.assn)_ tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.assn tptp.assn)|)) (= (ho_23836 x z) (ho_23836 y z)))) (= x y))))) (let ((_let_1386 (forall ((x |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z tptp.b)) (= (ho_18712 x z) (ho_18712 y z)))) (= x y))))) (let ((_let_1387 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.int)_ Bool tptp.int)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.int)_ Bool tptp.int)|)) (or (not (forall ((z tptp.set_o)) (= (ho_16899 x z) (ho_16899 y z)))) (= x y))))) (let ((_let_1388 (forall ((x |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)_ tptp.set_Pr4329608150637261639at_nat _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)_ tptp.set_Pr4329608150637261639at_nat _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)|)) (= (ho_24506 x z) (ho_24506 y z)))) (= x y))))) (let ((_let_1389 (forall ((x |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (= (ho_18711 x z) (ho_18711 y z)))) (= x y))))) (let ((_let_1390 (forall ((x |u_(-> tptp.code_natural _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> tptp.code_natural _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_18700 x z) (ho_18700 y z)))) (= x y))))) (let ((_let_1391 (forall ((x |u_(-> tptp.set_nat tptp.nat tptp.int)|) (y |u_(-> tptp.set_nat tptp.nat tptp.int)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_18136 x z) (ho_18136 y z)))) (= x y))))) (let ((_let_1392 (forall ((x |u_(-> tptp.code_natural _u_(-> tptp.code_integer tptp.code_natural)_ tptp.code_integer Bool)|) (y |u_(-> tptp.code_natural _u_(-> tptp.code_integer tptp.code_natural)_ tptp.code_integer Bool)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_15847 x z) (ho_15847 y z)))) (= x y))))) (let ((_let_1393 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.assn)_ _u_(-> Bool tptp.assn)_ Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.assn)_ _u_(-> Bool tptp.assn)_ Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_17176 x z) (ho_17176 y z)))) (= x y))))) (let ((_let_1394 (forall ((x |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z tptp.a)) (= (ho_18698 x z) (ho_18698 y z)))) (= x y))))) (let ((_let_1395 (forall ((x |u_(-> tptp.set_se6260736226359567993nt_int tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.set_se6260736226359567993nt_int tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.set_se6260736226359567993nt_int)) (= (ho_12655 x z) (ho_12655 y z)))) (= x y))))) (let ((_let_1396 (forall ((x |u_(-> Bool _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (y |u_(-> Bool _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (or (not (forall ((z Bool)) (= (ho_18694 x z) (ho_18694 y z)))) (= x y))))) (let ((_let_1397 (forall ((x |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (= (ho_24367 x z) (ho_24367 y z)))) (= x y))))) (let ((_let_1398 (forall ((x |u_(-> _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (y |u_(-> _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (or (not (forall ((z |u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (= (ho_18696 x z) (ho_18696 y z)))) (= x y))))) (let ((_let_1399 (forall ((x |u_(-> tptp.option_int tptp.option_nat)|) (y |u_(-> tptp.option_int tptp.option_nat)|)) (or (not (forall ((z tptp.option_int)) (= (ho_25735 x z) (ho_25735 y z)))) (= x y))))) (let ((_let_1400 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.set_nat Bool)_ tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.set_nat Bool)_ tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_19173 x z) (ho_19173 y z)))) (= x y))))) (let ((_let_1401 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.list_int tptp.rat tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.list_int tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_18686 x z) (ho_18686 y z)))) (= x y))))) (let ((_let_1402 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)_ tptp.produc2732055786443039994et_nat Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)_ tptp.produc2732055786443039994et_nat Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|)) (= (ho_25123 x z) (ho_25123 y z)))) (= x y))))) (let ((_let_1403 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.list_nat tptp.rat tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.list_nat tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_18680 x z) (ho_18680 y z)))) (= x y))))) (let ((_let_1404 (forall ((x |u_(-> _u_(-> tptp.nat tptp.set_nat)_ tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.set_nat)_ tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.set_nat)|)) (= (ho_14456 x z) (ho_14456 y z)))) (= x y))))) (let ((_let_1405 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)_ tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)_ tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_21982 x z) (ho_21982 y z)))) (= x y))))) (let ((_let_1406 (forall ((x |u_(-> tptp.list_nat tptp.rat tptp.nat tptp.rat)|) (y |u_(-> tptp.list_nat tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_18678 x z) (ho_18678 y z)))) (= x y))))) (let ((_let_1407 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit Bool)_ _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit Bool)_ _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit Bool)|)) (= (ho_22698 x z) (ho_22698 y z)))) (= x y))))) (let ((_let_1408 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.set_nat Bool)_ _u_(-> tptp.set_nat tptp.set_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_nat tptp.set_nat Bool)_ _u_(-> tptp.set_nat tptp.set_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.set_nat Bool)|)) (= (ho_24327 x z) (ho_24327 y z)))) (= x y))))) (let ((_let_1409 (forall ((x |u_(-> tptp.nat tptp.code_natural tptp.code_natural)|) (y |u_(-> tptp.nat tptp.code_natural tptp.code_natural)|)) (or (not (forall ((z tptp.nat)) (= (ho_20113 x z) (ho_20113 y z)))) (= x y))))) (let ((_let_1410 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.int tptp.list_int tptp.nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.int tptp.list_int tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_18670 x z) (ho_18670 y z)))) (= x y))))) (let ((_let_1411 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_int_int)|)) (= (ho_18759 x z) (ho_18759 y z)))) (= x y))))) (let ((_let_1412 (forall ((x |u_(-> _u_(-> tptp.set_int tptp.set_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_int tptp.set_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_int tptp.set_int Bool)|)) (= (ho_24336 x z) (ho_24336 y z)))) (= x y))))) (let ((_let_1413 (forall ((x |u_(-> tptp.int tptp.list_int tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.int tptp.list_int tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.int)) (= (ho_18671 x z) (ho_18671 y z)))) (= x y))))) (let ((_let_1414 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (= (ho_18747 x z) (ho_18747 y z)))) (= x y))))) (let ((_let_1415 (forall ((x |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.code_integer)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.code_integer)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.code_integer)|)) (= (ho_24590 x z) (ho_24590 y z)))) (= x y))))) (let ((_let_1416 (forall ((x |u_(-> Bool tptp.set_o tptp.set_o)|) (y |u_(-> Bool tptp.set_o tptp.set_o)|)) (or (not (forall ((z Bool)) (= (ho_19107 x z) (ho_19107 y z)))) (= x y))))) (let ((_let_1417 (forall ((x |u_(-> tptp.list_int tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.list_int tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.list_int)) (= (ho_18672 x z) (ho_18672 y z)))) (= x y))))) (let ((_let_1418 (forall ((x |u_(-> tptp.nat Bool tptp.assn)|) (y |u_(-> tptp.nat Bool tptp.assn)|)) (or (not (forall ((z tptp.nat)) (= (ho_20396 x z) (ho_20396 y z)))) (= x y))))) (let ((_let_1419 (forall ((x |u_(-> tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)|) (y |u_(-> tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)|)) (or (not (forall ((z tptp.produc3843707927480180839at_nat)) (= (ho_19112 x z) (ho_19112 y z)))) (= x y))))) (let ((_let_1420 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.list_nat tptp.nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.list_nat tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_18668 x z) (ho_18668 y z)))) (= x y))))) (let ((_let_1421 (forall ((x |u_(-> tptp.option4065278094766928714it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> tptp.option4065278094766928714it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z tptp.option4065278094766928714it_nat)) (= (ho_24282 x z) (ho_24282 y z)))) (= x y))))) (let ((_let_1422 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.list_int tptp.int tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.list_int tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_18662 x z) (ho_18662 y z)))) (= x y))))) (let ((_let_1423 (forall ((x |u_(-> tptp.int tptp.list_int tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.list_int tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_18659 x z) (ho_18659 y z)))) (= x y))))) (let ((_let_1424 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_natural)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.code_natural)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_natural)|)) (= (ho_11861 x z) (ho_11861 y z)))) (= x y))))) (let ((_let_1425 (forall ((x |u_(-> tptp.list_int tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.list_int tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_18660 x z) (ho_18660 y z)))) (= x y))))) (let ((_let_1426 (forall ((x |u_(-> _u_(-> tptp.num tptp.int)_ tptp.num tptp.int)|) (y |u_(-> _u_(-> tptp.num tptp.int)_ tptp.num tptp.int)|)) (or (not (forall ((z |u_(-> tptp.num tptp.int)|)) (= (ho_22693 x z) (ho_22693 y z)))) (= x y))))) (let ((_let_1427 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_26101 x z) (ho_26101 y z)))) (= x y))))) (let ((_let_1428 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.list_nat tptp.int tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.list_nat tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_18656 x z) (ho_18656 y z)))) (= x y))))) (let ((_let_1429 (forall ((x |u_(-> _u_(-> tptp.produc2115011035271226405et_int Bool)_ tptp.set_Pr2522554150109002629et_int)|) (y |u_(-> _u_(-> tptp.produc2115011035271226405et_int Bool)_ tptp.set_Pr2522554150109002629et_int)|)) (or (not (forall ((z |u_(-> tptp.produc2115011035271226405et_int Bool)|)) (= (ho_25608 x z) (ho_25608 y z)))) (= x y))))) (let ((_let_1430 (forall ((x |u_(-> tptp.nat tptp.list_nat tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.list_nat tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_18653 x z) (ho_18653 y z)))) (= x y))))) (let ((_let_1431 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.array_nat tptp.nat Bool)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.array_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_25565 x z) (ho_25565 y z)))) (= x y))))) (let ((_let_1432 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.set_nat tptp.set_Code_integer)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.set_nat tptp.set_Code_integer)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer)|)) (= (ho_25834 x z) (ho_25834 y z)))) (= x y))))) (let ((_let_1433 (forall ((x |u_(-> Bool tptp.list_o tptp.list_o)|) (y |u_(-> Bool tptp.list_o tptp.list_o)|)) (or (not (forall ((z Bool)) (= (ho_18647 x z) (ho_18647 y z)))) (= x y))))) (let ((_let_1434 (forall ((x |u_(-> _u_(-> Bool tptp.int)_ Bool tptp.list_o tptp.int tptp.nat tptp.int)|) (y |u_(-> _u_(-> Bool tptp.int)_ Bool tptp.list_o tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.int)|)) (= (ho_18643 x z) (ho_18643 y z)))) (= x y))))) (let ((_let_1435 (forall ((x |u_(-> tptp.list_P6935614879863011209it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.list_P6935614879863011209it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.list_P6935614879863011209it_nat)) (= (ho_24921 x z) (ho_24921 y z)))) (= x y))))) (let ((_let_1436 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.list_nat tptp.nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.list_nat tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_18664 x z) (ho_18664 y z)))) (= x y))))) (let ((_let_1437 (forall ((x |u_(-> tptp.option8956607266484857688it_nat tptp.option_num Bool)|) (y |u_(-> tptp.option8956607266484857688it_nat tptp.option_num Bool)|)) (or (not (forall ((z tptp.option8956607266484857688it_nat)) (= (ho_24412 x z) (ho_24412 y z)))) (= x y))))) (let ((_let_1438 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_natural)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_natural)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_natural)|)) (= (ho_15330 x z) (ho_15330 y z)))) (= x y))))) (let ((_let_1439 (forall ((x |u_(-> tptp.num tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.num tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.num)) (= (ho_18634 x z) (ho_18634 y z)))) (= x y))))) (let ((_let_1440 (forall ((x |u_(-> _u_(-> tptp.nat tptp.num tptp.option_num)_ tptp.product_prod_nat_num tptp.option_num)|) (y |u_(-> _u_(-> tptp.nat tptp.num tptp.option_num)_ tptp.product_prod_nat_num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.num tptp.option_num)|)) (= (ho_18625 x z) (ho_18625 y z)))) (= x y))))) (let ((_let_1441 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.produc9011797661310329043it_nat)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.produc9011797661310329043it_nat)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_24893 x z) (ho_24893 y z)))) (= x y))))) (let ((_let_1442 (forall ((x |u_(-> tptp.product_prod_nat_num tptp.option_num)|) (y |u_(-> tptp.product_prod_nat_num tptp.option_num)|)) (or (not (forall ((z tptp.product_prod_nat_num)) (= (ho_18626 x z) (ho_18626 y z)))) (= x y))))) (let ((_let_1443 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_11685 x z) (ho_11685 y z)))) (= x y))))) (let ((_let_1444 (forall ((x |u_(-> _u_(-> tptp.option_num tptp.nat)_ _u_(-> tptp.nat tptp.option_num)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.option_num tptp.nat)_ _u_(-> tptp.nat tptp.option_num)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.option_num tptp.nat)|)) (= (ho_18606 x z) (ho_18606 y z)))) (= x y))))) (let ((_let_1445 (forall ((x |u_(-> Bool Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_26124 x z) (ho_26124 y z)))) (= x y))))) (let ((_let_1446 (forall ((x |u_(-> tptp.list_int tptp.list_P3795440434834930179_o_int)|) (y |u_(-> tptp.list_int tptp.list_P3795440434834930179_o_int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_24787 x z) (ho_24787 y z)))) (= x y))))) (let ((_let_1447 (forall ((x |u_(-> tptp.list_nat tptp.heap_e7401611519738050253t_unit tptp.produc1730305018825802663t_unit)|) (y |u_(-> tptp.list_nat tptp.heap_e7401611519738050253t_unit tptp.produc1730305018825802663t_unit)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_11817 x z) (ho_11817 y z)))) (= x y))))) (let ((_let_1448 (forall ((x |u_(-> _u_(-> tptp.nat tptp.option_num)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.option_num)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.option_num)|)) (= (ho_18607 x z) (ho_18607 y z)))) (= x y))))) (let ((_let_1449 (forall ((x |u_(-> _u_(-> tptp.option_num Bool)_ _u_(-> tptp.nat tptp.option_num)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.option_num Bool)_ _u_(-> tptp.nat tptp.option_num)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.option_num Bool)|)) (= (ho_18602 x z) (ho_18602 y z)))) (= x y))))) (let ((_let_1450 (forall ((x |u_(-> tptp.nat tptp.rat Bool)|) (y |u_(-> tptp.nat tptp.rat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_24645 x z) (ho_24645 y z)))) (= x y))))) (let ((_let_1451 (forall ((x |u_(-> _u_(-> tptp.nat tptp.option_num)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.option_num)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.option_num)|)) (= (ho_18603 x z) (ho_18603 y z)))) (= x y))))) (let ((_let_1452 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.option_num)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_18599 x z) (ho_18599 y z)))) (= x y))))) (let ((_let_1453 (forall ((x |u_(-> _u_(-> Bool tptp.option_num)_ _u_(-> tptp.nat Bool)_ tptp.nat tptp.option_num)|) (y |u_(-> _u_(-> Bool tptp.option_num)_ _u_(-> tptp.nat Bool)_ tptp.nat tptp.option_num)|)) (or (not (forall ((z |u_(-> Bool tptp.option_num)|)) (= (ho_18593 x z) (ho_18593 y z)))) (= x y))))) (let ((_let_1454 (forall ((x |u_(-> _u_(-> tptp.produc3911288613690379145it_nat tptp.produc3911288613690379145it_nat Bool)_ tptp.produc3911288613690379145it_nat Bool)|) (y |u_(-> _u_(-> tptp.produc3911288613690379145it_nat tptp.produc3911288613690379145it_nat Bool)_ tptp.produc3911288613690379145it_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc3911288613690379145it_nat tptp.produc3911288613690379145it_nat Bool)|)) (= (ho_24441 x z) (ho_24441 y z)))) (= x y))))) (let ((_let_1455 (forall ((x |u_(-> Bool tptp.option_num)|) (y |u_(-> Bool tptp.option_num)|)) (or (not (forall ((z Bool)) (= (ho_18591 x z) (ho_18591 y z)))) (= x y))))) (let ((_let_1456 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.option_num)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_18594 x z) (ho_18594 y z)))) (= x y))))) (let ((_let_1457 (forall ((x |u_(-> _u_(-> Bool tptp.nat)_ _u_(-> tptp.nat Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> Bool tptp.nat)_ _u_(-> tptp.nat Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> Bool tptp.nat)|)) (= (ho_18590 x z) (ho_18590 y z)))) (= x y))))) (let ((_let_1458 (forall ((x |u_(-> _u_(-> tptp.set_int Bool)_ tptp.option_set_int Bool)|) (y |u_(-> _u_(-> tptp.set_int Bool)_ tptp.option_set_int Bool)|)) (or (not (forall ((z |u_(-> tptp.set_int Bool)|)) (= (ho_24224 x z) (ho_24224 y z)))) (= x y))))) (let ((_let_1459 (forall ((x |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_18588 x z) (ho_18588 y z)))) (= x y))))) (let ((_let_1460 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.num)_ tptp.produc8923325533196201883nteger tptp.num)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.num)_ tptp.produc8923325533196201883nteger tptp.num)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer tptp.num)|)) (= (ho_18551 x z) (ho_18551 y z)))) (= x y))))) (let ((_let_1461 (forall ((x |u_(-> tptp.option1583680563626158861at_nat tptp.option1583680563626158861at_nat)|) (y |u_(-> tptp.option1583680563626158861at_nat tptp.option1583680563626158861at_nat)|)) (or (not (forall ((z tptp.option1583680563626158861at_nat)) (= (ho_23583 x z) (ho_23583 y z)))) (= x y))))) (let ((_let_1462 (forall ((x |u_(-> _u_(-> tptp.array_nat tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat)_ tptp.produc1730305018825802663t_unit tptp.produc6751673265320737416it_nat)|) (y |u_(-> _u_(-> tptp.array_nat tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat)_ tptp.produc1730305018825802663t_unit tptp.produc6751673265320737416it_nat)|)) (or (not (forall ((z |u_(-> tptp.array_nat tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat)|)) (= (ho_11820 x z) (ho_11820 y z)))) (= x y))))) (let ((_let_1463 (forall ((x |u_(-> Bool tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> Bool tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z Bool)) (= (ho_22733 x z) (ho_22733 y z)))) (= x y))))) (let ((_let_1464 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.num)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.num)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_18552 x z) (ho_18552 y z)))) (= x y))))) (let ((_let_1465 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.int)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.int)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_18548 x z) (ho_18548 y z)))) (= x y))))) (let ((_let_1466 (forall ((x |u_(-> _u_(-> Bool tptp.code_integer)_ _u_(-> Bool tptp.code_integer)_ Bool tptp.code_integer)|) (y |u_(-> _u_(-> Bool tptp.code_integer)_ _u_(-> Bool tptp.code_integer)_ Bool tptp.code_integer)|)) (or (not (forall ((z |u_(-> Bool tptp.code_integer)|)) (= (ho_18521 x z) (ho_18521 y z)))) (= x y))))) (let ((_let_1467 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.code_integer)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer)|)) (= (ho_18518 x z) (ho_18518 y z)))) (= x y))))) (let ((_let_1468 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.code_integer)_ tptp.set_nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.set_nat tptp.code_integer)_ tptp.set_nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.code_integer)|)) (= (ho_18510 x z) (ho_18510 y z)))) (= x y))))) (let ((_let_1469 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_18494 x z) (ho_18494 y z)))) (= x y))))) (let ((_let_1470 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_25318 x z) (ho_25318 y z)))) (= x y))))) (let ((_let_1471 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_18495 x z) (ho_18495 y z)))) (= x y))))) (let ((_let_1472 (forall ((x |u_(-> tptp.set_Product_prod_o_o tptp.set_Product_prod_o_o)|) (y |u_(-> tptp.set_Product_prod_o_o tptp.set_Product_prod_o_o)|)) (or (not (forall ((z tptp.set_Product_prod_o_o)) (= (ho_24852 x z) (ho_24852 y z)))) (= x y))))) (let ((_let_1473 (forall ((x |u_(-> tptp.nat tptp.set_nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.set_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_19058 x z) (ho_19058 y z)))) (= x y))))) (let ((_let_1474 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_18491 x z) (ho_18491 y z)))) (= x y))))) (let ((_let_1475 (forall ((x |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ tptp.set_Pr958786334691620121nt_int tptp.nat)|) (y |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ tptp.set_Pr958786334691620121nt_int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)|)) (= (ho_18482 x z) (ho_18482 y z)))) (= x y))))) (let ((_let_1476 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.nat)_ tptp.produc8923325533196201883nteger tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.nat)_ tptp.produc8923325533196201883nteger tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer tptp.nat)|)) (= (ho_18473 x z) (ho_18473 y z)))) (= x y))))) (let ((_let_1477 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.nat)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.nat)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_18474 x z) (ho_18474 y z)))) (= x y))))) (let ((_let_1478 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_25855 x z) (ho_25855 y z)))) (= x y))))) (let ((_let_1479 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_21543 x z) (ho_21543 y z)))) (= x y))))) (let ((_let_1480 (forall ((x |u_(-> tptp.nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> tptp.nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_18340 x z) (ho_18340 y z)))) (= x y))))) (let ((_let_1481 (forall ((x |u_(-> tptp.set_Code_integer tptp.produc6491284506569428743nteger)|) (y |u_(-> tptp.set_Code_integer tptp.produc6491284506569428743nteger)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_25621 x z) (ho_25621 y z)))) (= x y))))) (let ((_let_1482 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.nat tptp.nat tptp.code_integer)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.nat tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_18274 x z) (ho_18274 y z)))) (= x y))))) (let ((_let_1483 (forall ((x |u_(-> _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.nat _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.nat _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.multis2468970476368604999at_nat)|)) (= (ho_18257 x z) (ho_18257 y z)))) (= x y))))) (let ((_let_1484 (forall ((x |u_(-> tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.option3562590408128118217it_nat)) (= (ho_22702 x z) (ho_22702 y z)))) (= x y))))) (let ((_let_1485 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_18258 x z) (ho_18258 y z)))) (= x y))))) (let ((_let_1486 (forall ((x |u_(-> Bool tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> Bool tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z Bool)) (= (ho_18254 x z) (ho_18254 y z)))) (= x y))))) (let ((_let_1487 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_18251 x z) (ho_18251 y z)))) (= x y))))) (let ((_let_1488 (forall ((x |u_(-> _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.multis2468970476368604999at_nat)|)) (= (ho_18252 x z) (ho_18252 y z)))) (= x y))))) (let ((_let_1489 (forall ((x |u_(-> tptp.list_P131111800688179804it_nat tptp.list_P7438302566501821706it_nat)|) (y |u_(-> tptp.list_P131111800688179804it_nat tptp.list_P7438302566501821706it_nat)|)) (or (not (forall ((z tptp.list_P131111800688179804it_nat)) (= (ho_24823 x z) (ho_24823 y z)))) (= x y))))) (let ((_let_1490 (forall ((x |u_(-> _u_(-> tptp.rat Bool)_ tptp.option_rat Bool)|) (y |u_(-> _u_(-> tptp.rat Bool)_ tptp.option_rat Bool)|)) (or (not (forall ((z |u_(-> tptp.rat Bool)|)) (= (ho_24195 x z) (ho_24195 y z)))) (= x y))))) (let ((_let_1491 (forall ((x |u_(-> tptp.rat tptp.rat tptp.rat tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat tptp.rat tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_18227 x z) (ho_18227 y z)))) (= x y))))) (let ((_let_1492 (forall ((x |u_(-> tptp.list_b tptp.nat tptp.b)|) (y |u_(-> tptp.list_b tptp.nat tptp.b)|)) (or (not (forall ((z tptp.list_b)) (= (ho_24819 x z) (ho_24819 y z)))) (= x y))))) (let ((_let_1493 (forall ((x |u_(-> tptp.rat tptp.rat tptp.nat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_18217 x z) (ho_18217 y z)))) (= x y))))) (let ((_let_1494 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_21538 x z) (ho_21538 y z)))) (= x y))))) (let ((_let_1495 (forall ((x |u_(-> tptp.num tptp.product_prod_nat_num)|) (y |u_(-> tptp.num tptp.product_prod_nat_num)|)) (or (not (forall ((z tptp.num)) (= (ho_18623 x z) (ho_18623 y z)))) (= x y))))) (let ((_let_1496 (forall ((x |u_(-> tptp.int tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_18196 x z) (ho_18196 y z)))) (= x y))))) (let ((_let_1497 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.nat tptp.code_integer)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_18194 x z) (ho_18194 y z)))) (= x y))))) (let ((_let_1498 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_18173 x z) (ho_18173 y z)))) (= x y))))) (let ((_let_1499 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_18170 x z) (ho_18170 y z)))) (= x y))))) (let ((_let_1500 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.set_nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.set_nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_18139 x z) (ho_18139 y z)))) (= x y))))) (let ((_let_1501 (forall ((x |u_(-> tptp.rat tptp.int tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.rat tptp.int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_20277 x z) (ho_20277 y z)))) (= x y))))) (let ((_let_1502 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.int)_ tptp.set_nat tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.int)_ tptp.set_nat tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.int)|)) (= (ho_18135 x z) (ho_18135 y z)))) (= x y))))) (let ((_let_1503 (forall ((x |u_(-> _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (y |u_(-> _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (or (not (forall ((z |u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (= (ho_18770 x z) (ho_18770 y z)))) (= x y))))) (let ((_let_1504 (forall ((x |u_(-> Bool tptp.code_natural tptp.code_natural tptp.code_natural)|) (y |u_(-> Bool tptp.code_natural tptp.code_natural tptp.code_natural)|)) (or (not (forall ((z Bool)) (= (ho_18793 x z) (ho_18793 y z)))) (= x y))))) (let ((_let_1505 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat tptp.int)_ tptp.set_int tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.nat tptp.int)_ tptp.set_int tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat tptp.int)|)) (= (ho_18128 x z) (ho_18128 y z)))) (= x y))))) (let ((_let_1506 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.rat Bool)|)) (= (ho_26094 x z) (ho_26094 y z)))) (= x y))))) (let ((_let_1507 (forall ((x |u_(-> tptp.assn _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.nat tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.assn _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.nat tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_23873 x z) (ho_23873 y z)))) (= x y))))) (let ((_let_1508 (forall ((x |u_(-> tptp.set_int tptp.nat tptp.int)|) (y |u_(-> tptp.set_int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_18129 x z) (ho_18129 y z)))) (= x y))))) (let ((_let_1509 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat tptp.int)_ tptp.set_nat tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.nat tptp.int)_ tptp.set_nat tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat tptp.int)|)) (= (ho_18125 x z) (ho_18125 y z)))) (= x y))))) (let ((_let_1510 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.set_int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.set_int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.int)|)) (= (ho_18121 x z) (ho_18121 y z)))) (= x y))))) (let ((_let_1511 (forall ((x |u_(-> tptp.nat tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_18800 x z) (ho_18800 y z)))) (= x y))))) (let ((_let_1512 (forall ((x |u_(-> tptp.set_o tptp.assn)|) (y |u_(-> tptp.set_o tptp.assn)|)) (or (not (forall ((z tptp.set_o)) (= (ho_25498 x z) (ho_25498 y z)))) (= x y))))) (let ((_let_1513 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.nat tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_18114 x z) (ho_18114 y z)))) (= x y))))) (let ((_let_1514 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int Bool)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_16932 x z) (ho_16932 y z)))) (= x y))))) (let ((_let_1515 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat tptp.rat)_ tptp.nat tptp.nat tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat tptp.rat)_ tptp.nat tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat tptp.rat)|)) (= (ho_18089 x z) (ho_18089 y z)))) (= x y))))) (let ((_let_1516 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer tptp.code_integer)_ tptp.nat tptp.nat tptp.code_integer tptp.code_integer)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer tptp.code_integer)_ tptp.nat tptp.nat tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer tptp.code_integer)|)) (= (ho_18084 x z) (ho_18084 y z)))) (= x y))))) (let ((_let_1517 (forall ((x |u_(-> tptp.set_int tptp.int tptp.int)|) (y |u_(-> tptp.set_int tptp.int tptp.int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_18122 x z) (ho_18122 y z)))) (= x y))))) (let ((_let_1518 (forall ((x |u_(-> tptp.set_Pr3286484037609594932et_nat _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.set_Pr3286484037609594932et_nat _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.set_Pr3286484037609594932et_nat)) (= (ho_21383 x z) (ho_21383 y z)))) (= x y))))) (let ((_let_1519 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_18067 x z) (ho_18067 y z)))) (= x y))))) (let ((_let_1520 (forall ((x |u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)|) (y |u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)|)) (or (not (forall ((z tptp.product_prod_num_num)) (= (ho_24452 x z) (ho_24452 y z)))) (= x y))))) (let ((_let_1521 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_18054 x z) (ho_18054 y z)))) (= x y))))) (let ((_let_1522 (forall ((x |u_(-> tptp.list_P131111800688179804it_nat tptp.nat tptp.produc6653097349344004940it_nat)|) (y |u_(-> tptp.list_P131111800688179804it_nat tptp.nat tptp.produc6653097349344004940it_nat)|)) (or (not (forall ((z tptp.list_P131111800688179804it_nat)) (= (ho_24817 x z) (ho_24817 y z)))) (= x y))))) (let ((_let_1523 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_18040 x z) (ho_18040 y z)))) (= x y))))) (let ((_let_1524 (forall ((x |u_(-> Bool tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat)|) (y |u_(-> Bool tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat)|)) (or (not (forall ((z Bool)) (= (ho_22430 x z) (ho_22430 y z)))) (= x y))))) (let ((_let_1525 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_11572 x z) (ho_11572 y z)))) (= x y))))) (let ((_let_1526 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_18041 x z) (ho_18041 y z)))) (= x y))))) (let ((_let_1527 (forall ((x |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (= (ho_25112 x z) (ho_25112 y z)))) (= x y))))) (let ((_let_1528 (forall ((x |u_(-> tptp.filter1242075044329608583at_nat Bool)|) (y |u_(-> tptp.filter1242075044329608583at_nat Bool)|)) (or (not (forall ((z tptp.filter1242075044329608583at_nat)) (= (ho_26087 x z) (ho_26087 y z)))) (= x y))))) (let ((_let_1529 (forall ((x |u_(-> tptp.option8956607266484857688it_nat _u_(-> tptp.produc7388388658123137530it_nat tptp.option8956607266484857688it_nat)_ tptp.option4065278094766928714it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.option8956607266484857688it_nat _u_(-> tptp.produc7388388658123137530it_nat tptp.option8956607266484857688it_nat)_ tptp.option4065278094766928714it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.option8956607266484857688it_nat)) (= (ho_23675 x z) (ho_23675 y z)))) (= x y))))) (let ((_let_1530 (forall ((x |u_(-> tptp.int tptp.int tptp.int tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int tptp.int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_18028 x z) (ho_18028 y z)))) (= x y))))) (let ((_let_1531 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.produc3843707927480180839at_nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.produc3843707927480180839at_nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_11430 x z) (ho_11430 y z)))) (= x y))))) (let ((_let_1532 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_24348 x z) (ho_24348 y z)))) (= x y))))) (let ((_let_1533 (forall ((x |u_(-> tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.option4065278094766928714it_nat)) (= (ho_11315 x z) (ho_11315 y z)))) (= x y))))) (let ((_let_1534 (forall ((x |u_(-> tptp.nat tptp.int tptp.assn)|) (y |u_(-> tptp.nat tptp.int tptp.assn)|)) (or (not (forall ((z tptp.nat)) (= (ho_20389 x z) (ho_20389 y z)))) (= x y))))) (let ((_let_1535 (forall ((x |u_(-> tptp.num tptp.num tptp.product_prod_int_int)|) (y |u_(-> tptp.num tptp.num tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.num)) (= (ho_20129 x z) (ho_20129 y z)))) (= x y))))) (let ((_let_1536 (forall ((x |u_(-> tptp.nat tptp.assn tptp.assn)|) (y |u_(-> tptp.nat tptp.assn tptp.assn)|)) (or (not (forall ((z tptp.nat)) (= (ho_17989 x z) (ho_17989 y z)))) (= x y))))) (let ((_let_1537 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)_ tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)_ tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_23095 x z) (ho_23095 y z)))) (= x y))))) (let ((_let_1538 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_17983 x z) (ho_17983 y z)))) (= x y))))) (let ((_let_1539 (forall ((x |u_(-> Bool Bool tptp.set_o)|) (y |u_(-> Bool Bool tptp.set_o)|)) (or (not (forall ((z Bool)) (= (ho_17978 x z) (ho_17978 y z)))) (= x y))))) (let ((_let_1540 (forall ((x |u_(-> _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ tptp.product_prod_num_num Bool)|) (y |u_(-> _u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)_ tptp.product_prod_num_num Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)|)) (= (ho_24454 x z) (ho_24454 y z)))) (= x y))))) (let ((_let_1541 (forall ((x |u_(-> _u_(-> tptp.option_num tptp.option_num)_ _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.option_num)|) (y |u_(-> _u_(-> tptp.option_num tptp.option_num)_ _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.option_num tptp.option_num)|)) (= (ho_18585 x z) (ho_18585 y z)))) (= x y))))) (let ((_let_1542 (forall ((x |u_(-> tptp.num tptp.nat)|) (y |u_(-> tptp.num tptp.nat)|)) (or (not (forall ((z tptp.num)) (= (ho_17974 x z) (ho_17974 y z)))) (= x y))))) (let ((_let_1543 (forall ((x |u_(-> tptp.nat tptp.num tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.num tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_17971 x z) (ho_17971 y z)))) (= x y))))) (let ((_let_1544 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_13848 x z) (ho_13848 y z)))) (= x y))))) (let ((_let_1545 (forall ((x |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr958786334691620121nt_int Bool)|)) (= (ho_23358 x z) (ho_23358 y z)))) (= x y))))) (let ((_let_1546 (forall ((x |u_(-> tptp.num tptp.nat Bool)|) (y |u_(-> tptp.num tptp.nat Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_17972 x z) (ho_17972 y z)))) (= x y))))) (let ((_let_1547 (forall ((x |u_(-> tptp.set_nat tptp.code_integer)|) (y |u_(-> tptp.set_nat tptp.code_integer)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_17951 x z) (ho_17951 y z)))) (= x y))))) (let ((_let_1548 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_24484 x z) (ho_24484 y z)))) (= x y))))) (let ((_let_1549 (forall ((x |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (= (ho_17912 x z) (ho_17912 y z)))) (= x y))))) (let ((_let_1550 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.heap_T3836121109492952855ay_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.heap_T3836121109492952855ay_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_15682 x z) (ho_15682 y z)))) (= x y))))) (let ((_let_1551 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.option1013472963438093988it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.option1013472963438093988it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_25481 x z) (ho_25481 y z)))) (= x y))))) (let ((_let_1552 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer)|)) (= (ho_17910 x z) (ho_17910 y z)))) (= x y))))) (let ((_let_1553 (forall ((x |u_(-> tptp.array_o tptp.list_o tptp.nat tptp.assn)|) (y |u_(-> tptp.array_o tptp.list_o tptp.nat tptp.assn)|)) (or (not (forall ((z tptp.array_o)) (= (ho_21054 x z) (ho_21054 y z)))) (= x y))))) (let ((_let_1554 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer)|)) (= (ho_17916 x z) (ho_17916 y z)))) (= x y))))) (let ((_let_1555 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_11424 x z) (ho_11424 y z)))) (= x y))))) (let ((_let_1556 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)|)) (= (ho_17907 x z) (ho_17907 y z)))) (= x y))))) (let ((_let_1557 (forall ((x |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)_ _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)_ _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat)_ tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)|)) (= (ho_24573 x z) (ho_24573 y z)))) (= x y))))) (let ((_let_1558 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.rat)|)) (= (ho_11506 x z) (ho_11506 y z)))) (= x y))))) (let ((_let_1559 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.code_integer)_ _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.code_integer)_ _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.nat)) (= (ho_17899 x z) (ho_17899 y z)))) (= x y))))) (let ((_let_1560 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_17419 x z) (ho_17419 y z)))) (= x y))))) (let ((_let_1561 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer)_ _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer)_ _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer)|)) (= (ho_17900 x z) (ho_17900 y z)))) (= x y))))) (let ((_let_1562 (forall ((x |u_(-> tptp.product_unit tptp.heap_T5738788834812785303t_unit)|) (y |u_(-> tptp.product_unit tptp.heap_T5738788834812785303t_unit)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_22586 x z) (ho_22586 y z)))) (= x y))))) (let ((_let_1563 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat Bool)|)) (= (ho_11764 x z) (ho_11764 y z)))) (= x y))))) (let ((_let_1564 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_17884 x z) (ho_17884 y z)))) (= x y))))) (let ((_let_1565 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat Bool)_ tptp.heap_T5660665574680485309rray_o)|) (y |u_(-> tptp.nat _u_(-> tptp.nat Bool)_ tptp.heap_T5660665574680485309rray_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_15671 x z) (ho_15671 y z)))) (= x y))))) (let ((_let_1566 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_17880 x z) (ho_17880 y z)))) (= x y))))) (let ((_let_1567 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_17881 x z) (ho_17881 y z)))) (= x y))))) (let ((_let_1568 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_13627 x z) (ho_13627 y z)))) (= x y))))) (let ((_let_1569 (forall ((x |u_(-> tptp.list_o tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat)|) (y |u_(-> tptp.list_o tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat)|)) (or (not (forall ((z tptp.list_o)) (= (ho_11815 x z) (ho_11815 y z)))) (= x y))))) (let ((_let_1570 (forall ((x |u_(-> tptp.list_nat tptp.list_nat Bool)|) (y |u_(-> tptp.list_nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_11277 x z) (ho_11277 y z)))) (= x y))))) (let ((_let_1571 (forall ((x |u_(-> tptp.set_int tptp.set_int tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.set_int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_11339 x z) (ho_11339 y z)))) (= x y))))) (let ((_let_1572 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_24342 x z) (ho_24342 y z)))) (= x y))))) (let ((_let_1573 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_13621 x z) (ho_13621 y z)))) (= x y))))) (let ((_let_1574 (forall ((x |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.option8963830502488799655at_nat)_ tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat)|) (y |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.option8963830502488799655at_nat)_ tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat)|)) (or (not (forall ((z |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.option8963830502488799655at_nat)|)) (= (ho_22213 x z) (ho_22213 y z)))) (= x y))))) (let ((_let_1575 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_13576 x z) (ho_13576 y z)))) (= x y))))) (let ((_let_1576 (forall ((x |u_(-> _u_(-> tptp.option_num tptp.option_num)_ tptp.option_num tptp.option_num)|) (y |u_(-> _u_(-> tptp.option_num tptp.option_num)_ tptp.option_num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.option_num tptp.option_num)|)) (= (ho_25732 x z) (ho_25732 y z)))) (= x y))))) (let ((_let_1577 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_13564 x z) (ho_13564 y z)))) (= x y))))) (let ((_let_1578 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_13562 x z) (ho_13562 y z)))) (= x y))))) (let ((_let_1579 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat Bool)|)) (= (ho_17322 x z) (ho_17322 y z)))) (= x y))))) (let ((_let_1580 (forall ((x |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)_ tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)_ tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)|)) (= (ho_21993 x z) (ho_21993 y z)))) (= x y))))) (let ((_let_1581 (forall ((x |u_(-> tptp.set_int tptp.set_int tptp.set_int tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.set_int tptp.set_int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_13555 x z) (ho_13555 y z)))) (= x y))))) (let ((_let_1582 (forall ((x |u_(-> tptp.set_nat tptp.option_set_nat)|) (y |u_(-> tptp.set_nat tptp.option_set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_13856 x z) (ho_13856 y z)))) (= x y))))) (let ((_let_1583 (forall ((x |u_(-> tptp.set_set_nat tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_set_nat tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_15164 x z) (ho_15164 y z)))) (= x y))))) (let ((_let_1584 (forall ((x |u_(-> _u_(-> tptp.set_nat Bool)_ tptp.set_nat Bool)|) (y |u_(-> _u_(-> tptp.set_nat Bool)_ tptp.set_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat Bool)|)) (= (ho_13344 x z) (ho_13344 y z)))) (= x y))))) (let ((_let_1585 (forall ((x |u_(-> tptp.code_natural tptp.code_natural tptp.produc7822875418678951345atural)|) (y |u_(-> tptp.code_natural tptp.code_natural tptp.produc7822875418678951345atural)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_25192 x z) (ho_25192 y z)))) (= x y))))) (let ((_let_1586 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_15050 x z) (ho_15050 y z)))) (= x y))))) (let ((_let_1587 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_13238 x z) (ho_13238 y z)))) (= x y))))) (let ((_let_1588 (forall ((x |u_(-> _u_(-> tptp.list_nat tptp.rat)_ _u_(-> tptp.list_nat tptp.rat)_ tptp.list_nat tptp.rat)|) (y |u_(-> _u_(-> tptp.list_nat tptp.rat)_ _u_(-> tptp.list_nat tptp.rat)_ tptp.list_nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.list_nat tptp.rat)|)) (= (ho_16304 x z) (ho_16304 y z)))) (= x y))))) (let ((_let_1589 (forall ((x |u_(-> tptp.num tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> tptp.num tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.num)) (= (ho_13125 x z) (ho_13125 y z)))) (= x y))))) (let ((_let_1590 (forall ((x |u_(-> tptp.set_o tptp.set_o tptp.set_o)|) (y |u_(-> tptp.set_o tptp.set_o tptp.set_o)|)) (or (not (forall ((z tptp.set_o)) (= (ho_20511 x z) (ho_20511 y z)))) (= x y))))) (let ((_let_1591 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_13574 x z) (ho_13574 y z)))) (= x y))))) (let ((_let_1592 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_int_int)|)) (= (ho_18764 x z) (ho_18764 y z)))) (= x y))))) (let ((_let_1593 (forall ((x |u_(-> tptp.array_o tptp.list_o tptp.nat Bool tptp.assn)|) (y |u_(-> tptp.array_o tptp.list_o tptp.nat Bool tptp.assn)|)) (or (not (forall ((z tptp.array_o)) (= (ho_20394 x z) (ho_20394 y z)))) (= x y))))) (let ((_let_1594 (forall ((x |u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)|) (y |u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)|)) (or (not (forall ((z tptp.int)) (= (ho_13228 x z) (ho_13228 y z)))) (= x y))))) (let ((_let_1595 (forall ((x |u_(-> tptp.nat tptp.list_nat tptp.nat)|) (y |u_(-> tptp.nat tptp.list_nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_15320 x z) (ho_15320 y z)))) (= x y))))) (let ((_let_1596 (forall ((x |u_(-> tptp.nat tptp.heap_Time_Heap_int)|) (y |u_(-> tptp.nat tptp.heap_Time_Heap_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_24726 x z) (ho_24726 y z)))) (= x y))))) (let ((_let_1597 (forall ((x |u_(-> _u_(-> Bool tptp.nat tptp.nat)_ tptp.set_o _u_(-> Bool tptp.nat Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> Bool tptp.nat tptp.nat)_ tptp.set_o _u_(-> Bool tptp.nat Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> Bool tptp.nat tptp.nat)|)) (= (ho_17352 x z) (ho_17352 y z)))) (= x y))))) (let ((_let_1598 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn)|)) (or (not (forall ((z tptp.nat)) (= (ho_17515 x z) (ho_17515 y z)))) (= x y))))) (let ((_let_1599 (forall ((x |u_(-> _u_(-> tptp.nat tptp.option_num)_ tptp.nat tptp.option_num)|) (y |u_(-> _u_(-> tptp.nat tptp.option_num)_ tptp.nat tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.option_num)|)) (= (ho_12588 x z) (ho_12588 y z)))) (= x y))))) (let ((_let_1600 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_13225 x z) (ho_13225 y z)))) (= x y))))) (let ((_let_1601 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_16940 x z) (ho_16940 y z)))) (= x y))))) (let ((_let_1602 (forall ((x |u_(-> _u_(-> 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)|) (y |u_(-> _u_(-> 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)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_13187 x z) (ho_13187 y z)))) (= x y))))) (let ((_let_1603 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_13154 x z) (ho_13154 y z)))) (= x y))))) (let ((_let_1604 (forall ((x |u_(-> tptp.nat tptp.option_num)|) (y |u_(-> tptp.nat tptp.option_num)|)) (or (not (forall ((z tptp.nat)) (= (ho_11174 x z) (ho_11174 y z)))) (= x y))))) (let ((_let_1605 (forall ((x |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_13151 x z) (ho_13151 y z)))) (= x y))))) (let ((_let_1606 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.rat)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.rat)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_11123 x z) (ho_11123 y z)))) (= x y))))) (let ((_let_1607 (forall ((x |u_(-> _u_(-> tptp.b tptp.heap_Time_Heap_a)_ tptp.b tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.heap_Time_Heap_a)_ tptp.b tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.heap_Time_Heap_a)|)) (= (ho_11302 x z) (ho_11302 y z)))) (= x y))))) (let ((_let_1608 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.code_integer tptp.int Bool)_ tptp.code_integer tptp.int)|) (y |u_(-> tptp.set_int _u_(-> tptp.code_integer tptp.int Bool)_ tptp.code_integer tptp.int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_17295 x z) (ho_17295 y z)))) (= x y))))) (let ((_let_1609 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_12622 x z) (ho_12622 y z)))) (= x y))))) (let ((_let_1610 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_17470 x z) (ho_17470 y z)))) (= x y))))) (let ((_let_1611 (forall ((x |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.b)) (= (ho_13118 x z) (ho_13118 y z)))) (= x y))))) (let ((_let_1612 (forall ((x |u_(-> tptp.int tptp.int tptp.nat tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_18277 x z) (ho_18277 y z)))) (= x y))))) (let ((_let_1613 (forall ((x |u_(-> tptp.list_rat tptp.list_rat)|) (y |u_(-> tptp.list_rat tptp.list_rat)|)) (or (not (forall ((z tptp.list_rat)) (= (ho_25018 x z) (ho_25018 y z)))) (= x y))))) (let ((_let_1614 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option4065278094766928714it_nat)_ tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option4065278094766928714it_nat)_ tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option4065278094766928714it_nat)|)) (= (ho_13110 x z) (ho_13110 y z)))) (= x y))))) (let ((_let_1615 (forall ((x |u_(-> tptp.set_Pr3444600963470892981et_nat Bool)|) (y |u_(-> tptp.set_Pr3444600963470892981et_nat Bool)|)) (or (not (forall ((z tptp.set_Pr3444600963470892981et_nat)) (= (ho_24880 x z) (ho_24880 y z)))) (= x y))))) (let ((_let_1616 (forall ((x |u_(-> tptp.rat _u_(-> tptp.rat tptp.assn)_ tptp.rat tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.rat _u_(-> tptp.rat tptp.assn)_ tptp.rat tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_23821 x z) (ho_23821 y z)))) (= x y))))) (let ((_let_1617 (forall ((x |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.b)) (= (ho_13107 x z) (ho_13107 y z)))) (= x y))))) (let ((_let_1618 (forall ((x |u_(-> tptp.nat Bool Bool)|) (y |u_(-> tptp.nat Bool Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_12191 x z) (ho_12191 y z)))) (= x y))))) (let ((_let_1619 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer)_ tptp.set_int tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer)_ tptp.set_int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15356 x z) (ho_15356 y z)))) (= x y))))) (let ((_let_1620 (forall ((x |u_(-> tptp.list_nat tptp.list_nat tptp.list_nat)|) (y |u_(-> tptp.list_nat tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_14655 x z) (ho_14655 y z)))) (= x y))))) (let ((_let_1621 (forall ((x |u_(-> _u_(-> tptp.a tptp.heap_Time_Heap_a)_ tptp.a tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.heap_Time_Heap_a)_ tptp.a tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.heap_Time_Heap_a)|)) (= (ho_13102 x z) (ho_13102 y z)))) (= x y))))) (let ((_let_1622 (forall ((x |u_(-> tptp.heap_T5738788834812785303t_unit tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.heap_T5738788834812785303t_unit tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.heap_T5738788834812785303t_unit)) (= (ho_11387 x z) (ho_11387 y z)))) (= x y))))) (let ((_let_1623 (forall ((x |u_(-> tptp.list_int tptp.rat tptp.nat tptp.rat)|) (y |u_(-> tptp.list_int tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.list_int)) (= (ho_18684 x z) (ho_18684 y z)))) (= x y))))) (let ((_let_1624 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer Bool)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer Bool)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer Bool)|)) (= (ho_14862 x z) (ho_14862 y z)))) (= x y))))) (let ((_let_1625 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_13100 x z) (ho_13100 y z)))) (= x y))))) (let ((_let_1626 (forall ((x |u_(-> tptp.assn tptp.option_assn)|) (y |u_(-> tptp.assn tptp.option_assn)|)) (or (not (forall ((z tptp.assn)) (= (ho_13864 x z) (ho_13864 y z)))) (= x y))))) (let ((_let_1627 (forall ((x |u_(-> tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.set_se6260736226359567993nt_int)) (= (ho_12887 x z) (ho_12887 y z)))) (= x y))))) (let ((_let_1628 (forall ((x |u_(-> tptp.set_set_nat tptp.set_set_nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_set_nat tptp.set_set_nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_12883 x z) (ho_12883 y z)))) (= x y))))) (let ((_let_1629 (forall ((x |u_(-> tptp.int tptp.set_int)|) (y |u_(-> tptp.int tptp.set_int)|)) (or (not (forall ((z tptp.int)) (= (ho_12416 x z) (ho_12416 y z)))) (= x y))))) (let ((_let_1630 (forall ((x |u_(-> tptp.list_P8198026277950538467nt_nat tptp.list_P8198026277950538467nt_nat)|) (y |u_(-> tptp.list_P8198026277950538467nt_nat tptp.list_P8198026277950538467nt_nat)|)) (or (not (forall ((z tptp.list_P8198026277950538467nt_nat)) (= (ho_24946 x z) (ho_24946 y z)))) (= x y))))) (let ((_let_1631 (forall ((x |u_(-> tptp.produc5011041761010125393t_unit tptp.produc8032495849646651230it_nat)|) (y |u_(-> tptp.produc5011041761010125393t_unit tptp.produc8032495849646651230it_nat)|)) (or (not (forall ((z tptp.produc5011041761010125393t_unit)) (= (ho_11813 x z) (ho_11813 y z)))) (= x y))))) (let ((_let_1632 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_24592 x z) (ho_24592 y z)))) (= x y))))) (let ((_let_1633 (forall ((x |u_(-> _u_(-> tptp.produc3843707927480180839at_nat Bool)_ tptp.set_Pr4329608150637261639at_nat)|) (y |u_(-> _u_(-> tptp.produc3843707927480180839at_nat Bool)_ tptp.set_Pr4329608150637261639at_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3843707927480180839at_nat Bool)|)) (= (ho_12817 x z) (ho_12817 y z)))) (= x y))))) (let ((_let_1634 (forall ((x |u_(-> tptp.set_int _u_(-> Bool tptp.int Bool)_ Bool tptp.nat)|) (y |u_(-> tptp.set_int _u_(-> Bool tptp.int Bool)_ Bool tptp.nat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_14899 x z) (ho_14899 y z)))) (= x y))))) (let ((_let_1635 (forall ((x |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.assn)|)) (= (ho_12034 x z) (ho_12034 y z)))) (= x y))))) (let ((_let_1636 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_12658 x z) (ho_12658 y z)))) (= x y))))) (let ((_let_1637 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.set_nat tptp.nat)_ tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.set_nat tptp.nat)_ tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_16937 x z) (ho_16937 y z)))) (= x y))))) (let ((_let_1638 (forall ((x |u_(-> Bool _u_(-> tptp.num Bool)_ tptp.option_num Bool)|) (y |u_(-> Bool _u_(-> tptp.num Bool)_ tptp.option_num Bool)|)) (or (not (forall ((z Bool)) (= (ho_22639 x z) (ho_22639 y z)))) (= x y))))) (let ((_let_1639 (forall ((x |u_(-> tptp.set_int tptp.set_int tptp.int tptp.set_int tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.set_int tptp.int tptp.set_int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_18966 x z) (ho_18966 y z)))) (= x y))))) (let ((_let_1640 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.set_nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_15362 x z) (ho_15362 y z)))) (= x y))))) (let ((_let_1641 (forall ((x |u_(-> _u_(-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat)_ tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat)_ tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat)|)) (= (ho_22528 x z) (ho_22528 y z)))) (= x y))))) (let ((_let_1642 (forall ((x |u_(-> _u_(-> tptp.int tptp.assn)_ _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn)|) (y |u_(-> _u_(-> tptp.int tptp.assn)_ _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.int tptp.assn)|)) (= (ho_15790 x z) (ho_15790 y z)))) (= x y))))) (let ((_let_1643 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat)_ tptp.heap_T3836121109492952855ay_nat)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat)_ tptp.heap_T3836121109492952855ay_nat)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat)|)) (= (ho_15684 x z) (ho_15684 y z)))) (= x y))))) (let ((_let_1644 (forall ((x |u_(-> _u_(-> tptp.assn tptp.assn Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.assn tptp.assn Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.assn tptp.assn Bool)|)) (= (ho_24332 x z) (ho_24332 y z)))) (= x y))))) (let ((_let_1645 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.set_nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.set_nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer)|)) (= (ho_17950 x z) (ho_17950 y z)))) (= x y))))) (let ((_let_1646 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_11373 x z) (ho_11373 y z)))) (= x y))))) (let ((_let_1647 (forall ((x |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.set_nat tptp.assn)|) (y |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.set_nat tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.assn)|)) (= (ho_25434 x z) (ho_25434 y z)))) (= x y))))) (let ((_let_1648 (forall ((x |u_(-> tptp.set_Code_integer tptp.rat)|) (y |u_(-> tptp.set_Code_integer tptp.rat)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_25494 x z) (ho_25494 y z)))) (= x y))))) (let ((_let_1649 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat Bool Bool)_ Bool tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat Bool Bool)_ Bool tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_12201 x z) (ho_12201 y z)))) (= x y))))) (let ((_let_1650 (forall ((x |u_(-> tptp.rat tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.rat tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_23823 x z) (ho_23823 y z)))) (= x y))))) (let ((_let_1651 (forall ((x |u_(-> tptp.num tptp.num Bool)|) (y |u_(-> tptp.num tptp.num Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_13978 x z) (ho_13978 y z)))) (= x y))))) (let ((_let_1652 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int Bool)|)) (= (ho_17381 x z) (ho_17381 y z)))) (= x y))))) (let ((_let_1653 (forall ((x |u_(-> tptp.product_prod_b_b tptp.set_Product_prod_b_b Bool)|) (y |u_(-> tptp.product_prod_b_b tptp.set_Product_prod_b_b Bool)|)) (or (not (forall ((z tptp.product_prod_b_b)) (= (ho_25070 x z) (ho_25070 y z)))) (= x y))))) (let ((_let_1654 (forall ((x |u_(-> tptp.set_nat tptp.set_set_nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_set_nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_12653 x z) (ho_12653 y z)))) (= x y))))) (let ((_let_1655 (forall ((x |u_(-> tptp.int _u_(-> tptp.num tptp.int)_ tptp.option_num tptp.int)|) (y |u_(-> tptp.int _u_(-> tptp.num tptp.int)_ tptp.option_num tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_24403 x z) (ho_24403 y z)))) (= x y))))) (let ((_let_1656 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.assn)_ _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer tptp.assn)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.assn)_ _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_16295 x z) (ho_16295 y z)))) (= x y))))) (let ((_let_1657 (forall ((x |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.code_integer)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.code_integer)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (= (ho_24589 x z) (ho_24589 y z)))) (= x y))))) (let ((_let_1658 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.int)|) (y |u_(-> tptp.set_nat _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.int)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_17321 x z) (ho_17321 y z)))) (= x y))))) (let ((_let_1659 (forall ((x |u_(-> _u_(-> tptp.list_nat tptp.nat)_ tptp.set_list_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.list_nat tptp.nat)_ tptp.set_list_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.list_nat tptp.nat)|)) (= (ho_15170 x z) (ho_15170 y z)))) (= x y))))) (let ((_let_1660 (forall ((x |u_(-> _u_(-> 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)|) (y |u_(-> _u_(-> 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)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_20040 x z) (ho_20040 y z)))) (= x y))))) (let ((_let_1661 (forall ((x |u_(-> tptp.multis2468970476368604999at_nat tptp.set_Pr8551490117392284871at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|) (y |u_(-> tptp.multis2468970476368604999at_nat tptp.set_Pr8551490117392284871at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|)) (or (not (forall ((z tptp.multis2468970476368604999at_nat)) (= (ho_12621 x z) (ho_12621 y z)))) (= x y))))) (let ((_let_1662 (forall ((x |u_(-> Bool tptp.option_set_o tptp.option_set_o tptp.option_set_o)|) (y |u_(-> Bool tptp.option_set_o tptp.option_set_o tptp.option_set_o)|)) (or (not (forall ((z Bool)) (= (ho_22425 x z) (ho_22425 y z)))) (= x y))))) (let ((_let_1663 (forall ((x |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|) (y |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|)) (or (not (forall ((z tptp.multis2468970476368604999at_nat)) (= (ho_12623 x z) (ho_12623 y z)))) (= x y))))) (let ((_let_1664 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.int tptp.int tptp.set_Pr958786334691620121nt_int tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.int tptp.int tptp.set_Pr958786334691620121nt_int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_13222 x z) (ho_13222 y z)))) (= x y))))) (let ((_let_1665 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_16860 x z) (ho_16860 y z)))) (= x y))))) (let ((_let_1666 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_12627 x z) (ho_12627 y z)))) (= x y))))) (let ((_let_1667 (forall ((x |u_(-> tptp.set_nat _u_(-> Bool tptp.nat Bool)_ Bool tptp.int)|) (y |u_(-> tptp.set_nat _u_(-> Bool tptp.nat Bool)_ Bool tptp.int)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_17329 x z) (ho_17329 y z)))) (= x y))))) (let ((_let_1668 (forall ((x |u_(-> tptp.nat tptp.produc8664842809031399944it_nat)|) (y |u_(-> tptp.nat tptp.produc8664842809031399944it_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_24924 x z) (ho_24924 y z)))) (= x y))))) (let ((_let_1669 (forall ((x |u_(-> tptp.num tptp.num tptp.set_num)|) (y |u_(-> tptp.num tptp.num tptp.set_num)|)) (or (not (forall ((z tptp.num)) (= (ho_25343 x z) (ho_25343 y z)))) (= x y))))) (let ((_let_1670 (forall ((x |u_(-> _u_(-> Bool Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_22450 x z) (ho_22450 y z)))) (= x y))))) (let ((_let_1671 (forall ((x |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|) (y |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|)) (or (not (forall ((z tptp.multis2468970476368604999at_nat)) (= (ho_12624 x z) (ho_12624 y z)))) (= x y))))) (let ((_let_1672 (forall ((x |u_(-> tptp.set_list_nat tptp.list_nat Bool)|) (y |u_(-> tptp.set_list_nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_12842 x z) (ho_12842 y z)))) (= x y))))) (let ((_let_1673 (forall ((x |u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (y |u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_11492 x z) (ho_11492 y z)))) (= x y))))) (let ((_let_1674 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_15828 x z) (ho_15828 y z)))) (= x y))))) (let ((_let_1675 (forall ((x |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (= (ho_18719 x z) (ho_18719 y z)))) (= x y))))) (let ((_let_1676 (forall ((x |u_(-> tptp.set_o tptp.int)|) (y |u_(-> tptp.set_o tptp.int)|)) (or (not (forall ((z tptp.set_o)) (= (ho_17312 x z) (ho_17312 y z)))) (= x y))))) (let ((_let_1677 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_17986 x z) (ho_17986 y z)))) (= x y))))) (let ((_let_1678 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_12611 x z) (ho_12611 y z)))) (= x y))))) (let ((_let_1679 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer)|)) (= (ho_15286 x z) (ho_15286 y z)))) (= x y))))) (let ((_let_1680 (forall ((x |u_(-> tptp.heap_T5738788834812785303t_unit tptp.nat)|) (y |u_(-> tptp.heap_T5738788834812785303t_unit tptp.nat)|)) (or (not (forall ((z tptp.heap_T5738788834812785303t_unit)) (= (ho_24676 x z) (ho_24676 y z)))) (= x y))))) (let ((_let_1681 (forall ((x |u_(-> tptp.num tptp.num tptp.nat tptp.int)|) (y |u_(-> tptp.num tptp.num tptp.nat tptp.int)|)) (or (not (forall ((z tptp.num)) (= (ho_13122 x z) (ho_13122 y z)))) (= x y))))) (let ((_let_1682 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.int)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.int)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_17325 x z) (ho_17325 y z)))) (= x y))))) (let ((_let_1683 (forall ((x |u_(-> _u_(-> tptp.list_nat tptp.rat)_ tptp.set_list_nat tptp.rat)|) (y |u_(-> _u_(-> tptp.list_nat tptp.rat)_ tptp.set_list_nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.list_nat tptp.rat)|)) (= (ho_25536 x z) (ho_25536 y z)))) (= x y))))) (let ((_let_1684 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_15183 x z) (ho_15183 y z)))) (= x y))))) (let ((_let_1685 (forall ((x |u_(-> tptp.set_int tptp.int)|) (y |u_(-> tptp.set_int tptp.int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_12563 x z) (ho_12563 y z)))) (= x y))))) (let ((_let_1686 (forall ((x |u_(-> tptp.num tptp.code_integer)|) (y |u_(-> tptp.num tptp.code_integer)|)) (or (not (forall ((z tptp.num)) (= (ho_12560 x z) (ho_12560 y z)))) (= x y))))) (let ((_let_1687 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.a)_ tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.a)_ tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit tptp.a)|)) (= (ho_22399 x z) (ho_22399 y z)))) (= x y))))) (let ((_let_1688 (forall ((x |u_(-> _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (y |u_(-> _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (or (not (forall ((z |u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (= (ho_18771 x z) (ho_18771 y z)))) (= x y))))) (let ((_let_1689 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_12539 x z) (ho_12539 y z)))) (= x y))))) (let ((_let_1690 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_13443 x z) (ho_13443 y z)))) (= x y))))) (let ((_let_1691 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_16319 x z) (ho_16319 y z)))) (= x y))))) (let ((_let_1692 (forall ((x |u_(-> tptp.list_P3795440434834930179_o_int tptp.nat)|) (y |u_(-> tptp.list_P3795440434834930179_o_int tptp.nat)|)) (or (not (forall ((z tptp.list_P3795440434834930179_o_int)) (= (ho_25009 x z) (ho_25009 y z)))) (= x y))))) (let ((_let_1693 (forall ((x |u_(-> Bool _u_(-> Bool tptp.nat)_ _u_(-> Bool tptp.nat)_ Bool tptp.nat)|) (y |u_(-> Bool _u_(-> Bool tptp.nat)_ _u_(-> Bool tptp.nat)_ Bool tptp.nat)|)) (or (not (forall ((z Bool)) (= (ho_15755 x z) (ho_15755 y z)))) (= x y))))) (let ((_let_1694 (forall ((x |u_(-> tptp.code_natural Bool)|) (y |u_(-> tptp.code_natural Bool)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_11864 x z) (ho_11864 y z)))) (= x y))))) (let ((_let_1695 (forall ((x |u_(-> tptp.num tptp.num tptp.num)|) (y |u_(-> tptp.num tptp.num tptp.num)|)) (or (not (forall ((z tptp.num)) (= (ho_12554 x z) (ho_12554 y z)))) (= x y))))) (let ((_let_1696 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_19110 x z) (ho_19110 y z)))) (= x y))))) (let ((_let_1697 (forall ((x |u_(-> tptp.list_num tptp.nat)|) (y |u_(-> tptp.list_num tptp.nat)|)) (or (not (forall ((z tptp.list_num)) (= (ho_24844 x z) (ho_24844 y z)))) (= x y))))) (let ((_let_1698 (forall ((x |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.nat Bool)_ tptp.code_natural Bool)|) (y |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.nat Bool)_ tptp.code_natural Bool)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_26050 x z) (ho_26050 y z)))) (= x y))))) (let ((_let_1699 (forall ((x |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_15259 x z) (ho_15259 y z)))) (= x y))))) (let ((_let_1700 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat tptp.int)_ tptp.set_Code_integer _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat tptp.int)_ tptp.set_Code_integer _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat tptp.int)|)) (= (ho_17324 x z) (ho_17324 y z)))) (= x y))))) (let ((_let_1701 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.int)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.int)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12550 x z) (ho_12550 y z)))) (= x y))))) (let ((_let_1702 (forall ((x |u_(-> Bool tptp.int tptp.int tptp.int)|) (y |u_(-> Bool tptp.int tptp.int tptp.int)|)) (or (not (forall ((z Bool)) (= (ho_12548 x z) (ho_12548 y z)))) (= x y))))) (let ((_let_1703 (forall ((x |u_(-> tptp.num tptp.num tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.num tptp.num tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.num)) (= (ho_20125 x z) (ho_20125 y z)))) (= x y))))) (let ((_let_1704 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_12579 x z) (ho_12579 y z)))) (= x y))))) (let ((_let_1705 (forall ((x |u_(-> tptp.list_o tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.list_o tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.list_o)) (= (ho_18645 x z) (ho_18645 y z)))) (= x y))))) (let ((_let_1706 (forall ((x |u_(-> tptp.code_natural tptp.int Bool)|) (y |u_(-> tptp.code_natural tptp.int Bool)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_24657 x z) (ho_24657 y z)))) (= x y))))) (let ((_let_1707 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_12542 x z) (ho_12542 y z)))) (= x y))))) (let ((_let_1708 (forall ((x |u_(-> tptp.int tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_11058 x z) (ho_11058 y z)))) (= x y))))) (let ((_let_1709 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.set_int _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.set_int _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int tptp.int)|)) (= (ho_17379 x z) (ho_17379 y z)))) (= x y))))) (let ((_let_1710 (forall ((x |u_(-> tptp.num tptp.nat tptp.code_integer)|) (y |u_(-> tptp.num tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.num)) (= (ho_19899 x z) (ho_19899 y z)))) (= x y))))) (let ((_let_1711 (forall ((x |u_(-> _u_(-> tptp.option_num tptp.option_num)_ _u_(-> tptp.nat tptp.option_num)_ tptp.nat tptp.option_num)|) (y |u_(-> _u_(-> tptp.option_num tptp.option_num)_ _u_(-> tptp.nat tptp.option_num)_ tptp.nat tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.option_num tptp.option_num)|)) (= (ho_18609 x z) (ho_18609 y z)))) (= x y))))) (let ((_let_1712 (forall ((x |u_(-> tptp.set_nat tptp.int)|) (y |u_(-> tptp.set_nat tptp.int)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_15313 x z) (ho_15313 y z)))) (= x y))))) (let ((_let_1713 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.int tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int tptp.int)|)) (= (ho_12275 x z) (ho_12275 y z)))) (= x y))))) (let ((_let_1714 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.int tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.int tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (= (ho_25930 x z) (ho_25930 y z)))) (= x y))))) (let ((_let_1715 (forall ((x |u_(-> tptp.rat tptp.nat tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.nat tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_12462 x z) (ho_12462 y z)))) (= x y))))) (let ((_let_1716 (forall ((x |u_(-> tptp.b tptp.product_prod_b_b)|) (y |u_(-> tptp.b tptp.product_prod_b_b)|)) (or (not (forall ((z tptp.b)) (= (ho_25068 x z) (ho_25068 y z)))) (= x y))))) (let ((_let_1717 (forall ((x |u_(-> tptp.produc1219242969750017639nt_int Bool)|) (y |u_(-> tptp.produc1219242969750017639nt_int Bool)|)) (or (not (forall ((z tptp.produc1219242969750017639nt_int)) (= (ho_26149 x z) (ho_26149 y z)))) (= x y))))) (let ((_let_1718 (forall ((x |u_(-> tptp.nat tptp.int tptp.int)|) (y |u_(-> tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_12273 x z) (ho_12273 y z)))) (= x y))))) (let ((_let_1719 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|)) (= (ho_25965 x z) (ho_25965 y z)))) (= x y))))) (let ((_let_1720 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_11064 x z) (ho_11064 y z)))) (= x y))))) (let ((_let_1721 (forall ((x |u_(-> tptp.nat tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.nat tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_12460 x z) (ho_12460 y z)))) (= x y))))) (let ((_let_1722 (forall ((x |u_(-> tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_13227 x z) (ho_13227 y z)))) (= x y))))) (let ((_let_1723 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.int)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.int)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.int)|)) (= (ho_17623 x z) (ho_17623 y z)))) (= x y))))) (let ((_let_1724 (forall ((x |u_(-> tptp.produc3925858234332021118et_nat tptp.produc6830853553727218525et_nat)|) (y |u_(-> tptp.produc3925858234332021118et_nat tptp.produc6830853553727218525et_nat)|)) (or (not (forall ((z tptp.produc3925858234332021118et_nat)) (= (ho_24869 x z) (ho_24869 y z)))) (= x y))))) (let ((_let_1725 (forall ((x |u_(-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.produc3843707927480180839at_nat)) (= (ho_19519 x z) (ho_19519 y z)))) (= x y))))) (let ((_let_1726 (forall ((x |u_(-> tptp.int tptp.int tptp.set_int)|) (y |u_(-> tptp.int tptp.int tptp.set_int)|)) (or (not (forall ((z tptp.int)) (= (ho_12415 x z) (ho_12415 y z)))) (= x y))))) (let ((_let_1727 (forall ((x |u_(-> tptp.list_int tptp.list_int Bool)|) (y |u_(-> tptp.list_int tptp.list_int Bool)|)) (or (not (forall ((z tptp.list_int)) (= (ho_20410 x z) (ho_20410 y z)))) (= x y))))) (let ((_let_1728 (forall ((x |u_(-> tptp.num tptp.num tptp.int)|) (y |u_(-> tptp.num tptp.num tptp.int)|)) (or (not (forall ((z tptp.num)) (= (ho_14521 x z) (ho_14521 y z)))) (= x y))))) (let ((_let_1729 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int Bool)|)) (= (ho_17386 x z) (ho_17386 y z)))) (= x y))))) (let ((_let_1730 (forall ((x |u_(-> tptp.list_b tptp.nat)|) (y |u_(-> tptp.list_b tptp.nat)|)) (or (not (forall ((z tptp.list_b)) (= (ho_24828 x z) (ho_24828 y z)))) (= x y))))) (let ((_let_1731 (forall ((x |u_(-> tptp.rat tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.rat tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_12412 x z) (ho_12412 y z)))) (= x y))))) (let ((_let_1732 (forall ((x |u_(-> tptp.option3562590408128118217it_nat tptp.nat)|) (y |u_(-> tptp.option3562590408128118217it_nat tptp.nat)|)) (or (not (forall ((z tptp.option3562590408128118217it_nat)) (= (ho_24666 x z) (ho_24666 y z)))) (= x y))))) (let ((_let_1733 (forall ((x |u_(-> tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_12413 x z) (ho_12413 y z)))) (= x y))))) (let ((_let_1734 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_25121 x z) (ho_25121 y z)))) (= x y))))) (let ((_let_1735 (forall ((x |u_(-> tptp.code_integer tptp.nat tptp.nat tptp.code_integer)|) (y |u_(-> tptp.code_integer tptp.nat tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12409 x z) (ho_12409 y z)))) (= x y))))) (let ((_let_1736 (forall ((x |u_(-> tptp.product_unit tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat)|) (y |u_(-> tptp.product_unit tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_22364 x z) (ho_22364 y z)))) (= x y))))) (let ((_let_1737 (forall ((x |u_(-> Bool tptp.num tptp.num tptp.num)|) (y |u_(-> Bool tptp.num tptp.num tptp.num)|)) (or (not (forall ((z Bool)) (= (ho_12556 x z) (ho_12556 y z)))) (= x y))))) (let ((_let_1738 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_11237 x z) (ho_11237 y z)))) (= x y))))) (let ((_let_1739 (forall ((x |u_(-> tptp.nat tptp.nat tptp.code_integer)|) (y |u_(-> tptp.nat tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.nat)) (= (ho_12410 x z) (ho_12410 y z)))) (= x y))))) (let ((_let_1740 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_11784 x z) (ho_11784 y z)))) (= x y))))) (let ((_let_1741 (forall ((x |u_(-> tptp.num tptp.rat)|) (y |u_(-> tptp.num tptp.rat)|)) (or (not (forall ((z tptp.num)) (= (ho_12457 x z) (ho_12457 y z)))) (= x y))))) (let ((_let_1742 (forall ((x |u_(-> tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.produc3843707927480180839at_nat)) (= (ho_12630 x z) (ho_12630 y z)))) (= x y))))) (let ((_let_1743 (forall ((x |u_(-> _u_(-> tptp.rat tptp.rat tptp.rat)_ _u_(-> tptp.rat tptp.rat Bool)_ _u_(-> tptp.rat tptp.rat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.rat tptp.rat tptp.rat)_ _u_(-> tptp.rat tptp.rat Bool)_ _u_(-> tptp.rat tptp.rat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.rat tptp.rat)|)) (= (ho_24338 x z) (ho_24338 y z)))) (= x y))))) (let ((_let_1744 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15567 x z) (ho_15567 y z)))) (= x y))))) (let ((_let_1745 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.produc7196121022310644452it_nat)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.produc7196121022310644452it_nat)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_11145 x z) (ho_11145 y z)))) (= x y))))) (let ((_let_1746 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (= (ho_18706 x z) (ho_18706 y z)))) (= x y))))) (let ((_let_1747 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (= (ho_25979 x z) (ho_25979 y z)))) (= x y))))) (let ((_let_1748 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12390 x z) (ho_12390 y z)))) (= x y))))) (let ((_let_1749 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.code_integer)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.code_integer)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_25777 x z) (ho_25777 y z)))) (= x y))))) (let ((_let_1750 (forall ((x |u_(-> tptp.list_int tptp.list_o tptp.list_P5087981734274514673_int_o)|) (y |u_(-> tptp.list_int tptp.list_o tptp.list_P5087981734274514673_int_o)|)) (or (not (forall ((z tptp.list_int)) (= (ho_24803 x z) (ho_24803 y z)))) (= x y))))) (let ((_let_1751 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_12255 x z) (ho_12255 y z)))) (= x y))))) (let ((_let_1752 (forall ((x |u_(-> tptp.list_o tptp.set_list_o Bool)|) (y |u_(-> tptp.list_o tptp.set_list_o Bool)|)) (or (not (forall ((z tptp.list_o)) (= (ho_25587 x z) (ho_25587 y z)))) (= x y))))) (let ((_let_1753 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat tptp.nat)_ tptp.nat tptp.code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat tptp.nat)_ tptp.nat tptp.code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat tptp.nat)|)) (= (ho_12240 x z) (ho_12240 y z)))) (= x y))))) (let ((_let_1754 (forall ((x |u_(-> tptp.set_int tptp.nat _u_(-> tptp.int tptp.nat)_ tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.nat _u_(-> tptp.int tptp.nat)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15877 x z) (ho_15877 y z)))) (= x y))))) (let ((_let_1755 (forall ((x |u_(-> tptp.heap_Time_Heap_nat _u_(-> tptp.nat tptp.assn)_ Bool)|) (y |u_(-> tptp.heap_Time_Heap_nat _u_(-> tptp.nat tptp.assn)_ Bool)|)) (or (not (forall ((z tptp.heap_Time_Heap_nat)) (= (ho_24696 x z) (ho_24696 y z)))) (= x y))))) (let ((_let_1756 (forall ((x |u_(-> _u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)_ tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|) (y |u_(-> _u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)_ tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|)) (= (ho_24365 x z) (ho_24365 y z)))) (= x y))))) (let ((_let_1757 (forall ((x |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ tptp.set_Pr958786334691620121nt_int tptp.nat)|) (y |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ tptp.set_Pr958786334691620121nt_int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)|)) (= (ho_18481 x z) (ho_18481 y z)))) (= x y))))) (let ((_let_1758 (forall ((x |u_(-> tptp.set_o Bool Bool)|) (y |u_(-> tptp.set_o Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_12571 x z) (ho_12571 y z)))) (= x y))))) (let ((_let_1759 (forall ((x |u_(-> tptp.product_prod_int_int tptp.set_int)|) (y |u_(-> tptp.product_prod_int_int tptp.set_int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_25140 x z) (ho_25140 y z)))) (= x y))))) (let ((_let_1760 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.int)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.int)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_25870 x z) (ho_25870 y z)))) (= x y))))) (let ((_let_1761 (forall ((x |u_(-> tptp.code_natural _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> tptp.code_natural _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_18755 x z) (ho_18755 y z)))) (= x y))))) (let ((_let_1762 (forall ((x |u_(-> tptp.rat tptp.rat tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_18281 x z) (ho_18281 y z)))) (= x y))))) (let ((_let_1763 (forall ((x |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_11407 x z) (ho_11407 y z)))) (= x y))))) (let ((_let_1764 (forall ((x |u_(-> _u_(-> tptp.array_o tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat)_ tptp.produc5011041761010125393t_unit tptp.produc8032495849646651230it_nat)|) (y |u_(-> _u_(-> tptp.array_o tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat)_ tptp.produc5011041761010125393t_unit tptp.produc8032495849646651230it_nat)|)) (or (not (forall ((z |u_(-> tptp.array_o tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat)|)) (= (ho_11812 x z) (ho_11812 y z)))) (= x y))))) (let ((_let_1765 (forall ((x |u_(-> tptp.nat tptp.list_int tptp.list_int)|) (y |u_(-> tptp.nat tptp.list_int tptp.list_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_24709 x z) (ho_24709 y z)))) (= x y))))) (let ((_let_1766 (forall ((x |u_(-> tptp.code_natural tptp.code_natural tptp.nat tptp.code_natural)|) (y |u_(-> tptp.code_natural tptp.code_natural tptp.nat tptp.code_natural)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_18198 x z) (ho_18198 y z)))) (= x y))))) (let ((_let_1767 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.int tptp.code_integer)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.int tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_15238 x z) (ho_15238 y z)))) (= x y))))) (let ((_let_1768 (forall ((x |u_(-> _u_(-> tptp.nat tptp.set_int)_ tptp.nat tptp.nat tptp.int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.set_int)_ tptp.nat tptp.nat tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.set_int)|)) (= (ho_21227 x z) (ho_21227 y z)))) (= x y))))) (let ((_let_1769 (forall ((x |u_(-> _u_(-> Bool tptp.nat tptp.int)_ tptp.nat Bool tptp.int)|) (y |u_(-> _u_(-> Bool tptp.nat tptp.int)_ tptp.nat Bool tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.nat tptp.int)|)) (= (ho_12233 x z) (ho_12233 y z)))) (= x y))))) (let ((_let_1770 (forall ((x |u_(-> tptp.product_prod_int_int tptp.set_set_nat)|) (y |u_(-> tptp.product_prod_int_int tptp.set_set_nat)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_25144 x z) (ho_25144 y z)))) (= x y))))) (let ((_let_1771 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_15406 x z) (ho_15406 y z)))) (= x y))))) (let ((_let_1772 (forall ((x |u_(-> tptp.num tptp.int)|) (y |u_(-> tptp.num tptp.int)|)) (or (not (forall ((z tptp.num)) (= (ho_12475 x z) (ho_12475 y z)))) (= x y))))) (let ((_let_1773 (forall ((x |u_(-> Bool tptp.list_o tptp.int tptp.nat tptp.int)|) (y |u_(-> Bool tptp.list_o tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z Bool)) (= (ho_18644 x z) (ho_18644 y z)))) (= x y))))) (let ((_let_1774 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_12228 x z) (ho_12228 y z)))) (= x y))))) (let ((_let_1775 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.int)|)) (= (ho_12327 x z) (ho_12327 y z)))) (= x y))))) (let ((_let_1776 (forall ((x |u_(-> tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat Bool)|) (y |u_(-> tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat Bool)|)) (or (not (forall ((z tptp.produc859450856879609959at_nat)) (= (ho_14481 x z) (ho_14481 y z)))) (= x y))))) (let ((_let_1777 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.a)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.a)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_22397 x z) (ho_22397 y z)))) (= x y))))) (let ((_let_1778 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.assn)_ _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer tptp.assn)|) (y |u_(-> _u_(-> tptp.code_integer tptp.assn)_ _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.assn)|)) (= (ho_15817 x z) (ho_15817 y z)))) (= x y))))) (let ((_let_1779 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.int _u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.int _u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_13231 x z) (ho_13231 y z)))) (= x y))))) (let ((_let_1780 (forall ((x |u_(-> tptp.set_set_nat tptp.set_nat)|) (y |u_(-> tptp.set_set_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_25846 x z) (ho_25846 y z)))) (= x y))))) (let ((_let_1781 (forall ((x |u_(-> tptp.nat tptp.code_integer tptp.int)|) (y |u_(-> tptp.nat tptp.code_integer tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_12226 x z) (ho_12226 y z)))) (= x y))))) (let ((_let_1782 (forall ((x |u_(-> tptp.list_o tptp.list_o Bool)|) (y |u_(-> tptp.list_o tptp.list_o Bool)|)) (or (not (forall ((z tptp.list_o)) (= (ho_20414 x z) (ho_20414 y z)))) (= x y))))) (let ((_let_1783 (forall ((x |u_(-> tptp.list_P131111800688179804it_nat tptp.list_P6935614879863011209it_nat)|) (y |u_(-> tptp.list_P131111800688179804it_nat tptp.list_P6935614879863011209it_nat)|)) (or (not (forall ((z tptp.list_P131111800688179804it_nat)) (= (ho_24985 x z) (ho_24985 y z)))) (= x y))))) (let ((_let_1784 (forall ((x |u_(-> tptp.set_list_nat tptp.set_list_nat tptp.list_nat Bool)|) (y |u_(-> tptp.set_list_nat tptp.set_list_nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_13259 x z) (ho_13259 y z)))) (= x y))))) (let ((_let_1785 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_16848 x z) (ho_16848 y z)))) (= x y))))) (let ((_let_1786 (forall ((x |u_(-> tptp.option_num Bool)|) (y |u_(-> tptp.option_num Bool)|)) (or (not (forall ((z tptp.option_num)) (= (ho_18600 x z) (ho_18600 y z)))) (= x y))))) (let ((_let_1787 (forall ((x |u_(-> _u_(-> Bool tptp.assn)_ Bool Bool)|) (y |u_(-> _u_(-> Bool tptp.assn)_ Bool Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.assn)|)) (= (ho_17173 x z) (ho_17173 y z)))) (= x y))))) (let ((_let_1788 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.option8963830502488799655at_nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.option8963830502488799655at_nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_13862 x z) (ho_13862 y z)))) (= x y))))) (let ((_let_1789 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int tptp.int)_ tptp.int tptp.code_integer tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int tptp.int)_ tptp.int tptp.code_integer tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int tptp.int)|)) (= (ho_12207 x z) (ho_12207 y z)))) (= x y))))) (let ((_let_1790 (forall ((x |u_(-> tptp.list_o tptp.heap_T5660665574680485309rray_o)|) (y |u_(-> tptp.list_o tptp.heap_T5660665574680485309rray_o)|)) (or (not (forall ((z tptp.list_o)) (= (ho_15667 x z) (ho_15667 y z)))) (= x y))))) (let ((_let_1791 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_12465 x z) (ho_12465 y z)))) (= x y))))) (let ((_let_1792 (forall ((x |u_(-> tptp.code_integer tptp.int tptp.int)|) (y |u_(-> tptp.code_integer tptp.int tptp.int)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12205 x z) (ho_12205 y z)))) (= x y))))) (let ((_let_1793 (forall ((x |u_(-> tptp.list_P7985473006766602707_nat_o tptp.list_P7985473006766602707_nat_o)|) (y |u_(-> tptp.list_P7985473006766602707_nat_o tptp.list_P7985473006766602707_nat_o)|)) (or (not (forall ((z tptp.list_P7985473006766602707_nat_o)) (= (ho_24967 x z) (ho_24967 y z)))) (= x y))))) (let ((_let_1794 (forall ((x |u_(-> tptp.assn tptp.assn tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.assn tptp.assn tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_13580 x z) (ho_13580 y z)))) (= x y))))) (let ((_let_1795 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.set_nat)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.set_nat)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_25173 x z) (ho_25173 y z)))) (= x y))))) (let ((_let_1796 (forall ((x |u_(-> tptp.int tptp.nat tptp.product_prod_int_nat)|) (y |u_(-> tptp.int tptp.nat tptp.product_prod_int_nat)|)) (or (not (forall ((z tptp.int)) (= (ho_24792 x z) (ho_24792 y z)))) (= x y))))) (let ((_let_1797 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int tptp.int)_ tptp.set_Code_integer _u_(-> tptp.code_integer tptp.int Bool)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int tptp.int)_ tptp.set_Code_integer _u_(-> tptp.code_integer tptp.int Bool)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int tptp.int)|)) (= (ho_17301 x z) (ho_17301 y z)))) (= x y))))) (let ((_let_1798 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.rat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.rat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.rat Bool)|)) (= (ho_25914 x z) (ho_25914 y z)))) (= x y))))) (let ((_let_1799 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)_ tptp.set_nat tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)_ tptp.set_nat tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_21987 x z) (ho_21987 y z)))) (= x y))))) (let ((_let_1800 (forall ((x |u_(-> tptp.produc7766336532480398636_nat_o Bool)|) (y |u_(-> tptp.produc7766336532480398636_nat_o Bool)|)) (or (not (forall ((z tptp.produc7766336532480398636_nat_o)) (= (ho_25243 x z) (ho_25243 y z)))) (= x y))))) (let ((_let_1801 (forall ((x |u_(-> tptp.rat tptp.set_rat Bool)|) (y |u_(-> tptp.rat tptp.set_rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_16779 x z) (ho_16779 y z)))) (= x y))))) (let ((_let_1802 (forall ((x |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer tptp.assn)|) (y |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer tptp.assn)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_17507 x z) (ho_17507 y z)))) (= x y))))) (let ((_let_1803 (forall ((x |u_(-> _u_(-> tptp.nat Bool tptp.nat)_ Bool tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat Bool tptp.nat)_ Bool tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool tptp.nat)|)) (= (ho_12197 x z) (ho_12197 y z)))) (= x y))))) (let ((_let_1804 (forall ((x |u_(-> _u_(-> tptp.list_nat Bool)_ tptp.set_list_nat)|) (y |u_(-> _u_(-> tptp.list_nat Bool)_ tptp.set_list_nat)|)) (or (not (forall ((z |u_(-> tptp.list_nat Bool)|)) (= (ho_11657 x z) (ho_11657 y z)))) (= x y))))) (let ((_let_1805 (forall ((x |u_(-> tptp.nat Bool tptp.nat)|) (y |u_(-> tptp.nat Bool tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_12195 x z) (ho_12195 y z)))) (= x y))))) (let ((_let_1806 (forall ((x |u_(-> tptp.nat tptp.produc6653097349344004940it_nat)|) (y |u_(-> tptp.nat tptp.produc6653097349344004940it_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11142 x z) (ho_11142 y z)))) (= x y))))) (let ((_let_1807 (forall ((x |u_(-> tptp.num tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.num tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_23807 x z) (ho_23807 y z)))) (= x y))))) (let ((_let_1808 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_15180 x z) (ho_15180 y z)))) (= x y))))) (let ((_let_1809 (forall ((x |u_(-> tptp.option4065278094766928714it_nat tptp.produc2207270350733924475it_nat)|) (y |u_(-> tptp.option4065278094766928714it_nat tptp.produc2207270350733924475it_nat)|)) (or (not (forall ((z tptp.option4065278094766928714it_nat)) (= (ho_24421 x z) (ho_24421 y z)))) (= x y))))) (let ((_let_1810 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.code_integer Bool)_ tptp.code_integer tptp.nat)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.code_integer Bool)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_15058 x z) (ho_15058 y z)))) (= x y))))) (let ((_let_1811 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int Bool)|)) (= (ho_12190 x z) (ho_12190 y z)))) (= x y))))) (let ((_let_1812 (forall ((x |u_(-> tptp.a tptp.assn)|) (y |u_(-> tptp.a tptp.assn)|)) (or (not (forall ((z tptp.a)) (= (ho_24264 x z) (ho_24264 y z)))) (= x y))))) (let ((_let_1813 (forall ((x |u_(-> tptp.rat tptp.product_prod_int_int)|) (y |u_(-> tptp.rat tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.rat)) (= (ho_11503 x z) (ho_11503 y z)))) (= x y))))) (let ((_let_1814 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat)_ _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat)_ _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.rat)|)) (= (ho_11121 x z) (ho_11121 y z)))) (= x y))))) (let ((_let_1815 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_11433 x z) (ho_11433 y z)))) (= x y))))) (let ((_let_1816 (forall ((x |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.assn)_ _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer tptp.assn)|) (y |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.assn)_ _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer tptp.assn)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_15816 x z) (ho_15816 y z)))) (= x y))))) (let ((_let_1817 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_24470 x z) (ho_24470 y z)))) (= x y))))) (let ((_let_1818 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int tptp.nat)_ tptp.int tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.int tptp.nat)_ tptp.int tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int tptp.nat)|)) (= (ho_12186 x z) (ho_12186 y z)))) (= x y))))) (let ((_let_1819 (forall ((x |u_(-> _u_(-> tptp.option_num tptp.int)_ _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.int)|) (y |u_(-> _u_(-> tptp.option_num tptp.int)_ _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.int)|)) (or (not (forall ((z |u_(-> tptp.option_num tptp.int)|)) (= (ho_22681 x z) (ho_22681 y z)))) (= x y))))) (let ((_let_1820 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.array_o tptp.nat Bool)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.array_o tptp.nat Bool)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_25571 x z) (ho_25571 y z)))) (= x y))))) (let ((_let_1821 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_o)|) (y |u_(-> tptp.nat tptp.product_prod_nat_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_24755 x z) (ho_24755 y z)))) (= x y))))) (let ((_let_1822 (forall ((x |u_(-> tptp.int tptp.nat tptp.nat)|) (y |u_(-> tptp.int tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.int)) (= (ho_12187 x z) (ho_12187 y z)))) (= x y))))) (let ((_let_1823 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat tptp.nat)_ tptp.set_nat _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat tptp.nat)_ tptp.set_nat _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat tptp.nat)|)) (= (ho_17336 x z) (ho_17336 y z)))) (= x y))))) (let ((_let_1824 (forall ((x |u_(-> tptp.nat _u_(-> tptp.num tptp.nat)_ tptp.option_num tptp.nat)|) (y |u_(-> tptp.nat _u_(-> tptp.num tptp.nat)_ tptp.option_num tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_25183 x z) (ho_25183 y z)))) (= x y))))) (let ((_let_1825 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_12182 x z) (ho_12182 y z)))) (= x y))))) (let ((_let_1826 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.set_int)_ tptp.product_prod_int_int tptp.set_int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.set_int)_ tptp.product_prod_int_int tptp.set_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.set_int)|)) (= (ho_25139 x z) (ho_25139 y z)))) (= x y))))) (let ((_let_1827 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.assn)_ _u_(-> tptp.nat tptp.assn)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.assn)_ _u_(-> tptp.nat tptp.assn)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_17166 x z) (ho_17166 y z)))) (= x y))))) (let ((_let_1828 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ Bool Bool Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ Bool Bool Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_11598 x z) (ho_11598 y z)))) (= x y))))) (let ((_let_1829 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.set_Pr958786334691620121nt_int)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.set_Pr958786334691620121nt_int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_14415 x z) (ho_14415 y z)))) (= x y))))) (let ((_let_1830 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int Bool)|)) (= (ho_12183 x z) (ho_12183 y z)))) (= x y))))) (let ((_let_1831 (forall ((x |u_(-> tptp.int _u_(-> tptp.int Bool)_ tptp.int _u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)_ tptp.int tptp.int Bool)|) (y |u_(-> tptp.int _u_(-> tptp.int Bool)_ tptp.int _u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_13230 x z) (ho_13230 y z)))) (= x y))))) (let ((_let_1832 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.code_integer tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.code_integer tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer Bool)|)) (= (ho_12179 x z) (ho_12179 y z)))) (= x y))))) (let ((_let_1833 (forall ((x |u_(-> tptp.code_integer tptp.nat)|) (y |u_(-> tptp.code_integer tptp.nat)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12176 x z) (ho_12176 y z)))) (= x y))))) (let ((_let_1834 (forall ((x |u_(-> tptp.list_nat tptp.nat tptp.nat)|) (y |u_(-> tptp.list_nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_15679 x z) (ho_15679 y z)))) (= x y))))) (let ((_let_1835 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.code_integer)_ _u_(-> Bool tptp.code_integer)_ Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.code_integer)_ _u_(-> Bool tptp.code_integer)_ Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_17198 x z) (ho_17198 y z)))) (= x y))))) (let ((_let_1836 (forall ((x |u_(-> tptp.produc1399344845416535567atural Bool)|) (y |u_(-> tptp.produc1399344845416535567atural Bool)|)) (or (not (forall ((z tptp.produc1399344845416535567atural)) (= (ho_25276 x z) (ho_25276 y z)))) (= x y))))) (let ((_let_1837 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_12544 x z) (ho_12544 y z)))) (= x y))))) (let ((_let_1838 (forall ((x |u_(-> tptp.set_nat tptp.set_set_nat)|) (y |u_(-> tptp.set_nat tptp.set_set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_12468 x z) (ho_12468 y z)))) (= x y))))) (let ((_let_1839 (forall ((x |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.produc1219242969750017639nt_int)|) (y |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.produc1219242969750017639nt_int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_24860 x z) (ho_24860 y z)))) (= x y))))) (let ((_let_1840 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer tptp.nat)_ tptp.code_integer tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer tptp.nat)_ tptp.code_integer tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer tptp.nat)|)) (= (ho_12174 x z) (ho_12174 y z)))) (= x y))))) (let ((_let_1841 (forall ((x |u_(-> tptp.code_integer tptp.nat tptp.nat)|) (y |u_(-> tptp.code_integer tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12175 x z) (ho_12175 y z)))) (= x y))))) (let ((_let_1842 (forall ((x |u_(-> tptp.b tptp.set_Pr4389693562480114009it_nat)|) (y |u_(-> tptp.b tptp.set_Pr4389693562480114009it_nat)|)) (or (not (forall ((z tptp.b)) (= (ho_25034 x z) (ho_25034 y z)))) (= x y))))) (let ((_let_1843 (forall ((x |u_(-> Bool Bool)|) (y |u_(-> Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_11194 x z) (ho_11194 y z)))) (= x y))))) (let ((_let_1844 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat Bool)|)) (= (ho_12229 x z) (ho_12229 y z)))) (= x y))))) (let ((_let_1845 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int)_ _u_(-> _u_(-> tptp.int tptp.int)_ tptp.code_integer tptp.code_integer)_ _u_(-> tptp.int tptp.int tptp.int)_ tptp.code_integer tptp.code_integer tptp.code_integer)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int)_ _u_(-> _u_(-> tptp.int tptp.int)_ tptp.code_integer tptp.code_integer)_ _u_(-> tptp.int tptp.int tptp.int)_ tptp.code_integer tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int)|)) (= (ho_12159 x z) (ho_12159 y z)))) (= x y))))) (let ((_let_1846 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ Bool tptp.nat)|) (y |u_(-> _u_(-> Bool Bool Bool)_ Bool tptp.nat)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_14908 x z) (ho_14908 y z)))) (= x y))))) (let ((_let_1847 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)_ tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)_ tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_23105 x z) (ho_23105 y z)))) (= x y))))) (let ((_let_1848 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.product_unit)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.product_unit)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_22403 x z) (ho_22403 y z)))) (= x y))))) (let ((_let_1849 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int tptp.int)_ tptp.code_integer tptp.code_integer)_ _u_(-> tptp.int tptp.int tptp.int)_ tptp.code_integer tptp.code_integer tptp.code_integer)|) (y |u_(-> _u_(-> _u_(-> tptp.int tptp.int)_ tptp.code_integer tptp.code_integer)_ _u_(-> tptp.int tptp.int tptp.int)_ tptp.code_integer tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int tptp.int)_ tptp.code_integer tptp.code_integer)|)) (= (ho_12160 x z) (ho_12160 y z)))) (= x y))))) (let ((_let_1850 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_22606 x z) (ho_22606 y z)))) (= x y))))) (let ((_let_1851 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int Bool)_ tptp.code_integer tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int Bool)_ tptp.code_integer tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int Bool)|)) (= (ho_17296 x z) (ho_17296 y z)))) (= x y))))) (let ((_let_1852 (forall ((x |u_(-> Bool tptp.product_prod_nat_o)|) (y |u_(-> Bool tptp.product_prod_nat_o)|)) (or (not (forall ((z Bool)) (= (ho_24749 x z) (ho_24749 y z)))) (= x y))))) (let ((_let_1853 (forall ((x |u_(-> _u_(-> Bool tptp.nat)_ Bool tptp.nat)|) (y |u_(-> _u_(-> Bool tptp.nat)_ Bool tptp.nat)|)) (or (not (forall ((z |u_(-> Bool tptp.nat)|)) (= (ho_15757 x z) (ho_15757 y z)))) (= x y))))) (let ((_let_1854 (forall ((x |u_(-> tptp.nat tptp.code_integer tptp.code_integer)|) (y |u_(-> tptp.nat tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z tptp.nat)) (= (ho_12439 x z) (ho_12439 y z)))) (= x y))))) (let ((_let_1855 (forall ((x |u_(-> tptp.code_integer tptp.int)|) (y |u_(-> tptp.code_integer tptp.int)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12154 x z) (ho_12154 y z)))) (= x y))))) (let ((_let_1856 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.nat)_ tptp.set_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.set_nat tptp.nat)_ tptp.set_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.nat)|)) (= (ho_14911 x z) (ho_14911 y z)))) (= x y))))) (let ((_let_1857 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_12253 x z) (ho_12253 y z)))) (= x y))))) (let ((_let_1858 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat Bool)|)) (= (ho_11554 x z) (ho_11554 y z)))) (= x y))))) (let ((_let_1859 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer)_ tptp.set_int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer)_ tptp.set_int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer)|)) (= (ho_15357 x z) (ho_15357 y z)))) (= x y))))) (let ((_let_1860 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.int Bool)_ tptp.int tptp.int)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.int Bool)_ tptp.int tptp.int)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_17302 x z) (ho_17302 y z)))) (= x y))))) (let ((_let_1861 (forall ((x |u_(-> tptp.code_integer tptp.code_integer)|) (y |u_(-> tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12130 x z) (ho_12130 y z)))) (= x y))))) (let ((_let_1862 (forall ((x |u_(-> _u_(-> tptp.b tptp.heap_Time_Heap_a)_ tptp.heap_Time_Heap_b tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.heap_Time_Heap_a)_ tptp.heap_Time_Heap_b tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.heap_Time_Heap_a)|)) (= (ho_19866 x z) (ho_19866 y z)))) (= x y))))) (let ((_let_1863 (forall ((x |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_13147 x z) (ho_13147 y z)))) (= x y))))) (let ((_let_1864 (forall ((x |u_(-> tptp.option4065278094766928714it_nat _u_(-> tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)_ tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.option4065278094766928714it_nat _u_(-> tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)_ tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.option4065278094766928714it_nat)) (= (ho_19882 x z) (ho_19882 y z)))) (= x y))))) (let ((_let_1865 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.code_integer tptp.code_integer)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_25999 x z) (ho_25999 y z)))) (= x y))))) (let ((_let_1866 (forall ((x |u_(-> tptp.list_b tptp.list_P131111800688179804it_nat tptp.list_P7438302566501821706it_nat)|) (y |u_(-> tptp.list_b tptp.list_P131111800688179804it_nat tptp.list_P7438302566501821706it_nat)|)) (or (not (forall ((z tptp.list_b)) (= (ho_24822 x z) (ho_24822 y z)))) (= x y))))) (let ((_let_1867 (forall ((x |u_(-> tptp.list_nat _u_(-> tptp.list_nat tptp.nat)_ tptp.list_nat Bool)|) (y |u_(-> tptp.list_nat _u_(-> tptp.list_nat tptp.nat)_ tptp.list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_16943 x z) (ho_16943 y z)))) (= x y))))) (let ((_let_1868 (forall ((x |u_(-> _u_(-> tptp.rat tptp.product_prod_int_int)_ _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.rat tptp.product_prod_int_int)_ _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.product_prod_int_int)|)) (= (ho_12141 x z) (ho_12141 y z)))) (= x y))))) (let ((_let_1869 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.nat)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.nat)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_24659 x z) (ho_24659 y z)))) (= x y))))) (let ((_let_1870 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat tptp.nat)_ tptp.set_nat _u_(-> tptp.int tptp.nat Bool)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat tptp.nat)_ tptp.set_nat _u_(-> tptp.int tptp.nat Bool)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat tptp.nat)|)) (= (ho_17344 x z) (ho_17344 y z)))) (= x y))))) (let ((_let_1871 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12129 x z) (ho_12129 y z)))) (= x y))))) (let ((_let_1872 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_25962 x z) (ho_25962 y z)))) (= x y))))) (let ((_let_1873 (forall ((x |u_(-> tptp.produc3658429121746597890et_nat tptp.set_nat)|) (y |u_(-> tptp.produc3658429121746597890et_nat tptp.set_nat)|)) (or (not (forall ((z tptp.produc3658429121746597890et_nat)) (= (ho_14620 x z) (ho_14620 y z)))) (= x y))))) (let ((_let_1874 (forall ((x |u_(-> tptp.product_unit tptp.product_unit)|) (y |u_(-> tptp.product_unit tptp.product_unit)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_25085 x z) (ho_25085 y z)))) (= x y))))) (let ((_let_1875 (forall ((x |u_(-> tptp.nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11293 x z) (ho_11293 y z)))) (= x y))))) (let ((_let_1876 (forall ((x |u_(-> tptp.int tptp.set_Pr958786334691620121nt_int tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.set_Pr958786334691620121nt_int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_13224 x z) (ho_13224 y z)))) (= x y))))) (let ((_let_1877 (forall ((x |u_(-> Bool tptp.code_integer Bool)|) (y |u_(-> Bool tptp.code_integer Bool)|)) (or (not (forall ((z Bool)) (= (ho_11583 x z) (ho_11583 y z)))) (= x y))))) (let ((_let_1878 (forall ((x |u_(-> tptp.set_Pr719794911490849221et_nat Bool)|) (y |u_(-> tptp.set_Pr719794911490849221et_nat Bool)|)) (or (not (forall ((z tptp.set_Pr719794911490849221et_nat)) (= (ho_25029 x z) (ho_25029 y z)))) (= x y))))) (let ((_let_1879 (forall ((x |u_(-> _u_(-> tptp.int tptp.assn)_ _u_(-> tptp.int tptp.assn)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.assn)_ _u_(-> tptp.int tptp.assn)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.assn)|)) (= (ho_12119 x z) (ho_12119 y z)))) (= x y))))) (let ((_let_1880 (forall ((x |u_(-> _u_(-> Bool tptp.int)_ tptp.list_o tptp.int tptp.nat tptp.int)|) (y |u_(-> _u_(-> Bool tptp.int)_ tptp.list_o tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.int)|)) (= (ho_18650 x z) (ho_18650 y z)))) (= x y))))) (let ((_let_1881 (forall ((x |u_(-> tptp.nat tptp.set_nat tptp.set_nat)|) (y |u_(-> tptp.nat tptp.set_nat tptp.set_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_19104 x z) (ho_19104 y z)))) (= x y))))) (let ((_let_1882 (forall ((x |u_(-> tptp.num tptp.num)|) (y |u_(-> tptp.num tptp.num)|)) (or (not (forall ((z tptp.num)) (= (ho_11030 x z) (ho_11030 y z)))) (= x y))))) (let ((_let_1883 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat tptp.nat)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_17357 x z) (ho_17357 y z)))) (= x y))))) (let ((_let_1884 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_25978 x z) (ho_25978 y z)))) (= x y))))) (let ((_let_1885 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_15269 x z) (ho_15269 y z)))) (= x y))))) (let ((_let_1886 (forall ((x |u_(-> tptp.nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11385 x z) (ho_11385 y z)))) (= x y))))) (let ((_let_1887 (forall ((x |u_(-> _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.assn)|)) (= (ho_23784 x z) (ho_23784 y z)))) (= x y))))) (let ((_let_1888 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer tptp.code_integer)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer)|)) (= (ho_17991 x z) (ho_17991 y z)))) (= x y))))) (let ((_let_1889 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool Bool)_ Bool tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer Bool Bool)_ Bool tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool Bool)|)) (= (ho_14847 x z) (ho_14847 y z)))) (= x y))))) (let ((_let_1890 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.nat)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.nat)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_12107 x z) (ho_12107 y z)))) (= x y))))) (let ((_let_1891 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12397 x z) (ho_12397 y z)))) (= x y))))) (let ((_let_1892 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_17221 x z) (ho_17221 y z)))) (= x y))))) (let ((_let_1893 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_17572 x z) (ho_17572 y z)))) (= x y))))) (let ((_let_1894 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.nat)_ tptp.int Bool)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.nat)_ tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_12063 x z) (ho_12063 y z)))) (= x y))))) (let ((_let_1895 (forall ((x |u_(-> tptp.nat tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_11239 x z) (ho_11239 y z)))) (= x y))))) (let ((_let_1896 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.nat tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.nat tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer Bool)|)) (= (ho_12171 x z) (ho_12171 y z)))) (= x y))))) (let ((_let_1897 (forall ((x |u_(-> tptp.nat tptp.assn)|) (y |u_(-> tptp.nat tptp.assn)|)) (or (not (forall ((z tptp.nat)) (= (ho_12032 x z) (ho_12032 y z)))) (= x y))))) (let ((_let_1898 (forall ((x |u_(-> Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z Bool)) (= (ho_12393 x z) (ho_12393 y z)))) (= x y))))) (let ((_let_1899 (forall ((x |u_(-> _u_(-> tptp.int tptp.assn)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.assn)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.assn)|)) (= (ho_12031 x z) (ho_12031 y z)))) (= x y))))) (let ((_let_1900 (forall ((x |u_(-> tptp.rat tptp.int tptp.rat)|) (y |u_(-> tptp.rat tptp.int tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_15306 x z) (ho_15306 y z)))) (= x y))))) (let ((_let_1901 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.set_o)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.set_o)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_25155 x z) (ho_25155 y z)))) (= x y))))) (let ((_let_1902 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.rat Bool)|)) (= (ho_25896 x z) (ho_25896 y z)))) (= x y))))) (let ((_let_1903 (forall ((x |u_(-> tptp.set_int tptp.set_int tptp.set_int Bool)|) (y |u_(-> tptp.set_int tptp.set_int tptp.set_int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_17415 x z) (ho_17415 y z)))) (= x y))))) (let ((_let_1904 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)|)) (= (ho_25908 x z) (ho_25908 y z)))) (= x y))))) (let ((_let_1905 (forall ((x |u_(-> Bool _u_(-> Bool Bool)_ Bool Bool)|) (y |u_(-> Bool _u_(-> Bool Bool)_ Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_19165 x z) (ho_19165 y z)))) (= x y))))) (let ((_let_1906 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.assn)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_12029 x z) (ho_12029 y z)))) (= x y))))) (let ((_let_1907 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_11878 x z) (ho_11878 y z)))) (= x y))))) (let ((_let_1908 (forall ((x |u_(-> tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat)|) (y |u_(-> tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat)|)) (or (not (forall ((z tptp.produc3925858234332021118et_nat)) (= (ho_25107 x z) (ho_25107 y z)))) (= x y))))) (let ((_let_1909 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.nat tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.nat tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_12170 x z) (ho_12170 y z)))) (= x y))))) (let ((_let_1910 (forall ((x |u_(-> _u_(-> tptp.produc50402934264563236_nat_o tptp.produc50402934264563236_nat_o Bool)_ tptp.produc50402934264563236_nat_o Bool)|) (y |u_(-> _u_(-> tptp.produc50402934264563236_nat_o tptp.produc50402934264563236_nat_o Bool)_ tptp.produc50402934264563236_nat_o Bool)|)) (or (not (forall ((z |u_(-> tptp.produc50402934264563236_nat_o tptp.produc50402934264563236_nat_o Bool)|)) (= (ho_25231 x z) (ho_25231 y z)))) (= x y))))) (let ((_let_1911 (forall ((x |u_(-> tptp.code_natural _u_(-> tptp.int tptp.code_natural)_ tptp.int Bool)|) (y |u_(-> tptp.code_natural _u_(-> tptp.int tptp.code_natural)_ tptp.int Bool)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_11869 x z) (ho_11869 y z)))) (= x y))))) (let ((_let_1912 (forall ((x |u_(-> Bool tptp.product_unit)|) (y |u_(-> Bool tptp.product_unit)|)) (or (not (forall ((z Bool)) (= (ho_22394 x z) (ho_22394 y z)))) (= x y))))) (let ((_let_1913 (forall ((x |u_(-> tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_12276 x z) (ho_12276 y z)))) (= x y))))) (let ((_let_1914 (forall ((x |u_(-> _u_(-> tptp.nat Bool Bool)_ Bool tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool Bool)_ Bool tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool Bool)|)) (= (ho_12202 x z) (ho_12202 y z)))) (= x y))))) (let ((_let_1915 (forall ((x |u_(-> tptp.int tptp.list_int tptp.list_int)|) (y |u_(-> tptp.int tptp.list_int tptp.list_int)|)) (or (not (forall ((z tptp.int)) (= (ho_14665 x z) (ho_14665 y z)))) (= x y))))) (let ((_let_1916 (forall ((x |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.multis2468970476368604999at_nat)) (= (ho_18816 x z) (ho_18816 y z)))) (= x y))))) (let ((_let_1917 (forall ((x |u_(-> tptp.set_nat tptp.set_set_nat tptp.set_set_nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_set_nat tptp.set_set_nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_19239 x z) (ho_19239 y z)))) (= x y))))) (let ((_let_1918 (forall ((x |u_(-> _u_(-> tptp.produc7388388658123137530it_nat Bool)_ tptp.option4065278094766928714it_nat Bool)|) (y |u_(-> _u_(-> tptp.produc7388388658123137530it_nat Bool)_ tptp.option4065278094766928714it_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc7388388658123137530it_nat Bool)|)) (= (ho_24445 x z) (ho_24445 y z)))) (= x y))))) (let ((_let_1919 (forall ((x |u_(-> tptp.list_P3521021558325789923at_int tptp.nat tptp.product_prod_nat_int)|) (y |u_(-> tptp.list_P3521021558325789923at_int tptp.nat tptp.product_prod_nat_int)|)) (or (not (forall ((z tptp.list_P3521021558325789923at_int)) (= (ho_24763 x z) (ho_24763 y z)))) (= x y))))) (let ((_let_1920 (forall ((x |u_(-> tptp.option_set_o tptp.set_o)|) (y |u_(-> tptp.option_set_o tptp.set_o)|)) (or (not (forall ((z tptp.option_set_o)) (= (ho_24535 x z) (ho_24535 y z)))) (= x y))))) (let ((_let_1921 (forall ((x |u_(-> tptp.int tptp.option_int)|) (y |u_(-> tptp.int tptp.option_int)|)) (or (not (forall ((z tptp.int)) (= (ho_14285 x z) (ho_14285 y z)))) (= x y))))) (let ((_let_1922 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.rat)_ Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.rat)_ Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_15128 x z) (ho_15128 y z)))) (= x y))))) (let ((_let_1923 (forall ((x |u_(-> tptp.code_natural tptp.code_natural Bool)|) (y |u_(-> tptp.code_natural tptp.code_natural Bool)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_11863 x z) (ho_11863 y z)))) (= x y))))) (let ((_let_1924 (forall ((x |u_(-> tptp.int tptp.int tptp.set_Pr958786334691620121nt_int tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int tptp.set_Pr958786334691620121nt_int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_13223 x z) (ho_13223 y z)))) (= x y))))) (let ((_let_1925 (forall ((x |u_(-> tptp.option_set_o tptp.option_set_o tptp.option_set_o)|) (y |u_(-> tptp.option_set_o tptp.option_set_o tptp.option_set_o)|)) (or (not (forall ((z tptp.option_set_o)) (= (ho_22426 x z) (ho_22426 y z)))) (= x y))))) (let ((_let_1926 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_11856 x z) (ho_11856 y z)))) (= x y))))) (let ((_let_1927 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.int)_ tptp.int Bool)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.int)_ tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_11852 x z) (ho_11852 y z)))) (= x y))))) (let ((_let_1928 (forall ((x |u_(-> tptp.num tptp.product_prod_int_int)|) (y |u_(-> tptp.num tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.num)) (= (ho_20130 x z) (ho_20130 y z)))) (= x y))))) (let ((_let_1929 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_12613 x z) (ho_12613 y z)))) (= x y))))) (let ((_let_1930 (forall ((x |u_(-> _u_(-> Bool tptp.nat Bool)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> Bool tptp.nat Bool)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.nat Bool)|)) (= (ho_17334 x z) (ho_17334 y z)))) (= x y))))) (let ((_let_1931 (forall ((x |u_(-> _u_(-> tptp.list_nat tptp.nat)_ tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.list_nat tptp.nat)_ tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.list_nat tptp.nat)|)) (= (ho_11848 x z) (ho_11848 y z)))) (= x y))))) (let ((_let_1932 (forall ((x |u_(-> tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o)|) (y |u_(-> tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z tptp.produc6271795597528267376eger_o)) (= (ho_26132 x z) (ho_26132 y z)))) (= x y))))) (let ((_let_1933 (forall ((x |u_(-> _u_(-> tptp.a tptp.heap_T5738788834812785303t_unit)_ tptp.a tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.heap_T5738788834812785303t_unit)_ tptp.a tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.heap_T5738788834812785303t_unit)|)) (= (ho_11382 x z) (ho_11382 y z)))) (= x y))))) (let ((_let_1934 (forall ((x |u_(-> _u_(-> Bool tptp.nat tptp.nat)_ tptp.nat Bool tptp.nat)|) (y |u_(-> _u_(-> Bool tptp.nat tptp.nat)_ tptp.nat Bool tptp.nat)|)) (or (not (forall ((z |u_(-> Bool tptp.nat tptp.nat)|)) (= (ho_12249 x z) (ho_12249 y z)))) (= x y))))) (let ((_let_1935 (forall ((x |u_(-> tptp.list_P7333126701944960589_nat_o tptp.nat)|) (y |u_(-> tptp.list_P7333126701944960589_nat_o tptp.nat)|)) (or (not (forall ((z tptp.list_P7333126701944960589_nat_o)) (= (ho_25001 x z) (ho_25001 y z)))) (= x y))))) (let ((_let_1936 (forall ((x |u_(-> _u_(-> tptp.a tptp.heap_Time_Heap_b)_ tptp.a tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.heap_Time_Heap_b)_ tptp.a tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.heap_Time_Heap_b)|)) (= (ho_11306 x z) (ho_11306 y z)))) (= x y))))) (let ((_let_1937 (forall ((x |u_(-> tptp.num tptp.option_num)|) (y |u_(-> tptp.num tptp.option_num)|)) (or (not (forall ((z tptp.num)) (= (ho_11028 x z) (ho_11028 y z)))) (= x y))))) (let ((_let_1938 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.rat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.rat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_25983 x z) (ho_25983 y z)))) (= x y))))) (let ((_let_1939 (forall ((x |u_(-> tptp.int tptp.int tptp.set_o)|) (y |u_(-> tptp.int tptp.int tptp.set_o)|)) (or (not (forall ((z tptp.int)) (= (ho_25128 x z) (ho_25128 y z)))) (= x y))))) (let ((_let_1940 (forall ((x |u_(-> _u_(-> tptp.option_num Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.option_num Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.option_num Bool)|)) (= (ho_22644 x z) (ho_22644 y z)))) (= x y))))) (let ((_let_1941 (forall ((x |u_(-> tptp.list_o tptp.heap_e7401611519738050253t_unit tptp.produc5011041761010125393t_unit)|) (y |u_(-> tptp.list_o tptp.heap_e7401611519738050253t_unit tptp.produc5011041761010125393t_unit)|)) (or (not (forall ((z tptp.list_o)) (= (ho_11809 x z) (ho_11809 y z)))) (= x y))))) (let ((_let_1942 (forall ((x |u_(-> Bool _u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ _u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|) (y |u_(-> Bool _u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ _u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (or (not (forall ((z Bool)) (= (ho_18737 x z) (ho_18737 y z)))) (= x y))))) (let ((_let_1943 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.code_integer tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.code_integer tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_12178 x z) (ho_12178 y z)))) (= x y))))) (let ((_let_1944 (forall ((x |u_(-> tptp.list_int tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat)|) (y |u_(-> tptp.list_int tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat)|)) (or (not (forall ((z tptp.list_int)) (= (ho_11807 x z) (ho_11807 y z)))) (= x y))))) (let ((_let_1945 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_15228 x z) (ho_15228 y z)))) (= x y))))) (let ((_let_1946 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_11785 x z) (ho_11785 y z)))) (= x y))))) (let ((_let_1947 (forall ((x |u_(-> tptp.produc4471711990508489141at_nat Bool)|) (y |u_(-> tptp.produc4471711990508489141at_nat Bool)|)) (or (not (forall ((z tptp.produc4471711990508489141at_nat)) (= (ho_24604 x z) (ho_24604 y z)))) (= x y))))) (let ((_let_1948 (forall ((x |u_(-> tptp.option_num tptp.num)|) (y |u_(-> tptp.option_num tptp.num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_11048 x z) (ho_11048 y z)))) (= x y))))) (let ((_let_1949 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.int)_ tptp.heap_T1346037964561226099ay_int)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.int)_ tptp.heap_T1346037964561226099ay_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_15661 x z) (ho_15661 y z)))) (= x y))))) (let ((_let_1950 (forall ((x |u_(-> tptp.product_prod_int_int tptp.set_se6260736226359567993nt_int)|) (y |u_(-> tptp.product_prod_int_int tptp.set_se6260736226359567993nt_int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_25149 x z) (ho_25149 y z)))) (= x y))))) (let ((_let_1951 (forall ((x |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)|) (y |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_11501 x z) (ho_11501 y z)))) (= x y))))) (let ((_let_1952 (forall ((x |u_(-> tptp.ref_Product_unit tptp.product_unit tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)|) (y |u_(-> tptp.ref_Product_unit tptp.product_unit tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)|)) (or (not (forall ((z tptp.ref_Product_unit)) (= (ho_25087 x z) (ho_25087 y z)))) (= x y))))) (let ((_let_1953 (forall ((x |u_(-> tptp.int tptp.list_int tptp.rat tptp.nat tptp.rat)|) (y |u_(-> tptp.int tptp.list_int tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_18683 x z) (ho_18683 y z)))) (= x y))))) (let ((_let_1954 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option8956607266484857688it_nat)_ tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option8956607266484857688it_nat)_ tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option8956607266484857688it_nat)|)) (= (ho_14313 x z) (ho_14313 y z)))) (= x y))))) (let ((_let_1955 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer Bool)_ tptp.code_integer tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer Bool)_ tptp.code_integer tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer Bool)|)) (= (ho_11755 x z) (ho_11755 y z)))) (= x y))))) (let ((_let_1956 (forall ((x |u_(-> tptp.set_nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_11705 x z) (ho_11705 y z)))) (= x y))))) (let ((_let_1957 (forall ((x |u_(-> tptp.nat tptp.num tptp.option_num)|) (y |u_(-> tptp.nat tptp.num tptp.option_num)|)) (or (not (forall ((z tptp.nat)) (= (ho_11033 x z) (ho_11033 y z)))) (= x y))))) (let ((_let_1958 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat Bool Bool)_ Bool tptp.nat)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat Bool Bool)_ Bool tptp.nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_17287 x z) (ho_17287 y z)))) (= x y))))) (let ((_let_1959 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.nat Bool)_ tptp.nat tptp.int)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.nat Bool)_ tptp.nat tptp.int)|)) (or (not (forall ((z tptp.set_o)) (= (ho_17333 x z) (ho_17333 y z)))) (= x y))))) (let ((_let_1960 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (= (ho_18756 x z) (ho_18756 y z)))) (= x y))))) (let ((_let_1961 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.code_integer)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.code_integer)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_11690 x z) (ho_11690 y z)))) (= x y))))) (let ((_let_1962 (forall ((x |u_(-> tptp.list_nat tptp.list_int tptp.list_P3521021558325789923at_int)|) (y |u_(-> tptp.list_nat tptp.list_int tptp.list_P3521021558325789923at_int)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_24760 x z) (ho_24760 y z)))) (= x y))))) (let ((_let_1963 (forall ((x |u_(-> tptp.nat tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.nat tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11314 x z) (ho_11314 y z)))) (= x y))))) (let ((_let_1964 (forall ((x |u_(-> tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_11508 x z) (ho_11508 y z)))) (= x y))))) (let ((_let_1965 (forall ((x |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (= (ho_18705 x z) (ho_18705 y z)))) (= x y))))) (let ((_let_1966 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.code_integer tptp.nat)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_17266 x z) (ho_17266 y z)))) (= x y))))) (let ((_let_1967 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_11260 x z) (ho_11260 y z)))) (= x y))))) (let ((_let_1968 (forall ((x |u_(-> tptp.list_o tptp.list_o)|) (y |u_(-> tptp.list_o tptp.list_o)|)) (or (not (forall ((z tptp.list_o)) (= (ho_18648 x z) (ho_18648 y z)))) (= x y))))) (let ((_let_1969 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)|)) (= (ho_24387 x z) (ho_24387 y z)))) (= x y))))) (let ((_let_1970 (forall ((x |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)_ tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)_ tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)|)) (= (ho_23096 x z) (ho_23096 y z)))) (= x y))))) (let ((_let_1971 (forall ((x |u_(-> tptp.set_int tptp.set_int tptp.set_set_int)|) (y |u_(-> tptp.set_int tptp.set_int tptp.set_set_int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_25337 x z) (ho_25337 y z)))) (= x y))))) (let ((_let_1972 (forall ((x |u_(-> tptp.code_integer tptp.assn)|) (y |u_(-> tptp.code_integer tptp.assn)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_15814 x z) (ho_15814 y z)))) (= x y))))) (let ((_let_1973 (forall ((x |u_(-> tptp.b tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.b tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.b)) (= (ho_11303 x z) (ho_11303 y z)))) (= x y))))) (let ((_let_1974 (forall ((x |u_(-> tptp.set_set_nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_set_nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_12650 x z) (ho_12650 y z)))) (= x y))))) (let ((_let_1975 (forall ((x |u_(-> tptp.list_int Bool)|) (y |u_(-> tptp.list_int Bool)|)) (or (not (forall ((z tptp.list_int)) (= (ho_20411 x z) (ho_20411 y z)))) (= x y))))) (let ((_let_1976 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_15246 x z) (ho_15246 y z)))) (= x y))))) (let ((_let_1977 (forall ((x |u_(-> tptp.nat tptp.nat tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_21238 x z) (ho_21238 y z)))) (= x y))))) (let ((_let_1978 (forall ((x |u_(-> _u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ _u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|) (y |u_(-> _u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ _u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (= (ho_18738 x z) (ho_18738 y z)))) (= x y))))) (let ((_let_1979 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.produc6751673265320737416it_nat)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.produc6751673265320737416it_nat)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_11163 x z) (ho_11163 y z)))) (= x y))))) (let ((_let_1980 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int Bool Bool)_ Bool tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int Bool Bool)_ Bool tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_14884 x z) (ho_14884 y z)))) (= x y))))) (let ((_let_1981 (forall ((x |u_(-> tptp.num tptp.set_num)|) (y |u_(-> tptp.num tptp.set_num)|)) (or (not (forall ((z tptp.num)) (= (ho_25344 x z) (ho_25344 y z)))) (= x y))))) (let ((_let_1982 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_11763 x z) (ho_11763 y z)))) (= x y))))) (let ((_let_1983 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.multis2468970476368604999at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.multis2468970476368604999at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_18822 x z) (ho_18822 y z)))) (= x y))))) (let ((_let_1984 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.list_P131111800688179804it_nat tptp.list_P131111800688179804it_nat)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.list_P131111800688179804it_nat tptp.list_P131111800688179804it_nat)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_24978 x z) (ho_24978 y z)))) (= x y))))) (let ((_let_1985 (forall ((x |u_(-> tptp.set_o _u_(-> tptp.set_o tptp.set_o Bool)_ _u_(-> tptp.set_o tptp.set_o Bool)_ Bool)|) (y |u_(-> tptp.set_o _u_(-> tptp.set_o tptp.set_o Bool)_ _u_(-> tptp.set_o tptp.set_o Bool)_ Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_24515 x z) (ho_24515 y z)))) (= x y))))) (let ((_let_1986 (forall ((x |u_(-> tptp.a tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.a tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.a)) (= (ho_11307 x z) (ho_11307 y z)))) (= x y))))) (let ((_let_1987 (forall ((x |u_(-> tptp.assn tptp.assn)|) (y |u_(-> tptp.assn tptp.assn)|)) (or (not (forall ((z tptp.assn)) (= (ho_15795 x z) (ho_15795 y z)))) (= x y))))) (let ((_let_1988 (forall ((x |u_(-> tptp.b tptp.heap_Time_Heap_a)|) (y |u_(-> tptp.b tptp.heap_Time_Heap_a)|)) (or (not (forall ((z tptp.b)) (= (ho_11300 x z) (ho_11300 y z)))) (= x y))))) (let ((_let_1989 (forall ((x |u_(-> _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (y |u_(-> _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (or (not (forall ((z |u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (= (ho_12602 x z) (ho_12602 y z)))) (= x y))))) (let ((_let_1990 (forall ((x |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.int)) (= (ho_11115 x z) (ho_11115 y z)))) (= x y))))) (let ((_let_1991 (forall ((x |u_(-> tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.heap_Time_Heap_a)) (= (ho_11295 x z) (ho_11295 y z)))) (= x y))))) (let ((_let_1992 (forall ((x |u_(-> tptp.int tptp.int tptp.set_se6260736226359567993nt_int)|) (y |u_(-> tptp.int tptp.int tptp.set_se6260736226359567993nt_int)|)) (or (not (forall ((z tptp.int)) (= (ho_25146 x z) (ho_25146 y z)))) (= x y))))) (let ((_let_1993 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_11054 x z) (ho_11054 y z)))) (= x y))))) (let ((_let_1994 (forall ((x |u_(-> tptp.option2498585697089621389at_nat tptp.option2498585697089621389at_nat)|) (y |u_(-> tptp.option2498585697089621389at_nat tptp.option2498585697089621389at_nat)|)) (or (not (forall ((z tptp.option2498585697089621389at_nat)) (= (ho_23590 x z) (ho_23590 y z)))) (= x y))))) (let ((_let_1995 (forall ((x |u_(-> tptp.set_set_nat tptp.set_nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_set_nat tptp.set_nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_18865 x z) (ho_18865 y z)))) (= x y))))) (let ((_let_1996 (forall ((x |u_(-> tptp.set_set_nat tptp.nat tptp.set_set_nat Bool)|) (y |u_(-> tptp.set_set_nat tptp.nat tptp.set_set_nat Bool)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_15166 x z) (ho_15166 y z)))) (= x y))))) (let ((_let_1997 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer)_ _u_(-> tptp.nat tptp.code_integer)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer)_ _u_(-> tptp.nat tptp.code_integer)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer)|)) (= (ho_17192 x z) (ho_17192 y z)))) (= x y))))) (let ((_let_1998 (forall ((x |u_(-> tptp.int tptp.int tptp.set_int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int tptp.set_int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_19507 x z) (ho_19507 y z)))) (= x y))))) (let ((_let_1999 (forall ((x |u_(-> tptp.list_o tptp.nat)|) (y |u_(-> tptp.list_o tptp.nat)|)) (or (not (forall ((z tptp.list_o)) (= (ho_11151 x z) (ho_11151 y z)))) (= x y))))) (let ((_let_2000 (forall ((x |u_(-> Bool _u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ _u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> Bool _u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ _u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z Bool)) (= (ho_18709 x z) (ho_18709 y z)))) (= x y))))) (let ((_let_2001 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.assn)_ _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.assn)_ _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_16291 x z) (ho_16291 y z)))) (= x y))))) (let ((_let_2002 (forall ((x |u_(-> tptp.set_nat tptp.int tptp.int)|) (y |u_(-> tptp.set_nat tptp.int tptp.int)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_18126 x z) (ho_18126 y z)))) (= x y))))) (let ((_let_2003 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_12459 x z) (ho_12459 y z)))) (= x y))))) (let ((_let_2004 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.produc8664842809031399944it_nat)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.produc8664842809031399944it_nat)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_25712 x z) (ho_25712 y z)))) (= x y))))) (let ((_let_2005 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_11377 x z) (ho_11377 y z)))) (= x y))))) (let ((_let_2006 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_16312 x z) (ho_16312 y z)))) (= x y))))) (let ((_let_2007 (forall ((x |u_(-> tptp.code_natural tptp.code_natural)|) (y |u_(-> tptp.code_natural tptp.code_natural)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_11477 x z) (ho_11477 y z)))) (= x y))))) (let ((_let_2008 (forall ((x |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.produc4166570645942440679at_nat)|) (y |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.produc4166570645942440679at_nat)|)) (or (not (forall ((z tptp.multis2468970476368604999at_nat)) (= (ho_12618 x z) (ho_12618 y z)))) (= x y))))) (let ((_let_2009 (forall ((x |u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|) (y |u_(-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (or (not (forall ((z tptp.produc3925858234332021118et_nat)) (= (ho_18730 x z) (ho_18730 y z)))) (= x y))))) (let ((_let_2010 (forall ((x |u_(-> tptp.nat tptp.int tptp.nat)|) (y |u_(-> tptp.nat tptp.int tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_12184 x z) (ho_12184 y z)))) (= x y))))) (let ((_let_2011 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_11215 x z) (ho_11215 y z)))) (= x y))))) (let ((_let_2012 (forall ((x |u_(-> tptp.rat tptp.nat tptp.rat tptp.nat tptp.rat)|) (y |u_(-> tptp.rat tptp.nat tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_17646 x z) (ho_17646 y z)))) (= x y))))) (let ((_let_2013 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15571 x z) (ho_15571 y z)))) (= x y))))) (let ((_let_2014 (forall ((x |u_(-> tptp.set_se6260736226359567993nt_int Bool)|) (y |u_(-> tptp.set_se6260736226359567993nt_int Bool)|)) (or (not (forall ((z tptp.set_se6260736226359567993nt_int)) (= (ho_11216 x z) (ho_11216 y z)))) (= x y))))) (let ((_let_2015 (forall ((x |u_(-> tptp.list_P5707943133018811711nt_int tptp.list_P5707943133018811711nt_int)|) (y |u_(-> tptp.list_P5707943133018811711nt_int tptp.list_P5707943133018811711nt_int)|)) (or (not (forall ((z tptp.list_P5707943133018811711nt_int)) (= (ho_24955 x z) (ho_24955 y z)))) (= x y))))) (let ((_let_2016 (forall ((x |u_(-> tptp.a tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.a tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.a)) (= (ho_11383 x z) (ho_11383 y z)))) (= x y))))) (let ((_let_2017 (forall ((x |u_(-> tptp.rat tptp.rat Bool)|) (y |u_(-> tptp.rat tptp.rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_14382 x z) (ho_14382 y z)))) (= x y))))) (let ((_let_2018 (forall ((x |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)_ _u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)_ _u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.b tptp.produc6653097349344004940it_nat Bool)|)) (= (ho_24381 x z) (ho_24381 y z)))) (= x y))))) (let ((_let_2019 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_15595 x z) (ho_15595 y z)))) (= x y))))) (let ((_let_2020 (forall ((x |u_(-> tptp.set_nat tptp.set_set_nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_11206 x z) (ho_11206 y z)))) (= x y))))) (let ((_let_2021 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_15051 x z) (ho_15051 y z)))) (= x y))))) (let ((_let_2022 (forall ((x |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.option8057788054806935849nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.option8057788054806935849nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (= (ho_25690 x z) (ho_25690 y z)))) (= x y))))) (let ((_let_2023 (forall ((x |u_(-> tptp.set_Pr4389693562480114009it_nat tptp.set_Pr2819221443900773171it_nat)|) (y |u_(-> tptp.set_Pr4389693562480114009it_nat tptp.set_Pr2819221443900773171it_nat)|)) (or (not (forall ((z tptp.set_Pr4389693562480114009it_nat)) (= (ho_25083 x z) (ho_25083 y z)))) (= x y))))) (let ((_let_2024 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_17090 x z) (ho_17090 y z)))) (= x y))))) (let ((_let_2025 (forall ((x |u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (y |u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (or (not (forall ((z tptp.produc7822875418678951345atural)) (= (ho_11493 x z) (ho_11493 y z)))) (= x y))))) (let ((_let_2026 (forall ((x |u_(-> Bool Bool Bool)|) (y |u_(-> Bool Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_11201 x z) (ho_11201 y z)))) (= x y))))) (let ((_let_2027 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_25952 x z) (ho_25952 y z)))) (= x y))))) (let ((_let_2028 (forall ((x |u_(-> tptp.array_nat tptp.produc6653097349344004940it_nat tptp.produc6751673265320737416it_nat)|) (y |u_(-> tptp.array_nat tptp.produc6653097349344004940it_nat tptp.produc6751673265320737416it_nat)|)) (or (not (forall ((z tptp.array_nat)) (= (ho_11162 x z) (ho_11162 y z)))) (= x y))))) (let ((_let_2029 (forall ((x |u_(-> Bool tptp.assn tptp.assn tptp.assn)|) (y |u_(-> Bool tptp.assn tptp.assn tptp.assn)|)) (or (not (forall ((z Bool)) (= (ho_15793 x z) (ho_15793 y z)))) (= x y))))) (let ((_let_2030 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_21404 x z) (ho_21404 y z)))) (= x y))))) (let ((_let_2031 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.code_integer)_ _u_(-> tptp.nat tptp.code_integer)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.code_integer)_ _u_(-> tptp.nat tptp.code_integer)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_17191 x z) (ho_17191 y z)))) (= x y))))) (let ((_let_2032 (forall ((x |u_(-> tptp.num _u_(-> tptp.num tptp.assn)_ tptp.num tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.num _u_(-> tptp.num tptp.assn)_ tptp.num tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_23809 x z) (ho_23809 y z)))) (= x y))))) (let ((_let_2033 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_natural)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_natural)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15334 x z) (ho_15334 y z)))) (= x y))))) (let ((_let_2034 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat)|)) (= (ho_15033 x z) (ho_15033 y z)))) (= x y))))) (let ((_let_2035 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.code_integer)_ _u_(-> tptp.set_nat tptp.code_integer)_ tptp.set_nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.set_nat tptp.code_integer)_ _u_(-> tptp.set_nat tptp.code_integer)_ tptp.set_nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.code_integer)|)) (= (ho_18509 x z) (ho_18509 y z)))) (= x y))))) (let ((_let_2036 (forall ((x |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)_ tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)_ tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)|)) (= (ho_13951 x z) (ho_13951 y z)))) (= x y))))) (let ((_let_2037 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_11053 x z) (ho_11053 y z)))) (= x y))))) (let ((_let_2038 (forall ((x |u_(-> tptp.produc4166570645942440679at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.produc4166570645942440679at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.produc4166570645942440679at_nat)) (= (ho_19706 x z) (ho_19706 y z)))) (= x y))))) (let ((_let_2039 (forall ((x |u_(-> _u_(-> Bool Bool)_ tptp.set_o)|) (y |u_(-> _u_(-> Bool Bool)_ tptp.set_o)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_11196 x z) (ho_11196 y z)))) (= x y))))) (let ((_let_2040 (forall ((x |u_(-> Bool _u_(-> Bool tptp.assn)_ _u_(-> Bool tptp.assn)_ Bool tptp.assn)|) (y |u_(-> Bool _u_(-> Bool tptp.assn)_ _u_(-> Bool tptp.assn)_ Bool tptp.assn)|)) (or (not (forall ((z Bool)) (= (ho_15808 x z) (ho_15808 y z)))) (= x y))))) (let ((_let_2041 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_18716 x z) (ho_18716 y z)))) (= x y))))) (let ((_let_2042 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_15342 x z) (ho_15342 y z)))) (= x y))))) (let ((_let_2043 (forall ((x |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_13559 x z) (ho_13559 y z)))) (= x y))))) (let ((_let_2044 (forall ((x |u_(-> Bool tptp.list_int tptp.list_int tptp.list_int)|) (y |u_(-> Bool tptp.list_int tptp.list_int tptp.list_int)|)) (or (not (forall ((z Bool)) (= (ho_14668 x z) (ho_14668 y z)))) (= x y))))) (let ((_let_2045 (forall ((x |u_(-> tptp.nat _u_(-> tptp.int tptp.nat)_ tptp.int Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.int tptp.nat)_ tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_11877 x z) (ho_11877 y z)))) (= x y))))) (let ((_let_2046 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)_ tptp.int tptp.int Bool)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_13232 x z) (ho_13232 y z)))) (= x y))))) (let ((_let_2047 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_15037 x z) (ho_15037 y z)))) (= x y))))) (let ((_let_2048 (forall ((x |u_(-> _u_(-> tptp.product_unit Bool)_ tptp.product_unit tptp.heap_T5738788834812785303t_unit)|) (y |u_(-> _u_(-> tptp.product_unit Bool)_ tptp.product_unit tptp.heap_T5738788834812785303t_unit)|)) (or (not (forall ((z |u_(-> tptp.product_unit Bool)|)) (= (ho_24529 x z) (ho_24529 y z)))) (= x y))))) (let ((_let_2049 (forall ((x |u_(-> tptp.list_o tptp.array_o tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat)|) (y |u_(-> tptp.list_o tptp.array_o tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat)|)) (or (not (forall ((z tptp.list_o)) (= (ho_11156 x z) (ho_11156 y z)))) (= x y))))) (let ((_let_2050 (forall ((x |u_(-> tptp.product_prod_int_int tptp.rat)|) (y |u_(-> tptp.product_prod_int_int tptp.rat)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_11117 x z) (ho_11117 y z)))) (= x y))))) (let ((_let_2051 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr1261947904930325089at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr1261947904930325089at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_18813 x z) (ho_18813 y z)))) (= x y))))) (let ((_let_2052 (forall ((x |u_(-> _u_(-> tptp.b tptp.heap_Time_Heap_b)_ tptp.b tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.heap_Time_Heap_b)_ tptp.b tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.heap_Time_Heap_b)|)) (= (ho_11318 x z) (ho_11318 y z)))) (= x y))))) (let ((_let_2053 (forall ((x |u_(-> tptp.set_Code_integer tptp.nat)|) (y |u_(-> tptp.set_Code_integer tptp.nat)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_14859 x z) (ho_14859 y z)))) (= x y))))) (let ((_let_2054 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11074 x z) (ho_11074 y z)))) (= x y))))) (let ((_let_2055 (forall ((x |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)|)) (= (ho_16871 x z) (ho_16871 y z)))) (= x y))))) (let ((_let_2056 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.set_int)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.set_int)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_11177 x z) (ho_11177 y z)))) (= x y))))) (let ((_let_2057 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.list_int tptp.int tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.list_int tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_18658 x z) (ho_18658 y z)))) (= x y))))) (let ((_let_2058 (forall ((x |u_(-> tptp.set_Pr7098220151150636591it_nat Bool)|) (y |u_(-> tptp.set_Pr7098220151150636591it_nat Bool)|)) (or (not (forall ((z tptp.set_Pr7098220151150636591it_nat)) (= (ho_21350 x z) (ho_21350 y z)))) (= x y))))) (let ((_let_2059 (forall ((x |u_(-> tptp.set_o _u_(-> tptp.code_integer Bool Bool)_ tptp.code_integer Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> tptp.code_integer Bool Bool)_ tptp.code_integer Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_11557 x z) (ho_11557 y z)))) (= x y))))) (let ((_let_2060 (forall ((x |u_(-> tptp.array_int tptp.produc6653097349344004940it_nat tptp.produc7196121022310644452it_nat)|) (y |u_(-> tptp.array_int tptp.produc6653097349344004940it_nat tptp.produc7196121022310644452it_nat)|)) (or (not (forall ((z tptp.array_int)) (= (ho_11144 x z) (ho_11144 y z)))) (= x y))))) (let ((_let_2061 (forall ((x |u_(-> tptp.set_o _u_(-> tptp.nat Bool Bool)_ tptp.nat tptp.nat)|) (y |u_(-> tptp.set_o _u_(-> tptp.nat Bool Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.set_o)) (= (ho_17283 x z) (ho_17283 y z)))) (= x y))))) (let ((_let_2062 (forall ((x |u_(-> tptp.int tptp.nat Bool)|) (y |u_(-> tptp.int tptp.nat Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_11574 x z) (ho_11574 y z)))) (= x y))))) (let ((_let_2063 (forall ((x |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr958786334691620121nt_int Bool)|)) (= (ho_15604 x z) (ho_15604 y z)))) (= x y))))) (let ((_let_2064 (forall ((x |u_(-> _u_(-> tptp.option_Code_integer tptp.option8057788054806935849nteger)_ tptp.option_Code_integer tptp.option7428179582072448501nteger)|) (y |u_(-> _u_(-> tptp.option_Code_integer tptp.option8057788054806935849nteger)_ tptp.option_Code_integer tptp.option7428179582072448501nteger)|)) (or (not (forall ((z |u_(-> tptp.option_Code_integer tptp.option8057788054806935849nteger)|)) (= (ho_25724 x z) (ho_25724 y z)))) (= x y))))) (let ((_let_2065 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_17052 x z) (ho_17052 y z)))) (= x y))))) (let ((_let_2066 (forall ((x |u_(-> _u_(-> Bool tptp.nat)_ _u_(-> Bool tptp.nat)_ Bool tptp.nat)|) (y |u_(-> _u_(-> Bool tptp.nat)_ _u_(-> Bool tptp.nat)_ Bool tptp.nat)|)) (or (not (forall ((z |u_(-> Bool tptp.nat)|)) (= (ho_15756 x z) (ho_15756 y z)))) (= x y))))) (let ((_let_2067 (forall ((x |u_(-> tptp.num tptp.num tptp.option_num)|) (y |u_(-> tptp.num tptp.num tptp.option_num)|)) (or (not (forall ((z tptp.num)) (= (ho_13932 x z) (ho_13932 y z)))) (= x y))))) (let ((_let_2068 (forall ((x |u_(-> tptp.nat tptp.product_prod_int_nat)|) (y |u_(-> tptp.nat tptp.product_prod_int_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_24793 x z) (ho_24793 y z)))) (= x y))))) (let ((_let_2069 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|)) (= (ho_24377 x z) (ho_24377 y z)))) (= x y))))) (let ((_let_2070 (forall ((x |u_(-> tptp.list_P4002435161011370285od_o_o tptp.nat tptp.product_prod_o_o)|) (y |u_(-> tptp.list_P4002435161011370285od_o_o tptp.nat tptp.product_prod_o_o)|)) (or (not (forall ((z tptp.list_P4002435161011370285od_o_o)) (= (ho_24780 x z) (ho_24780 y z)))) (= x y))))) (let ((_let_2071 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_17627 x z) (ho_17627 y z)))) (= x y))))) (let ((_let_2072 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_12394 x z) (ho_12394 y z)))) (= x y))))) (let ((_let_2073 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_20038 x z) (ho_20038 y z)))) (= x y))))) (let ((_let_2074 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_16265 x z) (ho_16265 y z)))) (= x y))))) (let ((_let_2075 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_natural)_ tptp.set_nat tptp.code_natural)|) (y |u_(-> _u_(-> tptp.nat tptp.code_natural)_ tptp.set_nat tptp.code_natural)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_natural)|)) (= (ho_25294 x z) (ho_25294 y z)))) (= x y))))) (let ((_let_2076 (forall ((x |u_(-> _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.option_num)|)) (= (ho_11171 x z) (ho_11171 y z)))) (= x y))))) (let ((_let_2077 (forall ((x |u_(-> tptp.produc3925858234332021118et_nat tptp.option5190343406534369742et_nat)|) (y |u_(-> tptp.produc3925858234332021118et_nat tptp.option5190343406534369742et_nat)|)) (or (not (forall ((z tptp.produc3925858234332021118et_nat)) (= (ho_24399 x z) (ho_24399 y z)))) (= x y))))) (let ((_let_2078 (forall ((x |u_(-> tptp.rat tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.rat tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_23819 x z) (ho_23819 y z)))) (= x y))))) (let ((_let_2079 (forall ((x |u_(-> _u_(-> tptp.nat tptp.option_num)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.option_num)|) (y |u_(-> _u_(-> tptp.nat tptp.option_num)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.option_num)|)) (= (ho_18598 x z) (ho_18598 y z)))) (= x y))))) (let ((_let_2080 (forall ((x |u_(-> tptp.list_nat tptp.array_nat tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat)|) (y |u_(-> tptp.list_nat tptp.array_nat tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_11165 x z) (ho_11165 y z)))) (= x y))))) (let ((_let_2081 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_13175 x z) (ho_13175 y z)))) (= x y))))) (let ((_let_2082 (forall ((x |u_(-> _u_(-> Bool tptp.code_integer Bool)_ Bool tptp.code_integer Bool)|) (y |u_(-> _u_(-> Bool tptp.code_integer Bool)_ Bool tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.code_integer Bool)|)) (= (ho_11586 x z) (ho_11586 y z)))) (= x y))))) (let ((_let_2083 (forall ((x |u_(-> tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_11190 x z) (ho_11190 y z)))) (= x y))))) (let ((_let_2084 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.nat)_ Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.nat)_ Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_15122 x z) (ho_15122 y z)))) (= x y))))) (let ((_let_2085 (forall ((x |u_(-> _u_(-> Bool tptp.nat Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> Bool tptp.nat Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> Bool tptp.nat Bool)|)) (= (ho_17354 x z) (ho_17354 y z)))) (= x y))))) (let ((_let_2086 (forall ((x |u_(-> tptp.set_o _u_(-> Bool Bool Bool)_ Bool tptp.nat)|) (y |u_(-> tptp.set_o _u_(-> Bool Bool Bool)_ Bool tptp.nat)|)) (or (not (forall ((z tptp.set_o)) (= (ho_14907 x z) (ho_14907 y z)))) (= x y))))) (let ((_let_2087 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_17069 x z) (ho_17069 y z)))) (= x y))))) (let ((_let_2088 (forall ((x |u_(-> tptp.list_nat tptp.nat)|) (y |u_(-> tptp.list_nat tptp.nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_11160 x z) (ho_11160 y z)))) (= x y))))) (let ((_let_2089 (forall ((x |u_(-> Bool tptp.set_o Bool)|) (y |u_(-> Bool tptp.set_o Bool)|)) (or (not (forall ((z Bool)) (= (ho_11198 x z) (ho_11198 y z)))) (= x y))))) (let ((_let_2090 (forall ((x |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.option2498585697089621389at_nat)_ tptp.option2498585697089621389at_nat tptp.option2498585697089621389at_nat)|) (y |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.option2498585697089621389at_nat)_ tptp.option2498585697089621389at_nat tptp.option2498585697089621389at_nat)|)) (or (not (forall ((z |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.option2498585697089621389at_nat)|)) (= (ho_23589 x z) (ho_23589 y z)))) (= x y))))) (let ((_let_2091 (forall ((x |u_(-> tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_12445 x z) (ho_12445 y z)))) (= x y))))) (let ((_let_2092 (forall ((x |u_(-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.produc3843707927480180839at_nat)) (= (ho_11262 x z) (ho_11262 y z)))) (= x y))))) (let ((_let_2093 (forall ((x |u_(-> tptp.set_int tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_11234 x z) (ho_11234 y z)))) (= x y))))) (let ((_let_2094 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_26148 x z) (ho_26148 y z)))) (= x y))))) (let ((_let_2095 (forall ((x |u_(-> tptp.produc3658429121746597890et_nat tptp.nat Bool)|) (y |u_(-> tptp.produc3658429121746597890et_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.produc3658429121746597890et_nat)) (= (ho_14618 x z) (ho_14618 y z)))) (= x y))))) (let ((_let_2096 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (= (ho_25865 x z) (ho_25865 y z)))) (= x y))))) (let ((_let_2097 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11075 x z) (ho_11075 y z)))) (= x y))))) (let ((_let_2098 (forall ((x |u_(-> tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_11240 x z) (ho_11240 y z)))) (= x y))))) (let ((_let_2099 (forall ((x |u_(-> tptp.set_Pr719794911490849221et_nat tptp.set_Pr7928877670098842301et_nat)|) (y |u_(-> tptp.set_Pr719794911490849221et_nat tptp.set_Pr7928877670098842301et_nat)|)) (or (not (forall ((z tptp.set_Pr719794911490849221et_nat)) (= (ho_25062 x z) (ho_25062 y z)))) (= x y))))) (let ((_let_2100 (forall ((x |u_(-> tptp.ref_Product_unit tptp.heap_T5738788834812785303t_unit)|) (y |u_(-> tptp.ref_Product_unit tptp.heap_T5738788834812785303t_unit)|)) (or (not (forall ((z tptp.ref_Product_unit)) (= (ho_24579 x z) (ho_24579 y z)))) (= x y))))) (let ((_let_2101 (forall ((x |u_(-> tptp.rat Bool)|) (y |u_(-> tptp.rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_14383 x z) (ho_14383 y z)))) (= x y))))) (let ((_let_2102 (forall ((x |u_(-> tptp.produc3925858234332021118et_nat tptp.set_Pr3286484037609594932et_nat Bool)|) (y |u_(-> tptp.produc3925858234332021118et_nat tptp.set_Pr3286484037609594932et_nat Bool)|)) (or (not (forall ((z tptp.produc3925858234332021118et_nat)) (= (ho_21385 x z) (ho_21385 y z)))) (= x y))))) (let ((_let_2103 (forall ((x |u_(-> _u_(-> tptp.code_natural tptp.nat)_ _u_(-> tptp.nat tptp.code_natural)_ _u_(-> tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural)|) (y |u_(-> _u_(-> tptp.code_natural tptp.nat)_ _u_(-> tptp.nat tptp.code_natural)_ _u_(-> tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural)|)) (or (not (forall ((z |u_(-> tptp.code_natural tptp.nat)|)) (= (ho_11485 x z) (ho_11485 y z)))) (= x y))))) (let ((_let_2104 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_18801 x z) (ho_18801 y z)))) (= x y))))) (let ((_let_2105 (forall ((x |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.nat)_ _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer tptp.nat)|) (y |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.nat)_ _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_15762 x z) (ho_15762 y z)))) (= x y))))) (let ((_let_2106 (forall ((x |u_(-> tptp.set_rat tptp.set_rat)|) (y |u_(-> tptp.set_rat tptp.set_rat)|)) (or (not (forall ((z tptp.set_rat)) (= (ho_25382 x z) (ho_25382 y z)))) (= x y))))) (let ((_let_2107 (forall ((x |u_(-> tptp.list_int tptp.nat)|) (y |u_(-> tptp.list_int tptp.nat)|)) (or (not (forall ((z tptp.list_int)) (= (ho_11137 x z) (ho_11137 y z)))) (= x y))))) (let ((_let_2108 (forall ((x |u_(-> _u_(-> 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)|) (y |u_(-> _u_(-> 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)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_20030 x z) (ho_20030 y z)))) (= x y))))) (let ((_let_2109 (forall ((x |u_(-> _u_(-> tptp.list_nat tptp.nat)_ tptp.nat tptp.list_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.list_nat tptp.nat)_ tptp.nat tptp.list_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.list_nat tptp.nat)|)) (= (ho_15821 x z) (ho_15821 y z)))) (= x y))))) (let ((_let_2110 (forall ((x |u_(-> _u_(-> tptp.rat tptp.set_Pr958786334691620121nt_int)_ _u_(-> tptp.set_Pr958786334691620121nt_int tptp.rat)_ tptp.set_se6260736226359567993nt_int Bool)|) (y |u_(-> _u_(-> tptp.rat tptp.set_Pr958786334691620121nt_int)_ _u_(-> tptp.set_Pr958786334691620121nt_int tptp.rat)_ tptp.set_se6260736226359567993nt_int Bool)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.set_Pr958786334691620121nt_int)|)) (= (ho_26114 x z) (ho_26114 y z)))) (= x y))))) (let ((_let_2111 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_17891 x z) (ho_17891 y z)))) (= x y))))) (let ((_let_2112 (forall ((x |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr958786334691620121nt_int Bool)|)) (= (ho_13346 x z) (ho_13346 y z)))) (= x y))))) (let ((_let_2113 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.option2498585697089621389at_nat)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.option2498585697089621389at_nat)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_14294 x z) (ho_14294 y z)))) (= x y))))) (let ((_let_2114 (forall ((x |u_(-> tptp.option_num tptp.num Bool)|) (y |u_(-> tptp.option_num tptp.num Bool)|)) (or (not (forall ((z tptp.option_num)) (= (ho_22642 x z) (ho_22642 y z)))) (= x y))))) (let ((_let_2115 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_11536 x z) (ho_11536 y z)))) (= x y))))) (let ((_let_2116 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int Bool)_ tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int Bool)_ tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_17460 x z) (ho_17460 y z)))) (= x y))))) (let ((_let_2117 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc5011041761010125393t_unit)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc5011041761010125393t_unit)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_11810 x z) (ho_11810 y z)))) (= x y))))) (let ((_let_2118 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.rat)_ _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer tptp.rat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.rat)_ _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.rat)|)) (= (ho_15042 x z) (ho_15042 y z)))) (= x y))))) (let ((_let_2119 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_25333 x z) (ho_25333 y z)))) (= x y))))) (let ((_let_2120 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_12405 x z) (ho_12405 y z)))) (= x y))))) (let ((_let_2121 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural tptp.code_natural)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural tptp.code_natural)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural)|)) (= (ho_11489 x z) (ho_11489 y z)))) (= x y))))) (let ((_let_2122 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_15148 x z) (ho_15148 y z)))) (= x y))))) (let ((_let_2123 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11139 x z) (ho_11139 y z)))) (= x y))))) (let ((_let_2124 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.produc859450856879609959at_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.produc859450856879609959at_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_14478 x z) (ho_14478 y z)))) (= x y))))) (let ((_let_2125 (forall ((x |u_(-> Bool tptp.set_int tptp.set_int tptp.set_int)|) (y |u_(-> Bool tptp.set_int tptp.set_int tptp.set_int)|)) (or (not (forall ((z Bool)) (= (ho_15193 x z) (ho_15193 y z)))) (= x y))))) (let ((_let_2126 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer Bool)_ tptp.code_integer tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer Bool)_ tptp.code_integer tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_11754 x z) (ho_11754 y z)))) (= x y))))) (let ((_let_2127 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.set_nat _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.set_nat _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_17356 x z) (ho_17356 y z)))) (= x y))))) (let ((_let_2128 (forall ((x |u_(-> tptp.num Bool)|) (y |u_(-> tptp.num Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_11035 x z) (ho_11035 y z)))) (= x y))))) (let ((_let_2129 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.heap_T1346037964561226099ay_int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.heap_T1346037964561226099ay_int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_15662 x z) (ho_15662 y z)))) (= x y))))) (let ((_let_2130 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_25325 x z) (ho_25325 y z)))) (= x y))))) (let ((_let_2131 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_17066 x z) (ho_17066 y z)))) (= x y))))) (let ((_let_2132 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_12540 x z) (ho_12540 y z)))) (= x y))))) (let ((_let_2133 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_17475 x z) (ho_17475 y z)))) (= x y))))) (let ((_let_2134 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_22290 x z) (ho_22290 y z)))) (= x y))))) (let ((_let_2135 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.code_integer)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.code_integer)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer)|)) (= (ho_12133 x z) (ho_12133 y z)))) (= x y))))) (let ((_let_2136 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_11374 x z) (ho_11374 y z)))) (= x y))))) (let ((_let_2137 (forall ((x |u_(-> tptp.code_integer tptp.nat Bool)|) (y |u_(-> tptp.code_integer tptp.nat Bool)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_11551 x z) (ho_11551 y z)))) (= x y))))) (let ((_let_2138 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_11686 x z) (ho_11686 y z)))) (= x y))))) (let ((_let_2139 (forall ((x |u_(-> tptp.option3562590408128118217it_nat _u_(-> tptp.produc7388388658123137530it_nat tptp.option3562590408128118217it_nat)_ tptp.option4065278094766928714it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.option3562590408128118217it_nat _u_(-> tptp.produc7388388658123137530it_nat tptp.option3562590408128118217it_nat)_ tptp.option4065278094766928714it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.option3562590408128118217it_nat)) (= (ho_19862 x z) (ho_19862 y z)))) (= x y))))) (let ((_let_2140 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_12189 x z) (ho_12189 y z)))) (= x y))))) (let ((_let_2141 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_11070 x z) (ho_11070 y z)))) (= x y))))) (let ((_let_2142 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_25957 x z) (ho_25957 y z)))) (= x y))))) (let ((_let_2143 (forall ((x |u_(-> tptp.int _u_(-> tptp.nat tptp.int)_ tptp.nat Bool)|) (y |u_(-> tptp.int _u_(-> tptp.nat tptp.int)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_11873 x z) (ho_11873 y z)))) (= x y))))) (let ((_let_2144 (forall ((x |u_(-> tptp.int tptp.code_natural)|) (y |u_(-> tptp.int tptp.code_natural)|)) (or (not (forall ((z tptp.int)) (= (ho_11867 x z) (ho_11867 y z)))) (= x y))))) (let ((_let_2145 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat tptp.int)_ tptp.set_nat _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat tptp.int)_ tptp.set_nat _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat tptp.int)|)) (= (ho_17320 x z) (ho_17320 y z)))) (= x y))))) (let ((_let_2146 (forall ((x |u_(-> tptp.produc8664842809031399944it_nat tptp.nat)|) (y |u_(-> tptp.produc8664842809031399944it_nat tptp.nat)|)) (or (not (forall ((z tptp.produc8664842809031399944it_nat)) (= (ho_24667 x z) (ho_24667 y z)))) (= x y))))) (let ((_let_2147 (forall ((x |u_(-> tptp.int tptp.code_integer Bool)|) (y |u_(-> tptp.int tptp.code_integer Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_11560 x z) (ho_11560 y z)))) (= x y))))) (let ((_let_2148 (forall ((x |u_(-> tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_11130 x z) (ho_11130 y z)))) (= x y))))) (let ((_let_2149 (forall ((x |u_(-> tptp.assn Bool)|) (y |u_(-> tptp.assn Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_14386 x z) (ho_14386 y z)))) (= x y))))) (let ((_let_2150 (forall ((x |u_(-> _u_(-> tptp.num Bool)_ tptp.option_num)|) (y |u_(-> _u_(-> tptp.num Bool)_ tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num Bool)|)) (= (ho_11037 x z) (ho_11037 y z)))) (= x y))))) (let ((_let_2151 (forall ((x |u_(-> _u_(-> tptp.nat tptp.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)|) (y |u_(-> _u_(-> tptp.nat tptp.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)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_13153 x z) (ho_13153 y z)))) (= x y))))) (let ((_let_2152 (forall ((x |u_(-> tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int Bool)|) (y |u_(-> tptp.set_se6260736226359567993nt_int tptp.set_se6260736226359567993nt_int Bool)|)) (or (not (forall ((z tptp.set_se6260736226359567993nt_int)) (= (ho_23361 x z) (ho_23361 y z)))) (= x y))))) (let ((_let_2153 (forall ((x |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ tptp.set_se6260736226359567993nt_int)|) (y |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ tptp.set_se6260736226359567993nt_int)|)) (or (not (forall ((z |u_(-> tptp.set_Pr958786334691620121nt_int Bool)|)) (= (ho_11213 x z) (ho_11213 y z)))) (= x y))))) (let ((_let_2154 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int)|)) (= (ho_26102 x z) (ho_26102 y z)))) (= x y))))) (let ((_let_2155 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat tptp.int)_ tptp.nat tptp.code_integer tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat tptp.int)_ tptp.nat tptp.code_integer tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat tptp.int)|)) (= (ho_12225 x z) (ho_12225 y z)))) (= x y))))) (let ((_let_2156 (forall ((x |u_(-> tptp.set_Code_integer Bool)|) (y |u_(-> tptp.set_Code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_11567 x z) (ho_11567 y z)))) (= x y))))) (let ((_let_2157 (forall ((x |u_(-> tptp.array_int tptp.list_int tptp.nat tptp.int tptp.assn)|) (y |u_(-> tptp.array_int tptp.list_int tptp.nat tptp.int tptp.assn)|)) (or (not (forall ((z tptp.array_int)) (= (ho_20387 x z) (ho_20387 y z)))) (= x y))))) (let ((_let_2158 (forall ((x |u_(-> tptp.assn tptp.heap_Time_Heap_nat _u_(-> tptp.nat tptp.assn)_ Bool)|) (y |u_(-> tptp.assn tptp.heap_Time_Heap_nat _u_(-> tptp.nat tptp.assn)_ Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_24695 x z) (ho_24695 y z)))) (= x y))))) (let ((_let_2159 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.rat)_ tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.rat)_ tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_15370 x z) (ho_15370 y z)))) (= x y))))) (let ((_let_2160 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.produc6653097349344004940it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.produc6653097349344004940it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_11141 x z) (ho_11141 y z)))) (= x y))))) (let ((_let_2161 (forall ((x |u_(-> tptp.set_nat tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_11343 x z) (ho_11343 y z)))) (= x y))))) (let ((_let_2162 (forall ((x |u_(-> tptp.nat tptp.int Bool)|) (y |u_(-> tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_11765 x z) (ho_11765 y z)))) (= x y))))) (let ((_let_2163 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.int Bool)_ tptp.int Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.int Bool)_ tptp.int Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_12220 x z) (ho_12220 y z)))) (= x y))))) (let ((_let_2164 (forall ((x |u_(-> tptp.int Bool tptp.int)|) (y |u_(-> tptp.int Bool tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_12217 x z) (ho_12217 y z)))) (= x y))))) (let ((_let_2165 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat Bool)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat Bool)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_17437 x z) (ho_17437 y z)))) (= x y))))) (let ((_let_2166 (forall ((x |u_(-> tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.option8956607266484857688it_nat)) (= (ho_11391 x z) (ho_11391 y z)))) (= x y))))) (let ((_let_2167 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_11553 x z) (ho_11553 y z)))) (= x y))))) (let ((_let_2168 (forall ((x |u_(-> tptp.list_nat Bool)|) (y |u_(-> tptp.list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_11278 x z) (ho_11278 y z)))) (= x y))))) (let ((_let_2169 (forall ((x |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)_ tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)_ tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)|)) (= (ho_24509 x z) (ho_24509 y z)))) (= x y))))) (let ((_let_2170 (forall ((x |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ _u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ _u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (= (ho_18710 x z) (ho_18710 y z)))) (= x y))))) (let ((_let_2171 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_15039 x z) (ho_15039 y z)))) (= x y))))) (let ((_let_2172 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.option2555668343544256180it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.option2555668343544256180it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_25486 x z) (ho_25486 y z)))) (= x y))))) (let ((_let_2173 (forall ((x |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11066 x z) (ho_11066 y z)))) (= x y))))) (let ((_let_2174 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_14915 x z) (ho_14915 y z)))) (= x y))))) (let ((_let_2175 (forall ((x |u_(-> tptp.rat tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_12444 x z) (ho_12444 y z)))) (= x y))))) (let ((_let_2176 (forall ((x |u_(-> tptp.option_num _u_(-> tptp.num tptp.option_num)_ tptp.option_num tptp.option_num)|) (y |u_(-> tptp.option_num _u_(-> tptp.num tptp.option_num)_ tptp.option_num tptp.option_num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_11039 x z) (ho_11039 y z)))) (= x y))))) (let ((_let_2177 (forall ((x |u_(-> tptp.rat tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_11511 x z) (ho_11511 y z)))) (= x y))))) (let ((_let_2178 (forall ((x |u_(-> Bool tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> Bool tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z Bool)) (= (ho_12027 x z) (ho_12027 y z)))) (= x y))))) (let ((_let_2179 (forall ((x |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.a)) (= (ho_13103 x z) (ho_13103 y z)))) (= x y))))) (let ((_let_2180 (forall ((x |u_(-> tptp.option1893999432384633940_int_o _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.option1893999432384633940_int_o)_ tptp.option1893999432384633940_int_o tptp.option1893999432384633940_int_o)|) (y |u_(-> tptp.option1893999432384633940_int_o _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.option1893999432384633940_int_o)_ tptp.option1893999432384633940_int_o tptp.option1893999432384633940_int_o)|)) (or (not (forall ((z tptp.option1893999432384633940_int_o)) (= (ho_22194 x z) (ho_22194 y z)))) (= x y))))) (let ((_let_2181 (forall ((x |u_(-> tptp.set_Pr4389693562480114009it_nat Bool)|) (y |u_(-> tptp.set_Pr4389693562480114009it_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4389693562480114009it_nat)) (= (ho_25043 x z) (ho_25043 y z)))) (= x y))))) (let ((_let_2182 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_17141 x z) (ho_17141 y z)))) (= x y))))) (let ((_let_2183 (forall ((x |u_(-> tptp.nat tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.nat tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11298 x z) (ho_11298 y z)))) (= x y))))) (let ((_let_2184 (forall ((x |u_(-> tptp.product_prod_int_int tptp.set_nat)|) (y |u_(-> tptp.product_prod_int_int tptp.set_nat)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_25136 x z) (ho_25136 y z)))) (= x y))))) (let ((_let_2185 (forall ((x |u_(-> tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_11059 x z) (ho_11059 y z)))) (= x y))))) (let ((_let_2186 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.set_nat _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.set_nat _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int tptp.int)|)) (= (ho_17384 x z) (ho_17384 y z)))) (= x y))))) (let ((_let_2187 (forall ((x |u_(-> _u_(-> Bool tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> _u_(-> Bool tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> Bool tptp.product_prod_int_int)|)) (= (ho_20077 x z) (ho_20077 y z)))) (= x y))))) (let ((_let_2188 (forall ((x |u_(-> tptp.int Bool)|) (y |u_(-> tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_11094 x z) (ho_11094 y z)))) (= x y))))) (let ((_let_2189 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_12252 x z) (ho_12252 y z)))) (= x y))))) (let ((_let_2190 (forall ((x |u_(-> tptp.heap_T5660665574680485309rray_o tptp.heap_e7401611519738050253t_unit tptp.option1013472963438093988it_nat)|) (y |u_(-> tptp.heap_T5660665574680485309rray_o tptp.heap_e7401611519738050253t_unit tptp.option1013472963438093988it_nat)|)) (or (not (forall ((z tptp.heap_T5660665574680485309rray_o)) (= (ho_25480 x z) (ho_25480 y z)))) (= x y))))) (let ((_let_2191 (forall ((x |u_(-> tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_11184 x z) (ho_11184 y z)))) (= x y))))) (let ((_let_2192 (forall ((x |u_(-> tptp.nat tptp.heap_Time_Heap_nat)|) (y |u_(-> tptp.nat tptp.heap_Time_Heap_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_24716 x z) (ho_24716 y z)))) (= x y))))) (let ((_let_2193 (forall ((x |u_(-> tptp.set_nat tptp.heap_e7401611519738050253t_unit tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.heap_e7401611519738050253t_unit tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_20385 x z) (ho_20385 y z)))) (= x y))))) (let ((_let_2194 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_13156 x z) (ho_13156 y z)))) (= x y))))) (let ((_let_2195 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_13569 x z) (ho_13569 y z)))) (= x y))))) (let ((_let_2196 (forall ((x |u_(-> tptp.set_Pr8693737435421807431at_nat tptp.set_Pr4329608150637261639at_nat)|) (y |u_(-> tptp.set_Pr8693737435421807431at_nat tptp.set_Pr4329608150637261639at_nat)|)) (or (not (forall ((z tptp.set_Pr8693737435421807431at_nat)) (= (ho_14493 x z) (ho_14493 y z)))) (= x y))))) (let ((_let_2197 (forall ((x |u_(-> tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_11093 x z) (ho_11093 y z)))) (= x y))))) (let ((_let_2198 (forall ((x |u_(-> tptp.rat tptp.nat tptp.rat)|) (y |u_(-> tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_12429 x z) (ho_12429 y z)))) (= x y))))) (let ((_let_2199 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|)) (= (ho_13149 x z) (ho_13149 y z)))) (= x y))))) (let ((_let_2200 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_11107 x z) (ho_11107 y z)))) (= x y))))) (let ((_let_2201 (forall ((x |u_(-> tptp.nat tptp.nat tptp.code_integer tptp.code_integer)|) (y |u_(-> tptp.nat tptp.nat tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z tptp.nat)) (= (ho_18085 x z) (ho_18085 y z)))) (= x y))))) (let ((_let_2202 (forall ((x |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int Bool)_ _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr958786334691620121nt_int Bool)|)) (= (ho_17106 x z) (ho_17106 y z)))) (= x y))))) (let ((_let_2203 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.rat)_ tptp.product_prod_nat_nat tptp.rat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.rat)_ tptp.product_prod_nat_nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.rat)|)) (= (ho_15020 x z) (ho_15020 y z)))) (= x y))))) (let ((_let_2204 (forall ((x |u_(-> tptp.set_o tptp.rat)|) (y |u_(-> tptp.set_o tptp.rat)|)) (or (not (forall ((z tptp.set_o)) (= (ho_25304 x z) (ho_25304 y z)))) (= x y))))) (let ((_let_2205 (forall ((x |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.multis2468970476368604999at_nat)) (= (ho_12615 x z) (ho_12615 y z)))) (= x y))))) (let ((_let_2206 (forall ((x |u_(-> Bool tptp.rat)|) (y |u_(-> Bool tptp.rat)|)) (or (not (forall ((z Bool)) (= (ho_15126 x z) (ho_15126 y z)))) (= x y))))) (let ((_let_2207 (forall ((x |u_(-> tptp.list_num tptp.list_num)|) (y |u_(-> tptp.list_num tptp.list_num)|)) (or (not (forall ((z tptp.list_num)) (= (ho_24997 x z) (ho_24997 y z)))) (= x y))))) (let ((_let_2208 (forall ((x |u_(-> _u_(-> tptp.num tptp.num)_ tptp.option_num tptp.num)|) (y |u_(-> _u_(-> tptp.num tptp.num)_ tptp.option_num tptp.num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num)|)) (= (ho_11047 x z) (ho_11047 y z)))) (= x y))))) (let ((_let_2209 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_12609 x z) (ho_12609 y z)))) (= x y))))) (let ((_let_2210 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_11388 x z) (ho_11388 y z)))) (= x y))))) (let ((_let_2211 (forall ((x |u_(-> tptp.nat tptp.nat tptp.set_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.set_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11420 x z) (ho_11420 y z)))) (= x y))))) (let ((_let_2212 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.rat)|)) (= (ho_15270 x z) (ho_15270 y z)))) (= x y))))) (let ((_let_2213 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.nat tptp.nat Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|)) (= (ho_13177 x z) (ho_13177 y z)))) (= x y))))) (let ((_let_2214 (forall ((x |u_(-> tptp.list_option_num tptp.list_option_num)|) (y |u_(-> tptp.list_option_num tptp.list_option_num)|)) (or (not (forall ((z tptp.list_option_num)) (= (ho_25289 x z) (ho_25289 y z)))) (= x y))))) (let ((_let_2215 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_18988 x z) (ho_18988 y z)))) (= x y))))) (let ((_let_2216 (forall ((x |u_(-> _u_(-> tptp.num tptp.option_num)_ tptp.option_num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num tptp.option_num)_ tptp.option_num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.option_num)|)) (= (ho_11040 x z) (ho_11040 y z)))) (= x y))))) (let ((_let_2217 (forall ((x |u_(-> tptp.set_o _u_(-> tptp.code_integer Bool Bool)_ tptp.code_integer tptp.nat)|) (y |u_(-> tptp.set_o _u_(-> tptp.code_integer Bool Bool)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z tptp.set_o)) (= (ho_14851 x z) (ho_14851 y z)))) (= x y))))) (let ((_let_2218 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.assn)_ _u_(-> tptp.int tptp.assn)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.assn)_ _u_(-> tptp.int tptp.assn)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_12118 x z) (ho_12118 y z)))) (= x y))))) (let ((_let_2219 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat Bool)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_11267 x z) (ho_11267 y z)))) (= x y))))) (let ((_let_2220 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.nat tptp.nat)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_17261 x z) (ho_17261 y z)))) (= x y))))) (let ((_let_2221 (forall ((x |u_(-> tptp.nat tptp.code_integer tptp.nat)|) (y |u_(-> tptp.nat tptp.code_integer tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_12172 x z) (ho_12172 y z)))) (= x y))))) (let ((_let_2222 (forall ((x |u_(-> tptp.list_nat tptp.list_P8198026277950538467nt_nat)|) (y |u_(-> tptp.list_nat tptp.list_P8198026277950538467nt_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_24796 x z) (ho_24796 y z)))) (= x y))))) (let ((_let_2223 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_11296 x z) (ho_11296 y z)))) (= x y))))) (let ((_let_2224 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.int)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.int)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_11680 x z) (ho_11680 y z)))) (= x y))))) (let ((_let_2225 (forall ((x |u_(-> tptp.set_int tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_int tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15138 x z) (ho_15138 y z)))) (= x y))))) (let ((_let_2226 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.nat Bool)_ tptp.nat tptp.nat)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.nat Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.set_o)) (= (ho_17353 x z) (ho_17353 y z)))) (= x y))))) (let ((_let_2227 (forall ((x |u_(-> tptp.nat tptp.product_unit)|) (y |u_(-> tptp.nat tptp.product_unit)|)) (or (not (forall ((z tptp.nat)) (= (ho_24733 x z) (ho_24733 y z)))) (= x y))))) (let ((_let_2228 (forall ((x |u_(-> tptp.int tptp.int tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_11103 x z) (ho_11103 y z)))) (= x y))))) (let ((_let_2229 (forall ((x |u_(-> tptp.int tptp.list_int)|) (y |u_(-> tptp.int tptp.list_int)|)) (or (not (forall ((z tptp.int)) (= (ho_14663 x z) (ho_14663 y z)))) (= x y))))) (let ((_let_2230 (forall ((x |u_(-> tptp.set_nat _u_(-> Bool tptp.nat Bool)_ Bool tptp.nat)|) (y |u_(-> tptp.set_nat _u_(-> Bool tptp.nat Bool)_ Bool tptp.nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_14903 x z) (ho_14903 y z)))) (= x y))))) (let ((_let_2231 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.assn)_ tptp.int tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.assn)_ tptp.int tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_23787 x z) (ho_23787 y z)))) (= x y))))) (let ((_let_2232 (forall ((x |u_(-> tptp.list_o tptp.list_P7333126701944960589_nat_o)|) (y |u_(-> tptp.list_o tptp.list_P7333126701944960589_nat_o)|)) (or (not (forall ((z tptp.list_o)) (= (ho_24752 x z) (ho_24752 y z)))) (= x y))))) (let ((_let_2233 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.set_nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.set_nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_17954 x z) (ho_17954 y z)))) (= x y))))) (let ((_let_2234 (forall ((x |u_(-> tptp.option8956607266484857688it_nat tptp.produc3911288613690379145it_nat)|) (y |u_(-> tptp.option8956607266484857688it_nat tptp.produc3911288613690379145it_nat)|)) (or (not (forall ((z tptp.option8956607266484857688it_nat)) (= (ho_24427 x z) (ho_24427 y z)))) (= x y))))) (let ((_let_2235 (forall ((x |u_(-> tptp.set_nat tptp.nat)|) (y |u_(-> tptp.set_nat tptp.nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_11109 x z) (ho_11109 y z)))) (= x y))))) (let ((_let_2236 (forall ((x |u_(-> tptp.code_integer tptp.int Bool)|) (y |u_(-> tptp.code_integer tptp.int Bool)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_11619 x z) (ho_11619 y z)))) (= x y))))) (let ((_let_2237 (forall ((x |u_(-> tptp.product_prod_o_o tptp.set_Product_prod_o_o Bool)|) (y |u_(-> tptp.product_prod_o_o tptp.set_Product_prod_o_o Bool)|)) (or (not (forall ((z tptp.product_prod_o_o)) (= (ho_24854 x z) (ho_24854 y z)))) (= x y))))) (let ((_let_2238 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_int_int)|)) (= (ho_26147 x z) (ho_26147 y z)))) (= x y))))) (let ((_let_2239 (forall ((x |u_(-> _u_(-> Bool tptp.int tptp.int)_ tptp.set_o _u_(-> Bool tptp.int Bool)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> Bool tptp.int tptp.int)_ tptp.set_o _u_(-> Bool tptp.int Bool)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.int tptp.int)|)) (= (ho_17314 x z) (ho_17314 y z)))) (= x y))))) (let ((_let_2240 (forall ((x |u_(-> tptp.int tptp.int tptp.rat)|) (y |u_(-> tptp.int tptp.int tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_11126 x z) (ho_11126 y z)))) (= x y))))) (let ((_let_2241 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_25948 x z) (ho_25948 y z)))) (= x y))))) (let ((_let_2242 (forall ((x |u_(-> tptp.list_int tptp.heap_e7401611519738050253t_unit tptp.produc3407818250607552075t_unit)|) (y |u_(-> tptp.list_int tptp.heap_e7401611519738050253t_unit tptp.produc3407818250607552075t_unit)|)) (or (not (forall ((z tptp.list_int)) (= (ho_11801 x z) (ho_11801 y z)))) (= x y))))) (let ((_let_2243 (forall ((x |u_(-> tptp.int tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> tptp.int tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.int)) (= (ho_11529 x z) (ho_11529 y z)))) (= x y))))) (let ((_let_2244 (forall ((x |u_(-> tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o)|) (y |u_(-> tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z tptp.produc6271795597528267376eger_o)) (= (ho_26133 x z) (ho_26133 y z)))) (= x y))))) (let ((_let_2245 (forall ((x |u_(-> _u_(-> tptp.num tptp.option_num)_ _u_(-> tptp.num tptp.num)_ tptp.num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num tptp.option_num)_ _u_(-> tptp.num tptp.num)_ tptp.num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.option_num)|)) (= (ho_22670 x z) (ho_22670 y z)))) (= x y))))) (let ((_let_2246 (forall ((x |u_(-> tptp.produc4166570645942440679at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.produc4166570645942440679at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.produc4166570645942440679at_nat)) (= (ho_12820 x z) (ho_12820 y z)))) (= x y))))) (let ((_let_2247 (forall ((x |u_(-> tptp.produc4928098042776334183_nat_o tptp.set_Pr2161125870931222855_nat_o Bool)|) (y |u_(-> tptp.produc4928098042776334183_nat_o tptp.set_Pr2161125870931222855_nat_o Bool)|)) (or (not (forall ((z tptp.produc4928098042776334183_nat_o)) (= (ho_25058 x z) (ho_25058 y z)))) (= x y))))) (let ((_let_2248 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (= (ho_16852 x z) (ho_16852 y z)))) (= x y))))) (let ((_let_2249 (forall ((x |u_(-> _u_(-> tptp.code_natural tptp.nat)_ _u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural tptp.code_natural)|) (y |u_(-> _u_(-> tptp.code_natural tptp.nat)_ _u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural tptp.code_natural)|)) (or (not (forall ((z |u_(-> tptp.code_natural tptp.nat)|)) (= (ho_11488 x z) (ho_11488 y z)))) (= x y))))) (let ((_let_2250 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)_ tptp.set_nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)_ tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)|)) (= (ho_21983 x z) (ho_21983 y z)))) (= x y))))) (let ((_let_2251 (forall ((x |u_(-> tptp.multis2468970476368604999at_nat Bool)|) (y |u_(-> tptp.multis2468970476368604999at_nat Bool)|)) (or (not (forall ((z tptp.multis2468970476368604999at_nat)) (= (ho_12625 x z) (ho_12625 y z)))) (= x y))))) (let ((_let_2252 (forall ((x |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_int)|) (y |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_int)|)) (or (not (forall ((z tptp.b)) (= (ho_25161 x z) (ho_25161 y z)))) (= x y))))) (let ((_let_2253 (forall ((x |u_(-> _u_(-> Bool tptp.nat Bool)_ tptp.nat Bool Bool)|) (y |u_(-> _u_(-> Bool tptp.nat Bool)_ tptp.nat Bool Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.nat Bool)|)) (= (ho_12237 x z) (ho_12237 y z)))) (= x y))))) (let ((_let_2254 (forall ((x |u_(-> tptp.nat tptp.set_nat)|) (y |u_(-> tptp.nat tptp.set_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11421 x z) (ho_11421 y z)))) (= x y))))) (let ((_let_2255 (forall ((x |u_(-> Bool tptp.nat Bool)|) (y |u_(-> Bool tptp.nat Bool)|)) (or (not (forall ((z Bool)) (= (ho_11592 x z) (ho_11592 y z)))) (= x y))))) (let ((_let_2256 (forall ((x |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)|) (y |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_20498 x z) (ho_20498 y z)))) (= x y))))) (let ((_let_2257 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.option2498585697089621389at_nat)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.option2498585697089621389at_nat)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_14296 x z) (ho_14296 y z)))) (= x y))))) (let ((_let_2258 (forall ((x |u_(-> _u_(-> tptp.assn tptp.assn tptp.assn)_ tptp.assn _u_(-> tptp.assn tptp.assn Bool)_ _u_(-> tptp.assn tptp.assn Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.assn tptp.assn tptp.assn)_ tptp.assn _u_(-> tptp.assn tptp.assn Bool)_ _u_(-> tptp.assn tptp.assn Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.assn tptp.assn tptp.assn)|)) (= (ho_24522 x z) (ho_24522 y z)))) (= x y))))) (let ((_let_2259 (forall ((x |u_(-> tptp.produc3500511559948749619nt_int Bool)|) (y |u_(-> tptp.produc3500511559948749619nt_int Bool)|)) (or (not (forall ((z tptp.produc3500511559948749619nt_int)) (= (ho_25221 x z) (ho_25221 y z)))) (= x y))))) (let ((_let_2260 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int Bool)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int Bool)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_17446 x z) (ho_17446 y z)))) (= x y))))) (let ((_let_2261 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_12538 x z) (ho_12538 y z)))) (= x y))))) (let ((_let_2262 (forall ((x |u_(-> tptp.list_P5087981734274514673_int_o tptp.nat tptp.product_prod_int_o)|) (y |u_(-> tptp.list_P5087981734274514673_int_o tptp.nat tptp.product_prod_int_o)|)) (or (not (forall ((z tptp.list_P5087981734274514673_int_o)) (= (ho_24806 x z) (ho_24806 y z)))) (= x y))))) (let ((_let_2263 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_18814 x z) (ho_18814 y z)))) (= x y))))) (let ((_let_2264 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.option1583680563626158861at_nat)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.option1583680563626158861at_nat)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_14292 x z) (ho_14292 y z)))) (= x y))))) (let ((_let_2265 (forall ((x |u_(-> tptp.set_nat _u_(-> Bool tptp.nat Bool)_ Bool tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> Bool tptp.nat Bool)_ Bool tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_11594 x z) (ho_11594 y z)))) (= x y))))) (let ((_let_2266 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.set_nat)_ tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.set_nat)_ tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_14455 x z) (ho_14455 y z)))) (= x y))))) (let ((_let_2267 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_13129 x z) (ho_13129 y z)))) (= x y))))) (let ((_let_2268 (forall ((x |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)_ tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)_ tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)|)) (= (ho_23103 x z) (ho_23103 y z)))) (= x y))))) (let ((_let_2269 (forall ((x |u_(-> tptp.set_o _u_(-> tptp.nat Bool Bool)_ tptp.nat Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> tptp.nat Bool Bool)_ tptp.nat Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_12193 x z) (ho_12193 y z)))) (= x y))))) (let ((_let_2270 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.num tptp.int)_ tptp.num tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.num tptp.int)_ tptp.num tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_22692 x z) (ho_22692 y z)))) (= x y))))) (let ((_let_2271 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.produc859450856879609959at_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.produc859450856879609959at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_14471 x z) (ho_14471 y z)))) (= x y))))) (let ((_let_2272 (forall ((x |u_(-> tptp.array_int tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat)|) (y |u_(-> tptp.array_int tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat)|)) (or (not (forall ((z tptp.array_int)) (= (ho_11148 x z) (ho_11148 y z)))) (= x y))))) (let ((_let_2273 (forall ((x |u_(-> tptp.a tptp.heap_T5738788834812785303t_unit)|) (y |u_(-> tptp.a tptp.heap_T5738788834812785303t_unit)|)) (or (not (forall ((z tptp.a)) (= (ho_11380 x z) (ho_11380 y z)))) (= x y))))) (let ((_let_2274 (forall ((x |u_(-> tptp.list_o tptp.nat tptp.nat)|) (y |u_(-> tptp.list_o tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.list_o)) (= (ho_18768 x z) (ho_18768 y z)))) (= x y))))) (let ((_let_2275 (forall ((x |u_(-> Bool tptp.nat tptp.nat tptp.nat)|) (y |u_(-> Bool tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z Bool)) (= (ho_12061 x z) (ho_12061 y z)))) (= x y))))) (let ((_let_2276 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_11149 x z) (ho_11149 y z)))) (= x y))))) (let ((_let_2277 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_13535 x z) (ho_13535 y z)))) (= x y))))) (let ((_let_2278 (forall ((x |u_(-> tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat)|) (y |u_(-> tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat)|)) (or (not (forall ((z tptp.set_Pr8693737435421807431at_nat)) (= (ho_14475 x z) (ho_14475 y z)))) (= x y))))) (let ((_let_2279 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_13624 x z) (ho_13624 y z)))) (= x y))))) (let ((_let_2280 (forall ((x |u_(-> _u_(-> tptp.a tptp.heap_T5738788834812785303t_unit)_ tptp.a tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.heap_T5738788834812785303t_unit)_ tptp.a tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.heap_T5738788834812785303t_unit)|)) (= (ho_14316 x z) (ho_14316 y z)))) (= x y))))) (let ((_let_2281 (forall ((x |u_(-> _u_(-> tptp.num tptp.nat)_ _u_(-> tptp.num tptp.num)_ tptp.num tptp.nat)|) (y |u_(-> _u_(-> tptp.num tptp.nat)_ _u_(-> tptp.num tptp.num)_ tptp.num tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.num tptp.nat)|)) (= (ho_25757 x z) (ho_25757 y z)))) (= x y))))) (let ((_let_2282 (forall ((x |u_(-> tptp.list_int tptp.array_int tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat)|) (y |u_(-> tptp.list_int tptp.array_int tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat)|)) (or (not (forall ((z tptp.list_int)) (= (ho_11147 x z) (ho_11147 y z)))) (= x y))))) (let ((_let_2283 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_21240 x z) (ho_21240 y z)))) (= x y))))) (let ((_let_2284 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.assn)_ _u_(-> tptp.int tptp.assn)_ tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.assn)_ _u_(-> tptp.int tptp.assn)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_17163 x z) (ho_17163 y z)))) (= x y))))) (let ((_let_2285 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.int tptp.code_integer Bool)_ tptp.int tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.int tptp.code_integer Bool)_ tptp.int tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_11562 x z) (ho_11562 y z)))) (= x y))))) (let ((_let_2286 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|)) (or (not (forall ((z tptp.int)) (= (ho_17561 x z) (ho_17561 y z)))) (= x y))))) (let ((_let_2287 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_13111 x z) (ho_13111 y z)))) (= x y))))) (let ((_let_2288 (forall ((x |u_(-> _u_(-> Bool Bool)_ _u_(-> Bool Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool)_ _u_(-> Bool Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_22449 x z) (ho_22449 y z)))) (= x y))))) (let ((_let_2289 (forall ((x |u_(-> tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.option3562590408128118217it_nat)) (= (ho_11299 x z) (ho_11299 y z)))) (= x y))))) (let ((_let_2290 (forall ((x |u_(-> tptp.set_o tptp.set_o Bool Bool)|) (y |u_(-> tptp.set_o tptp.set_o Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_12891 x z) (ho_12891 y z)))) (= x y))))) (let ((_let_2291 (forall ((x |u_(-> tptp.num tptp.code_natural)|) (y |u_(-> tptp.num tptp.code_natural)|)) (or (not (forall ((z tptp.num)) (= (ho_11474 x z) (ho_11474 y z)))) (= x y))))) (let ((_let_2292 (forall ((x |u_(-> _u_(-> tptp.assn tptp.option_assn)_ tptp.option_assn tptp.option_assn)|) (y |u_(-> _u_(-> tptp.assn tptp.option_assn)_ tptp.option_assn tptp.option_assn)|)) (or (not (forall ((z |u_(-> tptp.assn tptp.option_assn)|)) (= (ho_22219 x z) (ho_22219 y z)))) (= x y))))) (let ((_let_2293 (forall ((x |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z tptp.multis2468970476368604999at_nat)) (= (ho_14487 x z) (ho_14487 y z)))) (= x y))))) (let ((_let_2294 (forall ((x |u_(-> _u_(-> tptp.a tptp.heap_Time_Heap_a)_ tptp.a tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.heap_Time_Heap_a)_ tptp.a tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.heap_Time_Heap_a)|)) (= (ho_11290 x z) (ho_11290 y z)))) (= x y))))) (let ((_let_2295 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.set_int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.set_int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_14870 x z) (ho_14870 y z)))) (= x y))))) (let ((_let_2296 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.nat tptp.code_integer tptp.code_integer)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.nat tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_18272 x z) (ho_18272 y z)))) (= x y))))) (let ((_let_2297 (forall ((x |u_(-> tptp.nat tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_17246 x z) (ho_17246 y z)))) (= x y))))) (let ((_let_2298 (forall ((x |u_(-> tptp.produc3658429121746597890et_nat tptp.produc8111630337999740517et_nat)|) (y |u_(-> tptp.produc3658429121746597890et_nat tptp.produc8111630337999740517et_nat)|)) (or (not (forall ((z tptp.produc3658429121746597890et_nat)) (= (ho_25026 x z) (ho_25026 y z)))) (= x y))))) (let ((_let_2299 (forall ((x |u_(-> Bool _u_(-> tptp.int tptp.int Bool)_ tptp.product_prod_int_int Bool)|) (y |u_(-> Bool _u_(-> tptp.int tptp.int Bool)_ tptp.product_prod_int_int Bool)|)) (or (not (forall ((z Bool)) (= (ho_19812 x z) (ho_19812 y z)))) (= x y))))) (let ((_let_2300 (forall ((x |u_(-> _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.list_nat Bool)|)) (= (ho_11966 x z) (ho_11966 y z)))) (= x y))))) (let ((_let_2301 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int)_ _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.int)_ tptp.code_integer tptp.code_integer)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int)_ _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.int)_ tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int)|)) (= (ho_12156 x z) (ho_12156 y z)))) (= x y))))) (let ((_let_2302 (forall ((x |u_(-> tptp.list_nat tptp.set_list_nat Bool)|) (y |u_(-> tptp.list_nat tptp.set_list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_11659 x z) (ho_11659 y z)))) (= x y))))) (let ((_let_2303 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_11236 x z) (ho_11236 y z)))) (= x y))))) (let ((_let_2304 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_11167 x z) (ho_11167 y z)))) (= x y))))) (let ((_let_2305 (forall ((x |u_(-> _u_(-> tptp.produc8664842809031399944it_nat Bool)_ tptp.option8956607266484857688it_nat Bool)|) (y |u_(-> _u_(-> tptp.produc8664842809031399944it_nat Bool)_ tptp.option8956607266484857688it_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc8664842809031399944it_nat Bool)|)) (= (ho_24451 x z) (ho_24451 y z)))) (= x y))))) (let ((_let_2306 (forall ((x |u_(-> tptp.int tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_11104 x z) (ho_11104 y z)))) (= x y))))) (let ((_let_2307 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int Bool)_ tptp.int tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int Bool)_ tptp.int tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int Bool)|)) (= (ho_12211 x z) (ho_12211 y z)))) (= x y))))) (let ((_let_2308 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_11308 x z) (ho_11308 y z)))) (= x y))))) (let ((_let_2309 (forall ((x |u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)|) (y |u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)|)) (or (not (forall ((z tptp.produc2732055786443039994et_nat)) (= (ho_24474 x z) (ho_24474 y z)))) (= x y))))) (let ((_let_2310 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.nat Bool)_ tptp.nat Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.nat Bool)_ tptp.nat Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_12236 x z) (ho_12236 y z)))) (= x y))))) (let ((_let_2311 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer tptp.nat)_ tptp.set_nat _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer tptp.nat)_ tptp.set_nat _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer tptp.nat)|)) (= (ho_17265 x z) (ho_17265 y z)))) (= x y))))) (let ((_let_2312 (forall ((x |u_(-> tptp.set_set_int tptp.nat)|) (y |u_(-> tptp.set_set_int tptp.nat)|)) (or (not (forall ((z tptp.set_set_int)) (= (ho_25750 x z) (ho_25750 y z)))) (= x y))))) (let ((_let_2313 (forall ((x |u_(-> tptp.array_o tptp.produc6653097349344004940it_nat tptp.produc8032495849646651230it_nat)|) (y |u_(-> tptp.array_o tptp.produc6653097349344004940it_nat tptp.produc8032495849646651230it_nat)|)) (or (not (forall ((z tptp.array_o)) (= (ho_11153 x z) (ho_11153 y z)))) (= x y))))) (let ((_let_2314 (forall ((x |u_(-> tptp.int tptp.rat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.int tptp.rat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_20274 x z) (ho_20274 y z)))) (= x y))))) (let ((_let_2315 (forall ((x |u_(-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.produc3843707927480180839at_nat)) (= (ho_15263 x z) (ho_15263 y z)))) (= x y))))) (let ((_let_2316 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_17422 x z) (ho_17422 y z)))) (= x y))))) (let ((_let_2317 (forall ((x |u_(-> tptp.set_int tptp.set_int)|) (y |u_(-> tptp.set_int tptp.set_int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_11465 x z) (ho_11465 y z)))) (= x y))))) (let ((_let_2318 (forall ((x |u_(-> Bool tptp.option_set_nat tptp.option_set_nat tptp.option_set_nat)|) (y |u_(-> Bool tptp.option_set_nat tptp.option_set_nat tptp.option_set_nat)|)) (or (not (forall ((z Bool)) (= (ho_22418 x z) (ho_22418 y z)))) (= x y))))) (let ((_let_2319 (forall ((x |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12391 x z) (ho_12391 y z)))) (= x y))))) (let ((_let_2320 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer tptp.nat)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_16901 x z) (ho_16901 y z)))) (= x y))))) (let ((_let_2321 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc6999243976208994655_nat_o)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc6999243976208994655_nat_o)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (= (ho_25234 x z) (ho_25234 y z)))) (= x y))))) (let ((_let_2322 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_11571 x z) (ho_11571 y z)))) (= x y))))) (let ((_let_2323 (forall ((x |u_(-> _u_(-> tptp.produc7538756082594784606_nat_b tptp.produc7538756082594784606_nat_b Bool)_ tptp.produc7538756082594784606_nat_b Bool)|) (y |u_(-> _u_(-> tptp.produc7538756082594784606_nat_b tptp.produc7538756082594784606_nat_b Bool)_ tptp.produc7538756082594784606_nat_b Bool)|)) (or (not (forall ((z |u_(-> tptp.produc7538756082594784606_nat_b tptp.produc7538756082594784606_nat_b Bool)|)) (= (ho_25253 x z) (ho_25253 y z)))) (= x y))))) (let ((_let_2324 (forall ((x |u_(-> tptp.int tptp.int tptp.int tptp.option_int)|) (y |u_(-> tptp.int tptp.int tptp.int tptp.option_int)|)) (or (not (forall ((z tptp.int)) (= (ho_23574 x z) (ho_23574 y z)))) (= x y))))) (let ((_let_2325 (forall ((x |u_(-> tptp.num tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.num tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.num)) (= (ho_20126 x z) (ho_20126 y z)))) (= x y))))) (let ((_let_2326 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_15772 x z) (ho_15772 y z)))) (= x y))))) (let ((_let_2327 (forall ((x |u_(-> tptp.heap_Time_Heap_int _u_(-> tptp.int tptp.assn)_ Bool)|) (y |u_(-> tptp.heap_Time_Heap_int _u_(-> tptp.int tptp.assn)_ Bool)|)) (or (not (forall ((z tptp.heap_Time_Heap_int)) (= (ho_24729 x z) (ho_24729 y z)))) (= x y))))) (let ((_let_2328 (forall ((x |u_(-> tptp.option_num tptp.option_num)|) (y |u_(-> tptp.option_num tptp.option_num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_11041 x z) (ho_11041 y z)))) (= x y))))) (let ((_let_2329 (forall ((x |u_(-> tptp.set_Pr4389693562480114009it_nat tptp.set_Pr5508209795250834101it_nat)|) (y |u_(-> tptp.set_Pr4389693562480114009it_nat tptp.set_Pr5508209795250834101it_nat)|)) (or (not (forall ((z tptp.set_Pr4389693562480114009it_nat)) (= (ho_25074 x z) (ho_25074 y z)))) (= x y))))) (let ((_let_2330 (forall ((x |u_(-> _u_(-> tptp.produc4166570645942440679at_nat Bool)_ tptp.set_Pr8551490117392284871at_nat)|) (y |u_(-> _u_(-> tptp.produc4166570645942440679at_nat Bool)_ tptp.set_Pr8551490117392284871at_nat)|)) (or (not (forall ((z |u_(-> tptp.produc4166570645942440679at_nat Bool)|)) (= (ho_11269 x z) (ho_11269 y z)))) (= x y))))) (let ((_let_2331 (forall ((x |u_(-> tptp.set_o tptp.nat)|) (y |u_(-> tptp.set_o tptp.nat)|)) (or (not (forall ((z tptp.set_o)) (= (ho_14849 x z) (ho_14849 y z)))) (= x y))))) (let ((_let_2332 (forall ((x |u_(-> tptp.b tptp.heap_Time_Heap_b)|) (y |u_(-> tptp.b tptp.heap_Time_Heap_b)|)) (or (not (forall ((z tptp.b)) (= (ho_11316 x z) (ho_11316 y z)))) (= x y))))) (let ((_let_2333 (forall ((x |u_(-> Bool tptp.list_nat tptp.list_nat tptp.list_nat)|) (y |u_(-> Bool tptp.list_nat tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z Bool)) (= (ho_14654 x z) (ho_14654 y z)))) (= x y))))) (let ((_let_2334 (forall ((x |u_(-> tptp.rat tptp.list_nat tptp.rat)|) (y |u_(-> tptp.rat tptp.list_nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_15296 x z) (ho_15296 y z)))) (= x y))))) (let ((_let_2335 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_11324 x z) (ho_11324 y z)))) (= x y))))) (let ((_let_2336 (forall ((x |u_(-> tptp.nat tptp.nat tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_11322 x z) (ho_11322 y z)))) (= x y))))) (let ((_let_2337 (forall ((x |u_(-> _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (y |u_(-> _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ _u_(-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (or (not (forall ((z |u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (= (ho_18778 x z) (ho_18778 y z)))) (= x y))))) (let ((_let_2338 (forall ((x |u_(-> _u_(-> tptp.produc8664842809031399944it_nat tptp.produc7388388658123137530it_nat)_ tptp.option8956607266484857688it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.produc8664842809031399944it_nat tptp.produc7388388658123137530it_nat)_ tptp.option8956607266484857688it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc8664842809031399944it_nat tptp.produc7388388658123137530it_nat)|)) (= (ho_25674 x z) (ho_25674 y z)))) (= x y))))) (let ((_let_2339 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.int)|)) (= (ho_20089 x z) (ho_20089 y z)))) (= x y))))) (let ((_let_2340 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_24510 x z) (ho_24510 y z)))) (= x y))))) (let ((_let_2341 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.list_nat tptp.list_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_25825 x z) (ho_25825 y z)))) (= x y))))) (let ((_let_2342 (forall ((x |u_(-> tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.produc3658429121746597890et_nat)) (= (ho_11328 x z) (ho_11328 y z)))) (= x y))))) (let ((_let_2343 (forall ((x |u_(-> tptp.array_nat tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat)|) (y |u_(-> tptp.array_nat tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat)|)) (or (not (forall ((z tptp.array_nat)) (= (ho_11166 x z) (ho_11166 y z)))) (= x y))))) (let ((_let_2344 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.set_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_nat tptp.set_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.set_nat Bool)|)) (= (ho_24328 x z) (ho_24328 y z)))) (= x y))))) (let ((_let_2345 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer)_ tptp.set_int tptp.code_integer)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer)_ tptp.set_int tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer)|)) (= (ho_25300 x z) (ho_25300 y z)))) (= x y))))) (let ((_let_2346 (forall ((x |u_(-> _u_(-> Bool Bool)_ _u_(-> Bool tptp.code_integer)_ Bool tptp.code_integer)|) (y |u_(-> _u_(-> Bool Bool)_ _u_(-> Bool tptp.code_integer)_ Bool tptp.code_integer)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_17087 x z) (ho_17087 y z)))) (= x y))))) (let ((_let_2347 (forall ((x |u_(-> _u_(-> Bool tptp.assn)_ _u_(-> Bool tptp.assn)_ Bool tptp.assn)|) (y |u_(-> _u_(-> Bool tptp.assn)_ _u_(-> Bool tptp.assn)_ Bool tptp.assn)|)) (or (not (forall ((z |u_(-> Bool tptp.assn)|)) (= (ho_15809 x z) (ho_15809 y z)))) (= x y))))) (let ((_let_2348 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_11376 x z) (ho_11376 y z)))) (= x y))))) (let ((_let_2349 (forall ((x |u_(-> tptp.int tptp.set_int Bool)|) (y |u_(-> tptp.int tptp.set_int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_11179 x z) (ho_11179 y z)))) (= x y))))) (let ((_let_2350 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_11321 x z) (ho_11321 y z)))) (= x y))))) (let ((_let_2351 (forall ((x |u_(-> tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_11327 x z) (ho_11327 y z)))) (= x y))))) (let ((_let_2352 (forall ((x |u_(-> tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat Bool)|) (y |u_(-> tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat Bool)|)) (or (not (forall ((z tptp.produc3843707927480180839at_nat)) (= (ho_11259 x z) (ho_11259 y z)))) (= x y))))) (let ((_let_2353 (forall ((x |u_(-> _u_(-> tptp.rat tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.rat tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.product_prod_int_int)|)) (= (ho_11505 x z) (ho_11505 y z)))) (= x y))))) (let ((_let_2354 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_12395 x z) (ho_12395 y z)))) (= x y))))) (let ((_let_2355 (forall ((x |u_(-> tptp.int tptp.nat tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_12433 x z) (ho_12433 y z)))) (= x y))))) (let ((_let_2356 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ tptp.option1893999432384633940_int_o)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ tptp.option1893999432384633940_int_o)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_13844 x z) (ho_13844 y z)))) (= x y))))) (let ((_let_2357 (forall ((x |u_(-> _u_(-> tptp.num Bool)_ tptp.set_num)|) (y |u_(-> _u_(-> tptp.num Bool)_ tptp.set_num)|)) (or (not (forall ((z |u_(-> tptp.num Bool)|)) (= (ho_25366 x z) (ho_25366 y z)))) (= x y))))) (let ((_let_2358 (forall ((x |u_(-> tptp.set_Pr2161125870931222855_nat_o Bool)|) (y |u_(-> tptp.set_Pr2161125870931222855_nat_o Bool)|)) (or (not (forall ((z tptp.set_Pr2161125870931222855_nat_o)) (= (ho_25059 x z) (ho_25059 y z)))) (= x y))))) (let ((_let_2359 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_11188 x z) (ho_11188 y z)))) (= x y))))) (let ((_let_2360 (forall ((x |u_(-> tptp.nat tptp.num tptp.product_prod_nat_num)|) (y |u_(-> tptp.nat tptp.num tptp.product_prod_nat_num)|)) (or (not (forall ((z tptp.nat)) (= (ho_18622 x z) (ho_18622 y z)))) (= x y))))) (let ((_let_2361 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer)|)) (= (ho_11672 x z) (ho_11672 y z)))) (= x y))))) (let ((_let_2362 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.assn)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.assn)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_17169 x z) (ho_17169 y z)))) (= x y))))) (let ((_let_2363 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_24593 x z) (ho_24593 y z)))) (= x y))))) (let ((_let_2364 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_11384 x z) (ho_11384 y z)))) (= x y))))) (let ((_let_2365 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.option_nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.option_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_24187 x z) (ho_24187 y z)))) (= x y))))) (let ((_let_2366 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat tptp.rat)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)|)) (= (ho_12142 x z) (ho_12142 y z)))) (= x y))))) (let ((_let_2367 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_13953 x z) (ho_13953 y z)))) (= x y))))) (let ((_let_2368 (forall ((x |u_(-> tptp.nat tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.nat tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11390 x z) (ho_11390 y z)))) (= x y))))) (let ((_let_2369 (forall ((x |u_(-> _u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)_ tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> _u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)_ tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool)|)) (= (ho_18819 x z) (ho_18819 y z)))) (= x y))))) (let ((_let_2370 (forall ((x |u_(-> tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_11056 x z) (ho_11056 y z)))) (= x y))))) (let ((_let_2371 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ Bool)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ Bool)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_24504 x z) (ho_24504 y z)))) (= x y))))) (let ((_let_2372 (forall ((x |u_(-> tptp.int tptp.int tptp.option_int)|) (y |u_(-> tptp.int tptp.int tptp.option_int)|)) (or (not (forall ((z tptp.int)) (= (ho_14284 x z) (ho_14284 y z)))) (= x y))))) (let ((_let_2373 (forall ((x |u_(-> _u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)|)) (= (ho_24482 x z) (ho_24482 y z)))) (= x y))))) (let ((_let_2374 (forall ((x |u_(-> tptp.code_integer tptp.code_integer Bool)|) (y |u_(-> tptp.code_integer tptp.code_integer Bool)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_11614 x z) (ho_11614 y z)))) (= x y))))) (let ((_let_2375 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.rat)_ _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.rat)_ _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_17212 x z) (ho_17212 y z)))) (= x y))))) (let ((_let_2376 (forall ((x |u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat tptp.produc5657529347773406293et_nat)|) (y |u_(-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat tptp.produc5657529347773406293et_nat)|)) (or (not (forall ((z tptp.produc2732055786443039994et_nat)) (= (ho_24876 x z) (ho_24876 y z)))) (= x y))))) (let ((_let_2377 (forall ((x |u_(-> _u_(-> tptp.b tptp.heap_T5738788834812785303t_unit)_ tptp.b tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.heap_T5738788834812785303t_unit)_ tptp.b tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.heap_T5738788834812785303t_unit)|)) (= (ho_11396 x z) (ho_11396 y z)))) (= x y))))) (let ((_let_2378 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_13184 x z) (ho_13184 y z)))) (= x y))))) (let ((_let_2379 (forall ((x |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)_ tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)_ tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)|)) (= (ho_21990 x z) (ho_21990 y z)))) (= x y))))) (let ((_let_2380 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.product_prod_int_int tptp.rat)_ _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.product_prod_int_int tptp.rat)_ _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_11120 x z) (ho_11120 y z)))) (= x y))))) (let ((_let_2381 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_12146 x z) (ho_12146 y z)))) (= x y))))) (let ((_let_2382 (forall ((x |u_(-> Bool tptp.int)|) (y |u_(-> Bool tptp.int)|)) (or (not (forall ((z Bool)) (= (ho_12218 x z) (ho_12218 y z)))) (= x y))))) (let ((_let_2383 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.rat)_ _u_(-> tptp.product_prod_nat_nat tptp.rat)_ tptp.product_prod_nat_nat tptp.rat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.rat)_ _u_(-> tptp.product_prod_nat_nat tptp.rat)_ tptp.product_prod_nat_nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.rat)|)) (= (ho_15019 x z) (ho_15019 y z)))) (= x y))))) (let ((_let_2384 (forall ((x |u_(-> tptp.set_nat tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_15834 x z) (ho_15834 y z)))) (= x y))))) (let ((_let_2385 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.set_nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_11426 x z) (ho_11426 y z)))) (= x y))))) (let ((_let_2386 (forall ((x |u_(-> _u_(-> tptp.set_nat Bool)_ _u_(-> tptp.set_nat tptp.nat)_ tptp.set_nat Bool)|) (y |u_(-> _u_(-> tptp.set_nat Bool)_ _u_(-> tptp.set_nat tptp.nat)_ tptp.set_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat Bool)|)) (= (ho_17103 x z) (ho_17103 y z)))) (= x y))))) (let ((_let_2387 (forall ((x |u_(-> Bool tptp.code_integer)|) (y |u_(-> Bool tptp.code_integer)|)) (or (not (forall ((z Bool)) (= (ho_13199 x z) (ho_13199 y z)))) (= x y))))) (let ((_let_2388 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_11441 x z) (ho_11441 y z)))) (= x y))))) (let ((_let_2389 (forall ((x |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (= (ho_24512 x z) (ho_24512 y z)))) (= x y))))) (let ((_let_2390 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_natural)_ tptp.code_natural tptp.int tptp.code_natural)|) (y |u_(-> _u_(-> tptp.int tptp.code_natural)_ tptp.code_natural tptp.int tptp.code_natural)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_natural)|)) (= (ho_15852 x z) (ho_15852 y z)))) (= x y))))) (let ((_let_2391 (forall ((x |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)_ tptp.produc7388388658123137530it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)_ tptp.produc7388388658123137530it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)|)) (= (ho_23673 x z) (ho_23673 y z)))) (= x y))))) (let ((_let_2392 (forall ((x |u_(-> _u_(-> Bool Bool)_ _u_(-> Bool tptp.assn)_ Bool tptp.assn)|) (y |u_(-> _u_(-> Bool Bool)_ _u_(-> Bool tptp.assn)_ Bool tptp.assn)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_17072 x z) (ho_17072 y z)))) (= x y))))) (let ((_let_2393 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.code_integer Bool)_ tptp.code_integer tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.code_integer Bool)_ tptp.code_integer tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_11616 x z) (ho_11616 y z)))) (= x y))))) (let ((_let_2394 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat)|)) (= (ho_11440 x z) (ho_11440 y z)))) (= x y))))) (let ((_let_2395 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer)_ _u_(-> tptp.nat Bool)_ tptp.nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer)_ _u_(-> tptp.nat Bool)_ tptp.nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer)|)) (= (ho_17427 x z) (ho_17427 y z)))) (= x y))))) (let ((_let_2396 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.set_int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.set_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_11464 x z) (ho_11464 y z)))) (= x y))))) (let ((_let_2397 (forall ((x |u_(-> tptp.set_se6260736226359567993nt_int tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.set_se6260736226359567993nt_int tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.set_se6260736226359567993nt_int)) (= (ho_18871 x z) (ho_18871 y z)))) (= x y))))) (let ((_let_2398 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.set_nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_15371 x z) (ho_15371 y z)))) (= x y))))) (let ((_let_2399 (forall ((x |u_(-> _u_(-> tptp.rat tptp.rat Bool)_ tptp.list_rat Bool)|) (y |u_(-> _u_(-> tptp.rat tptp.rat Bool)_ tptp.list_rat Bool)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.rat Bool)|)) (= (ho_24834 x z) (ho_24834 y z)))) (= x y))))) (let ((_let_2400 (forall ((x |u_(-> tptp.set_int tptp.int _u_(-> tptp.int tptp.int)_ tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.int _u_(-> tptp.int tptp.int)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15830 x z) (ho_15830 y z)))) (= x y))))) (let ((_let_2401 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.assn)_ tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.assn)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_17158 x z) (ho_17158 y z)))) (= x y))))) (let ((_let_2402 (forall ((x |u_(-> tptp.nat _u_(-> tptp.list_nat tptp.nat)_ tptp.list_nat Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.list_nat tptp.nat)_ tptp.list_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_11847 x z) (ho_11847 y z)))) (= x y))))) (let ((_let_2403 (forall ((x |u_(-> _u_(-> tptp.int Bool Bool)_ tptp.int Bool Bool)|) (y |u_(-> _u_(-> tptp.int Bool Bool)_ tptp.int Bool Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool Bool)|)) (= (ho_11582 x z) (ho_11582 y z)))) (= x y))))) (let ((_let_2404 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 x z) (ho_11211 y z)))) (= x y))))) (let ((_let_2405 (forall ((x |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z tptp.multis2468970476368604999at_nat)) (= (ho_14485 x z) (ho_14485 y z)))) (= x y))))) (let ((_let_2406 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.set_int tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.set_int tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_17216 x z) (ho_17216 y z)))) (= x y))))) (let ((_let_2407 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_15767 x z) (ho_15767 y z)))) (= x y))))) (let ((_let_2408 (forall ((x |u_(-> tptp.b tptp.heap_T5738788834812785303t_unit)|) (y |u_(-> tptp.b tptp.heap_T5738788834812785303t_unit)|)) (or (not (forall ((z tptp.b)) (= (ho_11394 x z) (ho_11394 y z)))) (= x y))))) (let ((_let_2409 (forall ((x |u_(-> tptp.rat tptp.int Bool)|) (y |u_(-> tptp.rat tptp.int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_11514 x z) (ho_11514 y z)))) (= x y))))) (let ((_let_2410 (forall ((x |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat)|) (y |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat)|)) (or (not (forall ((z tptp.produc3658429121746597890et_nat)) (= (ho_25405 x z) (ho_25405 y z)))) (= x y))))) (let ((_let_2411 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.rat)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.rat)|) (y |u_(-> _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.rat)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ tptp.int tptp.rat)|)) (= (ho_11124 x z) (ho_11124 y z)))) (= x y))))) (let ((_let_2412 (forall ((x |u_(-> _u_(-> tptp.num tptp.num)_ _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.num tptp.int)_ tptp.num tptp.code_integer)|) (y |u_(-> _u_(-> tptp.num tptp.num)_ _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.num tptp.int)_ tptp.num tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num)|)) (= (ho_26015 x z) (ho_26015 y z)))) (= x y))))) (let ((_let_2413 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_19050 x z) (ho_19050 y z)))) (= x y))))) (let ((_let_2414 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int Bool)_ tptp.code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int Bool)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int Bool)|)) (= (ho_15065 x z) (ho_15065 y z)))) (= x y))))) (let ((_let_2415 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_11956 x z) (ho_11956 y z)))) (= x y))))) (let ((_let_2416 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (= (ho_25998 x z) (ho_25998 y z)))) (= x y))))) (let ((_let_2417 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural tptp.code_natural)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.code_natural tptp.code_natural tptp.code_natural)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_11490 x z) (ho_11490 y z)))) (= x y))))) (let ((_let_2418 (forall ((x |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.a)) (= (ho_13114 x z) (ho_13114 y z)))) (= x y))))) (let ((_let_2419 (forall ((x |u_(-> tptp.assn tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.assn tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_11347 x z) (ho_11347 y z)))) (= x y))))) (let ((_let_2420 (forall ((x |u_(-> tptp.nat tptp.code_natural)|) (y |u_(-> tptp.nat tptp.code_natural)|)) (or (not (forall ((z tptp.nat)) (= (ho_11481 x z) (ho_11481 y z)))) (= x y))))) (let ((_let_2421 (forall ((x |u_(-> _u_(-> tptp.nat Bool tptp.nat)_ tptp.set_nat _u_(-> tptp.nat Bool Bool)_ Bool tptp.nat)|) (y |u_(-> _u_(-> tptp.nat Bool tptp.nat)_ tptp.set_nat _u_(-> tptp.nat Bool Bool)_ Bool tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool tptp.nat)|)) (= (ho_17286 x z) (ho_17286 y z)))) (= x y))))) (let ((_let_2422 (forall ((x |u_(-> _u_(-> tptp.list_nat tptp.nat)_ tptp.list_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.list_nat tptp.nat)_ tptp.list_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.list_nat tptp.nat)|)) (= (ho_14913 x z) (ho_14913 y z)))) (= x y))))) (let ((_let_2423 (forall ((x |u_(-> _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (y |u_(-> _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (or (not (forall ((z |u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (= (ho_12595 x z) (ho_12595 y z)))) (= x y))))) (let ((_let_2424 (forall ((x |u_(-> tptp.ref_Product_unit tptp.product_unit)|) (y |u_(-> tptp.ref_Product_unit tptp.product_unit)|)) (or (not (forall ((z tptp.ref_Product_unit)) (= (ho_24577 x z) (ho_24577 y z)))) (= x y))))) (let ((_let_2425 (forall ((x |u_(-> _u_(-> tptp.produc3925858234332021118et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.produc3925858234332021118et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc3925858234332021118et_nat Bool)|)) (= (ho_24272 x z) (ho_24272 y z)))) (= x y))))) (let ((_let_2426 (forall ((x |u_(-> tptp.set_Pr8536935166611901872et_nat _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|) (y |u_(-> tptp.set_Pr8536935166611901872et_nat _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8536935166611901872et_nat)) (= (ho_21370 x z) (ho_21370 y z)))) (= x y))))) (let ((_let_2427 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_14314 x z) (ho_14314 y z)))) (= x y))))) (let ((_let_2428 (forall ((x |u_(-> tptp.set_list_nat tptp.set_list_nat Bool)|) (y |u_(-> tptp.set_list_nat tptp.set_list_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_15173 x z) (ho_15173 y z)))) (= x y))))) (let ((_let_2429 (forall ((x |u_(-> tptp.code_natural tptp.nat)|) (y |u_(-> tptp.code_natural tptp.nat)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_11483 x z) (ho_11483 y z)))) (= x y))))) (let ((_let_2430 (forall ((x |u_(-> tptp.produc3407818250607552075t_unit tptp.produc7196121022310644452it_nat)|) (y |u_(-> tptp.produc3407818250607552075t_unit tptp.produc7196121022310644452it_nat)|)) (or (not (forall ((z tptp.produc3407818250607552075t_unit)) (= (ho_11805 x z) (ho_11805 y z)))) (= x y))))) (let ((_let_2431 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.set_int tptp.set_int tptp.set_int)_ tptp.set_int tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.set_int tptp.set_int tptp.set_int)_ tptp.set_int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_21972 x z) (ho_21972 y z)))) (= x y))))) (let ((_let_2432 (forall ((x |u_(-> tptp.num tptp.set_num Bool)|) (y |u_(-> tptp.num tptp.set_num Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_25358 x z) (ho_25358 y z)))) (= x y))))) (let ((_let_2433 (forall ((x |u_(-> tptp.produc1730305018825802663t_unit tptp.produc6751673265320737416it_nat)|) (y |u_(-> tptp.produc1730305018825802663t_unit tptp.produc6751673265320737416it_nat)|)) (or (not (forall ((z tptp.produc1730305018825802663t_unit)) (= (ho_11821 x z) (ho_11821 y z)))) (= x y))))) (let ((_let_2434 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.produc8961450480463052793it_nat)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.produc8961450480463052793it_nat)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_25040 x z) (ho_25040 y z)))) (= x y))))) (let ((_let_2435 (forall ((x |u_(-> Bool tptp.nat)|) (y |u_(-> Bool tptp.nat)|)) (or (not (forall ((z Bool)) (= (ho_12199 x z) (ho_12199 y z)))) (= x y))))) (let ((_let_2436 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (= (ho_26005 x z) (ho_26005 y z)))) (= x y))))) (let ((_let_2437 (forall ((x |u_(-> tptp.code_natural tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (y |u_(-> tptp.code_natural tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_11495 x z) (ho_11495 y z)))) (= x y))))) (let ((_let_2438 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer tptp.assn)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer tptp.assn)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_16826 x z) (ho_16826 y z)))) (= x y))))) (let ((_let_2439 (forall ((x |u_(-> Bool tptp.int tptp.int)|) (y |u_(-> Bool tptp.int tptp.int)|)) (or (not (forall ((z Bool)) (= (ho_12214 x z) (ho_12214 y z)))) (= x y))))) (let ((_let_2440 (forall ((x |u_(-> tptp.option2498585697089621389at_nat _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.option2498585697089621389at_nat)_ tptp.option2498585697089621389at_nat tptp.option2498585697089621389at_nat)|) (y |u_(-> tptp.option2498585697089621389at_nat _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.option2498585697089621389at_nat)_ tptp.option2498585697089621389at_nat tptp.option2498585697089621389at_nat)|)) (or (not (forall ((z tptp.option2498585697089621389at_nat)) (= (ho_23588 x z) (ho_23588 y z)))) (= x y))))) (let ((_let_2441 (forall ((x |u_(-> _u_(-> Bool tptp.nat tptp.nat)_ tptp.set_nat _u_(-> Bool tptp.nat Bool)_ Bool tptp.nat)|) (y |u_(-> _u_(-> Bool tptp.nat tptp.nat)_ tptp.set_nat _u_(-> Bool tptp.nat Bool)_ Bool tptp.nat)|)) (or (not (forall ((z |u_(-> Bool tptp.nat tptp.nat)|)) (= (ho_17350 x z) (ho_17350 y z)))) (= x y))))) (let ((_let_2442 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_11507 x z) (ho_11507 y z)))) (= x y))))) (let ((_let_2443 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat)_ _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat)_ _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat)|)) (= (ho_15032 x z) (ho_15032 y z)))) (= x y))))) (let ((_let_2444 (forall ((x |u_(-> tptp.code_integer tptp.set_Code_integer Bool)|) (y |u_(-> tptp.code_integer tptp.set_Code_integer Bool)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_11566 x z) (ho_11566 y z)))) (= x y))))) (let ((_let_2445 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.nat)|) (y |u_(-> tptp.set_nat _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_14843 x z) (ho_14843 y z)))) (= x y))))) (let ((_let_2446 (forall ((x |u_(-> tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat Bool)|) (y |u_(-> tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat Bool)|)) (or (not (forall ((z tptp.produc4471711990508489141at_nat)) (= (ho_24601 x z) (ho_24601 y z)))) (= x y))))) (let ((_let_2447 (forall ((x |u_(-> tptp.list_nat tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.list_nat tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_18666 x z) (ho_18666 y z)))) (= x y))))) (let ((_let_2448 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_25842 x z) (ho_25842 y z)))) (= x y))))) (let ((_let_2449 (forall ((x |u_(-> tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_15573 x z) (ho_15573 y z)))) (= x y))))) (let ((_let_2450 (forall ((x |u_(-> Bool tptp.rat tptp.rat tptp.rat)|) (y |u_(-> Bool tptp.rat tptp.rat tptp.rat)|)) (or (not (forall ((z Bool)) (= (ho_11510 x z) (ho_11510 y z)))) (= x y))))) (let ((_let_2451 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_11069 x z) (ho_11069 y z)))) (= x y))))) (let ((_let_2452 (forall ((x |u_(-> Bool _u_(-> Bool tptp.int)_ _u_(-> Bool tptp.int)_ Bool tptp.int)|) (y |u_(-> Bool _u_(-> Bool tptp.int)_ _u_(-> Bool tptp.int)_ Bool tptp.int)|)) (or (not (forall ((z Bool)) (= (ho_15902 x z) (ho_15902 y z)))) (= x y))))) (let ((_let_2453 (forall ((x |u_(-> tptp.int tptp.product_prod_nat_nat)|) (y |u_(-> tptp.int tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.int)) (= (ho_11516 x z) (ho_11516 y z)))) (= x y))))) (let ((_let_2454 (forall ((x |u_(-> tptp.produc8664842809031399944it_nat tptp.list_P626663023886443800it_nat tptp.list_P626663023886443800it_nat)|) (y |u_(-> tptp.produc8664842809031399944it_nat tptp.list_P626663023886443800it_nat tptp.list_P626663023886443800it_nat)|)) (or (not (forall ((z tptp.produc8664842809031399944it_nat)) (= (ho_24993 x z) (ho_24993 y z)))) (= x y))))) (let ((_let_2455 (forall ((x |u_(-> tptp.code_integer tptp.nat tptp.code_integer tptp.code_integer)|) (y |u_(-> tptp.code_integer tptp.nat tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12438 x z) (ho_12438 y z)))) (= x y))))) (let ((_let_2456 (forall ((x |u_(-> _u_(-> tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural Bool)_ tptp.produc7822875418678951345atural Bool)|) (y |u_(-> _u_(-> tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural Bool)_ tptp.produc7822875418678951345atural Bool)|)) (or (not (forall ((z |u_(-> tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural Bool)|)) (= (ho_25197 x z) (ho_25197 y z)))) (= x y))))) (let ((_let_2457 (forall ((x |u_(-> tptp.list_P2321686559999237006et_nat tptp.list_P362550909693114634et_nat)|) (y |u_(-> tptp.list_P2321686559999237006et_nat tptp.list_P362550909693114634et_nat)|)) (or (not (forall ((z tptp.list_P2321686559999237006et_nat)) (= (ho_24970 x z) (ho_24970 y z)))) (= x y))))) (let ((_let_2458 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.code_integer)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer)|)) (= (ho_16843 x z) (ho_16843 y z)))) (= x y))))) (let ((_let_2459 (forall ((x |u_(-> _u_(-> Bool tptp.int Bool)_ Bool tptp.int Bool)|) (y |u_(-> _u_(-> Bool tptp.int Bool)_ Bool tptp.int Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.int Bool)|)) (= (ho_11591 x z) (ho_11591 y z)))) (= x y))))) (let ((_let_2460 (forall ((x |u_(-> tptp.nat tptp.rat tptp.nat tptp.rat)|) (y |u_(-> tptp.nat tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_17647 x z) (ho_17647 y z)))) (= x y))))) (let ((_let_2461 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_15231 x z) (ho_15231 y z)))) (= x y))))) (let ((_let_2462 (forall ((x |u_(-> _u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)_ _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)_ _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|)) (= (ho_25887 x z) (ho_25887 y z)))) (= x y))))) (let ((_let_2463 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_12608 x z) (ho_12608 y z)))) (= x y))))) (let ((_let_2464 (forall ((x |u_(-> tptp.int tptp.code_integer)|) (y |u_(-> tptp.int tptp.code_integer)|)) (or (not (forall ((z tptp.int)) (= (ho_11667 x z) (ho_11667 y z)))) (= x y))))) (let ((_let_2465 (forall ((x |u_(-> tptp.list_o tptp.nat Bool)|) (y |u_(-> tptp.list_o tptp.nat Bool)|)) (or (not (forall ((z tptp.list_o)) (= (ho_15669 x z) (ho_15669 y z)))) (= x y))))) (let ((_let_2466 (forall ((x |u_(-> tptp.int tptp.int tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> tptp.int tptp.int tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.int)) (= (ho_11528 x z) (ho_11528 y z)))) (= x y))))) (let ((_let_2467 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer Bool Bool)_ Bool tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer Bool Bool)_ Bool tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_14846 x z) (ho_14846 y z)))) (= x y))))) (let ((_let_2468 (forall ((x |u_(-> tptp.option_set_nat tptp.option_set_nat)|) (y |u_(-> tptp.option_set_nat tptp.option_set_nat)|)) (or (not (forall ((z tptp.option_set_nat)) (= (ho_22207 x z) (ho_22207 y z)))) (= x y))))) (let ((_let_2469 (forall ((x |u_(-> tptp.nat tptp.set_set_nat Bool)|) (y |u_(-> tptp.nat tptp.set_set_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_15167 x z) (ho_15167 y z)))) (= x y))))) (let ((_let_2470 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_15592 x z) (ho_15592 y z)))) (= x y))))) (let ((_let_2471 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool Bool)_ tptp.code_integer Bool Bool)|) (y |u_(-> _u_(-> tptp.code_integer Bool Bool)_ tptp.code_integer Bool Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool Bool)|)) (= (ho_11558 x z) (ho_11558 y z)))) (= x y))))) (let ((_let_2472 (forall ((x |u_(-> tptp.list_nat tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat)|) (y |u_(-> tptp.list_nat tptp.heap_e7401611519738050253t_unit tptp.produc6751673265320737416it_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_11823 x z) (ho_11823 y z)))) (= x y))))) (let ((_let_2473 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.code_integer)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.code_integer)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_12132 x z) (ho_12132 y z)))) (= x y))))) (let ((_let_2474 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer Bool)|)) (= (ho_17267 x z) (ho_17267 y z)))) (= x y))))) (let ((_let_2475 (forall ((x |u_(-> tptp.set_int Bool)|) (y |u_(-> tptp.set_int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_11180 x z) (ho_11180 y z)))) (= x y))))) (let ((_let_2476 (forall ((x |u_(-> _u_(-> tptp.num tptp.num tptp.num)_ tptp.num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num tptp.num tptp.num)_ tptp.num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num tptp.num)|)) (= (ho_22521 x z) (ho_22521 y z)))) (= x y))))) (let ((_let_2477 (forall ((x |u_(-> tptp.code_integer tptp.nat tptp.code_integer)|) (y |u_(-> tptp.code_integer tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12441 x z) (ho_12441 y z)))) (= x y))))) (let ((_let_2478 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (= (ho_25959 x z) (ho_25959 y z)))) (= x y))))) (let ((_let_2479 (forall ((x |u_(-> tptp.nat Bool tptp.int)|) (y |u_(-> tptp.nat Bool tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_12234 x z) (ho_12234 y z)))) (= x y))))) (let ((_let_2480 (forall ((x |u_(-> tptp.nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> tptp.nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_17673 x z) (ho_17673 y z)))) (= x y))))) (let ((_let_2481 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer)|)) (= (ho_24584 x z) (ho_24584 y z)))) (= x y))))) (let ((_let_2482 (forall ((x |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ _u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ _u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (= (ho_18724 x z) (ho_18724 y z)))) (= x y))))) (let ((_let_2483 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.list_nat tptp.int tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.list_nat tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_18652 x z) (ho_18652 y z)))) (= x y))))) (let ((_let_2484 (forall ((x |u_(-> _u_(-> tptp.set_set_nat Bool)_ tptp.set_set_set_nat)|) (y |u_(-> _u_(-> tptp.set_set_nat Bool)_ tptp.set_set_set_nat)|)) (or (not (forall ((z |u_(-> tptp.set_set_nat Bool)|)) (= (ho_25742 x z) (ho_25742 y z)))) (= x y))))) (let ((_let_2485 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat Bool)_ tptp.int tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.int tptp.nat Bool)_ tptp.int tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat Bool)|)) (= (ho_11577 x z) (ho_11577 y z)))) (= x y))))) (let ((_let_2486 (forall ((x |u_(-> tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.produc4166570645942440679at_nat)) (= (ho_11051 x z) (ho_11051 y z)))) (= x y))))) (let ((_let_2487 (forall ((x |u_(-> tptp.set_o _u_(-> tptp.int Bool Bool)_ tptp.int Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> tptp.int Bool Bool)_ tptp.int Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_11581 x z) (ho_11581 y z)))) (= x y))))) (let ((_let_2488 (forall ((x |u_(-> _u_(-> Bool tptp.int)_ Bool Bool)|) (y |u_(-> _u_(-> Bool tptp.int)_ Bool Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.int)|)) (= (ho_15116 x z) (ho_15116 y z)))) (= x y))))) (let ((_let_2489 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_17452 x z) (ho_17452 y z)))) (= x y))))) (let ((_let_2490 (forall ((x |u_(-> _u_(-> tptp.num tptp.assn)_ tptp.num tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.num tptp.assn)_ tptp.num tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.assn)|)) (= (ho_23810 x z) (ho_23810 y z)))) (= x y))))) (let ((_let_2491 (forall ((x |u_(-> _u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)|)) (= (ho_13233 x z) (ho_13233 y z)))) (= x y))))) (let ((_let_2492 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.code_integer tptp.code_integer tptp.code_integer)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.code_integer tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.int)|)) (= (ho_12161 x z) (ho_12161 y z)))) (= x y))))) (let ((_let_2493 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_13946 x z) (ho_13946 y z)))) (= x y))))) (let ((_let_2494 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_16275 x z) (ho_16275 y z)))) (= x y))))) (let ((_let_2495 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.code_integer)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.nat)) (= (ho_18578 x z) (ho_18578 y z)))) (= x y))))) (let ((_let_2496 (forall ((x |u_(-> Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (y |u_(-> Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z Bool)) (= (ho_13128 x z) (ho_13128 y z)))) (= x y))))) (let ((_let_2497 (forall ((x |u_(-> tptp.num tptp.product_prod_int_int tptp.product_prod_int_int)|) (y |u_(-> tptp.num tptp.product_prod_int_int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.num)) (= (ho_19912 x z) (ho_19912 y z)))) (= x y))))) (let ((_let_2498 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer Bool)_ tptp.code_integer tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer Bool)_ tptp.code_integer tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer Bool)|)) (= (ho_11617 x z) (ho_11617 y z)))) (= x y))))) (let ((_let_2499 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_11857 x z) (ho_11857 y z)))) (= x y))))) (let ((_let_2500 (forall ((x |u_(-> _u_(-> tptp.list_nat Bool)_ _u_(-> tptp.list_nat tptp.rat)_ _u_(-> tptp.list_nat tptp.rat)_ tptp.list_nat tptp.rat)|) (y |u_(-> _u_(-> tptp.list_nat Bool)_ _u_(-> tptp.list_nat tptp.rat)_ _u_(-> tptp.list_nat tptp.rat)_ tptp.list_nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.list_nat Bool)|)) (= (ho_16303 x z) (ho_16303 y z)))) (= x y))))) (let ((_let_2501 (forall ((x |u_(-> tptp.set_int _u_(-> Bool tptp.int Bool)_ Bool tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> Bool tptp.int Bool)_ Bool tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_11590 x z) (ho_11590 y z)))) (= x y))))) (let ((_let_2502 (forall ((x |u_(-> tptp.num _u_(-> tptp.num tptp.num)_ tptp.option_num tptp.num)|) (y |u_(-> tptp.num _u_(-> tptp.num tptp.num)_ tptp.option_num tptp.num)|)) (or (not (forall ((z tptp.num)) (= (ho_11046 x z) (ho_11046 y z)))) (= x y))))) (let ((_let_2503 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.code_integer)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.code_integer)|)) (or (not (forall ((z tptp.int)) (= (ho_17526 x z) (ho_17526 y z)))) (= x y))))) (let ((_let_2504 (forall ((x |u_(-> tptp.set_o _u_(-> Bool Bool Bool)_ Bool Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> Bool Bool Bool)_ Bool Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_11597 x z) (ho_11597 y z)))) (= x y))))) (let ((_let_2505 (forall ((x |u_(-> tptp.list_nat tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.list_nat tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_18654 x z) (ho_18654 y z)))) (= x y))))) (let ((_let_2506 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int Bool)_ tptp.code_integer tptp.int Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int Bool)_ tptp.code_integer tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int Bool)|)) (= (ho_11622 x z) (ho_11622 y z)))) (= x y))))) (let ((_let_2507 (forall ((x |u_(-> tptp.nat tptp.product_prod_int_o)|) (y |u_(-> tptp.nat tptp.product_prod_int_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_24807 x z) (ho_24807 y z)))) (= x y))))) (let ((_let_2508 (forall ((x |u_(-> tptp.a tptp.heap_Time_Heap_a)|) (y |u_(-> tptp.a tptp.heap_Time_Heap_a)|)) (or (not (forall ((z tptp.a)) (= (ho_11288 x z) (ho_11288 y z)))) (= x y))))) (let ((_let_2509 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool Bool)_ tptp.code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer Bool Bool)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool Bool)|)) (= (ho_14852 x z) (ho_14852 y z)))) (= x y))))) (let ((_let_2510 (forall ((x |u_(-> Bool tptp.int tptp.product_prod_o_int)|) (y |u_(-> Bool tptp.int tptp.product_prod_o_int)|)) (or (not (forall ((z Bool)) (= (ho_24783 x z) (ho_24783 y z)))) (= x y))))) (let ((_let_2511 (forall ((x |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)|)) (= (ho_24320 x z) (ho_24320 y z)))) (= x y))))) (let ((_let_2512 (forall ((x |u_(-> tptp.set_Code_integer tptp.code_integer)|) (y |u_(-> tptp.set_Code_integer tptp.code_integer)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_25491 x z) (ho_25491 y z)))) (= x y))))) (let ((_let_2513 (forall ((x |u_(-> tptp.multis2468970476368604999at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.multis2468970476368604999at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.multis2468970476368604999at_nat)) (= (ho_12616 x z) (ho_12616 y z)))) (= x y))))) (let ((_let_2514 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)_ _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)_ _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)|)) (= (ho_24630 x z) (ho_24630 y z)))) (= x y))))) (let ((_let_2515 (forall ((x |u_(-> tptp.b tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.b tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.b)) (= (ho_11397 x z) (ho_11397 y z)))) (= x y))))) (let ((_let_2516 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_13567 x z) (ho_13567 y z)))) (= x y))))) (let ((_let_2517 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_11158 x z) (ho_11158 y z)))) (= x y))))) (let ((_let_2518 (forall ((x |u_(-> tptp.nat tptp.code_integer)|) (y |u_(-> tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.nat)) (= (ho_11669 x z) (ho_11669 y z)))) (= x y))))) (let ((_let_2519 (forall ((x |u_(-> tptp.nat tptp.set_int)|) (y |u_(-> tptp.nat tptp.set_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_21223 x z) (ho_21223 y z)))) (= x y))))) (let ((_let_2520 (forall ((x |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_nat)|) (y |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.set_nat)|)) (or (not (forall ((z tptp.b)) (= (ho_25156 x z) (ho_25156 y z)))) (= x y))))) (let ((_let_2521 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_17151 x z) (ho_17151 y z)))) (= x y))))) (let ((_let_2522 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.option1893999432384633940_int_o)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.option1893999432384633940_int_o)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_13845 x z) (ho_13845 y z)))) (= x y))))) (let ((_let_2523 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_18726 x z) (ho_18726 y z)))) (= x y))))) (let ((_let_2524 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_13847 x z) (ho_13847 y z)))) (= x y))))) (let ((_let_2525 (forall ((x |u_(-> tptp.nat tptp.code_integer Bool)|) (y |u_(-> tptp.nat tptp.code_integer Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_12168 x z) (ho_12168 y z)))) (= x y))))) (let ((_let_2526 (forall ((x |u_(-> Bool tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|) (y |u_(-> Bool tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|)) (or (not (forall ((z Bool)) (= (ho_11525 x z) (ho_11525 y z)))) (= x y))))) (let ((_let_2527 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int)_ tptp.int tptp.code_integer tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int)_ tptp.int tptp.code_integer tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int)|)) (= (ho_15863 x z) (ho_15863 y z)))) (= x y))))) (let ((_let_2528 (forall ((x |u_(-> Bool tptp.num)|) (y |u_(-> Bool tptp.num)|)) (or (not (forall ((z Bool)) (= (ho_25523 x z) (ho_25523 y z)))) (= x y))))) (let ((_let_2529 (forall ((x |u_(-> tptp.a tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.a tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.a)) (= (ho_11291 x z) (ho_11291 y z)))) (= x y))))) (let ((_let_2530 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.assn)_ tptp.set_Code_integer tptp.assn)|) (y |u_(-> _u_(-> tptp.code_integer tptp.assn)_ tptp.set_Code_integer tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.assn)|)) (= (ho_25503 x z) (ho_25503 y z)))) (= x y))))) (let ((_let_2531 (forall ((x |u_(-> tptp.nat tptp.option_nat)|) (y |u_(-> tptp.nat tptp.option_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_13852 x z) (ho_13852 y z)))) (= x y))))) (let ((_let_2532 (forall ((x |u_(-> _u_(-> Bool tptp.product_unit)_ tptp.set_o Bool)|) (y |u_(-> _u_(-> Bool tptp.product_unit)_ tptp.set_o Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.product_unit)|)) (= (ho_26047 x z) (ho_26047 y z)))) (= x y))))) (let ((_let_2533 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.option1893999432384633940_int_o)_ tptp.option1893999432384633940_int_o tptp.option1893999432384633940_int_o)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.option1893999432384633940_int_o)_ tptp.option1893999432384633940_int_o tptp.option1893999432384633940_int_o)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.option1893999432384633940_int_o)|)) (= (ho_22195 x z) (ho_22195 y z)))) (= x y))))) (let ((_let_2534 (forall ((x |u_(-> tptp.set_nat tptp.set_nat tptp.option_set_nat)|) (y |u_(-> tptp.set_nat tptp.set_nat tptp.option_set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_13858 x z) (ho_13858 y z)))) (= x y))))) (let ((_let_2535 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.option8963830502488799655at_nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.option8963830502488799655at_nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_13860 x z) (ho_13860 y z)))) (= x y))))) (let ((_let_2536 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.code_integer)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer)|)) (= (ho_16837 x z) (ho_16837 y z)))) (= x y))))) (let ((_let_2537 (forall ((x |u_(-> tptp.option_num tptp.int)|) (y |u_(-> tptp.option_num tptp.int)|)) (or (not (forall ((z tptp.option_num)) (= (ho_22679 x z) (ho_22679 y z)))) (= x y))))) (let ((_let_2538 (forall ((x |u_(-> tptp.list_P3795440434834930179_o_int tptp.nat tptp.product_prod_o_int)|) (y |u_(-> tptp.list_P3795440434834930179_o_int tptp.nat tptp.product_prod_o_int)|)) (or (not (forall ((z tptp.list_P3795440434834930179_o_int)) (= (ho_24789 x z) (ho_24789 y z)))) (= x y))))) (let ((_let_2539 (forall ((x |u_(-> tptp.set_nat tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_20383 x z) (ho_20383 y z)))) (= x y))))) (let ((_let_2540 (forall ((x |u_(-> tptp.nat tptp.nat tptp.int tptp.int)|) (y |u_(-> tptp.nat tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_18076 x z) (ho_18076 y z)))) (= x y))))) (let ((_let_2541 (forall ((x |u_(-> tptp.produc7819656566062154093et_nat tptp.set_Pr5488025237498180813et_nat Bool)|) (y |u_(-> tptp.produc7819656566062154093et_nat tptp.set_Pr5488025237498180813et_nat Bool)|)) (or (not (forall ((z tptp.produc7819656566062154093et_nat)) (= (ho_25603 x z) (ho_25603 y z)))) (= x y))))) (let ((_let_2542 (forall ((x |u_(-> _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.multis2468970476368604999at_nat)|)) (= (ho_17675 x z) (ho_17675 y z)))) (= x y))))) (let ((_let_2543 (forall ((x |u_(-> tptp.nat tptp.list_nat tptp.rat tptp.nat tptp.rat)|) (y |u_(-> tptp.nat tptp.list_nat tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_18677 x z) (ho_18677 y z)))) (= x y))))) (let ((_let_2544 (forall ((x |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (= (ho_18810 x z) (ho_18810 y z)))) (= x y))))) (let ((_let_2545 (forall ((x |u_(-> _u_(-> tptp.num tptp.num tptp.num)_ tptp.num tptp.num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num tptp.num tptp.num)_ tptp.num tptp.num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num tptp.num)|)) (= (ho_13931 x z) (ho_13931 y z)))) (= x y))))) (let ((_let_2546 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_25020 x z) (ho_25020 y z)))) (= x y))))) (let ((_let_2547 (forall ((x |u_(-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.produc8664842809031399944it_nat)) (= (ho_13939 x z) (ho_13939 y z)))) (= x y))))) (let ((_let_2548 (forall ((x |u_(-> tptp.set_list_nat tptp.nat _u_(-> tptp.list_nat tptp.nat)_ tptp.list_nat Bool)|) (y |u_(-> tptp.set_list_nat tptp.nat _u_(-> tptp.list_nat tptp.nat)_ tptp.list_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_15823 x z) (ho_15823 y z)))) (= x y))))) (let ((_let_2549 (forall ((x |u_(-> tptp.int tptp.set_se6260736226359567993nt_int)|) (y |u_(-> tptp.int tptp.set_se6260736226359567993nt_int)|)) (or (not (forall ((z tptp.int)) (= (ho_25150 x z) (ho_25150 y z)))) (= x y))))) (let ((_let_2550 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.int)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.int)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_17385 x z) (ho_17385 y z)))) (= x y))))) (let ((_let_2551 (forall ((x |u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.int)|)) (= (ho_26146 x z) (ho_26146 y z)))) (= x y))))) (let ((_let_2552 (forall ((x |u_(-> _u_(-> tptp.product_unit tptp.product_unit)_ tptp.ref_Product_unit tptp.heap_T5738788834812785303t_unit)|) (y |u_(-> _u_(-> tptp.product_unit tptp.product_unit)_ tptp.ref_Product_unit tptp.heap_T5738788834812785303t_unit)|)) (or (not (forall ((z |u_(-> tptp.product_unit tptp.product_unit)|)) (= (ho_25091 x z) (ho_25091 y z)))) (= x y))))) (let ((_let_2553 (forall ((x |u_(-> tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.produc8664842809031399944it_nat)) (= (ho_13938 x z) (ho_13938 y z)))) (= x y))))) (let ((_let_2554 (forall ((x |u_(-> tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat)|) (y |u_(-> tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat)|)) (or (not (forall ((z tptp.produc8664842809031399944it_nat)) (= (ho_13935 x z) (ho_13935 y z)))) (= x y))))) (let ((_let_2555 (forall ((x |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|) (y |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_11526 x z) (ho_11526 y z)))) (= x y))))) (let ((_let_2556 (forall ((x |u_(-> _u_(-> tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat)_ tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat)_ tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat)|)) (= (ho_13937 x z) (ho_13937 y z)))) (= x y))))) (let ((_let_2557 (forall ((x |u_(-> tptp.multis2468970476368604999at_nat tptp.set_Pr8551490117392284871at_nat tptp.multis2468970476368604999at_nat tptp.produc4166570645942440679at_nat Bool)|) (y |u_(-> tptp.multis2468970476368604999at_nat tptp.set_Pr8551490117392284871at_nat tptp.multis2468970476368604999at_nat tptp.produc4166570645942440679at_nat Bool)|)) (or (not (forall ((z tptp.multis2468970476368604999at_nat)) (= (ho_18821 x z) (ho_18821 y z)))) (= x y))))) (let ((_let_2558 (forall ((x |u_(-> _u_(-> tptp.produc8664842809031399944it_nat Bool)_ tptp.list_P626663023886443800it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.produc8664842809031399944it_nat Bool)_ tptp.list_P626663023886443800it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc8664842809031399944it_nat Bool)|)) (= (ho_24928 x z) (ho_24928 y z)))) (= x y))))) (let ((_let_2559 (forall ((x |u_(-> tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat)|) (y |u_(-> tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat)|)) (or (not (forall ((z tptp.produc8664842809031399944it_nat)) (= (ho_13940 x z) (ho_13940 y z)))) (= x y))))) (let ((_let_2560 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.code_integer)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.code_integer)|)) (or (not (forall ((z tptp.set_int)) (= (ho_16842 x z) (ho_16842 y z)))) (= x y))))) (let ((_let_2561 (forall ((x |u_(-> tptp.array_int tptp.list_int tptp.nat tptp.assn)|) (y |u_(-> tptp.array_int tptp.list_int tptp.nat tptp.assn)|)) (or (not (forall ((z tptp.array_int)) (= (ho_21051 x z) (ho_21051 y z)))) (= x y))))) (let ((_let_2562 (forall ((x |u_(-> _u_(-> tptp.nat Bool Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat Bool Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool Bool)|)) (= (ho_17284 x z) (ho_17284 y z)))) (= x y))))) (let ((_let_2563 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.set_Pr719794911490849221et_nat)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.set_Pr719794911490849221et_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_25019 x z) (ho_25019 y z)))) (= x y))))) (let ((_let_2564 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_14484 x z) (ho_14484 y z)))) (= x y))))) (let ((_let_2565 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_nat)|) (y |u_(-> tptp.nat tptp.product_prod_nat_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11067 x z) (ho_11067 y z)))) (= x y))))) (let ((_let_2566 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_13945 x z) (ho_13945 y z)))) (= x y))))) (let ((_let_2567 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.rat Bool)|)) (= (ho_25897 x z) (ho_25897 y z)))) (= x y))))) (let ((_let_2568 (forall ((x |u_(-> tptp.list_nat tptp.int)|) (y |u_(-> tptp.list_nat tptp.int)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_15316 x z) (ho_15316 y z)))) (= x y))))) (let ((_let_2569 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_13942 x z) (ho_13942 y z)))) (= x y))))) (let ((_let_2570 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_15257 x z) (ho_15257 y z)))) (= x y))))) (let ((_let_2571 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit Bool)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit Bool)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_24268 x z) (ho_24268 y z)))) (= x y))))) (let ((_let_2572 (forall ((x |u_(-> tptp.set_Pr5508209795250834101it_nat Bool)|) (y |u_(-> tptp.set_Pr5508209795250834101it_nat Bool)|)) (or (not (forall ((z tptp.set_Pr5508209795250834101it_nat)) (= (ho_24888 x z) (ho_24888 y z)))) (= x y))))) (let ((_let_2573 (forall ((x |u_(-> tptp.set_Code_integer tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_Code_integer tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_15155 x z) (ho_15155 y z)))) (= x y))))) (let ((_let_2574 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11479 x z) (ho_11479 y z)))) (= x y))))) (let ((_let_2575 (forall ((x |u_(-> tptp.nat tptp.b)|) (y |u_(-> tptp.nat tptp.b)|)) (or (not (forall ((z tptp.nat)) (= (ho_24820 x z) (ho_24820 y z)))) (= x y))))) (let ((_let_2576 (forall ((x |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat)_ tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat)_ tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat)|)) (= (ho_13944 x z) (ho_13944 y z)))) (= x y))))) (let ((_let_2577 (forall ((x |u_(-> tptp.list_P7985473006766602707_nat_o tptp.list_P9062070895058802706et_nat tptp.list_P2321686559999237006et_nat)|) (y |u_(-> tptp.list_P7985473006766602707_nat_o tptp.list_P9062070895058802706et_nat tptp.list_P2321686559999237006et_nat)|)) (or (not (forall ((z tptp.list_P7985473006766602707_nat_o)) (= (ho_24957 x z) (ho_24957 y z)))) (= x y))))) (let ((_let_2578 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.code_integer)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_15234 x z) (ho_15234 y z)))) (= x y))))) (let ((_let_2579 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_13947 x z) (ho_13947 y z)))) (= x y))))) (let ((_let_2580 (forall ((x |u_(-> tptp.code_natural _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (y |u_(-> tptp.code_natural _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_12594 x z) (ho_12594 y z)))) (= x y))))) (let ((_let_2581 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_13952 x z) (ho_13952 y z)))) (= x y))))) (let ((_let_2582 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_13949 x z) (ho_13949 y z)))) (= x y))))) (let ((_let_2583 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_17421 x z) (ho_17421 y z)))) (= x y))))) (let ((_let_2584 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.assn)|)) (= (ho_16798 x z) (ho_16798 y z)))) (= x y))))) (let ((_let_2585 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_13954 x z) (ho_13954 y z)))) (= x y))))) (let ((_let_2586 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_13150 x z) (ho_13150 y z)))) (= x y))))) (let ((_let_2587 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.code_integer)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_25323 x z) (ho_25323 y z)))) (= x y))))) (let ((_let_2588 (forall ((x |u_(-> tptp.set_int tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_11467 x z) (ho_11467 y z)))) (= x y))))) (let ((_let_2589 (forall ((x |u_(-> tptp.b tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.b tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.b)) (= (ho_11319 x z) (ho_11319 y z)))) (= x y))))) (let ((_let_2590 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.int tptp.nat Bool)_ tptp.int tptp.nat)|) (y |u_(-> tptp.set_nat _u_(-> tptp.int tptp.nat Bool)_ tptp.int tptp.nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_14879 x z) (ho_14879 y z)))) (= x y))))) (let ((_let_2591 (forall ((x |u_(-> _u_(-> Bool Bool)_ _u_(-> Bool tptp.nat)_ Bool tptp.nat)|) (y |u_(-> _u_(-> Bool Bool)_ _u_(-> Bool tptp.nat)_ Bool tptp.nat)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_17117 x z) (ho_17117 y z)))) (= x y))))) (let ((_let_2592 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.option1583680563626158861at_nat)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.option1583680563626158861at_nat)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_14290 x z) (ho_14290 y z)))) (= x y))))) (let ((_let_2593 (forall ((x |u_(-> tptp.nat tptp.heap_Time_Heap_o)|) (y |u_(-> tptp.nat tptp.heap_Time_Heap_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_24719 x z) (ho_24719 y z)))) (= x y))))) (let ((_let_2594 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_14303 x z) (ho_14303 y z)))) (= x y))))) (let ((_let_2595 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_12121 x z) (ho_12121 y z)))) (= x y))))) (let ((_let_2596 (forall ((x |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.b)) (= (ho_14322 x z) (ho_14322 y z)))) (= x y))))) (let ((_let_2597 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.int)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_14686 x z) (ho_14686 y z)))) (= x y))))) (let ((_let_2598 (forall ((x |u_(-> tptp.assn tptp.assn Bool)|) (y |u_(-> tptp.assn tptp.assn Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_14385 x z) (ho_14385 y z)))) (= x y))))) (let ((_let_2599 (forall ((x |u_(-> tptp.set_int tptp.set_int Bool)|) (y |u_(-> tptp.set_int tptp.set_int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_14397 x z) (ho_14397 y z)))) (= x y))))) (let ((_let_2600 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.product_prod_int_int tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_14442 x z) (ho_14442 y z)))) (= x y))))) (let ((_let_2601 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.set_nat)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.set_nat)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_25160 x z) (ho_25160 y z)))) (= x y))))) (let ((_let_2602 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_25950 x z) (ho_25950 y z)))) (= x y))))) (let ((_let_2603 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ tptp.product_prod_int_int tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_14441 x z) (ho_14441 y z)))) (= x y))))) (let ((_let_2604 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.code_integer)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer)|)) (= (ho_17430 x z) (ho_17430 y z)))) (= x y))))) (let ((_let_2605 (forall ((x |u_(-> tptp.nat tptp.nat tptp.list_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.list_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_14445 x z) (ho_14445 y z)))) (= x y))))) (let ((_let_2606 (forall ((x |u_(-> tptp.nat tptp.list_nat tptp.list_nat)|) (y |u_(-> tptp.nat tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_14449 x z) (ho_14449 y z)))) (= x y))))) (let ((_let_2607 (forall ((x |u_(-> tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat)|) (y |u_(-> tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat)|)) (or (not (forall ((z tptp.set_Pr8693737435421807431at_nat)) (= (ho_14476 x z) (ho_14476 y z)))) (= x y))))) (let ((_let_2608 (forall ((x |u_(-> tptp.set_nat tptp.nat tptp.nat)|) (y |u_(-> tptp.set_nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_18140 x z) (ho_18140 y z)))) (= x y))))) (let ((_let_2609 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.set_int)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.set_int)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_25164 x z) (ho_25164 y z)))) (= x y))))) (let ((_let_2610 (forall ((x |u_(-> tptp.set_Product_prod_b_b Bool)|) (y |u_(-> tptp.set_Product_prod_b_b Bool)|)) (or (not (forall ((z tptp.set_Product_prod_b_b)) (= (ho_25071 x z) (ho_25071 y z)))) (= x y))))) (let ((_let_2611 (forall ((x |u_(-> tptp.produc859450856879609959at_nat Bool)|) (y |u_(-> tptp.produc859450856879609959at_nat Bool)|)) (or (not (forall ((z tptp.produc859450856879609959at_nat)) (= (ho_26145 x z) (ho_26145 y z)))) (= x y))))) (let ((_let_2612 (forall ((x |u_(-> tptp.code_natural tptp.code_natural tptp.code_natural)|) (y |u_(-> tptp.code_natural tptp.code_natural tptp.code_natural)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_11476 x z) (ho_11476 y z)))) (= x y))))) (let ((_let_2613 (forall ((x |u_(-> tptp.set_Pr8693737435421807431at_nat Bool)|) (y |u_(-> tptp.set_Pr8693737435421807431at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8693737435421807431at_nat)) (= (ho_14482 x z) (ho_14482 y z)))) (= x y))))) (let ((_let_2614 (forall ((x |u_(-> tptp.set_set_nat tptp.nat)|) (y |u_(-> tptp.set_set_nat tptp.nat)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_15162 x z) (ho_15162 y z)))) (= x y))))) (let ((_let_2615 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer Bool)_ tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer Bool)_ tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_17059 x z) (ho_17059 y z)))) (= x y))))) (let ((_let_2616 (forall ((x |u_(-> Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_26125 x z) (ho_26125 y z)))) (= x y))))) (let ((_let_2617 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_11853 x z) (ho_11853 y z)))) (= x y))))) (let ((_let_2618 (forall ((x |u_(-> tptp.code_integer tptp.set_Code_integer)|) (y |u_(-> tptp.code_integer tptp.set_Code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_25347 x z) (ho_25347 y z)))) (= x y))))) (let ((_let_2619 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.produc859450856879609959at_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.produc859450856879609959at_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_14479 x z) (ho_14479 y z)))) (= x y))))) (let ((_let_2620 (forall ((x |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat tptp.nat Bool)|) (y |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.produc3658429121746597890et_nat)) (= (ho_14617 x z) (ho_14617 y z)))) (= x y))))) (let ((_let_2621 (forall ((x |u_(-> tptp.list_int tptp.list_int)|) (y |u_(-> tptp.list_int tptp.list_int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_14666 x z) (ho_14666 y z)))) (= x y))))) (let ((_let_2622 (forall ((x |u_(-> tptp.nat tptp.list_nat Bool)|) (y |u_(-> tptp.nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_14643 x z) (ho_14643 y z)))) (= x y))))) (let ((_let_2623 (forall ((x |u_(-> _u_(-> Bool tptp.int tptp.int)_ tptp.int Bool tptp.int)|) (y |u_(-> _u_(-> Bool tptp.int tptp.int)_ tptp.int Bool tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.int tptp.int)|)) (= (ho_12216 x z) (ho_12216 y z)))) (= x y))))) (let ((_let_2624 (forall ((x |u_(-> tptp.nat Bool tptp.product_prod_nat_o)|) (y |u_(-> tptp.nat Bool tptp.product_prod_nat_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_24748 x z) (ho_24748 y z)))) (= x y))))) (let ((_let_2625 (forall ((x |u_(-> tptp.nat tptp.nat tptp.list_nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_14642 x z) (ho_14642 y z)))) (= x y))))) (let ((_let_2626 (forall ((x |u_(-> tptp.nat tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_12470 x z) (ho_12470 y z)))) (= x y))))) (let ((_let_2627 (forall ((x |u_(-> tptp.int tptp.int tptp.list_int)|) (y |u_(-> tptp.int tptp.int tptp.list_int)|)) (or (not (forall ((z tptp.int)) (= (ho_14662 x z) (ho_14662 y z)))) (= x y))))) (let ((_let_2628 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.rat)_ tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.rat)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15273 x z) (ho_15273 y z)))) (= x y))))) (let ((_let_2629 (forall ((x |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.produc3260487557148687353it_nat)_ tptp.option4065278094766928714it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.produc3260487557148687353it_nat)_ tptp.option4065278094766928714it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc7388388658123137530it_nat tptp.produc3260487557148687353it_nat)|)) (= (ho_25711 x z) (ho_25711 y z)))) (= x y))))) (let ((_let_2630 (forall ((x |u_(-> tptp.int tptp.rat)|) (y |u_(-> tptp.int tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_11127 x z) (ho_11127 y z)))) (= x y))))) (let ((_let_2631 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer tptp.nat)_ tptp.set_Code_integer _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer tptp.nat)_ tptp.set_Code_integer _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer tptp.nat)|)) (= (ho_17260 x z) (ho_17260 y z)))) (= x y))))) (let ((_let_2632 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.product_prod_int_int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ tptp.product_prod_int_int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.int)|)) (= (ho_14682 x z) (ho_14682 y z)))) (= x y))))) (let ((_let_2633 (forall ((x |u_(-> tptp.rat tptp.int)|) (y |u_(-> tptp.rat tptp.int)|)) (or (not (forall ((z tptp.rat)) (= (ho_14684 x z) (ho_14684 y z)))) (= x y))))) (let ((_let_2634 (forall ((x |u_(-> tptp.rat tptp.rat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.rat tptp.rat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_14698 x z) (ho_14698 y z)))) (= x y))))) (let ((_let_2635 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat Bool)|)) (= (ho_14844 x z) (ho_14844 y z)))) (= x y))))) (let ((_let_2636 (forall ((x |u_(-> _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.num)|) (y |u_(-> _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.option_num)|)) (= (ho_22677 x z) (ho_22677 y z)))) (= x y))))) (let ((_let_2637 (forall ((x |u_(-> tptp.option_num tptp.nat)|) (y |u_(-> tptp.option_num tptp.nat)|)) (or (not (forall ((z tptp.option_num)) (= (ho_18604 x z) (ho_18604 y z)))) (= x y))))) (let ((_let_2638 (forall ((x |u_(-> Bool Bool Bool Bool)|) (y |u_(-> Bool Bool Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_15255 x z) (ho_15255 y z)))) (= x y))))) (let ((_let_2639 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.set_nat)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.set_nat)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_25159 x z) (ho_25159 y z)))) (= x y))))) (let ((_let_2640 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.int)|) (y |u_(-> tptp.product_prod_nat_nat tptp.int)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_25527 x z) (ho_25527 y z)))) (= x y))))) (let ((_let_2641 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.set_Code_integer)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.set_Code_integer)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_14857 x z) (ho_14857 y z)))) (= x y))))) (let ((_let_2642 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_natural)_ tptp.code_natural tptp.nat tptp.code_natural)|) (y |u_(-> _u_(-> tptp.nat tptp.code_natural)_ tptp.code_natural tptp.nat tptp.code_natural)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_natural)|)) (= (ho_15837 x z) (ho_15837 y z)))) (= x y))))) (let ((_let_2643 (forall ((x |u_(-> _u_(-> tptp.rat tptp.assn)_ tptp.rat tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.rat tptp.assn)_ tptp.rat tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.assn)|)) (= (ho_23818 x z) (ho_23818 y z)))) (= x y))))) (let ((_let_2644 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.nat)_ tptp.set_nat Bool)|) (y |u_(-> _u_(-> tptp.set_nat tptp.nat)_ tptp.set_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.nat)|)) (= (ho_16865 x z) (ho_16865 y z)))) (= x y))))) (let ((_let_2645 (forall ((x |u_(-> tptp.list_P3521021558325789923at_int tptp.list_P3521021558325789923at_int)|) (y |u_(-> tptp.list_P3521021558325789923at_int tptp.list_P3521021558325789923at_int)|)) (or (not (forall ((z tptp.list_P3521021558325789923at_int)) (= (ho_24949 x z) (ho_24949 y z)))) (= x y))))) (let ((_let_2646 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_14874 x z) (ho_14874 y z)))) (= x y))))) (let ((_let_2647 (forall ((x |u_(-> tptp.list_int tptp.set_list_int Bool)|) (y |u_(-> tptp.list_int tptp.set_list_int Bool)|)) (or (not (forall ((z tptp.list_int)) (= (ho_25591 x z) (ho_25591 y z)))) (= x y))))) (let ((_let_2648 (forall ((x |u_(-> tptp.int tptp.int tptp.set_nat)|) (y |u_(-> tptp.int tptp.int tptp.set_nat)|)) (or (not (forall ((z tptp.int)) (= (ho_25133 x z) (ho_25133 y z)))) (= x y))))) (let ((_let_2649 (forall ((x |u_(-> tptp.array_o tptp.heap_Time_Heap_nat)|) (y |u_(-> tptp.array_o tptp.heap_Time_Heap_nat)|)) (or (not (forall ((z tptp.array_o)) (= (ho_24699 x z) (ho_24699 y z)))) (= x y))))) (let ((_let_2650 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_11292 x z) (ho_11292 y z)))) (= x y))))) (let ((_let_2651 (forall ((x |u_(-> _u_(-> Bool tptp.nat)_ tptp.set_o tptp.nat)|) (y |u_(-> _u_(-> Bool tptp.nat)_ tptp.set_o tptp.nat)|)) (or (not (forall ((z |u_(-> Bool tptp.nat)|)) (= (ho_17280 x z) (ho_17280 y z)))) (= x y))))) (let ((_let_2652 (forall ((x |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)|)) (= (ho_24324 x z) (ho_24324 y z)))) (= x y))))) (let ((_let_2653 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.set_int _u_(-> tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.set_int _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_21533 x z) (ho_21533 y z)))) (= x y))))) (let ((_let_2654 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option3562590408128118217it_nat)_ tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option3562590408128118217it_nat)_ tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option3562590408128118217it_nat)|)) (= (ho_13099 x z) (ho_13099 y z)))) (= x y))))) (let ((_let_2655 (forall ((x |u_(-> _u_(-> tptp.int Bool Bool)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int Bool Bool)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int Bool Bool)|)) (= (ho_14888 x z) (ho_14888 y z)))) (= x y))))) (let ((_let_2656 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_22758 x z) (ho_22758 y z)))) (= x y))))) (let ((_let_2657 (forall ((x |u_(-> tptp.num tptp.nat tptp.int)|) (y |u_(-> tptp.num tptp.nat tptp.int)|)) (or (not (forall ((z tptp.num)) (= (ho_13123 x z) (ho_13123 y z)))) (= x y))))) (let ((_let_2658 (forall ((x |u_(-> tptp.set_o _u_(-> tptp.int Bool Bool)_ tptp.int tptp.nat)|) (y |u_(-> tptp.set_o _u_(-> tptp.int Bool Bool)_ tptp.int tptp.nat)|)) (or (not (forall ((z tptp.set_o)) (= (ho_14887 x z) (ho_14887 y z)))) (= x y))))) (let ((_let_2659 (forall ((x |u_(-> _u_(-> Bool Bool)_ Bool Bool)|) (y |u_(-> _u_(-> Bool Bool)_ Bool Bool)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_17055 x z) (ho_17055 y z)))) (= x y))))) (let ((_let_2660 (forall ((x |u_(-> _u_(-> Bool tptp.nat tptp.int)_ tptp.set_o _u_(-> Bool tptp.nat Bool)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> Bool tptp.nat tptp.int)_ tptp.set_o _u_(-> Bool tptp.nat Bool)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.nat tptp.int)|)) (= (ho_17332 x z) (ho_17332 y z)))) (= x y))))) (let ((_let_2661 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat Bool)|)) (= (ho_17340 x z) (ho_17340 y z)))) (= x y))))) (let ((_let_2662 (forall ((x |u_(-> _u_(-> tptp.num tptp.option_num)_ _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num tptp.option_num)_ _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.option_num)|)) (= (ho_11170 x z) (ho_11170 y z)))) (= x y))))) (let ((_let_2663 (forall ((x |u_(-> _u_(-> Bool tptp.code_integer Bool)_ tptp.code_integer Bool Bool)|) (y |u_(-> _u_(-> Bool tptp.code_integer Bool)_ tptp.code_integer Bool Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.code_integer Bool)|)) (= (ho_14891 x z) (ho_14891 y z)))) (= x y))))) (let ((_let_2664 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_11681 x z) (ho_11681 y z)))) (= x y))))) (let ((_let_2665 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.code_integer Bool)_ tptp.code_integer Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.code_integer Bool)_ tptp.code_integer Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_14890 x z) (ho_14890 y z)))) (= x y))))) (let ((_let_2666 (forall ((x |u_(-> _u_(-> Bool tptp.code_integer Bool)_ Bool tptp.nat)|) (y |u_(-> _u_(-> Bool tptp.code_integer Bool)_ Bool tptp.nat)|)) (or (not (forall ((z |u_(-> Bool tptp.code_integer Bool)|)) (= (ho_14894 x z) (ho_14894 y z)))) (= x y))))) (let ((_let_2667 (forall ((x |u_(-> tptp.code_integer tptp.code_integer tptp.set_Code_integer)|) (y |u_(-> tptp.code_integer tptp.code_integer tptp.set_Code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_25346 x z) (ho_25346 y z)))) (= x y))))) (let ((_let_2668 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> Bool tptp.code_integer Bool)_ Bool tptp.nat)|) (y |u_(-> tptp.set_Code_integer _u_(-> Bool tptp.code_integer Bool)_ Bool tptp.nat)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_14893 x z) (ho_14893 y z)))) (= x y))))) (let ((_let_2669 (forall ((x |u_(-> _u_(-> Bool tptp.int Bool)_ Bool tptp.nat)|) (y |u_(-> _u_(-> Bool tptp.int Bool)_ Bool tptp.nat)|)) (or (not (forall ((z |u_(-> Bool tptp.int Bool)|)) (= (ho_14900 x z) (ho_14900 y z)))) (= x y))))) (let ((_let_2670 (forall ((x |u_(-> tptp.rat tptp.set_rat tptp.set_rat)|) (y |u_(-> tptp.rat tptp.set_rat tptp.set_rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_25449 x z) (ho_25449 y z)))) (= x y))))) (let ((_let_2671 (forall ((x |u_(-> _u_(-> Bool tptp.nat Bool)_ Bool tptp.nat)|) (y |u_(-> _u_(-> Bool tptp.nat Bool)_ Bool tptp.nat)|)) (or (not (forall ((z |u_(-> Bool tptp.nat Bool)|)) (= (ho_14904 x z) (ho_14904 y z)))) (= x y))))) (let ((_let_2672 (forall ((x |u_(-> tptp.nat tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> tptp.nat tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_15181 x z) (ho_15181 y z)))) (= x y))))) (let ((_let_2673 (forall ((x |u_(-> tptp.int tptp.assn)|) (y |u_(-> tptp.int tptp.assn)|)) (or (not (forall ((z tptp.int)) (= (ho_12025 x z) (ho_12025 y z)))) (= x y))))) (let ((_let_2674 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn)|)) (or (not (forall ((z tptp.set_int)) (= (ho_16831 x z) (ho_16831 y z)))) (= x y))))) (let ((_let_2675 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.rat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.rat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_15017 x z) (ho_15017 y z)))) (= x y))))) (let ((_let_2676 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_26012 x z) (ho_26012 y z)))) (= x y))))) (let ((_let_2677 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int)|)) (= (ho_15023 x z) (ho_15023 y z)))) (= x y))))) (let ((_let_2678 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_15027 x z) (ho_15027 y z)))) (= x y))))) (let ((_let_2679 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_15347 x z) (ho_15347 y z)))) (= x y))))) (let ((_let_2680 (forall ((x |u_(-> tptp.set_list_nat tptp.int)|) (y |u_(-> tptp.set_list_nat tptp.int)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_25704 x z) (ho_25704 y z)))) (= x y))))) (let ((_let_2681 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_15029 x z) (ho_15029 y z)))) (= x y))))) (let ((_let_2682 (forall ((x |u_(-> tptp.nat tptp.product_prod_o_nat)|) (y |u_(-> tptp.nat tptp.product_prod_o_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_24767 x z) (ho_24767 y z)))) (= x y))))) (let ((_let_2683 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.nat)_ _u_(-> tptp.set_nat tptp.nat)_ tptp.set_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.set_nat tptp.nat)_ _u_(-> tptp.set_nat tptp.nat)_ tptp.set_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.nat)|)) (= (ho_18479 x z) (ho_18479 y z)))) (= x y))))) (let ((_let_2684 (forall ((x |u_(-> _u_(-> tptp.nat Bool Bool)_ Bool tptp.nat)|) (y |u_(-> _u_(-> tptp.nat Bool Bool)_ Bool tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool Bool)|)) (= (ho_17288 x z) (ho_17288 y z)))) (= x y))))) (let ((_let_2685 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer tptp.rat)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_17120 x z) (ho_17120 y z)))) (= x y))))) (let ((_let_2686 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_15030 x z) (ho_15030 y z)))) (= x y))))) (let ((_let_2687 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_15893 x z) (ho_15893 y z)))) (= x y))))) (let ((_let_2688 (forall ((x |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (= (ho_24511 x z) (ho_24511 y z)))) (= x y))))) (let ((_let_2689 (forall ((x |u_(-> tptp.set_nat tptp.list_nat)|) (y |u_(-> tptp.set_nat tptp.list_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_25802 x z) (ho_25802 y z)))) (= x y))))) (let ((_let_2690 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat Bool)_ tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat Bool)_ tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_17451 x z) (ho_17451 y z)))) (= x y))))) (let ((_let_2691 (forall ((x |u_(-> tptp.rat tptp.rat tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_17640 x z) (ho_17640 y z)))) (= x y))))) (let ((_let_2692 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|)) (or (not (forall ((z tptp.int)) (= (ho_15882 x z) (ho_15882 y z)))) (= x y))))) (let ((_let_2693 (forall ((x |u_(-> tptp.list_b tptp.list_b)|) (y |u_(-> tptp.list_b tptp.list_b)|)) (or (not (forall ((z tptp.list_b)) (= (ho_24982 x z) (ho_24982 y z)))) (= x y))))) (let ((_let_2694 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.nat _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.nat _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer)|)) (= (ho_17903 x z) (ho_17903 y z)))) (= x y))))) (let ((_let_2695 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.produc6653097349344004940it_nat tptp.produc8961450480463052793it_nat)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.produc6653097349344004940it_nat tptp.produc8961450480463052793it_nat)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_25039 x z) (ho_25039 y z)))) (= x y))))) (let ((_let_2696 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_15047 x z) (ho_15047 y z)))) (= x y))))) (let ((_let_2697 (forall ((x |u_(-> tptp.set_int tptp.set_int tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.set_int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15512 x z) (ho_15512 y z)))) (= x y))))) (let ((_let_2698 (forall ((x |u_(-> tptp.int Bool tptp.product_prod_int_o)|) (y |u_(-> tptp.int Bool tptp.product_prod_int_o)|)) (or (not (forall ((z tptp.int)) (= (ho_24800 x z) (ho_24800 y z)))) (= x y))))) (let ((_let_2699 (forall ((x |u_(-> _u_(-> tptp.produc3843707927480180839at_nat Bool)_ tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> _u_(-> tptp.produc3843707927480180839at_nat Bool)_ tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc3843707927480180839at_nat Bool)|)) (= (ho_19186 x z) (ho_19186 y z)))) (= x y))))) (let ((_let_2700 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.code_integer)_ tptp.set_set_nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.set_nat tptp.code_integer)_ tptp.set_set_nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.code_integer)|)) (= (ho_25306 x z) (ho_25306 y z)))) (= x y))))) (let ((_let_2701 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_15048 x z) (ho_15048 y z)))) (= x y))))) (let ((_let_2702 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer tptp.assn)|) (y |u_(-> _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.assn)|)) (= (ho_15818 x z) (ho_15818 y z)))) (= x y))))) (let ((_let_2703 (forall ((x |u_(-> tptp.num tptp.nat tptp.option_num)|) (y |u_(-> tptp.num tptp.nat tptp.option_num)|)) (or (not (forall ((z tptp.num)) (= (ho_11173 x z) (ho_11173 y z)))) (= x y))))) (let ((_let_2704 (forall ((x |u_(-> Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o)|) (y |u_(-> Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z Bool)) (= (ho_26131 x z) (ho_26131 y z)))) (= x y))))) (let ((_let_2705 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer Bool)_ tptp.code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer Bool)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer Bool)|)) (= (ho_15059 x z) (ho_15059 y z)))) (= x y))))) (let ((_let_2706 (forall ((x |u_(-> tptp.rat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.rat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_11129 x z) (ho_11129 y z)))) (= x y))))) (let ((_let_2707 (forall ((x |u_(-> _u_(-> tptp.produc1219242969750017639nt_int Bool)_ tptp.set_Pr2560585780119916871nt_int)|) (y |u_(-> _u_(-> tptp.produc1219242969750017639nt_int Bool)_ tptp.set_Pr2560585780119916871nt_int)|)) (or (not (forall ((z |u_(-> tptp.produc1219242969750017639nt_int Bool)|)) (= (ho_25053 x z) (ho_25053 y z)))) (= x y))))) (let ((_let_2708 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.code_integer tptp.int Bool)_ tptp.code_integer tptp.nat)|) (y |u_(-> tptp.set_int _u_(-> tptp.code_integer tptp.int Bool)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15064 x z) (ho_15064 y z)))) (= x y))))) (let ((_let_2709 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.assn)_ Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.assn)_ Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_17172 x z) (ho_17172 y z)))) (= x y))))) (let ((_let_2710 (forall ((x |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.nat tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.nat tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.assn)|)) (= (ho_21237 x z) (ho_21237 y z)))) (= x y))))) (let ((_let_2711 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.int)_ Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.int)_ Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_15115 x z) (ho_15115 y z)))) (= x y))))) (let ((_let_2712 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_13219 x z) (ho_13219 y z)))) (= x y))))) (let ((_let_2713 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.int)_ tptp.set_set_nat tptp.int)|) (y |u_(-> _u_(-> tptp.set_nat tptp.int)_ tptp.set_set_nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.int)|)) (= (ho_25530 x z) (ho_25530 y z)))) (= x y))))) (let ((_let_2714 (forall ((x |u_(-> _u_(-> Bool tptp.rat)_ Bool Bool)|) (y |u_(-> _u_(-> Bool tptp.rat)_ Bool Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.rat)|)) (= (ho_15129 x z) (ho_15129 y z)))) (= x y))))) (let ((_let_2715 (forall ((x |u_(-> tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat Bool)|) (y |u_(-> tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat Bool)|)) (or (not (forall ((z tptp.produc8664842809031399944it_nat)) (= (ho_22715 x z) (ho_22715 y z)))) (= x y))))) (let ((_let_2716 (forall ((x |u_(-> _u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.option_Code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.option_Code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (= (ho_25679 x z) (ho_25679 y z)))) (= x y))))) (let ((_let_2717 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_14631 x z) (ho_14631 y z)))) (= x y))))) (let ((_let_2718 (forall ((x |u_(-> tptp.nat tptp.set_int Bool)|) (y |u_(-> tptp.nat tptp.set_int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_15141 x z) (ho_15141 y z)))) (= x y))))) (let ((_let_2719 (forall ((x |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ tptp.set_Pr958786334691620121nt_int Bool)|) (y |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ tptp.set_Pr958786334691620121nt_int Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)|)) (= (ho_16869 x z) (ho_16869 y z)))) (= x y))))) (let ((_let_2720 (forall ((x |u_(-> tptp.produc3843707927480180839at_nat Bool)|) (y |u_(-> tptp.produc3843707927480180839at_nat Bool)|)) (or (not (forall ((z tptp.produc3843707927480180839at_nat)) (= (ho_11263 x z) (ho_11263 y z)))) (= x y))))) (let ((_let_2721 (forall ((x |u_(-> tptp.produc50402934264563236_nat_o Bool)|) (y |u_(-> tptp.produc50402934264563236_nat_o Bool)|)) (or (not (forall ((z tptp.produc50402934264563236_nat_o)) (= (ho_25232 x z) (ho_25232 y z)))) (= x y))))) (let ((_let_2722 (forall ((x |u_(-> tptp.set_int tptp.nat tptp.set_int Bool)|) (y |u_(-> tptp.set_int tptp.nat tptp.set_int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15140 x z) (ho_15140 y z)))) (= x y))))) (let ((_let_2723 (forall ((x |u_(-> tptp.nat tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_15146 x z) (ho_15146 y z)))) (= x y))))) (let ((_let_2724 (forall ((x |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)_ tptp.set_Pr8551490117392284871at_nat _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)_ tptp.set_Pr8551490117392284871at_nat _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ _u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)|)) (= (ho_24503 x z) (ho_24503 y z)))) (= x y))))) (let ((_let_2725 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.rat)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_17455 x z) (ho_17455 y z)))) (= x y))))) (let ((_let_2726 (forall ((x |u_(-> tptp.set_Code_integer tptp.set_Code_integer Bool)|) (y |u_(-> tptp.set_Code_integer tptp.set_Code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_15153 x z) (ho_15153 y z)))) (= x y))))) (let ((_let_2727 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat tptp.nat)_ tptp.nat tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat tptp.nat)_ tptp.nat tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat tptp.nat)|)) (= (ho_12245 x z) (ho_12245 y z)))) (= x y))))) (let ((_let_2728 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_25395 x z) (ho_25395 y z)))) (= x y))))) (let ((_let_2729 (forall ((x |u_(-> tptp.set_nat tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_15157 x z) (ho_15157 y z)))) (= x y))))) (let ((_let_2730 (forall ((x |u_(-> tptp.list_o tptp.list_int tptp.list_P3795440434834930179_o_int)|) (y |u_(-> tptp.list_o tptp.list_int tptp.list_P3795440434834930179_o_int)|)) (or (not (forall ((z tptp.list_o)) (= (ho_24786 x z) (ho_24786 y z)))) (= x y))))) (let ((_let_2731 (forall ((x |u_(-> _u_(-> Bool tptp.code_integer)_ _u_(-> Bool tptp.code_integer)_ Bool Bool)|) (y |u_(-> _u_(-> Bool tptp.code_integer)_ _u_(-> Bool tptp.code_integer)_ Bool Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.code_integer)|)) (= (ho_17199 x z) (ho_17199 y z)))) (= x y))))) (let ((_let_2732 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_16279 x z) (ho_16279 y z)))) (= x y))))) (let ((_let_2733 (forall ((x |u_(-> tptp.assn _u_(-> tptp.assn tptp.assn tptp.assn)_ tptp.assn tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.assn _u_(-> tptp.assn tptp.assn tptp.assn)_ tptp.assn tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_22007 x z) (ho_22007 y z)))) (= x y))))) (let ((_let_2734 (forall ((x |u_(-> tptp.set_list_nat tptp.nat)|) (y |u_(-> tptp.set_list_nat tptp.nat)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_15171 x z) (ho_15171 y z)))) (= x y))))) (let ((_let_2735 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_12145 x z) (ho_12145 y z)))) (= x y))))) (let ((_let_2736 (forall ((x |u_(-> tptp.set_Code_integer tptp.set_Code_integer tptp.set_Code_integer Bool)|) (y |u_(-> tptp.set_Code_integer tptp.set_Code_integer tptp.set_Code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_17407 x z) (ho_17407 y z)))) (= x y))))) (let ((_let_2737 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_18702 x z) (ho_18702 y z)))) (= x y))))) (let ((_let_2738 (forall ((x |u_(-> tptp.nat tptp.set_list_nat Bool)|) (y |u_(-> tptp.nat tptp.set_list_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_15176 x z) (ho_15176 y z)))) (= x y))))) (let ((_let_2739 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.set_nat tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.set_nat tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int tptp.int)|)) (= (ho_18133 x z) (ho_18133 y z)))) (= x y))))) (let ((_let_2740 (forall ((x |u_(-> tptp.set_list_nat tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_list_nat tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_15178 x z) (ho_15178 y z)))) (= x y))))) (let ((_let_2741 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_24343 x z) (ho_24343 y z)))) (= x y))))) (let ((_let_2742 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer)|)) (= (ho_17084 x z) (ho_17084 y z)))) (= x y))))) (let ((_let_2743 (forall ((x |u_(-> tptp.heap_T5738788834812785303t_unit tptp.heap_e7401611519738050253t_unit Bool)|) (y |u_(-> tptp.heap_T5738788834812785303t_unit tptp.heap_e7401611519738050253t_unit Bool)|)) (or (not (forall ((z tptp.heap_T5738788834812785303t_unit)) (= (ho_24292 x z) (ho_24292 y z)))) (= x y))))) (let ((_let_2744 (forall ((x |u_(-> tptp.set_int tptp.set_int tptp.set_int)|) (y |u_(-> tptp.set_int tptp.set_int tptp.set_int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15194 x z) (ho_15194 y z)))) (= x y))))) (let ((_let_2745 (forall ((x |u_(-> tptp.list_int tptp.list_P3521021558325789923at_int)|) (y |u_(-> tptp.list_int tptp.list_P3521021558325789923at_int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_24761 x z) (ho_24761 y z)))) (= x y))))) (let ((_let_2746 (forall ((x |u_(-> _u_(-> tptp.list_nat Bool)_ tptp.list_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.list_nat Bool)_ tptp.list_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.list_nat Bool)|)) (= (ho_15219 x z) (ho_15219 y z)))) (= x y))))) (let ((_let_2747 (forall ((x |u_(-> tptp.set_list_nat _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|) (y |u_(-> tptp.set_list_nat _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_15221 x z) (ho_15221 y z)))) (= x y))))) (let ((_let_2748 (forall ((x |u_(-> tptp.code_integer tptp.rat)|) (y |u_(-> tptp.code_integer tptp.rat)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_15040 x z) (ho_15040 y z)))) (= x y))))) (let ((_let_2749 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_15225 x z) (ho_15225 y z)))) (= x y))))) (let ((_let_2750 (forall ((x |u_(-> tptp.list_nat tptp.list_nat)|) (y |u_(-> tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_14450 x z) (ho_14450 y z)))) (= x y))))) (let ((_let_2751 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_15241 x z) (ho_15241 y z)))) (= x y))))) (let ((_let_2752 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer tptp.rat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.rat)|)) (= (ho_15043 x z) (ho_15043 y z)))) (= x y))))) (let ((_let_2753 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_15244 x z) (ho_15244 y z)))) (= x y))))) (let ((_let_2754 (forall ((x |u_(-> tptp.nat tptp.rat)|) (y |u_(-> tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11498 x z) (ho_11498 y z)))) (= x y))))) (let ((_let_2755 (forall ((x |u_(-> tptp.list_nat tptp.list_nat tptp.list_nat Bool)|) (y |u_(-> tptp.list_nat tptp.list_nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_15261 x z) (ho_15261 y z)))) (= x y))))) (let ((_let_2756 (forall ((x |u_(-> tptp.produc3843707927480180839at_nat tptp.rat)|) (y |u_(-> tptp.produc3843707927480180839at_nat tptp.rat)|)) (or (not (forall ((z tptp.produc3843707927480180839at_nat)) (= (ho_25543 x z) (ho_25543 y z)))) (= x y))))) (let ((_let_2757 (forall ((x |u_(-> tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.heap_Time_Heap_a)) (= (ho_19877 x z) (ho_19877 y z)))) (= x y))))) (let ((_let_2758 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_15274 x z) (ho_15274 y z)))) (= x y))))) (let ((_let_2759 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer)|)) (= (ho_15282 x z) (ho_15282 y z)))) (= x y))))) (let ((_let_2760 (forall ((x |u_(-> tptp.multis2468970476368604999at_nat tptp.produc4166570645942440679at_nat)|) (y |u_(-> tptp.multis2468970476368604999at_nat tptp.produc4166570645942440679at_nat)|)) (or (not (forall ((z tptp.multis2468970476368604999at_nat)) (= (ho_12619 x z) (ho_12619 y z)))) (= x y))))) (let ((_let_2761 (forall ((x |u_(-> tptp.set_nat tptp.rat)|) (y |u_(-> tptp.set_nat tptp.rat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_15294 x z) (ho_15294 y z)))) (= x y))))) (let ((_let_2762 (forall ((x |u_(-> tptp.list_nat tptp.rat)|) (y |u_(-> tptp.list_nat tptp.rat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_15297 x z) (ho_15297 y z)))) (= x y))))) (let ((_let_2763 (forall ((x |u_(-> tptp.code_integer tptp.int tptp.code_integer)|) (y |u_(-> tptp.code_integer tptp.int tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_15301 x z) (ho_15301 y z)))) (= x y))))) (let ((_let_2764 (forall ((x |u_(-> tptp.int tptp.set_nat tptp.int)|) (y |u_(-> tptp.int tptp.set_nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_15312 x z) (ho_15312 y z)))) (= x y))))) (let ((_let_2765 (forall ((x |u_(-> tptp.int tptp.list_nat tptp.int)|) (y |u_(-> tptp.int tptp.list_nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_15315 x z) (ho_15315 y z)))) (= x y))))) (let ((_let_2766 (forall ((x |u_(-> tptp.nat tptp.set_nat tptp.nat)|) (y |u_(-> tptp.nat tptp.set_nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_15318 x z) (ho_15318 y z)))) (= x y))))) (let ((_let_2767 (forall ((x |u_(-> tptp.code_integer tptp.code_natural)|) (y |u_(-> tptp.code_integer tptp.code_natural)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_15327 x z) (ho_15327 y z)))) (= x y))))) (let ((_let_2768 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_21343 x z) (ho_21343 y z)))) (= x y))))) (let ((_let_2769 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_17473 x z) (ho_17473 y z)))) (= x y))))) (let ((_let_2770 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer)|)) (= (ho_17189 x z) (ho_17189 y z)))) (= x y))))) (let ((_let_2771 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat Bool)_ tptp.code_natural Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ tptp.code_natural tptp.code_natural Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat Bool)_ tptp.code_natural Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ tptp.code_natural tptp.code_natural Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat Bool)_ tptp.code_natural Bool)|)) (= (ho_26053 x z) (ho_26053 y z)))) (= x y))))) (let ((_let_2772 (forall ((x |u_(-> tptp.set_Pr7600907837789447088it_nat Bool)|) (y |u_(-> tptp.set_Pr7600907837789447088it_nat Bool)|)) (or (not (forall ((z tptp.set_Pr7600907837789447088it_nat)) (= (ho_21362 x z) (ho_21362 y z)))) (= x y))))) (let ((_let_2773 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.code_natural)_ tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.code_natural)_ tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_15329 x z) (ho_15329 y z)))) (= x y))))) (let ((_let_2774 (forall ((x |u_(-> Bool tptp.code_natural)|) (y |u_(-> Bool tptp.code_natural)|)) (or (not (forall ((z Bool)) (= (ho_15337 x z) (ho_15337 y z)))) (= x y))))) (let ((_let_2775 (forall ((x |u_(-> tptp.list_nat tptp.list_o tptp.list_P7333126701944960589_nat_o)|) (y |u_(-> tptp.list_nat tptp.list_o tptp.list_P7333126701944960589_nat_o)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_24751 x z) (ho_24751 y z)))) (= x y))))) (let ((_let_2776 (forall ((x |u_(-> _u_(-> Bool tptp.code_natural)_ Bool Bool)|) (y |u_(-> _u_(-> Bool tptp.code_natural)_ Bool Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.code_natural)|)) (= (ho_15340 x z) (ho_15340 y z)))) (= x y))))) (let ((_let_2777 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.code_integer)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.code_integer)_ tptp.int tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_17080 x z) (ho_17080 y z)))) (= x y))))) (let ((_let_2778 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.code_integer)_ tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.code_integer)_ tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_15379 x z) (ho_15379 y z)))) (= x y))))) (let ((_let_2779 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc4928098042776334183_nat_o)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc4928098042776334183_nat_o)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_25056 x z) (ho_25056 y z)))) (= x y))))) (let ((_let_2780 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat)|)) (= (ho_15348 x z) (ho_15348 y z)))) (= x y))))) (let ((_let_2781 (forall ((x |u_(-> tptp.list_int tptp.list_int tptp.list_int)|) (y |u_(-> tptp.list_int tptp.list_int tptp.list_int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_14669 x z) (ho_14669 y z)))) (= x y))))) (let ((_let_2782 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat Bool)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat Bool)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_22721 x z) (ho_22721 y z)))) (= x y))))) (let ((_let_2783 (forall ((x |u_(-> tptp.produc7196121022310644452it_nat tptp.option2555668343544256180it_nat)|) (y |u_(-> tptp.produc7196121022310644452it_nat tptp.option2555668343544256180it_nat)|)) (or (not (forall ((z tptp.produc7196121022310644452it_nat)) (= (ho_25483 x z) (ho_25483 y z)))) (= x y))))) (let ((_let_2784 (forall ((x |u_(-> tptp.set_Code_integer tptp.nat tptp.set_Code_integer Bool)|) (y |u_(-> tptp.set_Code_integer tptp.nat tptp.set_Code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_15150 x z) (ho_15150 y z)))) (= x y))))) (let ((_let_2785 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.int)_ tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.int)_ tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_15361 x z) (ho_15361 y z)))) (= x y))))) (let ((_let_2786 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.set_nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer)|)) (= (ho_15380 x z) (ho_15380 y z)))) (= x y))))) (let ((_let_2787 (forall ((x |u_(-> tptp.set_nat tptp.code_natural _u_(-> tptp.nat tptp.code_natural)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.code_natural _u_(-> tptp.nat tptp.code_natural)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_15841 x z) (ho_15841 y z)))) (= x y))))) (let ((_let_2788 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.option_set_nat)_ tptp.option_set_nat tptp.option_set_nat)|) (y |u_(-> _u_(-> tptp.set_nat tptp.option_set_nat)_ tptp.option_set_nat tptp.option_set_nat)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.option_set_nat)|)) (= (ho_22206 x z) (ho_22206 y z)))) (= x y))))) (let ((_let_2789 (forall ((x |u_(-> tptp.set_He475150555083384525t_unit tptp.heap_T5738788834812785303t_unit)|) (y |u_(-> tptp.set_He475150555083384525t_unit tptp.heap_T5738788834812785303t_unit)|)) (or (not (forall ((z tptp.set_He475150555083384525t_unit)) (= (ho_24606 x z) (ho_24606 y z)))) (= x y))))) (let ((_let_2790 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_15407 x z) (ho_15407 y z)))) (= x y))))) (let ((_let_2791 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_23624 x z) (ho_23624 y z)))) (= x y))))) (let ((_let_2792 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.set_Pr958786334691620121nt_int)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.set_Pr958786334691620121nt_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_24498 x z) (ho_24498 y z)))) (= x y))))) (let ((_let_2793 (forall ((x |u_(-> tptp.code_integer tptp.int tptp.int Bool)|) (y |u_(-> tptp.code_integer tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_15562 x z) (ho_15562 y z)))) (= x y))))) (let ((_let_2794 (forall ((x |u_(-> _u_(-> tptp.num tptp.num tptp.num)_ _u_(-> tptp.num tptp.num Bool)_ _u_(-> tptp.num tptp.num Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num tptp.num)_ _u_(-> tptp.num tptp.num Bool)_ _u_(-> tptp.num tptp.num Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num tptp.num)|)) (= (ho_25771 x z) (ho_25771 y z)))) (= x y))))) (let ((_let_2795 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer Bool)_ tptp.code_integer tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer Bool)_ tptp.code_integer tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer Bool)|)) (= (ho_15561 x z) (ho_15561 y z)))) (= x y))))) (let ((_let_2796 (forall ((x |u_(-> _u_(-> tptp.assn tptp.assn tptp.assn)_ tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.assn tptp.assn tptp.assn)_ tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.assn tptp.assn tptp.assn)|)) (= (ho_22003 x z) (ho_22003 y z)))) (= x y))))) (let ((_let_2797 (forall ((x |u_(-> _u_(-> tptp.nat Bool Bool)_ tptp.nat Bool Bool)|) (y |u_(-> _u_(-> tptp.nat Bool Bool)_ tptp.nat Bool Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool Bool)|)) (= (ho_12194 x z) (ho_12194 y z)))) (= x y))))) (let ((_let_2798 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer Bool)_ tptp.code_integer tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.code_integer Bool)_ tptp.code_integer tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_15560 x z) (ho_15560 y z)))) (= x y))))) (let ((_let_2799 (forall ((x |u_(-> tptp.list_P2321686559999237006et_nat tptp.list_P2321686559999237006et_nat)|) (y |u_(-> tptp.list_P2321686559999237006et_nat tptp.list_P2321686559999237006et_nat)|)) (or (not (forall ((z tptp.list_P2321686559999237006et_nat)) (= (ho_24961 x z) (ho_24961 y z)))) (= x y))))) (let ((_let_2800 (forall ((x |u_(-> _u_(-> tptp.num tptp.int)_ tptp.num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num tptp.int)_ tptp.num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.int)|)) (= (ho_22690 x z) (ho_22690 y z)))) (= x y))))) (let ((_let_2801 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_11365 x z) (ho_11365 y z)))) (= x y))))) (let ((_let_2802 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_15568 x z) (ho_15568 y z)))) (= x y))))) (let ((_let_2803 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.int Bool)_ tptp.int tptp.int)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.int Bool)_ tptp.int tptp.int)|)) (or (not (forall ((z tptp.set_o)) (= (ho_17315 x z) (ho_17315 y z)))) (= x y))))) (let ((_let_2804 (forall ((x |u_(-> tptp.nat tptp.nat tptp.int Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_21228 x z) (ho_21228 y z)))) (= x y))))) (let ((_let_2805 (forall ((x |u_(-> tptp.nat tptp.list_nat tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.list_nat tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_18665 x z) (ho_18665 y z)))) (= x y))))) (let ((_let_2806 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer Bool)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer Bool)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_15594 x z) (ho_15594 y z)))) (= x y))))) (let ((_let_2807 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat tptp.rat)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ tptp.rat tptp.rat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_12143 x z) (ho_12143 y z)))) (= x y))))) (let ((_let_2808 (forall ((x |u_(-> _u_(-> tptp.rat tptp.nat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.rat tptp.nat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.nat)|)) (= (ho_25330 x z) (ho_25330 y z)))) (= x y))))) (let ((_let_2809 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_15599 x z) (ho_15599 y z)))) (= x y))))) (let ((_let_2810 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.nat)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.nat)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_25551 x z) (ho_25551 y z)))) (= x y))))) (let ((_let_2811 (forall ((x |u_(-> _u_(-> tptp.set_nat Bool)_ _u_(-> tptp.set_nat Bool)_ tptp.set_nat Bool)|) (y |u_(-> _u_(-> tptp.set_nat Bool)_ _u_(-> tptp.set_nat Bool)_ tptp.set_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat Bool)|)) (= (ho_15602 x z) (ho_15602 y z)))) (= x y))))) (let ((_let_2812 (forall ((x |u_(-> _u_(-> tptp.list_nat Bool)_ _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.list_nat Bool)_ _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.list_nat Bool)|)) (= (ho_15606 x z) (ho_15606 y z)))) (= x y))))) (let ((_let_2813 (forall ((x |u_(-> tptp.list_int tptp.heap_T1346037964561226099ay_int)|) (y |u_(-> tptp.list_int tptp.heap_T1346037964561226099ay_int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_15657 x z) (ho_15657 y z)))) (= x y))))) (let ((_let_2814 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat)_ tptp.heap_T1346037964561226099ay_int)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat)_ tptp.heap_T1346037964561226099ay_int)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc7196121022310644452it_nat)|)) (= (ho_15664 x z) (ho_15664 y z)))) (= x y))))) (let ((_let_2815 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.heap_T5660665574680485309rray_o)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.heap_T5660665574680485309rray_o)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_15672 x z) (ho_15672 y z)))) (= x y))))) (let ((_let_2816 (forall ((x |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)_ tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.produc7388388658123137530it_nat)|)) (= (ho_18720 x z) (ho_18720 y z)))) (= x y))))) (let ((_let_2817 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat)_ tptp.heap_T5660665574680485309rray_o)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat)_ tptp.heap_T5660665574680485309rray_o)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc8032495849646651230it_nat)|)) (= (ho_15674 x z) (ho_15674 y z)))) (= x y))))) (let ((_let_2818 (forall ((x |u_(-> tptp.num tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.num tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_20359 x z) (ho_20359 y z)))) (= x y))))) (let ((_let_2819 (forall ((x |u_(-> tptp.list_nat tptp.heap_T3836121109492952855ay_nat)|) (y |u_(-> tptp.list_nat tptp.heap_T3836121109492952855ay_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_15677 x z) (ho_15677 y z)))) (= x y))))) (let ((_let_2820 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.heap_T3836121109492952855ay_nat)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.heap_T3836121109492952855ay_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_15681 x z) (ho_15681 y z)))) (= x y))))) (let ((_let_2821 (forall ((x |u_(-> _u_(-> tptp.nat tptp.set_int)_ tptp.nat tptp.int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.set_int)_ tptp.nat tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.set_int)|)) (= (ho_21225 x z) (ho_21225 y z)))) (= x y))))) (let ((_let_2822 (forall ((x |u_(-> Bool Bool tptp.product_prod_o_o)|) (y |u_(-> Bool Bool tptp.product_prod_o_o)|)) (or (not (forall ((z Bool)) (= (ho_24774 x z) (ho_24774 y z)))) (= x y))))) (let ((_let_2823 (forall ((x |u_(-> _u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (= (ho_22371 x z) (ho_22371 y z)))) (= x y))))) (let ((_let_2824 (forall ((x |u_(-> tptp.int _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|) (y |u_(-> tptp.int _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_25284 x z) (ho_25284 y z)))) (= x y))))) (let ((_let_2825 (forall ((x |u_(-> _u_(-> Bool tptp.rat)_ Bool tptp.rat)|) (y |u_(-> _u_(-> Bool tptp.rat)_ Bool tptp.rat)|)) (or (not (forall ((z |u_(-> Bool tptp.rat)|)) (= (ho_15779 x z) (ho_15779 y z)))) (= x y))))) (let ((_let_2826 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_16821 x z) (ho_16821 y z)))) (= x y))))) (let ((_let_2827 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.nat)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_17339 x z) (ho_17339 y z)))) (= x y))))) (let ((_let_2828 (forall ((x |u_(-> Bool _u_(-> Bool tptp.rat)_ _u_(-> Bool tptp.rat)_ Bool tptp.rat)|) (y |u_(-> Bool _u_(-> Bool tptp.rat)_ _u_(-> Bool tptp.rat)_ Bool tptp.rat)|)) (or (not (forall ((z Bool)) (= (ho_15777 x z) (ho_15777 y z)))) (= x y))))) (let ((_let_2829 (forall ((x |u_(-> tptp.option_int Bool)|) (y |u_(-> tptp.option_int Bool)|)) (or (not (forall ((z tptp.option_int)) (= (ho_24183 x z) (ho_24183 y z)))) (= x y))))) (let ((_let_2830 (forall ((x |u_(-> _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn)|) (y |u_(-> _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.int tptp.assn)|)) (= (ho_15791 x z) (ho_15791 y z)))) (= x y))))) (let ((_let_2831 (forall ((x |u_(-> tptp.option4065278094766928714it_nat _u_(-> tptp.produc3260487557148687353it_nat tptp.option4065278094766928714it_nat)_ tptp.option3562590408128118217it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.option4065278094766928714it_nat _u_(-> tptp.produc3260487557148687353it_nat tptp.option4065278094766928714it_nat)_ tptp.option3562590408128118217it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.option4065278094766928714it_nat)) (= (ho_19872 x z) (ho_19872 y z)))) (= x y))))) (let ((_let_2832 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.assn)_ _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.assn)_ _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn)|)) (or (not (forall ((z tptp.int)) (= (ho_15789 x z) (ho_15789 y z)))) (= x y))))) (let ((_let_2833 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (= (ho_20084 x z) (ho_20084 y z)))) (= x y))))) (let ((_let_2834 (forall ((x |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)_ tptp.produc7388388658123137530it_nat tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)_ tptp.produc7388388658123137530it_nat tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat)|)) (= (ho_19860 x z) (ho_19860 y z)))) (= x y))))) (let ((_let_2835 (forall ((x |u_(-> tptp.assn tptp.assn tptp.assn)|) (y |u_(-> tptp.assn tptp.assn tptp.assn)|)) (or (not (forall ((z tptp.assn)) (= (ho_15794 x z) (ho_15794 y z)))) (= x y))))) (let ((_let_2836 (forall ((x |u_(-> tptp.set_Pr8693737435421807431at_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr8693737435421807431at_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8693737435421807431at_nat)) (= (ho_22617 x z) (ho_22617 y z)))) (= x y))))) (let ((_let_2837 (forall ((x |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn)|) (y |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.assn)|)) (= (ho_15802 x z) (ho_15802 y z)))) (= x y))))) (let ((_let_2838 (forall ((x |u_(-> _u_(-> tptp.nat tptp.assn)_ _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn)|) (y |u_(-> _u_(-> tptp.nat tptp.assn)_ _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.assn)|)) (= (ho_15801 x z) (ho_15801 y z)))) (= x y))))) (let ((_let_2839 (forall ((x |u_(-> tptp.option_assn _u_(-> tptp.assn tptp.option_assn)_ tptp.option_assn tptp.option_assn)|) (y |u_(-> tptp.option_assn _u_(-> tptp.assn tptp.option_assn)_ tptp.option_assn tptp.option_assn)|)) (or (not (forall ((z tptp.option_assn)) (= (ho_22218 x z) (ho_22218 y z)))) (= x y))))) (let ((_let_2840 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_15250 x z) (ho_15250 y z)))) (= x y))))) (let ((_let_2841 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_natural)_ tptp.code_natural tptp.code_integer tptp.code_natural)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_natural)_ tptp.code_natural tptp.code_integer tptp.code_natural)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_natural)|)) (= (ho_15844 x z) (ho_15844 y z)))) (= x y))))) (let ((_let_2842 (forall ((x |u_(-> tptp.code_natural tptp.int tptp.code_natural)|) (y |u_(-> tptp.code_natural tptp.int tptp.code_natural)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_15853 x z) (ho_15853 y z)))) (= x y))))) (let ((_let_2843 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.int tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_15858 x z) (ho_15858 y z)))) (= x y))))) (let ((_let_2844 (forall ((x |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.assn tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.assn)|)) (= (ho_23801 x z) (ho_23801 y z)))) (= x y))))) (let ((_let_2845 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_12122 x z) (ho_12122 y z)))) (= x y))))) (let ((_let_2846 (forall ((x |u_(-> tptp.set_nat tptp.int _u_(-> tptp.nat tptp.int)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.int _u_(-> tptp.nat tptp.int)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_15860 x z) (ho_15860 y z)))) (= x y))))) (let ((_let_2847 (forall ((x |u_(-> _u_(-> tptp.int tptp.assn)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.assn)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.assn)|)) (= (ho_17159 x z) (ho_17159 y z)))) (= x y))))) (let ((_let_2848 (forall ((x |u_(-> tptp.rat tptp.rat tptp.set_rat)|) (y |u_(-> tptp.rat tptp.rat tptp.set_rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_25340 x z) (ho_25340 y z)))) (= x y))))) (let ((_let_2849 (forall ((x |u_(-> tptp.heap_Time_Heap_b tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.heap_Time_Heap_b tptp.heap_e7401611519738050253t_unit tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.heap_Time_Heap_b)) (= (ho_11311 x z) (ho_11311 y z)))) (= x y))))) (let ((_let_2850 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.nat tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.nat tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_15875 x z) (ho_15875 y z)))) (= x y))))) (let ((_let_2851 (forall ((x |u_(-> _u_(-> Bool tptp.int)_ Bool tptp.int)|) (y |u_(-> _u_(-> Bool tptp.int)_ Bool tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.int)|)) (= (ho_15904 x z) (ho_15904 y z)))) (= x y))))) (let ((_let_2852 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ tptp.int tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (= (ho_11125 x z) (ho_11125 y z)))) (= x y))))) (let ((_let_2853 (forall ((x |u_(-> tptp.int _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer Bool)|) (y |u_(-> tptp.int _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_15865 x z) (ho_15865 y z)))) (= x y))))) (let ((_let_2854 (forall ((x |u_(-> tptp.produc6653097349344004940it_nat tptp.produc6653097349344004940it_nat)|) (y |u_(-> tptp.produc6653097349344004940it_nat tptp.produc6653097349344004940it_nat)|)) (or (not (forall ((z tptp.produc6653097349344004940it_nat)) (= (ho_25416 x z) (ho_25416 y z)))) (= x y))))) (let ((_let_2855 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.code_integer)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_17075 x z) (ho_17075 y z)))) (= x y))))) (let ((_let_2856 (forall ((x |u_(-> _u_(-> Bool tptp.int)_ _u_(-> Bool tptp.int)_ Bool tptp.int)|) (y |u_(-> _u_(-> Bool tptp.int)_ _u_(-> Bool tptp.int)_ Bool tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.int)|)) (= (ho_15903 x z) (ho_15903 y z)))) (= x y))))) (let ((_let_2857 (forall ((x |u_(-> _u_(-> tptp.set_int tptp.set_int tptp.set_int)_ tptp.set_int tptp.set_int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.set_int tptp.set_int tptp.set_int)_ tptp.set_int tptp.set_int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.set_int tptp.set_int tptp.set_int)|)) (= (ho_21970 x z) (ho_21970 y z)))) (= x y))))) (let ((_let_2858 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_18080 x z) (ho_18080 y z)))) (= x y))))) (let ((_let_2859 (forall ((x |u_(-> tptp.set_Pr7577011563204128103nteger Bool)|) (y |u_(-> tptp.set_Pr7577011563204128103nteger Bool)|)) (or (not (forall ((z tptp.set_Pr7577011563204128103nteger)) (= (ho_25624 x z) (ho_25624 y z)))) (= x y))))) (let ((_let_2860 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_23367 x z) (ho_23367 y z)))) (= x y))))) (let ((_let_2861 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.int)_ _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.int)_ _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_16269 x z) (ho_16269 y z)))) (= x y))))) (let ((_let_2862 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_24494 x z) (ho_24494 y z)))) (= x y))))) (let ((_let_2863 (forall ((x |u_(-> tptp.nat tptp.set_Code_integer Bool)|) (y |u_(-> tptp.nat tptp.set_Code_integer Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_15151 x z) (ho_15151 y z)))) (= x y))))) (let ((_let_2864 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_16287 x z) (ho_16287 y z)))) (= x y))))) (let ((_let_2865 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.assn)_ _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.assn)_ _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_16299 x z) (ho_16299 y z)))) (= x y))))) (let ((_let_2866 (forall ((x |u_(-> tptp.heap_T5660665574680485309rray_o tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.array_o tptp.nat Bool)|) (y |u_(-> tptp.heap_T5660665574680485309rray_o tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.array_o tptp.nat Bool)|)) (or (not (forall ((z tptp.heap_T5660665574680485309rray_o)) (= (ho_25570 x z) (ho_25570 y z)))) (= x y))))) (let ((_let_2867 (forall ((x |u_(-> tptp.option_num _u_(-> tptp.num tptp.option_num)_ _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.option_num)|) (y |u_(-> tptp.option_num _u_(-> tptp.num tptp.option_num)_ _u_(-> tptp.num tptp.option_num)_ tptp.num tptp.option_num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_11169 x z) (ho_11169 y z)))) (= x y))))) (let ((_let_2868 (forall ((x |u_(-> Bool _u_(-> Bool tptp.code_integer)_ Bool tptp.code_integer)|) (y |u_(-> Bool _u_(-> Bool tptp.code_integer)_ Bool tptp.code_integer)|)) (or (not (forall ((z Bool)) (= (ho_17532 x z) (ho_17532 y z)))) (= x y))))) (let ((_let_2869 (forall ((x |u_(-> _u_(-> tptp.list_nat tptp.rat)_ tptp.list_nat tptp.rat)|) (y |u_(-> _u_(-> tptp.list_nat tptp.rat)_ tptp.list_nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.list_nat tptp.rat)|)) (= (ho_16305 x z) (ho_16305 y z)))) (= x y))))) (let ((_let_2870 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_12506 x z) (ho_12506 y z)))) (= x y))))) (let ((_let_2871 (forall ((x |u_(-> Bool _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> Bool _u_(-> tptp.int tptp.int Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z Bool)) (= (ho_19810 x z) (ho_19810 y z)))) (= x y))))) (let ((_let_2872 (forall ((x |u_(-> tptp.code_natural _u_(-> tptp.nat tptp.code_natural)_ tptp.nat Bool)|) (y |u_(-> tptp.code_natural _u_(-> tptp.nat tptp.code_natural)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_11860 x z) (ho_11860 y z)))) (= x y))))) (let ((_let_2873 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int)_ _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int)_ _u_(-> tptp.code_integer tptp.int)_ tptp.code_integer tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int)|)) (= (ho_15022 x z) (ho_15022 y z)))) (= x y))))) (let ((_let_2874 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.code_integer)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_16836 x z) (ho_16836 y z)))) (= x y))))) (let ((_let_2875 (forall ((x |u_(-> Bool Bool tptp.set_o Bool Bool)|) (y |u_(-> Bool Bool tptp.set_o Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_19513 x z) (ho_19513 y z)))) (= x y))))) (let ((_let_2876 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_17093 x z) (ho_17093 y z)))) (= x y))))) (let ((_let_2877 (forall ((x |u_(-> _u_(-> Bool tptp.code_integer)_ Bool tptp.code_integer)|) (y |u_(-> _u_(-> Bool tptp.code_integer)_ Bool tptp.code_integer)|)) (or (not (forall ((z |u_(-> Bool tptp.code_integer)|)) (= (ho_16847 x z) (ho_16847 y z)))) (= x y))))) (let ((_let_2878 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.code_integer)_ Bool tptp.code_integer)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.code_integer)_ Bool tptp.code_integer)|)) (or (not (forall ((z tptp.set_o)) (= (ho_16846 x z) (ho_16846 y z)))) (= x y))))) (let ((_let_2879 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.set_int tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.set_int tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int tptp.int)|)) (= (ho_18131 x z) (ho_18131 y z)))) (= x y))))) (let ((_let_2880 (forall ((x |u_(-> tptp.set_list_nat tptp.nat tptp.set_list_nat Bool)|) (y |u_(-> tptp.set_list_nat tptp.nat tptp.set_list_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_15175 x z) (ho_15175 y z)))) (= x y))))) (let ((_let_2881 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (= (ho_16850 x z) (ho_16850 y z)))) (= x y))))) (let ((_let_2882 (forall ((x |u_(-> tptp.a tptp.heap_Time_Heap_b)|) (y |u_(-> tptp.a tptp.heap_Time_Heap_b)|)) (or (not (forall ((z tptp.a)) (= (ho_11304 x z) (ho_11304 y z)))) (= x y))))) (let ((_let_2883 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_16858 x z) (ho_16858 y z)))) (= x y))))) (let ((_let_2884 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.nat)_ _u_(-> tptp.set_nat tptp.nat)_ tptp.set_nat Bool)|) (y |u_(-> _u_(-> tptp.set_nat tptp.nat)_ _u_(-> tptp.set_nat tptp.nat)_ tptp.set_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.nat)|)) (= (ho_16867 x z) (ho_16867 y z)))) (= x y))))) (let ((_let_2885 (forall ((x |u_(-> _u_(-> tptp.set_list_nat Bool)_ tptp.set_set_list_nat)|) (y |u_(-> _u_(-> tptp.set_list_nat Bool)_ tptp.set_set_list_nat)|)) (or (not (forall ((z |u_(-> tptp.set_list_nat Bool)|)) (= (ho_25738 x z) (ho_25738 y z)))) (= x y))))) (let ((_let_2886 (forall ((x |u_(-> _u_(-> tptp.list_nat tptp.nat)_ _u_(-> tptp.list_nat tptp.nat)_ tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.list_nat tptp.nat)_ _u_(-> tptp.list_nat tptp.nat)_ tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.list_nat tptp.nat)|)) (= (ho_16874 x z) (ho_16874 y z)))) (= x y))))) (let ((_let_2887 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_16906 x z) (ho_16906 y z)))) (= x y))))) (let ((_let_2888 (forall ((x |u_(-> tptp.option_set_int tptp.option_set_int tptp.option_set_int)|) (y |u_(-> tptp.option_set_int tptp.option_set_int tptp.option_set_int)|)) (or (not (forall ((z tptp.option_set_int)) (= (ho_22414 x z) (ho_22414 y z)))) (= x y))))) (let ((_let_2889 (forall ((x |u_(-> tptp.product_prod_nat_nat _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.product_prod_nat_nat _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_16925 x z) (ho_16925 y z)))) (= x y))))) (let ((_let_2890 (forall ((x |u_(-> tptp.product_prod_int_int tptp.option4624381673175914239nt_int)|) (y |u_(-> tptp.product_prod_int_int tptp.option4624381673175914239nt_int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_24397 x z) (ho_24397 y z)))) (= x y))))) (let ((_let_2891 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_15120 x z) (ho_15120 y z)))) (= x y))))) (let ((_let_2892 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_14502 x z) (ho_14502 y z)))) (= x y))))) (let ((_let_2893 (forall ((x |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer Bool)|) (y |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer Bool)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_16928 x z) (ho_16928 y z)))) (= x y))))) (let ((_let_2894 (forall ((x |u_(-> tptp.nat tptp.list_nat)|) (y |u_(-> tptp.nat tptp.list_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_14446 x z) (ho_14446 y z)))) (= x y))))) (let ((_let_2895 (forall ((x |u_(-> tptp.rat tptp.rat tptp.rat Bool)|) (y |u_(-> tptp.rat tptp.rat tptp.rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_17049 x z) (ho_17049 y z)))) (= x y))))) (let ((_let_2896 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer tptp.assn)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_17061 x z) (ho_17061 y z)))) (= x y))))) (let ((_let_2897 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)_ tptp.heap_T5738788834812785303t_unit)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)_ tptp.heap_T5738788834812785303t_unit)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|)) (= (ho_24314 x z) (ho_24314 y z)))) (= x y))))) (let ((_let_2898 (forall ((x |u_(-> tptp.set_nat tptp.assn)|) (y |u_(-> tptp.set_nat tptp.assn)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_25435 x z) (ho_25435 y z)))) (= x y))))) (let ((_let_2899 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_17097 x z) (ho_17097 y z)))) (= x y))))) (let ((_let_2900 (forall ((x |u_(-> tptp.heap_T5738788834812785303t_unit _u_(-> tptp.product_unit tptp.heap_Time_Heap_a)_ tptp.heap_Time_Heap_a)|) (y |u_(-> tptp.heap_T5738788834812785303t_unit _u_(-> tptp.product_unit tptp.heap_Time_Heap_a)_ tptp.heap_Time_Heap_a)|)) (or (not (forall ((z tptp.heap_T5738788834812785303t_unit)) (= (ho_24304 x z) (ho_24304 y z)))) (= x y))))) (let ((_let_2901 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_17099 x z) (ho_17099 y z)))) (= x y))))) (let ((_let_2902 (forall ((x |u_(-> _u_(-> tptp.list_nat Bool)_ _u_(-> tptp.list_nat tptp.nat)_ tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.list_nat Bool)_ _u_(-> tptp.list_nat tptp.nat)_ tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.list_nat Bool)|)) (= (ho_17109 x z) (ho_17109 y z)))) (= x y))))) (let ((_let_2903 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int tptp.nat)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_17114 x z) (ho_17114 y z)))) (= x y))))) (let ((_let_2904 (forall ((x |u_(-> tptp.list_int tptp.list_int tptp.list_P5707943133018811711nt_int)|) (y |u_(-> tptp.list_int tptp.list_int tptp.list_P5707943133018811711nt_int)|)) (or (not (forall ((z tptp.list_int)) (= (ho_24809 x z) (ho_24809 y z)))) (= x y))))) (let ((_let_2905 (forall ((x |u_(-> _u_(-> Bool tptp.rat)_ _u_(-> Bool tptp.rat)_ Bool Bool)|) (y |u_(-> _u_(-> Bool tptp.rat)_ _u_(-> Bool tptp.rat)_ Bool Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.rat)|)) (= (ho_17149 x z) (ho_17149 y z)))) (= x y))))) (let ((_let_2906 (forall ((x |u_(-> tptp.produc8032495849646651230it_nat tptp.option1013472963438093988it_nat)|) (y |u_(-> tptp.produc8032495849646651230it_nat tptp.option1013472963438093988it_nat)|)) (or (not (forall ((z tptp.produc8032495849646651230it_nat)) (= (ho_25478 x z) (ho_25478 y z)))) (= x y))))) (let ((_let_2907 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.rat)_ _u_(-> Bool tptp.rat)_ Bool Bool)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.rat)_ _u_(-> Bool tptp.rat)_ Bool Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_17148 x z) (ho_17148 y z)))) (= x y))))) (let ((_let_2908 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.int tptp.code_integer Bool)_ tptp.int tptp.nat)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.int tptp.code_integer Bool)_ tptp.int tptp.nat)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_14861 x z) (ho_14861 y z)))) (= x y))))) (let ((_let_2909 (forall ((x |u_(-> tptp.int tptp.set_o)|) (y |u_(-> tptp.int tptp.set_o)|)) (or (not (forall ((z tptp.int)) (= (ho_25132 x z) (ho_25132 y z)))) (= x y))))) (let ((_let_2910 (forall ((x |u_(-> tptp.list_nat _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|) (y |u_(-> tptp.list_nat _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_19181 x z) (ho_19181 y z)))) (= x y))))) (let ((_let_2911 (forall ((x |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.assn)_ _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer Bool)|) (y |u_(-> tptp.set_Code_integer _u_(-> tptp.code_integer tptp.assn)_ _u_(-> tptp.code_integer tptp.assn)_ tptp.code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_17154 x z) (ho_17154 y z)))) (= x y))))) (let ((_let_2912 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.nat)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_17277 x z) (ho_17277 y z)))) (= x y))))) (let ((_let_2913 (forall ((x |u_(-> tptp.filter_nat tptp.filter_nat tptp.filter1242075044329608583at_nat)|) (y |u_(-> tptp.filter_nat tptp.filter_nat tptp.filter1242075044329608583at_nat)|)) (or (not (forall ((z tptp.filter_nat)) (= (ho_26083 x z) (ho_26083 y z)))) (= x y))))) (let ((_let_2914 (forall ((x |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.a)) (= (ho_14317 x z) (ho_14317 y z)))) (= x y))))) (let ((_let_2915 (forall ((x |u_(-> _u_(-> tptp.produc2732055786443039994et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|) (y |u_(-> _u_(-> tptp.produc2732055786443039994et_nat Bool)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3925858234332021118et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc2732055786443039994et_nat Bool)|)) (= (ho_24274 x z) (ho_24274 y z)))) (= x y))))) (let ((_let_2916 (forall ((x |u_(-> _u_(-> tptp.nat tptp.assn)_ _u_(-> tptp.nat tptp.assn)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.assn)_ _u_(-> tptp.nat tptp.assn)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.assn)|)) (= (ho_17167 x z) (ho_17167 y z)))) (= x y))))) (let ((_let_2917 (forall ((x |u_(-> tptp.list_num Bool)|) (y |u_(-> tptp.list_num Bool)|)) (or (not (forall ((z tptp.list_num)) (= (ho_24842 x z) (ho_24842 y z)))) (= x y))))) (let ((_let_2918 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_17083 x z) (ho_17083 y z)))) (= x y))))) (let ((_let_2919 (forall ((x |u_(-> _u_(-> Bool tptp.nat)_ _u_(-> Bool tptp.nat)_ Bool Bool)|) (y |u_(-> _u_(-> Bool tptp.nat)_ _u_(-> Bool tptp.nat)_ Bool Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.nat)|)) (= (ho_17208 x z) (ho_17208 y z)))) (= x y))))) (let ((_let_2920 (forall ((x |u_(-> _u_(-> tptp.a tptp.heap_Time_Heap_a)_ tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.heap_Time_Heap_a)_ tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.heap_Time_Heap_a)|)) (= (ho_19857 x z) (ho_19857 y z)))) (= x y))))) (let ((_let_2921 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.rat)_ _u_(-> tptp.int tptp.rat)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_17220 x z) (ho_17220 y z)))) (= x y))))) (let ((_let_2922 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat)_ tptp.set_Code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat)_ tptp.set_Code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat)|)) (= (ho_17258 x z) (ho_17258 y z)))) (= x y))))) (let ((_let_2923 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer Bool)|)) (= (ho_17262 x z) (ho_17262 y z)))) (= x y))))) (let ((_let_2924 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)_ tptp.produc3260487557148687353it_nat Bool)|) (y |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)_ tptp.produc3260487557148687353it_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)|)) (= (ho_25127 x z) (ho_25127 y z)))) (= x y))))) (let ((_let_2925 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int tptp.int)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int tptp.int)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_20086 x z) (ho_20086 y z)))) (= x y))))) (let ((_let_2926 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int Bool)|)) (= (ho_17274 x z) (ho_17274 y z)))) (= x y))))) (let ((_let_2927 (forall ((x |u_(-> _u_(-> tptp.b tptp.heap_T5738788834812785303t_unit)_ tptp.b tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.b tptp.heap_T5738788834812785303t_unit)_ tptp.b tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.b tptp.heap_T5738788834812785303t_unit)|)) (= (ho_14321 x z) (ho_14321 y z)))) (= x y))))) (let ((_let_2928 (forall ((x |u_(-> tptp.set_nat tptp.filter_set_nat)|) (y |u_(-> tptp.set_nat tptp.filter_set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_26036 x z) (ho_26036 y z)))) (= x y))))) (let ((_let_2929 (forall ((x |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.produc3658429121746597890et_nat)) (= (ho_24641 x z) (ho_24641 y z)))) (= x y))))) (let ((_let_2930 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.nat)|) (y |u_(-> tptp.set_int _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_17273 x z) (ho_17273 y z)))) (= x y))))) (let ((_let_2931 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_11665 x z) (ho_11665 y z)))) (= x y))))) (let ((_let_2932 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_17732 x z) (ho_17732 y z)))) (= x y))))) (let ((_let_2933 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int tptp.nat)_ tptp.set_int _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.int tptp.nat)_ tptp.set_int _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int tptp.nat)|)) (= (ho_17272 x z) (ho_17272 y z)))) (= x y))))) (let ((_let_2934 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)_ tptp.produc3260487557148687353it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)_ tptp.produc3260487557148687353it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat)|)) (= (ho_23662 x z) (ho_23662 y z)))) (= x y))))) (let ((_let_2935 (forall ((x |u_(-> Bool tptp.assn)|) (y |u_(-> Bool tptp.assn)|)) (or (not (forall ((z Bool)) (= (ho_15806 x z) (ho_15806 y z)))) (= x y))))) (let ((_let_2936 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.int Bool)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int Bool)|)) (= (ho_17278 x z) (ho_17278 y z)))) (= x y))))) (let ((_let_2937 (forall ((x |u_(-> _u_(-> tptp.nat Bool tptp.nat)_ tptp.set_o _u_(-> tptp.nat Bool Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat Bool tptp.nat)_ tptp.set_o _u_(-> tptp.nat Bool Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool tptp.nat)|)) (= (ho_17282 x z) (ho_17282 y z)))) (= x y))))) (let ((_let_2938 (forall ((x |u_(-> tptp.set_Pr7600907837789447088it_nat tptp.set_Pr7600907837789447088it_nat)|) (y |u_(-> tptp.set_Pr7600907837789447088it_nat tptp.set_Pr7600907837789447088it_nat)|)) (or (not (forall ((z tptp.set_Pr7600907837789447088it_nat)) (= (ho_21368 x z) (ho_21368 y z)))) (= x y))))) (let ((_let_2939 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.assn)_ Bool tptp.assn)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.assn)_ Bool tptp.assn)|)) (or (not (forall ((z tptp.set_o)) (= (ho_16834 x z) (ho_16834 y z)))) (= x y))))) (let ((_let_2940 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_17292 x z) (ho_17292 y z)))) (= x y))))) (let ((_let_2941 (forall ((x |u_(-> Bool _u_(-> Bool tptp.assn)_ Bool tptp.assn)|) (y |u_(-> Bool _u_(-> Bool tptp.assn)_ Bool tptp.assn)|)) (or (not (forall ((z Bool)) (= (ho_17518 x z) (ho_17518 y z)))) (= x y))))) (let ((_let_2942 (forall ((x |u_(-> _u_(-> Bool tptp.rat)_ _u_(-> Bool tptp.rat)_ Bool tptp.rat)|) (y |u_(-> _u_(-> Bool tptp.rat)_ _u_(-> Bool tptp.rat)_ Bool tptp.rat)|)) (or (not (forall ((z |u_(-> Bool tptp.rat)|)) (= (ho_15778 x z) (ho_15778 y z)))) (= x y))))) (let ((_let_2943 (forall ((x |u_(-> tptp.set_Code_integer tptp.int)|) (y |u_(-> tptp.set_Code_integer tptp.int)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_17299 x z) (ho_17299 y z)))) (= x y))))) (let ((_let_2944 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int)_ tptp.set_Code_integer tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int)_ tptp.set_Code_integer tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int)|)) (= (ho_17298 x z) (ho_17298 y z)))) (= x y))))) (let ((_let_2945 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int Bool)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int Bool)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int Bool)|)) (= (ho_17303 x z) (ho_17303 y z)))) (= x y))))) (let ((_let_2946 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_21396 x z) (ho_21396 y z)))) (= x y))))) (let ((_let_2947 (forall ((x |u_(-> tptp.rat tptp.assn)|) (y |u_(-> tptp.rat tptp.assn)|)) (or (not (forall ((z tptp.rat)) (= (ho_23816 x z) (ho_23816 y z)))) (= x y))))) (let ((_let_2948 (forall ((x |u_(-> _u_(-> Bool tptp.int tptp.int)_ tptp.set_int _u_(-> Bool tptp.int Bool)_ Bool tptp.int)|) (y |u_(-> _u_(-> Bool tptp.int tptp.int)_ tptp.set_int _u_(-> Bool tptp.int Bool)_ Bool tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.int tptp.int)|)) (= (ho_17307 x z) (ho_17307 y z)))) (= x y))))) (let ((_let_2949 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.nat Bool)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.nat Bool)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_13235 x z) (ho_13235 y z)))) (= x y))))) (let ((_let_2950 (forall ((x |u_(-> Bool tptp.nat tptp.nat)|) (y |u_(-> Bool tptp.nat tptp.nat)|)) (or (not (forall ((z Bool)) (= (ho_12198 x z) (ho_12198 y z)))) (= x y))))) (let ((_let_2951 (forall ((x |u_(-> _u_(-> Bool tptp.int)_ tptp.set_o tptp.int)|) (y |u_(-> _u_(-> Bool tptp.int)_ tptp.set_o tptp.int)|)) (or (not (forall ((z |u_(-> Bool tptp.int)|)) (= (ho_17311 x z) (ho_17311 y z)))) (= x y))))) (let ((_let_2952 (forall ((x |u_(-> tptp.nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_11309 x z) (ho_11309 y z)))) (= x y))))) (let ((_let_2953 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.set_nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.set_nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_17318 x z) (ho_17318 y z)))) (= x y))))) (let ((_let_2954 (forall ((x |u_(-> tptp.list_P9062070895058802706et_nat tptp.list_P9062070895058802706et_nat)|) (y |u_(-> tptp.list_P9062070895058802706et_nat tptp.list_P9062070895058802706et_nat)|)) (or (not (forall ((z tptp.list_P9062070895058802706et_nat)) (= (ho_24964 x z) (ho_24964 y z)))) (= x y))))) (let ((_let_2955 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.set_int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_18492 x z) (ho_18492 y z)))) (= x y))))) (let ((_let_2956 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int tptp.nat)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ _u_(-> tptp.int tptp.nat)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_12044 x z) (ho_12044 y z)))) (= x y))))) (let ((_let_2957 (forall ((x |u_(-> tptp.set_set_nat Bool)|) (y |u_(-> tptp.set_set_nat Bool)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_11207 x z) (ho_11207 y z)))) (= x y))))) (let ((_let_2958 (forall ((x |u_(-> tptp.set_int tptp.multis2468970476368604999at_nat)|) (y |u_(-> tptp.set_int tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_25787 x z) (ho_25787 y z)))) (= x y))))) (let ((_let_2959 (forall ((x |u_(-> _u_(-> tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat Bool)_ tptp.produc4471711990508489141at_nat Bool)|) (y |u_(-> _u_(-> tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat Bool)_ tptp.produc4471711990508489141at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat Bool)|)) (= (ho_24603 x z) (ho_24603 y z)))) (= x y))))) (let ((_let_2960 (forall ((x |u_(-> _u_(-> tptp.int tptp.num)_ _u_(-> tptp.num tptp.int)_ tptp.num tptp.num)|) (y |u_(-> _u_(-> tptp.int tptp.num)_ _u_(-> tptp.num tptp.int)_ tptp.num tptp.num)|)) (or (not (forall ((z |u_(-> tptp.int tptp.num)|)) (= (ho_22685 x z) (ho_22685 y z)))) (= x y))))) (let ((_let_2961 (forall ((x |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_17917 x z) (ho_17917 y z)))) (= x y))))) (let ((_let_2962 (forall ((x |u_(-> _u_(-> Bool tptp.nat Bool)_ Bool tptp.nat Bool)|) (y |u_(-> _u_(-> Bool tptp.nat Bool)_ Bool tptp.nat Bool)|)) (or (not (forall ((z |u_(-> Bool tptp.nat Bool)|)) (= (ho_11595 x z) (ho_11595 y z)))) (= x y))))) (let ((_let_2963 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat Bool)|)) (= (ho_17326 x z) (ho_17326 y z)))) (= x y))))) (let ((_let_2964 (forall ((x |u_(-> tptp.set_o _u_(-> Bool tptp.rat)_ Bool tptp.rat)|) (y |u_(-> tptp.set_o _u_(-> Bool tptp.rat)_ Bool tptp.rat)|)) (or (not (forall ((z tptp.set_o)) (= (ho_16824 x z) (ho_16824 y z)))) (= x y))))) (let ((_let_2965 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat tptp.nat)_ tptp.set_Code_integer _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat tptp.nat)_ tptp.set_Code_integer _u_(-> tptp.code_integer tptp.nat Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat tptp.nat)|)) (= (ho_17338 x z) (ho_17338 y z)))) (= x y))))) (let ((_let_2966 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat Bool)|)) (= (ho_17348 x z) (ho_17348 y z)))) (= x y))))) (let ((_let_2967 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.nat)|) (y |u_(-> tptp.set_int _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_17347 x z) (ho_17347 y z)))) (= x y))))) (let ((_let_2968 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat tptp.nat)_ tptp.set_int _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat tptp.nat)_ tptp.set_int _u_(-> tptp.int tptp.nat Bool)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat tptp.nat)|)) (= (ho_17346 x z) (ho_17346 y z)))) (= x y))))) (let ((_let_2969 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_17829 x z) (ho_17829 y z)))) (= x y))))) (let ((_let_2970 (forall ((x |u_(-> tptp.set_int _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.int)|) (y |u_(-> tptp.set_int _u_(-> tptp.nat tptp.int Bool)_ tptp.nat tptp.int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_17380 x z) (ho_17380 y z)))) (= x y))))) (let ((_let_2971 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_25953 x z) (ho_25953 y z)))) (= x y))))) (let ((_let_2972 (forall ((x |u_(-> tptp.option_rat Bool)|) (y |u_(-> tptp.option_rat Bool)|)) (or (not (forall ((z tptp.option_rat)) (= (ho_24196 x z) (ho_24196 y z)))) (= x y))))) (let ((_let_2973 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.int)|)) (= (ho_25872 x z) (ho_25872 y z)))) (= x y))))) (let ((_let_2974 (forall ((x |u_(-> tptp.int _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn)|) (y |u_(-> tptp.int _u_(-> tptp.int tptp.assn)_ tptp.int tptp.assn)|)) (or (not (forall ((z tptp.int)) (= (ho_17512 x z) (ho_17512 y z)))) (= x y))))) (let ((_let_2975 (forall ((x |u_(-> tptp.int _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.int)|) (y |u_(-> tptp.int _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_18069 x z) (ho_18069 y z)))) (= x y))))) (let ((_let_2976 (forall ((x |u_(-> tptp.set_Code_integer tptp.set_Code_integer)|) (y |u_(-> tptp.set_Code_integer tptp.set_Code_integer)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_17410 x z) (ho_17410 y z)))) (= x y))))) (let ((_let_2977 (forall ((x |u_(-> tptp.list_P6935614879863011209it_nat tptp.nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> tptp.list_P6935614879863011209it_nat tptp.nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z tptp.list_P6935614879863011209it_nat)) (= (ho_24915 x z) (ho_24915 y z)))) (= x y))))) (let ((_let_2978 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int Bool)_ tptp.int tptp.code_integer)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int Bool)_ tptp.int tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer)|)) (= (ho_17434 x z) (ho_17434 y z)))) (= x y))))) (let ((_let_2979 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|)) (= (ho_25859 x z) (ho_25859 y z)))) (= x y))))) (let ((_let_2980 (forall ((x |u_(-> tptp.set_Product_prod_o_o Bool)|) (y |u_(-> tptp.set_Product_prod_o_o Bool)|)) (or (not (forall ((z tptp.set_Product_prod_o_o)) (= (ho_24855 x z) (ho_24855 y z)))) (= x y))))) (let ((_let_2981 (forall ((x |u_(-> tptp.option8057788054806935849nteger tptp.option7428179582072448501nteger)|) (y |u_(-> tptp.option8057788054806935849nteger tptp.option7428179582072448501nteger)|)) (or (not (forall ((z tptp.option8057788054806935849nteger)) (= (ho_25734 x z) (ho_25734 y z)))) (= x y))))) (let ((_let_2982 (forall ((x |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.product_unit)_ tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.heap_e7401611519738050253t_unit tptp.product_unit)_ tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.heap_e7401611519738050253t_unit tptp.product_unit)|)) (= (ho_22405 x z) (ho_22405 y z)))) (= x y))))) (let ((_let_2983 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.nat)_ _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ _u_(-> tptp.code_integer tptp.nat)_ _u_(-> tptp.code_integer tptp.nat)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_16271 x z) (ho_16271 y z)))) (= x y))))) (let ((_let_2984 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_nat_nat)|)) (= (ho_25977 x z) (ho_25977 y z)))) (= x y))))) (let ((_let_2985 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int)_ _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.int)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int)_ _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.int)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int)|)) (= (ho_17440 x z) (ho_17440 y z)))) (= x y))))) (let ((_let_2986 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat)_ _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat)_ _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat)|)) (= (ho_17442 x z) (ho_17442 y z)))) (= x y))))) (let ((_let_2987 (forall ((x |u_(-> _u_(-> tptp.set_o tptp.set_o tptp.set_o)_ tptp.set_o _u_(-> tptp.set_o tptp.set_o Bool)_ _u_(-> tptp.set_o tptp.set_o Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.set_o tptp.set_o tptp.set_o)_ tptp.set_o _u_(-> tptp.set_o tptp.set_o Bool)_ _u_(-> tptp.set_o tptp.set_o Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.set_o tptp.set_o tptp.set_o)|)) (= (ho_24514 x z) (ho_24514 y z)))) (= x y))))) (let ((_let_2988 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.rat)_ _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.rat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.rat)_ _u_(-> tptp.code_integer Bool)_ tptp.code_integer tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.rat)|)) (= (ho_17454 x z) (ho_17454 y z)))) (= x y))))) (let ((_let_2989 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.int tptp.rat)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.int tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_17461 x z) (ho_17461 y z)))) (= x y))))) (let ((_let_2990 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_17501 x z) (ho_17501 y z)))) (= x y))))) (let ((_let_2991 (forall ((x |u_(-> _u_(-> tptp.produc2732055786443039994et_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.produc2732055786443039994et_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.produc2732055786443039994et_nat Bool)|)) (= (ho_24479 x z) (ho_24479 y z)))) (= x y))))) (let ((_let_2992 (forall ((x |u_(-> tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat)|) (y |u_(-> tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat)|)) (or (not (forall ((z tptp.set_Pr7098220151150636591it_nat)) (= (ho_21355 x z) (ho_21355 y z)))) (= x y))))) (let ((_let_2993 (forall ((x |u_(-> Bool _u_(-> Bool tptp.rat)_ Bool tptp.rat)|) (y |u_(-> Bool _u_(-> Bool tptp.rat)_ Bool tptp.rat)|)) (or (not (forall ((z Bool)) (= (ho_17504 x z) (ho_17504 y z)))) (= x y))))) (let ((_let_2994 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.produc3843707927480180839at_nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.produc3843707927480180839at_nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_11429 x z) (ho_11429 y z)))) (= x y))))) (let ((_let_2995 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)_ _u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)_ tptp.a tptp.produc6653097349344004940it_nat Bool)|) (y |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)_ _u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)_ tptp.a tptp.produc6653097349344004940it_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc6653097349344004940it_nat Bool)|)) (= (ho_24361 x z) (ho_24361 y z)))) (= x y))))) (let ((_let_2996 (forall ((x |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.code_integer)|) (y |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_17521 x z) (ho_17521 y z)))) (= x y))))) (let ((_let_2997 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)_ tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat _u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)_ tptp.set_Pr1261947904930325089at_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_21992 x z) (ho_21992 y z)))) (= x y))))) (let ((_let_2998 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.nat)) (= (ho_17529 x z) (ho_17529 y z)))) (= x y))))) (let ((_let_2999 (forall ((x |u_(-> tptp.code_integer tptp.nat tptp.int)|) (y |u_(-> tptp.code_integer tptp.nat tptp.int)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_12223 x z) (ho_12223 y z)))) (= x y))))) (let ((_let_3000 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat Bool)|) (y |u_(-> tptp.produc3260487557148687353it_nat Bool)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_22719 x z) (ho_22719 y z)))) (= x y))))) (let ((_let_3001 (forall ((x |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer tptp.rat)|) (y |u_(-> tptp.code_integer _u_(-> tptp.code_integer tptp.rat)_ tptp.code_integer tptp.rat)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_17567 x z) (ho_17567 y z)))) (= x y))))) (let ((_let_3002 (forall ((x |u_(-> tptp.assn _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.produc3658429121746597890et_nat Bool)|) (y |u_(-> tptp.assn _u_(-> tptp.nat tptp.assn)_ tptp.nat tptp.produc3658429121746597890et_nat Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_23803 x z) (ho_23803 y z)))) (= x y))))) (let ((_let_3003 (forall ((x |u_(-> tptp.int tptp.int tptp.nat tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.int tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_17637 x z) (ho_17637 y z)))) (= x y))))) (let ((_let_3004 (forall ((x |u_(-> tptp.a tptp.product_prod_a_a)|) (y |u_(-> tptp.a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_25077 x z) (ho_25077 y z)))) (= x y))))) (let ((_let_3005 (forall ((x |u_(-> tptp.int tptp.nat tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.nat tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_17643 x z) (ho_17643 y z)))) (= x y))))) (let ((_let_3006 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc3407818250607552075t_unit)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.produc3407818250607552075t_unit)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_11802 x z) (ho_11802 y z)))) (= x y))))) (let ((_let_3007 (forall ((x |u_(-> tptp.option_Code_integer tptp.option8057788054806935849nteger)|) (y |u_(-> tptp.option_Code_integer tptp.option8057788054806935849nteger)|)) (or (not (forall ((z tptp.option_Code_integer)) (= (ho_25687 x z) (ho_25687 y z)))) (= x y))))) (let ((_let_3008 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_15143 x z) (ho_15143 y z)))) (= x y))))) (let ((_let_3009 (forall ((x |u_(-> Bool tptp.set_o)|) (y |u_(-> Bool tptp.set_o)|)) (or (not (forall ((z Bool)) (= (ho_17697 x z) (ho_17697 y z)))) (= x y))))) (let ((_let_3010 (forall ((x |u_(-> Bool tptp.int Bool)|) (y |u_(-> Bool tptp.int Bool)|)) (or (not (forall ((z Bool)) (= (ho_11588 x z) (ho_11588 y z)))) (= x y))))) (let ((_let_3011 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_17827 x z) (ho_17827 y z)))) (= x y))))) (let ((_let_3012 (forall ((x |u_(-> tptp.code_natural tptp.produc5728234346263159722nt_int tptp.produc3500511559948749619nt_int)|) (y |u_(-> tptp.code_natural tptp.produc5728234346263159722nt_int tptp.produc3500511559948749619nt_int)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_25215 x z) (ho_25215 y z)))) (= x y))))) (let ((_let_3013 (forall ((x |u_(-> tptp.produc3500511559948749619nt_int tptp.produc3500511559948749619nt_int Bool)|) (y |u_(-> tptp.produc3500511559948749619nt_int tptp.produc3500511559948749619nt_int Bool)|)) (or (not (forall ((z tptp.produc3500511559948749619nt_int)) (= (ho_25218 x z) (ho_25218 y z)))) (= x y))))) (let ((_let_3014 (forall ((x |u_(-> _u_(-> tptp.produc3500511559948749619nt_int tptp.produc3500511559948749619nt_int Bool)_ tptp.produc3500511559948749619nt_int Bool)|) (y |u_(-> _u_(-> tptp.produc3500511559948749619nt_int tptp.produc3500511559948749619nt_int Bool)_ tptp.produc3500511559948749619nt_int Bool)|)) (or (not (forall ((z |u_(-> tptp.produc3500511559948749619nt_int tptp.produc3500511559948749619nt_int Bool)|)) (= (ho_25220 x z) (ho_25220 y z)))) (= x y))))) (let ((_let_3015 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc8628075524815789655_nat_o)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc8628075524815789655_nat_o)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat Bool)|)) (= (ho_25224 x z) (ho_25224 y z)))) (= x y))))) (let ((_let_3016 (forall ((x |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc8628075524815789655_nat_o)|) (y |u_(-> _u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc8628075524815789655_nat_o)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.produc3658429121746597890et_nat Bool)_ tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (= (ho_25223 x z) (ho_25223 y z)))) (= x y))))) (let ((_let_3017 (forall ((x |u_(-> tptp.produc8628075524815789655_nat_o tptp.produc50402934264563236_nat_o)|) (y |u_(-> tptp.produc8628075524815789655_nat_o tptp.produc50402934264563236_nat_o)|)) (or (not (forall ((z tptp.produc8628075524815789655_nat_o)) (= (ho_25227 x z) (ho_25227 y z)))) (= x y))))) (let ((_let_3018 (forall ((x |u_(-> tptp.code_natural tptp.produc8628075524815789655_nat_o tptp.produc50402934264563236_nat_o)|) (y |u_(-> tptp.code_natural tptp.produc8628075524815789655_nat_o tptp.produc50402934264563236_nat_o)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_25226 x z) (ho_25226 y z)))) (= x y))))) (let ((_let_3019 (forall ((x |u_(-> tptp.produc6999243976208994655_nat_o tptp.produc7766336532480398636_nat_o)|) (y |u_(-> tptp.produc6999243976208994655_nat_o tptp.produc7766336532480398636_nat_o)|)) (or (not (forall ((z tptp.produc6999243976208994655_nat_o)) (= (ho_25238 x z) (ho_25238 y z)))) (= x y))))) (let ((_let_3020 (forall ((x |u_(-> tptp.code_natural tptp.produc6999243976208994655_nat_o tptp.produc7766336532480398636_nat_o)|) (y |u_(-> tptp.code_natural tptp.produc6999243976208994655_nat_o tptp.produc7766336532480398636_nat_o)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_25237 x z) (ho_25237 y z)))) (= x y))))) (let ((_let_3021 (forall ((x |u_(-> tptp.produc7766336532480398636_nat_o tptp.produc7766336532480398636_nat_o Bool)|) (y |u_(-> tptp.produc7766336532480398636_nat_o tptp.produc7766336532480398636_nat_o Bool)|)) (or (not (forall ((z tptp.produc7766336532480398636_nat_o)) (= (ho_25240 x z) (ho_25240 y z)))) (= x y))))) (let ((_let_3022 (forall ((x |u_(-> _u_(-> tptp.produc7766336532480398636_nat_o tptp.produc7766336532480398636_nat_o Bool)_ tptp.produc7766336532480398636_nat_o Bool)|) (y |u_(-> _u_(-> tptp.produc7766336532480398636_nat_o tptp.produc7766336532480398636_nat_o Bool)_ tptp.produc7766336532480398636_nat_o Bool)|)) (or (not (forall ((z |u_(-> tptp.produc7766336532480398636_nat_o tptp.produc7766336532480398636_nat_o Bool)|)) (= (ho_25242 x z) (ho_25242 y z)))) (= x y))))) (let ((_let_3023 (forall ((x |u_(-> tptp.produc8449588929630179473_nat_b tptp.produc7538756082594784606_nat_b)|) (y |u_(-> tptp.produc8449588929630179473_nat_b tptp.produc7538756082594784606_nat_b)|)) (or (not (forall ((z tptp.produc8449588929630179473_nat_b)) (= (ho_25249 x z) (ho_25249 y z)))) (= x y))))) (let ((_let_3024 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.list_nat tptp.list_nat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_25829 x z) (ho_25829 y z)))) (= x y))))) (let ((_let_3025 (forall ((x |u_(-> tptp.code_natural tptp.produc8449588929630179473_nat_b tptp.produc7538756082594784606_nat_b)|) (y |u_(-> tptp.code_natural tptp.produc8449588929630179473_nat_b tptp.produc7538756082594784606_nat_b)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_25248 x z) (ho_25248 y z)))) (= x y))))) (let ((_let_3026 (forall ((x |u_(-> tptp.a tptp.produc2763251018811306770_nat_a)|) (y |u_(-> tptp.a tptp.produc2763251018811306770_nat_a)|)) (or (not (forall ((z tptp.a)) (= (ho_25257 x z) (ho_25257 y z)))) (= x y))))) (let ((_let_3027 (forall ((x |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.a tptp.produc2763251018811306770_nat_a)|) (y |u_(-> _u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)_ tptp.a tptp.produc2763251018811306770_nat_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat)|)) (= (ho_25256 x z) (ho_25256 y z)))) (= x y))))) (let ((_let_3028 (forall ((x |u_(-> tptp.produc2763251018811306770_nat_a tptp.produc7140141985219958623_nat_a)|) (y |u_(-> tptp.produc2763251018811306770_nat_a tptp.produc7140141985219958623_nat_a)|)) (or (not (forall ((z tptp.produc2763251018811306770_nat_a)) (= (ho_25260 x z) (ho_25260 y z)))) (= x y))))) (let ((_let_3029 (forall ((x |u_(-> tptp.code_natural tptp.produc2763251018811306770_nat_a tptp.produc7140141985219958623_nat_a)|) (y |u_(-> tptp.code_natural tptp.produc2763251018811306770_nat_a tptp.produc7140141985219958623_nat_a)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_25259 x z) (ho_25259 y z)))) (= x y))))) (let ((_let_3030 (forall ((x |u_(-> tptp.produc7140141985219958623_nat_a Bool)|) (y |u_(-> tptp.produc7140141985219958623_nat_a Bool)|)) (or (not (forall ((z tptp.produc7140141985219958623_nat_a)) (= (ho_25265 x z) (ho_25265 y z)))) (= x y))))) (let ((_let_3031 (forall ((x |u_(-> tptp.produc7140141985219958623_nat_a tptp.produc7140141985219958623_nat_a Bool)|) (y |u_(-> tptp.produc7140141985219958623_nat_a tptp.produc7140141985219958623_nat_a Bool)|)) (or (not (forall ((z tptp.produc7140141985219958623_nat_a)) (= (ho_25262 x z) (ho_25262 y z)))) (= x y))))) (let ((_let_3032 (forall ((x |u_(-> _u_(-> tptp.produc7140141985219958623_nat_a tptp.produc7140141985219958623_nat_a Bool)_ tptp.produc7140141985219958623_nat_a Bool)|) (y |u_(-> _u_(-> tptp.produc7140141985219958623_nat_a tptp.produc7140141985219958623_nat_a Bool)_ tptp.produc7140141985219958623_nat_a Bool)|)) (or (not (forall ((z |u_(-> tptp.produc7140141985219958623_nat_a tptp.produc7140141985219958623_nat_a Bool)|)) (= (ho_25264 x z) (ho_25264 y z)))) (= x y))))) (let ((_let_3033 (forall ((x |u_(-> tptp.code_natural tptp.produc7250841696378415494atural)|) (y |u_(-> tptp.code_natural tptp.produc7250841696378415494atural)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_25268 x z) (ho_25268 y z)))) (= x y))))) (let ((_let_3034 (forall ((x |u_(-> tptp.list_option_num tptp.nat tptp.option_num)|) (y |u_(-> tptp.list_option_num tptp.nat tptp.option_num)|)) (or (not (forall ((z tptp.list_option_num)) (= (ho_25286 x z) (ho_25286 y z)))) (= x y))))) (let ((_let_3035 (forall ((x |u_(-> _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.code_natural tptp.produc7250841696378415494atural)|) (y |u_(-> _u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)_ tptp.code_natural tptp.produc7250841696378415494atural)|)) (or (not (forall ((z |u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|)) (= (ho_25267 x z) (ho_25267 y z)))) (= x y))))) (let ((_let_3036 (forall ((x |u_(-> tptp.code_natural tptp.produc7250841696378415494atural tptp.produc1399344845416535567atural)|) (y |u_(-> tptp.code_natural tptp.produc7250841696378415494atural tptp.produc1399344845416535567atural)|)) (or (not (forall ((z tptp.code_natural)) (= (ho_25270 x z) (ho_25270 y z)))) (= x y))))) (let ((_let_3037 (forall ((x |u_(-> tptp.produc1399344845416535567atural tptp.produc1399344845416535567atural Bool)|) (y |u_(-> tptp.produc1399344845416535567atural tptp.produc1399344845416535567atural Bool)|)) (or (not (forall ((z tptp.produc1399344845416535567atural)) (= (ho_25273 x z) (ho_25273 y z)))) (= x y))))) (let ((_let_3038 (forall ((x |u_(-> Bool _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> Bool _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z Bool)) (= (ho_25280 x z) (ho_25280 y z)))) (= x y))))) (let ((_let_3039 (forall ((x |u_(-> tptp.option_num tptp.list_option_num tptp.list_option_num)|) (y |u_(-> tptp.option_num tptp.list_option_num tptp.list_option_num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_25288 x z) (ho_25288 y z)))) (= x y))))) (let ((_let_3040 (forall ((x |u_(-> tptp.set_int tptp.rat)|) (y |u_(-> tptp.set_int tptp.rat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_25292 x z) (ho_25292 y z)))) (= x y))))) (let ((_let_3041 (forall ((x |u_(-> tptp.set_nat tptp.code_natural)|) (y |u_(-> tptp.set_nat tptp.code_natural)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_25295 x z) (ho_25295 y z)))) (= x y))))) (let ((_let_3042 (forall ((x |u_(-> tptp.set_o tptp.code_integer)|) (y |u_(-> tptp.set_o tptp.code_integer)|)) (or (not (forall ((z tptp.set_o)) (= (ho_25298 x z) (ho_25298 y z)))) (= x y))))) (let ((_let_3043 (forall ((x |u_(-> _u_(-> Bool tptp.code_integer)_ tptp.set_o tptp.code_integer)|) (y |u_(-> _u_(-> Bool tptp.code_integer)_ tptp.set_o tptp.code_integer)|)) (or (not (forall ((z |u_(-> Bool tptp.code_integer)|)) (= (ho_25297 x z) (ho_25297 y z)))) (= x y))))) (let ((_let_3044 (forall ((x |u_(-> tptp.set_int tptp.code_integer)|) (y |u_(-> tptp.set_int tptp.code_integer)|)) (or (not (forall ((z tptp.set_int)) (= (ho_25301 x z) (ho_25301 y z)))) (= x y))))) (let ((_let_3045 (forall ((x |u_(-> _u_(-> Bool tptp.rat)_ tptp.set_o tptp.rat)|) (y |u_(-> _u_(-> Bool tptp.rat)_ tptp.set_o tptp.rat)|)) (or (not (forall ((z |u_(-> Bool tptp.rat)|)) (= (ho_25303 x z) (ho_25303 y z)))) (= x y))))) (let ((_let_3046 (forall ((x |u_(-> tptp.set_set_nat tptp.code_integer)|) (y |u_(-> tptp.set_set_nat tptp.code_integer)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_25307 x z) (ho_25307 y z)))) (= x y))))) (let ((_let_3047 (forall ((x |u_(-> tptp.set_set_nat tptp.rat)|) (y |u_(-> tptp.set_set_nat tptp.rat)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_25310 x z) (ho_25310 y z)))) (= x y))))) (let ((_let_3048 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.rat)_ tptp.set_set_nat tptp.rat)|) (y |u_(-> _u_(-> tptp.set_nat tptp.rat)_ tptp.set_set_nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.rat)|)) (= (ho_25309 x z) (ho_25309 y z)))) (= x y))))) (let ((_let_3049 (forall ((x |u_(-> tptp.set_se6260736226359567993nt_int tptp.nat)|) (y |u_(-> tptp.set_se6260736226359567993nt_int tptp.nat)|)) (or (not (forall ((z tptp.set_se6260736226359567993nt_int)) (= (ho_25313 x z) (ho_25313 y z)))) (= x y))))) (let ((_let_3050 (forall ((x |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ tptp.set_se6260736226359567993nt_int tptp.nat)|) (y |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)_ tptp.set_se6260736226359567993nt_int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.set_Pr958786334691620121nt_int tptp.nat)|)) (= (ho_25312 x z) (ho_25312 y z)))) (= x y))))) (let ((_let_3051 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.code_integer)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer)|)) (= (ho_25315 x z) (ho_25315 y z)))) (= x y))))) (let ((_let_3052 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.rat)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_25317 x z) (ho_25317 y z)))) (= x y))))) (let ((_let_3053 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_25320 x z) (ho_25320 y z)))) (= x y))))) (let ((_let_3054 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.code_integer)|) (y |u_(-> _u_(-> tptp.int tptp.code_integer)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_integer)|)) (= (ho_25322 x z) (ho_25322 y z)))) (= x y))))) (let ((_let_3055 (forall ((x |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.code_integer)|)) (= (ho_25328 x z) (ho_25328 y z)))) (= x y))))) (let ((_let_3056 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.nat)_ _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.nat)_ _u_(-> tptp.nat tptp.code_integer)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.nat)|)) (= (ho_25327 x z) (ho_25327 y z)))) (= x y))))) (let ((_let_3057 (forall ((x |u_(-> tptp.set_int tptp.set_set_int)|) (y |u_(-> tptp.set_int tptp.set_set_int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_25338 x z) (ho_25338 y z)))) (= x y))))) (let ((_let_3058 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_25351 x z) (ho_25351 y z)))) (= x y))))) (let ((_let_3059 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_25350 x z) (ho_25350 y z)))) (= x y))))) (let ((_let_3060 (forall ((x |u_(-> tptp.set_set_int Bool)|) (y |u_(-> tptp.set_set_int Bool)|)) (or (not (forall ((z tptp.set_set_int)) (= (ho_25356 x z) (ho_25356 y z)))) (= x y))))) (let ((_let_3061 (forall ((x |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_25971 x z) (ho_25971 y z)))) (= x y))))) (let ((_let_3062 (forall ((x |u_(-> tptp.set_int tptp.set_set_int Bool)|) (y |u_(-> tptp.set_int tptp.set_set_int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_25355 x z) (ho_25355 y z)))) (= x y))))) (let ((_let_3063 (forall ((x |u_(-> tptp.set_num Bool)|) (y |u_(-> tptp.set_num Bool)|)) (or (not (forall ((z tptp.set_num)) (= (ho_25359 x z) (ho_25359 y z)))) (= x y))))) (let ((_let_3064 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.option4277301481530639448it_nat)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.option4277301481530639448it_nat)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_25476 x z) (ho_25476 y z)))) (= x y))))) (let ((_let_3065 (forall ((x |u_(-> _u_(-> tptp.set_int Bool)_ tptp.set_set_int)|) (y |u_(-> _u_(-> tptp.set_int Bool)_ tptp.set_set_int)|)) (or (not (forall ((z |u_(-> tptp.set_int Bool)|)) (= (ho_25362 x z) (ho_25362 y z)))) (= x y))))) (let ((_let_3066 (forall ((x |u_(-> _u_(-> tptp.rat Bool)_ tptp.set_rat)|) (y |u_(-> _u_(-> tptp.rat Bool)_ tptp.set_rat)|)) (or (not (forall ((z |u_(-> tptp.rat Bool)|)) (= (ho_25364 x z) (ho_25364 y z)))) (= x y))))) (let ((_let_3067 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)|)) (= (ho_25817 x z) (ho_25817 y z)))) (= x y))))) (let ((_let_3068 (forall ((x |u_(-> tptp.assn tptp.set_assn)|) (y |u_(-> tptp.assn tptp.set_assn)|)) (or (not (forall ((z tptp.assn)) (= (ho_25369 x z) (ho_25369 y z)))) (= x y))))) (let ((_let_3069 (forall ((x |u_(-> tptp.set_set_int tptp.set_set_int Bool)|) (y |u_(-> tptp.set_set_int tptp.set_set_int Bool)|)) (or (not (forall ((z tptp.set_set_int)) (= (ho_25371 x z) (ho_25371 y z)))) (= x y))))) (let ((_let_3070 (forall ((x |u_(-> tptp.set_num tptp.set_num Bool)|) (y |u_(-> tptp.set_num tptp.set_num Bool)|)) (or (not (forall ((z tptp.set_num)) (= (ho_25375 x z) (ho_25375 y z)))) (= x y))))) (let ((_let_3071 (forall ((x |u_(-> tptp.set_nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> tptp.set_nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_25379 x z) (ho_25379 y z)))) (= x y))))) (let ((_let_3072 (forall ((x |u_(-> _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.set_nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ tptp.set_nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.multis2468970476368604999at_nat)|)) (= (ho_25378 x z) (ho_25378 y z)))) (= x y))))) (let ((_let_3073 (forall ((x |u_(-> tptp.set_rat tptp.set_rat tptp.set_rat)|) (y |u_(-> tptp.set_rat tptp.set_rat tptp.set_rat)|)) (or (not (forall ((z tptp.set_rat)) (= (ho_25381 x z) (ho_25381 y z)))) (= x y))))) (let ((_let_3074 (forall ((x |u_(-> tptp.set_num tptp.set_num)|) (y |u_(-> tptp.set_num tptp.set_num)|)) (or (not (forall ((z tptp.set_num)) (= (ho_25385 x z) (ho_25385 y z)))) (= x y))))) (let ((_let_3075 (forall ((x |u_(-> tptp.set_num tptp.set_num tptp.set_num)|) (y |u_(-> tptp.set_num tptp.set_num tptp.set_num)|)) (or (not (forall ((z tptp.set_num)) (= (ho_25384 x z) (ho_25384 y z)))) (= x y))))) (let ((_let_3076 (forall ((x |u_(-> tptp.set_assn Bool)|) (y |u_(-> tptp.set_assn Bool)|)) (or (not (forall ((z tptp.set_assn)) (= (ho_25389 x z) (ho_25389 y z)))) (= x y))))) (let ((_let_3077 (forall ((x |u_(-> tptp.set_assn tptp.set_assn Bool)|) (y |u_(-> tptp.set_assn tptp.set_assn Bool)|)) (or (not (forall ((z tptp.set_assn)) (= (ho_25388 x z) (ho_25388 y z)))) (= x y))))) (let ((_let_3078 (forall ((x |u_(-> _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.multis2468970476368604999at_nat)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.multis2468970476368604999at_nat)|)) (= (ho_25394 x z) (ho_25394 y z)))) (= x y))))) (let ((_let_3079 (forall ((x |u_(-> tptp.nat tptp.nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> tptp.nat tptp.nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_25398 x z) (ho_25398 y z)))) (= x y))))) (let ((_let_3080 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.array_int tptp.nat Bool)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.array_int tptp.nat Bool)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_25579 x z) (ho_25579 y z)))) (= x y))))) (let ((_let_3081 (forall ((x |u_(-> _u_(-> tptp.nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)_ tptp.nat tptp.nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)_ tptp.nat tptp.nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat)|)) (= (ho_25397 x z) (ho_25397 y z)))) (= x y))))) (let ((_let_3082 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.product_prod_nat_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.product_prod_nat_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_25400 x z) (ho_25400 y z)))) (= x y))))) (let ((_let_3083 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.set_Pr1261947904930325089at_nat tptp.nat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.set_Pr1261947904930325089at_nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (= (ho_25402 x z) (ho_25402 y z)))) (= x y))))) (let ((_let_3084 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.product_prod_int_int tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.product_prod_int_int tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_25404 x z) (ho_25404 y z)))) (= x y))))) (let ((_let_3085 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat)|)) (= (ho_25407 x z) (ho_25407 y z)))) (= x y))))) (let ((_let_3086 (forall ((x |u_(-> _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|) (y |u_(-> _u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)|)) (= (ho_25409 x z) (ho_25409 y z)))) (= x y))))) (let ((_let_3087 (forall ((x |u_(-> tptp.produc3925858234332021118et_nat tptp.produc3658429121746597890et_nat)|) (y |u_(-> tptp.produc3925858234332021118et_nat tptp.produc3658429121746597890et_nat)|)) (or (not (forall ((z tptp.produc3925858234332021118et_nat)) (= (ho_25410 x z) (ho_25410 y z)))) (= x y))))) (let ((_let_3088 (forall ((x |u_(-> _u_(-> tptp.produc3925858234332021118et_nat tptp.produc3658429121746597890et_nat)_ tptp.produc2732055786443039994et_nat tptp.produc3925858234332021118et_nat)|) (y |u_(-> _u_(-> tptp.produc3925858234332021118et_nat tptp.produc3658429121746597890et_nat)_ tptp.produc2732055786443039994et_nat tptp.produc3925858234332021118et_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3925858234332021118et_nat tptp.produc3658429121746597890et_nat)|)) (= (ho_25412 x z) (ho_25412 y z)))) (= x y))))) (let ((_let_3089 (forall ((x |u_(-> _u_(-> tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat)|) (y |u_(-> _u_(-> tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat)_ tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat)|)) (= (ho_25415 x z) (ho_25415 y z)))) (= x y))))) (let ((_let_3090 (forall ((x |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc6653097349344004940it_nat)_ tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc6653097349344004940it_nat)_ tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc6653097349344004940it_nat tptp.produc6653097349344004940it_nat)|)) (= (ho_25418 x z) (ho_25418 y z)))) (= x y))))) (let ((_let_3091 (forall ((x |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc6653097349344004940it_nat)_ tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> _u_(-> tptp.produc6653097349344004940it_nat tptp.produc6653097349344004940it_nat)_ tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc6653097349344004940it_nat tptp.produc6653097349344004940it_nat)|)) (= (ho_25420 x z) (ho_25420 y z)))) (= x y))))) (let ((_let_3092 (forall ((x |u_(-> _u_(-> tptp.option_int tptp.option_int)_ tptp.option_int tptp.nat)|) (y |u_(-> _u_(-> tptp.option_int tptp.option_int)_ tptp.option_int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.option_int tptp.option_int)|)) (= (ho_25755 x z) (ho_25755 y z)))) (= x y))))) (let ((_let_3093 (forall ((x |u_(-> tptp.assn tptp.set_assn Bool)|) (y |u_(-> tptp.assn tptp.set_assn Bool)|)) (or (not (forall ((z tptp.assn)) (= (ho_25426 x z) (ho_25426 y z)))) (= x y))))) (let ((_let_3094 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc5966032636589952099nteger)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc5966032636589952099nteger)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_25438 x z) (ho_25438 y z)))) (= x y))))) (let ((_let_3095 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.produc8923325533196201883nteger tptp.produc5966032636589952099nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.produc8923325533196201883nteger tptp.produc5966032636589952099nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (= (ho_25437 x z) (ho_25437 y z)))) (= x y))))) (let ((_let_3096 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.code_integer)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ _u_(-> tptp.code_integer tptp.code_integer)_ tptp.code_integer tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer)|)) (= (ho_25440 x z) (ho_25440 y z)))) (= x y))))) (let ((_let_3097 (forall ((x |u_(-> tptp.nat tptp.nat tptp.assn tptp.assn)|) (y |u_(-> tptp.nat tptp.nat tptp.assn tptp.assn)|)) (or (not (forall ((z tptp.nat)) (= (ho_25447 x z) (ho_25447 y z)))) (= x y))))) (let ((_let_3098 (forall ((x |u_(-> _u_(-> tptp.nat tptp.assn tptp.assn)_ tptp.nat tptp.nat tptp.assn tptp.assn)|) (y |u_(-> _u_(-> tptp.nat tptp.assn tptp.assn)_ tptp.nat tptp.nat tptp.assn tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.assn tptp.assn)|)) (= (ho_25446 x z) (ho_25446 y z)))) (= x y))))) (let ((_let_3099 (forall ((x |u_(-> tptp.num tptp.set_num tptp.set_num)|) (y |u_(-> tptp.num tptp.set_num tptp.set_num)|)) (or (not (forall ((z tptp.num)) (= (ho_25451 x z) (ho_25451 y z)))) (= x y))))) (let ((_let_3100 (forall ((x |u_(-> _u_(-> tptp.assn Bool)_ tptp.set_assn)|) (y |u_(-> _u_(-> tptp.assn Bool)_ tptp.set_assn)|)) (or (not (forall ((z |u_(-> tptp.assn Bool)|)) (= (ho_25456 x z) (ho_25456 y z)))) (= x y))))) (let ((_let_3101 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.int)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.int)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_25463 x z) (ho_25463 y z)))) (= x y))))) (let ((_let_3102 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int)_ tptp.set_Pr1261947904930325089at_nat tptp.int)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int)_ tptp.set_Pr1261947904930325089at_nat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int)|)) (= (ho_25462 x z) (ho_25462 y z)))) (= x y))))) (let ((_let_3103 (forall ((x |u_(-> tptp.set_assn tptp.set_assn)|) (y |u_(-> tptp.set_assn tptp.set_assn)|)) (or (not (forall ((z tptp.set_assn)) (= (ho_25466 x z) (ho_25466 y z)))) (= x y))))) (let ((_let_3104 (forall ((x |u_(-> tptp.assn tptp.set_assn tptp.set_assn)|) (y |u_(-> tptp.assn tptp.set_assn tptp.set_assn)|)) (or (not (forall ((z tptp.assn)) (= (ho_25465 x z) (ho_25465 y z)))) (= x y))))) (let ((_let_3105 (forall ((x |u_(-> tptp.set_assn tptp.set_assn tptp.set_assn)|) (y |u_(-> tptp.set_assn tptp.set_assn tptp.set_assn)|)) (or (not (forall ((z tptp.set_assn)) (= (ho_25468 x z) (ho_25468 y z)))) (= x y))))) (let ((_let_3106 (forall ((x |u_(-> tptp.produc6751673265320737416it_nat tptp.option4277301481530639448it_nat)|) (y |u_(-> tptp.produc6751673265320737416it_nat tptp.option4277301481530639448it_nat)|)) (or (not (forall ((z tptp.produc6751673265320737416it_nat)) (= (ho_25473 x z) (ho_25473 y z)))) (= x y))))) (let ((_let_3107 (forall ((x |u_(-> tptp.heap_T3836121109492952855ay_nat tptp.heap_e7401611519738050253t_unit tptp.option4277301481530639448it_nat)|) (y |u_(-> tptp.heap_T3836121109492952855ay_nat tptp.heap_e7401611519738050253t_unit tptp.option4277301481530639448it_nat)|)) (or (not (forall ((z tptp.heap_T3836121109492952855ay_nat)) (= (ho_25475 x z) (ho_25475 y z)))) (= x y))))) (let ((_let_3108 (forall ((x |u_(-> tptp.heap_T1346037964561226099ay_int tptp.heap_e7401611519738050253t_unit tptp.option2555668343544256180it_nat)|) (y |u_(-> tptp.heap_T1346037964561226099ay_int tptp.heap_e7401611519738050253t_unit tptp.option2555668343544256180it_nat)|)) (or (not (forall ((z tptp.heap_T1346037964561226099ay_int)) (= (ho_25485 x z) (ho_25485 y z)))) (= x y))))) (let ((_let_3109 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.set_Code_integer tptp.code_integer)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.set_Code_integer tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer)|)) (= (ho_25490 x z) (ho_25490 y z)))) (= x y))))) (let ((_let_3110 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.rat)_ tptp.set_Code_integer tptp.rat)|) (y |u_(-> _u_(-> tptp.code_integer tptp.rat)_ tptp.set_Code_integer tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.rat)|)) (= (ho_25493 x z) (ho_25493 y z)))) (= x y))))) (let ((_let_3111 (forall ((x |u_(-> _u_(-> Bool tptp.assn)_ tptp.set_o tptp.assn)|) (y |u_(-> _u_(-> Bool tptp.assn)_ tptp.set_o tptp.assn)|)) (or (not (forall ((z |u_(-> Bool tptp.assn)|)) (= (ho_25497 x z) (ho_25497 y z)))) (= x y))))) (let ((_let_3112 (forall ((x |u_(-> tptp.set_int tptp.assn)|) (y |u_(-> tptp.set_int tptp.assn)|)) (or (not (forall ((z tptp.set_int)) (= (ho_25501 x z) (ho_25501 y z)))) (= x y))))) (let ((_let_3113 (forall ((x |u_(-> _u_(-> tptp.int tptp.assn)_ tptp.set_int tptp.assn)|) (y |u_(-> _u_(-> tptp.int tptp.assn)_ tptp.set_int tptp.assn)|)) (or (not (forall ((z |u_(-> tptp.int tptp.assn)|)) (= (ho_25500 x z) (ho_25500 y z)))) (= x y))))) (let ((_let_3114 (forall ((x |u_(-> _u_(-> tptp.set_Code_integer Bool)_ tptp.set_set_Code_integer)|) (y |u_(-> _u_(-> tptp.set_Code_integer Bool)_ tptp.set_set_Code_integer)|)) (or (not (forall ((z |u_(-> tptp.set_Code_integer Bool)|)) (= (ho_25513 x z) (ho_25513 y z)))) (= x y))))) (let ((_let_3115 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_25818 x z) (ho_25818 y z)))) (= x y))))) (let ((_let_3116 (forall ((x |u_(-> tptp.set_set_Code_integer Bool)|) (y |u_(-> tptp.set_set_Code_integer Bool)|)) (or (not (forall ((z tptp.set_set_Code_integer)) (= (ho_25515 x z) (ho_25515 y z)))) (= x y))))) (let ((_let_3117 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)|)) (= (ho_25974 x z) (ho_25974 y z)))) (= x y))))) (let ((_let_3118 (forall ((x |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat Bool)_ tptp.set_se7855581050983116737at_nat)|) (y |u_(-> _u_(-> tptp.set_Pr1261947904930325089at_nat Bool)_ tptp.set_se7855581050983116737at_nat)|)) (or (not (forall ((z |u_(-> tptp.set_Pr1261947904930325089at_nat Bool)|)) (= (ho_25517 x z) (ho_25517 y z)))) (= x y))))) (let ((_let_3119 (forall ((x |u_(-> tptp.set_se7855581050983116737at_nat Bool)|) (y |u_(-> tptp.set_se7855581050983116737at_nat Bool)|)) (or (not (forall ((z tptp.set_se7855581050983116737at_nat)) (= (ho_25519 x z) (ho_25519 y z)))) (= x y))))) (let ((_let_3120 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.rat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.rat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_25526 x z) (ho_25526 y z)))) (= x y))))) (let ((_let_3121 (forall ((x |u_(-> tptp.set_set_nat tptp.int)|) (y |u_(-> tptp.set_set_nat tptp.int)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_25531 x z) (ho_25531 y z)))) (= x y))))) (let ((_let_3122 (forall ((x |u_(-> tptp.set_list_nat tptp.rat)|) (y |u_(-> tptp.set_list_nat tptp.rat)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_25537 x z) (ho_25537 y z)))) (= x y))))) (let ((_let_3123 (forall ((x |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.rat)|) (y |u_(-> tptp.set_Pr8551490117392284871at_nat tptp.rat)|)) (or (not (forall ((z tptp.set_Pr8551490117392284871at_nat)) (= (ho_25541 x z) (ho_25541 y z)))) (= x y))))) (let ((_let_3124 (forall ((x |u_(-> tptp.produc4166570645942440679at_nat tptp.rat)|) (y |u_(-> tptp.produc4166570645942440679at_nat tptp.rat)|)) (or (not (forall ((z tptp.produc4166570645942440679at_nat)) (= (ho_25538 x z) (ho_25538 y z)))) (= x y))))) (let ((_let_3125 (forall ((x |u_(-> _u_(-> tptp.produc4166570645942440679at_nat tptp.rat)_ tptp.set_Pr8551490117392284871at_nat tptp.rat)|) (y |u_(-> _u_(-> tptp.produc4166570645942440679at_nat tptp.rat)_ tptp.set_Pr8551490117392284871at_nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.produc4166570645942440679at_nat tptp.rat)|)) (= (ho_25540 x z) (ho_25540 y z)))) (= x y))))) (let ((_let_3126 (forall ((x |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.rat)|) (y |u_(-> tptp.set_Pr4329608150637261639at_nat tptp.rat)|)) (or (not (forall ((z tptp.set_Pr4329608150637261639at_nat)) (= (ho_25546 x z) (ho_25546 y z)))) (= x y))))) (let ((_let_3127 (forall ((x |u_(-> _u_(-> tptp.produc3843707927480180839at_nat tptp.rat)_ tptp.set_Pr4329608150637261639at_nat tptp.rat)|) (y |u_(-> _u_(-> tptp.produc3843707927480180839at_nat tptp.rat)_ tptp.set_Pr4329608150637261639at_nat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.produc3843707927480180839at_nat tptp.rat)|)) (= (ho_25545 x z) (ho_25545 y z)))) (= x y))))) (let ((_let_3128 (forall ((x |u_(-> tptp.produc4166570645942440679at_nat tptp.nat)|) (y |u_(-> tptp.produc4166570645942440679at_nat tptp.nat)|)) (or (not (forall ((z tptp.produc4166570645942440679at_nat)) (= (ho_25548 x z) (ho_25548 y z)))) (= x y))))) (let ((_let_3129 (forall ((x |u_(-> tptp.produc3843707927480180839at_nat tptp.nat)|) (y |u_(-> tptp.produc3843707927480180839at_nat tptp.nat)|)) (or (not (forall ((z tptp.produc3843707927480180839at_nat)) (= (ho_25552 x z) (ho_25552 y z)))) (= x y))))) (let ((_let_3130 (forall ((x |u_(-> tptp.set_int tptp.code_natural)|) (y |u_(-> tptp.set_int tptp.code_natural)|)) (or (not (forall ((z tptp.set_int)) (= (ho_25558 x z) (ho_25558 y z)))) (= x y))))) (let ((_let_3131 (forall ((x |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.num)_ tptp.option4065278094766928714it_nat tptp.option_num)|) (y |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.num)_ tptp.option4065278094766928714it_nat tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.produc7388388658123137530it_nat tptp.num)|)) (= (ho_25657 x z) (ho_25657 y z)))) (= x y))))) (let ((_let_3132 (forall ((x |u_(-> _u_(-> tptp.int tptp.code_natural)_ tptp.set_int tptp.code_natural)|) (y |u_(-> _u_(-> tptp.int tptp.code_natural)_ tptp.set_int tptp.code_natural)|)) (or (not (forall ((z |u_(-> tptp.int tptp.code_natural)|)) (= (ho_25557 x z) (ho_25557 y z)))) (= x y))))) (let ((_let_3133 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_26007 x z) (ho_26007 y z)))) (= x y))))) (let ((_let_3134 (forall ((x |u_(-> tptp.set_Code_integer tptp.code_natural)|) (y |u_(-> tptp.set_Code_integer tptp.code_natural)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_25561 x z) (ho_25561 y z)))) (= x y))))) (let ((_let_3135 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_natural)_ tptp.set_Code_integer tptp.code_natural)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_natural)_ tptp.set_Code_integer tptp.code_natural)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_natural)|)) (= (ho_25560 x z) (ho_25560 y z)))) (= x y))))) (let ((_let_3136 (forall ((x |u_(-> tptp.array_nat tptp.nat Bool)|) (y |u_(-> tptp.array_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.array_nat)) (= (ho_25566 x z) (ho_25566 y z)))) (= x y))))) (let ((_let_3137 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.set_nat tptp.set_int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.set_nat tptp.set_int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_25837 x z) (ho_25837 y z)))) (= x y))))) (let ((_let_3138 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.array_nat tptp.nat Bool)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.array_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_25564 x z) (ho_25564 y z)))) (= x y))))) (let ((_let_3139 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.set_int tptp.set_nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.set_int tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_26027 x z) (ho_26027 y z)))) (= x y))))) (let ((_let_3140 (forall ((x |u_(-> tptp.heap_T3836121109492952855ay_nat tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.array_nat tptp.nat Bool)|) (y |u_(-> tptp.heap_T3836121109492952855ay_nat tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.array_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.heap_T3836121109492952855ay_nat)) (= (ho_25563 x z) (ho_25563 y z)))) (= x y))))) (let ((_let_3141 (forall ((x |u_(-> tptp.array_o tptp.nat Bool)|) (y |u_(-> tptp.array_o tptp.nat Bool)|)) (or (not (forall ((z tptp.array_o)) (= (ho_25573 x z) (ho_25573 y z)))) (= x y))))) (let ((_let_3142 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.array_o tptp.nat Bool)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.array_o tptp.nat Bool)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_25572 x z) (ho_25572 y z)))) (= x y))))) (let ((_let_3143 (forall ((x |u_(-> tptp.array_o tptp.heap_e7401611519738050253t_unit tptp.produc5011041761010125393t_unit)|) (y |u_(-> tptp.array_o tptp.heap_e7401611519738050253t_unit tptp.produc5011041761010125393t_unit)|)) (or (not (forall ((z tptp.array_o)) (= (ho_25575 x z) (ho_25575 y z)))) (= x y))))) (let ((_let_3144 (forall ((x |u_(-> tptp.array_int tptp.nat Bool)|) (y |u_(-> tptp.array_int tptp.nat Bool)|)) (or (not (forall ((z tptp.array_int)) (= (ho_25580 x z) (ho_25580 y z)))) (= x y))))) (let ((_let_3145 (forall ((x |u_(-> tptp.set_int tptp.produc2115011035271226405et_int)|) (y |u_(-> tptp.set_int tptp.produc2115011035271226405et_int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_25611 x z) (ho_25611 y z)))) (= x y))))) (let ((_let_3146 (forall ((x |u_(-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.array_int tptp.nat Bool)|) (y |u_(-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.array_int tptp.nat Bool)|)) (or (not (forall ((z tptp.heap_e7401611519738050253t_unit)) (= (ho_25578 x z) (ho_25578 y z)))) (= x y))))) (let ((_let_3147 (forall ((x |u_(-> tptp.heap_T1346037964561226099ay_int tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.array_int tptp.nat Bool)|) (y |u_(-> tptp.heap_T1346037964561226099ay_int tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.array_int tptp.nat Bool)|)) (or (not (forall ((z tptp.heap_T1346037964561226099ay_int)) (= (ho_25577 x z) (ho_25577 y z)))) (= x y))))) (let ((_let_3148 (forall ((x |u_(-> tptp.array_int tptp.heap_e7401611519738050253t_unit tptp.produc3407818250607552075t_unit)|) (y |u_(-> tptp.array_int tptp.heap_e7401611519738050253t_unit tptp.produc3407818250607552075t_unit)|)) (or (not (forall ((z tptp.array_int)) (= (ho_25582 x z) (ho_25582 y z)))) (= x y))))) (let ((_let_3149 (forall ((x |u_(-> tptp.set_list_o Bool)|) (y |u_(-> tptp.set_list_o Bool)|)) (or (not (forall ((z tptp.set_list_o)) (= (ho_25588 x z) (ho_25588 y z)))) (= x y))))) (let ((_let_3150 (forall ((x |u_(-> tptp.set_list_int Bool)|) (y |u_(-> tptp.set_list_int Bool)|)) (or (not (forall ((z tptp.set_list_int)) (= (ho_25592 x z) (ho_25592 y z)))) (= x y))))) (let ((_let_3151 (forall ((x |u_(-> tptp.produc7819656566062154093et_nat Bool)|) (y |u_(-> tptp.produc7819656566062154093et_nat Bool)|)) (or (not (forall ((z tptp.produc7819656566062154093et_nat)) (= (ho_26144 x z) (ho_26144 y z)))) (= x y))))) (let ((_let_3152 (forall ((x |u_(-> _u_(-> tptp.set_nat tptp.set_nat Bool)_ tptp.produc7819656566062154093et_nat Bool)|) (y |u_(-> _u_(-> tptp.set_nat tptp.set_nat Bool)_ tptp.produc7819656566062154093et_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.set_nat tptp.set_nat Bool)|)) (= (ho_25596 x z) (ho_25596 y z)))) (= x y))))) (let ((_let_3153 (forall ((x |u_(-> _u_(-> tptp.produc7819656566062154093et_nat Bool)_ tptp.set_Pr5488025237498180813et_nat)|) (y |u_(-> _u_(-> tptp.produc7819656566062154093et_nat Bool)_ tptp.set_Pr5488025237498180813et_nat)|)) (or (not (forall ((z |u_(-> tptp.produc7819656566062154093et_nat Bool)|)) (= (ho_25598 x z) (ho_25598 y z)))) (= x y))))) (let ((_let_3154 (forall ((x |u_(-> tptp.set_nat tptp.produc7819656566062154093et_nat)|) (y |u_(-> tptp.set_nat tptp.produc7819656566062154093et_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_25601 x z) (ho_25601 y z)))) (= x y))))) (let ((_let_3155 (forall ((x |u_(-> tptp.set_nat tptp.set_nat tptp.produc7819656566062154093et_nat)|) (y |u_(-> tptp.set_nat tptp.set_nat tptp.produc7819656566062154093et_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_25600 x z) (ho_25600 y z)))) (= x y))))) (let ((_let_3156 (forall ((x |u_(-> tptp.produc2115011035271226405et_int Bool)|) (y |u_(-> tptp.produc2115011035271226405et_int Bool)|)) (or (not (forall ((z tptp.produc2115011035271226405et_int)) (= (ho_26143 x z) (ho_26143 y z)))) (= x y))))) (let ((_let_3157 (forall ((x |u_(-> _u_(-> tptp.set_int tptp.set_int Bool)_ tptp.produc2115011035271226405et_int Bool)|) (y |u_(-> _u_(-> tptp.set_int tptp.set_int Bool)_ tptp.produc2115011035271226405et_int Bool)|)) (or (not (forall ((z |u_(-> tptp.set_int tptp.set_int Bool)|)) (= (ho_25606 x z) (ho_25606 y z)))) (= x y))))) (let ((_let_3158 (forall ((x |u_(-> tptp.set_Pr2522554150109002629et_int Bool)|) (y |u_(-> tptp.set_Pr2522554150109002629et_int Bool)|)) (or (not (forall ((z tptp.set_Pr2522554150109002629et_int)) (= (ho_25614 x z) (ho_25614 y z)))) (= x y))))) (let ((_let_3159 (forall ((x |u_(-> tptp.produc2115011035271226405et_int tptp.set_Pr2522554150109002629et_int Bool)|) (y |u_(-> tptp.produc2115011035271226405et_int tptp.set_Pr2522554150109002629et_int Bool)|)) (or (not (forall ((z tptp.produc2115011035271226405et_int)) (= (ho_25613 x z) (ho_25613 y z)))) (= x y))))) (let ((_let_3160 (forall ((x |u_(-> tptp.produc6491284506569428743nteger Bool)|) (y |u_(-> tptp.produc6491284506569428743nteger Bool)|)) (or (not (forall ((z tptp.produc6491284506569428743nteger)) (= (ho_26142 x z) (ho_26142 y z)))) (= x y))))) (let ((_let_3161 (forall ((x |u_(-> _u_(-> tptp.set_Code_integer tptp.set_Code_integer Bool)_ tptp.produc6491284506569428743nteger Bool)|) (y |u_(-> _u_(-> tptp.set_Code_integer tptp.set_Code_integer Bool)_ tptp.produc6491284506569428743nteger Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Code_integer tptp.set_Code_integer Bool)|)) (= (ho_25616 x z) (ho_25616 y z)))) (= x y))))) (let ((_let_3162 (forall ((x |u_(-> _u_(-> tptp.produc6491284506569428743nteger Bool)_ tptp.set_Pr7577011563204128103nteger)|) (y |u_(-> _u_(-> tptp.produc6491284506569428743nteger Bool)_ tptp.set_Pr7577011563204128103nteger)|)) (or (not (forall ((z |u_(-> tptp.produc6491284506569428743nteger Bool)|)) (= (ho_25618 x z) (ho_25618 y z)))) (= x y))))) (let ((_let_3163 (forall ((x |u_(-> tptp.set_Code_integer tptp.set_Code_integer tptp.produc6491284506569428743nteger)|) (y |u_(-> tptp.set_Code_integer tptp.set_Code_integer tptp.produc6491284506569428743nteger)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_25620 x z) (ho_25620 y z)))) (= x y))))) (let ((_let_3164 (forall ((x |u_(-> tptp.produc6491284506569428743nteger tptp.set_Pr7577011563204128103nteger Bool)|) (y |u_(-> tptp.produc6491284506569428743nteger tptp.set_Pr7577011563204128103nteger Bool)|)) (or (not (forall ((z tptp.produc6491284506569428743nteger)) (= (ho_25623 x z) (ho_25623 y z)))) (= x y))))) (let ((_let_3165 (forall ((x |u_(-> tptp.set_o tptp.code_natural)|) (y |u_(-> tptp.set_o tptp.code_natural)|)) (or (not (forall ((z tptp.set_o)) (= (ho_25637 x z) (ho_25637 y z)))) (= x y))))) (let ((_let_3166 (forall ((x |u_(-> _u_(-> Bool tptp.code_natural)_ tptp.set_o tptp.code_natural)|) (y |u_(-> _u_(-> Bool tptp.code_natural)_ tptp.set_o tptp.code_natural)|)) (or (not (forall ((z |u_(-> Bool tptp.code_natural)|)) (= (ho_25636 x z) (ho_25636 y z)))) (= x y))))) (let ((_let_3167 (forall ((x |u_(-> _u_(-> tptp.num tptp.num)_ tptp.option_num tptp.option_num)|) (y |u_(-> _u_(-> tptp.num tptp.num)_ tptp.option_num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num)|)) (= (ho_25639 x z) (ho_25639 y z)))) (= x y))))) (let ((_let_3168 (forall ((x |u_(-> tptp.option_num tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.option_num tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.option_num)) (= (ho_25646 x z) (ho_25646 y z)))) (= x y))))) (let ((_let_3169 (forall ((x |u_(-> _u_(-> tptp.num tptp.produc7388388658123137530it_nat)_ tptp.option_num tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.num tptp.produc7388388658123137530it_nat)_ tptp.option_num tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.num tptp.produc7388388658123137530it_nat)|)) (= (ho_25645 x z) (ho_25645 y z)))) (= x y))))) (let ((_let_3170 (forall ((x |u_(-> tptp.num tptp.produc3260487557148687353it_nat)|) (y |u_(-> tptp.num tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z tptp.num)) (= (ho_25647 x z) (ho_25647 y z)))) (= x y))))) (let ((_let_3171 (forall ((x |u_(-> tptp.option_num tptp.option3562590408128118217it_nat)|) (y |u_(-> tptp.option_num tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z tptp.option_num)) (= (ho_25650 x z) (ho_25650 y z)))) (= x y))))) (let ((_let_3172 (forall ((x |u_(-> _u_(-> tptp.num tptp.produc3260487557148687353it_nat)_ tptp.option_num tptp.option3562590408128118217it_nat)|) (y |u_(-> _u_(-> tptp.num tptp.produc3260487557148687353it_nat)_ tptp.option_num tptp.option3562590408128118217it_nat)|)) (or (not (forall ((z |u_(-> tptp.num tptp.produc3260487557148687353it_nat)|)) (= (ho_25649 x z) (ho_25649 y z)))) (= x y))))) (let ((_let_3173 (forall ((x |u_(-> tptp.num tptp.produc8664842809031399944it_nat)|) (y |u_(-> tptp.num tptp.produc8664842809031399944it_nat)|)) (or (not (forall ((z tptp.num)) (= (ho_25651 x z) (ho_25651 y z)))) (= x y))))) (let ((_let_3174 (forall ((x |u_(-> tptp.option_num tptp.option8956607266484857688it_nat)|) (y |u_(-> tptp.option_num tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z tptp.option_num)) (= (ho_25654 x z) (ho_25654 y z)))) (= x y))))) (let ((_let_3175 (forall ((x |u_(-> _u_(-> tptp.num tptp.produc8664842809031399944it_nat)_ tptp.option_num tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.num tptp.produc8664842809031399944it_nat)_ tptp.option_num tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.num tptp.produc8664842809031399944it_nat)|)) (= (ho_25653 x z) (ho_25653 y z)))) (= x y))))) (let ((_let_3176 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.num)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.num)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_25655 x z) (ho_25655 y z)))) (= x y))))) (let ((_let_3177 (forall ((x |u_(-> tptp.option4065278094766928714it_nat tptp.option_num)|) (y |u_(-> tptp.option4065278094766928714it_nat tptp.option_num)|)) (or (not (forall ((z tptp.option4065278094766928714it_nat)) (= (ho_25658 x z) (ho_25658 y z)))) (= x y))))) (let ((_let_3178 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.num)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.num)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_25659 x z) (ho_25659 y z)))) (= x y))))) (let ((_let_3179 (forall ((x |u_(-> tptp.option3562590408128118217it_nat tptp.option_num)|) (y |u_(-> tptp.option3562590408128118217it_nat tptp.option_num)|)) (or (not (forall ((z tptp.option3562590408128118217it_nat)) (= (ho_25662 x z) (ho_25662 y z)))) (= x y))))) (let ((_let_3180 (forall ((x |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.num)_ tptp.option3562590408128118217it_nat tptp.option_num)|) (y |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.num)_ tptp.option3562590408128118217it_nat tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.produc3260487557148687353it_nat tptp.num)|)) (= (ho_25661 x z) (ho_25661 y z)))) (= x y))))) (let ((_let_3181 (forall ((x |u_(-> tptp.produc8664842809031399944it_nat tptp.num)|) (y |u_(-> tptp.produc8664842809031399944it_nat tptp.num)|)) (or (not (forall ((z tptp.produc8664842809031399944it_nat)) (= (ho_25663 x z) (ho_25663 y z)))) (= x y))))) (let ((_let_3182 (forall ((x |u_(-> tptp.option8956607266484857688it_nat tptp.option_num)|) (y |u_(-> tptp.option8956607266484857688it_nat tptp.option_num)|)) (or (not (forall ((z tptp.option8956607266484857688it_nat)) (= (ho_25666 x z) (ho_25666 y z)))) (= x y))))) (let ((_let_3183 (forall ((x |u_(-> _u_(-> tptp.produc8664842809031399944it_nat tptp.num)_ tptp.option8956607266484857688it_nat tptp.option_num)|) (y |u_(-> _u_(-> tptp.produc8664842809031399944it_nat tptp.num)_ tptp.option8956607266484857688it_nat tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.produc8664842809031399944it_nat tptp.num)|)) (= (ho_25665 x z) (ho_25665 y z)))) (= x y))))) (let ((_let_3184 (forall ((x |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)_ tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)_ tptp.option4065278094766928714it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc7388388658123137530it_nat tptp.produc7388388658123137530it_nat)|)) (= (ho_25668 x z) (ho_25668 y z)))) (= x y))))) (let ((_let_3185 (forall ((x |u_(-> tptp.produc3260487557148687353it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> tptp.produc3260487557148687353it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z tptp.produc3260487557148687353it_nat)) (= (ho_25669 x z) (ho_25669 y z)))) (= x y))))) (let ((_let_3186 (forall ((x |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.produc7388388658123137530it_nat)_ tptp.option3562590408128118217it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> _u_(-> tptp.produc3260487557148687353it_nat tptp.produc7388388658123137530it_nat)_ tptp.option3562590408128118217it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc3260487557148687353it_nat tptp.produc7388388658123137530it_nat)|)) (= (ho_25671 x z) (ho_25671 y z)))) (= x y))))) (let ((_let_3187 (forall ((x |u_(-> tptp.produc8664842809031399944it_nat tptp.produc7388388658123137530it_nat)|) (y |u_(-> tptp.produc8664842809031399944it_nat tptp.produc7388388658123137530it_nat)|)) (or (not (forall ((z tptp.produc8664842809031399944it_nat)) (= (ho_25672 x z) (ho_25672 y z)))) (= x y))))) (let ((_let_3188 (forall ((x |u_(-> tptp.option8956607266484857688it_nat tptp.option4065278094766928714it_nat)|) (y |u_(-> tptp.option8956607266484857688it_nat tptp.option4065278094766928714it_nat)|)) (or (not (forall ((z tptp.option8956607266484857688it_nat)) (= (ho_25675 x z) (ho_25675 y z)))) (= x y))))) (let ((_let_3189 (forall ((x |u_(-> tptp.option_Code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.option_Code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.option_Code_integer)) (= (ho_25681 x z) (ho_25681 y z)))) (= x y))))) (let ((_let_3190 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.option_Code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.option_Code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (= (ho_25680 x z) (ho_25680 y z)))) (= x y))))) (let ((_let_3191 (forall ((x |u_(-> tptp.option_Code_integer tptp.option_Code_integer)|) (y |u_(-> tptp.option_Code_integer tptp.option_Code_integer)|)) (or (not (forall ((z tptp.option_Code_integer)) (= (ho_25684 x z) (ho_25684 y z)))) (= x y))))) (let ((_let_3192 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.option_Code_integer tptp.option_Code_integer)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.option_Code_integer tptp.option_Code_integer)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer)|)) (= (ho_25683 x z) (ho_25683 y z)))) (= x y))))) (let ((_let_3193 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)_ tptp.option_Code_integer tptp.option8057788054806935849nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)_ tptp.option_Code_integer tptp.option8057788054806935849nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer tptp.code_integer)|)) (= (ho_25686 x z) (ho_25686 y z)))) (= x y))))) (let ((_let_3194 (forall ((x |u_(-> tptp.option8057788054806935849nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.option8057788054806935849nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.option8057788054806935849nteger)) (= (ho_25691 x z) (ho_25691 y z)))) (= x y))))) (let ((_let_3195 (forall ((x |u_(-> _u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.option8057788054806935849nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> _u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.option8057788054806935849nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (= (ho_25689 x z) (ho_25689 y z)))) (= x y))))) (let ((_let_3196 (forall ((x |u_(-> tptp.option_int tptp.nat)|) (y |u_(-> tptp.option_int tptp.nat)|)) (or (not (forall ((z tptp.option_int)) (= (ho_25695 x z) (ho_25695 y z)))) (= x y))))) (let ((_let_3197 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.option_int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.option_int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_25694 x z) (ho_25694 y z)))) (= x y))))) (let ((_let_3198 (forall ((x |u_(-> tptp.nat _u_(-> tptp.int tptp.nat)_ tptp.option_int tptp.nat)|) (y |u_(-> tptp.nat _u_(-> tptp.int tptp.nat)_ tptp.option_int tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_25693 x z) (ho_25693 y z)))) (= x y))))) (let ((_let_3199 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.option_int tptp.option_int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.option_int tptp.option_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_25697 x z) (ho_25697 y z)))) (= x y))))) (let ((_let_3200 (forall ((x |u_(-> tptp.produc7388388658123137530it_nat tptp.produc3260487557148687353it_nat)|) (y |u_(-> tptp.produc7388388658123137530it_nat tptp.produc3260487557148687353it_nat)|)) (or (not (forall ((z tptp.produc7388388658123137530it_nat)) (= (ho_25709 x z) (ho_25709 y z)))) (= x y))))) (let ((_let_3201 (forall ((x |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.produc8664842809031399944it_nat)_ tptp.option4065278094766928714it_nat tptp.option8956607266484857688it_nat)|) (y |u_(-> _u_(-> tptp.produc7388388658123137530it_nat tptp.produc8664842809031399944it_nat)_ tptp.option4065278094766928714it_nat tptp.option8956607266484857688it_nat)|)) (or (not (forall ((z |u_(-> tptp.produc7388388658123137530it_nat tptp.produc8664842809031399944it_nat)|)) (= (ho_25714 x z) (ho_25714 y z)))) (= x y))))) (let ((_let_3202 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.option_Code_integer tptp.option7428179582072448501nteger)|) (y |u_(-> _u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.option_Code_integer tptp.option7428179582072448501nteger)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (= (ho_25716 x z) (ho_25716 y z)))) (= x y))))) (let ((_let_3203 (forall ((x |u_(-> _u_(-> tptp.option_Code_integer tptp.option7428179582072448501nteger)_ _u_(-> tptp.option_Code_integer tptp.option_Code_integer)_ tptp.option_Code_integer tptp.option7428179582072448501nteger)|) (y |u_(-> _u_(-> tptp.option_Code_integer tptp.option7428179582072448501nteger)_ _u_(-> tptp.option_Code_integer tptp.option_Code_integer)_ tptp.option_Code_integer tptp.option7428179582072448501nteger)|)) (or (not (forall ((z |u_(-> tptp.option_Code_integer tptp.option7428179582072448501nteger)|)) (= (ho_25718 x z) (ho_25718 y z)))) (= x y))))) (let ((_let_3204 (forall ((x |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.option8057788054806935849nteger tptp.option7428179582072448501nteger)|) (y |u_(-> _u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)_ tptp.option8057788054806935849nteger tptp.option7428179582072448501nteger)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (= (ho_25721 x z) (ho_25721 y z)))) (= x y))))) (let ((_let_3205 (forall ((x |u_(-> _u_(-> tptp.option8057788054806935849nteger tptp.option7428179582072448501nteger)_ _u_(-> tptp.option_Code_integer tptp.option8057788054806935849nteger)_ tptp.option_Code_integer tptp.option7428179582072448501nteger)|) (y |u_(-> _u_(-> tptp.option8057788054806935849nteger tptp.option7428179582072448501nteger)_ _u_(-> tptp.option_Code_integer tptp.option8057788054806935849nteger)_ tptp.option_Code_integer tptp.option7428179582072448501nteger)|)) (or (not (forall ((z |u_(-> tptp.option8057788054806935849nteger tptp.option7428179582072448501nteger)|)) (= (ho_25723 x z) (ho_25723 y z)))) (= x y))))) (let ((_let_3206 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.option_int tptp.option_nat)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ tptp.option_int tptp.option_nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_25726 x z) (ho_25726 y z)))) (= x y))))) (let ((_let_3207 (forall ((x |u_(-> _u_(-> tptp.option_int tptp.option_int)_ tptp.option_int tptp.option_nat)|) (y |u_(-> _u_(-> tptp.option_int tptp.option_int)_ tptp.option_int tptp.option_nat)|)) (or (not (forall ((z |u_(-> tptp.option_int tptp.option_int)|)) (= (ho_25729 x z) (ho_25729 y z)))) (= x y))))) (let ((_let_3208 (forall ((x |u_(-> _u_(-> tptp.option_int tptp.option_nat)_ _u_(-> tptp.option_int tptp.option_int)_ tptp.option_int tptp.option_nat)|) (y |u_(-> _u_(-> tptp.option_int tptp.option_nat)_ _u_(-> tptp.option_int tptp.option_int)_ tptp.option_int tptp.option_nat)|)) (or (not (forall ((z |u_(-> tptp.option_int tptp.option_nat)|)) (= (ho_25728 x z) (ho_25728 y z)))) (= x y))))) (let ((_let_3209 (forall ((x |u_(-> _u_(-> tptp.option_num tptp.option_num)_ _u_(-> tptp.option_num tptp.option_num)_ tptp.option_num tptp.option_num)|) (y |u_(-> _u_(-> tptp.option_num tptp.option_num)_ _u_(-> tptp.option_num tptp.option_num)_ tptp.option_num tptp.option_num)|)) (or (not (forall ((z |u_(-> tptp.option_num tptp.option_num)|)) (= (ho_25731 x z) (ho_25731 y z)))) (= x y))))) (let ((_let_3210 (forall ((x |u_(-> tptp.set_set_list_nat tptp.nat)|) (y |u_(-> tptp.set_set_list_nat tptp.nat)|)) (or (not (forall ((z tptp.set_set_list_nat)) (= (ho_25740 x z) (ho_25740 y z)))) (= x y))))) (let ((_let_3211 (forall ((x |u_(-> tptp.set_set_set_nat tptp.nat)|) (y |u_(-> tptp.set_set_set_nat tptp.nat)|)) (or (not (forall ((z tptp.set_set_set_nat)) (= (ho_25744 x z) (ho_25744 y z)))) (= x y))))) (let ((_let_3212 (forall ((x |u_(-> tptp.set_set_Code_integer tptp.nat)|) (y |u_(-> tptp.set_set_Code_integer tptp.nat)|)) (or (not (forall ((z tptp.set_set_Code_integer)) (= (ho_25746 x z) (ho_25746 y z)))) (= x y))))) (let ((_let_3213 (forall ((x |u_(-> tptp.set_se7855581050983116737at_nat tptp.nat)|) (y |u_(-> tptp.set_se7855581050983116737at_nat tptp.nat)|)) (or (not (forall ((z tptp.set_se7855581050983116737at_nat)) (= (ho_25748 x z) (ho_25748 y z)))) (= x y))))) (let ((_let_3214 (forall ((x |u_(-> _u_(-> tptp.option_int tptp.nat)_ _u_(-> tptp.option_int tptp.option_int)_ tptp.option_int tptp.nat)|) (y |u_(-> _u_(-> tptp.option_int tptp.nat)_ _u_(-> tptp.option_int tptp.option_int)_ tptp.option_int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.option_int tptp.nat)|)) (= (ho_25754 x z) (ho_25754 y z)))) (= x y))))) (let ((_let_3215 (forall ((x |u_(-> _u_(-> tptp.option_num tptp.nat)_ _u_(-> tptp.option_num tptp.option_num)_ tptp.option_num tptp.nat)|) (y |u_(-> _u_(-> tptp.option_num tptp.nat)_ _u_(-> tptp.option_num tptp.option_num)_ tptp.option_num tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.option_num tptp.nat)|)) (= (ho_25760 x z) (ho_25760 y z)))) (= x y))))) (let ((_let_3216 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_25769 x z) (ho_25769 y z)))) (= x y))))) (let ((_let_3217 (forall ((x |u_(-> _u_(-> tptp.num tptp.num Bool)_ _u_(-> tptp.num tptp.num Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num Bool)_ _u_(-> tptp.num tptp.num Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num Bool)|)) (= (ho_25772 x z) (ho_25772 y z)))) (= x y))))) (let ((_let_3218 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.code_integer)|) (y |u_(-> tptp.product_prod_nat_nat tptp.code_integer)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_25774 x z) (ho_25774 y z)))) (= x y))))) (let ((_let_3219 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_25781 x z) (ho_25781 y z)))) (= x y))))) (let ((_let_3220 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_25778 x z) (ho_25778 y z)))) (= x y))))) (let ((_let_3221 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.multis2468970476368604999at_nat)_ tptp.set_Pr1261947904930325089at_nat tptp.multis2468970476368604999at_nat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.multis2468970476368604999at_nat)_ tptp.set_Pr1261947904930325089at_nat tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.multis2468970476368604999at_nat)|)) (= (ho_25780 x z) (ho_25780 y z)))) (= x y))))) (let ((_let_3222 (forall ((x |u_(-> tptp.int tptp.multis2468970476368604999at_nat)|) (y |u_(-> tptp.int tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z tptp.int)) (= (ho_25784 x z) (ho_25784 y z)))) (= x y))))) (let ((_let_3223 (forall ((x |u_(-> _u_(-> tptp.int tptp.multis2468970476368604999at_nat)_ tptp.set_int tptp.multis2468970476368604999at_nat)|) (y |u_(-> _u_(-> tptp.int tptp.multis2468970476368604999at_nat)_ tptp.set_int tptp.multis2468970476368604999at_nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.multis2468970476368604999at_nat)|)) (= (ho_25786 x z) (ho_25786 y z)))) (= x y))))) (let ((_let_3224 (forall ((x |u_(-> tptp.num tptp.num tptp.product_prod_num_num)|) (y |u_(-> tptp.num tptp.num tptp.product_prod_num_num)|)) (or (not (forall ((z tptp.num)) (= (ho_25789 x z) (ho_25789 y z)))) (= x y))))) (let ((_let_3225 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_25798 x z) (ho_25798 y z)))) (= x y))))) (let ((_let_3226 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_25810 x z) (ho_25810 y z)))) (= x y))))) (let ((_let_3227 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int)|)) (= (ho_25809 x z) (ho_25809 y z)))) (= x y))))) (let ((_let_3228 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_nat_nat)|)) (= (ho_25808 x z) (ho_25808 y z)))) (= x y))))) (let ((_let_3229 (forall ((x |u_(-> tptp.produc5835291356934675326atural tptp.code_natural)|) (y |u_(-> tptp.produc5835291356934675326atural tptp.code_natural)|)) (or (not (forall ((z tptp.produc5835291356934675326atural)) (= (ho_25812 x z) (ho_25812 y z)))) (= x y))))) (let ((_let_3230 (forall ((x |u_(-> tptp.nat tptp.nat tptp.product_prod_int_int)|) (y |u_(-> tptp.nat tptp.nat tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_25814 x z) (ho_25814 y z)))) (= x y))))) (let ((_let_3231 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ tptp.int tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_nat_nat)|)) (= (ho_25816 x z) (ho_25816 y z)))) (= x y))))) (let ((_let_3232 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ tptp.list_int tptp.list_int)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ tptp.list_int tptp.list_int)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_25823 x z) (ho_25823 y z)))) (= x y))))) (let ((_let_3233 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.set_Code_integer tptp.set_Code_integer)|) (y |u_(-> _u_(-> tptp.code_integer tptp.code_integer)_ tptp.set_Code_integer tptp.set_Code_integer)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.code_integer)|)) (= (ho_25832 x z) (ho_25832 y z)))) (= x y))))) (let ((_let_3234 (forall ((x |u_(-> tptp.set_nat tptp.set_Code_integer)|) (y |u_(-> tptp.set_nat tptp.set_Code_integer)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_25835 x z) (ho_25835 y z)))) (= x y))))) (let ((_let_3235 (forall ((x |u_(-> tptp.set_nat tptp.set_int)|) (y |u_(-> tptp.set_nat tptp.set_int)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_25838 x z) (ho_25838 y z)))) (= x y))))) (let ((_let_3236 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_25840 x z) (ho_25840 y z)))) (= x y))))) (let ((_let_3237 (forall ((x |u_(-> _u_(-> tptp.nat tptp.set_nat)_ tptp.set_nat tptp.set_set_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.set_nat)_ tptp.set_nat tptp.set_set_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.set_nat)|)) (= (ho_25844 x z) (ho_25844 y z)))) (= x y))))) (let ((_let_3238 (forall ((x |u_(-> tptp.produc3658429121746597890et_nat tptp.heap_e7401611519738050253t_unit)|) (y |u_(-> tptp.produc3658429121746597890et_nat tptp.heap_e7401611519738050253t_unit)|)) (or (not (forall ((z tptp.produc3658429121746597890et_nat)) (= (ho_25850 x z) (ho_25850 y z)))) (= x y))))) (let ((_let_3239 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_25856 x z) (ho_25856 y z)))) (= x y))))) (let ((_let_3240 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_25862 x z) (ho_25862 y z)))) (= x y))))) (let ((_let_3241 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_25864 x z) (ho_25864 y z)))) (= x y))))) (let ((_let_3242 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.int)|)) (= (ho_25873 x z) (ho_25873 y z)))) (= x y))))) (let ((_let_3243 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_25890 x z) (ho_25890 y z)))) (= x y))))) (let ((_let_3244 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_25868 x z) (ho_25868 y z)))) (= x y))))) (let ((_let_3245 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_25867 x z) (ho_25867 y z)))) (= x y))))) (let ((_let_3246 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.int)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.int)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (= (ho_25871 x z) (ho_25871 y z)))) (= x y))))) (let ((_let_3247 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_25881 x z) (ho_25881 y z)))) (= x y))))) (let ((_let_3248 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_25880 x z) (ho_25880 y z)))) (= x y))))) (let ((_let_3249 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_26141 x z) (ho_26141 y z)))) (= x y))))) (let ((_let_3250 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_25876 x z) (ho_25876 y z)))) (= x y))))) (let ((_let_3251 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_25875 x z) (ho_25875 y z)))) (= x y))))) (let ((_let_3252 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)|)) (= (ho_25879 x z) (ho_25879 y z)))) (= x y))))) (let ((_let_3253 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat)_ Bool)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_25878 x z) (ho_25878 y z)))) (= x y))))) (let ((_let_3254 (forall ((x |u_(-> _u_(-> tptp.num tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num tptp.int)|)) (= (ho_25889 x z) (ho_25889 y z)))) (= x y))))) (let ((_let_3255 (forall ((x |u_(-> _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num tptp.int)|)) (= (ho_25888 x z) (ho_25888 y z)))) (= x y))))) (let ((_let_3256 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_25884 x z) (ho_25884 y z)))) (= x y))))) (let ((_let_3257 (forall ((x |u_(-> _u_(-> tptp.num tptp.num Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num Bool)|)) (= (ho_25883 x z) (ho_25883 y z)))) (= x y))))) (let ((_let_3258 (forall ((x |u_(-> _u_(-> tptp.num tptp.num Bool)_ _u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)_ _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num Bool)_ _u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)_ _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num Bool)|)) (= (ho_25886 x z) (ho_25886 y z)))) (= x y))))) (let ((_let_3259 (forall ((x |u_(-> _u_(-> tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int)|)) (= (ho_25891 x z) (ho_25891 y z)))) (= x y))))) (let ((_let_3260 (forall ((x |u_(-> _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.rat tptp.rat)|)) (= (ho_25902 x z) (ho_25902 y z)))) (= x y))))) (let ((_let_3261 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_25901 x z) (ho_25901 y z)))) (= x y))))) (let ((_let_3262 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_25911 x z) (ho_25911 y z)))) (= x y))))) (let ((_let_3263 (forall ((x |u_(-> tptp.product_prod_int_int tptp.rat Bool)|) (y |u_(-> tptp.product_prod_int_int tptp.rat Bool)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_25894 x z) (ho_25894 y z)))) (= x y))))) (let ((_let_3264 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)|)) (= (ho_25900 x z) (ho_25900 y z)))) (= x y))))) (let ((_let_3265 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.rat tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.rat Bool)|)) (= (ho_25899 x z) (ho_25899 y z)))) (= x y))))) (let ((_let_3266 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (= (ho_25909 x z) (ho_25909 y z)))) (= x y))))) (let ((_let_3267 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_int_int)|)) (= (ho_26140 x z) (ho_26140 y z)))) (= x y))))) (let ((_let_3268 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.rat Bool)|)) (= (ho_25905 x z) (ho_25905 y z)))) (= x y))))) (let ((_let_3269 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.product_prod_int_int tptp.rat Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_25904 x z) (ho_25904 y z)))) (= x y))))) (let ((_let_3270 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.rat)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_25907 x z) (ho_25907 y z)))) (= x y))))) (let ((_let_3271 (forall ((x |u_(-> _u_(-> tptp.rat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> tptp.rat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.rat)|)) (= (ho_25912 x z) (ho_25912 y z)))) (= x y))))) (let ((_let_3272 (forall ((x |u_(-> _u_(-> tptp.rat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.rat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.rat Bool)|)) (= (ho_25917 x z) (ho_25917 y z)))) (= x y))))) (let ((_let_3273 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.rat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.rat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_25916 x z) (ho_25916 y z)))) (= x y))))) (let ((_let_3274 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.rat Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.rat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_25915 x z) (ho_25915 y z)))) (= x y))))) (let ((_let_3275 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_25926 x z) (ho_25926 y z)))) (= x y))))) (let ((_let_3276 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_25937 x z) (ho_25937 y z)))) (= x y))))) (let ((_let_3277 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|) (y |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_25919 x z) (ho_25919 y z)))) (= x y))))) (let ((_let_3278 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (= (ho_25922 x z) (ho_25922 y z)))) (= x y))))) (let ((_let_3279 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (= (ho_25921 x z) (ho_25921 y z)))) (= x y))))) (let ((_let_3280 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)|)) (= (ho_25925 x z) (ho_25925 y z)))) (= x y))))) (let ((_let_3281 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.int tptp.int tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (= (ho_25924 x z) (ho_25924 y z)))) (= x y))))) (let ((_let_3282 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.int tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.int tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_25929 x z) (ho_25929 y z)))) (= x y))))) (let ((_let_3283 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.int tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.int tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (= (ho_25928 x z) (ho_25928 y z)))) (= x y))))) (let ((_let_3284 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_25936 x z) (ho_25936 y z)))) (= x y))))) (let ((_let_3285 (forall ((x |u_(-> _u_(-> tptp.nat tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.product_prod_nat_nat)|)) (= (ho_25935 x z) (ho_25935 y z)))) (= x y))))) (let ((_let_3286 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.nat tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.nat tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_25933 x z) (ho_25933 y z)))) (= x y))))) (let ((_let_3287 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_25944 x z) (ho_25944 y z)))) (= x y))))) (let ((_let_3288 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_26139 x z) (ho_26139 y z)))) (= x y))))) (let ((_let_3289 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_25940 x z) (ho_25940 y z)))) (= x y))))) (let ((_let_3290 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (= (ho_25939 x z) (ho_25939 y z)))) (= x y))))) (let ((_let_3291 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (= (ho_25943 x z) (ho_25943 y z)))) (= x y))))) (let ((_let_3292 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (= (ho_25942 x z) (ho_25942 y z)))) (= x y))))) (let ((_let_3293 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|)) (= (ho_25954 x z) (ho_25954 y z)))) (= x y))))) (let ((_let_3294 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_25947 x z) (ho_25947 y z)))) (= x y))))) (let ((_let_3295 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ Bool)|)) (= (ho_25951 x z) (ho_25951 y z)))) (= x y))))) (let ((_let_3296 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (= (ho_25958 x z) (ho_25958 y z)))) (= x y))))) (let ((_let_3297 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_25956 x z) (ho_25956 y z)))) (= x y))))) (let ((_let_3298 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_25961 x z) (ho_25961 y z)))) (= x y))))) (let ((_let_3299 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_25964 x z) (ho_25964 y z)))) (= x y))))) (let ((_let_3300 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_25967 x z) (ho_25967 y z)))) (= x y))))) (let ((_let_3301 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_26138 x z) (ho_26138 y z)))) (= x y))))) (let ((_let_3302 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_nat_nat)|)) (= (ho_25970 x z) (ho_25970 y z)))) (= x y))))) (let ((_let_3303 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_nat_nat)|)) (= (ho_25973 x z) (ho_25973 y z)))) (= x y))))) (let ((_let_3304 (forall ((x |u_(-> _u_(-> tptp.rat tptp.product_prod_int_int)_ _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ tptp.rat Bool)|) (y |u_(-> _u_(-> tptp.rat tptp.product_prod_int_int)_ _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ tptp.rat Bool)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.product_prod_int_int)|)) (= (ho_25981 x z) (ho_25981 y z)))) (= x y))))) (let ((_let_3305 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.code_integer tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.code_integer tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_25990 x z) (ho_25990 y z)))) (= x y))))) (let ((_let_3306 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_26137 x z) (ho_26137 y z)))) (= x y))))) (let ((_let_3307 (forall ((x |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.int Bool)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.int Bool)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_25986 x z) (ho_25986 y z)))) (= x y))))) (let ((_let_3308 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int)_ _u_(-> Bool Bool)_ _u_(-> tptp.int Bool)_ tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int)_ _u_(-> Bool Bool)_ _u_(-> tptp.int Bool)_ tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int)|)) (= (ho_25985 x z) (ho_25985 y z)))) (= x y))))) (let ((_let_3309 (forall ((x |u_(-> _u_(-> tptp.code_integer tptp.int)_ _u_(-> _u_(-> tptp.int Bool)_ tptp.code_integer Bool)_ _u_(-> tptp.int tptp.int Bool)_ tptp.code_integer tptp.code_integer Bool)|) (y |u_(-> _u_(-> tptp.code_integer tptp.int)_ _u_(-> _u_(-> tptp.int Bool)_ tptp.code_integer Bool)_ _u_(-> tptp.int tptp.int Bool)_ tptp.code_integer tptp.code_integer Bool)|)) (or (not (forall ((z |u_(-> tptp.code_integer tptp.int)|)) (= (ho_25988 x z) (ho_25988 y z)))) (= x y))))) (let ((_let_3310 (forall ((x |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (= (ho_25997 x z) (ho_25997 y z)))) (= x y))))) (let ((_let_3311 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_int_int)|)) (= (ho_26136 x z) (ho_26136 y z)))) (= x y))))) (let ((_let_3312 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_25993 x z) (ho_25993 y z)))) (= x y))))) (let ((_let_3313 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)|)) (= (ho_25996 x z) (ho_25996 y z)))) (= x y))))) (let ((_let_3314 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ _u_(-> tptp.int tptp.int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_25995 x z) (ho_25995 y z)))) (= x y))))) (let ((_let_3315 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_26006 x z) (ho_26006 y z)))) (= x y))))) (let ((_let_3316 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_26008 x z) (ho_26008 y z)))) (= x y))))) (let ((_let_3317 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_26002 x z) (ho_26002 y z)))) (= x y))))) (let ((_let_3318 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_26001 x z) (ho_26001 y z)))) (= x y))))) (let ((_let_3319 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_26004 x z) (ho_26004 y z)))) (= x y))))) (let ((_let_3320 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int)|)) (= (ho_26009 x z) (ho_26009 y z)))) (= x y))))) (let ((_let_3321 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ _u_(-> tptp.product_prod_int_int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)|)) (= (ho_26011 x z) (ho_26011 y z)))) (= x y))))) (let ((_let_3322 (forall ((x |u_(-> tptp.num tptp.num tptp.code_integer)|) (y |u_(-> tptp.num tptp.num tptp.code_integer)|)) (or (not (forall ((z tptp.num)) (= (ho_26021 x z) (ho_26021 y z)))) (= x y))))) (let ((_let_3323 (forall ((x |u_(-> _u_(-> tptp.num tptp.num tptp.int)_ tptp.num tptp.num tptp.code_integer)|) (y |u_(-> _u_(-> tptp.num tptp.num tptp.int)_ tptp.num tptp.num tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num tptp.int)|)) (= (ho_26020 x z) (ho_26020 y z)))) (= x y))))) (let ((_let_3324 (forall ((x |u_(-> _u_(-> tptp.num tptp.int)_ tptp.num tptp.code_integer)|) (y |u_(-> _u_(-> tptp.num tptp.int)_ tptp.num tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.num tptp.int)|)) (= (ho_26135 x z) (ho_26135 y z)))) (= x y))))) (let ((_let_3325 (forall ((x |u_(-> _u_(-> _u_(-> tptp.num tptp.int)_ tptp.num tptp.code_integer)_ _u_(-> tptp.num tptp.num tptp.int)_ tptp.num tptp.num tptp.code_integer)|) (y |u_(-> _u_(-> _u_(-> tptp.num tptp.int)_ tptp.num tptp.code_integer)_ _u_(-> tptp.num tptp.num tptp.int)_ tptp.num tptp.num tptp.code_integer)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.num tptp.int)_ tptp.num tptp.code_integer)|)) (= (ho_26019 x z) (ho_26019 y z)))) (= x y))))) (let ((_let_3326 (forall ((x |u_(-> _u_(-> tptp.num tptp.num)_ _u_(-> _u_(-> tptp.num tptp.int)_ tptp.num tptp.code_integer)_ _u_(-> tptp.num tptp.num tptp.int)_ tptp.num tptp.num tptp.code_integer)|) (y |u_(-> _u_(-> tptp.num tptp.num)_ _u_(-> _u_(-> tptp.num tptp.int)_ tptp.num tptp.code_integer)_ _u_(-> tptp.num tptp.num tptp.int)_ tptp.num tptp.num tptp.code_integer)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num)|)) (= (ho_26018 x z) (ho_26018 y z)))) (= x y))))) (let ((_let_3327 (forall ((x |u_(-> tptp.set_int tptp.set_nat)|) (y |u_(-> tptp.set_int tptp.set_nat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_26028 x z) (ho_26028 y z)))) (= x y))))) (let ((_let_3328 (forall ((x |u_(-> _u_(-> tptp.nat tptp.set_nat)_ tptp.filter_set_nat tptp.filter_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.set_nat)_ tptp.filter_set_nat tptp.filter_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.set_nat)|)) (= (ho_26038 x z) (ho_26038 y z)))) (= x y))))) (let ((_let_3329 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_26042 x z) (ho_26042 y z)))) (= x y))))) (let ((_let_3330 (forall ((x |u_(-> _u_(-> tptp.product_unit Bool)_ _u_(-> Bool tptp.product_unit)_ tptp.set_o Bool)|) (y |u_(-> _u_(-> tptp.product_unit Bool)_ _u_(-> Bool tptp.product_unit)_ tptp.set_o Bool)|)) (or (not (forall ((z |u_(-> tptp.product_unit Bool)|)) (= (ho_26046 x z) (ho_26046 y z)))) (= x y))))) (let ((_let_3331 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.code_natural tptp.code_natural Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.code_natural tptp.code_natural Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_26054 x z) (ho_26054 y z)))) (= x y))))) (let ((_let_3332 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.code_natural Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.code_natural Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_26134 x z) (ho_26134 y z)))) (= x y))))) (let ((_let_3333 (forall ((x |u_(-> _u_(-> tptp.code_natural tptp.nat)_ _u_(-> Bool Bool)_ _u_(-> tptp.nat Bool)_ tptp.code_natural Bool)|) (y |u_(-> _u_(-> tptp.code_natural tptp.nat)_ _u_(-> Bool Bool)_ _u_(-> tptp.nat Bool)_ tptp.code_natural Bool)|)) (or (not (forall ((z |u_(-> tptp.code_natural tptp.nat)|)) (= (ho_26049 x z) (ho_26049 y z)))) (= x y))))) (let ((_let_3334 (forall ((x |u_(-> _u_(-> tptp.code_natural tptp.nat)_ _u_(-> _u_(-> tptp.nat Bool)_ tptp.code_natural Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ tptp.code_natural tptp.code_natural Bool)|) (y |u_(-> _u_(-> tptp.code_natural tptp.nat)_ _u_(-> _u_(-> tptp.nat Bool)_ tptp.code_natural Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ tptp.code_natural tptp.code_natural Bool)|)) (or (not (forall ((z |u_(-> tptp.code_natural tptp.nat)|)) (= (ho_26052 x z) (ho_26052 y z)))) (= x y))))) (let ((_let_3335 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.filter_nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.filter_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_26056 x z) (ho_26056 y z)))) (= x y))))) (let ((_let_3336 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr8693737435421807431at_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr8693737435421807431at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_26061 x z) (ho_26061 y z)))) (= x y))))) (let ((_let_3337 (forall ((x |u_(-> tptp.produc1319942482725812455at_nat Bool)|) (y |u_(-> tptp.produc1319942482725812455at_nat Bool)|)) (or (not (forall ((z tptp.produc1319942482725812455at_nat)) (= (ho_26068 x z) (ho_26068 y z)))) (= x y))))) (let ((_let_3338 (forall ((x |u_(-> tptp.multis2468970476368604999at_nat tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.multis2468970476368604999at_nat tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.multis2468970476368604999at_nat)) (= (ho_26070 x z) (ho_26070 y z)))) (= x y))))) (let ((_let_3339 (forall ((x |u_(-> tptp.set_nat tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_26072 x z) (ho_26072 y z)))) (= x y))))) (let ((_let_3340 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.filter1242075044329608583at_nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.filter1242075044329608583at_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_26086 x z) (ho_26086 y z)))) (= x y))))) (let ((_let_3341 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.list_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.list_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_26091 x z) (ho_26091 y z)))) (= x y))))) (let ((_let_3342 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.list_nat)_ tptp.product_prod_nat_nat tptp.list_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.list_nat)_ tptp.product_prod_nat_nat tptp.list_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.list_nat)|)) (= (ho_26090 x z) (ho_26090 y z)))) (= x y))))) (let ((_let_3343 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (= (ho_26100 x z) (ho_26100 y z)))) (= x y))))) (let ((_let_3344 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_26097 x z) (ho_26097 y z)))) (= x y))))) (let ((_let_3345 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_26096 x z) (ho_26096 y z)))) (= x y))))) (let ((_let_3346 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)_ _u_(-> tptp.product_prod_nat_nat tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_26099 x z) (ho_26099 y z)))) (= x y))))) (let ((_let_3347 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_26105 x z) (ho_26105 y z)))) (= x y))))) (let ((_let_3348 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_26107 x z) (ho_26107 y z)))) (= x y))))) (let ((_let_3349 (forall ((x |u_(-> tptp.set_Pr958786334691620121nt_int tptp.rat)|) (y |u_(-> tptp.set_Pr958786334691620121nt_int tptp.rat)|)) (or (not (forall ((z tptp.set_Pr958786334691620121nt_int)) (= (ho_26110 x z) (ho_26110 y z)))) (= x y))))) (let ((_let_3350 (forall ((x |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int tptp.rat)_ tptp.set_se6260736226359567993nt_int Bool)|) (y |u_(-> _u_(-> tptp.set_Pr958786334691620121nt_int tptp.rat)_ tptp.set_se6260736226359567993nt_int Bool)|)) (or (not (forall ((z |u_(-> tptp.set_Pr958786334691620121nt_int tptp.rat)|)) (= (ho_26115 x z) (ho_26115 y z)))) (= x y))))) (let ((_let_3351 (forall ((x |u_(-> Bool tptp.char)|) (y |u_(-> Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_26127 x z) (ho_26127 y z)))) (= x y))))) (let ((_let_3352 (forall ((x |u_(-> Bool Bool tptp.char)|) (y |u_(-> Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_26126 x z) (ho_26126 y z)))) (= x y))))) (let ((_let_3353 (forall ((x |u_(-> Bool Bool Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_26123 x z) (ho_26123 y z)))) (= x y))))) (let ((_let_3354 (forall ((x |u_(-> Bool Bool Bool Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_26122 x z) (ho_26122 y z)))) (= x y))))) (let ((_let_3355 (forall ((x |u_(-> Bool Bool Bool Bool Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool Bool Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_26121 x z) (ho_26121 y z)))) (= x y))))) (let ((_let_3356 (forall ((x |u_(-> Bool Bool Bool Bool Bool Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool Bool Bool Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_26120 x z) (ho_26120 y z)))) (= x y))))) (let ((_let_3357 (forall ((x |u_(-> tptp.char tptp.code_integer)|) (y |u_(-> tptp.char tptp.code_integer)|)) (or (not (forall ((z tptp.char)) (= (ho_26129 x z) (ho_26129 y z)))) (= x y))))) (let ((_let_3358 (forall ((BOUND_VARIABLE_1323704 tptp.num)) (= (ho_11028 k_11027 BOUND_VARIABLE_1323704) (ho_11028 k_11031 (ho_11030 k_11029 BOUND_VARIABLE_1323704)))))) (let ((_let_3359 (forall ((BOUND_VARIABLE_1323690 tptp.nat) (BOUND_VARIABLE_1323691 tptp.num)) (= (ho_11041 (ho_11040 (ho_11039 k_11038 (ho_11037 k_11036 k_11034)) k_11027) (ho_11028 (ho_11033 k_11032 BOUND_VARIABLE_1323690) BOUND_VARIABLE_1323691)) (ho_11028 (ho_11033 k_11042 BOUND_VARIABLE_1323690) BOUND_VARIABLE_1323691))))) (let ((_let_3360 (forall ((BOUND_VARIABLE_1323680 tptp.nat) (BOUND_VARIABLE_1323681 tptp.num)) (= (ho_11028 (ho_11033 k_11043 BOUND_VARIABLE_1323680) BOUND_VARIABLE_1323681) (ho_11028 k_11031 (ho_11048 (ho_11047 (ho_11046 k_11045 tptp.one) k_11044) (ho_11028 (ho_11033 k_11032 BOUND_VARIABLE_1323680) BOUND_VARIABLE_1323681))))))) (let ((_let_3361 (forall ((BOUND_VARIABLE_1323673 tptp.produc4166570645942440679at_nat) (BOUND_VARIABLE_1323674 tptp.produc4166570645942440679at_nat)) (= (= BOUND_VARIABLE_1323673 BOUND_VARIABLE_1323674) (ho_11051 (ho_11050 k_11049 BOUND_VARIABLE_1323673) BOUND_VARIABLE_1323674))))) (let ((_let_3362 (forall ((BOUND_VARIABLE_1323651 tptp.nat) (BOUND_VARIABLE_1323652 tptp.nat)) (= (ho_11054 (ho_11053 k_11052 BOUND_VARIABLE_1323651) BOUND_VARIABLE_1323652) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1323651 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323652)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1323652 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323651)) (ho_11056 k_11055 K3))))))))))) (let ((_let_3363 (forall ((BOUND_VARIABLE_1323632 tptp.nat) (BOUND_VARIABLE_1323633 tptp.nat) (BOUND_VARIABLE_1323634 tptp.nat) (BOUND_VARIABLE_1323635 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 (ho_11063 k_11062 BOUND_VARIABLE_1323632) BOUND_VARIABLE_1323633) BOUND_VARIABLE_1323634) BOUND_VARIABLE_1323635) (or (ho_11070 (ho_11069 k_11068 (ho_11067 (ho_11066 k_11065 BOUND_VARIABLE_1323632) BOUND_VARIABLE_1323634)) tptp.less_than) (and (= BOUND_VARIABLE_1323632 BOUND_VARIABLE_1323634) (ho_11070 (ho_11069 k_11068 (ho_11067 (ho_11066 k_11065 BOUND_VARIABLE_1323633) BOUND_VARIABLE_1323635)) tptp.less_than))))))) (let ((_let_3364 (forall ((BOUND_VARIABLE_1323606 tptp.nat) (BOUND_VARIABLE_1323607 tptp.nat) (BOUND_VARIABLE_1323608 tptp.nat) (BOUND_VARIABLE_1323609 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 (ho_11063 k_11071 BOUND_VARIABLE_1323606) BOUND_VARIABLE_1323607) BOUND_VARIABLE_1323608) BOUND_VARIABLE_1323609) (not (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323608)) (ho_11056 k_11055 BOUND_VARIABLE_1323607))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323606)) (ho_11056 k_11055 BOUND_VARIABLE_1323609))))) (ho_11056 k_11055 K3))))))))))) (let ((_let_3365 (forall ((BOUND_VARIABLE_1323572 tptp.nat) (BOUND_VARIABLE_1323573 tptp.nat) (BOUND_VARIABLE_1323574 tptp.nat) (BOUND_VARIABLE_1323575 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 (ho_11063 k_11072 BOUND_VARIABLE_1323572) BOUND_VARIABLE_1323573) BOUND_VARIABLE_1323574) BOUND_VARIABLE_1323575) (and (not (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323574)) (ho_11056 k_11055 BOUND_VARIABLE_1323573))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323572)) (ho_11056 k_11055 BOUND_VARIABLE_1323575))))) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323574)) (ho_11056 k_11055 BOUND_VARIABLE_1323573))))) (ho_11056 k_11055 K3))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323572)) (ho_11056 k_11055 BOUND_VARIABLE_1323575))))))))))) (let ((_let_3366 (forall ((BOUND_VARIABLE_1323552 tptp.nat) (BOUND_VARIABLE_1323553 tptp.nat) (BOUND_VARIABLE_1323554 tptp.nat) (BOUND_VARIABLE_1323555 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11075 (ho_11074 k_11073 BOUND_VARIABLE_1323552) BOUND_VARIABLE_1323553) BOUND_VARIABLE_1323554) BOUND_VARIABLE_1323555) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323552)) (ho_11056 k_11055 BOUND_VARIABLE_1323555)))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323553)) (ho_11056 k_11055 BOUND_VARIABLE_1323554)))))))) (let ((_let_3367 (forall ((BOUND_VARIABLE_1323532 tptp.nat) (BOUND_VARIABLE_1323533 tptp.nat) (BOUND_VARIABLE_1323534 tptp.nat) (BOUND_VARIABLE_1323535 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11075 (ho_11074 k_11076 BOUND_VARIABLE_1323532) BOUND_VARIABLE_1323533) BOUND_VARIABLE_1323534) BOUND_VARIABLE_1323535) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323532)) (ho_11056 k_11055 BOUND_VARIABLE_1323535)))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323533)) (ho_11056 k_11055 BOUND_VARIABLE_1323534)))))))) (let ((_let_3368 (forall ((BOUND_VARIABLE_1323512 tptp.nat) (BOUND_VARIABLE_1323513 tptp.nat) (BOUND_VARIABLE_1323514 tptp.nat) (BOUND_VARIABLE_1323515 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11075 (ho_11074 k_11077 BOUND_VARIABLE_1323512) BOUND_VARIABLE_1323513) BOUND_VARIABLE_1323514) BOUND_VARIABLE_1323515) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323512)) (ho_11056 k_11055 BOUND_VARIABLE_1323514)))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323513)) (ho_11056 k_11055 BOUND_VARIABLE_1323515)))))))) (let ((_let_3369 (forall ((BOUND_VARIABLE_1323492 tptp.nat) (BOUND_VARIABLE_1323493 tptp.nat) (BOUND_VARIABLE_1323494 tptp.nat) (BOUND_VARIABLE_1323495 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11075 (ho_11074 k_11078 BOUND_VARIABLE_1323492) BOUND_VARIABLE_1323493) BOUND_VARIABLE_1323494) BOUND_VARIABLE_1323495) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323492)) (ho_11056 k_11055 BOUND_VARIABLE_1323494)))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323493)) (ho_11056 k_11055 BOUND_VARIABLE_1323495)))))))) (let ((_let_3370 (forall ((BOUND_VARIABLE_1323466 tptp.nat) (BOUND_VARIABLE_1323467 tptp.nat) (BOUND_VARIABLE_1323468 tptp.nat) (BOUND_VARIABLE_1323469 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 (ho_11063 k_11079 BOUND_VARIABLE_1323466) BOUND_VARIABLE_1323467) BOUND_VARIABLE_1323468) BOUND_VARIABLE_1323469) (not (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323468)) (ho_11056 k_11055 BOUND_VARIABLE_1323467))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323466)) (ho_11056 k_11055 BOUND_VARIABLE_1323469))))) (ho_11056 k_11055 K3))))))))))) (let ((_let_3371 (forall ((BOUND_VARIABLE_1323440 tptp.nat) (BOUND_VARIABLE_1323441 tptp.nat) (BOUND_VARIABLE_1323442 tptp.nat) (BOUND_VARIABLE_1323443 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 (ho_11063 k_11080 BOUND_VARIABLE_1323440) BOUND_VARIABLE_1323441) BOUND_VARIABLE_1323442) BOUND_VARIABLE_1323443) (not (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323442)) (ho_11056 k_11055 BOUND_VARIABLE_1323441))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323440)) (ho_11056 k_11055 BOUND_VARIABLE_1323443))))) (ho_11056 k_11055 K3))))))))))) (let ((_let_3372 (forall ((BOUND_VARIABLE_1323406 tptp.nat) (BOUND_VARIABLE_1323407 tptp.nat) (BOUND_VARIABLE_1323408 tptp.nat) (BOUND_VARIABLE_1323409 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 (ho_11063 k_11081 BOUND_VARIABLE_1323406) BOUND_VARIABLE_1323407) BOUND_VARIABLE_1323408) BOUND_VARIABLE_1323409) (and (not (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323408)) (ho_11056 k_11055 BOUND_VARIABLE_1323407))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323406)) (ho_11056 k_11055 BOUND_VARIABLE_1323409))))) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323408)) (ho_11056 k_11055 BOUND_VARIABLE_1323407))))) (ho_11056 k_11055 K3))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323406)) (ho_11056 k_11055 BOUND_VARIABLE_1323409))))))))))) (let ((_let_3373 (forall ((BOUND_VARIABLE_1323372 tptp.nat) (BOUND_VARIABLE_1323373 tptp.nat) (BOUND_VARIABLE_1323374 tptp.nat) (BOUND_VARIABLE_1323375 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 (ho_11063 k_11082 BOUND_VARIABLE_1323372) BOUND_VARIABLE_1323373) BOUND_VARIABLE_1323374) BOUND_VARIABLE_1323375) (and (not (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323374)) (ho_11056 k_11055 BOUND_VARIABLE_1323373))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323372)) (ho_11056 k_11055 BOUND_VARIABLE_1323375))))) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323374)) (ho_11056 k_11055 BOUND_VARIABLE_1323373))))) (ho_11056 k_11055 K3))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323372)) (ho_11056 k_11055 BOUND_VARIABLE_1323375))))))))))) (let ((_let_3374 (forall ((BOUND_VARIABLE_1323353 tptp.nat) (BOUND_VARIABLE_1323354 tptp.nat) (BOUND_VARIABLE_1323355 tptp.nat) (BOUND_VARIABLE_1323356 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 (ho_11063 k_11083 BOUND_VARIABLE_1323353) BOUND_VARIABLE_1323354) BOUND_VARIABLE_1323355) BOUND_VARIABLE_1323356) (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323355)) (ho_11056 k_11055 BOUND_VARIABLE_1323354))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323353)) (ho_11056 k_11055 BOUND_VARIABLE_1323356)))))))) (let ((_let_3375 (forall ((BOUND_VARIABLE_1323319 tptp.nat) (BOUND_VARIABLE_1323320 tptp.nat) (BOUND_VARIABLE_1323321 tptp.nat) (BOUND_VARIABLE_1323322 tptp.nat)) (let ((_let_1 (ho_11056 k_11055 BOUND_VARIABLE_1323321))) (let ((_let_2 (ho_11058 k_11085 (ho_11056 k_11055 BOUND_VARIABLE_1323320)))) (let ((_let_3 (ho_11056 k_11055 BOUND_VARIABLE_1323322))) (let ((_let_4 (ho_11058 k_11085 (ho_11056 k_11055 BOUND_VARIABLE_1323319)))) (= (ho_11067 (ho_11066 (ho_11075 (ho_11074 k_11084 BOUND_VARIABLE_1323319) BOUND_VARIABLE_1323320) BOUND_VARIABLE_1323321) BOUND_VARIABLE_1323322) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_4 _let_1)))) (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_2 _let_3)))))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_4 _let_3)))) (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_2 _let_1)))))))))))))) (let ((_let_3376 (forall ((BOUND_VARIABLE_1323285 tptp.nat) (BOUND_VARIABLE_1323286 tptp.nat) (BOUND_VARIABLE_1323287 tptp.nat) (BOUND_VARIABLE_1323288 tptp.nat)) (let ((_let_1 (ho_11056 k_11055 BOUND_VARIABLE_1323287))) (let ((_let_2 (ho_11058 k_11085 (ho_11056 k_11055 BOUND_VARIABLE_1323286)))) (let ((_let_3 (ho_11056 k_11055 BOUND_VARIABLE_1323288))) (let ((_let_4 (ho_11058 k_11085 (ho_11056 k_11055 BOUND_VARIABLE_1323285)))) (= (ho_11067 (ho_11066 (ho_11075 (ho_11074 k_11086 BOUND_VARIABLE_1323285) BOUND_VARIABLE_1323286) BOUND_VARIABLE_1323287) BOUND_VARIABLE_1323288) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_4 _let_1)))) (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_2 _let_3)))))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_4 _let_3)))) (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_2 _let_1)))))))))))))) (let ((_let_3377 (forall ((BOUND_VARIABLE_1323265 tptp.nat) (BOUND_VARIABLE_1323266 tptp.nat) (BOUND_VARIABLE_1323267 tptp.nat) (BOUND_VARIABLE_1323268 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11075 (ho_11074 k_11087 BOUND_VARIABLE_1323265) BOUND_VARIABLE_1323266) BOUND_VARIABLE_1323267) BOUND_VARIABLE_1323268) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323265)) (ho_11056 k_11055 BOUND_VARIABLE_1323268)))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323266)) (ho_11056 k_11055 BOUND_VARIABLE_1323267)))))))) (let ((_let_3378 (forall ((BOUND_VARIABLE_1323245 tptp.nat) (BOUND_VARIABLE_1323246 tptp.nat) (BOUND_VARIABLE_1323247 tptp.nat) (BOUND_VARIABLE_1323248 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11075 (ho_11074 k_11088 BOUND_VARIABLE_1323245) BOUND_VARIABLE_1323246) BOUND_VARIABLE_1323247) BOUND_VARIABLE_1323248) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323245)) (ho_11056 k_11055 BOUND_VARIABLE_1323247)))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323246)) (ho_11056 k_11055 BOUND_VARIABLE_1323248)))))))) (let ((_let_3379 (forall ((BOUND_VARIABLE_1323219 tptp.nat) (BOUND_VARIABLE_1323220 tptp.nat) (BOUND_VARIABLE_1323221 tptp.nat) (BOUND_VARIABLE_1323222 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 (ho_11063 k_11089 BOUND_VARIABLE_1323219) BOUND_VARIABLE_1323220) BOUND_VARIABLE_1323221) BOUND_VARIABLE_1323222) (not (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323221)) (ho_11056 k_11055 BOUND_VARIABLE_1323220))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323219)) (ho_11056 k_11055 BOUND_VARIABLE_1323222))))) (ho_11056 k_11055 K3))))))))))) (let ((_let_3380 (forall ((BOUND_VARIABLE_1323185 tptp.nat) (BOUND_VARIABLE_1323186 tptp.nat) (BOUND_VARIABLE_1323187 tptp.nat) (BOUND_VARIABLE_1323188 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 (ho_11063 k_11090 BOUND_VARIABLE_1323185) BOUND_VARIABLE_1323186) BOUND_VARIABLE_1323187) BOUND_VARIABLE_1323188) (and (not (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323187)) (ho_11056 k_11055 BOUND_VARIABLE_1323186))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323185)) (ho_11056 k_11055 BOUND_VARIABLE_1323188))))) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323187)) (ho_11056 k_11055 BOUND_VARIABLE_1323186))))) (ho_11056 k_11055 K3))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323185)) (ho_11056 k_11055 BOUND_VARIABLE_1323188))))))))))) (let ((_let_3381 (forall ((BOUND_VARIABLE_1323151 tptp.nat) (BOUND_VARIABLE_1323152 tptp.nat) (BOUND_VARIABLE_1323153 tptp.nat) (BOUND_VARIABLE_1323154 tptp.nat)) (let ((_let_1 (ho_11056 k_11055 BOUND_VARIABLE_1323153))) (let ((_let_2 (ho_11058 k_11085 (ho_11056 k_11055 BOUND_VARIABLE_1323152)))) (let ((_let_3 (ho_11056 k_11055 BOUND_VARIABLE_1323154))) (let ((_let_4 (ho_11058 k_11085 (ho_11056 k_11055 BOUND_VARIABLE_1323151)))) (= (ho_11067 (ho_11066 (ho_11075 (ho_11074 k_11091 BOUND_VARIABLE_1323151) BOUND_VARIABLE_1323152) BOUND_VARIABLE_1323153) BOUND_VARIABLE_1323154) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_4 _let_1)))) (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_2 _let_3)))))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_4 _let_3)))) (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_2 _let_1)))))))))))))) (let ((_let_3382 (forall ((BOUND_VARIABLE_1323142 tptp.int) (BOUND_VARIABLE_1323143 tptp.int)) (= (ho_11094 (ho_11093 k_11092 BOUND_VARIABLE_1323142) BOUND_VARIABLE_1323143) (= BOUND_VARIABLE_1323142 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1323143) BOUND_VARIABLE_1323142)))))) (let ((_let_3383 (forall ((BOUND_VARIABLE_1323128 tptp.int) (BOUND_VARIABLE_1323129 tptp.int)) (= (ho_11094 (ho_11093 k_11096 BOUND_VARIABLE_1323128) BOUND_VARIABLE_1323129) (and (= BOUND_VARIABLE_1323128 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1323129) BOUND_VARIABLE_1323128)) (not (= BOUND_VARIABLE_1323129 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1323128) BOUND_VARIABLE_1323129)))))))) (let ((_let_3384 (forall ((BOUND_VARIABLE_1323108 tptp.nat) (BOUND_VARIABLE_1323109 tptp.nat) (BOUND_VARIABLE_1323110 tptp.nat) (BOUND_VARIABLE_1323111 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11075 (ho_11074 k_11097 BOUND_VARIABLE_1323108) BOUND_VARIABLE_1323109) BOUND_VARIABLE_1323110) BOUND_VARIABLE_1323111) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323108)) (ho_11056 k_11055 BOUND_VARIABLE_1323111)))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323109)) (ho_11056 k_11055 BOUND_VARIABLE_1323110)))))))) (let ((_let_3385 (forall ((BOUND_VARIABLE_1323088 tptp.nat) (BOUND_VARIABLE_1323089 tptp.nat) (BOUND_VARIABLE_1323090 tptp.nat) (BOUND_VARIABLE_1323091 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11075 (ho_11074 k_11098 BOUND_VARIABLE_1323088) BOUND_VARIABLE_1323089) BOUND_VARIABLE_1323090) BOUND_VARIABLE_1323091) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323088)) (ho_11056 k_11055 BOUND_VARIABLE_1323090)))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323089)) (ho_11056 k_11055 BOUND_VARIABLE_1323091)))))))) (let ((_let_3386 (forall ((BOUND_VARIABLE_1323054 tptp.nat) (BOUND_VARIABLE_1323055 tptp.nat) (BOUND_VARIABLE_1323056 tptp.nat) (BOUND_VARIABLE_1323057 tptp.nat)) (let ((_let_1 (ho_11056 k_11055 BOUND_VARIABLE_1323056))) (let ((_let_2 (ho_11058 k_11085 (ho_11056 k_11055 BOUND_VARIABLE_1323055)))) (let ((_let_3 (ho_11056 k_11055 BOUND_VARIABLE_1323057))) (let ((_let_4 (ho_11058 k_11085 (ho_11056 k_11055 BOUND_VARIABLE_1323054)))) (= (ho_11067 (ho_11066 (ho_11075 (ho_11074 k_11099 BOUND_VARIABLE_1323054) BOUND_VARIABLE_1323055) BOUND_VARIABLE_1323056) BOUND_VARIABLE_1323057) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_4 _let_1)))) (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_2 _let_3)))))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_4 _let_3)))) (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_2 _let_1)))))))))))))) (let ((_let_3387 (forall ((BOUND_VARIABLE_1323020 tptp.nat) (BOUND_VARIABLE_1323021 tptp.nat) (BOUND_VARIABLE_1323022 tptp.nat) (BOUND_VARIABLE_1323023 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 (ho_11063 k_11100 BOUND_VARIABLE_1323020) BOUND_VARIABLE_1323021) BOUND_VARIABLE_1323022) BOUND_VARIABLE_1323023) (and (not (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323022)) (ho_11056 k_11055 BOUND_VARIABLE_1323021))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323020)) (ho_11056 k_11055 BOUND_VARIABLE_1323023))))) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323022)) (ho_11056 k_11055 BOUND_VARIABLE_1323021))))) (ho_11056 k_11055 K3))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1323020)) (ho_11056 k_11055 BOUND_VARIABLE_1323023))))))))))) (let ((_let_3388 (forall ((BOUND_VARIABLE_1322994 tptp.nat) (BOUND_VARIABLE_1322995 tptp.nat) (BOUND_VARIABLE_1322996 tptp.nat) (BOUND_VARIABLE_1322997 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 (ho_11063 k_11101 BOUND_VARIABLE_1322994) BOUND_VARIABLE_1322995) BOUND_VARIABLE_1322996) BOUND_VARIABLE_1322997) (not (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1322996)) (ho_11056 k_11055 BOUND_VARIABLE_1322995))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1322994)) (ho_11056 k_11055 BOUND_VARIABLE_1322997))))) (ho_11056 k_11055 K3))))))))))) (let ((_let_3389 (forall ((BOUND_VARIABLE_1322974 tptp.int) (BOUND_VARIABLE_1322975 tptp.int) (BOUND_VARIABLE_1322976 tptp.int) (BOUND_VARIABLE_1322977 tptp.int)) (let ((_let_1 (ho_11059 (ho_11058 k_11085 BOUND_VARIABLE_1322975) BOUND_VARIABLE_1322977))) (let ((_let_2 (ho_11059 (ho_11058 k_11085 BOUND_VARIABLE_1322974) BOUND_VARIABLE_1322976))) (= (ho_11094 (ho_11093 (ho_11104 (ho_11103 k_11102 BOUND_VARIABLE_1322974) BOUND_VARIABLE_1322975) BOUND_VARIABLE_1322976) BOUND_VARIABLE_1322977) (and (= _let_2 (ho_11059 (ho_11058 k_11095 _let_1) _let_2)) (not (= _let_1 (ho_11059 (ho_11058 k_11095 _let_2) _let_1)))))))))) (let ((_let_3390 (forall ((BOUND_VARIABLE_1322943 tptp.rat) (BOUND_VARIABLE_1322944 tptp.product_prod_int_int)) (let ((_let_1 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1322944))) (let ((_let_3 (ho_11111 k_11112 BOUND_VARIABLE_1322944))) (= (and (= BOUND_VARIABLE_1322943 (ho_11127 (ho_11126 (ho_11125 (ho_11124 (ho_11123 k_11122 k_11118) (ho_11121 (ho_11120 k_11119 k_11118) k_11116)) k_11114) _let_3) _let_2)) (ho_11094 (ho_11093 k_11113 _let_3) _let_2) (= _let_2 (ho_11059 (ho_11058 k_11095 _let_1) _let_2)) (not (= _let_1 (ho_11059 (ho_11058 k_11095 _let_2) _let_1)))) (ho_11130 (ho_11129 k_11128 BOUND_VARIABLE_1322943) BOUND_VARIABLE_1322944)))))))) (let ((_let_3391 (forall ((BOUND_VARIABLE_1322928 tptp.int) (BOUND_VARIABLE_1322929 tptp.int) (BOUND_VARIABLE_1322930 tptp.int) (BOUND_VARIABLE_1322931 tptp.int)) (let ((_let_1 (ho_11059 (ho_11058 k_11085 BOUND_VARIABLE_1322929) BOUND_VARIABLE_1322930))) (= (ho_11094 (ho_11093 (ho_11104 (ho_11103 k_11131 BOUND_VARIABLE_1322928) BOUND_VARIABLE_1322929) BOUND_VARIABLE_1322930) BOUND_VARIABLE_1322931) (= _let_1 (ho_11059 (ho_11058 k_11095 (ho_11059 (ho_11058 k_11085 BOUND_VARIABLE_1322928) BOUND_VARIABLE_1322931)) _let_1))))))) (let ((_let_3392 (forall ((BOUND_VARIABLE_1322897 tptp.rat) (BOUND_VARIABLE_1322898 tptp.product_prod_int_int)) (let ((_let_1 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1322898))) (let ((_let_3 (ho_11111 k_11112 BOUND_VARIABLE_1322898))) (= (and (= BOUND_VARIABLE_1322897 (ho_11127 (ho_11126 (ho_11125 (ho_11124 (ho_11123 k_11122 k_11118) (ho_11121 (ho_11120 k_11119 k_11118) k_11116)) k_11114) _let_3) _let_2)) (ho_11094 (ho_11093 k_11113 _let_3) _let_2) (= _let_2 (ho_11059 (ho_11058 k_11095 _let_1) _let_2)) (not (= _let_1 (ho_11059 (ho_11058 k_11095 _let_2) _let_1)))) (ho_11130 (ho_11129 k_11132 BOUND_VARIABLE_1322897) BOUND_VARIABLE_1322898)))))))) (let ((_let_3393 (forall ((BOUND_VARIABLE_1322888 tptp.int) (BOUND_VARIABLE_1322889 tptp.int)) (= (ho_11094 (ho_11093 k_11133 BOUND_VARIABLE_1322888) BOUND_VARIABLE_1322889) (= BOUND_VARIABLE_1322888 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1322889) BOUND_VARIABLE_1322888)))))) (let ((_let_3394 (forall ((BOUND_VARIABLE_1322874 tptp.nat) (BOUND_VARIABLE_1322875 tptp.nat)) (= (ho_11054 (ho_11053 k_11134 BOUND_VARIABLE_1322874) BOUND_VARIABLE_1322875) (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1322874 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1322875)) (ho_11056 k_11055 K3))))))))))) (let ((_let_3395 (forall ((BOUND_VARIABLE_1322852 tptp.nat) (BOUND_VARIABLE_1322853 tptp.nat)) (= (ho_11054 (ho_11053 k_11135 BOUND_VARIABLE_1322852) BOUND_VARIABLE_1322853) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1322852 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1322853)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1322853 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1322852)) (ho_11056 k_11055 K3))))))))))) (let ((_let_3396 (forall ((BOUND_VARIABLE_1322831 tptp.list_int) (BOUND_VARIABLE_1322832 tptp.array_int) (BOUND_VARIABLE_1322833 tptp.heap_e7401611519738050253t_unit)) (= (ho_11145 (ho_11144 k_11143 BOUND_VARIABLE_1322832) (ho_11142 (ho_11141 k_11140 BOUND_VARIABLE_1322833) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (ho_11056 k_11055 (ho_11137 k_11136 BOUND_VARIABLE_1322831)))))) (ho_11149 (ho_11148 (ho_11147 k_11146 BOUND_VARIABLE_1322831) BOUND_VARIABLE_1322832) BOUND_VARIABLE_1322833))))) (let ((_let_3397 (forall ((BOUND_VARIABLE_1322810 tptp.list_o) (BOUND_VARIABLE_1322811 tptp.array_o) (BOUND_VARIABLE_1322812 tptp.heap_e7401611519738050253t_unit)) (= (ho_11154 (ho_11153 k_11152 BOUND_VARIABLE_1322811) (ho_11142 (ho_11141 k_11140 BOUND_VARIABLE_1322812) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (ho_11056 k_11055 (ho_11151 k_11150 BOUND_VARIABLE_1322810)))))) (ho_11158 (ho_11157 (ho_11156 k_11155 BOUND_VARIABLE_1322810) BOUND_VARIABLE_1322811) BOUND_VARIABLE_1322812))))) (let ((_let_3398 (forall ((BOUND_VARIABLE_1322789 tptp.list_nat) (BOUND_VARIABLE_1322790 tptp.array_nat) (BOUND_VARIABLE_1322791 tptp.heap_e7401611519738050253t_unit)) (= (ho_11163 (ho_11162 k_11161 BOUND_VARIABLE_1322790) (ho_11142 (ho_11141 k_11140 BOUND_VARIABLE_1322791) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (ho_11056 k_11055 (ho_11160 k_11159 BOUND_VARIABLE_1322789)))))) (ho_11167 (ho_11166 (ho_11165 k_11164 BOUND_VARIABLE_1322789) BOUND_VARIABLE_1322790) BOUND_VARIABLE_1322791))))) (let ((_let_3399 (forall ((BOUND_VARIABLE_1322750 tptp.num) (BOUND_VARIABLE_1322751 tptp.nat)) (= (ho_11028 (ho_11171 (ho_11170 (ho_11169 k_11168 (ho_11028 k_11031 tptp.one)) (ho_11033 k_11042 BOUND_VARIABLE_1322751)) (ho_11033 k_11043 BOUND_VARIABLE_1322751)) BOUND_VARIABLE_1322750) (ho_11174 (ho_11173 k_11172 BOUND_VARIABLE_1322750) BOUND_VARIABLE_1322751))))) (let ((_let_3400 (forall ((BOUND_VARIABLE_1322736 tptp.int) (BOUND_VARIABLE_1322737 tptp.int)) (= (or (= BOUND_VARIABLE_1322736 BOUND_VARIABLE_1322737) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1322737) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11181 BOUND_VARIABLE_1322736) BOUND_VARIABLE_1322737))))) (let ((_let_3401 (forall ((BOUND_VARIABLE_1322722 tptp.int) (BOUND_VARIABLE_1322723 tptp.int)) (= (or (= BOUND_VARIABLE_1322722 BOUND_VARIABLE_1322723) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1322723) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11182 BOUND_VARIABLE_1322722) BOUND_VARIABLE_1322723))))) (let ((_let_3402 (forall ((BOUND_VARIABLE_1322708 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1322709 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1322708 BOUND_VARIABLE_1322709) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1322709) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_11187 BOUND_VARIABLE_1322708) BOUND_VARIABLE_1322709))))) (let ((_let_3403 (forall ((BOUND_VARIABLE_1322694 tptp.nat) (BOUND_VARIABLE_1322695 tptp.nat)) (= (or (= BOUND_VARIABLE_1322694 BOUND_VARIABLE_1322695) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1322695) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11192 BOUND_VARIABLE_1322694) BOUND_VARIABLE_1322695))))) (let ((_let_3404 (forall ((BOUND_VARIABLE_1322680 Bool) (BOUND_VARIABLE_1322681 Bool)) (= (or (= BOUND_VARIABLE_1322680 BOUND_VARIABLE_1322681) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1322681) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11200 BOUND_VARIABLE_1322680) BOUND_VARIABLE_1322681))))) (let ((_let_3405 (forall ((BOUND_VARIABLE_1322666 tptp.set_nat) (BOUND_VARIABLE_1322667 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1322666 BOUND_VARIABLE_1322667) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1322667) (ho_11204 k_11203 k_11202))) (ho_11191 (ho_11209 k_11208 BOUND_VARIABLE_1322666) BOUND_VARIABLE_1322667))))) (let ((_let_3406 (forall ((BOUND_VARIABLE_1322652 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1322653 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1322652 BOUND_VARIABLE_1322653) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1322653) (ho_11213 k_11212 k_11210))) (ho_11211 (ho_11218 k_11217 BOUND_VARIABLE_1322652) BOUND_VARIABLE_1322653))))) (let ((_let_3407 (forall ((BOUND_VARIABLE_1322638 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1322639 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1322638 BOUND_VARIABLE_1322639) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1322639) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_11219 BOUND_VARIABLE_1322638) BOUND_VARIABLE_1322639))))) (let ((_let_3408 (forall ((BOUND_VARIABLE_1322624 tptp.int) (BOUND_VARIABLE_1322625 tptp.int)) (= (or (= BOUND_VARIABLE_1322624 BOUND_VARIABLE_1322625) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1322625) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11220 BOUND_VARIABLE_1322624) BOUND_VARIABLE_1322625))))) (let ((_let_3409 (forall ((BOUND_VARIABLE_1322610 tptp.int) (BOUND_VARIABLE_1322611 tptp.int)) (= (or (= BOUND_VARIABLE_1322610 BOUND_VARIABLE_1322611) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1322611) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11221 BOUND_VARIABLE_1322610) BOUND_VARIABLE_1322611))))) (let ((_let_3410 (forall ((BOUND_VARIABLE_1322596 tptp.nat) (BOUND_VARIABLE_1322597 tptp.nat)) (= (or (= BOUND_VARIABLE_1322596 BOUND_VARIABLE_1322597) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1322597) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11222 BOUND_VARIABLE_1322596) BOUND_VARIABLE_1322597))))) (let ((_let_3411 (forall ((BOUND_VARIABLE_1322582 Bool) (BOUND_VARIABLE_1322583 Bool)) (= (or (= BOUND_VARIABLE_1322582 BOUND_VARIABLE_1322583) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1322583) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11223 BOUND_VARIABLE_1322582) BOUND_VARIABLE_1322583))))) (let ((_let_3412 (forall ((BOUND_VARIABLE_1322568 tptp.set_nat) (BOUND_VARIABLE_1322569 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1322568 BOUND_VARIABLE_1322569) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1322569) (ho_11204 k_11203 k_11202))) (ho_11191 (ho_11209 k_11224 BOUND_VARIABLE_1322568) BOUND_VARIABLE_1322569))))) (let ((_let_3413 (forall ((BOUND_VARIABLE_1322554 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1322555 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1322554 BOUND_VARIABLE_1322555) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1322555) (ho_11213 k_11212 k_11210))) (ho_11211 (ho_11218 k_11225 BOUND_VARIABLE_1322554) BOUND_VARIABLE_1322555))))) (let ((_let_3414 (forall ((BOUND_VARIABLE_1322540 tptp.int) (BOUND_VARIABLE_1322541 tptp.int)) (= (or (= BOUND_VARIABLE_1322540 BOUND_VARIABLE_1322541) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1322541) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11226 BOUND_VARIABLE_1322540) BOUND_VARIABLE_1322541))))) (let ((_let_3415 (forall ((BOUND_VARIABLE_1322526 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1322527 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1322526 BOUND_VARIABLE_1322527) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1322527) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_11227 BOUND_VARIABLE_1322526) BOUND_VARIABLE_1322527))))) (let ((_let_3416 (forall ((BOUND_VARIABLE_1322512 tptp.nat) (BOUND_VARIABLE_1322513 tptp.nat)) (= (or (= BOUND_VARIABLE_1322512 BOUND_VARIABLE_1322513) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1322513) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11228 BOUND_VARIABLE_1322512) BOUND_VARIABLE_1322513))))) (let ((_let_3417 (forall ((BOUND_VARIABLE_1322498 tptp.int) (BOUND_VARIABLE_1322499 tptp.int)) (= (or (= BOUND_VARIABLE_1322498 BOUND_VARIABLE_1322499) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1322499) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11229 BOUND_VARIABLE_1322498) BOUND_VARIABLE_1322499))))) (let ((_let_3418 (forall ((BOUND_VARIABLE_1322484 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1322485 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1322484 BOUND_VARIABLE_1322485) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1322485) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_11230 BOUND_VARIABLE_1322484) BOUND_VARIABLE_1322485))))) (let ((_let_3419 (forall ((BOUND_VARIABLE_1322470 tptp.nat) (BOUND_VARIABLE_1322471 tptp.nat)) (= (or (= BOUND_VARIABLE_1322470 BOUND_VARIABLE_1322471) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1322471) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11231 BOUND_VARIABLE_1322470) BOUND_VARIABLE_1322471))))) (let ((_let_3420 (forall ((BOUND_VARIABLE_1322459 tptp.int) (BOUND_VARIABLE_1322460 tptp.set_int) (BOUND_VARIABLE_1322461 tptp.int)) (= (or (= BOUND_VARIABLE_1322459 BOUND_VARIABLE_1322461) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1322461) BOUND_VARIABLE_1322460)) (ho_11094 (ho_11234 (ho_11233 k_11232 BOUND_VARIABLE_1322459) BOUND_VARIABLE_1322460) BOUND_VARIABLE_1322461))))) (let ((_let_3421 (forall ((BOUND_VARIABLE_1322448 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1322449 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1322450 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1322448 BOUND_VARIABLE_1322450) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1322450) BOUND_VARIABLE_1322449)) (ho_11184 (ho_11237 (ho_11236 k_11235 BOUND_VARIABLE_1322448) BOUND_VARIABLE_1322449) BOUND_VARIABLE_1322450))))) (let ((_let_3422 (forall ((BOUND_VARIABLE_1322437 tptp.nat) (BOUND_VARIABLE_1322438 tptp.set_nat) (BOUND_VARIABLE_1322439 tptp.nat)) (= (or (= BOUND_VARIABLE_1322437 BOUND_VARIABLE_1322439) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1322439) BOUND_VARIABLE_1322438)) (ho_11054 (ho_11240 (ho_11239 k_11238 BOUND_VARIABLE_1322437) BOUND_VARIABLE_1322438) BOUND_VARIABLE_1322439))))) (let ((_let_3423 (forall ((BOUND_VARIABLE_1322423 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1322424 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1322423 BOUND_VARIABLE_1322424) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1322424) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_11241 BOUND_VARIABLE_1322423) BOUND_VARIABLE_1322424))))) (let ((_let_3424 (forall ((BOUND_VARIABLE_1322409 tptp.int) (BOUND_VARIABLE_1322410 tptp.int)) (= (or (= BOUND_VARIABLE_1322409 BOUND_VARIABLE_1322410) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1322410) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11242 BOUND_VARIABLE_1322409) BOUND_VARIABLE_1322410))))) (let ((_let_3425 (forall ((BOUND_VARIABLE_1322395 tptp.nat) (BOUND_VARIABLE_1322396 tptp.nat)) (= (or (= BOUND_VARIABLE_1322395 BOUND_VARIABLE_1322396) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1322396) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11243 BOUND_VARIABLE_1322395) BOUND_VARIABLE_1322396))))) (let ((_let_3426 (forall ((BOUND_VARIABLE_1322381 Bool) (BOUND_VARIABLE_1322382 Bool)) (= (or (= BOUND_VARIABLE_1322381 BOUND_VARIABLE_1322382) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1322382) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11244 BOUND_VARIABLE_1322381) BOUND_VARIABLE_1322382))))) (let ((_let_3427 (forall ((BOUND_VARIABLE_1322367 tptp.set_nat) (BOUND_VARIABLE_1322368 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1322367 BOUND_VARIABLE_1322368) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1322368) (ho_11204 k_11203 k_11202))) (ho_11191 (ho_11209 k_11245 BOUND_VARIABLE_1322367) BOUND_VARIABLE_1322368))))) (let ((_let_3428 (forall ((BOUND_VARIABLE_1322353 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1322354 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1322353 BOUND_VARIABLE_1322354) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1322354) (ho_11213 k_11212 k_11210))) (ho_11211 (ho_11218 k_11246 BOUND_VARIABLE_1322353) BOUND_VARIABLE_1322354))))) (let ((_let_3429 (forall ((BOUND_VARIABLE_1322339 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1322340 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1322339 BOUND_VARIABLE_1322340) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1322340) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_11247 BOUND_VARIABLE_1322339) BOUND_VARIABLE_1322340))))) (let ((_let_3430 (forall ((BOUND_VARIABLE_1322325 tptp.int) (BOUND_VARIABLE_1322326 tptp.int)) (= (or (= BOUND_VARIABLE_1322325 BOUND_VARIABLE_1322326) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1322326) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11248 BOUND_VARIABLE_1322325) BOUND_VARIABLE_1322326))))) (let ((_let_3431 (forall ((BOUND_VARIABLE_1322311 tptp.nat) (BOUND_VARIABLE_1322312 tptp.nat)) (= (or (= BOUND_VARIABLE_1322311 BOUND_VARIABLE_1322312) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1322312) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11249 BOUND_VARIABLE_1322311) BOUND_VARIABLE_1322312))))) (let ((_let_3432 (forall ((BOUND_VARIABLE_1322297 Bool) (BOUND_VARIABLE_1322298 Bool)) (= (or (= BOUND_VARIABLE_1322297 BOUND_VARIABLE_1322298) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1322298) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11250 BOUND_VARIABLE_1322297) BOUND_VARIABLE_1322298))))) (let ((_let_3433 (forall ((BOUND_VARIABLE_1322283 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1322284 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1322283 BOUND_VARIABLE_1322284) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1322284) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_11251 BOUND_VARIABLE_1322283) BOUND_VARIABLE_1322284))))) (let ((_let_3434 (forall ((BOUND_VARIABLE_1322269 tptp.int) (BOUND_VARIABLE_1322270 tptp.int)) (= (or (= BOUND_VARIABLE_1322269 BOUND_VARIABLE_1322270) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1322270) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11252 BOUND_VARIABLE_1322269) BOUND_VARIABLE_1322270))))) (let ((_let_3435 (forall ((BOUND_VARIABLE_1322255 tptp.nat) (BOUND_VARIABLE_1322256 tptp.nat)) (= (or (= BOUND_VARIABLE_1322255 BOUND_VARIABLE_1322256) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1322256) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11253 BOUND_VARIABLE_1322255) BOUND_VARIABLE_1322256))))) (let ((_let_3436 (forall ((BOUND_VARIABLE_1322241 Bool) (BOUND_VARIABLE_1322242 Bool)) (= (or (= BOUND_VARIABLE_1322241 BOUND_VARIABLE_1322242) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1322242) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11254 BOUND_VARIABLE_1322241) BOUND_VARIABLE_1322242))))) (let ((_let_3437 (forall ((BOUND_VARIABLE_1322227 tptp.int) (BOUND_VARIABLE_1322228 tptp.int)) (= (or (= BOUND_VARIABLE_1322227 BOUND_VARIABLE_1322228) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1322228) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11255 BOUND_VARIABLE_1322227) BOUND_VARIABLE_1322228))))) (let ((_let_3438 (forall ((BOUND_VARIABLE_1322213 tptp.nat) (BOUND_VARIABLE_1322214 tptp.nat)) (= (or (= BOUND_VARIABLE_1322213 BOUND_VARIABLE_1322214) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1322214) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11256 BOUND_VARIABLE_1322213) BOUND_VARIABLE_1322214))))) (let ((_let_3439 (forall ((BOUND_VARIABLE_1322199 Bool) (BOUND_VARIABLE_1322200 Bool)) (= (or (= BOUND_VARIABLE_1322199 BOUND_VARIABLE_1322200) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1322200) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11257 BOUND_VARIABLE_1322199) BOUND_VARIABLE_1322200))))) (let ((_let_3440 (forall ((BOUND_VARIABLE_1322189 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1322190 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1322189 BOUND_VARIABLE_1322190) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1322190) tptp.bot_bo228742789529271731at_nat)) (ho_11263 (ho_11262 k_11261 BOUND_VARIABLE_1322189) BOUND_VARIABLE_1322190))))) (let ((_let_3441 (forall ((BOUND_VARIABLE_1322182 tptp.produc4166570645942440679at_nat) (BOUND_VARIABLE_1322183 tptp.produc4166570645942440679at_nat)) (= (= BOUND_VARIABLE_1322182 BOUND_VARIABLE_1322183) (ho_11051 (ho_11050 k_11264 BOUND_VARIABLE_1322182) BOUND_VARIABLE_1322183))))) (let ((_let_3442 (forall ((BOUND_VARIABLE_1322158 tptp.produc4166570645942440679at_nat) (BOUND_VARIABLE_1322159 tptp.produc4166570645942440679at_nat)) (let ((_let_1 (ho_11266 k_11265 BOUND_VARIABLE_1322159))) (= (or (ho_11267 _let_1 (ho_11269 k_11268 (ho_11050 k_11049 BOUND_VARIABLE_1322158))) (ho_11267 _let_1 tptp.bot_bo8422036546324065075at_nat)) (ho_11051 (ho_11050 k_11270 BOUND_VARIABLE_1322158) BOUND_VARIABLE_1322159)))))) (let ((_let_3443 (forall ((BOUND_VARIABLE_1322151 tptp.nat) (BOUND_VARIABLE_1322152 tptp.nat)) (= (= BOUND_VARIABLE_1322151 BOUND_VARIABLE_1322152) (ho_11054 (ho_11053 k_11271 BOUND_VARIABLE_1322151) BOUND_VARIABLE_1322152))))) (let ((_let_3444 (forall ((BOUND_VARIABLE_1322144 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1322145 tptp.produc3843707927480180839at_nat)) (= (= BOUND_VARIABLE_1322144 BOUND_VARIABLE_1322145) (ho_11263 (ho_11262 k_11272 BOUND_VARIABLE_1322144) BOUND_VARIABLE_1322145))))) (let ((_let_3445 (forall ((BOUND_VARIABLE_1322137 tptp.int) (BOUND_VARIABLE_1322138 tptp.int)) (= (= BOUND_VARIABLE_1322137 BOUND_VARIABLE_1322138) (ho_11094 (ho_11093 k_11273 BOUND_VARIABLE_1322137) BOUND_VARIABLE_1322138))))) (let ((_let_3446 (forall ((BOUND_VARIABLE_1322130 tptp.set_nat) (BOUND_VARIABLE_1322131 tptp.set_nat)) (= (= BOUND_VARIABLE_1322130 BOUND_VARIABLE_1322131) (ho_11191 (ho_11209 k_11274 BOUND_VARIABLE_1322130) BOUND_VARIABLE_1322131))))) (let ((_let_3447 (forall ((BOUND_VARIABLE_1322123 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1322124 tptp.set_Pr958786334691620121nt_int)) (= (= BOUND_VARIABLE_1322123 BOUND_VARIABLE_1322124) (ho_11211 (ho_11218 k_11275 BOUND_VARIABLE_1322123) BOUND_VARIABLE_1322124))))) (let ((_let_3448 (forall ((BOUND_VARIABLE_1322116 tptp.list_nat) (BOUND_VARIABLE_1322117 tptp.list_nat)) (= (= BOUND_VARIABLE_1322116 BOUND_VARIABLE_1322117) (ho_11278 (ho_11277 k_11276 BOUND_VARIABLE_1322116) BOUND_VARIABLE_1322117))))) (let ((_let_3449 (forall ((BOUND_VARIABLE_1322109 Bool) (BOUND_VARIABLE_1322110 Bool)) (= (= BOUND_VARIABLE_1322109 BOUND_VARIABLE_1322110) (ho_11194 (ho_11201 k_11279 BOUND_VARIABLE_1322109) BOUND_VARIABLE_1322110))))) (let ((_let_3450 (forall ((BOUND_VARIABLE_1322095 tptp.int) (BOUND_VARIABLE_1322096 tptp.int)) (= (or (= BOUND_VARIABLE_1322095 BOUND_VARIABLE_1322096) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1322096) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11280 BOUND_VARIABLE_1322095) BOUND_VARIABLE_1322096))))) (let ((_let_3451 (forall ((BOUND_VARIABLE_1322081 tptp.nat) (BOUND_VARIABLE_1322082 tptp.nat)) (= (or (= BOUND_VARIABLE_1322081 BOUND_VARIABLE_1322082) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1322082) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11281 BOUND_VARIABLE_1322081) BOUND_VARIABLE_1322082))))) (let ((_let_3452 (forall ((BOUND_VARIABLE_1322067 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1322068 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1322067 BOUND_VARIABLE_1322068) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1322068) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_11282 BOUND_VARIABLE_1322067) BOUND_VARIABLE_1322068))))) (let ((_let_3453 (forall ((BOUND_VARIABLE_1322053 tptp.int) (BOUND_VARIABLE_1322054 tptp.int)) (= (or (= BOUND_VARIABLE_1322053 BOUND_VARIABLE_1322054) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1322054) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11283 BOUND_VARIABLE_1322053) BOUND_VARIABLE_1322054))))) (let ((_let_3454 (forall ((BOUND_VARIABLE_1322039 tptp.nat) (BOUND_VARIABLE_1322040 tptp.nat)) (= (or (= BOUND_VARIABLE_1322039 BOUND_VARIABLE_1322040) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1322040) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11284 BOUND_VARIABLE_1322039) BOUND_VARIABLE_1322040))))) (let ((_let_3455 (forall ((BOUND_VARIABLE_1322025 Bool) (BOUND_VARIABLE_1322026 Bool)) (= (or (= BOUND_VARIABLE_1322025 BOUND_VARIABLE_1322026) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1322026) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11285 BOUND_VARIABLE_1322025) BOUND_VARIABLE_1322026))))) (let ((_let_3456 (forall ((BOUND_VARIABLE_1322018 tptp.produc4166570645942440679at_nat) (BOUND_VARIABLE_1322019 tptp.produc4166570645942440679at_nat)) (= (= BOUND_VARIABLE_1322018 BOUND_VARIABLE_1322019) (ho_11051 (ho_11050 k_11286 BOUND_VARIABLE_1322018) BOUND_VARIABLE_1322019))))) (let ((_let_3457 (forall ((BOUND_VARIABLE_1322011 tptp.produc4166570645942440679at_nat) (BOUND_VARIABLE_1322012 tptp.produc4166570645942440679at_nat)) (= (= BOUND_VARIABLE_1322011 BOUND_VARIABLE_1322012) (ho_11051 (ho_11050 k_11287 BOUND_VARIABLE_1322011) BOUND_VARIABLE_1322012))))) (let ((_let_3458 (forall ((BOUND_VARIABLE_1344705 |u_(-> tptp.a tptp.heap_Time_Heap_a)|) (BOUND_VARIABLE_1321999 tptp.a) (BOUND_VARIABLE_1322000 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1322001 tptp.nat)) (= (ho_11293 (ho_11292 (ho_11291 (ho_11290 k_11289 BOUND_VARIABLE_1344705) BOUND_VARIABLE_1321999) BOUND_VARIABLE_1322000) BOUND_VARIABLE_1322001) (ho_11299 (ho_11298 k_11297 BOUND_VARIABLE_1322001) (ho_11296 (ho_11295 k_11294 (ho_11288 BOUND_VARIABLE_1344705 BOUND_VARIABLE_1321999)) BOUND_VARIABLE_1322000)))))) (let ((_let_3459 (forall ((BOUND_VARIABLE_1344753 |u_(-> tptp.b tptp.heap_Time_Heap_a)|) (BOUND_VARIABLE_1321986 tptp.b) (BOUND_VARIABLE_1321987 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321988 tptp.nat)) (= (ho_11293 (ho_11292 (ho_11303 (ho_11302 k_11301 BOUND_VARIABLE_1344753) BOUND_VARIABLE_1321986) BOUND_VARIABLE_1321987) BOUND_VARIABLE_1321988) (ho_11299 (ho_11298 k_11297 BOUND_VARIABLE_1321988) (ho_11296 (ho_11295 k_11294 (ho_11300 BOUND_VARIABLE_1344753 BOUND_VARIABLE_1321986)) BOUND_VARIABLE_1321987)))))) (let ((_let_3460 (forall ((BOUND_VARIABLE_1344782 |u_(-> tptp.a tptp.heap_Time_Heap_b)|) (BOUND_VARIABLE_1321973 tptp.a) (BOUND_VARIABLE_1321974 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321975 tptp.nat)) (= (ho_11309 (ho_11308 (ho_11307 (ho_11306 k_11305 BOUND_VARIABLE_1344782) BOUND_VARIABLE_1321973) BOUND_VARIABLE_1321974) BOUND_VARIABLE_1321975) (ho_11315 (ho_11314 k_11313 BOUND_VARIABLE_1321975) (ho_11312 (ho_11311 k_11310 (ho_11304 BOUND_VARIABLE_1344782 BOUND_VARIABLE_1321973)) BOUND_VARIABLE_1321974)))))) (let ((_let_3461 (forall ((BOUND_VARIABLE_1344830 |u_(-> tptp.b tptp.heap_Time_Heap_b)|) (BOUND_VARIABLE_1321960 tptp.b) (BOUND_VARIABLE_1321961 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321962 tptp.nat)) (= (ho_11309 (ho_11308 (ho_11319 (ho_11318 k_11317 BOUND_VARIABLE_1344830) BOUND_VARIABLE_1321960) BOUND_VARIABLE_1321961) BOUND_VARIABLE_1321962) (ho_11315 (ho_11314 k_11313 BOUND_VARIABLE_1321962) (ho_11312 (ho_11311 k_11310 (ho_11316 BOUND_VARIABLE_1344830 BOUND_VARIABLE_1321960)) BOUND_VARIABLE_1321961)))))) (let ((_let_3462 (forall ((BOUND_VARIABLE_1321938 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1321939 tptp.nat) (BOUND_VARIABLE_1321940 tptp.nat) (BOUND_VARIABLE_1321941 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1321942 tptp.nat) (BOUND_VARIABLE_1321943 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11324 (ho_11323 (ho_11322 (ho_11321 k_11320 BOUND_VARIABLE_1321938) BOUND_VARIABLE_1321939) BOUND_VARIABLE_1321940) BOUND_VARIABLE_1321941) BOUND_VARIABLE_1321942) BOUND_VARIABLE_1321943) (or (ho_11070 (ho_11069 k_11068 (ho_11067 (ho_11066 k_11065 BOUND_VARIABLE_1321939) BOUND_VARIABLE_1321942)) BOUND_VARIABLE_1321938) (and (= BOUND_VARIABLE_1321939 BOUND_VARIABLE_1321942) (ho_11070 (ho_11069 k_11068 (ho_11067 (ho_11066 k_11065 BOUND_VARIABLE_1321940) BOUND_VARIABLE_1321943)) BOUND_VARIABLE_1321941))))))) (let ((_let_3463 (forall ((BOUND_VARIABLE_1321930 tptp.set_int) (BOUND_VARIABLE_1321931 tptp.int)) (= (ho_11094 (ho_11234 k_11325 BOUND_VARIABLE_1321930) BOUND_VARIABLE_1321931) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1321931) BOUND_VARIABLE_1321930))))) (let ((_let_3464 (forall ((BOUND_VARIABLE_1321919 tptp.assn) (BOUND_VARIABLE_1321920 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 k_11326 BOUND_VARIABLE_1321919) BOUND_VARIABLE_1321920) (and (ho_11328 k_11330 BOUND_VARIABLE_1321920) (not (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321919) BOUND_VARIABLE_1321920))))))) (let ((_let_3465 (forall ((BOUND_VARIABLE_1321911 tptp.set_nat) (BOUND_VARIABLE_1321912 tptp.nat)) (= (ho_11054 (ho_11240 k_11331 BOUND_VARIABLE_1321911) BOUND_VARIABLE_1321912) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1321912) BOUND_VARIABLE_1321911))))) (let ((_let_3466 (forall ((BOUND_VARIABLE_1321903 tptp.set_int) (BOUND_VARIABLE_1321904 tptp.int)) (= (ho_11094 (ho_11234 k_11332 BOUND_VARIABLE_1321903) BOUND_VARIABLE_1321904) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1321904) BOUND_VARIABLE_1321903))))) (let ((_let_3467 (forall ((BOUND_VARIABLE_1321892 tptp.assn) (BOUND_VARIABLE_1321893 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 k_11333 BOUND_VARIABLE_1321892) BOUND_VARIABLE_1321893) (and (ho_11328 k_11330 BOUND_VARIABLE_1321893) (not (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321892) BOUND_VARIABLE_1321893))))))) (let ((_let_3468 (forall ((BOUND_VARIABLE_1321884 tptp.set_nat) (BOUND_VARIABLE_1321885 tptp.nat)) (= (ho_11054 (ho_11240 k_11334 BOUND_VARIABLE_1321884) BOUND_VARIABLE_1321885) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1321885) BOUND_VARIABLE_1321884))))) (let ((_let_3469 (forall ((BOUND_VARIABLE_1321876 tptp.set_int) (BOUND_VARIABLE_1321877 tptp.int)) (= (ho_11094 (ho_11234 k_11335 BOUND_VARIABLE_1321876) BOUND_VARIABLE_1321877) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1321877) BOUND_VARIABLE_1321876))))) (let ((_let_3470 (forall ((BOUND_VARIABLE_1321865 tptp.assn) (BOUND_VARIABLE_1321866 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 k_11336 BOUND_VARIABLE_1321865) BOUND_VARIABLE_1321866) (and (ho_11328 k_11330 BOUND_VARIABLE_1321866) (not (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321865) BOUND_VARIABLE_1321866))))))) (let ((_let_3471 (forall ((BOUND_VARIABLE_1321857 tptp.set_nat) (BOUND_VARIABLE_1321858 tptp.nat)) (= (ho_11054 (ho_11240 k_11337 BOUND_VARIABLE_1321857) BOUND_VARIABLE_1321858) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1321858) BOUND_VARIABLE_1321857))))) (let ((_let_3472 (forall ((BOUND_VARIABLE_1321846 tptp.set_int) (BOUND_VARIABLE_1321847 tptp.set_int) (BOUND_VARIABLE_1321848 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1321848))) (= (ho_11094 (ho_11234 (ho_11339 k_11338 BOUND_VARIABLE_1321846) BOUND_VARIABLE_1321847) BOUND_VARIABLE_1321848) (and (ho_11180 _let_1 BOUND_VARIABLE_1321846) (ho_11180 _let_1 BOUND_VARIABLE_1321847))))))) (let ((_let_3473 (forall ((BOUND_VARIABLE_1321835 tptp.set_int) (BOUND_VARIABLE_1321836 tptp.set_int) (BOUND_VARIABLE_1321837 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1321837))) (= (ho_11094 (ho_11234 (ho_11339 k_11340 BOUND_VARIABLE_1321835) BOUND_VARIABLE_1321836) BOUND_VARIABLE_1321837) (and (ho_11180 _let_1 BOUND_VARIABLE_1321835) (ho_11180 _let_1 BOUND_VARIABLE_1321836))))))) (let ((_let_3474 (forall ((BOUND_VARIABLE_1321824 tptp.set_int) (BOUND_VARIABLE_1321825 tptp.set_int) (BOUND_VARIABLE_1321826 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1321826))) (= (ho_11094 (ho_11234 (ho_11339 k_11341 BOUND_VARIABLE_1321824) BOUND_VARIABLE_1321825) BOUND_VARIABLE_1321826) (or (ho_11180 _let_1 BOUND_VARIABLE_1321824) (ho_11180 _let_1 BOUND_VARIABLE_1321825))))))) (let ((_let_3475 (forall ((BOUND_VARIABLE_1321813 tptp.set_nat) (BOUND_VARIABLE_1321814 tptp.set_nat) (BOUND_VARIABLE_1321815 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1321815))) (= (ho_11054 (ho_11240 (ho_11343 k_11342 BOUND_VARIABLE_1321813) BOUND_VARIABLE_1321814) BOUND_VARIABLE_1321815) (and (ho_11191 _let_1 BOUND_VARIABLE_1321813) (ho_11191 _let_1 BOUND_VARIABLE_1321814))))))) (let ((_let_3476 (forall ((BOUND_VARIABLE_1321802 tptp.set_nat) (BOUND_VARIABLE_1321803 tptp.set_nat) (BOUND_VARIABLE_1321804 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1321804))) (= (ho_11054 (ho_11240 (ho_11343 k_11344 BOUND_VARIABLE_1321802) BOUND_VARIABLE_1321803) BOUND_VARIABLE_1321804) (and (ho_11191 _let_1 BOUND_VARIABLE_1321802) (ho_11191 _let_1 BOUND_VARIABLE_1321803))))))) (let ((_let_3477 (forall ((BOUND_VARIABLE_1321791 tptp.set_nat) (BOUND_VARIABLE_1321792 tptp.set_nat) (BOUND_VARIABLE_1321793 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1321793))) (= (ho_11054 (ho_11240 (ho_11343 k_11345 BOUND_VARIABLE_1321791) BOUND_VARIABLE_1321792) BOUND_VARIABLE_1321793) (or (ho_11191 _let_1 BOUND_VARIABLE_1321791) (ho_11191 _let_1 BOUND_VARIABLE_1321792))))))) (let ((_let_3478 (forall ((BOUND_VARIABLE_1321779 tptp.assn) (BOUND_VARIABLE_1321780 tptp.assn) (BOUND_VARIABLE_1321781 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 (ho_11347 k_11346 BOUND_VARIABLE_1321779) BOUND_VARIABLE_1321780) BOUND_VARIABLE_1321781) (and (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321779) BOUND_VARIABLE_1321781) (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321780) BOUND_VARIABLE_1321781)))))) (let ((_let_3479 (forall ((BOUND_VARIABLE_1321767 tptp.assn) (BOUND_VARIABLE_1321768 tptp.assn) (BOUND_VARIABLE_1321769 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 (ho_11347 k_11348 BOUND_VARIABLE_1321767) BOUND_VARIABLE_1321768) BOUND_VARIABLE_1321769) (and (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321767) BOUND_VARIABLE_1321769) (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321768) BOUND_VARIABLE_1321769)))))) (let ((_let_3480 (forall ((BOUND_VARIABLE_1321755 tptp.assn) (BOUND_VARIABLE_1321756 tptp.assn) (BOUND_VARIABLE_1321757 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 (ho_11347 k_11349 BOUND_VARIABLE_1321755) BOUND_VARIABLE_1321756) BOUND_VARIABLE_1321757) (or (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321755) BOUND_VARIABLE_1321757) (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321756) BOUND_VARIABLE_1321757)))))) (let ((_let_3481 (forall ((BOUND_VARIABLE_1321744 tptp.set_int) (BOUND_VARIABLE_1321745 tptp.set_int) (BOUND_VARIABLE_1321746 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1321746))) (= (ho_11094 (ho_11234 (ho_11339 k_11350 BOUND_VARIABLE_1321744) BOUND_VARIABLE_1321745) BOUND_VARIABLE_1321746) (and (ho_11180 _let_1 BOUND_VARIABLE_1321744) (ho_11180 _let_1 BOUND_VARIABLE_1321745))))))) (let ((_let_3482 (forall ((BOUND_VARIABLE_1321733 tptp.set_int) (BOUND_VARIABLE_1321734 tptp.set_int) (BOUND_VARIABLE_1321735 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1321735))) (= (ho_11094 (ho_11234 (ho_11339 k_11351 BOUND_VARIABLE_1321733) BOUND_VARIABLE_1321734) BOUND_VARIABLE_1321735) (or (ho_11180 _let_1 BOUND_VARIABLE_1321733) (ho_11180 _let_1 BOUND_VARIABLE_1321734))))))) (let ((_let_3483 (forall ((BOUND_VARIABLE_1321722 tptp.set_int) (BOUND_VARIABLE_1321723 tptp.set_int) (BOUND_VARIABLE_1321724 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1321724))) (= (ho_11094 (ho_11234 (ho_11339 k_11352 BOUND_VARIABLE_1321722) BOUND_VARIABLE_1321723) BOUND_VARIABLE_1321724) (or (ho_11180 _let_1 BOUND_VARIABLE_1321722) (ho_11180 _let_1 BOUND_VARIABLE_1321723))))))) (let ((_let_3484 (forall ((BOUND_VARIABLE_1321711 tptp.set_nat) (BOUND_VARIABLE_1321712 tptp.set_nat) (BOUND_VARIABLE_1321713 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1321713))) (= (ho_11054 (ho_11240 (ho_11343 k_11353 BOUND_VARIABLE_1321711) BOUND_VARIABLE_1321712) BOUND_VARIABLE_1321713) (and (ho_11191 _let_1 BOUND_VARIABLE_1321711) (ho_11191 _let_1 BOUND_VARIABLE_1321712))))))) (let ((_let_3485 (forall ((BOUND_VARIABLE_1321700 tptp.set_nat) (BOUND_VARIABLE_1321701 tptp.set_nat) (BOUND_VARIABLE_1321702 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1321702))) (= (ho_11054 (ho_11240 (ho_11343 k_11354 BOUND_VARIABLE_1321700) BOUND_VARIABLE_1321701) BOUND_VARIABLE_1321702) (or (ho_11191 _let_1 BOUND_VARIABLE_1321700) (ho_11191 _let_1 BOUND_VARIABLE_1321701))))))) (let ((_let_3486 (forall ((BOUND_VARIABLE_1321689 tptp.set_nat) (BOUND_VARIABLE_1321690 tptp.set_nat) (BOUND_VARIABLE_1321691 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1321691))) (= (ho_11054 (ho_11240 (ho_11343 k_11355 BOUND_VARIABLE_1321689) BOUND_VARIABLE_1321690) BOUND_VARIABLE_1321691) (or (ho_11191 _let_1 BOUND_VARIABLE_1321689) (ho_11191 _let_1 BOUND_VARIABLE_1321690))))))) (let ((_let_3487 (forall ((BOUND_VARIABLE_1321677 tptp.assn) (BOUND_VARIABLE_1321678 tptp.assn) (BOUND_VARIABLE_1321679 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 (ho_11347 k_11356 BOUND_VARIABLE_1321677) BOUND_VARIABLE_1321678) BOUND_VARIABLE_1321679) (and (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321677) BOUND_VARIABLE_1321679) (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321678) BOUND_VARIABLE_1321679)))))) (let ((_let_3488 (forall ((BOUND_VARIABLE_1321665 tptp.assn) (BOUND_VARIABLE_1321666 tptp.assn) (BOUND_VARIABLE_1321667 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 (ho_11347 k_11357 BOUND_VARIABLE_1321665) BOUND_VARIABLE_1321666) BOUND_VARIABLE_1321667) (or (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321665) BOUND_VARIABLE_1321667) (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321666) BOUND_VARIABLE_1321667)))))) (let ((_let_3489 (forall ((BOUND_VARIABLE_1321653 tptp.assn) (BOUND_VARIABLE_1321654 tptp.assn) (BOUND_VARIABLE_1321655 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 (ho_11347 k_11358 BOUND_VARIABLE_1321653) BOUND_VARIABLE_1321654) BOUND_VARIABLE_1321655) (or (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321653) BOUND_VARIABLE_1321655) (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321654) BOUND_VARIABLE_1321655)))))) (let ((_let_3490 (forall ((BOUND_VARIABLE_1321642 tptp.set_nat) (BOUND_VARIABLE_1321643 tptp.set_nat) (BOUND_VARIABLE_1321644 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1321644))) (= (ho_11054 (ho_11240 (ho_11343 k_11359 BOUND_VARIABLE_1321642) BOUND_VARIABLE_1321643) BOUND_VARIABLE_1321644) (and (ho_11191 _let_1 BOUND_VARIABLE_1321642) (ho_11191 _let_1 BOUND_VARIABLE_1321643))))))) (let ((_let_3491 (forall ((BOUND_VARIABLE_1321631 tptp.set_nat) (BOUND_VARIABLE_1321632 tptp.set_nat) (BOUND_VARIABLE_1321633 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1321633))) (= (ho_11054 (ho_11240 (ho_11343 k_11360 BOUND_VARIABLE_1321631) BOUND_VARIABLE_1321632) BOUND_VARIABLE_1321633) (and (ho_11191 _let_1 BOUND_VARIABLE_1321631) (ho_11191 _let_1 BOUND_VARIABLE_1321632))))))) (let ((_let_3492 (forall ((BOUND_VARIABLE_1321620 tptp.set_nat) (BOUND_VARIABLE_1321621 tptp.set_nat) (BOUND_VARIABLE_1321622 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1321622))) (= (ho_11054 (ho_11240 (ho_11343 k_11361 BOUND_VARIABLE_1321620) BOUND_VARIABLE_1321621) BOUND_VARIABLE_1321622) (or (ho_11191 _let_1 BOUND_VARIABLE_1321620) (ho_11191 _let_1 BOUND_VARIABLE_1321621))))))) (let ((_let_3493 (forall ((BOUND_VARIABLE_1321609 tptp.set_nat) (BOUND_VARIABLE_1321610 tptp.set_nat) (BOUND_VARIABLE_1321611 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1321611))) (= (ho_11054 (ho_11240 (ho_11343 k_11362 BOUND_VARIABLE_1321609) BOUND_VARIABLE_1321610) BOUND_VARIABLE_1321611) (or (ho_11191 _let_1 BOUND_VARIABLE_1321609) (ho_11191 _let_1 BOUND_VARIABLE_1321610))))))) (let ((_let_3494 (forall ((BOUND_VARIABLE_1321598 tptp.set_nat) (BOUND_VARIABLE_1321599 tptp.set_nat) (BOUND_VARIABLE_1321600 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1321600))) (= (ho_11054 (ho_11240 (ho_11343 k_11363 BOUND_VARIABLE_1321598) BOUND_VARIABLE_1321599) BOUND_VARIABLE_1321600) (and (ho_11191 _let_1 BOUND_VARIABLE_1321598) (ho_11191 _let_1 BOUND_VARIABLE_1321599))))))) (let ((_let_3495 (forall ((BOUND_VARIABLE_1321587 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1321588 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1321589 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1321589))) (= (ho_11184 (ho_11237 (ho_11365 k_11364 BOUND_VARIABLE_1321587) BOUND_VARIABLE_1321588) BOUND_VARIABLE_1321589) (and (ho_11070 _let_1 BOUND_VARIABLE_1321587) (ho_11070 _let_1 BOUND_VARIABLE_1321588))))))) (let ((_let_3496 (forall ((BOUND_VARIABLE_1321575 tptp.assn) (BOUND_VARIABLE_1321576 tptp.assn) (BOUND_VARIABLE_1321577 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 (ho_11347 k_11366 BOUND_VARIABLE_1321575) BOUND_VARIABLE_1321576) BOUND_VARIABLE_1321577) (and (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321575) BOUND_VARIABLE_1321577) (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321576) BOUND_VARIABLE_1321577)))))) (let ((_let_3497 (forall ((BOUND_VARIABLE_1345336 |u_(-> tptp.a tptp.heap_Time_Heap_a)|) (BOUND_VARIABLE_1321563 tptp.a) (BOUND_VARIABLE_1321564 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321565 tptp.nat)) (= (ho_11293 (ho_11292 (ho_11291 (ho_11290 k_11367 BOUND_VARIABLE_1345336) BOUND_VARIABLE_1321563) BOUND_VARIABLE_1321564) BOUND_VARIABLE_1321565) (ho_11299 (ho_11298 k_11297 BOUND_VARIABLE_1321565) (ho_11296 (ho_11295 k_11294 (ho_11288 BOUND_VARIABLE_1345336 BOUND_VARIABLE_1321563)) BOUND_VARIABLE_1321564)))))) (let ((_let_3498 (forall ((BOUND_VARIABLE_1345354 |u_(-> tptp.a tptp.heap_Time_Heap_b)|) (BOUND_VARIABLE_1321550 tptp.a) (BOUND_VARIABLE_1321551 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321552 tptp.nat)) (= (ho_11309 (ho_11308 (ho_11307 (ho_11306 k_11368 BOUND_VARIABLE_1345354) BOUND_VARIABLE_1321550) BOUND_VARIABLE_1321551) BOUND_VARIABLE_1321552) (ho_11315 (ho_11314 k_11313 BOUND_VARIABLE_1321552) (ho_11312 (ho_11311 k_11310 (ho_11304 BOUND_VARIABLE_1345354 BOUND_VARIABLE_1321550)) BOUND_VARIABLE_1321551)))))) (let ((_let_3499 (forall ((BOUND_VARIABLE_1345372 |u_(-> tptp.b tptp.heap_Time_Heap_a)|) (BOUND_VARIABLE_1321537 tptp.b) (BOUND_VARIABLE_1321538 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321539 tptp.nat)) (= (ho_11293 (ho_11292 (ho_11303 (ho_11302 k_11369 BOUND_VARIABLE_1345372) BOUND_VARIABLE_1321537) BOUND_VARIABLE_1321538) BOUND_VARIABLE_1321539) (ho_11299 (ho_11298 k_11297 BOUND_VARIABLE_1321539) (ho_11296 (ho_11295 k_11294 (ho_11300 BOUND_VARIABLE_1345372 BOUND_VARIABLE_1321537)) BOUND_VARIABLE_1321538)))))) (let ((_let_3500 (forall ((BOUND_VARIABLE_1345390 |u_(-> tptp.b tptp.heap_Time_Heap_b)|) (BOUND_VARIABLE_1321524 tptp.b) (BOUND_VARIABLE_1321525 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321526 tptp.nat)) (= (ho_11309 (ho_11308 (ho_11319 (ho_11318 k_11370 BOUND_VARIABLE_1345390) BOUND_VARIABLE_1321524) BOUND_VARIABLE_1321525) BOUND_VARIABLE_1321526) (ho_11315 (ho_11314 k_11313 BOUND_VARIABLE_1321526) (ho_11312 (ho_11311 k_11310 (ho_11316 BOUND_VARIABLE_1345390 BOUND_VARIABLE_1321524)) BOUND_VARIABLE_1321525)))))) (let ((_let_3501 (forall ((BOUND_VARIABLE_1321512 tptp.set_nat) (BOUND_VARIABLE_1321513 tptp.set_nat) (BOUND_VARIABLE_1321514 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1321514))) (= (ho_11054 (ho_11240 (ho_11343 k_11371 BOUND_VARIABLE_1321512) BOUND_VARIABLE_1321513) BOUND_VARIABLE_1321514) (or (ho_11191 _let_1 BOUND_VARIABLE_1321512) (ho_11191 _let_1 BOUND_VARIABLE_1321513))))))) (let ((_let_3502 (forall ((BOUND_VARIABLE_1321501 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1321502 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1321503 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (ho_11259 k_11258 BOUND_VARIABLE_1321503))) (= (ho_11263 (ho_11374 (ho_11373 k_11372 BOUND_VARIABLE_1321501) BOUND_VARIABLE_1321502) BOUND_VARIABLE_1321503) (or (ho_11260 _let_1 BOUND_VARIABLE_1321501) (ho_11260 _let_1 BOUND_VARIABLE_1321502))))))) (let ((_let_3503 (forall ((BOUND_VARIABLE_1321490 tptp.set_Pr8551490117392284871at_nat) (BOUND_VARIABLE_1321491 tptp.set_Pr8551490117392284871at_nat) (BOUND_VARIABLE_1321492 tptp.produc4166570645942440679at_nat)) (let ((_let_1 (ho_11266 k_11265 BOUND_VARIABLE_1321492))) (= (ho_11051 (ho_11377 (ho_11376 k_11375 BOUND_VARIABLE_1321490) BOUND_VARIABLE_1321491) BOUND_VARIABLE_1321492) (or (ho_11267 _let_1 BOUND_VARIABLE_1321490) (ho_11267 _let_1 BOUND_VARIABLE_1321491))))))) (let ((_let_3504 (forall ((BOUND_VARIABLE_1345459 |u_(-> tptp.a tptp.heap_Time_Heap_a)|) (BOUND_VARIABLE_1321478 tptp.a) (BOUND_VARIABLE_1321479 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321480 tptp.nat)) (= (ho_11293 (ho_11292 (ho_11291 (ho_11290 k_11378 BOUND_VARIABLE_1345459) BOUND_VARIABLE_1321478) BOUND_VARIABLE_1321479) BOUND_VARIABLE_1321480) (ho_11299 (ho_11298 k_11297 BOUND_VARIABLE_1321480) (ho_11296 (ho_11295 k_11294 (ho_11288 BOUND_VARIABLE_1345459 BOUND_VARIABLE_1321478)) BOUND_VARIABLE_1321479)))))) (let ((_let_3505 (forall ((BOUND_VARIABLE_1345477 |u_(-> tptp.a tptp.heap_Time_Heap_b)|) (BOUND_VARIABLE_1321465 tptp.a) (BOUND_VARIABLE_1321466 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321467 tptp.nat)) (= (ho_11309 (ho_11308 (ho_11307 (ho_11306 k_11379 BOUND_VARIABLE_1345477) BOUND_VARIABLE_1321465) BOUND_VARIABLE_1321466) BOUND_VARIABLE_1321467) (ho_11315 (ho_11314 k_11313 BOUND_VARIABLE_1321467) (ho_11312 (ho_11311 k_11310 (ho_11304 BOUND_VARIABLE_1345477 BOUND_VARIABLE_1321465)) BOUND_VARIABLE_1321466)))))) (let ((_let_3506 (forall ((BOUND_VARIABLE_1345497 |u_(-> tptp.a tptp.heap_T5738788834812785303t_unit)|) (BOUND_VARIABLE_1321452 tptp.a) (BOUND_VARIABLE_1321453 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321454 tptp.nat)) (= (ho_11385 (ho_11384 (ho_11383 (ho_11382 k_11381 BOUND_VARIABLE_1345497) BOUND_VARIABLE_1321452) BOUND_VARIABLE_1321453) BOUND_VARIABLE_1321454) (ho_11391 (ho_11390 k_11389 BOUND_VARIABLE_1321454) (ho_11388 (ho_11387 k_11386 (ho_11380 BOUND_VARIABLE_1345497 BOUND_VARIABLE_1321452)) BOUND_VARIABLE_1321453)))))) (let ((_let_3507 (forall ((BOUND_VARIABLE_1345544 |u_(-> tptp.b tptp.heap_Time_Heap_a)|) (BOUND_VARIABLE_1321439 tptp.b) (BOUND_VARIABLE_1321440 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321441 tptp.nat)) (= (ho_11293 (ho_11292 (ho_11303 (ho_11302 k_11392 BOUND_VARIABLE_1345544) BOUND_VARIABLE_1321439) BOUND_VARIABLE_1321440) BOUND_VARIABLE_1321441) (ho_11299 (ho_11298 k_11297 BOUND_VARIABLE_1321441) (ho_11296 (ho_11295 k_11294 (ho_11300 BOUND_VARIABLE_1345544 BOUND_VARIABLE_1321439)) BOUND_VARIABLE_1321440)))))) (let ((_let_3508 (forall ((BOUND_VARIABLE_1345562 |u_(-> tptp.b tptp.heap_Time_Heap_b)|) (BOUND_VARIABLE_1321426 tptp.b) (BOUND_VARIABLE_1321427 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321428 tptp.nat)) (= (ho_11309 (ho_11308 (ho_11319 (ho_11318 k_11393 BOUND_VARIABLE_1345562) BOUND_VARIABLE_1321426) BOUND_VARIABLE_1321427) BOUND_VARIABLE_1321428) (ho_11315 (ho_11314 k_11313 BOUND_VARIABLE_1321428) (ho_11312 (ho_11311 k_11310 (ho_11316 BOUND_VARIABLE_1345562 BOUND_VARIABLE_1321426)) BOUND_VARIABLE_1321427)))))) (let ((_let_3509 (forall ((BOUND_VARIABLE_1345581 |u_(-> tptp.b tptp.heap_T5738788834812785303t_unit)|) (BOUND_VARIABLE_1321413 tptp.b) (BOUND_VARIABLE_1321414 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321415 tptp.nat)) (= (ho_11385 (ho_11384 (ho_11397 (ho_11396 k_11395 BOUND_VARIABLE_1345581) BOUND_VARIABLE_1321413) BOUND_VARIABLE_1321414) BOUND_VARIABLE_1321415) (ho_11391 (ho_11390 k_11389 BOUND_VARIABLE_1321415) (ho_11388 (ho_11387 k_11386 (ho_11394 BOUND_VARIABLE_1345581 BOUND_VARIABLE_1321413)) BOUND_VARIABLE_1321414)))))) (let ((_let_3510 (forall ((BOUND_VARIABLE_1345608 |u_(-> tptp.a tptp.heap_Time_Heap_a)|) (BOUND_VARIABLE_1321400 tptp.a) (BOUND_VARIABLE_1321401 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321402 tptp.nat)) (= (ho_11293 (ho_11292 (ho_11291 (ho_11290 k_11398 BOUND_VARIABLE_1345608) BOUND_VARIABLE_1321400) BOUND_VARIABLE_1321401) BOUND_VARIABLE_1321402) (ho_11299 (ho_11298 k_11297 BOUND_VARIABLE_1321402) (ho_11296 (ho_11295 k_11294 (ho_11288 BOUND_VARIABLE_1345608 BOUND_VARIABLE_1321400)) BOUND_VARIABLE_1321401)))))) (let ((_let_3511 (forall ((BOUND_VARIABLE_1345626 |u_(-> tptp.a tptp.heap_Time_Heap_b)|) (BOUND_VARIABLE_1321387 tptp.a) (BOUND_VARIABLE_1321388 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321389 tptp.nat)) (= (ho_11309 (ho_11308 (ho_11307 (ho_11306 k_11399 BOUND_VARIABLE_1345626) BOUND_VARIABLE_1321387) BOUND_VARIABLE_1321388) BOUND_VARIABLE_1321389) (ho_11315 (ho_11314 k_11313 BOUND_VARIABLE_1321389) (ho_11312 (ho_11311 k_11310 (ho_11304 BOUND_VARIABLE_1345626 BOUND_VARIABLE_1321387)) BOUND_VARIABLE_1321388)))))) (let ((_let_3512 (forall ((BOUND_VARIABLE_1345644 |u_(-> tptp.b tptp.heap_Time_Heap_a)|) (BOUND_VARIABLE_1321374 tptp.b) (BOUND_VARIABLE_1321375 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321376 tptp.nat)) (= (ho_11293 (ho_11292 (ho_11303 (ho_11302 k_11400 BOUND_VARIABLE_1345644) BOUND_VARIABLE_1321374) BOUND_VARIABLE_1321375) BOUND_VARIABLE_1321376) (ho_11299 (ho_11298 k_11297 BOUND_VARIABLE_1321376) (ho_11296 (ho_11295 k_11294 (ho_11300 BOUND_VARIABLE_1345644 BOUND_VARIABLE_1321374)) BOUND_VARIABLE_1321375)))))) (let ((_let_3513 (forall ((BOUND_VARIABLE_1345662 |u_(-> tptp.b tptp.heap_Time_Heap_b)|) (BOUND_VARIABLE_1321361 tptp.b) (BOUND_VARIABLE_1321362 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1321363 tptp.nat)) (= (ho_11309 (ho_11308 (ho_11319 (ho_11318 k_11401 BOUND_VARIABLE_1345662) BOUND_VARIABLE_1321361) BOUND_VARIABLE_1321362) BOUND_VARIABLE_1321363) (ho_11315 (ho_11314 k_11313 BOUND_VARIABLE_1321363) (ho_11312 (ho_11311 k_11310 (ho_11316 BOUND_VARIABLE_1345662 BOUND_VARIABLE_1321361)) BOUND_VARIABLE_1321362)))))) (let ((_let_3514 (forall ((BOUND_VARIABLE_1321348 tptp.assn) (BOUND_VARIABLE_1321349 tptp.assn) (BOUND_VARIABLE_1321350 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 (ho_11347 k_11402 BOUND_VARIABLE_1321348) BOUND_VARIABLE_1321349) BOUND_VARIABLE_1321350) (and (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321348) BOUND_VARIABLE_1321350) (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321349) BOUND_VARIABLE_1321350)))))) (let ((_let_3515 (forall ((BOUND_VARIABLE_1321336 tptp.assn) (BOUND_VARIABLE_1321337 tptp.assn) (BOUND_VARIABLE_1321338 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 (ho_11347 k_11403 BOUND_VARIABLE_1321336) BOUND_VARIABLE_1321337) BOUND_VARIABLE_1321338) (and (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321336) BOUND_VARIABLE_1321338) (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1321337) BOUND_VARIABLE_1321338)))))) (let ((_let_3516 (forall ((BOUND_VARIABLE_1321325 tptp.set_int) (BOUND_VARIABLE_1321326 tptp.set_int) (BOUND_VARIABLE_1321327 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1321327))) (= (ho_11094 (ho_11234 (ho_11339 k_11404 BOUND_VARIABLE_1321325) BOUND_VARIABLE_1321326) BOUND_VARIABLE_1321327) (or (ho_11180 _let_1 BOUND_VARIABLE_1321325) (ho_11180 _let_1 BOUND_VARIABLE_1321326))))))) (let ((_let_3517 (forall ((BOUND_VARIABLE_1321314 tptp.set_int) (BOUND_VARIABLE_1321315 tptp.set_int) (BOUND_VARIABLE_1321316 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1321316))) (= (ho_11094 (ho_11234 (ho_11339 k_11405 BOUND_VARIABLE_1321314) BOUND_VARIABLE_1321315) BOUND_VARIABLE_1321316) (or (ho_11180 _let_1 BOUND_VARIABLE_1321314) (ho_11180 _let_1 BOUND_VARIABLE_1321315))))))) (let ((_let_3518 (forall ((BOUND_VARIABLE_1321287 tptp.product_prod_int_int) (BOUND_VARIABLE_1321288 tptp.product_prod_int_int)) (let ((_let_1 (ho_11111 k_11110 BOUND_VARIABLE_1321288))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1321287))) (let ((_let_3 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (= (ho_11130 (ho_11407 k_11406 BOUND_VARIABLE_1321287) BOUND_VARIABLE_1321288) (and (not (= _let_3 _let_2)) (not (= _let_3 _let_1)) (= (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321288)) _let_2) (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321287)) _let_1)))))))))) (let ((_let_3519 (forall ((BOUND_VARIABLE_1321260 tptp.product_prod_int_int) (BOUND_VARIABLE_1321261 tptp.product_prod_int_int)) (let ((_let_1 (ho_11111 k_11110 BOUND_VARIABLE_1321261))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1321260))) (let ((_let_3 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (= (ho_11130 (ho_11407 k_11408 BOUND_VARIABLE_1321260) BOUND_VARIABLE_1321261) (and (not (= _let_3 _let_2)) (not (= _let_3 _let_1)) (= (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321261)) _let_2) (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321260)) _let_1)))))))))) (let ((_let_3520 (forall ((BOUND_VARIABLE_1321233 tptp.product_prod_int_int) (BOUND_VARIABLE_1321234 tptp.product_prod_int_int)) (let ((_let_1 (ho_11111 k_11110 BOUND_VARIABLE_1321234))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1321233))) (let ((_let_3 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (= (ho_11130 (ho_11407 k_11409 BOUND_VARIABLE_1321233) BOUND_VARIABLE_1321234) (and (not (= _let_3 _let_2)) (not (= _let_3 _let_1)) (= (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321234)) _let_2) (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321233)) _let_1)))))))))) (let ((_let_3521 (forall ((BOUND_VARIABLE_1321206 tptp.product_prod_int_int) (BOUND_VARIABLE_1321207 tptp.product_prod_int_int)) (let ((_let_1 (ho_11111 k_11110 BOUND_VARIABLE_1321207))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1321206))) (let ((_let_3 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (= (ho_11130 (ho_11407 k_11410 BOUND_VARIABLE_1321206) BOUND_VARIABLE_1321207) (and (not (= _let_3 _let_2)) (not (= _let_3 _let_1)) (= (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321207)) _let_2) (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321206)) _let_1)))))))))) (let ((_let_3522 (forall ((BOUND_VARIABLE_1321179 tptp.product_prod_int_int) (BOUND_VARIABLE_1321180 tptp.product_prod_int_int)) (let ((_let_1 (ho_11111 k_11110 BOUND_VARIABLE_1321180))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1321179))) (let ((_let_3 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (= (ho_11130 (ho_11407 k_11411 BOUND_VARIABLE_1321179) BOUND_VARIABLE_1321180) (and (not (= _let_3 _let_2)) (not (= _let_3 _let_1)) (= (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321180)) _let_2) (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321179)) _let_1)))))))))) (let ((_let_3523 (forall ((BOUND_VARIABLE_1321152 tptp.product_prod_int_int) (BOUND_VARIABLE_1321153 tptp.product_prod_int_int)) (let ((_let_1 (ho_11111 k_11110 BOUND_VARIABLE_1321153))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1321152))) (let ((_let_3 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (= (ho_11130 (ho_11407 k_11412 BOUND_VARIABLE_1321152) BOUND_VARIABLE_1321153) (and (not (= _let_3 _let_2)) (not (= _let_3 _let_1)) (= (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321153)) _let_2) (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321152)) _let_1)))))))))) (let ((_let_3524 (forall ((BOUND_VARIABLE_1321125 tptp.product_prod_int_int) (BOUND_VARIABLE_1321126 tptp.product_prod_int_int)) (let ((_let_1 (ho_11111 k_11110 BOUND_VARIABLE_1321126))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1321125))) (let ((_let_3 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (= (ho_11130 (ho_11407 k_11413 BOUND_VARIABLE_1321125) BOUND_VARIABLE_1321126) (and (not (= _let_3 _let_2)) (not (= _let_3 _let_1)) (= (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321126)) _let_2) (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321125)) _let_1)))))))))) (let ((_let_3525 (forall ((BOUND_VARIABLE_1321098 tptp.product_prod_int_int) (BOUND_VARIABLE_1321099 tptp.product_prod_int_int)) (let ((_let_1 (ho_11111 k_11110 BOUND_VARIABLE_1321099))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1321098))) (let ((_let_3 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (= (ho_11130 (ho_11407 k_11414 BOUND_VARIABLE_1321098) BOUND_VARIABLE_1321099) (and (not (= _let_3 _let_2)) (not (= _let_3 _let_1)) (= (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321099)) _let_2) (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321098)) _let_1)))))))))) (let ((_let_3526 (forall ((BOUND_VARIABLE_1321071 tptp.product_prod_int_int) (BOUND_VARIABLE_1321072 tptp.product_prod_int_int)) (let ((_let_1 (ho_11111 k_11110 BOUND_VARIABLE_1321072))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1321071))) (let ((_let_3 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (= (ho_11130 (ho_11407 k_11415 BOUND_VARIABLE_1321071) BOUND_VARIABLE_1321072) (and (not (= _let_3 _let_2)) (not (= _let_3 _let_1)) (= (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321072)) _let_2) (ho_11059 (ho_11058 k_11085 (ho_11111 k_11112 BOUND_VARIABLE_1321071)) _let_1)))))))))) (let ((_let_3527 (forall ((BOUND_VARIABLE_1321064 tptp.int) (BOUND_VARIABLE_1321065 tptp.int)) (= (= BOUND_VARIABLE_1321064 BOUND_VARIABLE_1321065) (ho_11094 (ho_11093 k_11416 BOUND_VARIABLE_1321064) BOUND_VARIABLE_1321065))))) (let ((_let_3528 (forall ((BOUND_VARIABLE_1321057 tptp.int) (BOUND_VARIABLE_1321058 tptp.int)) (= (= BOUND_VARIABLE_1321057 BOUND_VARIABLE_1321058) (ho_11094 (ho_11093 k_11417 BOUND_VARIABLE_1321057) BOUND_VARIABLE_1321058))))) (let ((_let_3529 (forall ((BOUND_VARIABLE_1321035 tptp.nat) (BOUND_VARIABLE_1321036 tptp.nat)) (= (ho_11054 (ho_11053 k_11418 BOUND_VARIABLE_1321035) BOUND_VARIABLE_1321036) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1321035 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1321036)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1321036 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1321035)) (ho_11056 k_11055 K3))))))))))) (let ((_let_3530 (forall ((BOUND_VARIABLE_1320995 tptp.nat) (BOUND_VARIABLE_1320996 tptp.nat)) (= (ho_11107 k_11106 (ho_11053 k_11052 BOUND_VARIABLE_1320995)) (ho_11421 (ho_11420 k_11419 BOUND_VARIABLE_1320995) BOUND_VARIABLE_1320996))))) (let ((_let_3531 (forall ((BOUND_VARIABLE_1320985 tptp.nat) (BOUND_VARIABLE_1320986 tptp.nat)) (= (ho_11421 (ho_11426 k_11425 (ho_11186 k_11185 (ho_11424 k_11423 k_11422))) BOUND_VARIABLE_1320985) (ho_11421 (ho_11420 k_11427 BOUND_VARIABLE_1320985) BOUND_VARIABLE_1320986))))) (let ((_let_3532 (forall ((BOUND_VARIABLE_1320971 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (ho_11186 k_11185 k_11183))) (= (or (= BOUND_VARIABLE_1320971 (ho_11430 (ho_11429 k_11428 _let_1) _let_1)) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1320971) tptp.bot_bo228742789529271731at_nat)) (ho_11263 k_11431 BOUND_VARIABLE_1320971)))))) (let ((_let_3533 (forall ((BOUND_VARIABLE_1320928 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320929 tptp.nat) (BOUND_VARIABLE_1320930 tptp.nat)) (= (ho_11184 (ho_11424 k_11423 (ho_11064 (ho_11063 k_11062 BOUND_VARIABLE_1320929) BOUND_VARIABLE_1320930)) BOUND_VARIABLE_1320928) (ho_11054 (ho_11053 (ho_11433 k_11432 BOUND_VARIABLE_1320928) BOUND_VARIABLE_1320929) BOUND_VARIABLE_1320930))))) (let ((_let_3534 (forall ((BOUND_VARIABLE_1320920 tptp.nat) (BOUND_VARIABLE_1320921 tptp.nat)) (= (ho_11054 (ho_11053 k_11434 BOUND_VARIABLE_1320920) BOUND_VARIABLE_1320921) (ho_11054 (ho_11053 k_11435 BOUND_VARIABLE_1320921) BOUND_VARIABLE_1320920))))) (let ((_let_3535 (forall ((BOUND_VARIABLE_1320900 tptp.nat) (BOUND_VARIABLE_1320901 tptp.nat) (BOUND_VARIABLE_1320902 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 k_11436 BOUND_VARIABLE_1320900) BOUND_VARIABLE_1320901) BOUND_VARIABLE_1320902) (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1320900 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11085 (ho_11056 k_11055 BOUND_VARIABLE_1320902)) (ho_11056 k_11055 BOUND_VARIABLE_1320901))))) (ho_11056 k_11055 K3))))))))))) (let ((_let_3536 (forall ((BOUND_VARIABLE_1320849 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320850 tptp.nat) (BOUND_VARIABLE_1320851 tptp.nat)) (= (ho_11184 (ho_11424 k_11423 (ho_11064 (ho_11063 k_11071 BOUND_VARIABLE_1320850) BOUND_VARIABLE_1320851)) BOUND_VARIABLE_1320849) (ho_11054 (ho_11053 (ho_11433 k_11437 BOUND_VARIABLE_1320849) BOUND_VARIABLE_1320850) BOUND_VARIABLE_1320851))))) (let ((_let_3537 (forall ((BOUND_VARIABLE_1320782 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320783 tptp.nat) (BOUND_VARIABLE_1320784 tptp.nat)) (= (ho_11184 (ho_11424 k_11423 (ho_11064 (ho_11063 k_11072 BOUND_VARIABLE_1320783) BOUND_VARIABLE_1320784)) BOUND_VARIABLE_1320782) (ho_11054 (ho_11053 (ho_11433 k_11438 BOUND_VARIABLE_1320782) BOUND_VARIABLE_1320783) BOUND_VARIABLE_1320784))))) (let ((_let_3538 (forall ((BOUND_VARIABLE_1320741 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320742 tptp.nat) (BOUND_VARIABLE_1320743 tptp.nat)) (= (ho_11441 (ho_11440 k_11439 (ho_11075 (ho_11074 k_11073 BOUND_VARIABLE_1320742) BOUND_VARIABLE_1320743)) BOUND_VARIABLE_1320741) (ho_11067 (ho_11066 (ho_11443 k_11442 BOUND_VARIABLE_1320741) BOUND_VARIABLE_1320742) BOUND_VARIABLE_1320743))))) (let ((_let_3539 (forall ((BOUND_VARIABLE_1320700 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320701 tptp.nat) (BOUND_VARIABLE_1320702 tptp.nat)) (= (ho_11441 (ho_11440 k_11439 (ho_11075 (ho_11074 k_11076 BOUND_VARIABLE_1320701) BOUND_VARIABLE_1320702)) BOUND_VARIABLE_1320700) (ho_11067 (ho_11066 (ho_11443 k_11444 BOUND_VARIABLE_1320700) BOUND_VARIABLE_1320701) BOUND_VARIABLE_1320702))))) (let ((_let_3540 (forall ((BOUND_VARIABLE_1320659 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320660 tptp.nat) (BOUND_VARIABLE_1320661 tptp.nat)) (= (ho_11441 (ho_11440 k_11439 (ho_11075 (ho_11074 k_11077 BOUND_VARIABLE_1320660) BOUND_VARIABLE_1320661)) BOUND_VARIABLE_1320659) (ho_11067 (ho_11066 (ho_11443 k_11445 BOUND_VARIABLE_1320659) BOUND_VARIABLE_1320660) BOUND_VARIABLE_1320661))))) (let ((_let_3541 (forall ((BOUND_VARIABLE_1320618 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320619 tptp.nat) (BOUND_VARIABLE_1320620 tptp.nat)) (= (ho_11441 (ho_11440 k_11439 (ho_11075 (ho_11074 k_11078 BOUND_VARIABLE_1320619) BOUND_VARIABLE_1320620)) BOUND_VARIABLE_1320618) (ho_11067 (ho_11066 (ho_11443 k_11446 BOUND_VARIABLE_1320618) BOUND_VARIABLE_1320619) BOUND_VARIABLE_1320620))))) (let ((_let_3542 (forall ((BOUND_VARIABLE_1320567 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320568 tptp.nat) (BOUND_VARIABLE_1320569 tptp.nat)) (= (ho_11184 (ho_11424 k_11423 (ho_11064 (ho_11063 k_11079 BOUND_VARIABLE_1320568) BOUND_VARIABLE_1320569)) BOUND_VARIABLE_1320567) (ho_11054 (ho_11053 (ho_11433 k_11447 BOUND_VARIABLE_1320567) BOUND_VARIABLE_1320568) BOUND_VARIABLE_1320569))))) (let ((_let_3543 (forall ((BOUND_VARIABLE_1320516 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320517 tptp.nat) (BOUND_VARIABLE_1320518 tptp.nat)) (= (ho_11184 (ho_11424 k_11423 (ho_11064 (ho_11063 k_11080 BOUND_VARIABLE_1320517) BOUND_VARIABLE_1320518)) BOUND_VARIABLE_1320516) (ho_11054 (ho_11053 (ho_11433 k_11448 BOUND_VARIABLE_1320516) BOUND_VARIABLE_1320517) BOUND_VARIABLE_1320518))))) (let ((_let_3544 (forall ((BOUND_VARIABLE_1320449 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320450 tptp.nat) (BOUND_VARIABLE_1320451 tptp.nat)) (= (ho_11184 (ho_11424 k_11423 (ho_11064 (ho_11063 k_11081 BOUND_VARIABLE_1320450) BOUND_VARIABLE_1320451)) BOUND_VARIABLE_1320449) (ho_11054 (ho_11053 (ho_11433 k_11449 BOUND_VARIABLE_1320449) BOUND_VARIABLE_1320450) BOUND_VARIABLE_1320451))))) (let ((_let_3545 (forall ((BOUND_VARIABLE_1320382 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320383 tptp.nat) (BOUND_VARIABLE_1320384 tptp.nat)) (= (ho_11184 (ho_11424 k_11423 (ho_11064 (ho_11063 k_11082 BOUND_VARIABLE_1320383) BOUND_VARIABLE_1320384)) BOUND_VARIABLE_1320382) (ho_11054 (ho_11053 (ho_11433 k_11450 BOUND_VARIABLE_1320382) BOUND_VARIABLE_1320383) BOUND_VARIABLE_1320384))))) (let ((_let_3546 (forall ((BOUND_VARIABLE_1320363 tptp.nat) (BOUND_VARIABLE_1320364 tptp.nat) (BOUND_VARIABLE_1320365 tptp.nat) (BOUND_VARIABLE_1320366 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 (ho_11063 k_11451 BOUND_VARIABLE_1320363) BOUND_VARIABLE_1320364) BOUND_VARIABLE_1320365) BOUND_VARIABLE_1320366) (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1320365)) (ho_11056 k_11055 BOUND_VARIABLE_1320364))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1320363)) (ho_11056 k_11055 BOUND_VARIABLE_1320366)))))))) (let ((_let_3547 (forall ((BOUND_VARIABLE_1320326 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320327 tptp.nat) (BOUND_VARIABLE_1320328 tptp.nat)) (= (ho_11184 (ho_11424 k_11423 (ho_11064 (ho_11063 k_11083 BOUND_VARIABLE_1320327) BOUND_VARIABLE_1320328)) BOUND_VARIABLE_1320326) (ho_11054 (ho_11053 (ho_11433 k_11452 BOUND_VARIABLE_1320326) BOUND_VARIABLE_1320327) BOUND_VARIABLE_1320328))))) (let ((_let_3548 (forall ((BOUND_VARIABLE_1320257 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320258 tptp.nat) (BOUND_VARIABLE_1320259 tptp.nat)) (= (ho_11441 (ho_11440 k_11439 (ho_11075 (ho_11074 k_11084 BOUND_VARIABLE_1320258) BOUND_VARIABLE_1320259)) BOUND_VARIABLE_1320257) (ho_11067 (ho_11066 (ho_11443 k_11453 BOUND_VARIABLE_1320257) BOUND_VARIABLE_1320258) BOUND_VARIABLE_1320259))))) (let ((_let_3549 (forall ((BOUND_VARIABLE_1320188 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320189 tptp.nat) (BOUND_VARIABLE_1320190 tptp.nat)) (= (ho_11441 (ho_11440 k_11439 (ho_11075 (ho_11074 k_11086 BOUND_VARIABLE_1320189) BOUND_VARIABLE_1320190)) BOUND_VARIABLE_1320188) (ho_11067 (ho_11066 (ho_11443 k_11454 BOUND_VARIABLE_1320188) BOUND_VARIABLE_1320189) BOUND_VARIABLE_1320190))))) (let ((_let_3550 (forall ((BOUND_VARIABLE_1320147 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320148 tptp.nat) (BOUND_VARIABLE_1320149 tptp.nat)) (= (ho_11441 (ho_11440 k_11439 (ho_11075 (ho_11074 k_11087 BOUND_VARIABLE_1320148) BOUND_VARIABLE_1320149)) BOUND_VARIABLE_1320147) (ho_11067 (ho_11066 (ho_11443 k_11455 BOUND_VARIABLE_1320147) BOUND_VARIABLE_1320148) BOUND_VARIABLE_1320149))))) (let ((_let_3551 (forall ((BOUND_VARIABLE_1320106 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320107 tptp.nat) (BOUND_VARIABLE_1320108 tptp.nat)) (= (ho_11441 (ho_11440 k_11439 (ho_11075 (ho_11074 k_11088 BOUND_VARIABLE_1320107) BOUND_VARIABLE_1320108)) BOUND_VARIABLE_1320106) (ho_11067 (ho_11066 (ho_11443 k_11456 BOUND_VARIABLE_1320106) BOUND_VARIABLE_1320107) BOUND_VARIABLE_1320108))))) (let ((_let_3552 (forall ((BOUND_VARIABLE_1320055 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1320056 tptp.nat) (BOUND_VARIABLE_1320057 tptp.nat)) (= (ho_11184 (ho_11424 k_11423 (ho_11064 (ho_11063 k_11089 BOUND_VARIABLE_1320056) BOUND_VARIABLE_1320057)) BOUND_VARIABLE_1320055) (ho_11054 (ho_11053 (ho_11433 k_11457 BOUND_VARIABLE_1320055) BOUND_VARIABLE_1320056) BOUND_VARIABLE_1320057))))) (let ((_let_3553 (forall ((BOUND_VARIABLE_1319988 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1319989 tptp.nat) (BOUND_VARIABLE_1319990 tptp.nat)) (= (ho_11184 (ho_11424 k_11423 (ho_11064 (ho_11063 k_11090 BOUND_VARIABLE_1319989) BOUND_VARIABLE_1319990)) BOUND_VARIABLE_1319988) (ho_11054 (ho_11053 (ho_11433 k_11458 BOUND_VARIABLE_1319988) BOUND_VARIABLE_1319989) BOUND_VARIABLE_1319990))))) (let ((_let_3554 (forall ((BOUND_VARIABLE_1319919 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1319920 tptp.nat) (BOUND_VARIABLE_1319921 tptp.nat)) (= (ho_11441 (ho_11440 k_11439 (ho_11075 (ho_11074 k_11091 BOUND_VARIABLE_1319920) BOUND_VARIABLE_1319921)) BOUND_VARIABLE_1319919) (ho_11067 (ho_11066 (ho_11443 k_11459 BOUND_VARIABLE_1319919) BOUND_VARIABLE_1319920) BOUND_VARIABLE_1319921))))) (let ((_let_3555 (forall ((BOUND_VARIABLE_1319897 tptp.nat) (BOUND_VARIABLE_1319898 tptp.nat)) (= (ho_11054 (ho_11053 k_11460 BOUND_VARIABLE_1319897) BOUND_VARIABLE_1319898) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1319897 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1319898)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1319898 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1319897)) (ho_11056 k_11055 K3))))))))))) (let ((_let_3556 (forall ((BOUND_VARIABLE_1319883 tptp.nat) (BOUND_VARIABLE_1319884 tptp.nat)) (= (ho_11054 (ho_11053 k_11461 BOUND_VARIABLE_1319883) BOUND_VARIABLE_1319884) (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1319883 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1319884)) (ho_11056 k_11055 K3))))))))))) (let ((_let_3557 (forall ((BOUND_VARIABLE_1319853 tptp.set_int) (BOUND_VARIABLE_1319854 tptp.int) (BOUND_VARIABLE_1319855 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1319855))) (= (or (ho_11180 _let_1 (ho_11465 (ho_11464 k_11463 k_11462) BOUND_VARIABLE_1319853)) (ho_11180 _let_1 (ho_11177 k_11176 (ho_11093 k_11092 BOUND_VARIABLE_1319854)))) (ho_11094 (ho_11093 (ho_11467 k_11466 BOUND_VARIABLE_1319853) BOUND_VARIABLE_1319854) BOUND_VARIABLE_1319855)))))) (let ((_let_3558 (forall ((BOUND_VARIABLE_1319839 tptp.int) (BOUND_VARIABLE_1319840 tptp.int)) (= (ho_11094 (ho_11093 k_11468 BOUND_VARIABLE_1319839) BOUND_VARIABLE_1319840) (and (= BOUND_VARIABLE_1319839 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1319840) BOUND_VARIABLE_1319839)) (not (= BOUND_VARIABLE_1319840 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1319839) BOUND_VARIABLE_1319840)))))))) (let ((_let_3559 (forall ((BOUND_VARIABLE_1319799 tptp.set_int) (BOUND_VARIABLE_1319800 tptp.int) (BOUND_VARIABLE_1319801 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1319801))) (= (or (ho_11180 _let_1 (ho_11465 (ho_11464 k_11463 k_11462) BOUND_VARIABLE_1319799)) (ho_11180 _let_1 (ho_11177 k_11176 (ho_11093 k_11096 BOUND_VARIABLE_1319800)))) (ho_11094 (ho_11093 (ho_11467 k_11469 BOUND_VARIABLE_1319799) BOUND_VARIABLE_1319800) BOUND_VARIABLE_1319801)))))) (let ((_let_3560 (forall ((BOUND_VARIABLE_1319758 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1319759 tptp.nat) (BOUND_VARIABLE_1319760 tptp.nat)) (= (ho_11441 (ho_11440 k_11439 (ho_11075 (ho_11074 k_11097 BOUND_VARIABLE_1319759) BOUND_VARIABLE_1319760)) BOUND_VARIABLE_1319758) (ho_11067 (ho_11066 (ho_11443 k_11470 BOUND_VARIABLE_1319758) BOUND_VARIABLE_1319759) BOUND_VARIABLE_1319760))))) (let ((_let_3561 (forall ((BOUND_VARIABLE_1319717 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1319718 tptp.nat) (BOUND_VARIABLE_1319719 tptp.nat)) (= (ho_11441 (ho_11440 k_11439 (ho_11075 (ho_11074 k_11098 BOUND_VARIABLE_1319718) BOUND_VARIABLE_1319719)) BOUND_VARIABLE_1319717) (ho_11067 (ho_11066 (ho_11443 k_11471 BOUND_VARIABLE_1319717) BOUND_VARIABLE_1319718) BOUND_VARIABLE_1319719))))) (let ((_let_3562 (forall ((BOUND_VARIABLE_1319648 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1319649 tptp.nat) (BOUND_VARIABLE_1319650 tptp.nat)) (= (ho_11441 (ho_11440 k_11439 (ho_11075 (ho_11074 k_11099 BOUND_VARIABLE_1319649) BOUND_VARIABLE_1319650)) BOUND_VARIABLE_1319648) (ho_11067 (ho_11066 (ho_11443 k_11472 BOUND_VARIABLE_1319648) BOUND_VARIABLE_1319649) BOUND_VARIABLE_1319650))))) (let ((_let_3563 (forall ((BOUND_VARIABLE_1319629 tptp.code_natural) (BOUND_VARIABLE_1319630 tptp.code_natural) (BOUND_VARIABLE_1319631 tptp.produc7822875418678951345atural)) (= (ho_11493 (ho_11492 k_11491 (ho_11477 (ho_11476 (ho_11490 (ho_11489 (ho_11488 k_11487 k_11482) (ho_11486 (ho_11485 k_11484 k_11482) k_11480)) k_11478) BOUND_VARIABLE_1319630) (ho_11477 (ho_11476 k_11475 BOUND_VARIABLE_1319629) (ho_11474 k_11473 (ho_11030 k_11044 (ho_11030 k_11029 (ho_11030 k_11029 (ho_11030 k_11044 (ho_11030 k_11029 (ho_11030 k_11044 (ho_11030 k_11029 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 (ho_11030 k_11044 tptp.one)))))))))))))))))))))))))))))))))) BOUND_VARIABLE_1319631) (ho_11493 (ho_11492 (ho_11495 k_11494 BOUND_VARIABLE_1319629) BOUND_VARIABLE_1319630) BOUND_VARIABLE_1319631))))) (let ((_let_3564 (forall ((BOUND_VARIABLE_1319598 tptp.rat) (BOUND_VARIABLE_1319599 tptp.product_prod_int_int)) (let ((_let_1 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1319599))) (let ((_let_3 (ho_11111 k_11112 BOUND_VARIABLE_1319599))) (= (and (= BOUND_VARIABLE_1319598 (ho_11127 (ho_11126 (ho_11125 (ho_11124 (ho_11123 k_11122 k_11118) (ho_11121 (ho_11120 k_11119 k_11118) k_11116)) k_11114) _let_3) _let_2)) (ho_11094 (ho_11093 k_11113 _let_3) _let_2) (= _let_2 (ho_11059 (ho_11058 k_11095 _let_1) _let_2)) (not (= _let_1 (ho_11059 (ho_11058 k_11095 _let_2) _let_1)))) (ho_11130 (ho_11129 k_11496 BOUND_VARIABLE_1319598) BOUND_VARIABLE_1319599)))))))) (let ((_let_3565 (forall ((BOUND_VARIABLE_1319499 tptp.rat) (BOUND_VARIABLE_1319500 tptp.int)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (let ((_let_2 (ho_11056 k_11055 (ho_11139 k_11138 _let_1)))) (let ((_let_3 (ho_11059 (ho_11058 k_11057 BOUND_VARIABLE_1319500) _let_2))) (let ((_let_4 (ho_11507 (ho_11506 (ho_11505 k_11504 k_11502) k_11116) k_11500))) (let ((_let_5 (ho_11056 k_11055 _let_1))) (let ((_let_6 (ho_11058 k_11095 _let_5))) (let ((_let_7 (ho_11508 (ho_11511 (ho_11510 k_11509 (and (= _let_5 (ho_11059 (ho_11058 k_11095 _let_3) _let_5)) (not (= _let_3 (ho_11059 _let_6 _let_3))))) (ho_11508 _let_4 (ho_11498 k_11497 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 _let_3)) _let_2))))) (ho_11498 k_11497 (ho_11061 k_11060 _let_3))))) (= (and (= BOUND_VARIABLE_1319499 (ho_11508 (ho_11511 k_11512 (ho_11508 (ho_11511 (ho_11510 k_11509 (and (= _let_5 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1319500) _let_5)) (not (= BOUND_VARIABLE_1319500 (ho_11059 _let_6 BOUND_VARIABLE_1319500))))) (ho_11508 _let_4 (ho_11498 k_11497 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 BOUND_VARIABLE_1319500)) _let_2))))) (ho_11498 k_11497 (ho_11061 k_11060 BOUND_VARIABLE_1319500)))) BOUND_VARIABLE_1319499)) (= _let_7 (ho_11508 (ho_11511 k_11512 BOUND_VARIABLE_1319499) _let_7)) (not (= BOUND_VARIABLE_1319499 (ho_11508 (ho_11511 k_11512 _let_7) BOUND_VARIABLE_1319499)))) (ho_11094 (ho_11514 k_11513 BOUND_VARIABLE_1319499) BOUND_VARIABLE_1319500)))))))))))) (let ((_let_3566 (forall ((BOUND_VARIABLE_1319431 tptp.int) (BOUND_VARIABLE_1319432 tptp.nat) (BOUND_VARIABLE_1319433 tptp.nat)) (= (ho_11184 (ho_11424 k_11423 (ho_11064 (ho_11063 k_11100 BOUND_VARIABLE_1319432) BOUND_VARIABLE_1319433)) (ho_11516 k_11515 BOUND_VARIABLE_1319431)) (ho_11054 (ho_11053 (ho_11518 k_11517 BOUND_VARIABLE_1319431) BOUND_VARIABLE_1319432) BOUND_VARIABLE_1319433))))) (let ((_let_3567 (forall ((BOUND_VARIABLE_1319379 tptp.int) (BOUND_VARIABLE_1319380 tptp.nat) (BOUND_VARIABLE_1319381 tptp.nat)) (= (ho_11184 (ho_11424 k_11423 (ho_11064 (ho_11063 k_11101 BOUND_VARIABLE_1319380) BOUND_VARIABLE_1319381)) (ho_11516 k_11515 BOUND_VARIABLE_1319379)) (ho_11054 (ho_11053 (ho_11518 k_11519 BOUND_VARIABLE_1319379) BOUND_VARIABLE_1319380) BOUND_VARIABLE_1319381))))) (let ((_let_3568 (forall ((BOUND_VARIABLE_1319310 tptp.int) (BOUND_VARIABLE_1319311 tptp.int) (BOUND_VARIABLE_1319312 tptp.int) (BOUND_VARIABLE_1319313 tptp.int)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (let ((_let_2 (ho_11056 k_11055 (ho_11139 k_11138 _let_1)))) (let ((_let_3 (ho_11521 (ho_11115 k_11520 (ho_11059 (ho_11058 k_11057 (ho_11059 (ho_11058 k_11085 BOUND_VARIABLE_1319310) BOUND_VARIABLE_1319313)) (ho_11059 (ho_11058 k_11085 BOUND_VARIABLE_1319312) BOUND_VARIABLE_1319311))) (ho_11059 (ho_11058 k_11085 BOUND_VARIABLE_1319311) BOUND_VARIABLE_1319313)))) (let ((_let_4 (ho_11111 k_11110 _let_3))) (let ((_let_5 (ho_11111 k_11112 _let_3))) (let ((_let_6 (ho_11059 (ho_11058 k_11522 _let_5) _let_4))) (let ((_let_7 (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 _let_6)) _let_2))) (let ((_let_8 (ho_11058 k_11523 _let_4))) (let ((_let_9 (ho_11058 k_11523 _let_5))) (let ((_let_10 (ho_11056 k_11055 _let_1))) (= (ho_11501 (ho_11526 (ho_11525 k_11524 (and (= _let_4 (ho_11059 (ho_11058 k_11095 _let_10) _let_4)) (not (= _let_10 (ho_11059 (ho_11058 k_11095 _let_4) _let_10))))) (ho_11521 (ho_11115 k_11520 (ho_11059 _let_9 _let_6)) (ho_11059 _let_8 _let_6))) (ho_11501 (ho_11526 (ho_11525 k_11524 (= _let_10 _let_4)) (ho_11521 (ho_11115 k_11520 _let_10) _let_2)) (ho_11521 (ho_11115 k_11520 (ho_11059 _let_9 _let_7)) (ho_11059 _let_8 _let_7)))) (ho_11521 (ho_11115 (ho_11529 (ho_11528 k_11527 BOUND_VARIABLE_1319310) BOUND_VARIABLE_1319311) BOUND_VARIABLE_1319312) BOUND_VARIABLE_1319313))))))))))))))) (let ((_let_3569 (forall ((BOUND_VARIABLE_1319279 tptp.rat) (BOUND_VARIABLE_1319280 tptp.product_prod_int_int)) (let ((_let_1 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1319280))) (let ((_let_3 (ho_11111 k_11112 BOUND_VARIABLE_1319280))) (= (and (= BOUND_VARIABLE_1319279 (ho_11127 (ho_11126 (ho_11125 (ho_11124 (ho_11123 k_11122 k_11118) (ho_11121 (ho_11120 k_11119 k_11118) k_11116)) k_11114) _let_3) _let_2)) (ho_11094 (ho_11093 k_11113 _let_3) _let_2) (= _let_2 (ho_11059 (ho_11058 k_11095 _let_1) _let_2)) (not (= _let_1 (ho_11059 (ho_11058 k_11095 _let_2) _let_1)))) (ho_11130 (ho_11129 k_11530 BOUND_VARIABLE_1319279) BOUND_VARIABLE_1319280)))))))) (let ((_let_3570 (forall ((BOUND_VARIABLE_1319214 tptp.int) (BOUND_VARIABLE_1319215 tptp.int) (BOUND_VARIABLE_1319216 tptp.int) (BOUND_VARIABLE_1319217 tptp.int)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (let ((_let_2 (ho_11056 k_11055 (ho_11139 k_11138 _let_1)))) (let ((_let_3 (ho_11521 (ho_11115 k_11520 (ho_11059 (ho_11058 k_11085 BOUND_VARIABLE_1319214) BOUND_VARIABLE_1319216)) (ho_11059 (ho_11058 k_11085 BOUND_VARIABLE_1319215) BOUND_VARIABLE_1319217)))) (let ((_let_4 (ho_11111 k_11110 _let_3))) (let ((_let_5 (ho_11111 k_11112 _let_3))) (let ((_let_6 (ho_11059 (ho_11058 k_11522 _let_5) _let_4))) (let ((_let_7 (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 _let_6)) _let_2))) (let ((_let_8 (ho_11058 k_11523 _let_4))) (let ((_let_9 (ho_11058 k_11523 _let_5))) (let ((_let_10 (ho_11056 k_11055 _let_1))) (= (ho_11501 (ho_11526 (ho_11525 k_11524 (and (= _let_4 (ho_11059 (ho_11058 k_11095 _let_10) _let_4)) (not (= _let_10 (ho_11059 (ho_11058 k_11095 _let_4) _let_10))))) (ho_11521 (ho_11115 k_11520 (ho_11059 _let_9 _let_6)) (ho_11059 _let_8 _let_6))) (ho_11501 (ho_11526 (ho_11525 k_11524 (= _let_10 _let_4)) (ho_11521 (ho_11115 k_11520 _let_10) _let_2)) (ho_11521 (ho_11115 k_11520 (ho_11059 _let_9 _let_7)) (ho_11059 _let_8 _let_7)))) (ho_11521 (ho_11115 (ho_11529 (ho_11528 k_11531 BOUND_VARIABLE_1319214) BOUND_VARIABLE_1319215) BOUND_VARIABLE_1319216) BOUND_VARIABLE_1319217))))))))))))))) (let ((_let_3571 (forall ((BOUND_VARIABLE_1319183 tptp.rat) (BOUND_VARIABLE_1319184 tptp.product_prod_int_int)) (let ((_let_1 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1319184))) (let ((_let_3 (ho_11111 k_11112 BOUND_VARIABLE_1319184))) (= (and (= BOUND_VARIABLE_1319183 (ho_11127 (ho_11126 (ho_11125 (ho_11124 (ho_11123 k_11122 k_11118) (ho_11121 (ho_11120 k_11119 k_11118) k_11116)) k_11114) _let_3) _let_2)) (ho_11094 (ho_11093 k_11113 _let_3) _let_2) (= _let_2 (ho_11059 (ho_11058 k_11095 _let_1) _let_2)) (not (= _let_1 (ho_11059 (ho_11058 k_11095 _let_2) _let_1)))) (ho_11130 (ho_11129 k_11532 BOUND_VARIABLE_1319183) BOUND_VARIABLE_1319184)))))))) (let ((_let_3572 (forall ((BOUND_VARIABLE_1319118 tptp.int) (BOUND_VARIABLE_1319119 tptp.int) (BOUND_VARIABLE_1319120 tptp.int) (BOUND_VARIABLE_1319121 tptp.int)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (let ((_let_2 (ho_11056 k_11055 (ho_11139 k_11138 _let_1)))) (let ((_let_3 (ho_11521 (ho_11115 k_11520 (ho_11059 (ho_11058 k_11085 BOUND_VARIABLE_1319118) BOUND_VARIABLE_1319121)) (ho_11059 (ho_11058 k_11085 BOUND_VARIABLE_1319119) BOUND_VARIABLE_1319120)))) (let ((_let_4 (ho_11111 k_11110 _let_3))) (let ((_let_5 (ho_11111 k_11112 _let_3))) (let ((_let_6 (ho_11059 (ho_11058 k_11522 _let_5) _let_4))) (let ((_let_7 (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 _let_6)) _let_2))) (let ((_let_8 (ho_11058 k_11523 _let_4))) (let ((_let_9 (ho_11058 k_11523 _let_5))) (let ((_let_10 (ho_11056 k_11055 _let_1))) (= (ho_11501 (ho_11526 (ho_11525 k_11524 (and (= _let_4 (ho_11059 (ho_11058 k_11095 _let_10) _let_4)) (not (= _let_10 (ho_11059 (ho_11058 k_11095 _let_4) _let_10))))) (ho_11521 (ho_11115 k_11520 (ho_11059 _let_9 _let_6)) (ho_11059 _let_8 _let_6))) (ho_11501 (ho_11526 (ho_11525 k_11524 (= _let_10 _let_4)) (ho_11521 (ho_11115 k_11520 _let_10) _let_2)) (ho_11521 (ho_11115 k_11520 (ho_11059 _let_9 _let_7)) (ho_11059 _let_8 _let_7)))) (ho_11521 (ho_11115 (ho_11529 (ho_11528 k_11533 BOUND_VARIABLE_1319118) BOUND_VARIABLE_1319119) BOUND_VARIABLE_1319120) BOUND_VARIABLE_1319121))))))))))))))) (let ((_let_3573 (forall ((BOUND_VARIABLE_1319087 tptp.rat) (BOUND_VARIABLE_1319088 tptp.product_prod_int_int)) (let ((_let_1 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1319088))) (let ((_let_3 (ho_11111 k_11112 BOUND_VARIABLE_1319088))) (= (and (= BOUND_VARIABLE_1319087 (ho_11127 (ho_11126 (ho_11125 (ho_11124 (ho_11123 k_11122 k_11118) (ho_11121 (ho_11120 k_11119 k_11118) k_11116)) k_11114) _let_3) _let_2)) (ho_11094 (ho_11093 k_11113 _let_3) _let_2) (= _let_2 (ho_11059 (ho_11058 k_11095 _let_1) _let_2)) (not (= _let_1 (ho_11059 (ho_11058 k_11095 _let_2) _let_1)))) (ho_11130 (ho_11129 k_11534 BOUND_VARIABLE_1319087) BOUND_VARIABLE_1319088)))))))) (let ((_let_3574 (forall ((BOUND_VARIABLE_1319030 tptp.rat) (BOUND_VARIABLE_1319031 tptp.int) (BOUND_VARIABLE_1319032 tptp.int)) (= (ho_11130 (ho_11538 k_11537 (ho_11104 (ho_11103 k_11102 BOUND_VARIABLE_1319032) BOUND_VARIABLE_1319031)) (ho_11536 k_11535 (ho_11129 k_11128 BOUND_VARIABLE_1319030))) (ho_11094 (ho_11093 (ho_11540 k_11539 BOUND_VARIABLE_1319030) BOUND_VARIABLE_1319031) BOUND_VARIABLE_1319032))))) (let ((_let_3575 (forall ((BOUND_VARIABLE_1318999 tptp.rat) (BOUND_VARIABLE_1319000 tptp.product_prod_int_int)) (let ((_let_1 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1319000))) (let ((_let_3 (ho_11111 k_11112 BOUND_VARIABLE_1319000))) (= (and (= BOUND_VARIABLE_1318999 (ho_11127 (ho_11126 (ho_11125 (ho_11124 (ho_11123 k_11122 k_11118) (ho_11121 (ho_11120 k_11119 k_11118) k_11116)) k_11114) _let_3) _let_2)) (ho_11094 (ho_11093 k_11113 _let_3) _let_2) (= _let_2 (ho_11059 (ho_11058 k_11095 _let_1) _let_2)) (not (= _let_1 (ho_11059 (ho_11058 k_11095 _let_2) _let_1)))) (ho_11130 (ho_11129 k_11541 BOUND_VARIABLE_1318999) BOUND_VARIABLE_1319000)))))))) (let ((_let_3576 (forall ((BOUND_VARIABLE_1318952 tptp.rat) (BOUND_VARIABLE_1318953 tptp.int) (BOUND_VARIABLE_1318954 tptp.int)) (= (ho_11130 (ho_11538 k_11537 (ho_11104 (ho_11103 k_11131 BOUND_VARIABLE_1318953) BOUND_VARIABLE_1318954)) (ho_11536 k_11535 (ho_11129 k_11132 BOUND_VARIABLE_1318952))) (ho_11094 (ho_11093 (ho_11540 k_11542 BOUND_VARIABLE_1318952) BOUND_VARIABLE_1318953) BOUND_VARIABLE_1318954))))) (let ((_let_3577 (forall ((BOUND_VARIABLE_1318921 tptp.rat) (BOUND_VARIABLE_1318922 tptp.product_prod_int_int)) (let ((_let_1 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1318922))) (let ((_let_3 (ho_11111 k_11112 BOUND_VARIABLE_1318922))) (= (and (= BOUND_VARIABLE_1318921 (ho_11127 (ho_11126 (ho_11125 (ho_11124 (ho_11123 k_11122 k_11118) (ho_11121 (ho_11120 k_11119 k_11118) k_11116)) k_11114) _let_3) _let_2)) (ho_11094 (ho_11093 k_11113 _let_3) _let_2) (= _let_2 (ho_11059 (ho_11058 k_11095 _let_1) _let_2)) (not (= _let_1 (ho_11059 (ho_11058 k_11095 _let_2) _let_1)))) (ho_11130 (ho_11129 k_11543 BOUND_VARIABLE_1318921) BOUND_VARIABLE_1318922)))))))) (let ((_let_3578 (forall ((BOUND_VARIABLE_1318832 tptp.int) (BOUND_VARIABLE_1318833 tptp.int) (BOUND_VARIABLE_1318834 tptp.int) (BOUND_VARIABLE_1318835 tptp.int)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (let ((_let_2 (ho_11056 k_11055 (ho_11139 k_11138 _let_1)))) (let ((_let_3 (ho_11521 (ho_11115 k_11520 (ho_11059 (ho_11058 k_11057 (ho_11059 (ho_11058 k_11085 BOUND_VARIABLE_1318832) BOUND_VARIABLE_1318835)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11059 (ho_11058 k_11085 BOUND_VARIABLE_1318834) BOUND_VARIABLE_1318833))) _let_2))) (ho_11059 (ho_11058 k_11085 BOUND_VARIABLE_1318833) BOUND_VARIABLE_1318835)))) (let ((_let_4 (ho_11111 k_11110 _let_3))) (let ((_let_5 (ho_11111 k_11112 _let_3))) (let ((_let_6 (ho_11059 (ho_11058 k_11522 _let_5) _let_4))) (let ((_let_7 (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 _let_6)) _let_2))) (let ((_let_8 (ho_11058 k_11523 _let_4))) (let ((_let_9 (ho_11058 k_11523 _let_5))) (let ((_let_10 (ho_11056 k_11055 _let_1))) (= (ho_11501 (ho_11526 (ho_11525 k_11524 (and (= _let_4 (ho_11059 (ho_11058 k_11095 _let_10) _let_4)) (not (= _let_10 (ho_11059 (ho_11058 k_11095 _let_4) _let_10))))) (ho_11521 (ho_11115 k_11520 (ho_11059 _let_9 _let_6)) (ho_11059 _let_8 _let_6))) (ho_11501 (ho_11526 (ho_11525 k_11524 (= _let_10 _let_4)) (ho_11521 (ho_11115 k_11520 _let_10) _let_2)) (ho_11521 (ho_11115 k_11520 (ho_11059 _let_9 _let_7)) (ho_11059 _let_8 _let_7)))) (ho_11521 (ho_11115 (ho_11529 (ho_11528 k_11544 BOUND_VARIABLE_1318832) BOUND_VARIABLE_1318833) BOUND_VARIABLE_1318834) BOUND_VARIABLE_1318835))))))))))))))) (let ((_let_3579 (forall ((BOUND_VARIABLE_1318801 tptp.rat) (BOUND_VARIABLE_1318802 tptp.product_prod_int_int)) (let ((_let_1 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1318802))) (let ((_let_3 (ho_11111 k_11112 BOUND_VARIABLE_1318802))) (= (and (= BOUND_VARIABLE_1318801 (ho_11127 (ho_11126 (ho_11125 (ho_11124 (ho_11123 k_11122 k_11118) (ho_11121 (ho_11120 k_11119 k_11118) k_11116)) k_11114) _let_3) _let_2)) (ho_11094 (ho_11093 k_11113 _let_3) _let_2) (= _let_2 (ho_11059 (ho_11058 k_11095 _let_1) _let_2)) (not (= _let_1 (ho_11059 (ho_11058 k_11095 _let_2) _let_1)))) (ho_11130 (ho_11129 k_11545 BOUND_VARIABLE_1318801) BOUND_VARIABLE_1318802)))))))) (let ((_let_3580 (forall ((BOUND_VARIABLE_1318781 tptp.nat) (BOUND_VARIABLE_1318782 tptp.nat) (BOUND_VARIABLE_1318783 tptp.nat) (BOUND_VARIABLE_1318784 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11075 (ho_11074 k_11546 BOUND_VARIABLE_1318781) BOUND_VARIABLE_1318782) BOUND_VARIABLE_1318783) BOUND_VARIABLE_1318784) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1318781)) (ho_11056 k_11055 BOUND_VARIABLE_1318784)))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1318782)) (ho_11056 k_11055 BOUND_VARIABLE_1318783)))))))) (let ((_let_3581 (forall ((BOUND_VARIABLE_1318761 tptp.nat) (BOUND_VARIABLE_1318762 tptp.nat) (BOUND_VARIABLE_1318763 tptp.nat) (BOUND_VARIABLE_1318764 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11075 (ho_11074 k_11547 BOUND_VARIABLE_1318761) BOUND_VARIABLE_1318762) BOUND_VARIABLE_1318763) BOUND_VARIABLE_1318764) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1318761)) (ho_11056 k_11055 BOUND_VARIABLE_1318763)))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1318762)) (ho_11056 k_11055 BOUND_VARIABLE_1318764)))))))) (let ((_let_3582 (forall ((BOUND_VARIABLE_1318735 tptp.nat) (BOUND_VARIABLE_1318736 tptp.nat) (BOUND_VARIABLE_1318737 tptp.nat) (BOUND_VARIABLE_1318738 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 (ho_11063 k_11548 BOUND_VARIABLE_1318735) BOUND_VARIABLE_1318736) BOUND_VARIABLE_1318737) BOUND_VARIABLE_1318738) (not (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1318737)) (ho_11056 k_11055 BOUND_VARIABLE_1318736))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1318735)) (ho_11056 k_11055 BOUND_VARIABLE_1318738))))) (ho_11056 k_11055 K3))))))))))) (let ((_let_3583 (forall ((BOUND_VARIABLE_1318701 tptp.nat) (BOUND_VARIABLE_1318702 tptp.nat) (BOUND_VARIABLE_1318703 tptp.nat) (BOUND_VARIABLE_1318704 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 (ho_11063 k_11549 BOUND_VARIABLE_1318701) BOUND_VARIABLE_1318702) BOUND_VARIABLE_1318703) BOUND_VARIABLE_1318704) (and (not (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1318703)) (ho_11056 k_11055 BOUND_VARIABLE_1318702))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1318701)) (ho_11056 k_11055 BOUND_VARIABLE_1318704))))) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1318703)) (ho_11056 k_11055 BOUND_VARIABLE_1318702))))) (ho_11056 k_11055 K3))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1318701)) (ho_11056 k_11055 BOUND_VARIABLE_1318704))))))))))) (let ((_let_3584 (forall ((BOUND_VARIABLE_1318667 tptp.nat) (BOUND_VARIABLE_1318668 tptp.nat) (BOUND_VARIABLE_1318669 tptp.nat) (BOUND_VARIABLE_1318670 tptp.nat)) (let ((_let_1 (ho_11056 k_11055 BOUND_VARIABLE_1318669))) (let ((_let_2 (ho_11058 k_11085 (ho_11056 k_11055 BOUND_VARIABLE_1318668)))) (let ((_let_3 (ho_11056 k_11055 BOUND_VARIABLE_1318670))) (let ((_let_4 (ho_11058 k_11085 (ho_11056 k_11055 BOUND_VARIABLE_1318667)))) (= (ho_11067 (ho_11066 (ho_11075 (ho_11074 k_11550 BOUND_VARIABLE_1318667) BOUND_VARIABLE_1318668) BOUND_VARIABLE_1318669) BOUND_VARIABLE_1318670) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_4 _let_1)))) (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_2 _let_3)))))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_4 _let_3)))) (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_2 _let_1)))))))))))))) (let ((_let_3585 (forall ((BOUND_VARIABLE_1318654 tptp.set_nat) (BOUND_VARIABLE_1347274 |u_(-> tptp.code_integer tptp.nat Bool)|) (BOUND_VARIABLE_1318656 tptp.code_integer) (BOUND_VARIABLE_1318657 tptp.nat)) (= (ho_11054 (ho_11551 (ho_11554 (ho_11553 k_11552 BOUND_VARIABLE_1318654) BOUND_VARIABLE_1347274) BOUND_VARIABLE_1318656) BOUND_VARIABLE_1318657) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1318657) BOUND_VARIABLE_1318654) (ho_11054 (ho_11551 BOUND_VARIABLE_1347274 BOUND_VARIABLE_1318656) BOUND_VARIABLE_1318657)))))) (let ((_let_3586 (forall ((BOUND_VARIABLE_1318641 tptp.set_o) (BOUND_VARIABLE_1347303 |u_(-> tptp.code_integer Bool Bool)|) (BOUND_VARIABLE_1318643 tptp.code_integer) (BOUND_VARIABLE_1318644 Bool)) (= (ho_11194 (ho_11555 (ho_11558 (ho_11557 k_11556 BOUND_VARIABLE_1318641) BOUND_VARIABLE_1347303) BOUND_VARIABLE_1318643) BOUND_VARIABLE_1318644) (and (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1318644) BOUND_VARIABLE_1318641) (ho_11194 (ho_11555 BOUND_VARIABLE_1347303 BOUND_VARIABLE_1318643) BOUND_VARIABLE_1318644)))))) (let ((_let_3587 (forall ((BOUND_VARIABLE_1318632 tptp.int) (BOUND_VARIABLE_1318633 tptp.int)) (= (ho_11094 (ho_11093 k_11559 BOUND_VARIABLE_1318632) BOUND_VARIABLE_1318633) (= BOUND_VARIABLE_1318632 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318633) BOUND_VARIABLE_1318632)))))) (let ((_let_3588 (forall ((BOUND_VARIABLE_1318619 tptp.set_Code_integer) (BOUND_VARIABLE_1347342 |u_(-> tptp.int tptp.code_integer Bool)|) (BOUND_VARIABLE_1318621 tptp.int) (BOUND_VARIABLE_1318622 tptp.code_integer)) (= (ho_11564 (ho_11560 (ho_11563 (ho_11562 k_11561 BOUND_VARIABLE_1318619) BOUND_VARIABLE_1347342) BOUND_VARIABLE_1318621) BOUND_VARIABLE_1318622) (and (ho_11567 (ho_11566 k_11565 BOUND_VARIABLE_1318622) BOUND_VARIABLE_1318619) (ho_11564 (ho_11560 BOUND_VARIABLE_1347342 BOUND_VARIABLE_1318621) BOUND_VARIABLE_1318622)))))) (let ((_let_3589 (forall ((BOUND_VARIABLE_1318610 tptp.int) (BOUND_VARIABLE_1318611 tptp.int)) (= (ho_11094 (ho_11093 k_11568 BOUND_VARIABLE_1318610) BOUND_VARIABLE_1318611) (= BOUND_VARIABLE_1318610 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318611) BOUND_VARIABLE_1318610)))))) (let ((_let_3590 (forall ((BOUND_VARIABLE_1318601 tptp.int) (BOUND_VARIABLE_1318602 tptp.int)) (= (ho_11094 (ho_11093 k_11569 BOUND_VARIABLE_1318601) BOUND_VARIABLE_1318602) (= BOUND_VARIABLE_1318601 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318602) BOUND_VARIABLE_1318601)))))) (let ((_let_3591 (forall ((BOUND_VARIABLE_1318588 tptp.set_int) (BOUND_VARIABLE_1347400 |u_(-> tptp.int tptp.int Bool)|) (BOUND_VARIABLE_1318590 tptp.int) (BOUND_VARIABLE_1318591 tptp.int)) (= (ho_11094 (ho_11093 (ho_11572 (ho_11571 k_11570 BOUND_VARIABLE_1318588) BOUND_VARIABLE_1347400) BOUND_VARIABLE_1318590) BOUND_VARIABLE_1318591) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1318591) BOUND_VARIABLE_1318588) (ho_11094 (ho_11093 BOUND_VARIABLE_1347400 BOUND_VARIABLE_1318590) BOUND_VARIABLE_1318591)))))) (let ((_let_3592 (forall ((BOUND_VARIABLE_1318579 tptp.int) (BOUND_VARIABLE_1318580 tptp.int)) (= (ho_11094 (ho_11093 k_11573 BOUND_VARIABLE_1318579) BOUND_VARIABLE_1318580) (= BOUND_VARIABLE_1318579 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318580) BOUND_VARIABLE_1318579)))))) (let ((_let_3593 (forall ((BOUND_VARIABLE_1318566 tptp.set_nat) (BOUND_VARIABLE_1347437 |u_(-> tptp.int tptp.nat Bool)|) (BOUND_VARIABLE_1318568 tptp.int) (BOUND_VARIABLE_1318569 tptp.nat)) (= (ho_11054 (ho_11574 (ho_11577 (ho_11576 k_11575 BOUND_VARIABLE_1318566) BOUND_VARIABLE_1347437) BOUND_VARIABLE_1318568) BOUND_VARIABLE_1318569) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1318569) BOUND_VARIABLE_1318566) (ho_11054 (ho_11574 BOUND_VARIABLE_1347437 BOUND_VARIABLE_1318568) BOUND_VARIABLE_1318569)))))) (let ((_let_3594 (forall ((BOUND_VARIABLE_1318557 tptp.int) (BOUND_VARIABLE_1318558 tptp.int)) (= (ho_11094 (ho_11093 k_11578 BOUND_VARIABLE_1318557) BOUND_VARIABLE_1318558) (= BOUND_VARIABLE_1318557 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318558) BOUND_VARIABLE_1318557)))))) (let ((_let_3595 (forall ((BOUND_VARIABLE_1318544 tptp.set_o) (BOUND_VARIABLE_1347476 |u_(-> tptp.int Bool Bool)|) (BOUND_VARIABLE_1318546 tptp.int) (BOUND_VARIABLE_1318547 Bool)) (= (ho_11194 (ho_11579 (ho_11582 (ho_11581 k_11580 BOUND_VARIABLE_1318544) BOUND_VARIABLE_1347476) BOUND_VARIABLE_1318546) BOUND_VARIABLE_1318547) (and (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1318547) BOUND_VARIABLE_1318544) (ho_11194 (ho_11579 BOUND_VARIABLE_1347476 BOUND_VARIABLE_1318546) BOUND_VARIABLE_1318547)))))) (let ((_let_3596 (forall ((BOUND_VARIABLE_1318531 tptp.set_Code_integer) (BOUND_VARIABLE_1347505 |u_(-> Bool tptp.code_integer Bool)|) (BOUND_VARIABLE_1318533 Bool) (BOUND_VARIABLE_1318534 tptp.code_integer)) (= (ho_11564 (ho_11583 (ho_11586 (ho_11585 k_11584 BOUND_VARIABLE_1318531) BOUND_VARIABLE_1347505) BOUND_VARIABLE_1318533) BOUND_VARIABLE_1318534) (and (ho_11567 (ho_11566 k_11565 BOUND_VARIABLE_1318534) BOUND_VARIABLE_1318531) (ho_11564 (ho_11583 BOUND_VARIABLE_1347505 BOUND_VARIABLE_1318533) BOUND_VARIABLE_1318534)))))) (let ((_let_3597 (forall ((BOUND_VARIABLE_1318522 tptp.int) (BOUND_VARIABLE_1318523 tptp.int)) (= (ho_11094 (ho_11093 k_11587 BOUND_VARIABLE_1318522) BOUND_VARIABLE_1318523) (= BOUND_VARIABLE_1318522 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318523) BOUND_VARIABLE_1318522)))))) (let ((_let_3598 (forall ((BOUND_VARIABLE_1318509 tptp.set_int) (BOUND_VARIABLE_1347544 |u_(-> Bool tptp.int Bool)|) (BOUND_VARIABLE_1318511 Bool) (BOUND_VARIABLE_1318512 tptp.int)) (= (ho_11094 (ho_11588 (ho_11591 (ho_11590 k_11589 BOUND_VARIABLE_1318509) BOUND_VARIABLE_1347544) BOUND_VARIABLE_1318511) BOUND_VARIABLE_1318512) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1318512) BOUND_VARIABLE_1318509) (ho_11094 (ho_11588 BOUND_VARIABLE_1347544 BOUND_VARIABLE_1318511) BOUND_VARIABLE_1318512)))))) (let ((_let_3599 (forall ((BOUND_VARIABLE_1318496 tptp.set_nat) (BOUND_VARIABLE_1347573 |u_(-> Bool tptp.nat Bool)|) (BOUND_VARIABLE_1318498 Bool) (BOUND_VARIABLE_1318499 tptp.nat)) (= (ho_11054 (ho_11592 (ho_11595 (ho_11594 k_11593 BOUND_VARIABLE_1318496) BOUND_VARIABLE_1347573) BOUND_VARIABLE_1318498) BOUND_VARIABLE_1318499) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1318499) BOUND_VARIABLE_1318496) (ho_11054 (ho_11592 BOUND_VARIABLE_1347573 BOUND_VARIABLE_1318498) BOUND_VARIABLE_1318499)))))) (let ((_let_3600 (forall ((BOUND_VARIABLE_1318483 tptp.set_o) (BOUND_VARIABLE_1347601 |u_(-> Bool Bool Bool)|) (BOUND_VARIABLE_1318485 Bool) (BOUND_VARIABLE_1318486 Bool)) (= (ho_11194 (ho_11201 (ho_11598 (ho_11597 k_11596 BOUND_VARIABLE_1318483) BOUND_VARIABLE_1347601) BOUND_VARIABLE_1318485) BOUND_VARIABLE_1318486) (and (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1318486) BOUND_VARIABLE_1318483) (ho_11194 (ho_11201 BOUND_VARIABLE_1347601 BOUND_VARIABLE_1318485) BOUND_VARIABLE_1318486)))))) (let ((_let_3601 (forall ((BOUND_VARIABLE_1318474 tptp.int) (BOUND_VARIABLE_1318475 tptp.int)) (= (ho_11094 (ho_11093 k_11599 BOUND_VARIABLE_1318474) BOUND_VARIABLE_1318475) (= BOUND_VARIABLE_1318474 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318475) BOUND_VARIABLE_1318474)))))) (let ((_let_3602 (forall ((BOUND_VARIABLE_1318465 tptp.int) (BOUND_VARIABLE_1318466 tptp.int)) (= (ho_11094 (ho_11093 k_11600 BOUND_VARIABLE_1318465) BOUND_VARIABLE_1318466) (= BOUND_VARIABLE_1318465 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318466) BOUND_VARIABLE_1318465)))))) (let ((_let_3603 (forall ((BOUND_VARIABLE_1318456 tptp.int) (BOUND_VARIABLE_1318457 tptp.int)) (= (ho_11094 (ho_11093 k_11601 BOUND_VARIABLE_1318456) BOUND_VARIABLE_1318457) (= BOUND_VARIABLE_1318456 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318457) BOUND_VARIABLE_1318456)))))) (let ((_let_3604 (forall ((BOUND_VARIABLE_1318447 tptp.int) (BOUND_VARIABLE_1318448 tptp.int)) (= (ho_11094 (ho_11093 k_11602 BOUND_VARIABLE_1318447) BOUND_VARIABLE_1318448) (= BOUND_VARIABLE_1318447 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318448) BOUND_VARIABLE_1318447)))))) (let ((_let_3605 (forall ((BOUND_VARIABLE_1318438 tptp.int) (BOUND_VARIABLE_1318439 tptp.int)) (= (ho_11094 (ho_11093 k_11603 BOUND_VARIABLE_1318438) BOUND_VARIABLE_1318439) (= BOUND_VARIABLE_1318438 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318439) BOUND_VARIABLE_1318438)))))) (let ((_let_3606 (forall ((BOUND_VARIABLE_1318429 tptp.int) (BOUND_VARIABLE_1318430 tptp.int)) (= (ho_11094 (ho_11093 k_11604 BOUND_VARIABLE_1318429) BOUND_VARIABLE_1318430) (= BOUND_VARIABLE_1318429 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318430) BOUND_VARIABLE_1318429)))))) (let ((_let_3607 (forall ((BOUND_VARIABLE_1318420 tptp.int) (BOUND_VARIABLE_1318421 tptp.int)) (= (ho_11094 (ho_11093 k_11605 BOUND_VARIABLE_1318420) BOUND_VARIABLE_1318421) (= BOUND_VARIABLE_1318420 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318421) BOUND_VARIABLE_1318420)))))) (let ((_let_3608 (forall ((BOUND_VARIABLE_1318411 tptp.int) (BOUND_VARIABLE_1318412 tptp.int)) (= (ho_11094 (ho_11093 k_11606 BOUND_VARIABLE_1318411) BOUND_VARIABLE_1318412) (= BOUND_VARIABLE_1318411 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318412) BOUND_VARIABLE_1318411)))))) (let ((_let_3609 (forall ((BOUND_VARIABLE_1318402 tptp.int) (BOUND_VARIABLE_1318403 tptp.int)) (= (ho_11094 (ho_11093 k_11607 BOUND_VARIABLE_1318402) BOUND_VARIABLE_1318403) (= BOUND_VARIABLE_1318402 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318403) BOUND_VARIABLE_1318402)))))) (let ((_let_3610 (forall ((BOUND_VARIABLE_1318393 tptp.int) (BOUND_VARIABLE_1318394 tptp.int)) (= (ho_11094 (ho_11093 k_11608 BOUND_VARIABLE_1318393) BOUND_VARIABLE_1318394) (= BOUND_VARIABLE_1318393 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318394) BOUND_VARIABLE_1318393)))))) (let ((_let_3611 (forall ((BOUND_VARIABLE_1318384 tptp.int) (BOUND_VARIABLE_1318385 tptp.int)) (= (ho_11094 (ho_11093 k_11609 BOUND_VARIABLE_1318384) BOUND_VARIABLE_1318385) (= BOUND_VARIABLE_1318384 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318385) BOUND_VARIABLE_1318384)))))) (let ((_let_3612 (forall ((BOUND_VARIABLE_1318375 tptp.int) (BOUND_VARIABLE_1318376 tptp.int)) (= (ho_11094 (ho_11093 k_11610 BOUND_VARIABLE_1318375) BOUND_VARIABLE_1318376) (= BOUND_VARIABLE_1318375 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318376) BOUND_VARIABLE_1318375)))))) (let ((_let_3613 (forall ((BOUND_VARIABLE_1318366 tptp.int) (BOUND_VARIABLE_1318367 tptp.int)) (= (ho_11094 (ho_11093 k_11611 BOUND_VARIABLE_1318366) BOUND_VARIABLE_1318367) (= BOUND_VARIABLE_1318366 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318367) BOUND_VARIABLE_1318366)))))) (let ((_let_3614 (forall ((BOUND_VARIABLE_1318357 tptp.int) (BOUND_VARIABLE_1318358 tptp.int)) (= (ho_11094 (ho_11093 k_11612 BOUND_VARIABLE_1318357) BOUND_VARIABLE_1318358) (= BOUND_VARIABLE_1318357 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318358) BOUND_VARIABLE_1318357)))))) (let ((_let_3615 (forall ((BOUND_VARIABLE_1318344 tptp.set_nat) (BOUND_VARIABLE_1347767 |u_(-> Bool tptp.nat Bool)|) (BOUND_VARIABLE_1318346 Bool) (BOUND_VARIABLE_1318347 tptp.nat)) (= (ho_11054 (ho_11592 (ho_11595 (ho_11594 k_11613 BOUND_VARIABLE_1318344) BOUND_VARIABLE_1347767) BOUND_VARIABLE_1318346) BOUND_VARIABLE_1318347) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1318347) BOUND_VARIABLE_1318344) (ho_11054 (ho_11592 BOUND_VARIABLE_1347767 BOUND_VARIABLE_1318346) BOUND_VARIABLE_1318347)))))) (let ((_let_3616 (forall ((BOUND_VARIABLE_1318331 tptp.set_Code_integer) (BOUND_VARIABLE_1347786 |u_(-> tptp.code_integer tptp.code_integer Bool)|) (BOUND_VARIABLE_1318333 tptp.code_integer) (BOUND_VARIABLE_1318334 tptp.code_integer)) (= (ho_11564 (ho_11614 (ho_11617 (ho_11616 k_11615 BOUND_VARIABLE_1318331) BOUND_VARIABLE_1347786) BOUND_VARIABLE_1318333) BOUND_VARIABLE_1318334) (and (ho_11567 (ho_11566 k_11565 BOUND_VARIABLE_1318334) BOUND_VARIABLE_1318331) (ho_11564 (ho_11614 BOUND_VARIABLE_1347786 BOUND_VARIABLE_1318333) BOUND_VARIABLE_1318334)))))) (let ((_let_3617 (forall ((BOUND_VARIABLE_1318322 tptp.int) (BOUND_VARIABLE_1318323 tptp.int)) (= (ho_11094 (ho_11093 k_11618 BOUND_VARIABLE_1318322) BOUND_VARIABLE_1318323) (= BOUND_VARIABLE_1318322 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318323) BOUND_VARIABLE_1318322)))))) (let ((_let_3618 (forall ((BOUND_VARIABLE_1318309 tptp.set_int) (BOUND_VARIABLE_1347825 |u_(-> tptp.code_integer tptp.int Bool)|) (BOUND_VARIABLE_1318311 tptp.code_integer) (BOUND_VARIABLE_1318312 tptp.int)) (= (ho_11094 (ho_11619 (ho_11622 (ho_11621 k_11620 BOUND_VARIABLE_1318309) BOUND_VARIABLE_1347825) BOUND_VARIABLE_1318311) BOUND_VARIABLE_1318312) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1318312) BOUND_VARIABLE_1318309) (ho_11094 (ho_11619 BOUND_VARIABLE_1347825 BOUND_VARIABLE_1318311) BOUND_VARIABLE_1318312)))))) (let ((_let_3619 (forall ((BOUND_VARIABLE_1318296 tptp.set_o) (BOUND_VARIABLE_1347853 |u_(-> tptp.code_integer Bool Bool)|) (BOUND_VARIABLE_1318298 tptp.code_integer) (BOUND_VARIABLE_1318299 Bool)) (= (ho_11194 (ho_11555 (ho_11558 (ho_11557 k_11623 BOUND_VARIABLE_1318296) BOUND_VARIABLE_1347853) BOUND_VARIABLE_1318298) BOUND_VARIABLE_1318299) (and (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1318299) BOUND_VARIABLE_1318296) (ho_11194 (ho_11555 BOUND_VARIABLE_1347853 BOUND_VARIABLE_1318298) BOUND_VARIABLE_1318299)))))) (let ((_let_3620 (forall ((BOUND_VARIABLE_1318287 tptp.int) (BOUND_VARIABLE_1318288 tptp.int)) (= (ho_11094 (ho_11093 k_11624 BOUND_VARIABLE_1318287) BOUND_VARIABLE_1318288) (= BOUND_VARIABLE_1318287 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318288) BOUND_VARIABLE_1318287)))))) (let ((_let_3621 (forall ((BOUND_VARIABLE_1318274 tptp.set_Code_integer) (BOUND_VARIABLE_1347881 |u_(-> tptp.int tptp.code_integer Bool)|) (BOUND_VARIABLE_1318276 tptp.int) (BOUND_VARIABLE_1318277 tptp.code_integer)) (= (ho_11564 (ho_11560 (ho_11563 (ho_11562 k_11625 BOUND_VARIABLE_1318274) BOUND_VARIABLE_1347881) BOUND_VARIABLE_1318276) BOUND_VARIABLE_1318277) (and (ho_11567 (ho_11566 k_11565 BOUND_VARIABLE_1318277) BOUND_VARIABLE_1318274) (ho_11564 (ho_11560 BOUND_VARIABLE_1347881 BOUND_VARIABLE_1318276) BOUND_VARIABLE_1318277)))))) (let ((_let_3622 (forall ((BOUND_VARIABLE_1318265 tptp.int) (BOUND_VARIABLE_1318266 tptp.int)) (= (ho_11094 (ho_11093 k_11626 BOUND_VARIABLE_1318265) BOUND_VARIABLE_1318266) (= BOUND_VARIABLE_1318265 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318266) BOUND_VARIABLE_1318265)))))) (let ((_let_3623 (forall ((BOUND_VARIABLE_1318256 tptp.int) (BOUND_VARIABLE_1318257 tptp.int)) (= (ho_11094 (ho_11093 k_11627 BOUND_VARIABLE_1318256) BOUND_VARIABLE_1318257) (= BOUND_VARIABLE_1318256 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318257) BOUND_VARIABLE_1318256)))))) (let ((_let_3624 (forall ((BOUND_VARIABLE_1318243 tptp.set_int) (BOUND_VARIABLE_1347919 |u_(-> tptp.int tptp.int Bool)|) (BOUND_VARIABLE_1318245 tptp.int) (BOUND_VARIABLE_1318246 tptp.int)) (= (ho_11094 (ho_11093 (ho_11572 (ho_11571 k_11628 BOUND_VARIABLE_1318243) BOUND_VARIABLE_1347919) BOUND_VARIABLE_1318245) BOUND_VARIABLE_1318246) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1318246) BOUND_VARIABLE_1318243) (ho_11094 (ho_11093 BOUND_VARIABLE_1347919 BOUND_VARIABLE_1318245) BOUND_VARIABLE_1318246)))))) (let ((_let_3625 (forall ((BOUND_VARIABLE_1318234 tptp.int) (BOUND_VARIABLE_1318235 tptp.int)) (= (ho_11094 (ho_11093 k_11629 BOUND_VARIABLE_1318234) BOUND_VARIABLE_1318235) (= BOUND_VARIABLE_1318234 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318235) BOUND_VARIABLE_1318234)))))) (let ((_let_3626 (forall ((BOUND_VARIABLE_1318221 tptp.set_o) (BOUND_VARIABLE_1347947 |u_(-> tptp.int Bool Bool)|) (BOUND_VARIABLE_1318223 tptp.int) (BOUND_VARIABLE_1318224 Bool)) (= (ho_11194 (ho_11579 (ho_11582 (ho_11581 k_11630 BOUND_VARIABLE_1318221) BOUND_VARIABLE_1347947) BOUND_VARIABLE_1318223) BOUND_VARIABLE_1318224) (and (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1318224) BOUND_VARIABLE_1318221) (ho_11194 (ho_11579 BOUND_VARIABLE_1347947 BOUND_VARIABLE_1318223) BOUND_VARIABLE_1318224)))))) (let ((_let_3627 (forall ((BOUND_VARIABLE_1318208 tptp.set_Code_integer) (BOUND_VARIABLE_1347965 |u_(-> Bool tptp.code_integer Bool)|) (BOUND_VARIABLE_1318210 Bool) (BOUND_VARIABLE_1318211 tptp.code_integer)) (= (ho_11564 (ho_11583 (ho_11586 (ho_11585 k_11631 BOUND_VARIABLE_1318208) BOUND_VARIABLE_1347965) BOUND_VARIABLE_1318210) BOUND_VARIABLE_1318211) (and (ho_11567 (ho_11566 k_11565 BOUND_VARIABLE_1318211) BOUND_VARIABLE_1318208) (ho_11564 (ho_11583 BOUND_VARIABLE_1347965 BOUND_VARIABLE_1318210) BOUND_VARIABLE_1318211)))))) (let ((_let_3628 (forall ((BOUND_VARIABLE_1318199 tptp.int) (BOUND_VARIABLE_1318200 tptp.int)) (= (ho_11094 (ho_11093 k_11632 BOUND_VARIABLE_1318199) BOUND_VARIABLE_1318200) (= BOUND_VARIABLE_1318199 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318200) BOUND_VARIABLE_1318199)))))) (let ((_let_3629 (forall ((BOUND_VARIABLE_1318186 tptp.set_int) (BOUND_VARIABLE_1347993 |u_(-> Bool tptp.int Bool)|) (BOUND_VARIABLE_1318188 Bool) (BOUND_VARIABLE_1318189 tptp.int)) (= (ho_11094 (ho_11588 (ho_11591 (ho_11590 k_11633 BOUND_VARIABLE_1318186) BOUND_VARIABLE_1347993) BOUND_VARIABLE_1318188) BOUND_VARIABLE_1318189) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1318189) BOUND_VARIABLE_1318186) (ho_11094 (ho_11588 BOUND_VARIABLE_1347993 BOUND_VARIABLE_1318188) BOUND_VARIABLE_1318189)))))) (let ((_let_3630 (forall ((BOUND_VARIABLE_1318173 tptp.set_o) (BOUND_VARIABLE_1348011 |u_(-> Bool Bool Bool)|) (BOUND_VARIABLE_1318175 Bool) (BOUND_VARIABLE_1318176 Bool)) (= (ho_11194 (ho_11201 (ho_11598 (ho_11597 k_11634 BOUND_VARIABLE_1318173) BOUND_VARIABLE_1348011) BOUND_VARIABLE_1318175) BOUND_VARIABLE_1318176) (and (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1318176) BOUND_VARIABLE_1318173) (ho_11194 (ho_11201 BOUND_VARIABLE_1348011 BOUND_VARIABLE_1318175) BOUND_VARIABLE_1318176)))))) (let ((_let_3631 (forall ((BOUND_VARIABLE_1318164 tptp.int) (BOUND_VARIABLE_1318165 tptp.int)) (= (ho_11094 (ho_11093 k_11635 BOUND_VARIABLE_1318164) BOUND_VARIABLE_1318165) (= BOUND_VARIABLE_1318164 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318165) BOUND_VARIABLE_1318164)))))) (let ((_let_3632 (forall ((BOUND_VARIABLE_1318155 tptp.int) (BOUND_VARIABLE_1318156 tptp.int)) (= (ho_11094 (ho_11093 k_11636 BOUND_VARIABLE_1318155) BOUND_VARIABLE_1318156) (= BOUND_VARIABLE_1318155 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318156) BOUND_VARIABLE_1318155)))))) (let ((_let_3633 (forall ((BOUND_VARIABLE_1318146 tptp.int) (BOUND_VARIABLE_1318147 tptp.int)) (= (ho_11094 (ho_11093 k_11637 BOUND_VARIABLE_1318146) BOUND_VARIABLE_1318147) (= BOUND_VARIABLE_1318146 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318147) BOUND_VARIABLE_1318146)))))) (let ((_let_3634 (forall ((BOUND_VARIABLE_1318137 tptp.int) (BOUND_VARIABLE_1318138 tptp.int)) (= (ho_11094 (ho_11093 k_11638 BOUND_VARIABLE_1318137) BOUND_VARIABLE_1318138) (= BOUND_VARIABLE_1318137 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318138) BOUND_VARIABLE_1318137)))))) (let ((_let_3635 (forall ((BOUND_VARIABLE_1318128 tptp.int) (BOUND_VARIABLE_1318129 tptp.int)) (= (ho_11094 (ho_11093 k_11639 BOUND_VARIABLE_1318128) BOUND_VARIABLE_1318129) (= BOUND_VARIABLE_1318128 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318129) BOUND_VARIABLE_1318128)))))) (let ((_let_3636 (forall ((BOUND_VARIABLE_1318119 tptp.int) (BOUND_VARIABLE_1318120 tptp.int)) (= (ho_11094 (ho_11093 k_11640 BOUND_VARIABLE_1318119) BOUND_VARIABLE_1318120) (= BOUND_VARIABLE_1318119 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318120) BOUND_VARIABLE_1318119)))))) (let ((_let_3637 (forall ((BOUND_VARIABLE_1318110 tptp.int) (BOUND_VARIABLE_1318111 tptp.int)) (= (ho_11094 (ho_11093 k_11641 BOUND_VARIABLE_1318110) BOUND_VARIABLE_1318111) (= BOUND_VARIABLE_1318110 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318111) BOUND_VARIABLE_1318110)))))) (let ((_let_3638 (forall ((BOUND_VARIABLE_1318099 tptp.set_int) (BOUND_VARIABLE_1318100 tptp.set_int) (BOUND_VARIABLE_1318101 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1318101))) (= (ho_11094 (ho_11234 (ho_11339 k_11642 BOUND_VARIABLE_1318099) BOUND_VARIABLE_1318100) BOUND_VARIABLE_1318101) (or (ho_11180 _let_1 BOUND_VARIABLE_1318099) (ho_11180 _let_1 BOUND_VARIABLE_1318100))))))) (let ((_let_3639 (forall ((BOUND_VARIABLE_1318088 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1318089 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1318090 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1318090))) (= (ho_11184 (ho_11237 (ho_11365 k_11643 BOUND_VARIABLE_1318088) BOUND_VARIABLE_1318089) BOUND_VARIABLE_1318090) (and (ho_11070 _let_1 BOUND_VARIABLE_1318088) (ho_11070 _let_1 BOUND_VARIABLE_1318089))))))) (let ((_let_3640 (forall ((BOUND_VARIABLE_1318077 tptp.set_nat) (BOUND_VARIABLE_1318078 tptp.set_nat) (BOUND_VARIABLE_1318079 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1318079))) (= (ho_11054 (ho_11240 (ho_11343 k_11644 BOUND_VARIABLE_1318077) BOUND_VARIABLE_1318078) BOUND_VARIABLE_1318079) (or (ho_11191 _let_1 BOUND_VARIABLE_1318077) (ho_11191 _let_1 BOUND_VARIABLE_1318078))))))) (let ((_let_3641 (forall ((BOUND_VARIABLE_1318066 tptp.set_int) (BOUND_VARIABLE_1318067 tptp.set_int) (BOUND_VARIABLE_1318068 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1318068))) (= (ho_11094 (ho_11234 (ho_11339 k_11645 BOUND_VARIABLE_1318066) BOUND_VARIABLE_1318067) BOUND_VARIABLE_1318068) (or (ho_11180 _let_1 BOUND_VARIABLE_1318066) (ho_11180 _let_1 BOUND_VARIABLE_1318067))))))) (let ((_let_3642 (forall ((BOUND_VARIABLE_1318055 tptp.set_int) (BOUND_VARIABLE_1318056 tptp.set_int) (BOUND_VARIABLE_1318057 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1318057))) (= (ho_11094 (ho_11234 (ho_11339 k_11646 BOUND_VARIABLE_1318055) BOUND_VARIABLE_1318056) BOUND_VARIABLE_1318057) (or (ho_11180 _let_1 BOUND_VARIABLE_1318055) (ho_11180 _let_1 BOUND_VARIABLE_1318056))))))) (let ((_let_3643 (forall ((BOUND_VARIABLE_1318046 tptp.int) (BOUND_VARIABLE_1318047 tptp.int)) (= (ho_11094 (ho_11093 k_11647 BOUND_VARIABLE_1318046) BOUND_VARIABLE_1318047) (= BOUND_VARIABLE_1318046 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318047) BOUND_VARIABLE_1318046)))))) (let ((_let_3644 (forall ((BOUND_VARIABLE_1318037 tptp.int) (BOUND_VARIABLE_1318038 tptp.int)) (= (ho_11094 (ho_11093 k_11648 BOUND_VARIABLE_1318037) BOUND_VARIABLE_1318038) (= BOUND_VARIABLE_1318037 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318038) BOUND_VARIABLE_1318037)))))) (let ((_let_3645 (forall ((BOUND_VARIABLE_1318028 tptp.int) (BOUND_VARIABLE_1318029 tptp.int)) (= (ho_11094 (ho_11093 k_11649 BOUND_VARIABLE_1318028) BOUND_VARIABLE_1318029) (= BOUND_VARIABLE_1318028 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1318029) BOUND_VARIABLE_1318028)))))) (let ((_let_3646 (forall ((BOUND_VARIABLE_1318014 tptp.int) (BOUND_VARIABLE_1318015 tptp.int)) (= (or (= BOUND_VARIABLE_1318014 BOUND_VARIABLE_1318015) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1318015) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11650 BOUND_VARIABLE_1318014) BOUND_VARIABLE_1318015))))) (let ((_let_3647 (forall ((BOUND_VARIABLE_1318000 tptp.nat) (BOUND_VARIABLE_1318001 tptp.nat)) (= (or (= BOUND_VARIABLE_1318000 BOUND_VARIABLE_1318001) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1318001) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11651 BOUND_VARIABLE_1318000) BOUND_VARIABLE_1318001))))) (let ((_let_3648 (forall ((BOUND_VARIABLE_1317986 Bool) (BOUND_VARIABLE_1317987 Bool)) (= (or (= BOUND_VARIABLE_1317986 BOUND_VARIABLE_1317987) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1317987) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11652 BOUND_VARIABLE_1317986) BOUND_VARIABLE_1317987))))) (let ((_let_3649 (forall ((BOUND_VARIABLE_1317972 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1317973 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1317972 BOUND_VARIABLE_1317973) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1317973) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_11653 BOUND_VARIABLE_1317972) BOUND_VARIABLE_1317973))))) (let ((_let_3650 (forall ((BOUND_VARIABLE_1317958 tptp.set_nat) (BOUND_VARIABLE_1317959 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1317958 BOUND_VARIABLE_1317959) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1317959) (ho_11204 k_11203 k_11202))) (ho_11191 (ho_11209 k_11654 BOUND_VARIABLE_1317958) BOUND_VARIABLE_1317959))))) (let ((_let_3651 (forall ((BOUND_VARIABLE_1317944 tptp.list_nat) (BOUND_VARIABLE_1317945 tptp.list_nat)) (= (or (= BOUND_VARIABLE_1317944 BOUND_VARIABLE_1317945) (ho_11660 (ho_11659 k_11658 BOUND_VARIABLE_1317945) (ho_11657 k_11656 k_11655))) (ho_11278 (ho_11277 k_11661 BOUND_VARIABLE_1317944) BOUND_VARIABLE_1317945))))) (let ((_let_3652 (forall ((BOUND_VARIABLE_1317934 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1317935 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11262 k_11662 BOUND_VARIABLE_1317934) BOUND_VARIABLE_1317935) (or (= BOUND_VARIABLE_1317934 BOUND_VARIABLE_1317935) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1317935) tptp.bot_bo228742789529271731at_nat)))))) (let ((_let_3653 (forall ((BOUND_VARIABLE_1317916 tptp.set_int) (BOUND_VARIABLE_1348274 |u_(-> tptp.int tptp.rat)|) (BOUND_VARIABLE_1317918 tptp.int)) (= (ho_11094 (ho_11665 (ho_11664 k_11663 BOUND_VARIABLE_1317916) BOUND_VARIABLE_1348274) BOUND_VARIABLE_1317918) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1317918) BOUND_VARIABLE_1317916) (not (= (ho_11127 BOUND_VARIABLE_1348274 BOUND_VARIABLE_1317918) (ho_11498 k_11497 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))))))) (let ((_let_3654 (forall ((BOUND_VARIABLE_1317907 tptp.int) (BOUND_VARIABLE_1317908 tptp.int)) (= (ho_11094 (ho_11093 k_11666 BOUND_VARIABLE_1317907) BOUND_VARIABLE_1317908) (= BOUND_VARIABLE_1317907 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317908) BOUND_VARIABLE_1317907)))))) (let ((_let_3655 (forall ((BOUND_VARIABLE_1317889 tptp.set_int) (BOUND_VARIABLE_1348311 |u_(-> tptp.int tptp.code_integer)|) (BOUND_VARIABLE_1317891 tptp.int)) (= (ho_11094 (ho_11672 (ho_11671 k_11670 BOUND_VARIABLE_1317889) BOUND_VARIABLE_1348311) BOUND_VARIABLE_1317891) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1317891) BOUND_VARIABLE_1317889) (not (= (ho_11667 BOUND_VARIABLE_1348311 BOUND_VARIABLE_1317891) (ho_11669 k_11668 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))))))) (let ((_let_3656 (forall ((BOUND_VARIABLE_1317880 tptp.int) (BOUND_VARIABLE_1317881 tptp.int)) (= (ho_11094 (ho_11093 k_11673 BOUND_VARIABLE_1317880) BOUND_VARIABLE_1317881) (= BOUND_VARIABLE_1317880 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317881) BOUND_VARIABLE_1317880)))))) (let ((_let_3657 (forall ((BOUND_VARIABLE_1317871 tptp.int) (BOUND_VARIABLE_1317872 tptp.int)) (= (ho_11094 (ho_11093 k_11674 BOUND_VARIABLE_1317871) BOUND_VARIABLE_1317872) (= BOUND_VARIABLE_1317871 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317872) BOUND_VARIABLE_1317871)))))) (let ((_let_3658 (forall ((BOUND_VARIABLE_1317862 tptp.int) (BOUND_VARIABLE_1317863 tptp.int)) (= (ho_11094 (ho_11093 k_11675 BOUND_VARIABLE_1317862) BOUND_VARIABLE_1317863) (= BOUND_VARIABLE_1317862 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317863) BOUND_VARIABLE_1317862)))))) (let ((_let_3659 (forall ((BOUND_VARIABLE_1317853 tptp.int) (BOUND_VARIABLE_1317854 tptp.int)) (= (ho_11094 (ho_11093 k_11676 BOUND_VARIABLE_1317853) BOUND_VARIABLE_1317854) (= BOUND_VARIABLE_1317853 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317854) BOUND_VARIABLE_1317853)))))) (let ((_let_3660 (forall ((BOUND_VARIABLE_1317835 tptp.set_int) (BOUND_VARIABLE_1348383 |u_(-> tptp.int tptp.code_integer)|) (BOUND_VARIABLE_1317837 tptp.int)) (= (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1317837) BOUND_VARIABLE_1317835) (not (= (ho_11669 k_11668 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11667 BOUND_VARIABLE_1348383 BOUND_VARIABLE_1317837)))) (ho_11094 (ho_11672 (ho_11671 k_11677 BOUND_VARIABLE_1317835) BOUND_VARIABLE_1348383) BOUND_VARIABLE_1317837))))) (let ((_let_3661 (forall ((BOUND_VARIABLE_1317821 tptp.int) (BOUND_VARIABLE_1317822 tptp.int)) (= (or (= BOUND_VARIABLE_1317821 BOUND_VARIABLE_1317822) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1317822) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11678 BOUND_VARIABLE_1317821) BOUND_VARIABLE_1317822))))) (let ((_let_3662 (forall ((BOUND_VARIABLE_1317803 tptp.set_nat) (BOUND_VARIABLE_1348410 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1317805 tptp.nat)) (= (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1317805) BOUND_VARIABLE_1317803) (not (= (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11056 BOUND_VARIABLE_1348410 BOUND_VARIABLE_1317805)))) (ho_11054 (ho_11681 (ho_11680 k_11679 BOUND_VARIABLE_1317803) BOUND_VARIABLE_1348410) BOUND_VARIABLE_1317805))))) (let ((_let_3663 (forall ((BOUND_VARIABLE_1317789 tptp.nat) (BOUND_VARIABLE_1317790 tptp.nat)) (= (or (= BOUND_VARIABLE_1317789 BOUND_VARIABLE_1317790) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1317790) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11682 BOUND_VARIABLE_1317789) BOUND_VARIABLE_1317790))))) (let ((_let_3664 (forall ((BOUND_VARIABLE_1317775 Bool) (BOUND_VARIABLE_1317776 Bool)) (= (or (= BOUND_VARIABLE_1317775 BOUND_VARIABLE_1317776) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1317776) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11683 BOUND_VARIABLE_1317775) BOUND_VARIABLE_1317776))))) (let ((_let_3665 (forall ((BOUND_VARIABLE_1317757 tptp.set_nat) (BOUND_VARIABLE_1348455 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1317759 tptp.nat)) (= (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1317759) BOUND_VARIABLE_1317757) (not (= (ho_11498 k_11497 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11498 BOUND_VARIABLE_1348455 BOUND_VARIABLE_1317759)))) (ho_11054 (ho_11686 (ho_11685 k_11684 BOUND_VARIABLE_1317757) BOUND_VARIABLE_1348455) BOUND_VARIABLE_1317759))))) (let ((_let_3666 (forall ((BOUND_VARIABLE_1317743 tptp.nat) (BOUND_VARIABLE_1317744 tptp.nat)) (= (or (= BOUND_VARIABLE_1317743 BOUND_VARIABLE_1317744) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1317744) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11687 BOUND_VARIABLE_1317743) BOUND_VARIABLE_1317744))))) (let ((_let_3667 (forall ((BOUND_VARIABLE_1317729 Bool) (BOUND_VARIABLE_1317730 Bool)) (= (or (= BOUND_VARIABLE_1317729 BOUND_VARIABLE_1317730) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1317730) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11688 BOUND_VARIABLE_1317729) BOUND_VARIABLE_1317730))))) (let ((_let_3668 (forall ((BOUND_VARIABLE_1317711 tptp.set_nat) (BOUND_VARIABLE_1348500 |u_(-> tptp.nat tptp.code_integer)|) (BOUND_VARIABLE_1317713 tptp.nat)) (= (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1317713) BOUND_VARIABLE_1317711) (not (= (ho_11669 k_11668 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11669 BOUND_VARIABLE_1348500 BOUND_VARIABLE_1317713)))) (ho_11054 (ho_11691 (ho_11690 k_11689 BOUND_VARIABLE_1317711) BOUND_VARIABLE_1348500) BOUND_VARIABLE_1317713))))) (let ((_let_3669 (forall ((BOUND_VARIABLE_1317697 tptp.nat) (BOUND_VARIABLE_1317698 tptp.nat)) (= (or (= BOUND_VARIABLE_1317697 BOUND_VARIABLE_1317698) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1317698) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11692 BOUND_VARIABLE_1317697) BOUND_VARIABLE_1317698))))) (let ((_let_3670 (forall ((BOUND_VARIABLE_1317683 Bool) (BOUND_VARIABLE_1317684 Bool)) (= (or (= BOUND_VARIABLE_1317683 BOUND_VARIABLE_1317684) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1317684) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11693 BOUND_VARIABLE_1317683) BOUND_VARIABLE_1317684))))) (let ((_let_3671 (forall ((BOUND_VARIABLE_1317674 tptp.int) (BOUND_VARIABLE_1317675 tptp.int)) (= (ho_11094 (ho_11093 k_11694 BOUND_VARIABLE_1317674) BOUND_VARIABLE_1317675) (= BOUND_VARIABLE_1317674 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317675) BOUND_VARIABLE_1317674)))))) (let ((_let_3672 (forall ((BOUND_VARIABLE_1317665 tptp.int) (BOUND_VARIABLE_1317666 tptp.int)) (= (ho_11094 (ho_11093 k_11695 BOUND_VARIABLE_1317665) BOUND_VARIABLE_1317666) (= BOUND_VARIABLE_1317665 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317666) BOUND_VARIABLE_1317665)))))) (let ((_let_3673 (forall ((BOUND_VARIABLE_1317654 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1317655 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1317656 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1317656))) (= (ho_11184 (ho_11237 (ho_11365 k_11696 BOUND_VARIABLE_1317654) BOUND_VARIABLE_1317655) BOUND_VARIABLE_1317656) (and (ho_11070 _let_1 BOUND_VARIABLE_1317654) (ho_11070 _let_1 BOUND_VARIABLE_1317655))))))) (let ((_let_3674 (forall ((BOUND_VARIABLE_1317645 tptp.int) (BOUND_VARIABLE_1317646 tptp.int)) (= (ho_11094 (ho_11093 k_11697 BOUND_VARIABLE_1317645) BOUND_VARIABLE_1317646) (= BOUND_VARIABLE_1317645 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317646) BOUND_VARIABLE_1317645)))))) (let ((_let_3675 (forall ((BOUND_VARIABLE_1317615 tptp.set_int) (BOUND_VARIABLE_1317616 tptp.int) (BOUND_VARIABLE_1317617 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1317617))) (= (or (ho_11180 _let_1 (ho_11465 (ho_11464 k_11463 k_11462) BOUND_VARIABLE_1317615)) (ho_11180 _let_1 (ho_11177 k_11176 (ho_11093 k_11133 BOUND_VARIABLE_1317616)))) (ho_11094 (ho_11093 (ho_11467 k_11698 BOUND_VARIABLE_1317615) BOUND_VARIABLE_1317616) BOUND_VARIABLE_1317617)))))) (let ((_let_3676 (forall ((BOUND_VARIABLE_1317604 tptp.set_int) (BOUND_VARIABLE_1317605 tptp.set_int) (BOUND_VARIABLE_1317606 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1317606))) (= (ho_11094 (ho_11234 (ho_11339 k_11699 BOUND_VARIABLE_1317604) BOUND_VARIABLE_1317605) BOUND_VARIABLE_1317606) (or (ho_11180 _let_1 BOUND_VARIABLE_1317604) (ho_11180 _let_1 BOUND_VARIABLE_1317605))))))) (let ((_let_3677 (forall ((BOUND_VARIABLE_1317593 tptp.set_int) (BOUND_VARIABLE_1317594 tptp.set_int) (BOUND_VARIABLE_1317595 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1317595))) (= (ho_11094 (ho_11234 (ho_11339 k_11700 BOUND_VARIABLE_1317593) BOUND_VARIABLE_1317594) BOUND_VARIABLE_1317595) (or (ho_11180 _let_1 BOUND_VARIABLE_1317593) (ho_11180 _let_1 BOUND_VARIABLE_1317594))))))) (let ((_let_3678 (forall ((BOUND_VARIABLE_1317585 tptp.set_nat) (BOUND_VARIABLE_1317586 tptp.nat)) (= (ho_11054 (ho_11240 k_11701 BOUND_VARIABLE_1317585) BOUND_VARIABLE_1317586) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1317586) BOUND_VARIABLE_1317585))))) (let ((_let_3679 (forall ((BOUND_VARIABLE_1317577 tptp.set_nat) (BOUND_VARIABLE_1317578 tptp.nat)) (= (ho_11054 (ho_11240 k_11702 BOUND_VARIABLE_1317577) BOUND_VARIABLE_1317578) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1317578) BOUND_VARIABLE_1317577))))) (let ((_let_3680 (forall ((BOUND_VARIABLE_1317563 tptp.nat) (BOUND_VARIABLE_1317564 tptp.nat)) (= (ho_11054 (ho_11053 k_11703 BOUND_VARIABLE_1317563) BOUND_VARIABLE_1317564) (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1317563 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1317564)) (ho_11056 k_11055 K3))))))))))) (let ((_let_3681 (forall ((BOUND_VARIABLE_1317532 tptp.set_nat) (BOUND_VARIABLE_1317533 tptp.nat) (BOUND_VARIABLE_1317534 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1317534))) (= (or (ho_11191 _let_1 BOUND_VARIABLE_1317532) (ho_11191 _let_1 (ho_11107 k_11106 (ho_11053 k_11134 BOUND_VARIABLE_1317533)))) (ho_11054 (ho_11053 (ho_11705 k_11704 BOUND_VARIABLE_1317532) BOUND_VARIABLE_1317533) BOUND_VARIABLE_1317534)))))) (let ((_let_3682 (forall ((BOUND_VARIABLE_1317510 tptp.nat) (BOUND_VARIABLE_1317511 tptp.nat)) (= (ho_11054 (ho_11053 k_11706 BOUND_VARIABLE_1317510) BOUND_VARIABLE_1317511) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1317510 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1317511)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1317511 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1317510)) (ho_11056 k_11055 K3))))))))))) (let ((_let_3683 (forall ((BOUND_VARIABLE_1317463 tptp.set_nat) (BOUND_VARIABLE_1317464 tptp.nat) (BOUND_VARIABLE_1317465 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1317465))) (= (or (ho_11191 _let_1 BOUND_VARIABLE_1317463) (ho_11191 _let_1 (ho_11107 k_11106 (ho_11053 k_11135 BOUND_VARIABLE_1317464)))) (ho_11054 (ho_11053 (ho_11705 k_11707 BOUND_VARIABLE_1317463) BOUND_VARIABLE_1317464) BOUND_VARIABLE_1317465)))))) (let ((_let_3684 (forall ((BOUND_VARIABLE_1317441 tptp.nat) (BOUND_VARIABLE_1317442 tptp.nat)) (= (ho_11054 (ho_11053 k_11708 BOUND_VARIABLE_1317441) BOUND_VARIABLE_1317442) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1317441 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1317442)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1317442 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1317441)) (ho_11056 k_11055 K3))))))))))) (let ((_let_3685 (forall ((BOUND_VARIABLE_1317432 tptp.int) (BOUND_VARIABLE_1317433 tptp.int)) (= (ho_11094 (ho_11093 k_11709 BOUND_VARIABLE_1317432) BOUND_VARIABLE_1317433) (= BOUND_VARIABLE_1317432 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317433) BOUND_VARIABLE_1317432)))))) (let ((_let_3686 (forall ((BOUND_VARIABLE_1317423 tptp.int) (BOUND_VARIABLE_1317424 tptp.int)) (= (ho_11094 (ho_11093 k_11710 BOUND_VARIABLE_1317423) BOUND_VARIABLE_1317424) (= BOUND_VARIABLE_1317423 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317424) BOUND_VARIABLE_1317423)))))) (let ((_let_3687 (forall ((BOUND_VARIABLE_1317409 tptp.int) (BOUND_VARIABLE_1317410 tptp.int)) (= (or (= BOUND_VARIABLE_1317409 BOUND_VARIABLE_1317410) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1317410) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11711 BOUND_VARIABLE_1317409) BOUND_VARIABLE_1317410))))) (let ((_let_3688 (forall ((BOUND_VARIABLE_1317395 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1317396 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1317395 BOUND_VARIABLE_1317396) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1317396) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_11712 BOUND_VARIABLE_1317395) BOUND_VARIABLE_1317396))))) (let ((_let_3689 (forall ((BOUND_VARIABLE_1317381 tptp.nat) (BOUND_VARIABLE_1317382 tptp.nat)) (= (or (= BOUND_VARIABLE_1317381 BOUND_VARIABLE_1317382) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1317382) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11713 BOUND_VARIABLE_1317381) BOUND_VARIABLE_1317382))))) (let ((_let_3690 (forall ((BOUND_VARIABLE_1317367 Bool) (BOUND_VARIABLE_1317368 Bool)) (= (or (= BOUND_VARIABLE_1317367 BOUND_VARIABLE_1317368) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1317368) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11714 BOUND_VARIABLE_1317367) BOUND_VARIABLE_1317368))))) (let ((_let_3691 (forall ((BOUND_VARIABLE_1317353 tptp.set_nat) (BOUND_VARIABLE_1317354 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1317353 BOUND_VARIABLE_1317354) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1317354) (ho_11204 k_11203 k_11202))) (ho_11191 (ho_11209 k_11715 BOUND_VARIABLE_1317353) BOUND_VARIABLE_1317354))))) (let ((_let_3692 (forall ((BOUND_VARIABLE_1317339 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1317340 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1317339 BOUND_VARIABLE_1317340) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1317340) (ho_11213 k_11212 k_11210))) (ho_11211 (ho_11218 k_11716 BOUND_VARIABLE_1317339) BOUND_VARIABLE_1317340))))) (let ((_let_3693 (forall ((BOUND_VARIABLE_1317330 tptp.int) (BOUND_VARIABLE_1317331 tptp.int)) (= (ho_11094 (ho_11093 k_11717 BOUND_VARIABLE_1317330) BOUND_VARIABLE_1317331) (= BOUND_VARIABLE_1317330 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317331) BOUND_VARIABLE_1317330)))))) (let ((_let_3694 (forall ((BOUND_VARIABLE_1317321 tptp.int) (BOUND_VARIABLE_1317322 tptp.int)) (= (ho_11094 (ho_11093 k_11718 BOUND_VARIABLE_1317321) BOUND_VARIABLE_1317322) (= BOUND_VARIABLE_1317321 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317322) BOUND_VARIABLE_1317321)))))) (let ((_let_3695 (forall ((BOUND_VARIABLE_1317307 tptp.int) (BOUND_VARIABLE_1317308 tptp.int)) (= (or (= BOUND_VARIABLE_1317307 BOUND_VARIABLE_1317308) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1317308) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11719 BOUND_VARIABLE_1317307) BOUND_VARIABLE_1317308))))) (let ((_let_3696 (forall ((BOUND_VARIABLE_1317293 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1317294 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1317293 BOUND_VARIABLE_1317294) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1317294) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_11720 BOUND_VARIABLE_1317293) BOUND_VARIABLE_1317294))))) (let ((_let_3697 (forall ((BOUND_VARIABLE_1317279 tptp.nat) (BOUND_VARIABLE_1317280 tptp.nat)) (= (or (= BOUND_VARIABLE_1317279 BOUND_VARIABLE_1317280) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1317280) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11721 BOUND_VARIABLE_1317279) BOUND_VARIABLE_1317280))))) (let ((_let_3698 (forall ((BOUND_VARIABLE_1317265 Bool) (BOUND_VARIABLE_1317266 Bool)) (= (or (= BOUND_VARIABLE_1317265 BOUND_VARIABLE_1317266) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1317266) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11722 BOUND_VARIABLE_1317265) BOUND_VARIABLE_1317266))))) (let ((_let_3699 (forall ((BOUND_VARIABLE_1317251 tptp.set_nat) (BOUND_VARIABLE_1317252 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1317251 BOUND_VARIABLE_1317252) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1317252) (ho_11204 k_11203 k_11202))) (ho_11191 (ho_11209 k_11723 BOUND_VARIABLE_1317251) BOUND_VARIABLE_1317252))))) (let ((_let_3700 (forall ((BOUND_VARIABLE_1317237 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1317238 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1317237 BOUND_VARIABLE_1317238) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1317238) (ho_11213 k_11212 k_11210))) (ho_11211 (ho_11218 k_11724 BOUND_VARIABLE_1317237) BOUND_VARIABLE_1317238))))) (let ((_let_3701 (forall ((BOUND_VARIABLE_1317228 tptp.int) (BOUND_VARIABLE_1317229 tptp.int)) (= (ho_11094 (ho_11093 k_11725 BOUND_VARIABLE_1317228) BOUND_VARIABLE_1317229) (= BOUND_VARIABLE_1317228 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317229) BOUND_VARIABLE_1317228)))))) (let ((_let_3702 (forall ((BOUND_VARIABLE_1317219 tptp.int) (BOUND_VARIABLE_1317220 tptp.int)) (= (ho_11094 (ho_11093 k_11726 BOUND_VARIABLE_1317219) BOUND_VARIABLE_1317220) (= BOUND_VARIABLE_1317219 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317220) BOUND_VARIABLE_1317219)))))) (let ((_let_3703 (forall ((BOUND_VARIABLE_1317210 tptp.int) (BOUND_VARIABLE_1317211 tptp.int)) (= (ho_11094 (ho_11093 k_11727 BOUND_VARIABLE_1317210) BOUND_VARIABLE_1317211) (= BOUND_VARIABLE_1317210 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317211) BOUND_VARIABLE_1317210)))))) (let ((_let_3704 (forall ((BOUND_VARIABLE_1317201 tptp.int) (BOUND_VARIABLE_1317202 tptp.int)) (= (ho_11094 (ho_11093 k_11728 BOUND_VARIABLE_1317201) BOUND_VARIABLE_1317202) (= BOUND_VARIABLE_1317201 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317202) BOUND_VARIABLE_1317201)))))) (let ((_let_3705 (forall ((BOUND_VARIABLE_1317192 tptp.int) (BOUND_VARIABLE_1317193 tptp.int)) (= (ho_11094 (ho_11093 k_11729 BOUND_VARIABLE_1317192) BOUND_VARIABLE_1317193) (= BOUND_VARIABLE_1317192 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317193) BOUND_VARIABLE_1317192)))))) (let ((_let_3706 (forall ((BOUND_VARIABLE_1317183 tptp.int) (BOUND_VARIABLE_1317184 tptp.int)) (= (ho_11094 (ho_11093 k_11730 BOUND_VARIABLE_1317183) BOUND_VARIABLE_1317184) (= BOUND_VARIABLE_1317183 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317184) BOUND_VARIABLE_1317183)))))) (let ((_let_3707 (forall ((BOUND_VARIABLE_1317174 tptp.int) (BOUND_VARIABLE_1317175 tptp.int)) (= (ho_11094 (ho_11093 k_11731 BOUND_VARIABLE_1317174) BOUND_VARIABLE_1317175) (= BOUND_VARIABLE_1317174 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317175) BOUND_VARIABLE_1317174)))))) (let ((_let_3708 (forall ((BOUND_VARIABLE_1317165 tptp.int) (BOUND_VARIABLE_1317166 tptp.int)) (= (ho_11094 (ho_11093 k_11732 BOUND_VARIABLE_1317165) BOUND_VARIABLE_1317166) (= BOUND_VARIABLE_1317165 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317166) BOUND_VARIABLE_1317165)))))) (let ((_let_3709 (forall ((BOUND_VARIABLE_1317156 tptp.int) (BOUND_VARIABLE_1317157 tptp.int)) (= (ho_11094 (ho_11093 k_11733 BOUND_VARIABLE_1317156) BOUND_VARIABLE_1317157) (= BOUND_VARIABLE_1317156 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317157) BOUND_VARIABLE_1317156)))))) (let ((_let_3710 (forall ((BOUND_VARIABLE_1317147 tptp.int) (BOUND_VARIABLE_1317148 tptp.int)) (= (ho_11094 (ho_11093 k_11734 BOUND_VARIABLE_1317147) BOUND_VARIABLE_1317148) (= BOUND_VARIABLE_1317147 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317148) BOUND_VARIABLE_1317147)))))) (let ((_let_3711 (forall ((BOUND_VARIABLE_1317136 tptp.set_int) (BOUND_VARIABLE_1317137 tptp.set_int) (BOUND_VARIABLE_1317138 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1317138))) (= (ho_11094 (ho_11234 (ho_11339 k_11735 BOUND_VARIABLE_1317136) BOUND_VARIABLE_1317137) BOUND_VARIABLE_1317138) (or (ho_11180 _let_1 BOUND_VARIABLE_1317136) (ho_11180 _let_1 BOUND_VARIABLE_1317137))))))) (let ((_let_3712 (forall ((BOUND_VARIABLE_1317127 tptp.int) (BOUND_VARIABLE_1317128 tptp.int)) (= (ho_11094 (ho_11093 k_11736 BOUND_VARIABLE_1317127) BOUND_VARIABLE_1317128) (= BOUND_VARIABLE_1317127 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317128) BOUND_VARIABLE_1317127)))))) (let ((_let_3713 (forall ((BOUND_VARIABLE_1317118 tptp.int) (BOUND_VARIABLE_1317119 tptp.int)) (= (ho_11094 (ho_11093 k_11737 BOUND_VARIABLE_1317118) BOUND_VARIABLE_1317119) (= BOUND_VARIABLE_1317118 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317119) BOUND_VARIABLE_1317118)))))) (let ((_let_3714 (forall ((BOUND_VARIABLE_1317107 tptp.set_int) (BOUND_VARIABLE_1317108 tptp.set_int) (BOUND_VARIABLE_1317109 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1317109))) (= (ho_11094 (ho_11234 (ho_11339 k_11738 BOUND_VARIABLE_1317107) BOUND_VARIABLE_1317108) BOUND_VARIABLE_1317109) (or (ho_11180 _let_1 BOUND_VARIABLE_1317107) (ho_11180 _let_1 BOUND_VARIABLE_1317108))))))) (let ((_let_3715 (forall ((BOUND_VARIABLE_1317098 tptp.int) (BOUND_VARIABLE_1317099 tptp.int)) (= (ho_11094 (ho_11093 k_11739 BOUND_VARIABLE_1317098) BOUND_VARIABLE_1317099) (= BOUND_VARIABLE_1317098 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317099) BOUND_VARIABLE_1317098)))))) (let ((_let_3716 (forall ((BOUND_VARIABLE_1317089 tptp.int) (BOUND_VARIABLE_1317090 tptp.int)) (= (ho_11094 (ho_11093 k_11740 BOUND_VARIABLE_1317089) BOUND_VARIABLE_1317090) (= BOUND_VARIABLE_1317089 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317090) BOUND_VARIABLE_1317089)))))) (let ((_let_3717 (forall ((BOUND_VARIABLE_1317080 tptp.int) (BOUND_VARIABLE_1317081 tptp.int)) (= (ho_11094 (ho_11093 k_11741 BOUND_VARIABLE_1317080) BOUND_VARIABLE_1317081) (= BOUND_VARIABLE_1317080 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317081) BOUND_VARIABLE_1317080)))))) (let ((_let_3718 (forall ((BOUND_VARIABLE_1317069 tptp.set_int) (BOUND_VARIABLE_1317070 tptp.set_int) (BOUND_VARIABLE_1317071 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1317071))) (= (ho_11094 (ho_11234 (ho_11339 k_11742 BOUND_VARIABLE_1317069) BOUND_VARIABLE_1317070) BOUND_VARIABLE_1317071) (or (ho_11180 _let_1 BOUND_VARIABLE_1317069) (ho_11180 _let_1 BOUND_VARIABLE_1317070))))))) (let ((_let_3719 (forall ((BOUND_VARIABLE_1317060 tptp.int) (BOUND_VARIABLE_1317061 tptp.int)) (= (ho_11094 (ho_11093 k_11743 BOUND_VARIABLE_1317060) BOUND_VARIABLE_1317061) (= BOUND_VARIABLE_1317060 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317061) BOUND_VARIABLE_1317060)))))) (let ((_let_3720 (forall ((BOUND_VARIABLE_1317051 tptp.int) (BOUND_VARIABLE_1317052 tptp.int)) (= (ho_11094 (ho_11093 k_11744 BOUND_VARIABLE_1317051) BOUND_VARIABLE_1317052) (= BOUND_VARIABLE_1317051 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317052) BOUND_VARIABLE_1317051)))))) (let ((_let_3721 (forall ((BOUND_VARIABLE_1317042 tptp.int) (BOUND_VARIABLE_1317043 tptp.int)) (= (ho_11094 (ho_11093 k_11745 BOUND_VARIABLE_1317042) BOUND_VARIABLE_1317043) (= BOUND_VARIABLE_1317042 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317043) BOUND_VARIABLE_1317042)))))) (let ((_let_3722 (forall ((BOUND_VARIABLE_1317033 tptp.int) (BOUND_VARIABLE_1317034 tptp.int)) (= (ho_11094 (ho_11093 k_11746 BOUND_VARIABLE_1317033) BOUND_VARIABLE_1317034) (= BOUND_VARIABLE_1317033 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317034) BOUND_VARIABLE_1317033)))))) (let ((_let_3723 (forall ((BOUND_VARIABLE_1317024 tptp.int) (BOUND_VARIABLE_1317025 tptp.int)) (= (ho_11094 (ho_11093 k_11747 BOUND_VARIABLE_1317024) BOUND_VARIABLE_1317025) (= BOUND_VARIABLE_1317024 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317025) BOUND_VARIABLE_1317024)))))) (let ((_let_3724 (forall ((BOUND_VARIABLE_1317015 tptp.int) (BOUND_VARIABLE_1317016 tptp.int)) (= (ho_11094 (ho_11093 k_11748 BOUND_VARIABLE_1317015) BOUND_VARIABLE_1317016) (= BOUND_VARIABLE_1317015 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317016) BOUND_VARIABLE_1317015)))))) (let ((_let_3725 (forall ((BOUND_VARIABLE_1317006 tptp.int) (BOUND_VARIABLE_1317007 tptp.int)) (= (ho_11094 (ho_11093 k_11749 BOUND_VARIABLE_1317006) BOUND_VARIABLE_1317007) (= BOUND_VARIABLE_1317006 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1317007) BOUND_VARIABLE_1317006)))))) (let ((_let_3726 (forall ((BOUND_VARIABLE_1316997 tptp.int) (BOUND_VARIABLE_1316998 tptp.int)) (= (ho_11094 (ho_11093 k_11750 BOUND_VARIABLE_1316997) BOUND_VARIABLE_1316998) (= BOUND_VARIABLE_1316997 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316998) BOUND_VARIABLE_1316997)))))) (let ((_let_3727 (forall ((BOUND_VARIABLE_1316988 tptp.int) (BOUND_VARIABLE_1316989 tptp.int)) (= (ho_11094 (ho_11093 k_11751 BOUND_VARIABLE_1316988) BOUND_VARIABLE_1316989) (= BOUND_VARIABLE_1316988 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316989) BOUND_VARIABLE_1316988)))))) (let ((_let_3728 (forall ((BOUND_VARIABLE_1316979 tptp.int) (BOUND_VARIABLE_1316980 tptp.int)) (= (ho_11094 (ho_11093 k_11752 BOUND_VARIABLE_1316979) BOUND_VARIABLE_1316980) (= BOUND_VARIABLE_1316979 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316980) BOUND_VARIABLE_1316979)))))) (let ((_let_3729 (forall ((BOUND_VARIABLE_1316966 tptp.set_int) (BOUND_VARIABLE_1349195 |u_(-> tptp.int tptp.code_integer Bool)|) (BOUND_VARIABLE_1316968 tptp.code_integer) (BOUND_VARIABLE_1316969 tptp.int)) (= (ho_11094 (ho_11619 (ho_11755 (ho_11754 k_11753 BOUND_VARIABLE_1316966) BOUND_VARIABLE_1349195) BOUND_VARIABLE_1316968) BOUND_VARIABLE_1316969) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1316969) BOUND_VARIABLE_1316966) (ho_11564 (ho_11560 BOUND_VARIABLE_1349195 BOUND_VARIABLE_1316969) BOUND_VARIABLE_1316968)))))) (let ((_let_3730 (forall ((BOUND_VARIABLE_1316957 tptp.int) (BOUND_VARIABLE_1316958 tptp.int)) (= (ho_11094 (ho_11093 k_11756 BOUND_VARIABLE_1316957) BOUND_VARIABLE_1316958) (= BOUND_VARIABLE_1316957 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316958) BOUND_VARIABLE_1316957)))))) (let ((_let_3731 (forall ((BOUND_VARIABLE_1316948 tptp.int) (BOUND_VARIABLE_1316949 tptp.int)) (= (ho_11094 (ho_11093 k_11757 BOUND_VARIABLE_1316948) BOUND_VARIABLE_1316949) (= BOUND_VARIABLE_1316948 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316949) BOUND_VARIABLE_1316948)))))) (let ((_let_3732 (forall ((BOUND_VARIABLE_1316939 tptp.int) (BOUND_VARIABLE_1316940 tptp.int)) (= (ho_11094 (ho_11093 k_11758 BOUND_VARIABLE_1316939) BOUND_VARIABLE_1316940) (= BOUND_VARIABLE_1316939 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316940) BOUND_VARIABLE_1316939)))))) (let ((_let_3733 (forall ((BOUND_VARIABLE_1316926 tptp.set_int) (BOUND_VARIABLE_1349251 |u_(-> tptp.int tptp.int Bool)|) (BOUND_VARIABLE_1316928 tptp.int) (BOUND_VARIABLE_1316929 tptp.int)) (= (ho_11094 (ho_11093 (ho_11572 (ho_11571 k_11759 BOUND_VARIABLE_1316926) BOUND_VARIABLE_1349251) BOUND_VARIABLE_1316928) BOUND_VARIABLE_1316929) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1316929) BOUND_VARIABLE_1316926) (ho_11094 (ho_11093 BOUND_VARIABLE_1349251 BOUND_VARIABLE_1316929) BOUND_VARIABLE_1316928)))))) (let ((_let_3734 (forall ((BOUND_VARIABLE_1316917 tptp.int) (BOUND_VARIABLE_1316918 tptp.int)) (= (ho_11094 (ho_11093 k_11760 BOUND_VARIABLE_1316917) BOUND_VARIABLE_1316918) (= BOUND_VARIABLE_1316917 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316918) BOUND_VARIABLE_1316917)))))) (let ((_let_3735 (forall ((BOUND_VARIABLE_1316908 tptp.int) (BOUND_VARIABLE_1316909 tptp.int)) (= (ho_11094 (ho_11093 k_11761 BOUND_VARIABLE_1316908) BOUND_VARIABLE_1316909) (= BOUND_VARIABLE_1316908 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316909) BOUND_VARIABLE_1316908)))))) (let ((_let_3736 (forall ((BOUND_VARIABLE_1316895 tptp.set_int) (BOUND_VARIABLE_1349289 |u_(-> tptp.int tptp.nat Bool)|) (BOUND_VARIABLE_1316897 tptp.nat) (BOUND_VARIABLE_1316898 tptp.int)) (= (ho_11094 (ho_11765 (ho_11764 (ho_11763 k_11762 BOUND_VARIABLE_1316895) BOUND_VARIABLE_1349289) BOUND_VARIABLE_1316897) BOUND_VARIABLE_1316898) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1316898) BOUND_VARIABLE_1316895) (ho_11054 (ho_11574 BOUND_VARIABLE_1349289 BOUND_VARIABLE_1316898) BOUND_VARIABLE_1316897)))))) (let ((_let_3737 (forall ((BOUND_VARIABLE_1316886 tptp.int) (BOUND_VARIABLE_1316887 tptp.int)) (= (ho_11094 (ho_11093 k_11766 BOUND_VARIABLE_1316886) BOUND_VARIABLE_1316887) (= BOUND_VARIABLE_1316886 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316887) BOUND_VARIABLE_1316886)))))) (let ((_let_3738 (forall ((BOUND_VARIABLE_1316877 tptp.int) (BOUND_VARIABLE_1316878 tptp.int)) (= (ho_11094 (ho_11093 k_11767 BOUND_VARIABLE_1316877) BOUND_VARIABLE_1316878) (= BOUND_VARIABLE_1316877 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316878) BOUND_VARIABLE_1316877)))))) (let ((_let_3739 (forall ((BOUND_VARIABLE_1316868 tptp.int) (BOUND_VARIABLE_1316869 tptp.int)) (= (ho_11094 (ho_11093 k_11768 BOUND_VARIABLE_1316868) BOUND_VARIABLE_1316869) (= BOUND_VARIABLE_1316868 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316869) BOUND_VARIABLE_1316868)))))) (let ((_let_3740 (forall ((BOUND_VARIABLE_1316859 tptp.int) (BOUND_VARIABLE_1316860 tptp.int)) (= (ho_11094 (ho_11093 k_11769 BOUND_VARIABLE_1316859) BOUND_VARIABLE_1316860) (= BOUND_VARIABLE_1316859 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316860) BOUND_VARIABLE_1316859)))))) (let ((_let_3741 (forall ((BOUND_VARIABLE_1316851 tptp.int) (BOUND_VARIABLE_1316852 tptp.int)) (= (ho_11094 (ho_11093 k_11770 BOUND_VARIABLE_1316851) BOUND_VARIABLE_1316852) (ho_11094 (ho_11093 k_11771 BOUND_VARIABLE_1316852) BOUND_VARIABLE_1316851))))) (let ((_let_3742 (forall ((BOUND_VARIABLE_1316842 tptp.int) (BOUND_VARIABLE_1316843 tptp.int)) (= (ho_11094 (ho_11093 k_11772 BOUND_VARIABLE_1316842) BOUND_VARIABLE_1316843) (= BOUND_VARIABLE_1316842 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316843) BOUND_VARIABLE_1316842)))))) (let ((_let_3743 (forall ((BOUND_VARIABLE_1316825 tptp.int) (BOUND_VARIABLE_1316826 tptp.int) (BOUND_VARIABLE_1316827 tptp.int)) (let ((_let_1 (ho_11058 k_11095 BOUND_VARIABLE_1316827))) (= (ho_11094 (ho_11093 (ho_11104 k_11773 BOUND_VARIABLE_1316825) BOUND_VARIABLE_1316826) BOUND_VARIABLE_1316827) (and (= BOUND_VARIABLE_1316825 (ho_11059 _let_1 BOUND_VARIABLE_1316825)) (= BOUND_VARIABLE_1316827 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316826) BOUND_VARIABLE_1316827)) (not (= BOUND_VARIABLE_1316826 (ho_11059 _let_1 BOUND_VARIABLE_1316826))))))))) (let ((_let_3744 (forall ((BOUND_VARIABLE_1316816 tptp.int) (BOUND_VARIABLE_1316817 tptp.int)) (= (ho_11094 (ho_11093 k_11774 BOUND_VARIABLE_1316816) BOUND_VARIABLE_1316817) (= BOUND_VARIABLE_1316816 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316817) BOUND_VARIABLE_1316816)))))) (let ((_let_3745 (forall ((BOUND_VARIABLE_1316798 tptp.int) (BOUND_VARIABLE_1316799 tptp.int) (BOUND_VARIABLE_1316800 tptp.int)) (= (ho_11094 (ho_11093 (ho_11104 k_11775 BOUND_VARIABLE_1316798) BOUND_VARIABLE_1316799) BOUND_VARIABLE_1316800) (and (= BOUND_VARIABLE_1316800 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316798) BOUND_VARIABLE_1316800)) (= BOUND_VARIABLE_1316799 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316800) BOUND_VARIABLE_1316799)) (not (= BOUND_VARIABLE_1316800 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316799) BOUND_VARIABLE_1316800)))))))) (let ((_let_3746 (forall ((BOUND_VARIABLE_1316789 tptp.int) (BOUND_VARIABLE_1316790 tptp.int)) (= (ho_11094 (ho_11093 k_11776 BOUND_VARIABLE_1316789) BOUND_VARIABLE_1316790) (= BOUND_VARIABLE_1316789 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316790) BOUND_VARIABLE_1316789)))))) (let ((_let_3747 (forall ((BOUND_VARIABLE_1316768 tptp.int) (BOUND_VARIABLE_1316769 tptp.int) (BOUND_VARIABLE_1316770 tptp.int)) (let ((_let_1 (ho_11058 k_11095 BOUND_VARIABLE_1316770))) (= (ho_11094 (ho_11093 (ho_11104 k_11777 BOUND_VARIABLE_1316768) BOUND_VARIABLE_1316769) BOUND_VARIABLE_1316770) (and (= BOUND_VARIABLE_1316770 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316768) BOUND_VARIABLE_1316770)) (not (= BOUND_VARIABLE_1316768 (ho_11059 _let_1 BOUND_VARIABLE_1316768))) (= BOUND_VARIABLE_1316769 (ho_11059 _let_1 BOUND_VARIABLE_1316769)) (not (= BOUND_VARIABLE_1316770 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316769) BOUND_VARIABLE_1316770))))))))) (let ((_let_3748 (forall ((BOUND_VARIABLE_1316759 tptp.int) (BOUND_VARIABLE_1316760 tptp.int)) (= (ho_11094 (ho_11093 k_11778 BOUND_VARIABLE_1316759) BOUND_VARIABLE_1316760) (= BOUND_VARIABLE_1316759 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316760) BOUND_VARIABLE_1316759)))))) (let ((_let_3749 (forall ((BOUND_VARIABLE_1316745 tptp.int) (BOUND_VARIABLE_1316746 tptp.int) (BOUND_VARIABLE_1316747 tptp.int)) (= (ho_11094 (ho_11093 (ho_11104 k_11779 BOUND_VARIABLE_1316745) BOUND_VARIABLE_1316746) BOUND_VARIABLE_1316747) (and (= BOUND_VARIABLE_1316747 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316745) BOUND_VARIABLE_1316747)) (= BOUND_VARIABLE_1316746 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316747) BOUND_VARIABLE_1316746))))))) (let ((_let_3750 (forall ((BOUND_VARIABLE_1316736 tptp.int) (BOUND_VARIABLE_1316737 tptp.int)) (= (ho_11094 (ho_11093 k_11780 BOUND_VARIABLE_1316736) BOUND_VARIABLE_1316737) (= BOUND_VARIABLE_1316736 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316737) BOUND_VARIABLE_1316736)))))) (let ((_let_3751 (forall ((BOUND_VARIABLE_1316727 tptp.int) (BOUND_VARIABLE_1316728 tptp.int)) (= (ho_11094 (ho_11093 k_11781 BOUND_VARIABLE_1316727) BOUND_VARIABLE_1316728) (= BOUND_VARIABLE_1316727 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316728) BOUND_VARIABLE_1316727)))))) (let ((_let_3752 (forall ((BOUND_VARIABLE_1316718 tptp.int) (BOUND_VARIABLE_1316719 tptp.int)) (= (ho_11094 (ho_11093 k_11782 BOUND_VARIABLE_1316718) BOUND_VARIABLE_1316719) (= BOUND_VARIABLE_1316718 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316719) BOUND_VARIABLE_1316718)))))) (let ((_let_3753 (forall ((BOUND_VARIABLE_1349516 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_1349515 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_1316710 tptp.int)) (= (ho_11094 (ho_11785 (ho_11784 k_11783 BOUND_VARIABLE_1349516) BOUND_VARIABLE_1349515) BOUND_VARIABLE_1316710) (or (ho_11094 BOUND_VARIABLE_1349516 BOUND_VARIABLE_1316710) (ho_11094 BOUND_VARIABLE_1349515 BOUND_VARIABLE_1316710)))))) (let ((_let_3754 (forall ((BOUND_VARIABLE_1316699 tptp.int) (BOUND_VARIABLE_1316700 tptp.int)) (= (ho_11094 (ho_11093 k_11786 BOUND_VARIABLE_1316699) BOUND_VARIABLE_1316700) (= BOUND_VARIABLE_1316699 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316700) BOUND_VARIABLE_1316699)))))) (let ((_let_3755 (forall ((BOUND_VARIABLE_1316690 tptp.int) (BOUND_VARIABLE_1316691 tptp.int)) (= (ho_11094 (ho_11093 k_11787 BOUND_VARIABLE_1316690) BOUND_VARIABLE_1316691) (= BOUND_VARIABLE_1316690 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316691) BOUND_VARIABLE_1316690)))))) (let ((_let_3756 (forall ((BOUND_VARIABLE_1316681 tptp.int) (BOUND_VARIABLE_1316682 tptp.int)) (= (ho_11094 (ho_11093 k_11788 BOUND_VARIABLE_1316681) BOUND_VARIABLE_1316682) (= BOUND_VARIABLE_1316681 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316682) BOUND_VARIABLE_1316681)))))) (let ((_let_3757 (forall ((BOUND_VARIABLE_1349568 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_1349567 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_1316673 tptp.int)) (= (ho_11094 (ho_11785 (ho_11784 k_11789 BOUND_VARIABLE_1349568) BOUND_VARIABLE_1349567) BOUND_VARIABLE_1316673) (and (ho_11094 BOUND_VARIABLE_1349568 BOUND_VARIABLE_1316673) (ho_11094 BOUND_VARIABLE_1349567 BOUND_VARIABLE_1316673)))))) (let ((_let_3758 (forall ((BOUND_VARIABLE_1316662 tptp.int) (BOUND_VARIABLE_1316663 tptp.int)) (= (ho_11094 (ho_11093 k_11790 BOUND_VARIABLE_1316662) BOUND_VARIABLE_1316663) (= BOUND_VARIABLE_1316662 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316663) BOUND_VARIABLE_1316662)))))) (let ((_let_3759 (forall ((BOUND_VARIABLE_1316653 tptp.int) (BOUND_VARIABLE_1316654 tptp.int)) (= (ho_11094 (ho_11093 k_11791 BOUND_VARIABLE_1316653) BOUND_VARIABLE_1316654) (= BOUND_VARIABLE_1316653 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316654) BOUND_VARIABLE_1316653)))))) (let ((_let_3760 (forall ((BOUND_VARIABLE_1316644 tptp.int) (BOUND_VARIABLE_1316645 tptp.int)) (= (ho_11094 (ho_11093 k_11792 BOUND_VARIABLE_1316644) BOUND_VARIABLE_1316645) (= BOUND_VARIABLE_1316644 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316645) BOUND_VARIABLE_1316644)))))) (let ((_let_3761 (forall ((BOUND_VARIABLE_1316633 tptp.set_int) (BOUND_VARIABLE_1316634 tptp.set_int) (BOUND_VARIABLE_1316635 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1316635))) (= (ho_11094 (ho_11234 (ho_11339 k_11793 BOUND_VARIABLE_1316633) BOUND_VARIABLE_1316634) BOUND_VARIABLE_1316635) (or (ho_11180 _let_1 BOUND_VARIABLE_1316633) (ho_11180 _let_1 BOUND_VARIABLE_1316634))))))) (let ((_let_3762 (forall ((BOUND_VARIABLE_1316624 tptp.int) (BOUND_VARIABLE_1316625 tptp.int)) (= (ho_11094 (ho_11093 k_11794 BOUND_VARIABLE_1316624) BOUND_VARIABLE_1316625) (= BOUND_VARIABLE_1316624 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316625) BOUND_VARIABLE_1316624)))))) (let ((_let_3763 (forall ((BOUND_VARIABLE_1316615 tptp.int) (BOUND_VARIABLE_1316616 tptp.int)) (= (ho_11094 (ho_11093 k_11795 BOUND_VARIABLE_1316615) BOUND_VARIABLE_1316616) (= BOUND_VARIABLE_1316615 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316616) BOUND_VARIABLE_1316615)))))) (let ((_let_3764 (forall ((BOUND_VARIABLE_1316606 tptp.int) (BOUND_VARIABLE_1316607 tptp.int)) (= (ho_11094 (ho_11093 k_11796 BOUND_VARIABLE_1316606) BOUND_VARIABLE_1316607) (= BOUND_VARIABLE_1316606 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316607) BOUND_VARIABLE_1316606)))))) (let ((_let_3765 (forall ((BOUND_VARIABLE_1316595 tptp.set_int) (BOUND_VARIABLE_1316596 tptp.set_int) (BOUND_VARIABLE_1316597 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1316597))) (= (ho_11094 (ho_11234 (ho_11339 k_11797 BOUND_VARIABLE_1316595) BOUND_VARIABLE_1316596) BOUND_VARIABLE_1316597) (or (ho_11180 _let_1 BOUND_VARIABLE_1316595) (ho_11180 _let_1 BOUND_VARIABLE_1316596))))))) (let ((_let_3766 (forall ((BOUND_VARIABLE_1316584 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1316585 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1316586 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1316586))) (= (ho_11184 (ho_11237 (ho_11365 k_11798 BOUND_VARIABLE_1316584) BOUND_VARIABLE_1316585) BOUND_VARIABLE_1316586) (and (ho_11070 _let_1 BOUND_VARIABLE_1316584) (ho_11070 _let_1 BOUND_VARIABLE_1316585))))))) (let ((_let_3767 (forall ((BOUND_VARIABLE_1316573 tptp.set_nat) (BOUND_VARIABLE_1316574 tptp.set_nat) (BOUND_VARIABLE_1316575 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1316575))) (= (ho_11054 (ho_11240 (ho_11343 k_11799 BOUND_VARIABLE_1316573) BOUND_VARIABLE_1316574) BOUND_VARIABLE_1316575) (or (ho_11191 _let_1 BOUND_VARIABLE_1316573) (ho_11191 _let_1 BOUND_VARIABLE_1316574))))))) (let ((_let_3768 (forall ((BOUND_VARIABLE_1316541 tptp.list_int) (BOUND_VARIABLE_1316542 tptp.heap_e7401611519738050253t_unit)) (= (ho_11805 (ho_11804 k_11803 (ho_11147 k_11146 BOUND_VARIABLE_1316541)) (ho_11802 (ho_11801 k_11800 BOUND_VARIABLE_1316541) BOUND_VARIABLE_1316542)) (ho_11149 (ho_11807 k_11806 BOUND_VARIABLE_1316541) BOUND_VARIABLE_1316542))))) (let ((_let_3769 (forall ((BOUND_VARIABLE_1316509 tptp.list_o) (BOUND_VARIABLE_1316510 tptp.heap_e7401611519738050253t_unit)) (= (ho_11813 (ho_11812 k_11811 (ho_11156 k_11155 BOUND_VARIABLE_1316509)) (ho_11810 (ho_11809 k_11808 BOUND_VARIABLE_1316509) BOUND_VARIABLE_1316510)) (ho_11158 (ho_11815 k_11814 BOUND_VARIABLE_1316509) BOUND_VARIABLE_1316510))))) (let ((_let_3770 (forall ((BOUND_VARIABLE_1316477 tptp.list_nat) (BOUND_VARIABLE_1316478 tptp.heap_e7401611519738050253t_unit)) (= (ho_11821 (ho_11820 k_11819 (ho_11165 k_11164 BOUND_VARIABLE_1316477)) (ho_11818 (ho_11817 k_11816 BOUND_VARIABLE_1316477) BOUND_VARIABLE_1316478)) (ho_11167 (ho_11823 k_11822 BOUND_VARIABLE_1316477) BOUND_VARIABLE_1316478))))) (let ((_let_3771 (forall ((BOUND_VARIABLE_1316468 tptp.int) (BOUND_VARIABLE_1316469 tptp.int)) (= (ho_11094 (ho_11093 k_11824 BOUND_VARIABLE_1316468) BOUND_VARIABLE_1316469) (= BOUND_VARIABLE_1316468 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316469) BOUND_VARIABLE_1316468)))))) (let ((_let_3772 (forall ((BOUND_VARIABLE_1316459 tptp.int) (BOUND_VARIABLE_1316460 tptp.int)) (= (ho_11094 (ho_11093 k_11825 BOUND_VARIABLE_1316459) BOUND_VARIABLE_1316460) (= BOUND_VARIABLE_1316459 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316460) BOUND_VARIABLE_1316459)))))) (let ((_let_3773 (forall ((BOUND_VARIABLE_1316450 tptp.int) (BOUND_VARIABLE_1316451 tptp.int)) (= (ho_11094 (ho_11093 k_11826 BOUND_VARIABLE_1316450) BOUND_VARIABLE_1316451) (= BOUND_VARIABLE_1316450 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316451) BOUND_VARIABLE_1316450)))))) (let ((_let_3774 (forall ((BOUND_VARIABLE_1316441 tptp.int) (BOUND_VARIABLE_1316442 tptp.int)) (= (ho_11094 (ho_11093 k_11827 BOUND_VARIABLE_1316441) BOUND_VARIABLE_1316442) (= BOUND_VARIABLE_1316441 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316442) BOUND_VARIABLE_1316441)))))) (let ((_let_3775 (forall ((BOUND_VARIABLE_1316427 Bool) (BOUND_VARIABLE_1316428 Bool)) (= (or (= BOUND_VARIABLE_1316427 BOUND_VARIABLE_1316428) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1316428) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11828 BOUND_VARIABLE_1316427) BOUND_VARIABLE_1316428))))) (let ((_let_3776 (forall ((BOUND_VARIABLE_1316413 tptp.int) (BOUND_VARIABLE_1316414 tptp.int)) (= (or (= BOUND_VARIABLE_1316413 BOUND_VARIABLE_1316414) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1316414) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11829 BOUND_VARIABLE_1316413) BOUND_VARIABLE_1316414))))) (let ((_let_3777 (forall ((BOUND_VARIABLE_1316404 tptp.int) (BOUND_VARIABLE_1316405 tptp.int)) (= (ho_11094 (ho_11093 k_11830 BOUND_VARIABLE_1316404) BOUND_VARIABLE_1316405) (= BOUND_VARIABLE_1316404 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316405) BOUND_VARIABLE_1316404)))))) (let ((_let_3778 (forall ((BOUND_VARIABLE_1316390 tptp.nat) (BOUND_VARIABLE_1316391 tptp.nat)) (= (or (= BOUND_VARIABLE_1316390 BOUND_VARIABLE_1316391) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1316391) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11831 BOUND_VARIABLE_1316390) BOUND_VARIABLE_1316391))))) (let ((_let_3779 (forall ((BOUND_VARIABLE_1316376 Bool) (BOUND_VARIABLE_1316377 Bool)) (= (or (= BOUND_VARIABLE_1316376 BOUND_VARIABLE_1316377) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1316377) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11832 BOUND_VARIABLE_1316376) BOUND_VARIABLE_1316377))))) (let ((_let_3780 (forall ((BOUND_VARIABLE_1316362 tptp.int) (BOUND_VARIABLE_1316363 tptp.int)) (= (or (= BOUND_VARIABLE_1316362 BOUND_VARIABLE_1316363) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1316363) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11833 BOUND_VARIABLE_1316362) BOUND_VARIABLE_1316363))))) (let ((_let_3781 (forall ((BOUND_VARIABLE_1316353 tptp.int) (BOUND_VARIABLE_1316354 tptp.int)) (= (ho_11094 (ho_11093 k_11834 BOUND_VARIABLE_1316353) BOUND_VARIABLE_1316354) (= BOUND_VARIABLE_1316353 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316354) BOUND_VARIABLE_1316353)))))) (let ((_let_3782 (forall ((BOUND_VARIABLE_1316339 tptp.nat) (BOUND_VARIABLE_1316340 tptp.nat)) (= (or (= BOUND_VARIABLE_1316339 BOUND_VARIABLE_1316340) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1316340) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11835 BOUND_VARIABLE_1316339) BOUND_VARIABLE_1316340))))) (let ((_let_3783 (forall ((BOUND_VARIABLE_1316325 Bool) (BOUND_VARIABLE_1316326 Bool)) (= (or (= BOUND_VARIABLE_1316325 BOUND_VARIABLE_1316326) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1316326) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11836 BOUND_VARIABLE_1316325) BOUND_VARIABLE_1316326))))) (let ((_let_3784 (forall ((BOUND_VARIABLE_1316311 Bool) (BOUND_VARIABLE_1316312 Bool)) (= (or (= BOUND_VARIABLE_1316311 BOUND_VARIABLE_1316312) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1316312) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11837 BOUND_VARIABLE_1316311) BOUND_VARIABLE_1316312))))) (let ((_let_3785 (forall ((BOUND_VARIABLE_1316302 tptp.int) (BOUND_VARIABLE_1316303 tptp.int)) (= (ho_11094 (ho_11093 k_11838 BOUND_VARIABLE_1316302) BOUND_VARIABLE_1316303) (= BOUND_VARIABLE_1316302 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316303) BOUND_VARIABLE_1316302)))))) (let ((_let_3786 (forall ((BOUND_VARIABLE_1316288 tptp.int) (BOUND_VARIABLE_1316289 tptp.int)) (= (or (= BOUND_VARIABLE_1316288 BOUND_VARIABLE_1316289) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1316289) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11839 BOUND_VARIABLE_1316288) BOUND_VARIABLE_1316289))))) (let ((_let_3787 (forall ((BOUND_VARIABLE_1316274 tptp.nat) (BOUND_VARIABLE_1316275 tptp.nat)) (= (or (= BOUND_VARIABLE_1316274 BOUND_VARIABLE_1316275) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1316275) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11840 BOUND_VARIABLE_1316274) BOUND_VARIABLE_1316275))))) (let ((_let_3788 (forall ((BOUND_VARIABLE_1316260 Bool) (BOUND_VARIABLE_1316261 Bool)) (= (or (= BOUND_VARIABLE_1316260 BOUND_VARIABLE_1316261) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1316261) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11841 BOUND_VARIABLE_1316260) BOUND_VARIABLE_1316261))))) (let ((_let_3789 (forall ((BOUND_VARIABLE_1316251 tptp.int) (BOUND_VARIABLE_1316252 tptp.int)) (= (ho_11094 (ho_11093 k_11842 BOUND_VARIABLE_1316251) BOUND_VARIABLE_1316252) (= BOUND_VARIABLE_1316251 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316252) BOUND_VARIABLE_1316251)))))) (let ((_let_3790 (forall ((BOUND_VARIABLE_1316237 tptp.int) (BOUND_VARIABLE_1316238 tptp.int)) (= (or (= BOUND_VARIABLE_1316237 BOUND_VARIABLE_1316238) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1316238) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11843 BOUND_VARIABLE_1316237) BOUND_VARIABLE_1316238))))) (let ((_let_3791 (forall ((BOUND_VARIABLE_1316223 tptp.nat) (BOUND_VARIABLE_1316224 tptp.nat)) (= (or (= BOUND_VARIABLE_1316223 BOUND_VARIABLE_1316224) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1316224) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11844 BOUND_VARIABLE_1316223) BOUND_VARIABLE_1316224))))) (let ((_let_3792 (forall ((BOUND_VARIABLE_1316209 Bool) (BOUND_VARIABLE_1316210 Bool)) (= (or (= BOUND_VARIABLE_1316209 BOUND_VARIABLE_1316210) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1316210) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11845 BOUND_VARIABLE_1316209) BOUND_VARIABLE_1316210))))) (let ((_let_3793 (forall ((BOUND_VARIABLE_1316199 tptp.nat) (BOUND_VARIABLE_1350004 |u_(-> tptp.list_nat tptp.nat)|) (BOUND_VARIABLE_1316201 tptp.list_nat)) (= (ho_11278 (ho_11848 (ho_11847 k_11846 BOUND_VARIABLE_1316199) BOUND_VARIABLE_1350004) BOUND_VARIABLE_1316201) (ho_11054 (ho_11053 k_11435 BOUND_VARIABLE_1316199) (ho_11160 BOUND_VARIABLE_1350004 BOUND_VARIABLE_1316201)))))) (let ((_let_3794 (forall ((BOUND_VARIABLE_1316188 tptp.nat) (BOUND_VARIABLE_1350026 |u_(-> tptp.list_nat tptp.nat)|) (BOUND_VARIABLE_1316190 tptp.list_nat)) (= (ho_11278 (ho_11848 (ho_11847 k_11849 BOUND_VARIABLE_1316188) BOUND_VARIABLE_1350026) BOUND_VARIABLE_1316190) (not (ho_11054 (ho_11053 k_11435 BOUND_VARIABLE_1316188) (ho_11160 BOUND_VARIABLE_1350026 BOUND_VARIABLE_1316190))))))) (let ((_let_3795 (forall ((BOUND_VARIABLE_1316179 tptp.int) (BOUND_VARIABLE_1316180 tptp.int)) (= (ho_11094 (ho_11093 k_11850 BOUND_VARIABLE_1316179) BOUND_VARIABLE_1316180) (= BOUND_VARIABLE_1316179 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316180) BOUND_VARIABLE_1316179)))))) (let ((_let_3796 (forall ((BOUND_VARIABLE_1316169 tptp.int) (BOUND_VARIABLE_1350051 |u_(-> tptp.int tptp.int)|) (BOUND_VARIABLE_1316171 tptp.int)) (= (ho_11094 (ho_11853 (ho_11852 k_11851 BOUND_VARIABLE_1316169) BOUND_VARIABLE_1350051) BOUND_VARIABLE_1316171) (ho_11094 (ho_11093 k_11771 BOUND_VARIABLE_1316169) (ho_11059 BOUND_VARIABLE_1350051 BOUND_VARIABLE_1316171)))))) (let ((_let_3797 (forall ((BOUND_VARIABLE_1316158 tptp.int) (BOUND_VARIABLE_1350073 |u_(-> tptp.int tptp.int)|) (BOUND_VARIABLE_1316160 tptp.int)) (= (ho_11094 (ho_11853 (ho_11852 k_11854 BOUND_VARIABLE_1316158) BOUND_VARIABLE_1350073) BOUND_VARIABLE_1316160) (not (ho_11094 (ho_11093 k_11771 BOUND_VARIABLE_1316158) (ho_11059 BOUND_VARIABLE_1350073 BOUND_VARIABLE_1316160))))))) (let ((_let_3798 (forall ((BOUND_VARIABLE_1316148 tptp.nat) (BOUND_VARIABLE_1350088 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1316150 tptp.nat)) (= (ho_11054 (ho_11857 (ho_11856 k_11855 BOUND_VARIABLE_1316148) BOUND_VARIABLE_1350088) BOUND_VARIABLE_1316150) (ho_11054 (ho_11053 k_11435 BOUND_VARIABLE_1316148) (ho_11139 BOUND_VARIABLE_1350088 BOUND_VARIABLE_1316150)))))) (let ((_let_3799 (forall ((BOUND_VARIABLE_1316137 tptp.nat) (BOUND_VARIABLE_1350110 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1316139 tptp.nat)) (= (ho_11054 (ho_11857 (ho_11856 k_11858 BOUND_VARIABLE_1316137) BOUND_VARIABLE_1350110) BOUND_VARIABLE_1316139) (not (ho_11054 (ho_11053 k_11435 BOUND_VARIABLE_1316137) (ho_11139 BOUND_VARIABLE_1350110 BOUND_VARIABLE_1316139))))))) (let ((_let_3800 (forall ((BOUND_VARIABLE_1316127 tptp.code_natural) (BOUND_VARIABLE_1350125 |u_(-> tptp.nat tptp.code_natural)|) (BOUND_VARIABLE_1316129 tptp.nat)) (= (ho_11054 (ho_11861 (ho_11860 k_11859 BOUND_VARIABLE_1316127) BOUND_VARIABLE_1350125) BOUND_VARIABLE_1316129) (ho_11864 (ho_11863 k_11862 BOUND_VARIABLE_1316127) (ho_11481 BOUND_VARIABLE_1350125 BOUND_VARIABLE_1316129)))))) (let ((_let_3801 (forall ((BOUND_VARIABLE_1316116 tptp.code_natural) (BOUND_VARIABLE_1350154 |u_(-> tptp.nat tptp.code_natural)|) (BOUND_VARIABLE_1316118 tptp.nat)) (= (ho_11054 (ho_11861 (ho_11860 k_11865 BOUND_VARIABLE_1316116) BOUND_VARIABLE_1350154) BOUND_VARIABLE_1316118) (not (ho_11864 (ho_11863 k_11862 BOUND_VARIABLE_1316116) (ho_11481 BOUND_VARIABLE_1350154 BOUND_VARIABLE_1316118))))))) (let ((_let_3802 (forall ((BOUND_VARIABLE_1316107 tptp.int) (BOUND_VARIABLE_1316108 tptp.int)) (= (ho_11094 (ho_11093 k_11866 BOUND_VARIABLE_1316107) BOUND_VARIABLE_1316108) (= BOUND_VARIABLE_1316107 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316108) BOUND_VARIABLE_1316107)))))) (let ((_let_3803 (forall ((BOUND_VARIABLE_1316097 tptp.code_natural) (BOUND_VARIABLE_1350180 |u_(-> tptp.int tptp.code_natural)|) (BOUND_VARIABLE_1316099 tptp.int)) (= (ho_11094 (ho_11870 (ho_11869 k_11868 BOUND_VARIABLE_1316097) BOUND_VARIABLE_1350180) BOUND_VARIABLE_1316099) (ho_11864 (ho_11863 k_11862 BOUND_VARIABLE_1316097) (ho_11867 BOUND_VARIABLE_1350180 BOUND_VARIABLE_1316099)))))) (let ((_let_3804 (forall ((BOUND_VARIABLE_1316086 tptp.code_natural) (BOUND_VARIABLE_1350204 |u_(-> tptp.int tptp.code_natural)|) (BOUND_VARIABLE_1316088 tptp.int)) (= (ho_11094 (ho_11870 (ho_11869 k_11871 BOUND_VARIABLE_1316086) BOUND_VARIABLE_1350204) BOUND_VARIABLE_1316088) (not (ho_11864 (ho_11863 k_11862 BOUND_VARIABLE_1316086) (ho_11867 BOUND_VARIABLE_1350204 BOUND_VARIABLE_1316088))))))) (let ((_let_3805 (forall ((BOUND_VARIABLE_1316076 tptp.int) (BOUND_VARIABLE_1350219 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1316078 tptp.nat)) (= (ho_11054 (ho_11681 (ho_11873 k_11872 BOUND_VARIABLE_1316076) BOUND_VARIABLE_1350219) BOUND_VARIABLE_1316078) (ho_11094 (ho_11093 k_11771 BOUND_VARIABLE_1316076) (ho_11056 BOUND_VARIABLE_1350219 BOUND_VARIABLE_1316078)))))) (let ((_let_3806 (forall ((BOUND_VARIABLE_1316065 tptp.int) (BOUND_VARIABLE_1350237 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1316067 tptp.nat)) (= (ho_11054 (ho_11681 (ho_11873 k_11874 BOUND_VARIABLE_1316065) BOUND_VARIABLE_1350237) BOUND_VARIABLE_1316067) (not (ho_11094 (ho_11093 k_11771 BOUND_VARIABLE_1316065) (ho_11056 BOUND_VARIABLE_1350237 BOUND_VARIABLE_1316067))))))) (let ((_let_3807 (forall ((BOUND_VARIABLE_1316056 tptp.int) (BOUND_VARIABLE_1316057 tptp.int)) (= (ho_11094 (ho_11093 k_11875 BOUND_VARIABLE_1316056) BOUND_VARIABLE_1316057) (= BOUND_VARIABLE_1316056 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316057) BOUND_VARIABLE_1316056)))))) (let ((_let_3808 (forall ((BOUND_VARIABLE_1316046 tptp.nat) (BOUND_VARIABLE_1350262 |u_(-> tptp.int tptp.nat)|) (BOUND_VARIABLE_1316048 tptp.int)) (= (ho_11094 (ho_11878 (ho_11877 k_11876 BOUND_VARIABLE_1316046) BOUND_VARIABLE_1350262) BOUND_VARIABLE_1316048) (ho_11054 (ho_11053 k_11435 BOUND_VARIABLE_1316046) (ho_11061 BOUND_VARIABLE_1350262 BOUND_VARIABLE_1316048)))))) (let ((_let_3809 (forall ((BOUND_VARIABLE_1316035 tptp.nat) (BOUND_VARIABLE_1350284 |u_(-> tptp.int tptp.nat)|) (BOUND_VARIABLE_1316037 tptp.int)) (= (ho_11094 (ho_11878 (ho_11877 k_11879 BOUND_VARIABLE_1316035) BOUND_VARIABLE_1350284) BOUND_VARIABLE_1316037) (not (ho_11054 (ho_11053 k_11435 BOUND_VARIABLE_1316035) (ho_11061 BOUND_VARIABLE_1350284 BOUND_VARIABLE_1316037))))))) (let ((_let_3810 (forall ((BOUND_VARIABLE_1316026 tptp.int) (BOUND_VARIABLE_1316027 tptp.int)) (= (ho_11094 (ho_11093 k_11880 BOUND_VARIABLE_1316026) BOUND_VARIABLE_1316027) (= BOUND_VARIABLE_1316026 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316027) BOUND_VARIABLE_1316026)))))) (let ((_let_3811 (forall ((BOUND_VARIABLE_1316012 tptp.int) (BOUND_VARIABLE_1316013 tptp.int)) (= (or (= BOUND_VARIABLE_1316012 BOUND_VARIABLE_1316013) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1316013) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11881 BOUND_VARIABLE_1316012) BOUND_VARIABLE_1316013))))) (let ((_let_3812 (forall ((BOUND_VARIABLE_1316003 tptp.int) (BOUND_VARIABLE_1316004 tptp.int)) (= (ho_11094 (ho_11093 k_11882 BOUND_VARIABLE_1316003) BOUND_VARIABLE_1316004) (= BOUND_VARIABLE_1316003 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1316004) BOUND_VARIABLE_1316003)))))) (let ((_let_3813 (forall ((BOUND_VARIABLE_1315989 tptp.int) (BOUND_VARIABLE_1315990 tptp.int)) (= (or (= BOUND_VARIABLE_1315989 BOUND_VARIABLE_1315990) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1315990) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11883 BOUND_VARIABLE_1315989) BOUND_VARIABLE_1315990))))) (let ((_let_3814 (forall ((BOUND_VARIABLE_1315975 tptp.nat) (BOUND_VARIABLE_1315976 tptp.nat)) (= (or (= BOUND_VARIABLE_1315975 BOUND_VARIABLE_1315976) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1315976) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11884 BOUND_VARIABLE_1315975) BOUND_VARIABLE_1315976))))) (let ((_let_3815 (forall ((BOUND_VARIABLE_1315961 tptp.nat) (BOUND_VARIABLE_1315962 tptp.nat)) (= (or (= BOUND_VARIABLE_1315961 BOUND_VARIABLE_1315962) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1315962) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11885 BOUND_VARIABLE_1315961) BOUND_VARIABLE_1315962))))) (let ((_let_3816 (forall ((BOUND_VARIABLE_1315947 Bool) (BOUND_VARIABLE_1315948 Bool)) (= (or (= BOUND_VARIABLE_1315947 BOUND_VARIABLE_1315948) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1315948) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11886 BOUND_VARIABLE_1315947) BOUND_VARIABLE_1315948))))) (let ((_let_3817 (forall ((BOUND_VARIABLE_1315933 Bool) (BOUND_VARIABLE_1315934 Bool)) (= (or (= BOUND_VARIABLE_1315933 BOUND_VARIABLE_1315934) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1315934) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11887 BOUND_VARIABLE_1315933) BOUND_VARIABLE_1315934))))) (let ((_let_3818 (forall ((BOUND_VARIABLE_1315919 Bool) (BOUND_VARIABLE_1315920 Bool)) (= (or (= BOUND_VARIABLE_1315919 BOUND_VARIABLE_1315920) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1315920) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11888 BOUND_VARIABLE_1315919) BOUND_VARIABLE_1315920))))) (let ((_let_3819 (forall ((BOUND_VARIABLE_1315910 tptp.int) (BOUND_VARIABLE_1315911 tptp.int)) (= (ho_11094 (ho_11093 k_11889 BOUND_VARIABLE_1315910) BOUND_VARIABLE_1315911) (= BOUND_VARIABLE_1315910 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315911) BOUND_VARIABLE_1315910)))))) (let ((_let_3820 (forall ((BOUND_VARIABLE_1315901 tptp.int) (BOUND_VARIABLE_1315902 tptp.int)) (= (ho_11094 (ho_11093 k_11890 BOUND_VARIABLE_1315901) BOUND_VARIABLE_1315902) (= BOUND_VARIABLE_1315901 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315902) BOUND_VARIABLE_1315901)))))) (let ((_let_3821 (forall ((BOUND_VARIABLE_1315892 tptp.int) (BOUND_VARIABLE_1315893 tptp.int)) (= (ho_11094 (ho_11093 k_11891 BOUND_VARIABLE_1315892) BOUND_VARIABLE_1315893) (= BOUND_VARIABLE_1315892 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315893) BOUND_VARIABLE_1315892)))))) (let ((_let_3822 (forall ((BOUND_VARIABLE_1315883 tptp.int) (BOUND_VARIABLE_1315884 tptp.int)) (= (ho_11094 (ho_11093 k_11892 BOUND_VARIABLE_1315883) BOUND_VARIABLE_1315884) (= BOUND_VARIABLE_1315883 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315884) BOUND_VARIABLE_1315883)))))) (let ((_let_3823 (forall ((BOUND_VARIABLE_1315874 tptp.int) (BOUND_VARIABLE_1315875 tptp.int)) (= (ho_11094 (ho_11093 k_11893 BOUND_VARIABLE_1315874) BOUND_VARIABLE_1315875) (= BOUND_VARIABLE_1315874 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315875) BOUND_VARIABLE_1315874)))))) (let ((_let_3824 (forall ((BOUND_VARIABLE_1315865 tptp.int) (BOUND_VARIABLE_1315866 tptp.int)) (= (ho_11094 (ho_11093 k_11894 BOUND_VARIABLE_1315865) BOUND_VARIABLE_1315866) (= BOUND_VARIABLE_1315865 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315866) BOUND_VARIABLE_1315865)))))) (let ((_let_3825 (forall ((BOUND_VARIABLE_1315856 tptp.int) (BOUND_VARIABLE_1315857 tptp.int)) (= (ho_11094 (ho_11093 k_11895 BOUND_VARIABLE_1315856) BOUND_VARIABLE_1315857) (= BOUND_VARIABLE_1315856 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315857) BOUND_VARIABLE_1315856)))))) (let ((_let_3826 (forall ((BOUND_VARIABLE_1315847 tptp.int) (BOUND_VARIABLE_1315848 tptp.int)) (= (ho_11094 (ho_11093 k_11896 BOUND_VARIABLE_1315847) BOUND_VARIABLE_1315848) (= BOUND_VARIABLE_1315847 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315848) BOUND_VARIABLE_1315847)))))) (let ((_let_3827 (forall ((BOUND_VARIABLE_1315836 tptp.set_int) (BOUND_VARIABLE_1315837 tptp.set_int) (BOUND_VARIABLE_1315838 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1315838))) (= (ho_11094 (ho_11234 (ho_11339 k_11897 BOUND_VARIABLE_1315836) BOUND_VARIABLE_1315837) BOUND_VARIABLE_1315838) (or (ho_11180 _let_1 BOUND_VARIABLE_1315836) (ho_11180 _let_1 BOUND_VARIABLE_1315837))))))) (let ((_let_3828 (forall ((BOUND_VARIABLE_1315827 tptp.int) (BOUND_VARIABLE_1315828 tptp.int)) (= (ho_11094 (ho_11093 k_11898 BOUND_VARIABLE_1315827) BOUND_VARIABLE_1315828) (= BOUND_VARIABLE_1315827 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315828) BOUND_VARIABLE_1315827)))))) (let ((_let_3829 (forall ((BOUND_VARIABLE_1315816 tptp.set_int) (BOUND_VARIABLE_1315817 tptp.set_int) (BOUND_VARIABLE_1315818 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1315818))) (= (ho_11094 (ho_11234 (ho_11339 k_11899 BOUND_VARIABLE_1315816) BOUND_VARIABLE_1315817) BOUND_VARIABLE_1315818) (or (ho_11180 _let_1 BOUND_VARIABLE_1315816) (ho_11180 _let_1 BOUND_VARIABLE_1315817))))))) (let ((_let_3830 (forall ((BOUND_VARIABLE_1315807 tptp.int) (BOUND_VARIABLE_1315808 tptp.int)) (= (ho_11094 (ho_11093 k_11900 BOUND_VARIABLE_1315807) BOUND_VARIABLE_1315808) (= BOUND_VARIABLE_1315807 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315808) BOUND_VARIABLE_1315807)))))) (let ((_let_3831 (forall ((BOUND_VARIABLE_1315796 tptp.set_int) (BOUND_VARIABLE_1315797 tptp.set_int) (BOUND_VARIABLE_1315798 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1315798))) (= (ho_11094 (ho_11234 (ho_11339 k_11901 BOUND_VARIABLE_1315796) BOUND_VARIABLE_1315797) BOUND_VARIABLE_1315798) (or (ho_11180 _let_1 BOUND_VARIABLE_1315796) (ho_11180 _let_1 BOUND_VARIABLE_1315797))))))) (let ((_let_3832 (forall ((BOUND_VARIABLE_1315787 tptp.int) (BOUND_VARIABLE_1315788 tptp.int)) (= (ho_11094 (ho_11093 k_11902 BOUND_VARIABLE_1315787) BOUND_VARIABLE_1315788) (= BOUND_VARIABLE_1315787 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315788) BOUND_VARIABLE_1315787)))))) (let ((_let_3833 (forall ((BOUND_VARIABLE_1315778 tptp.int) (BOUND_VARIABLE_1315779 tptp.int)) (= (ho_11094 (ho_11093 k_11903 BOUND_VARIABLE_1315778) BOUND_VARIABLE_1315779) (= BOUND_VARIABLE_1315778 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315779) BOUND_VARIABLE_1315778)))))) (let ((_let_3834 (forall ((BOUND_VARIABLE_1315769 tptp.int) (BOUND_VARIABLE_1315770 tptp.int)) (= (ho_11094 (ho_11093 k_11904 BOUND_VARIABLE_1315769) BOUND_VARIABLE_1315770) (= BOUND_VARIABLE_1315769 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315770) BOUND_VARIABLE_1315769)))))) (let ((_let_3835 (forall ((BOUND_VARIABLE_1315760 tptp.int) (BOUND_VARIABLE_1315761 tptp.int)) (= (ho_11094 (ho_11093 k_11905 BOUND_VARIABLE_1315760) BOUND_VARIABLE_1315761) (= BOUND_VARIABLE_1315760 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315761) BOUND_VARIABLE_1315760)))))) (let ((_let_3836 (forall ((BOUND_VARIABLE_1315751 tptp.int) (BOUND_VARIABLE_1315752 tptp.int)) (= (ho_11094 (ho_11093 k_11906 BOUND_VARIABLE_1315751) BOUND_VARIABLE_1315752) (= BOUND_VARIABLE_1315751 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315752) BOUND_VARIABLE_1315751)))))) (let ((_let_3837 (forall ((BOUND_VARIABLE_1315742 tptp.int) (BOUND_VARIABLE_1315743 tptp.int)) (= (ho_11094 (ho_11093 k_11907 BOUND_VARIABLE_1315742) BOUND_VARIABLE_1315743) (= BOUND_VARIABLE_1315742 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315743) BOUND_VARIABLE_1315742)))))) (let ((_let_3838 (forall ((BOUND_VARIABLE_1315733 tptp.int) (BOUND_VARIABLE_1315734 tptp.int)) (= (ho_11094 (ho_11093 k_11908 BOUND_VARIABLE_1315733) BOUND_VARIABLE_1315734) (= BOUND_VARIABLE_1315733 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315734) BOUND_VARIABLE_1315733)))))) (let ((_let_3839 (forall ((BOUND_VARIABLE_1315724 tptp.int) (BOUND_VARIABLE_1315725 tptp.int)) (= (ho_11094 (ho_11093 k_11909 BOUND_VARIABLE_1315724) BOUND_VARIABLE_1315725) (= BOUND_VARIABLE_1315724 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315725) BOUND_VARIABLE_1315724)))))) (let ((_let_3840 (forall ((BOUND_VARIABLE_1315715 tptp.int) (BOUND_VARIABLE_1315716 tptp.int)) (= (ho_11094 (ho_11093 k_11910 BOUND_VARIABLE_1315715) BOUND_VARIABLE_1315716) (= BOUND_VARIABLE_1315715 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315716) BOUND_VARIABLE_1315715)))))) (let ((_let_3841 (forall ((BOUND_VARIABLE_1315706 tptp.int) (BOUND_VARIABLE_1315707 tptp.int)) (= (ho_11094 (ho_11093 k_11911 BOUND_VARIABLE_1315706) BOUND_VARIABLE_1315707) (= BOUND_VARIABLE_1315706 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315707) BOUND_VARIABLE_1315706)))))) (let ((_let_3842 (forall ((BOUND_VARIABLE_1315697 tptp.int) (BOUND_VARIABLE_1315698 tptp.int)) (= (ho_11094 (ho_11093 k_11912 BOUND_VARIABLE_1315697) BOUND_VARIABLE_1315698) (= BOUND_VARIABLE_1315697 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315698) BOUND_VARIABLE_1315697)))))) (let ((_let_3843 (forall ((BOUND_VARIABLE_1315688 tptp.int) (BOUND_VARIABLE_1315689 tptp.int)) (= (ho_11094 (ho_11093 k_11913 BOUND_VARIABLE_1315688) BOUND_VARIABLE_1315689) (= BOUND_VARIABLE_1315688 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315689) BOUND_VARIABLE_1315688)))))) (let ((_let_3844 (forall ((BOUND_VARIABLE_1315679 tptp.int) (BOUND_VARIABLE_1315680 tptp.int)) (= (ho_11094 (ho_11093 k_11914 BOUND_VARIABLE_1315679) BOUND_VARIABLE_1315680) (= BOUND_VARIABLE_1315679 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315680) BOUND_VARIABLE_1315679)))))) (let ((_let_3845 (forall ((BOUND_VARIABLE_1315670 tptp.int) (BOUND_VARIABLE_1315671 tptp.int)) (= (ho_11094 (ho_11093 k_11915 BOUND_VARIABLE_1315670) BOUND_VARIABLE_1315671) (= BOUND_VARIABLE_1315670 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315671) BOUND_VARIABLE_1315670)))))) (let ((_let_3846 (forall ((BOUND_VARIABLE_1315661 tptp.int) (BOUND_VARIABLE_1315662 tptp.int)) (= (ho_11094 (ho_11093 k_11916 BOUND_VARIABLE_1315661) BOUND_VARIABLE_1315662) (= BOUND_VARIABLE_1315661 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315662) BOUND_VARIABLE_1315661)))))) (let ((_let_3847 (forall ((BOUND_VARIABLE_1315652 tptp.int) (BOUND_VARIABLE_1315653 tptp.int)) (= (ho_11094 (ho_11093 k_11917 BOUND_VARIABLE_1315652) BOUND_VARIABLE_1315653) (= BOUND_VARIABLE_1315652 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315653) BOUND_VARIABLE_1315652)))))) (let ((_let_3848 (forall ((BOUND_VARIABLE_1315643 tptp.int) (BOUND_VARIABLE_1315644 tptp.int)) (= (ho_11094 (ho_11093 k_11918 BOUND_VARIABLE_1315643) BOUND_VARIABLE_1315644) (= BOUND_VARIABLE_1315643 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315644) BOUND_VARIABLE_1315643)))))) (let ((_let_3849 (forall ((BOUND_VARIABLE_1315634 tptp.int) (BOUND_VARIABLE_1315635 tptp.int)) (= (ho_11094 (ho_11093 k_11919 BOUND_VARIABLE_1315634) BOUND_VARIABLE_1315635) (= BOUND_VARIABLE_1315634 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315635) BOUND_VARIABLE_1315634)))))) (let ((_let_3850 (forall ((BOUND_VARIABLE_1315625 tptp.int) (BOUND_VARIABLE_1315626 tptp.int)) (= (ho_11094 (ho_11093 k_11920 BOUND_VARIABLE_1315625) BOUND_VARIABLE_1315626) (= BOUND_VARIABLE_1315625 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315626) BOUND_VARIABLE_1315625)))))) (let ((_let_3851 (forall ((BOUND_VARIABLE_1315616 tptp.int) (BOUND_VARIABLE_1315617 tptp.int)) (= (ho_11094 (ho_11093 k_11921 BOUND_VARIABLE_1315616) BOUND_VARIABLE_1315617) (= BOUND_VARIABLE_1315616 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315617) BOUND_VARIABLE_1315616)))))) (let ((_let_3852 (forall ((BOUND_VARIABLE_1315607 tptp.int) (BOUND_VARIABLE_1315608 tptp.int)) (= (ho_11094 (ho_11093 k_11922 BOUND_VARIABLE_1315607) BOUND_VARIABLE_1315608) (= BOUND_VARIABLE_1315607 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315608) BOUND_VARIABLE_1315607)))))) (let ((_let_3853 (forall ((BOUND_VARIABLE_1315598 tptp.int) (BOUND_VARIABLE_1315599 tptp.int)) (= (ho_11094 (ho_11093 k_11923 BOUND_VARIABLE_1315598) BOUND_VARIABLE_1315599) (= BOUND_VARIABLE_1315598 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315599) BOUND_VARIABLE_1315598)))))) (let ((_let_3854 (forall ((BOUND_VARIABLE_1315589 tptp.int) (BOUND_VARIABLE_1315590 tptp.int)) (= (ho_11094 (ho_11093 k_11924 BOUND_VARIABLE_1315589) BOUND_VARIABLE_1315590) (= BOUND_VARIABLE_1315589 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315590) BOUND_VARIABLE_1315589)))))) (let ((_let_3855 (forall ((BOUND_VARIABLE_1315580 tptp.int) (BOUND_VARIABLE_1315581 tptp.int)) (= (ho_11094 (ho_11093 k_11925 BOUND_VARIABLE_1315580) BOUND_VARIABLE_1315581) (= BOUND_VARIABLE_1315580 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315581) BOUND_VARIABLE_1315580)))))) (let ((_let_3856 (forall ((BOUND_VARIABLE_1315571 tptp.int) (BOUND_VARIABLE_1315572 tptp.int)) (= (ho_11094 (ho_11093 k_11926 BOUND_VARIABLE_1315571) BOUND_VARIABLE_1315572) (= BOUND_VARIABLE_1315571 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315572) BOUND_VARIABLE_1315571)))))) (let ((_let_3857 (forall ((BOUND_VARIABLE_1315562 tptp.int) (BOUND_VARIABLE_1315563 tptp.int)) (= (ho_11094 (ho_11093 k_11927 BOUND_VARIABLE_1315562) BOUND_VARIABLE_1315563) (= BOUND_VARIABLE_1315562 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315563) BOUND_VARIABLE_1315562)))))) (let ((_let_3858 (forall ((BOUND_VARIABLE_1315553 tptp.int) (BOUND_VARIABLE_1315554 tptp.int)) (= (ho_11094 (ho_11093 k_11928 BOUND_VARIABLE_1315553) BOUND_VARIABLE_1315554) (= BOUND_VARIABLE_1315553 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315554) BOUND_VARIABLE_1315553)))))) (let ((_let_3859 (forall ((BOUND_VARIABLE_1315544 tptp.int) (BOUND_VARIABLE_1315545 tptp.int)) (= (ho_11094 (ho_11093 k_11929 BOUND_VARIABLE_1315544) BOUND_VARIABLE_1315545) (= BOUND_VARIABLE_1315544 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315545) BOUND_VARIABLE_1315544)))))) (let ((_let_3860 (forall ((BOUND_VARIABLE_1315530 tptp.int) (BOUND_VARIABLE_1315531 tptp.int)) (= (or (= BOUND_VARIABLE_1315530 BOUND_VARIABLE_1315531) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1315531) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11930 BOUND_VARIABLE_1315530) BOUND_VARIABLE_1315531))))) (let ((_let_3861 (forall ((BOUND_VARIABLE_1315521 tptp.int) (BOUND_VARIABLE_1315522 tptp.int)) (= (ho_11094 (ho_11093 k_11931 BOUND_VARIABLE_1315521) BOUND_VARIABLE_1315522) (= BOUND_VARIABLE_1315521 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315522) BOUND_VARIABLE_1315521)))))) (let ((_let_3862 (forall ((BOUND_VARIABLE_1315507 tptp.int) (BOUND_VARIABLE_1315508 tptp.int)) (= (or (= BOUND_VARIABLE_1315507 BOUND_VARIABLE_1315508) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1315508) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11932 BOUND_VARIABLE_1315507) BOUND_VARIABLE_1315508))))) (let ((_let_3863 (forall ((BOUND_VARIABLE_1315493 tptp.nat) (BOUND_VARIABLE_1315494 tptp.nat)) (= (or (= BOUND_VARIABLE_1315493 BOUND_VARIABLE_1315494) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1315494) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11933 BOUND_VARIABLE_1315493) BOUND_VARIABLE_1315494))))) (let ((_let_3864 (forall ((BOUND_VARIABLE_1315479 tptp.nat) (BOUND_VARIABLE_1315480 tptp.nat)) (= (or (= BOUND_VARIABLE_1315479 BOUND_VARIABLE_1315480) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1315480) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11934 BOUND_VARIABLE_1315479) BOUND_VARIABLE_1315480))))) (let ((_let_3865 (forall ((BOUND_VARIABLE_1315465 Bool) (BOUND_VARIABLE_1315466 Bool)) (= (or (= BOUND_VARIABLE_1315465 BOUND_VARIABLE_1315466) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1315466) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11935 BOUND_VARIABLE_1315465) BOUND_VARIABLE_1315466))))) (let ((_let_3866 (forall ((BOUND_VARIABLE_1315451 Bool) (BOUND_VARIABLE_1315452 Bool)) (= (or (= BOUND_VARIABLE_1315451 BOUND_VARIABLE_1315452) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1315452) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11936 BOUND_VARIABLE_1315451) BOUND_VARIABLE_1315452))))) (let ((_let_3867 (forall ((BOUND_VARIABLE_1315437 Bool) (BOUND_VARIABLE_1315438 Bool)) (= (or (= BOUND_VARIABLE_1315437 BOUND_VARIABLE_1315438) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1315438) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11937 BOUND_VARIABLE_1315437) BOUND_VARIABLE_1315438))))) (let ((_let_3868 (forall ((BOUND_VARIABLE_1315428 tptp.int) (BOUND_VARIABLE_1315429 tptp.int)) (= (ho_11094 (ho_11093 k_11938 BOUND_VARIABLE_1315428) BOUND_VARIABLE_1315429) (= BOUND_VARIABLE_1315428 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315429) BOUND_VARIABLE_1315428)))))) (let ((_let_3869 (forall ((BOUND_VARIABLE_1315414 tptp.int) (BOUND_VARIABLE_1315415 tptp.int)) (= (or (= BOUND_VARIABLE_1315414 BOUND_VARIABLE_1315415) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1315415) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11939 BOUND_VARIABLE_1315414) BOUND_VARIABLE_1315415))))) (let ((_let_3870 (forall ((BOUND_VARIABLE_1315405 tptp.int) (BOUND_VARIABLE_1315406 tptp.int)) (= (ho_11094 (ho_11093 k_11940 BOUND_VARIABLE_1315405) BOUND_VARIABLE_1315406) (= BOUND_VARIABLE_1315405 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315406) BOUND_VARIABLE_1315405)))))) (let ((_let_3871 (forall ((BOUND_VARIABLE_1315391 tptp.int) (BOUND_VARIABLE_1315392 tptp.int)) (= (or (= BOUND_VARIABLE_1315391 BOUND_VARIABLE_1315392) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1315392) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_11941 BOUND_VARIABLE_1315391) BOUND_VARIABLE_1315392))))) (let ((_let_3872 (forall ((BOUND_VARIABLE_1315377 tptp.nat) (BOUND_VARIABLE_1315378 tptp.nat)) (= (or (= BOUND_VARIABLE_1315377 BOUND_VARIABLE_1315378) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1315378) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11942 BOUND_VARIABLE_1315377) BOUND_VARIABLE_1315378))))) (let ((_let_3873 (forall ((BOUND_VARIABLE_1315363 tptp.nat) (BOUND_VARIABLE_1315364 tptp.nat)) (= (or (= BOUND_VARIABLE_1315363 BOUND_VARIABLE_1315364) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1315364) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_11943 BOUND_VARIABLE_1315363) BOUND_VARIABLE_1315364))))) (let ((_let_3874 (forall ((BOUND_VARIABLE_1315349 Bool) (BOUND_VARIABLE_1315350 Bool)) (= (or (= BOUND_VARIABLE_1315349 BOUND_VARIABLE_1315350) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1315350) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11944 BOUND_VARIABLE_1315349) BOUND_VARIABLE_1315350))))) (let ((_let_3875 (forall ((BOUND_VARIABLE_1315335 Bool) (BOUND_VARIABLE_1315336 Bool)) (= (or (= BOUND_VARIABLE_1315335 BOUND_VARIABLE_1315336) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1315336) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11945 BOUND_VARIABLE_1315335) BOUND_VARIABLE_1315336))))) (let ((_let_3876 (forall ((BOUND_VARIABLE_1315321 Bool) (BOUND_VARIABLE_1315322 Bool)) (= (or (= BOUND_VARIABLE_1315321 BOUND_VARIABLE_1315322) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1315322) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_11946 BOUND_VARIABLE_1315321) BOUND_VARIABLE_1315322))))) (let ((_let_3877 (forall ((BOUND_VARIABLE_1315312 tptp.int) (BOUND_VARIABLE_1315313 tptp.int)) (= (ho_11094 (ho_11093 k_11947 BOUND_VARIABLE_1315312) BOUND_VARIABLE_1315313) (= BOUND_VARIABLE_1315312 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315313) BOUND_VARIABLE_1315312)))))) (let ((_let_3878 (forall ((BOUND_VARIABLE_1315303 tptp.int) (BOUND_VARIABLE_1315304 tptp.int)) (= (ho_11094 (ho_11093 k_11948 BOUND_VARIABLE_1315303) BOUND_VARIABLE_1315304) (= BOUND_VARIABLE_1315303 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315304) BOUND_VARIABLE_1315303)))))) (let ((_let_3879 (forall ((BOUND_VARIABLE_1315294 tptp.int) (BOUND_VARIABLE_1315295 tptp.int)) (= (ho_11094 (ho_11093 k_11949 BOUND_VARIABLE_1315294) BOUND_VARIABLE_1315295) (= BOUND_VARIABLE_1315294 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315295) BOUND_VARIABLE_1315294)))))) (let ((_let_3880 (forall ((BOUND_VARIABLE_1315285 tptp.int) (BOUND_VARIABLE_1315286 tptp.int)) (= (ho_11094 (ho_11093 k_11950 BOUND_VARIABLE_1315285) BOUND_VARIABLE_1315286) (= BOUND_VARIABLE_1315285 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315286) BOUND_VARIABLE_1315285)))))) (let ((_let_3881 (forall ((BOUND_VARIABLE_1315276 tptp.int) (BOUND_VARIABLE_1315277 tptp.int)) (= (ho_11094 (ho_11093 k_11951 BOUND_VARIABLE_1315276) BOUND_VARIABLE_1315277) (= BOUND_VARIABLE_1315276 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315277) BOUND_VARIABLE_1315276)))))) (let ((_let_3882 (forall ((BOUND_VARIABLE_1315267 tptp.int) (BOUND_VARIABLE_1315268 tptp.int)) (= (ho_11094 (ho_11093 k_11952 BOUND_VARIABLE_1315267) BOUND_VARIABLE_1315268) (= BOUND_VARIABLE_1315267 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315268) BOUND_VARIABLE_1315267)))))) (let ((_let_3883 (forall ((BOUND_VARIABLE_1315258 tptp.int) (BOUND_VARIABLE_1315259 tptp.int)) (= (ho_11094 (ho_11093 k_11953 BOUND_VARIABLE_1315258) BOUND_VARIABLE_1315259) (= BOUND_VARIABLE_1315258 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315259) BOUND_VARIABLE_1315258)))))) (let ((_let_3884 (forall ((BOUND_VARIABLE_1315249 tptp.int) (BOUND_VARIABLE_1315250 tptp.int)) (= (ho_11094 (ho_11093 k_11954 BOUND_VARIABLE_1315249) BOUND_VARIABLE_1315250) (= BOUND_VARIABLE_1315249 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315250) BOUND_VARIABLE_1315249)))))) (let ((_let_3885 (forall ((BOUND_VARIABLE_1351057 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_1315241 tptp.nat)) (= (ho_11054 (ho_11956 k_11955 BOUND_VARIABLE_1351057) BOUND_VARIABLE_1315241) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1315241) (ho_11107 k_11106 BOUND_VARIABLE_1351057)))))) (let ((_let_3886 (forall ((BOUND_VARIABLE_1315231 tptp.int) (BOUND_VARIABLE_1315232 tptp.int)) (= (ho_11094 (ho_11093 k_11957 BOUND_VARIABLE_1315231) BOUND_VARIABLE_1315232) (= BOUND_VARIABLE_1315231 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315232) BOUND_VARIABLE_1315231)))))) (let ((_let_3887 (forall ((BOUND_VARIABLE_1351082 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_1315223 tptp.int)) (= (ho_11094 (ho_11785 k_11958 BOUND_VARIABLE_1351082) BOUND_VARIABLE_1315223) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1315223) (ho_11177 k_11176 BOUND_VARIABLE_1351082)))))) (let ((_let_3888 (forall ((BOUND_VARIABLE_1351094 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_1315214 tptp.nat)) (= (ho_11054 (ho_11956 k_11959 BOUND_VARIABLE_1351094) BOUND_VARIABLE_1315214) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1315214) (ho_11107 k_11106 BOUND_VARIABLE_1351094)))))) (let ((_let_3889 (forall ((BOUND_VARIABLE_1315204 tptp.int) (BOUND_VARIABLE_1315205 tptp.int)) (= (ho_11094 (ho_11093 k_11960 BOUND_VARIABLE_1315204) BOUND_VARIABLE_1315205) (= BOUND_VARIABLE_1315204 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315205) BOUND_VARIABLE_1315204)))))) (let ((_let_3890 (forall ((BOUND_VARIABLE_1351116 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_1315196 tptp.int)) (= (ho_11094 (ho_11785 k_11961 BOUND_VARIABLE_1351116) BOUND_VARIABLE_1315196) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1315196) (ho_11177 k_11176 BOUND_VARIABLE_1351116)))))) (let ((_let_3891 (forall ((BOUND_VARIABLE_1351128 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_1315187 tptp.nat)) (= (ho_11054 (ho_11956 k_11962 BOUND_VARIABLE_1351128) BOUND_VARIABLE_1315187) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1315187) (ho_11107 k_11106 BOUND_VARIABLE_1351128)))))) (let ((_let_3892 (forall ((BOUND_VARIABLE_1315177 tptp.int) (BOUND_VARIABLE_1315178 tptp.int)) (= (ho_11094 (ho_11093 k_11963 BOUND_VARIABLE_1315177) BOUND_VARIABLE_1315178) (= BOUND_VARIABLE_1315177 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315178) BOUND_VARIABLE_1315177)))))) (let ((_let_3893 (forall ((BOUND_VARIABLE_1351150 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_1315169 tptp.int)) (= (ho_11094 (ho_11785 k_11964 BOUND_VARIABLE_1351150) BOUND_VARIABLE_1315169) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1315169) (ho_11177 k_11176 BOUND_VARIABLE_1351150)))))) (let ((_let_3894 (forall ((BOUND_VARIABLE_1351162 |u_(-> tptp.list_nat Bool)|) (BOUND_VARIABLE_1315160 tptp.list_nat)) (= (ho_11278 (ho_11966 k_11965 BOUND_VARIABLE_1351162) BOUND_VARIABLE_1315160) (ho_11660 (ho_11659 k_11658 BOUND_VARIABLE_1315160) (ho_11657 k_11656 BOUND_VARIABLE_1351162)))))) (let ((_let_3895 (forall ((BOUND_VARIABLE_1315150 tptp.int) (BOUND_VARIABLE_1315151 tptp.int)) (= (ho_11094 (ho_11093 k_11967 BOUND_VARIABLE_1315150) BOUND_VARIABLE_1315151) (= BOUND_VARIABLE_1315150 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315151) BOUND_VARIABLE_1315150)))))) (let ((_let_3896 (forall ((BOUND_VARIABLE_1351187 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_1315142 tptp.int)) (= (ho_11094 (ho_11785 k_11968 BOUND_VARIABLE_1351187) BOUND_VARIABLE_1315142) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1315142) (ho_11177 k_11176 BOUND_VARIABLE_1351187)))))) (let ((_let_3897 (forall ((BOUND_VARIABLE_1351199 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_1315133 tptp.nat)) (= (ho_11054 (ho_11956 k_11969 BOUND_VARIABLE_1351199) BOUND_VARIABLE_1315133) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1315133) (ho_11107 k_11106 BOUND_VARIABLE_1351199)))))) (let ((_let_3898 (forall ((BOUND_VARIABLE_1351211 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_1315124 tptp.nat)) (= (ho_11054 (ho_11956 k_11970 BOUND_VARIABLE_1351211) BOUND_VARIABLE_1315124) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1315124) (ho_11107 k_11106 BOUND_VARIABLE_1351211)))))) (let ((_let_3899 (forall ((BOUND_VARIABLE_1351223 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_1315115 tptp.nat)) (= (ho_11054 (ho_11956 k_11971 BOUND_VARIABLE_1351223) BOUND_VARIABLE_1315115) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1315115) (ho_11107 k_11106 BOUND_VARIABLE_1351223)))))) (let ((_let_3900 (forall ((BOUND_VARIABLE_1315105 tptp.int) (BOUND_VARIABLE_1315106 tptp.int)) (= (ho_11094 (ho_11093 k_11972 BOUND_VARIABLE_1315105) BOUND_VARIABLE_1315106) (= BOUND_VARIABLE_1315105 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315106) BOUND_VARIABLE_1315105)))))) (let ((_let_3901 (forall ((BOUND_VARIABLE_1351245 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_1315097 tptp.int)) (= (ho_11094 (ho_11785 k_11973 BOUND_VARIABLE_1351245) BOUND_VARIABLE_1315097) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1315097) (ho_11177 k_11176 BOUND_VARIABLE_1351245)))))) (let ((_let_3902 (forall ((BOUND_VARIABLE_1315087 tptp.int) (BOUND_VARIABLE_1315088 tptp.int)) (= (ho_11094 (ho_11093 k_11974 BOUND_VARIABLE_1315087) BOUND_VARIABLE_1315088) (= BOUND_VARIABLE_1315087 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315088) BOUND_VARIABLE_1315087)))))) (let ((_let_3903 (forall ((BOUND_VARIABLE_1351267 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_1315079 tptp.int)) (= (ho_11094 (ho_11785 k_11975 BOUND_VARIABLE_1351267) BOUND_VARIABLE_1315079) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1315079) (ho_11177 k_11176 BOUND_VARIABLE_1351267)))))) (let ((_let_3904 (forall ((BOUND_VARIABLE_1315069 tptp.int) (BOUND_VARIABLE_1315070 tptp.int)) (= (ho_11094 (ho_11093 k_11976 BOUND_VARIABLE_1315069) BOUND_VARIABLE_1315070) (= BOUND_VARIABLE_1315069 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315070) BOUND_VARIABLE_1315069)))))) (let ((_let_3905 (forall ((BOUND_VARIABLE_1315060 tptp.int) (BOUND_VARIABLE_1315061 tptp.int)) (= (ho_11094 (ho_11093 k_11977 BOUND_VARIABLE_1315060) BOUND_VARIABLE_1315061) (= BOUND_VARIABLE_1315060 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315061) BOUND_VARIABLE_1315060)))))) (let ((_let_3906 (forall ((BOUND_VARIABLE_1315051 tptp.int) (BOUND_VARIABLE_1315052 tptp.int)) (= (ho_11094 (ho_11093 k_11978 BOUND_VARIABLE_1315051) BOUND_VARIABLE_1315052) (= BOUND_VARIABLE_1315051 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315052) BOUND_VARIABLE_1315051)))))) (let ((_let_3907 (forall ((BOUND_VARIABLE_1315042 tptp.int) (BOUND_VARIABLE_1315043 tptp.int)) (= (ho_11094 (ho_11093 k_11979 BOUND_VARIABLE_1315042) BOUND_VARIABLE_1315043) (= BOUND_VARIABLE_1315042 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315043) BOUND_VARIABLE_1315042)))))) (let ((_let_3908 (forall ((BOUND_VARIABLE_1315033 tptp.int) (BOUND_VARIABLE_1315034 tptp.int)) (= (ho_11094 (ho_11093 k_11980 BOUND_VARIABLE_1315033) BOUND_VARIABLE_1315034) (= BOUND_VARIABLE_1315033 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315034) BOUND_VARIABLE_1315033)))))) (let ((_let_3909 (forall ((BOUND_VARIABLE_1315024 tptp.int) (BOUND_VARIABLE_1315025 tptp.int)) (= (ho_11094 (ho_11093 k_11981 BOUND_VARIABLE_1315024) BOUND_VARIABLE_1315025) (= BOUND_VARIABLE_1315024 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315025) BOUND_VARIABLE_1315024)))))) (let ((_let_3910 (forall ((BOUND_VARIABLE_1315015 tptp.int) (BOUND_VARIABLE_1315016 tptp.int)) (= (ho_11094 (ho_11093 k_11982 BOUND_VARIABLE_1315015) BOUND_VARIABLE_1315016) (= BOUND_VARIABLE_1315015 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315016) BOUND_VARIABLE_1315015)))))) (let ((_let_3911 (forall ((BOUND_VARIABLE_1315006 tptp.int) (BOUND_VARIABLE_1315007 tptp.int)) (= (ho_11094 (ho_11093 k_11983 BOUND_VARIABLE_1315006) BOUND_VARIABLE_1315007) (= BOUND_VARIABLE_1315006 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1315007) BOUND_VARIABLE_1315006)))))) (let ((_let_3912 (forall ((BOUND_VARIABLE_1314997 tptp.int) (BOUND_VARIABLE_1314998 tptp.int)) (= (ho_11094 (ho_11093 k_11984 BOUND_VARIABLE_1314997) BOUND_VARIABLE_1314998) (= BOUND_VARIABLE_1314997 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314998) BOUND_VARIABLE_1314997)))))) (let ((_let_3913 (forall ((BOUND_VARIABLE_1314988 tptp.int) (BOUND_VARIABLE_1314989 tptp.int)) (= (ho_11094 (ho_11093 k_11985 BOUND_VARIABLE_1314988) BOUND_VARIABLE_1314989) (= BOUND_VARIABLE_1314988 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314989) BOUND_VARIABLE_1314988)))))) (let ((_let_3914 (forall ((BOUND_VARIABLE_1314979 tptp.int) (BOUND_VARIABLE_1314980 tptp.int)) (= (ho_11094 (ho_11093 k_11986 BOUND_VARIABLE_1314979) BOUND_VARIABLE_1314980) (= BOUND_VARIABLE_1314979 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314980) BOUND_VARIABLE_1314979)))))) (let ((_let_3915 (forall ((BOUND_VARIABLE_1314970 tptp.int) (BOUND_VARIABLE_1314971 tptp.int)) (= (ho_11094 (ho_11093 k_11987 BOUND_VARIABLE_1314970) BOUND_VARIABLE_1314971) (= BOUND_VARIABLE_1314970 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314971) BOUND_VARIABLE_1314970)))))) (let ((_let_3916 (forall ((BOUND_VARIABLE_1314961 tptp.int) (BOUND_VARIABLE_1314962 tptp.int)) (= (ho_11094 (ho_11093 k_11988 BOUND_VARIABLE_1314961) BOUND_VARIABLE_1314962) (= BOUND_VARIABLE_1314961 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314962) BOUND_VARIABLE_1314961)))))) (let ((_let_3917 (forall ((BOUND_VARIABLE_1314952 tptp.int) (BOUND_VARIABLE_1314953 tptp.int)) (= (ho_11094 (ho_11093 k_11989 BOUND_VARIABLE_1314952) BOUND_VARIABLE_1314953) (= BOUND_VARIABLE_1314952 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314953) BOUND_VARIABLE_1314952)))))) (let ((_let_3918 (forall ((BOUND_VARIABLE_1314943 tptp.int) (BOUND_VARIABLE_1314944 tptp.int)) (= (ho_11094 (ho_11093 k_11990 BOUND_VARIABLE_1314943) BOUND_VARIABLE_1314944) (= BOUND_VARIABLE_1314943 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314944) BOUND_VARIABLE_1314943)))))) (let ((_let_3919 (forall ((BOUND_VARIABLE_1314934 tptp.int) (BOUND_VARIABLE_1314935 tptp.int)) (= (ho_11094 (ho_11093 k_11991 BOUND_VARIABLE_1314934) BOUND_VARIABLE_1314935) (= BOUND_VARIABLE_1314934 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314935) BOUND_VARIABLE_1314934)))))) (let ((_let_3920 (forall ((BOUND_VARIABLE_1314925 tptp.int) (BOUND_VARIABLE_1314926 tptp.int)) (= (ho_11094 (ho_11093 k_11992 BOUND_VARIABLE_1314925) BOUND_VARIABLE_1314926) (= BOUND_VARIABLE_1314925 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314926) BOUND_VARIABLE_1314925)))))) (let ((_let_3921 (forall ((BOUND_VARIABLE_1314916 tptp.int) (BOUND_VARIABLE_1314917 tptp.int)) (= (ho_11094 (ho_11093 k_11993 BOUND_VARIABLE_1314916) BOUND_VARIABLE_1314917) (= BOUND_VARIABLE_1314916 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314917) BOUND_VARIABLE_1314916)))))) (let ((_let_3922 (forall ((BOUND_VARIABLE_1314907 tptp.int) (BOUND_VARIABLE_1314908 tptp.int)) (= (ho_11094 (ho_11093 k_11994 BOUND_VARIABLE_1314907) BOUND_VARIABLE_1314908) (= BOUND_VARIABLE_1314907 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314908) BOUND_VARIABLE_1314907)))))) (let ((_let_3923 (forall ((BOUND_VARIABLE_1314898 tptp.int) (BOUND_VARIABLE_1314899 tptp.int)) (= (ho_11094 (ho_11093 k_11995 BOUND_VARIABLE_1314898) BOUND_VARIABLE_1314899) (= BOUND_VARIABLE_1314898 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314899) BOUND_VARIABLE_1314898)))))) (let ((_let_3924 (forall ((BOUND_VARIABLE_1314889 tptp.int) (BOUND_VARIABLE_1314890 tptp.int)) (= (ho_11094 (ho_11093 k_11996 BOUND_VARIABLE_1314889) BOUND_VARIABLE_1314890) (= BOUND_VARIABLE_1314889 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314890) BOUND_VARIABLE_1314889)))))) (let ((_let_3925 (forall ((BOUND_VARIABLE_1314880 tptp.int) (BOUND_VARIABLE_1314881 tptp.int)) (= (ho_11094 (ho_11093 k_11997 BOUND_VARIABLE_1314880) BOUND_VARIABLE_1314881) (= BOUND_VARIABLE_1314880 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314881) BOUND_VARIABLE_1314880)))))) (let ((_let_3926 (forall ((BOUND_VARIABLE_1314871 tptp.int) (BOUND_VARIABLE_1314872 tptp.int)) (= (ho_11094 (ho_11093 k_11998 BOUND_VARIABLE_1314871) BOUND_VARIABLE_1314872) (= BOUND_VARIABLE_1314871 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314872) BOUND_VARIABLE_1314871)))))) (let ((_let_3927 (forall ((BOUND_VARIABLE_1314862 tptp.int) (BOUND_VARIABLE_1314863 tptp.int)) (= (ho_11094 (ho_11093 k_11999 BOUND_VARIABLE_1314862) BOUND_VARIABLE_1314863) (= BOUND_VARIABLE_1314862 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314863) BOUND_VARIABLE_1314862)))))) (let ((_let_3928 (forall ((BOUND_VARIABLE_1314853 tptp.int) (BOUND_VARIABLE_1314854 tptp.int)) (= (ho_11094 (ho_11093 k_12000 BOUND_VARIABLE_1314853) BOUND_VARIABLE_1314854) (= BOUND_VARIABLE_1314853 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314854) BOUND_VARIABLE_1314853)))))) (let ((_let_3929 (forall ((BOUND_VARIABLE_1314844 tptp.int) (BOUND_VARIABLE_1314845 tptp.int)) (= (ho_11094 (ho_11093 k_12001 BOUND_VARIABLE_1314844) BOUND_VARIABLE_1314845) (= BOUND_VARIABLE_1314844 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314845) BOUND_VARIABLE_1314844)))))) (let ((_let_3930 (forall ((BOUND_VARIABLE_1314835 tptp.int) (BOUND_VARIABLE_1314836 tptp.int)) (= (ho_11094 (ho_11093 k_12002 BOUND_VARIABLE_1314835) BOUND_VARIABLE_1314836) (= BOUND_VARIABLE_1314835 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314836) BOUND_VARIABLE_1314835)))))) (let ((_let_3931 (forall ((BOUND_VARIABLE_1314826 tptp.int) (BOUND_VARIABLE_1314827 tptp.int)) (= (ho_11094 (ho_11093 k_12003 BOUND_VARIABLE_1314826) BOUND_VARIABLE_1314827) (= BOUND_VARIABLE_1314826 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314827) BOUND_VARIABLE_1314826)))))) (let ((_let_3932 (forall ((BOUND_VARIABLE_1314817 tptp.int) (BOUND_VARIABLE_1314818 tptp.int)) (= (ho_11094 (ho_11093 k_12004 BOUND_VARIABLE_1314817) BOUND_VARIABLE_1314818) (= BOUND_VARIABLE_1314817 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314818) BOUND_VARIABLE_1314817)))))) (let ((_let_3933 (forall ((BOUND_VARIABLE_1314808 tptp.int) (BOUND_VARIABLE_1314809 tptp.int)) (= (ho_11094 (ho_11093 k_12005 BOUND_VARIABLE_1314808) BOUND_VARIABLE_1314809) (= BOUND_VARIABLE_1314808 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314809) BOUND_VARIABLE_1314808)))))) (let ((_let_3934 (forall ((BOUND_VARIABLE_1314799 tptp.int) (BOUND_VARIABLE_1314800 tptp.int)) (= (ho_11094 (ho_11093 k_12006 BOUND_VARIABLE_1314799) BOUND_VARIABLE_1314800) (= BOUND_VARIABLE_1314799 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314800) BOUND_VARIABLE_1314799)))))) (let ((_let_3935 (forall ((BOUND_VARIABLE_1314790 tptp.int) (BOUND_VARIABLE_1314791 tptp.int)) (= (ho_11094 (ho_11093 k_12007 BOUND_VARIABLE_1314790) BOUND_VARIABLE_1314791) (= BOUND_VARIABLE_1314790 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314791) BOUND_VARIABLE_1314790)))))) (let ((_let_3936 (forall ((BOUND_VARIABLE_1314781 tptp.int) (BOUND_VARIABLE_1314782 tptp.int)) (= (ho_11094 (ho_11093 k_12008 BOUND_VARIABLE_1314781) BOUND_VARIABLE_1314782) (= BOUND_VARIABLE_1314781 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314782) BOUND_VARIABLE_1314781)))))) (let ((_let_3937 (forall ((BOUND_VARIABLE_1314772 tptp.int) (BOUND_VARIABLE_1314773 tptp.int)) (= (ho_11094 (ho_11093 k_12009 BOUND_VARIABLE_1314772) BOUND_VARIABLE_1314773) (= BOUND_VARIABLE_1314772 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314773) BOUND_VARIABLE_1314772)))))) (let ((_let_3938 (forall ((BOUND_VARIABLE_1314763 tptp.int) (BOUND_VARIABLE_1314764 tptp.int)) (= (ho_11094 (ho_11093 k_12010 BOUND_VARIABLE_1314763) BOUND_VARIABLE_1314764) (= BOUND_VARIABLE_1314763 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314764) BOUND_VARIABLE_1314763)))))) (let ((_let_3939 (forall ((BOUND_VARIABLE_1314754 tptp.int) (BOUND_VARIABLE_1314755 tptp.int)) (= (ho_11094 (ho_11093 k_12011 BOUND_VARIABLE_1314754) BOUND_VARIABLE_1314755) (= BOUND_VARIABLE_1314754 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314755) BOUND_VARIABLE_1314754)))))) (let ((_let_3940 (forall ((BOUND_VARIABLE_1314745 tptp.int) (BOUND_VARIABLE_1314746 tptp.int)) (= (ho_11094 (ho_11093 k_12012 BOUND_VARIABLE_1314745) BOUND_VARIABLE_1314746) (= BOUND_VARIABLE_1314745 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314746) BOUND_VARIABLE_1314745)))))) (let ((_let_3941 (forall ((BOUND_VARIABLE_1314736 tptp.int) (BOUND_VARIABLE_1314737 tptp.int)) (= (ho_11094 (ho_11093 k_12013 BOUND_VARIABLE_1314736) BOUND_VARIABLE_1314737) (= BOUND_VARIABLE_1314736 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314737) BOUND_VARIABLE_1314736)))))) (let ((_let_3942 (forall ((BOUND_VARIABLE_1314727 tptp.int) (BOUND_VARIABLE_1314728 tptp.int)) (= (ho_11094 (ho_11093 k_12014 BOUND_VARIABLE_1314727) BOUND_VARIABLE_1314728) (= BOUND_VARIABLE_1314727 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314728) BOUND_VARIABLE_1314727)))))) (let ((_let_3943 (forall ((BOUND_VARIABLE_1314718 tptp.int) (BOUND_VARIABLE_1314719 tptp.int)) (= (ho_11094 (ho_11093 k_12015 BOUND_VARIABLE_1314718) BOUND_VARIABLE_1314719) (= BOUND_VARIABLE_1314718 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314719) BOUND_VARIABLE_1314718)))))) (let ((_let_3944 (forall ((BOUND_VARIABLE_1314709 tptp.int) (BOUND_VARIABLE_1314710 tptp.int)) (= (ho_11094 (ho_11093 k_12016 BOUND_VARIABLE_1314709) BOUND_VARIABLE_1314710) (= BOUND_VARIABLE_1314709 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314710) BOUND_VARIABLE_1314709)))))) (let ((_let_3945 (forall ((BOUND_VARIABLE_1314700 tptp.int) (BOUND_VARIABLE_1314701 tptp.int)) (= (ho_11094 (ho_11093 k_12017 BOUND_VARIABLE_1314700) BOUND_VARIABLE_1314701) (= BOUND_VARIABLE_1314700 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314701) BOUND_VARIABLE_1314700)))))) (let ((_let_3946 (forall ((BOUND_VARIABLE_1314691 tptp.int) (BOUND_VARIABLE_1314692 tptp.int)) (= (ho_11094 (ho_11093 k_12018 BOUND_VARIABLE_1314691) BOUND_VARIABLE_1314692) (= BOUND_VARIABLE_1314691 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314692) BOUND_VARIABLE_1314691)))))) (let ((_let_3947 (forall ((BOUND_VARIABLE_1314682 tptp.int) (BOUND_VARIABLE_1314683 tptp.int)) (= (ho_11094 (ho_11093 k_12019 BOUND_VARIABLE_1314682) BOUND_VARIABLE_1314683) (= BOUND_VARIABLE_1314682 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314683) BOUND_VARIABLE_1314682)))))) (let ((_let_3948 (forall ((BOUND_VARIABLE_1351717 |u_(-> tptp.int tptp.nat)|) (BOUND_VARIABLE_1314672 tptp.int)) (= (= (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11061 BOUND_VARIABLE_1351717 BOUND_VARIABLE_1314672)) (ho_11094 (ho_11878 k_12020 BOUND_VARIABLE_1351717) BOUND_VARIABLE_1314672))))) (let ((_let_3949 (forall ((BOUND_VARIABLE_1314662 tptp.int) (BOUND_VARIABLE_1314663 tptp.int)) (= (ho_11094 (ho_11093 k_12021 BOUND_VARIABLE_1314662) BOUND_VARIABLE_1314663) (= BOUND_VARIABLE_1314662 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314663) BOUND_VARIABLE_1314662)))))) (let ((_let_3950 (forall ((BOUND_VARIABLE_1351738 |u_(-> tptp.int tptp.rat)|) (BOUND_VARIABLE_1314652 tptp.int)) (= (ho_11094 (ho_11665 k_12022 BOUND_VARIABLE_1351738) BOUND_VARIABLE_1314652) (= (ho_11127 BOUND_VARIABLE_1351738 BOUND_VARIABLE_1314652) (ho_11498 k_11497 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))))))) (let ((_let_3951 (forall ((BOUND_VARIABLE_1351750 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1314641 tptp.nat)) (= (= (ho_11498 k_11497 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (ho_11498 BOUND_VARIABLE_1351750 BOUND_VARIABLE_1314641)) (ho_11054 (ho_11686 k_12023 BOUND_VARIABLE_1351750) BOUND_VARIABLE_1314641))))) (let ((_let_3952 (forall ((BOUND_VARIABLE_1314631 tptp.int) (BOUND_VARIABLE_1314632 tptp.int)) (= (ho_11094 (ho_11093 k_12024 BOUND_VARIABLE_1314631) BOUND_VARIABLE_1314632) (= BOUND_VARIABLE_1314631 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314632) BOUND_VARIABLE_1314631)))))) (let ((_let_3953 (forall ((BOUND_VARIABLE_1351772 |u_(-> tptp.int tptp.assn)|) (BOUND_VARIABLE_1314624 tptp.int)) (= (ho_11094 (ho_12031 k_12030 BOUND_VARIABLE_1351772) BOUND_VARIABLE_1314624) (= (ho_12025 BOUND_VARIABLE_1351772 BOUND_VARIABLE_1314624) (ho_12029 k_12028 (ho_12027 k_12026 true))))))) (let ((_let_3954 (forall ((BOUND_VARIABLE_1351801 |u_(-> tptp.nat tptp.assn)|) (BOUND_VARIABLE_1314616 tptp.nat)) (= (= (ho_12029 k_12028 (ho_12027 k_12026 true)) (ho_12032 BOUND_VARIABLE_1351801 BOUND_VARIABLE_1314616)) (ho_11054 (ho_12034 k_12033 BOUND_VARIABLE_1351801) BOUND_VARIABLE_1314616))))) (let ((_let_3955 (forall ((BOUND_VARIABLE_1314606 tptp.int) (BOUND_VARIABLE_1314607 tptp.int)) (= (ho_11094 (ho_11093 k_12035 BOUND_VARIABLE_1314606) BOUND_VARIABLE_1314607) (= BOUND_VARIABLE_1314606 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314607) BOUND_VARIABLE_1314606)))))) (let ((_let_3956 (forall ((BOUND_VARIABLE_1351828 |u_(-> tptp.int tptp.code_integer)|) (BOUND_VARIABLE_1314596 tptp.int)) (= (ho_11094 (ho_11672 k_12036 BOUND_VARIABLE_1351828) BOUND_VARIABLE_1314596) (= (ho_11667 BOUND_VARIABLE_1351828 BOUND_VARIABLE_1314596) (ho_11669 k_11668 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))))))) (let ((_let_3957 (forall ((BOUND_VARIABLE_1351840 |u_(-> tptp.nat tptp.code_integer)|) (BOUND_VARIABLE_1314585 tptp.nat)) (= (= (ho_11669 k_11668 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (ho_11669 BOUND_VARIABLE_1351840 BOUND_VARIABLE_1314585)) (ho_11054 (ho_11691 k_12037 BOUND_VARIABLE_1351840) BOUND_VARIABLE_1314585))))) (let ((_let_3958 (forall ((BOUND_VARIABLE_1314575 tptp.int) (BOUND_VARIABLE_1314576 tptp.int)) (= (ho_11094 (ho_11093 k_12038 BOUND_VARIABLE_1314575) BOUND_VARIABLE_1314576) (= BOUND_VARIABLE_1314575 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314576) BOUND_VARIABLE_1314575)))))) (let ((_let_3959 (forall ((BOUND_VARIABLE_1314566 tptp.int) (BOUND_VARIABLE_1314567 tptp.int)) (= (ho_11094 (ho_11093 k_12039 BOUND_VARIABLE_1314566) BOUND_VARIABLE_1314567) (= BOUND_VARIABLE_1314566 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314567) BOUND_VARIABLE_1314566)))))) (let ((_let_3960 (forall ((BOUND_VARIABLE_1314557 tptp.int) (BOUND_VARIABLE_1314558 tptp.int)) (= (ho_11094 (ho_11093 k_12040 BOUND_VARIABLE_1314557) BOUND_VARIABLE_1314558) (= BOUND_VARIABLE_1314557 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314558) BOUND_VARIABLE_1314557)))))) (let ((_let_3961 (forall ((BOUND_VARIABLE_1351881 |u_(-> tptp.int tptp.nat)|) (BOUND_VARIABLE_1314529 tptp.int)) (= (ho_11094 (ho_11878 k_12041 BOUND_VARIABLE_1351881) BOUND_VARIABLE_1314529) (and (not (forall ((K3 tptp.nat)) (not (= (ho_11061 BOUND_VARIABLE_1351881 BOUND_VARIABLE_1314529) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= (ho_11109 k_11108 (ho_11107 k_11106 k_11105)) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 BOUND_VARIABLE_1351881 BOUND_VARIABLE_1314529))) (ho_11056 k_11055 K3))))))))))) (let ((_let_3962 (forall ((BOUND_VARIABLE_1314519 tptp.int) (BOUND_VARIABLE_1314520 tptp.int)) (= (ho_11094 (ho_11093 k_12042 BOUND_VARIABLE_1314519) BOUND_VARIABLE_1314520) (= BOUND_VARIABLE_1314519 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314520) BOUND_VARIABLE_1314519)))))) (let ((_let_3963 (forall ((BOUND_VARIABLE_1351922 |u_(-> tptp.int tptp.nat)|) (BOUND_VARIABLE_1351916 |u_(-> tptp.int tptp.nat)|) (BOUND_VARIABLE_1314475 tptp.int)) (= (and (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 _let_1)) (ho_11056 k_11055 K3))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 BOUND_VARIABLE_1351922 BOUND_VARIABLE_1314475))) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 (ho_11061 BOUND_VARIABLE_1351916 BOUND_VARIABLE_1314475)))) (ho_11056 k_11055 (ho_11139 k_11138 _let_1)))))))))) (forall ((K3 tptp.nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (not (= _let_1 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 BOUND_VARIABLE_1351922 BOUND_VARIABLE_1314475))) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 (ho_11061 BOUND_VARIABLE_1351916 BOUND_VARIABLE_1314475)))) (ho_11056 k_11055 (ho_11139 k_11138 _let_1))))))) (ho_11056 k_11055 K3)))))))) (ho_11094 (ho_11878 (ho_12044 k_12043 BOUND_VARIABLE_1351922) BOUND_VARIABLE_1351916) BOUND_VARIABLE_1314475))))) (let ((_let_3964 (forall ((BOUND_VARIABLE_1314464 tptp.int) (BOUND_VARIABLE_1314465 tptp.int)) (= (ho_11094 (ho_11093 k_12045 BOUND_VARIABLE_1314464) BOUND_VARIABLE_1314465) (= BOUND_VARIABLE_1314464 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314465) BOUND_VARIABLE_1314464)))))) (let ((_let_3965 (forall ((BOUND_VARIABLE_1351964 |u_(-> tptp.nat tptp.int)|) (BOUND_VARIABLE_1314454 tptp.nat)) (= (= (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11056 BOUND_VARIABLE_1351964 BOUND_VARIABLE_1314454)) (ho_11054 (ho_11681 k_12046 BOUND_VARIABLE_1351964) BOUND_VARIABLE_1314454))))) (let ((_let_3966 (forall ((BOUND_VARIABLE_1314444 tptp.int) (BOUND_VARIABLE_1314445 tptp.int)) (= (ho_11094 (ho_11093 k_12047 BOUND_VARIABLE_1314444) BOUND_VARIABLE_1314445) (= BOUND_VARIABLE_1314444 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314445) BOUND_VARIABLE_1314444)))))) (let ((_let_3967 (forall ((BOUND_VARIABLE_1351985 |u_(-> tptp.int tptp.nat)|) (BOUND_VARIABLE_1314434 tptp.int)) (= (= (ho_11109 k_11108 (ho_11107 k_11106 k_11105)) (ho_11061 BOUND_VARIABLE_1351985 BOUND_VARIABLE_1314434)) (ho_11094 (ho_11878 k_12048 BOUND_VARIABLE_1351985) BOUND_VARIABLE_1314434))))) (let ((_let_3968 (forall ((BOUND_VARIABLE_1314424 tptp.int) (BOUND_VARIABLE_1314425 tptp.int)) (= (ho_11094 (ho_11093 k_12049 BOUND_VARIABLE_1314424) BOUND_VARIABLE_1314425) (= BOUND_VARIABLE_1314424 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314425) BOUND_VARIABLE_1314424)))))) (let ((_let_3969 (forall ((BOUND_VARIABLE_1352006 |u_(-> tptp.int tptp.rat)|) (BOUND_VARIABLE_1314414 tptp.int)) (= (= (ho_11498 k_11497 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11127 BOUND_VARIABLE_1352006 BOUND_VARIABLE_1314414)) (ho_11094 (ho_11665 k_12050 BOUND_VARIABLE_1352006) BOUND_VARIABLE_1314414))))) (let ((_let_3970 (forall ((BOUND_VARIABLE_1352017 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_1314403 tptp.nat)) (= (= (ho_11498 k_11497 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11498 BOUND_VARIABLE_1352017 BOUND_VARIABLE_1314403)) (ho_11054 (ho_11686 k_12051 BOUND_VARIABLE_1352017) BOUND_VARIABLE_1314403))))) (let ((_let_3971 (forall ((BOUND_VARIABLE_1314393 tptp.int) (BOUND_VARIABLE_1314394 tptp.int)) (= (ho_11094 (ho_11093 k_12052 BOUND_VARIABLE_1314393) BOUND_VARIABLE_1314394) (= BOUND_VARIABLE_1314393 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314394) BOUND_VARIABLE_1314393)))))) (let ((_let_3972 (forall ((BOUND_VARIABLE_1352038 |u_(-> tptp.int tptp.code_integer)|) (BOUND_VARIABLE_1314383 tptp.int)) (= (= (ho_11669 k_11668 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11667 BOUND_VARIABLE_1352038 BOUND_VARIABLE_1314383)) (ho_11094 (ho_11672 k_12053 BOUND_VARIABLE_1352038) BOUND_VARIABLE_1314383))))) (let ((_let_3973 (forall ((BOUND_VARIABLE_1352049 |u_(-> tptp.nat tptp.code_integer)|) (BOUND_VARIABLE_1314372 tptp.nat)) (= (= (ho_11669 k_11668 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11669 BOUND_VARIABLE_1352049 BOUND_VARIABLE_1314372)) (ho_11054 (ho_11691 k_12054 BOUND_VARIABLE_1352049) BOUND_VARIABLE_1314372))))) (let ((_let_3974 (forall ((BOUND_VARIABLE_1314362 tptp.int) (BOUND_VARIABLE_1314363 tptp.int)) (= (ho_11094 (ho_11093 k_12055 BOUND_VARIABLE_1314362) BOUND_VARIABLE_1314363) (= BOUND_VARIABLE_1314362 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314363) BOUND_VARIABLE_1314362)))))) (let ((_let_3975 (forall ((BOUND_VARIABLE_1314353 tptp.int) (BOUND_VARIABLE_1314354 tptp.int)) (= (ho_11094 (ho_11093 k_12056 BOUND_VARIABLE_1314353) BOUND_VARIABLE_1314354) (= BOUND_VARIABLE_1314353 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314354) BOUND_VARIABLE_1314353)))))) (let ((_let_3976 (forall ((BOUND_VARIABLE_1314344 tptp.int) (BOUND_VARIABLE_1314345 tptp.int)) (= (ho_11094 (ho_11093 k_12057 BOUND_VARIABLE_1314344) BOUND_VARIABLE_1314345) (= BOUND_VARIABLE_1314344 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314345) BOUND_VARIABLE_1314344)))))) (let ((_let_3977 (forall ((BOUND_VARIABLE_1352090 |u_(-> tptp.int tptp.nat)|) (BOUND_VARIABLE_1314316 tptp.int)) (= (and (not (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (ho_11056 k_11055 K3))) (ho_11061 BOUND_VARIABLE_1352090 BOUND_VARIABLE_1314316))))) (forall ((K3 tptp.nat)) (not (= (ho_11109 k_11108 (ho_11107 k_11106 k_11105)) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 BOUND_VARIABLE_1352090 BOUND_VARIABLE_1314316))) (ho_11056 k_11055 K3))))))) (ho_11094 (ho_11878 k_12058 BOUND_VARIABLE_1352090) BOUND_VARIABLE_1314316))))) (let ((_let_3978 (forall ((BOUND_VARIABLE_1314306 tptp.int) (BOUND_VARIABLE_1314307 tptp.int)) (= (ho_11094 (ho_11093 k_12059 BOUND_VARIABLE_1314306) BOUND_VARIABLE_1314307) (= BOUND_VARIABLE_1314306 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314307) BOUND_VARIABLE_1314306)))))) (let ((_let_3979 (forall ((BOUND_VARIABLE_1314271 tptp.int) (BOUND_VARIABLE_1352122 |u_(-> tptp.int tptp.nat)|) (BOUND_VARIABLE_1314273 tptp.int)) (= (and (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_11061 BOUND_VARIABLE_1352122 BOUND_VARIABLE_1314273))) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (ho_11056 k_11055 K3))) (ho_11139 (ho_11479 (ho_12061 k_12060 (= BOUND_VARIABLE_1314271 BOUND_VARIABLE_1314273)) (ho_11139 k_11138 _let_1)) _let_1)))))) (forall ((K3 tptp.nat)) (let ((_let_1 (ho_11061 BOUND_VARIABLE_1352122 BOUND_VARIABLE_1314273))) (not (= (ho_11109 k_11108 (ho_11107 k_11106 k_11105)) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11139 (ho_11479 (ho_12061 k_12060 (= BOUND_VARIABLE_1314271 BOUND_VARIABLE_1314273)) (ho_11139 k_11138 _let_1)) _let_1))) (ho_11056 k_11055 K3)))))))) (ho_11094 (ho_11878 (ho_12063 k_12062 BOUND_VARIABLE_1314271) BOUND_VARIABLE_1352122) BOUND_VARIABLE_1314273))))) (let ((_let_3980 (forall ((BOUND_VARIABLE_1314262 tptp.int) (BOUND_VARIABLE_1314263 tptp.int)) (= (ho_11094 (ho_11093 k_12064 BOUND_VARIABLE_1314262) BOUND_VARIABLE_1314263) (= BOUND_VARIABLE_1314262 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314263) BOUND_VARIABLE_1314262)))))) (let ((_let_3981 (forall ((BOUND_VARIABLE_1314253 tptp.int) (BOUND_VARIABLE_1314254 tptp.int)) (= (ho_11094 (ho_11093 k_12065 BOUND_VARIABLE_1314253) BOUND_VARIABLE_1314254) (= BOUND_VARIABLE_1314253 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314254) BOUND_VARIABLE_1314253)))))) (let ((_let_3982 (forall ((BOUND_VARIABLE_1314244 tptp.int) (BOUND_VARIABLE_1314245 tptp.int)) (= (ho_11094 (ho_11093 k_12066 BOUND_VARIABLE_1314244) BOUND_VARIABLE_1314245) (= BOUND_VARIABLE_1314244 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314245) BOUND_VARIABLE_1314244)))))) (let ((_let_3983 (forall ((BOUND_VARIABLE_1314235 tptp.int) (BOUND_VARIABLE_1314236 tptp.int)) (= (ho_11094 (ho_11093 k_12067 BOUND_VARIABLE_1314235) BOUND_VARIABLE_1314236) (= BOUND_VARIABLE_1314235 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314236) BOUND_VARIABLE_1314235)))))) (let ((_let_3984 (forall ((BOUND_VARIABLE_1314226 tptp.int) (BOUND_VARIABLE_1314227 tptp.int)) (= (ho_11094 (ho_11093 k_12068 BOUND_VARIABLE_1314226) BOUND_VARIABLE_1314227) (= BOUND_VARIABLE_1314226 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314227) BOUND_VARIABLE_1314226)))))) (let ((_let_3985 (forall ((BOUND_VARIABLE_1314217 tptp.int) (BOUND_VARIABLE_1314218 tptp.int)) (= (ho_11094 (ho_11093 k_12069 BOUND_VARIABLE_1314217) BOUND_VARIABLE_1314218) (= BOUND_VARIABLE_1314217 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314218) BOUND_VARIABLE_1314217)))))) (let ((_let_3986 (forall ((BOUND_VARIABLE_1314208 tptp.int) (BOUND_VARIABLE_1314209 tptp.int)) (= (ho_11094 (ho_11093 k_12070 BOUND_VARIABLE_1314208) BOUND_VARIABLE_1314209) (= BOUND_VARIABLE_1314208 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314209) BOUND_VARIABLE_1314208)))))) (let ((_let_3987 (forall ((BOUND_VARIABLE_1314199 tptp.int) (BOUND_VARIABLE_1314200 tptp.int)) (= (ho_11094 (ho_11093 k_12071 BOUND_VARIABLE_1314199) BOUND_VARIABLE_1314200) (= BOUND_VARIABLE_1314199 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314200) BOUND_VARIABLE_1314199)))))) (let ((_let_3988 (forall ((BOUND_VARIABLE_1314190 tptp.int) (BOUND_VARIABLE_1314191 tptp.int)) (= (ho_11094 (ho_11093 k_12072 BOUND_VARIABLE_1314190) BOUND_VARIABLE_1314191) (= BOUND_VARIABLE_1314190 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314191) BOUND_VARIABLE_1314190)))))) (let ((_let_3989 (forall ((BOUND_VARIABLE_1314181 tptp.int) (BOUND_VARIABLE_1314182 tptp.int)) (= (ho_11094 (ho_11093 k_12073 BOUND_VARIABLE_1314181) BOUND_VARIABLE_1314182) (= BOUND_VARIABLE_1314181 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314182) BOUND_VARIABLE_1314181)))))) (let ((_let_3990 (forall ((BOUND_VARIABLE_1314172 tptp.int) (BOUND_VARIABLE_1314173 tptp.int)) (= (ho_11094 (ho_11093 k_12074 BOUND_VARIABLE_1314172) BOUND_VARIABLE_1314173) (= BOUND_VARIABLE_1314172 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314173) BOUND_VARIABLE_1314172)))))) (let ((_let_3991 (forall ((BOUND_VARIABLE_1314163 tptp.int) (BOUND_VARIABLE_1314164 tptp.int)) (= (ho_11094 (ho_11093 k_12075 BOUND_VARIABLE_1314163) BOUND_VARIABLE_1314164) (= BOUND_VARIABLE_1314163 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314164) BOUND_VARIABLE_1314163)))))) (let ((_let_3992 (forall ((BOUND_VARIABLE_1314154 tptp.int) (BOUND_VARIABLE_1314155 tptp.int)) (= (ho_11094 (ho_11093 k_12076 BOUND_VARIABLE_1314154) BOUND_VARIABLE_1314155) (= BOUND_VARIABLE_1314154 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314155) BOUND_VARIABLE_1314154)))))) (let ((_let_3993 (forall ((BOUND_VARIABLE_1314145 tptp.int) (BOUND_VARIABLE_1314146 tptp.int)) (= (ho_11094 (ho_11093 k_12077 BOUND_VARIABLE_1314145) BOUND_VARIABLE_1314146) (= BOUND_VARIABLE_1314145 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314146) BOUND_VARIABLE_1314145)))))) (let ((_let_3994 (forall ((BOUND_VARIABLE_1314136 tptp.int) (BOUND_VARIABLE_1314137 tptp.int)) (= (ho_11094 (ho_11093 k_12078 BOUND_VARIABLE_1314136) BOUND_VARIABLE_1314137) (= BOUND_VARIABLE_1314136 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314137) BOUND_VARIABLE_1314136)))))) (let ((_let_3995 (forall ((BOUND_VARIABLE_1314127 tptp.int) (BOUND_VARIABLE_1314128 tptp.int)) (= (ho_11094 (ho_11093 k_12079 BOUND_VARIABLE_1314127) BOUND_VARIABLE_1314128) (= BOUND_VARIABLE_1314127 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314128) BOUND_VARIABLE_1314127)))))) (let ((_let_3996 (forall ((BOUND_VARIABLE_1314118 tptp.int) (BOUND_VARIABLE_1314119 tptp.int)) (= (ho_11094 (ho_11093 k_12080 BOUND_VARIABLE_1314118) BOUND_VARIABLE_1314119) (= BOUND_VARIABLE_1314118 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314119) BOUND_VARIABLE_1314118)))))) (let ((_let_3997 (forall ((BOUND_VARIABLE_1314109 tptp.int) (BOUND_VARIABLE_1314110 tptp.int)) (= (ho_11094 (ho_11093 k_12081 BOUND_VARIABLE_1314109) BOUND_VARIABLE_1314110) (= BOUND_VARIABLE_1314109 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314110) BOUND_VARIABLE_1314109)))))) (let ((_let_3998 (forall ((BOUND_VARIABLE_1314100 tptp.int) (BOUND_VARIABLE_1314101 tptp.int)) (= (ho_11094 (ho_11093 k_12082 BOUND_VARIABLE_1314100) BOUND_VARIABLE_1314101) (= BOUND_VARIABLE_1314100 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314101) BOUND_VARIABLE_1314100)))))) (let ((_let_3999 (forall ((BOUND_VARIABLE_1314091 tptp.int) (BOUND_VARIABLE_1314092 tptp.int)) (= (ho_11094 (ho_11093 k_12083 BOUND_VARIABLE_1314091) BOUND_VARIABLE_1314092) (= BOUND_VARIABLE_1314091 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314092) BOUND_VARIABLE_1314091)))))) (let ((_let_4000 (forall ((BOUND_VARIABLE_1314082 tptp.int) (BOUND_VARIABLE_1314083 tptp.int)) (= (ho_11094 (ho_11093 k_12084 BOUND_VARIABLE_1314082) BOUND_VARIABLE_1314083) (= BOUND_VARIABLE_1314082 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314083) BOUND_VARIABLE_1314082)))))) (let ((_let_4001 (forall ((BOUND_VARIABLE_1314073 tptp.int) (BOUND_VARIABLE_1314074 tptp.int)) (= (ho_11094 (ho_11093 k_12085 BOUND_VARIABLE_1314073) BOUND_VARIABLE_1314074) (= BOUND_VARIABLE_1314073 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314074) BOUND_VARIABLE_1314073)))))) (let ((_let_4002 (forall ((BOUND_VARIABLE_1314064 tptp.int) (BOUND_VARIABLE_1314065 tptp.int)) (= (ho_11094 (ho_11093 k_12086 BOUND_VARIABLE_1314064) BOUND_VARIABLE_1314065) (= BOUND_VARIABLE_1314064 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314065) BOUND_VARIABLE_1314064)))))) (let ((_let_4003 (forall ((BOUND_VARIABLE_1314055 tptp.int) (BOUND_VARIABLE_1314056 tptp.int)) (= (ho_11094 (ho_11093 k_12087 BOUND_VARIABLE_1314055) BOUND_VARIABLE_1314056) (= BOUND_VARIABLE_1314055 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314056) BOUND_VARIABLE_1314055)))))) (let ((_let_4004 (forall ((BOUND_VARIABLE_1314046 tptp.int) (BOUND_VARIABLE_1314047 tptp.int)) (= (ho_11094 (ho_11093 k_12088 BOUND_VARIABLE_1314046) BOUND_VARIABLE_1314047) (= BOUND_VARIABLE_1314046 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314047) BOUND_VARIABLE_1314046)))))) (let ((_let_4005 (forall ((BOUND_VARIABLE_1314037 tptp.int) (BOUND_VARIABLE_1314038 tptp.int)) (= (ho_11094 (ho_11093 k_12089 BOUND_VARIABLE_1314037) BOUND_VARIABLE_1314038) (= BOUND_VARIABLE_1314037 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314038) BOUND_VARIABLE_1314037)))))) (let ((_let_4006 (forall ((BOUND_VARIABLE_1314028 tptp.int) (BOUND_VARIABLE_1314029 tptp.int)) (= (ho_11094 (ho_11093 k_12090 BOUND_VARIABLE_1314028) BOUND_VARIABLE_1314029) (= BOUND_VARIABLE_1314028 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314029) BOUND_VARIABLE_1314028)))))) (let ((_let_4007 (forall ((BOUND_VARIABLE_1314019 tptp.int) (BOUND_VARIABLE_1314020 tptp.int)) (= (ho_11094 (ho_11093 k_12091 BOUND_VARIABLE_1314019) BOUND_VARIABLE_1314020) (= BOUND_VARIABLE_1314019 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314020) BOUND_VARIABLE_1314019)))))) (let ((_let_4008 (forall ((BOUND_VARIABLE_1314010 tptp.int) (BOUND_VARIABLE_1314011 tptp.int)) (= (ho_11094 (ho_11093 k_12092 BOUND_VARIABLE_1314010) BOUND_VARIABLE_1314011) (= BOUND_VARIABLE_1314010 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314011) BOUND_VARIABLE_1314010)))))) (let ((_let_4009 (forall ((BOUND_VARIABLE_1314001 tptp.int) (BOUND_VARIABLE_1314002 tptp.int)) (= (ho_11094 (ho_11093 k_12093 BOUND_VARIABLE_1314001) BOUND_VARIABLE_1314002) (= BOUND_VARIABLE_1314001 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1314002) BOUND_VARIABLE_1314001)))))) (let ((_let_4010 (forall ((BOUND_VARIABLE_1313992 tptp.int) (BOUND_VARIABLE_1313993 tptp.int)) (= (ho_11094 (ho_11093 k_12094 BOUND_VARIABLE_1313992) BOUND_VARIABLE_1313993) (= BOUND_VARIABLE_1313992 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313993) BOUND_VARIABLE_1313992)))))) (let ((_let_4011 (forall ((BOUND_VARIABLE_1313983 tptp.int) (BOUND_VARIABLE_1313984 tptp.int)) (= (ho_11094 (ho_11093 k_12095 BOUND_VARIABLE_1313983) BOUND_VARIABLE_1313984) (= BOUND_VARIABLE_1313983 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313984) BOUND_VARIABLE_1313983)))))) (let ((_let_4012 (forall ((BOUND_VARIABLE_1313974 tptp.int) (BOUND_VARIABLE_1313975 tptp.int)) (= (ho_11094 (ho_11093 k_12096 BOUND_VARIABLE_1313974) BOUND_VARIABLE_1313975) (= BOUND_VARIABLE_1313974 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313975) BOUND_VARIABLE_1313974)))))) (let ((_let_4013 (forall ((BOUND_VARIABLE_1313965 tptp.int) (BOUND_VARIABLE_1313966 tptp.int)) (= (ho_11094 (ho_11093 k_12097 BOUND_VARIABLE_1313965) BOUND_VARIABLE_1313966) (= BOUND_VARIABLE_1313965 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313966) BOUND_VARIABLE_1313965)))))) (let ((_let_4014 (forall ((BOUND_VARIABLE_1313956 tptp.int) (BOUND_VARIABLE_1313957 tptp.int)) (= (ho_11094 (ho_11093 k_12098 BOUND_VARIABLE_1313956) BOUND_VARIABLE_1313957) (= BOUND_VARIABLE_1313956 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313957) BOUND_VARIABLE_1313956)))))) (let ((_let_4015 (forall ((BOUND_VARIABLE_1313947 tptp.int) (BOUND_VARIABLE_1313948 tptp.int)) (= (ho_11094 (ho_11093 k_12099 BOUND_VARIABLE_1313947) BOUND_VARIABLE_1313948) (= BOUND_VARIABLE_1313947 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313948) BOUND_VARIABLE_1313947)))))) (let ((_let_4016 (forall ((BOUND_VARIABLE_1313938 tptp.int) (BOUND_VARIABLE_1313939 tptp.int)) (= (ho_11094 (ho_11093 k_12100 BOUND_VARIABLE_1313938) BOUND_VARIABLE_1313939) (= BOUND_VARIABLE_1313938 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313939) BOUND_VARIABLE_1313938)))))) (let ((_let_4017 (forall ((BOUND_VARIABLE_1313929 tptp.int) (BOUND_VARIABLE_1313930 tptp.int)) (= (ho_11094 (ho_11093 k_12101 BOUND_VARIABLE_1313929) BOUND_VARIABLE_1313930) (= BOUND_VARIABLE_1313929 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313930) BOUND_VARIABLE_1313929)))))) (let ((_let_4018 (forall ((BOUND_VARIABLE_1313920 tptp.int) (BOUND_VARIABLE_1313921 tptp.int)) (= (ho_11094 (ho_11093 k_12102 BOUND_VARIABLE_1313920) BOUND_VARIABLE_1313921) (= BOUND_VARIABLE_1313920 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313921) BOUND_VARIABLE_1313920)))))) (let ((_let_4019 (forall ((BOUND_VARIABLE_1313911 tptp.int) (BOUND_VARIABLE_1313912 tptp.int)) (= (ho_11094 (ho_11093 k_12103 BOUND_VARIABLE_1313911) BOUND_VARIABLE_1313912) (= BOUND_VARIABLE_1313911 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313912) BOUND_VARIABLE_1313911)))))) (let ((_let_4020 (forall ((BOUND_VARIABLE_1352558 |u_(-> tptp.int tptp.nat)|) (BOUND_VARIABLE_1313883 tptp.int)) (= (and (not (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (ho_11056 k_11055 K3))) (ho_11061 BOUND_VARIABLE_1352558 BOUND_VARIABLE_1313883))))) (forall ((K3 tptp.nat)) (not (= (ho_11109 k_11108 (ho_11107 k_11106 k_11105)) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 BOUND_VARIABLE_1352558 BOUND_VARIABLE_1313883))) (ho_11056 k_11055 K3))))))) (ho_11094 (ho_11878 k_12104 BOUND_VARIABLE_1352558) BOUND_VARIABLE_1313883))))) (let ((_let_4021 (forall ((BOUND_VARIABLE_1313873 tptp.int) (BOUND_VARIABLE_1313874 tptp.int)) (= (ho_11094 (ho_11093 k_12105 BOUND_VARIABLE_1313873) BOUND_VARIABLE_1313874) (= BOUND_VARIABLE_1313873 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313874) BOUND_VARIABLE_1313873)))))) (let ((_let_4022 (forall ((BOUND_VARIABLE_1352592 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_1352590 |u_(-> tptp.int tptp.nat)|) (BOUND_VARIABLE_1313836 tptp.int)) (= (and (not (forall ((K3 tptp.nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 _let_1)) (ho_11056 k_11055 K3))) (ho_11139 (ho_11479 (ho_12061 k_12060 (ho_11094 BOUND_VARIABLE_1352592 BOUND_VARIABLE_1313836)) (ho_11061 BOUND_VARIABLE_1352590 BOUND_VARIABLE_1313836)) _let_1)))))) (forall ((K3 tptp.nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (not (= _let_1 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11139 (ho_11479 (ho_12061 k_12060 (ho_11094 BOUND_VARIABLE_1352592 BOUND_VARIABLE_1313836)) (ho_11061 BOUND_VARIABLE_1352590 BOUND_VARIABLE_1313836)) _let_1))) (ho_11056 k_11055 K3)))))))) (ho_11094 (ho_11878 (ho_12107 k_12106 BOUND_VARIABLE_1352592) BOUND_VARIABLE_1352590) BOUND_VARIABLE_1313836))))) (let ((_let_4023 (forall ((BOUND_VARIABLE_1313825 tptp.int) (BOUND_VARIABLE_1313826 tptp.int)) (= (ho_11094 (ho_11093 k_12108 BOUND_VARIABLE_1313825) BOUND_VARIABLE_1313826) (= BOUND_VARIABLE_1313825 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313826) BOUND_VARIABLE_1313825)))))) (let ((_let_4024 (forall ((BOUND_VARIABLE_1313816 tptp.int) (BOUND_VARIABLE_1313817 tptp.int)) (= (ho_11094 (ho_11093 k_12109 BOUND_VARIABLE_1313816) BOUND_VARIABLE_1313817) (= BOUND_VARIABLE_1313816 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313817) BOUND_VARIABLE_1313816)))))) (let ((_let_4025 (forall ((BOUND_VARIABLE_1313807 tptp.int) (BOUND_VARIABLE_1313808 tptp.int)) (= (ho_11094 (ho_11093 k_12110 BOUND_VARIABLE_1313807) BOUND_VARIABLE_1313808) (= BOUND_VARIABLE_1313807 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313808) BOUND_VARIABLE_1313807)))))) (let ((_let_4026 (forall ((BOUND_VARIABLE_1313798 tptp.int) (BOUND_VARIABLE_1313799 tptp.int)) (= (ho_11094 (ho_11093 k_12111 BOUND_VARIABLE_1313798) BOUND_VARIABLE_1313799) (= BOUND_VARIABLE_1313798 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313799) BOUND_VARIABLE_1313798)))))) (let ((_let_4027 (forall ((BOUND_VARIABLE_1313785 tptp.set_int) (BOUND_VARIABLE_1352663 |u_(-> tptp.int tptp.assn)|) (BOUND_VARIABLE_1313787 tptp.int)) (= (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313787) BOUND_VARIABLE_1313785) (not (= (ho_12029 k_12028 (ho_12027 k_12026 true)) (ho_12025 BOUND_VARIABLE_1352663 BOUND_VARIABLE_1313787)))) (ho_11094 (ho_12031 (ho_12113 k_12112 BOUND_VARIABLE_1313785) BOUND_VARIABLE_1352663) BOUND_VARIABLE_1313787))))) (let ((_let_4028 (forall ((BOUND_VARIABLE_1313776 tptp.int) (BOUND_VARIABLE_1313777 tptp.int)) (= (ho_11094 (ho_11093 k_12114 BOUND_VARIABLE_1313776) BOUND_VARIABLE_1313777) (= BOUND_VARIABLE_1313776 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313777) BOUND_VARIABLE_1313776)))))) (let ((_let_4029 (forall ((BOUND_VARIABLE_1313763 tptp.set_int) (BOUND_VARIABLE_1352694 |u_(-> tptp.int tptp.assn)|) (BOUND_VARIABLE_1313765 tptp.int)) (= (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313765) BOUND_VARIABLE_1313763) (not (= (ho_12029 k_12028 (ho_12027 k_12026 true)) (ho_12025 BOUND_VARIABLE_1352694 BOUND_VARIABLE_1313765)))) (ho_11094 (ho_12031 (ho_12113 k_12115 BOUND_VARIABLE_1313763) BOUND_VARIABLE_1352694) BOUND_VARIABLE_1313765))))) (let ((_let_4030 (forall ((BOUND_VARIABLE_1313754 tptp.int) (BOUND_VARIABLE_1313755 tptp.int)) (= (ho_11094 (ho_11093 k_12116 BOUND_VARIABLE_1313754) BOUND_VARIABLE_1313755) (= BOUND_VARIABLE_1313754 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313755) BOUND_VARIABLE_1313754)))))) (let ((_let_4031 (forall ((BOUND_VARIABLE_1313734 tptp.set_int) (BOUND_VARIABLE_1352726 |u_(-> tptp.int tptp.assn)|) (BOUND_VARIABLE_1352725 |u_(-> tptp.int tptp.assn)|) (BOUND_VARIABLE_1313737 tptp.int)) (= (ho_11094 (ho_12031 (ho_12119 (ho_12118 k_12117 BOUND_VARIABLE_1313734) BOUND_VARIABLE_1352726) BOUND_VARIABLE_1352725) BOUND_VARIABLE_1313737) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313737) BOUND_VARIABLE_1313734) (not (= (ho_12029 k_12028 (ho_12027 k_12026 true)) (ho_12029 k_12028 (ho_12122 (ho_12121 k_12120 (ho_11327 k_11329 (ho_12025 BOUND_VARIABLE_1352726 BOUND_VARIABLE_1313737))) (ho_11327 k_11329 (ho_12025 BOUND_VARIABLE_1352725 BOUND_VARIABLE_1313737))))))))))) (let ((_let_4032 (forall ((BOUND_VARIABLE_1313725 tptp.int) (BOUND_VARIABLE_1313726 tptp.int)) (= (ho_11094 (ho_11093 k_12123 BOUND_VARIABLE_1313725) BOUND_VARIABLE_1313726) (= BOUND_VARIABLE_1313725 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313726) BOUND_VARIABLE_1313725)))))) (let ((_let_4033 (forall ((BOUND_VARIABLE_1313707 tptp.set_int) (BOUND_VARIABLE_1352773 |u_(-> tptp.int tptp.code_integer)|) (BOUND_VARIABLE_1313709 tptp.int)) (= (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313709) BOUND_VARIABLE_1313707) (not (= (ho_11669 k_11668 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (ho_11667 BOUND_VARIABLE_1352773 BOUND_VARIABLE_1313709)))) (ho_11094 (ho_11672 (ho_11671 k_12124 BOUND_VARIABLE_1313707) BOUND_VARIABLE_1352773) BOUND_VARIABLE_1313709))))) (let ((_let_4034 (forall ((BOUND_VARIABLE_1313698 tptp.int) (BOUND_VARIABLE_1313699 tptp.int)) (= (ho_11094 (ho_11093 k_12125 BOUND_VARIABLE_1313698) BOUND_VARIABLE_1313699) (= BOUND_VARIABLE_1313698 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313699) BOUND_VARIABLE_1313698)))))) (let ((_let_4035 (forall ((BOUND_VARIABLE_1313680 tptp.set_int) (BOUND_VARIABLE_1352800 |u_(-> tptp.int tptp.code_integer)|) (BOUND_VARIABLE_1313682 tptp.int)) (= (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313682) BOUND_VARIABLE_1313680) (not (= (ho_11669 k_11668 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (ho_11667 BOUND_VARIABLE_1352800 BOUND_VARIABLE_1313682)))) (ho_11094 (ho_11672 (ho_11671 k_12126 BOUND_VARIABLE_1313680) BOUND_VARIABLE_1352800) BOUND_VARIABLE_1313682))))) (let ((_let_4036 (forall ((BOUND_VARIABLE_1313671 tptp.int) (BOUND_VARIABLE_1313672 tptp.int)) (= (ho_11094 (ho_11093 k_12127 BOUND_VARIABLE_1313671) BOUND_VARIABLE_1313672) (= BOUND_VARIABLE_1313671 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313672) BOUND_VARIABLE_1313671)))))) (let ((_let_4037 (forall ((BOUND_VARIABLE_1313649 tptp.set_int) (BOUND_VARIABLE_1352829 |u_(-> tptp.int tptp.code_integer)|) (BOUND_VARIABLE_1352827 |u_(-> tptp.int tptp.code_integer)|) (BOUND_VARIABLE_1313652 tptp.int)) (= (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313652) BOUND_VARIABLE_1313649) (not (= (ho_11669 k_11668 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (ho_12130 (ho_12129 k_12128 (ho_11667 BOUND_VARIABLE_1352829 BOUND_VARIABLE_1313652)) (ho_11667 BOUND_VARIABLE_1352827 BOUND_VARIABLE_1313652))))) (ho_11094 (ho_11672 (ho_12133 (ho_12132 k_12131 BOUND_VARIABLE_1313649) BOUND_VARIABLE_1352829) BOUND_VARIABLE_1352827) BOUND_VARIABLE_1313652))))) (let ((_let_4038 (forall ((BOUND_VARIABLE_1313640 tptp.int) (BOUND_VARIABLE_1313641 tptp.int)) (= (ho_11094 (ho_11093 k_12134 BOUND_VARIABLE_1313640) BOUND_VARIABLE_1313641) (= BOUND_VARIABLE_1313640 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313641) BOUND_VARIABLE_1313640)))))) (let ((_let_4039 (forall ((BOUND_VARIABLE_1313622 tptp.set_int) (BOUND_VARIABLE_1352875 |u_(-> tptp.int tptp.rat)|) (BOUND_VARIABLE_1313624 tptp.int)) (= (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313624) BOUND_VARIABLE_1313622) (not (= (ho_11498 k_11497 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11127 BOUND_VARIABLE_1352875 BOUND_VARIABLE_1313624)))) (ho_11094 (ho_11665 (ho_11664 k_12135 BOUND_VARIABLE_1313622) BOUND_VARIABLE_1352875) BOUND_VARIABLE_1313624))))) (let ((_let_4040 (forall ((BOUND_VARIABLE_1313613 tptp.int) (BOUND_VARIABLE_1313614 tptp.int)) (= (ho_11094 (ho_11093 k_12136 BOUND_VARIABLE_1313613) BOUND_VARIABLE_1313614) (= BOUND_VARIABLE_1313613 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313614) BOUND_VARIABLE_1313613)))))) (let ((_let_4041 (forall ((BOUND_VARIABLE_1313595 tptp.set_int) (BOUND_VARIABLE_1352902 |u_(-> tptp.int tptp.rat)|) (BOUND_VARIABLE_1313597 tptp.int)) (= (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313597) BOUND_VARIABLE_1313595) (not (= (ho_11498 k_11497 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11127 BOUND_VARIABLE_1352902 BOUND_VARIABLE_1313597)))) (ho_11094 (ho_11665 (ho_11664 k_12137 BOUND_VARIABLE_1313595) BOUND_VARIABLE_1352902) BOUND_VARIABLE_1313597))))) (let ((_let_4042 (forall ((BOUND_VARIABLE_1313586 tptp.int) (BOUND_VARIABLE_1313587 tptp.int)) (= (ho_11094 (ho_11093 k_12138 BOUND_VARIABLE_1313586) BOUND_VARIABLE_1313587) (= BOUND_VARIABLE_1313586 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313587) BOUND_VARIABLE_1313586)))))) (let ((_let_4043 (forall ((BOUND_VARIABLE_1313562 tptp.set_int) (BOUND_VARIABLE_1352931 |u_(-> tptp.int tptp.rat)|) (BOUND_VARIABLE_1352929 |u_(-> tptp.int tptp.rat)|) (BOUND_VARIABLE_1313565 tptp.int)) (= (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313565) BOUND_VARIABLE_1313562) (not (= (ho_11498 k_11497 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11508 (ho_11511 (ho_12143 (ho_12142 (ho_12141 k_12140 k_11502) (ho_11506 (ho_11505 k_11504 k_11502) k_11116)) k_12139) (ho_11127 BOUND_VARIABLE_1352931 BOUND_VARIABLE_1313565)) (ho_11127 BOUND_VARIABLE_1352929 BOUND_VARIABLE_1313565))))) (ho_11094 (ho_11665 (ho_12146 (ho_12145 k_12144 BOUND_VARIABLE_1313562) BOUND_VARIABLE_1352931) BOUND_VARIABLE_1352929) BOUND_VARIABLE_1313565))))) (let ((_let_4044 (forall ((BOUND_VARIABLE_1313553 tptp.int) (BOUND_VARIABLE_1313554 tptp.int)) (= (ho_11094 (ho_11093 k_12147 BOUND_VARIABLE_1313553) BOUND_VARIABLE_1313554) (= BOUND_VARIABLE_1313553 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313554) BOUND_VARIABLE_1313553)))))) (let ((_let_4045 (forall ((BOUND_VARIABLE_1313535 tptp.set_int) (BOUND_VARIABLE_1352987 |u_(-> tptp.int tptp.code_integer)|) (BOUND_VARIABLE_1313537 tptp.int)) (= (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313537) BOUND_VARIABLE_1313535) (not (= (ho_11669 k_11668 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11667 BOUND_VARIABLE_1352987 BOUND_VARIABLE_1313537)))) (ho_11094 (ho_11672 (ho_11671 k_12148 BOUND_VARIABLE_1313535) BOUND_VARIABLE_1352987) BOUND_VARIABLE_1313537))))) (let ((_let_4046 (forall ((BOUND_VARIABLE_1313526 tptp.int) (BOUND_VARIABLE_1313527 tptp.int)) (= (ho_11094 (ho_11093 k_12149 BOUND_VARIABLE_1313526) BOUND_VARIABLE_1313527) (= BOUND_VARIABLE_1313526 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313527) BOUND_VARIABLE_1313526)))))) (let ((_let_4047 (forall ((BOUND_VARIABLE_1313508 tptp.set_int) (BOUND_VARIABLE_1353014 |u_(-> tptp.int tptp.code_integer)|) (BOUND_VARIABLE_1313510 tptp.int)) (= (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313510) BOUND_VARIABLE_1313508) (not (= (ho_11669 k_11668 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11667 BOUND_VARIABLE_1353014 BOUND_VARIABLE_1313510)))) (ho_11094 (ho_11672 (ho_11671 k_12150 BOUND_VARIABLE_1313508) BOUND_VARIABLE_1353014) BOUND_VARIABLE_1313510))))) (let ((_let_4048 (forall ((BOUND_VARIABLE_1313499 tptp.int) (BOUND_VARIABLE_1313500 tptp.int)) (= (ho_11094 (ho_11093 k_12151 BOUND_VARIABLE_1313499) BOUND_VARIABLE_1313500) (= BOUND_VARIABLE_1313499 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313500) BOUND_VARIABLE_1313499)))))) (let ((_let_4049 (forall ((BOUND_VARIABLE_1313477 tptp.set_int) (BOUND_VARIABLE_1353043 |u_(-> tptp.int tptp.code_integer)|) (BOUND_VARIABLE_1353041 |u_(-> tptp.int tptp.code_integer)|) (BOUND_VARIABLE_1313480 tptp.int)) (= (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313480) BOUND_VARIABLE_1313477) (not (= (ho_11669 k_11668 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_12130 (ho_12129 (ho_12161 (ho_12160 (ho_12159 k_12158 k_12153) (ho_12157 (ho_12156 k_12155 k_12153) k_12152)) k_11057) (ho_11667 BOUND_VARIABLE_1353043 BOUND_VARIABLE_1313480)) (ho_11667 BOUND_VARIABLE_1353041 BOUND_VARIABLE_1313480))))) (ho_11094 (ho_11672 (ho_12133 (ho_12132 k_12162 BOUND_VARIABLE_1313477) BOUND_VARIABLE_1353043) BOUND_VARIABLE_1353041) BOUND_VARIABLE_1313480))))) (let ((_let_4050 (forall ((BOUND_VARIABLE_1313468 tptp.int) (BOUND_VARIABLE_1313469 tptp.int)) (= (ho_11094 (ho_11093 k_12163 BOUND_VARIABLE_1313468) BOUND_VARIABLE_1313469) (= BOUND_VARIABLE_1313468 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313469) BOUND_VARIABLE_1313468)))))) (let ((_let_4051 (forall ((BOUND_VARIABLE_1313459 tptp.int) (BOUND_VARIABLE_1313460 tptp.int)) (= (ho_11094 (ho_11093 k_12164 BOUND_VARIABLE_1313459) BOUND_VARIABLE_1313460) (= BOUND_VARIABLE_1313459 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313460) BOUND_VARIABLE_1313459)))))) (let ((_let_4052 (forall ((BOUND_VARIABLE_1313450 tptp.int) (BOUND_VARIABLE_1313451 tptp.int)) (= (ho_11094 (ho_11093 k_12165 BOUND_VARIABLE_1313450) BOUND_VARIABLE_1313451) (= BOUND_VARIABLE_1313450 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313451) BOUND_VARIABLE_1313450)))))) (let ((_let_4053 (forall ((BOUND_VARIABLE_1313441 tptp.int) (BOUND_VARIABLE_1313442 tptp.int)) (= (ho_11094 (ho_11093 k_12166 BOUND_VARIABLE_1313441) BOUND_VARIABLE_1313442) (= BOUND_VARIABLE_1313441 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313442) BOUND_VARIABLE_1313441)))))) (let ((_let_4054 (forall ((BOUND_VARIABLE_1313432 tptp.int) (BOUND_VARIABLE_1313433 tptp.int)) (= (ho_11094 (ho_11093 k_12167 BOUND_VARIABLE_1313432) BOUND_VARIABLE_1313433) (= BOUND_VARIABLE_1313432 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313433) BOUND_VARIABLE_1313432)))))) (let ((_let_4055 (forall ((BOUND_VARIABLE_1313419 tptp.set_Code_integer) (BOUND_VARIABLE_1353153 |u_(-> tptp.nat tptp.code_integer Bool)|) (BOUND_VARIABLE_1313421 tptp.nat) (BOUND_VARIABLE_1313422 tptp.code_integer)) (= (ho_11564 (ho_12168 (ho_12171 (ho_12170 k_12169 BOUND_VARIABLE_1313419) BOUND_VARIABLE_1353153) BOUND_VARIABLE_1313421) BOUND_VARIABLE_1313422) (and (ho_11567 (ho_11566 k_11565 BOUND_VARIABLE_1313422) BOUND_VARIABLE_1313419) (ho_11564 (ho_12168 BOUND_VARIABLE_1353153 BOUND_VARIABLE_1313421) BOUND_VARIABLE_1313422)))))) (let ((_let_4056 (forall ((BOUND_VARIABLE_1353181 |u_(-> tptp.nat tptp.code_integer tptp.nat)|) (BOUND_VARIABLE_1313411 tptp.code_integer) (BOUND_VARIABLE_1313412 tptp.nat)) (= (ho_11139 (ho_12175 (ho_12174 k_12173 BOUND_VARIABLE_1353181) BOUND_VARIABLE_1313411) BOUND_VARIABLE_1313412) (ho_12176 (ho_12172 BOUND_VARIABLE_1353181 BOUND_VARIABLE_1313412) BOUND_VARIABLE_1313411))))) (let ((_let_4057 (forall ((BOUND_VARIABLE_1313397 tptp.set_nat) (BOUND_VARIABLE_1353207 |u_(-> tptp.nat tptp.code_integer Bool)|) (BOUND_VARIABLE_1313399 tptp.code_integer) (BOUND_VARIABLE_1313400 tptp.nat)) (= (ho_11054 (ho_11551 (ho_12179 (ho_12178 k_12177 BOUND_VARIABLE_1313397) BOUND_VARIABLE_1353207) BOUND_VARIABLE_1313399) BOUND_VARIABLE_1313400) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1313400) BOUND_VARIABLE_1313397) (ho_11564 (ho_12168 BOUND_VARIABLE_1353207 BOUND_VARIABLE_1313400) BOUND_VARIABLE_1313399)))))) (let ((_let_4058 (forall ((BOUND_VARIABLE_1313388 tptp.int) (BOUND_VARIABLE_1313389 tptp.int)) (= (ho_11094 (ho_11093 k_12180 BOUND_VARIABLE_1313388) BOUND_VARIABLE_1313389) (= BOUND_VARIABLE_1313388 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313389) BOUND_VARIABLE_1313388)))))) (let ((_let_4059 (forall ((BOUND_VARIABLE_1313375 tptp.set_int) (BOUND_VARIABLE_1353243 |u_(-> tptp.nat tptp.int Bool)|) (BOUND_VARIABLE_1313377 tptp.nat) (BOUND_VARIABLE_1313378 tptp.int)) (= (ho_11094 (ho_11765 (ho_12183 (ho_12182 k_12181 BOUND_VARIABLE_1313375) BOUND_VARIABLE_1353243) BOUND_VARIABLE_1313377) BOUND_VARIABLE_1313378) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313378) BOUND_VARIABLE_1313375) (ho_11094 (ho_11765 BOUND_VARIABLE_1353243 BOUND_VARIABLE_1313377) BOUND_VARIABLE_1313378)))))) (let ((_let_4060 (forall ((BOUND_VARIABLE_1353269 |u_(-> tptp.nat tptp.int tptp.nat)|) (BOUND_VARIABLE_1313367 tptp.int) (BOUND_VARIABLE_1313368 tptp.nat)) (= (ho_11139 (ho_12187 (ho_12186 k_12185 BOUND_VARIABLE_1353269) BOUND_VARIABLE_1313367) BOUND_VARIABLE_1313368) (ho_11061 (ho_12184 BOUND_VARIABLE_1353269 BOUND_VARIABLE_1313368) BOUND_VARIABLE_1313367))))) (let ((_let_4061 (forall ((BOUND_VARIABLE_1313353 tptp.set_nat) (BOUND_VARIABLE_1353292 |u_(-> tptp.nat tptp.int Bool)|) (BOUND_VARIABLE_1313355 tptp.int) (BOUND_VARIABLE_1313356 tptp.nat)) (= (ho_11054 (ho_11574 (ho_12190 (ho_12189 k_12188 BOUND_VARIABLE_1313353) BOUND_VARIABLE_1353292) BOUND_VARIABLE_1313355) BOUND_VARIABLE_1313356) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1313356) BOUND_VARIABLE_1313353) (ho_11094 (ho_11765 BOUND_VARIABLE_1353292 BOUND_VARIABLE_1313356) BOUND_VARIABLE_1313355)))))) (let ((_let_4062 (forall ((BOUND_VARIABLE_1313340 tptp.set_o) (BOUND_VARIABLE_1353319 |u_(-> tptp.nat Bool Bool)|) (BOUND_VARIABLE_1313342 tptp.nat) (BOUND_VARIABLE_1313343 Bool)) (= (ho_11194 (ho_12191 (ho_12194 (ho_12193 k_12192 BOUND_VARIABLE_1313340) BOUND_VARIABLE_1353319) BOUND_VARIABLE_1313342) BOUND_VARIABLE_1313343) (and (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1313343) BOUND_VARIABLE_1313340) (ho_11194 (ho_12191 BOUND_VARIABLE_1353319 BOUND_VARIABLE_1313342) BOUND_VARIABLE_1313343)))))) (let ((_let_4063 (forall ((BOUND_VARIABLE_1353347 |u_(-> tptp.nat Bool tptp.nat)|) (BOUND_VARIABLE_1313332 Bool) (BOUND_VARIABLE_1313333 tptp.nat)) (= (ho_11139 (ho_12198 (ho_12197 k_12196 BOUND_VARIABLE_1353347) BOUND_VARIABLE_1313332) BOUND_VARIABLE_1313333) (ho_12199 (ho_12195 BOUND_VARIABLE_1353347 BOUND_VARIABLE_1313333) BOUND_VARIABLE_1313332))))) (let ((_let_4064 (forall ((BOUND_VARIABLE_1313318 tptp.set_nat) (BOUND_VARIABLE_1353373 |u_(-> tptp.nat Bool Bool)|) (BOUND_VARIABLE_1313320 Bool) (BOUND_VARIABLE_1313321 tptp.nat)) (= (ho_11054 (ho_11592 (ho_12202 (ho_12201 k_12200 BOUND_VARIABLE_1313318) BOUND_VARIABLE_1353373) BOUND_VARIABLE_1313320) BOUND_VARIABLE_1313321) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1313321) BOUND_VARIABLE_1313318) (ho_11194 (ho_12191 BOUND_VARIABLE_1353373 BOUND_VARIABLE_1313321) BOUND_VARIABLE_1313320)))))) (let ((_let_4065 (forall ((BOUND_VARIABLE_1313309 tptp.int) (BOUND_VARIABLE_1313310 tptp.int)) (= (ho_11094 (ho_11093 k_12203 BOUND_VARIABLE_1313309) BOUND_VARIABLE_1313310) (= BOUND_VARIABLE_1313309 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313310) BOUND_VARIABLE_1313309)))))) (let ((_let_4066 (forall ((BOUND_VARIABLE_1313296 tptp.set_int) (BOUND_VARIABLE_1353409 |u_(-> tptp.code_integer tptp.int Bool)|) (BOUND_VARIABLE_1313298 tptp.code_integer) (BOUND_VARIABLE_1313299 tptp.int)) (= (ho_11094 (ho_11619 (ho_11622 (ho_11621 k_12204 BOUND_VARIABLE_1313296) BOUND_VARIABLE_1353409) BOUND_VARIABLE_1313298) BOUND_VARIABLE_1313299) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313299) BOUND_VARIABLE_1313296) (ho_11094 (ho_11619 BOUND_VARIABLE_1353409 BOUND_VARIABLE_1313298) BOUND_VARIABLE_1313299)))))) (let ((_let_4067 (forall ((BOUND_VARIABLE_1353427 |u_(-> tptp.code_integer tptp.int tptp.int)|) (BOUND_VARIABLE_1313288 tptp.int) (BOUND_VARIABLE_1313289 tptp.code_integer)) (= (ho_12154 (ho_12208 (ho_12207 k_12206 BOUND_VARIABLE_1353427) BOUND_VARIABLE_1313288) BOUND_VARIABLE_1313289) (ho_11059 (ho_12205 BOUND_VARIABLE_1353427 BOUND_VARIABLE_1313289) BOUND_VARIABLE_1313288))))) (let ((_let_4068 (forall ((BOUND_VARIABLE_1313274 tptp.set_Code_integer) (BOUND_VARIABLE_1353450 |u_(-> tptp.code_integer tptp.int Bool)|) (BOUND_VARIABLE_1313276 tptp.int) (BOUND_VARIABLE_1313277 tptp.code_integer)) (= (ho_11564 (ho_11560 (ho_12211 (ho_12210 k_12209 BOUND_VARIABLE_1313274) BOUND_VARIABLE_1353450) BOUND_VARIABLE_1313276) BOUND_VARIABLE_1313277) (and (ho_11567 (ho_11566 k_11565 BOUND_VARIABLE_1313277) BOUND_VARIABLE_1313274) (ho_11094 (ho_11619 BOUND_VARIABLE_1353450 BOUND_VARIABLE_1313277) BOUND_VARIABLE_1313276)))))) (let ((_let_4069 (forall ((BOUND_VARIABLE_1313265 tptp.int) (BOUND_VARIABLE_1313266 tptp.int)) (= (ho_11094 (ho_11093 k_12212 BOUND_VARIABLE_1313265) BOUND_VARIABLE_1313266) (= BOUND_VARIABLE_1313265 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313266) BOUND_VARIABLE_1313265)))))) (let ((_let_4070 (forall ((BOUND_VARIABLE_1313252 tptp.set_int) (BOUND_VARIABLE_1353486 |u_(-> Bool tptp.int Bool)|) (BOUND_VARIABLE_1313254 Bool) (BOUND_VARIABLE_1313255 tptp.int)) (= (ho_11094 (ho_11588 (ho_11591 (ho_11590 k_12213 BOUND_VARIABLE_1313252) BOUND_VARIABLE_1353486) BOUND_VARIABLE_1313254) BOUND_VARIABLE_1313255) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313255) BOUND_VARIABLE_1313252) (ho_11094 (ho_11588 BOUND_VARIABLE_1353486 BOUND_VARIABLE_1313254) BOUND_VARIABLE_1313255)))))) (let ((_let_4071 (forall ((BOUND_VARIABLE_1353504 |u_(-> Bool tptp.int tptp.int)|) (BOUND_VARIABLE_1313244 tptp.int) (BOUND_VARIABLE_1313245 Bool)) (= (ho_12218 (ho_12217 (ho_12216 k_12215 BOUND_VARIABLE_1353504) BOUND_VARIABLE_1313244) BOUND_VARIABLE_1313245) (ho_11059 (ho_12214 BOUND_VARIABLE_1353504 BOUND_VARIABLE_1313245) BOUND_VARIABLE_1313244))))) (let ((_let_4072 (forall ((BOUND_VARIABLE_1313230 tptp.set_o) (BOUND_VARIABLE_1353530 |u_(-> Bool tptp.int Bool)|) (BOUND_VARIABLE_1313232 tptp.int) (BOUND_VARIABLE_1313233 Bool)) (= (ho_11194 (ho_11579 (ho_12221 (ho_12220 k_12219 BOUND_VARIABLE_1313230) BOUND_VARIABLE_1353530) BOUND_VARIABLE_1313232) BOUND_VARIABLE_1313233) (and (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1313233) BOUND_VARIABLE_1313230) (ho_11094 (ho_11588 BOUND_VARIABLE_1353530 BOUND_VARIABLE_1313233) BOUND_VARIABLE_1313232)))))) (let ((_let_4073 (forall ((BOUND_VARIABLE_1313217 tptp.set_nat) (BOUND_VARIABLE_1353556 |u_(-> tptp.code_integer tptp.nat Bool)|) (BOUND_VARIABLE_1313219 tptp.code_integer) (BOUND_VARIABLE_1313220 tptp.nat)) (= (ho_11054 (ho_11551 (ho_11554 (ho_11553 k_12222 BOUND_VARIABLE_1313217) BOUND_VARIABLE_1353556) BOUND_VARIABLE_1313219) BOUND_VARIABLE_1313220) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1313220) BOUND_VARIABLE_1313217) (ho_11054 (ho_11551 BOUND_VARIABLE_1353556 BOUND_VARIABLE_1313219) BOUND_VARIABLE_1313220)))))) (let ((_let_4074 (forall ((BOUND_VARIABLE_1353574 |u_(-> tptp.code_integer tptp.nat tptp.int)|) (BOUND_VARIABLE_1313209 tptp.nat) (BOUND_VARIABLE_1313210 tptp.code_integer)) (= (ho_12154 (ho_12226 (ho_12225 k_12224 BOUND_VARIABLE_1353574) BOUND_VARIABLE_1313209) BOUND_VARIABLE_1313210) (ho_11056 (ho_12223 BOUND_VARIABLE_1353574 BOUND_VARIABLE_1313210) BOUND_VARIABLE_1313209))))) (let ((_let_4075 (forall ((BOUND_VARIABLE_1313195 tptp.set_Code_integer) (BOUND_VARIABLE_1353597 |u_(-> tptp.code_integer tptp.nat Bool)|) (BOUND_VARIABLE_1313197 tptp.nat) (BOUND_VARIABLE_1313198 tptp.code_integer)) (= (ho_11564 (ho_12168 (ho_12229 (ho_12228 k_12227 BOUND_VARIABLE_1313195) BOUND_VARIABLE_1353597) BOUND_VARIABLE_1313197) BOUND_VARIABLE_1313198) (and (ho_11567 (ho_11566 k_11565 BOUND_VARIABLE_1313198) BOUND_VARIABLE_1313195) (ho_11054 (ho_11551 BOUND_VARIABLE_1353597 BOUND_VARIABLE_1313198) BOUND_VARIABLE_1313197)))))) (let ((_let_4076 (forall ((BOUND_VARIABLE_1313182 tptp.set_nat) (BOUND_VARIABLE_1353623 |u_(-> Bool tptp.nat Bool)|) (BOUND_VARIABLE_1313184 Bool) (BOUND_VARIABLE_1313185 tptp.nat)) (= (ho_11054 (ho_11592 (ho_11595 (ho_11594 k_12230 BOUND_VARIABLE_1313182) BOUND_VARIABLE_1353623) BOUND_VARIABLE_1313184) BOUND_VARIABLE_1313185) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1313185) BOUND_VARIABLE_1313182) (ho_11054 (ho_11592 BOUND_VARIABLE_1353623 BOUND_VARIABLE_1313184) BOUND_VARIABLE_1313185)))))) (let ((_let_4077 (forall ((BOUND_VARIABLE_1353641 |u_(-> Bool tptp.nat tptp.int)|) (BOUND_VARIABLE_1313174 tptp.nat) (BOUND_VARIABLE_1313175 Bool)) (= (ho_12218 (ho_12234 (ho_12233 k_12232 BOUND_VARIABLE_1353641) BOUND_VARIABLE_1313174) BOUND_VARIABLE_1313175) (ho_11056 (ho_12231 BOUND_VARIABLE_1353641 BOUND_VARIABLE_1313175) BOUND_VARIABLE_1313174))))) (let ((_let_4078 (forall ((BOUND_VARIABLE_1313160 tptp.set_o) (BOUND_VARIABLE_1353664 |u_(-> Bool tptp.nat Bool)|) (BOUND_VARIABLE_1313162 tptp.nat) (BOUND_VARIABLE_1313163 Bool)) (= (ho_11194 (ho_12191 (ho_12237 (ho_12236 k_12235 BOUND_VARIABLE_1313160) BOUND_VARIABLE_1353664) BOUND_VARIABLE_1313162) BOUND_VARIABLE_1313163) (and (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1313163) BOUND_VARIABLE_1313160) (ho_11054 (ho_11592 BOUND_VARIABLE_1353664 BOUND_VARIABLE_1313163) BOUND_VARIABLE_1313162)))))) (let ((_let_4079 (forall ((BOUND_VARIABLE_1313147 tptp.set_nat) (BOUND_VARIABLE_1353690 |u_(-> tptp.code_integer tptp.nat Bool)|) (BOUND_VARIABLE_1313149 tptp.code_integer) (BOUND_VARIABLE_1313150 tptp.nat)) (= (ho_11054 (ho_11551 (ho_11554 (ho_11553 k_12238 BOUND_VARIABLE_1313147) BOUND_VARIABLE_1353690) BOUND_VARIABLE_1313149) BOUND_VARIABLE_1313150) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1313150) BOUND_VARIABLE_1313147) (ho_11054 (ho_11551 BOUND_VARIABLE_1353690 BOUND_VARIABLE_1313149) BOUND_VARIABLE_1313150)))))) (let ((_let_4080 (forall ((BOUND_VARIABLE_1353707 |u_(-> tptp.code_integer tptp.nat tptp.nat)|) (BOUND_VARIABLE_1313139 tptp.nat) (BOUND_VARIABLE_1313140 tptp.code_integer)) (= (ho_12176 (ho_12172 (ho_12240 k_12239 BOUND_VARIABLE_1353707) BOUND_VARIABLE_1313139) BOUND_VARIABLE_1313140) (ho_11139 (ho_12175 BOUND_VARIABLE_1353707 BOUND_VARIABLE_1313140) BOUND_VARIABLE_1313139))))) (let ((_let_4081 (forall ((BOUND_VARIABLE_1313125 tptp.set_Code_integer) (BOUND_VARIABLE_1353725 |u_(-> tptp.code_integer tptp.nat Bool)|) (BOUND_VARIABLE_1313127 tptp.nat) (BOUND_VARIABLE_1313128 tptp.code_integer)) (= (ho_11564 (ho_12168 (ho_12229 (ho_12228 k_12241 BOUND_VARIABLE_1313125) BOUND_VARIABLE_1353725) BOUND_VARIABLE_1313127) BOUND_VARIABLE_1313128) (and (ho_11567 (ho_11566 k_11565 BOUND_VARIABLE_1313128) BOUND_VARIABLE_1313125) (ho_11054 (ho_11551 BOUND_VARIABLE_1353725 BOUND_VARIABLE_1313128) BOUND_VARIABLE_1313127)))))) (let ((_let_4082 (forall ((BOUND_VARIABLE_1313116 tptp.int) (BOUND_VARIABLE_1313117 tptp.int)) (= (ho_11094 (ho_11093 k_12242 BOUND_VARIABLE_1313116) BOUND_VARIABLE_1313117) (= BOUND_VARIABLE_1313116 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1313117) BOUND_VARIABLE_1313116)))))) (let ((_let_4083 (forall ((BOUND_VARIABLE_1313103 tptp.set_nat) (BOUND_VARIABLE_1353753 |u_(-> tptp.int tptp.nat Bool)|) (BOUND_VARIABLE_1313105 tptp.int) (BOUND_VARIABLE_1313106 tptp.nat)) (= (ho_11054 (ho_11574 (ho_11577 (ho_11576 k_12243 BOUND_VARIABLE_1313103) BOUND_VARIABLE_1353753) BOUND_VARIABLE_1313105) BOUND_VARIABLE_1313106) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1313106) BOUND_VARIABLE_1313103) (ho_11054 (ho_11574 BOUND_VARIABLE_1353753 BOUND_VARIABLE_1313105) BOUND_VARIABLE_1313106)))))) (let ((_let_4084 (forall ((BOUND_VARIABLE_1353770 |u_(-> tptp.int tptp.nat tptp.nat)|) (BOUND_VARIABLE_1313095 tptp.nat) (BOUND_VARIABLE_1313096 tptp.int)) (= (ho_11061 (ho_12184 (ho_12245 k_12244 BOUND_VARIABLE_1353770) BOUND_VARIABLE_1313095) BOUND_VARIABLE_1313096) (ho_11139 (ho_12187 BOUND_VARIABLE_1353770 BOUND_VARIABLE_1313096) BOUND_VARIABLE_1313095))))) (let ((_let_4085 (forall ((BOUND_VARIABLE_1313081 tptp.set_int) (BOUND_VARIABLE_1353788 |u_(-> tptp.int tptp.nat Bool)|) (BOUND_VARIABLE_1313083 tptp.nat) (BOUND_VARIABLE_1313084 tptp.int)) (= (ho_11094 (ho_11765 (ho_11764 (ho_11763 k_12246 BOUND_VARIABLE_1313081) BOUND_VARIABLE_1353788) BOUND_VARIABLE_1313083) BOUND_VARIABLE_1313084) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1313084) BOUND_VARIABLE_1313081) (ho_11054 (ho_11574 BOUND_VARIABLE_1353788 BOUND_VARIABLE_1313084) BOUND_VARIABLE_1313083)))))) (let ((_let_4086 (forall ((BOUND_VARIABLE_1313068 tptp.set_nat) (BOUND_VARIABLE_1353806 |u_(-> Bool tptp.nat Bool)|) (BOUND_VARIABLE_1313070 Bool) (BOUND_VARIABLE_1313071 tptp.nat)) (= (ho_11054 (ho_11592 (ho_11595 (ho_11594 k_12247 BOUND_VARIABLE_1313068) BOUND_VARIABLE_1353806) BOUND_VARIABLE_1313070) BOUND_VARIABLE_1313071) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1313071) BOUND_VARIABLE_1313068) (ho_11054 (ho_11592 BOUND_VARIABLE_1353806 BOUND_VARIABLE_1313070) BOUND_VARIABLE_1313071)))))) (let ((_let_4087 (forall ((BOUND_VARIABLE_1353823 |u_(-> Bool tptp.nat tptp.nat)|) (BOUND_VARIABLE_1313060 tptp.nat) (BOUND_VARIABLE_1313061 Bool)) (= (ho_12199 (ho_12195 (ho_12249 k_12248 BOUND_VARIABLE_1353823) BOUND_VARIABLE_1313060) BOUND_VARIABLE_1313061) (ho_11139 (ho_12198 BOUND_VARIABLE_1353823 BOUND_VARIABLE_1313061) BOUND_VARIABLE_1313060))))) (let ((_let_4088 (forall ((BOUND_VARIABLE_1313046 tptp.set_o) (BOUND_VARIABLE_1353841 |u_(-> Bool tptp.nat Bool)|) (BOUND_VARIABLE_1313048 tptp.nat) (BOUND_VARIABLE_1313049 Bool)) (= (ho_11194 (ho_12191 (ho_12237 (ho_12236 k_12250 BOUND_VARIABLE_1313046) BOUND_VARIABLE_1353841) BOUND_VARIABLE_1313048) BOUND_VARIABLE_1313049) (and (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1313049) BOUND_VARIABLE_1313046) (ho_11054 (ho_11592 BOUND_VARIABLE_1353841 BOUND_VARIABLE_1313049) BOUND_VARIABLE_1313048)))))) (let ((_let_4089 (forall ((BOUND_VARIABLE_1313033 tptp.set_nat) (BOUND_VARIABLE_1353859 |u_(-> tptp.nat tptp.nat Bool)|) (BOUND_VARIABLE_1313035 tptp.nat) (BOUND_VARIABLE_1313036 tptp.nat)) (= (ho_11054 (ho_11053 (ho_12253 (ho_12252 k_12251 BOUND_VARIABLE_1313033) BOUND_VARIABLE_1353859) BOUND_VARIABLE_1313035) BOUND_VARIABLE_1313036) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1313036) BOUND_VARIABLE_1313033) (ho_11054 (ho_11053 BOUND_VARIABLE_1353859 BOUND_VARIABLE_1313035) BOUND_VARIABLE_1313036)))))) (let ((_let_4090 (forall ((BOUND_VARIABLE_1353884 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1313025 tptp.nat) (BOUND_VARIABLE_1313026 tptp.nat)) (= (ho_11139 (ho_11479 (ho_12255 k_12254 BOUND_VARIABLE_1353884) BOUND_VARIABLE_1313025) BOUND_VARIABLE_1313026) (ho_11139 (ho_11479 BOUND_VARIABLE_1353884 BOUND_VARIABLE_1313026) BOUND_VARIABLE_1313025))))) (let ((_let_4091 (forall ((BOUND_VARIABLE_1313011 tptp.set_nat) (BOUND_VARIABLE_1353902 |u_(-> tptp.nat tptp.nat Bool)|) (BOUND_VARIABLE_1313013 tptp.nat) (BOUND_VARIABLE_1313014 tptp.nat)) (= (ho_11054 (ho_11053 (ho_12253 (ho_12252 k_12256 BOUND_VARIABLE_1313011) BOUND_VARIABLE_1353902) BOUND_VARIABLE_1313013) BOUND_VARIABLE_1313014) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1313014) BOUND_VARIABLE_1313011) (ho_11054 (ho_11053 BOUND_VARIABLE_1353902 BOUND_VARIABLE_1313014) BOUND_VARIABLE_1313013)))))) (let ((_let_4092 (forall ((BOUND_VARIABLE_1312998 tptp.set_Code_integer) (BOUND_VARIABLE_1353920 |u_(-> tptp.nat tptp.code_integer Bool)|) (BOUND_VARIABLE_1313000 tptp.nat) (BOUND_VARIABLE_1313001 tptp.code_integer)) (= (ho_11564 (ho_12168 (ho_12171 (ho_12170 k_12257 BOUND_VARIABLE_1312998) BOUND_VARIABLE_1353920) BOUND_VARIABLE_1313000) BOUND_VARIABLE_1313001) (and (ho_11567 (ho_11566 k_11565 BOUND_VARIABLE_1313001) BOUND_VARIABLE_1312998) (ho_11564 (ho_12168 BOUND_VARIABLE_1353920 BOUND_VARIABLE_1313000) BOUND_VARIABLE_1313001)))))) (let ((_let_4093 (forall ((BOUND_VARIABLE_1353937 |u_(-> tptp.nat tptp.code_integer tptp.nat)|) (BOUND_VARIABLE_1312990 tptp.code_integer) (BOUND_VARIABLE_1312991 tptp.nat)) (= (ho_11139 (ho_12175 (ho_12174 k_12258 BOUND_VARIABLE_1353937) BOUND_VARIABLE_1312990) BOUND_VARIABLE_1312991) (ho_12176 (ho_12172 BOUND_VARIABLE_1353937 BOUND_VARIABLE_1312991) BOUND_VARIABLE_1312990))))) (let ((_let_4094 (forall ((BOUND_VARIABLE_1312976 tptp.set_nat) (BOUND_VARIABLE_1353951 |u_(-> tptp.nat tptp.code_integer Bool)|) (BOUND_VARIABLE_1312978 tptp.code_integer) (BOUND_VARIABLE_1312979 tptp.nat)) (= (ho_11054 (ho_11551 (ho_12179 (ho_12178 k_12259 BOUND_VARIABLE_1312976) BOUND_VARIABLE_1353951) BOUND_VARIABLE_1312978) BOUND_VARIABLE_1312979) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1312979) BOUND_VARIABLE_1312976) (ho_11564 (ho_12168 BOUND_VARIABLE_1353951 BOUND_VARIABLE_1312979) BOUND_VARIABLE_1312978)))))) (let ((_let_4095 (forall ((BOUND_VARIABLE_1312967 tptp.int) (BOUND_VARIABLE_1312968 tptp.int)) (= (ho_11094 (ho_11093 k_12260 BOUND_VARIABLE_1312967) BOUND_VARIABLE_1312968) (= BOUND_VARIABLE_1312967 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312968) BOUND_VARIABLE_1312967)))))) (let ((_let_4096 (forall ((BOUND_VARIABLE_1312954 tptp.set_int) (BOUND_VARIABLE_1353979 |u_(-> tptp.nat tptp.int Bool)|) (BOUND_VARIABLE_1312956 tptp.nat) (BOUND_VARIABLE_1312957 tptp.int)) (= (ho_11094 (ho_11765 (ho_12183 (ho_12182 k_12261 BOUND_VARIABLE_1312954) BOUND_VARIABLE_1353979) BOUND_VARIABLE_1312956) BOUND_VARIABLE_1312957) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1312957) BOUND_VARIABLE_1312954) (ho_11094 (ho_11765 BOUND_VARIABLE_1353979 BOUND_VARIABLE_1312956) BOUND_VARIABLE_1312957)))))) (let ((_let_4097 (forall ((BOUND_VARIABLE_1353996 |u_(-> tptp.nat tptp.int tptp.nat)|) (BOUND_VARIABLE_1312946 tptp.int) (BOUND_VARIABLE_1312947 tptp.nat)) (= (ho_11139 (ho_12187 (ho_12186 k_12262 BOUND_VARIABLE_1353996) BOUND_VARIABLE_1312946) BOUND_VARIABLE_1312947) (ho_11061 (ho_12184 BOUND_VARIABLE_1353996 BOUND_VARIABLE_1312947) BOUND_VARIABLE_1312946))))) (let ((_let_4098 (forall ((BOUND_VARIABLE_1312932 tptp.set_nat) (BOUND_VARIABLE_1354010 |u_(-> tptp.nat tptp.int Bool)|) (BOUND_VARIABLE_1312934 tptp.int) (BOUND_VARIABLE_1312935 tptp.nat)) (= (ho_11054 (ho_11574 (ho_12190 (ho_12189 k_12263 BOUND_VARIABLE_1312932) BOUND_VARIABLE_1354010) BOUND_VARIABLE_1312934) BOUND_VARIABLE_1312935) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1312935) BOUND_VARIABLE_1312932) (ho_11094 (ho_11765 BOUND_VARIABLE_1354010 BOUND_VARIABLE_1312935) BOUND_VARIABLE_1312934)))))) (let ((_let_4099 (forall ((BOUND_VARIABLE_1312919 tptp.set_o) (BOUND_VARIABLE_1354028 |u_(-> tptp.nat Bool Bool)|) (BOUND_VARIABLE_1312921 tptp.nat) (BOUND_VARIABLE_1312922 Bool)) (= (ho_11194 (ho_12191 (ho_12194 (ho_12193 k_12264 BOUND_VARIABLE_1312919) BOUND_VARIABLE_1354028) BOUND_VARIABLE_1312921) BOUND_VARIABLE_1312922) (and (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1312922) BOUND_VARIABLE_1312919) (ho_11194 (ho_12191 BOUND_VARIABLE_1354028 BOUND_VARIABLE_1312921) BOUND_VARIABLE_1312922)))))) (let ((_let_4100 (forall ((BOUND_VARIABLE_1354045 |u_(-> tptp.nat Bool tptp.nat)|) (BOUND_VARIABLE_1312911 Bool) (BOUND_VARIABLE_1312912 tptp.nat)) (= (ho_11139 (ho_12198 (ho_12197 k_12265 BOUND_VARIABLE_1354045) BOUND_VARIABLE_1312911) BOUND_VARIABLE_1312912) (ho_12199 (ho_12195 BOUND_VARIABLE_1354045 BOUND_VARIABLE_1312912) BOUND_VARIABLE_1312911))))) (let ((_let_4101 (forall ((BOUND_VARIABLE_1312897 tptp.set_nat) (BOUND_VARIABLE_1354059 |u_(-> tptp.nat Bool Bool)|) (BOUND_VARIABLE_1312899 Bool) (BOUND_VARIABLE_1312900 tptp.nat)) (= (ho_11054 (ho_11592 (ho_12202 (ho_12201 k_12266 BOUND_VARIABLE_1312897) BOUND_VARIABLE_1354059) BOUND_VARIABLE_1312899) BOUND_VARIABLE_1312900) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1312900) BOUND_VARIABLE_1312897) (ho_11194 (ho_12191 BOUND_VARIABLE_1354059 BOUND_VARIABLE_1312900) BOUND_VARIABLE_1312899)))))) (let ((_let_4102 (forall ((BOUND_VARIABLE_1312888 tptp.int) (BOUND_VARIABLE_1312889 tptp.int)) (= (ho_11094 (ho_11093 k_12267 BOUND_VARIABLE_1312888) BOUND_VARIABLE_1312889) (= BOUND_VARIABLE_1312888 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312889) BOUND_VARIABLE_1312888)))))) (let ((_let_4103 (forall ((BOUND_VARIABLE_1312875 tptp.set_int) (BOUND_VARIABLE_1354087 |u_(-> tptp.code_integer tptp.int Bool)|) (BOUND_VARIABLE_1312877 tptp.code_integer) (BOUND_VARIABLE_1312878 tptp.int)) (= (ho_11094 (ho_11619 (ho_11622 (ho_11621 k_12268 BOUND_VARIABLE_1312875) BOUND_VARIABLE_1354087) BOUND_VARIABLE_1312877) BOUND_VARIABLE_1312878) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1312878) BOUND_VARIABLE_1312875) (ho_11094 (ho_11619 BOUND_VARIABLE_1354087 BOUND_VARIABLE_1312877) BOUND_VARIABLE_1312878)))))) (let ((_let_4104 (forall ((BOUND_VARIABLE_1354104 |u_(-> tptp.code_integer tptp.int tptp.int)|) (BOUND_VARIABLE_1312867 tptp.int) (BOUND_VARIABLE_1312868 tptp.code_integer)) (= (ho_12154 (ho_12208 (ho_12207 k_12269 BOUND_VARIABLE_1354104) BOUND_VARIABLE_1312867) BOUND_VARIABLE_1312868) (ho_11059 (ho_12205 BOUND_VARIABLE_1354104 BOUND_VARIABLE_1312868) BOUND_VARIABLE_1312867))))) (let ((_let_4105 (forall ((BOUND_VARIABLE_1312853 tptp.set_Code_integer) (BOUND_VARIABLE_1354118 |u_(-> tptp.code_integer tptp.int Bool)|) (BOUND_VARIABLE_1312855 tptp.int) (BOUND_VARIABLE_1312856 tptp.code_integer)) (= (ho_11564 (ho_11560 (ho_12211 (ho_12210 k_12270 BOUND_VARIABLE_1312853) BOUND_VARIABLE_1354118) BOUND_VARIABLE_1312855) BOUND_VARIABLE_1312856) (and (ho_11567 (ho_11566 k_11565 BOUND_VARIABLE_1312856) BOUND_VARIABLE_1312853) (ho_11094 (ho_11619 BOUND_VARIABLE_1354118 BOUND_VARIABLE_1312856) BOUND_VARIABLE_1312855)))))) (let ((_let_4106 (forall ((BOUND_VARIABLE_1312844 tptp.int) (BOUND_VARIABLE_1312845 tptp.int)) (= (ho_11094 (ho_11093 k_12271 BOUND_VARIABLE_1312844) BOUND_VARIABLE_1312845) (= BOUND_VARIABLE_1312844 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312845) BOUND_VARIABLE_1312844)))))) (let ((_let_4107 (forall ((BOUND_VARIABLE_1312831 tptp.set_int) (BOUND_VARIABLE_1354146 |u_(-> tptp.nat tptp.int Bool)|) (BOUND_VARIABLE_1312833 tptp.nat) (BOUND_VARIABLE_1312834 tptp.int)) (= (ho_11094 (ho_11765 (ho_12183 (ho_12182 k_12272 BOUND_VARIABLE_1312831) BOUND_VARIABLE_1354146) BOUND_VARIABLE_1312833) BOUND_VARIABLE_1312834) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1312834) BOUND_VARIABLE_1312831) (ho_11094 (ho_11765 BOUND_VARIABLE_1354146 BOUND_VARIABLE_1312833) BOUND_VARIABLE_1312834)))))) (let ((_let_4108 (forall ((BOUND_VARIABLE_1354164 |u_(-> tptp.nat tptp.int tptp.int)|) (BOUND_VARIABLE_1312823 tptp.int) (BOUND_VARIABLE_1312824 tptp.nat)) (= (ho_11056 (ho_12276 (ho_12275 k_12274 BOUND_VARIABLE_1354164) BOUND_VARIABLE_1312823) BOUND_VARIABLE_1312824) (ho_11059 (ho_12273 BOUND_VARIABLE_1354164 BOUND_VARIABLE_1312824) BOUND_VARIABLE_1312823))))) (let ((_let_4109 (forall ((BOUND_VARIABLE_1312809 tptp.set_nat) (BOUND_VARIABLE_1354187 |u_(-> tptp.nat tptp.int Bool)|) (BOUND_VARIABLE_1312811 tptp.int) (BOUND_VARIABLE_1312812 tptp.nat)) (= (ho_11054 (ho_11574 (ho_12190 (ho_12189 k_12277 BOUND_VARIABLE_1312809) BOUND_VARIABLE_1354187) BOUND_VARIABLE_1312811) BOUND_VARIABLE_1312812) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1312812) BOUND_VARIABLE_1312809) (ho_11094 (ho_11765 BOUND_VARIABLE_1354187 BOUND_VARIABLE_1312812) BOUND_VARIABLE_1312811)))))) (let ((_let_4110 (forall ((BOUND_VARIABLE_1312800 tptp.int) (BOUND_VARIABLE_1312801 tptp.int)) (= (ho_11094 (ho_11093 k_12278 BOUND_VARIABLE_1312800) BOUND_VARIABLE_1312801) (= BOUND_VARIABLE_1312800 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312801) BOUND_VARIABLE_1312800)))))) (let ((_let_4111 (forall ((BOUND_VARIABLE_1312787 tptp.set_int) (BOUND_VARIABLE_1354215 |u_(-> Bool tptp.int Bool)|) (BOUND_VARIABLE_1312789 Bool) (BOUND_VARIABLE_1312790 tptp.int)) (= (ho_11094 (ho_11588 (ho_11591 (ho_11590 k_12279 BOUND_VARIABLE_1312787) BOUND_VARIABLE_1354215) BOUND_VARIABLE_1312789) BOUND_VARIABLE_1312790) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1312790) BOUND_VARIABLE_1312787) (ho_11094 (ho_11588 BOUND_VARIABLE_1354215 BOUND_VARIABLE_1312789) BOUND_VARIABLE_1312790)))))) (let ((_let_4112 (forall ((BOUND_VARIABLE_1354232 |u_(-> Bool tptp.int tptp.int)|) (BOUND_VARIABLE_1312779 tptp.int) (BOUND_VARIABLE_1312780 Bool)) (= (ho_12218 (ho_12217 (ho_12216 k_12280 BOUND_VARIABLE_1354232) BOUND_VARIABLE_1312779) BOUND_VARIABLE_1312780) (ho_11059 (ho_12214 BOUND_VARIABLE_1354232 BOUND_VARIABLE_1312780) BOUND_VARIABLE_1312779))))) (let ((_let_4113 (forall ((BOUND_VARIABLE_1312765 tptp.set_o) (BOUND_VARIABLE_1354246 |u_(-> Bool tptp.int Bool)|) (BOUND_VARIABLE_1312767 tptp.int) (BOUND_VARIABLE_1312768 Bool)) (= (ho_11194 (ho_11579 (ho_12221 (ho_12220 k_12281 BOUND_VARIABLE_1312765) BOUND_VARIABLE_1354246) BOUND_VARIABLE_1312767) BOUND_VARIABLE_1312768) (and (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1312768) BOUND_VARIABLE_1312765) (ho_11094 (ho_11588 BOUND_VARIABLE_1354246 BOUND_VARIABLE_1312768) BOUND_VARIABLE_1312767)))))) (let ((_let_4114 (forall ((BOUND_VARIABLE_1312752 tptp.set_nat) (BOUND_VARIABLE_1354264 |u_(-> tptp.code_integer tptp.nat Bool)|) (BOUND_VARIABLE_1312754 tptp.code_integer) (BOUND_VARIABLE_1312755 tptp.nat)) (= (ho_11054 (ho_11551 (ho_11554 (ho_11553 k_12282 BOUND_VARIABLE_1312752) BOUND_VARIABLE_1354264) BOUND_VARIABLE_1312754) BOUND_VARIABLE_1312755) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1312755) BOUND_VARIABLE_1312752) (ho_11054 (ho_11551 BOUND_VARIABLE_1354264 BOUND_VARIABLE_1312754) BOUND_VARIABLE_1312755)))))) (let ((_let_4115 (forall ((BOUND_VARIABLE_1354281 |u_(-> tptp.code_integer tptp.nat tptp.nat)|) (BOUND_VARIABLE_1312744 tptp.nat) (BOUND_VARIABLE_1312745 tptp.code_integer)) (= (ho_12176 (ho_12172 (ho_12240 k_12283 BOUND_VARIABLE_1354281) BOUND_VARIABLE_1312744) BOUND_VARIABLE_1312745) (ho_11139 (ho_12175 BOUND_VARIABLE_1354281 BOUND_VARIABLE_1312745) BOUND_VARIABLE_1312744))))) (let ((_let_4116 (forall ((BOUND_VARIABLE_1312730 tptp.set_Code_integer) (BOUND_VARIABLE_1354295 |u_(-> tptp.code_integer tptp.nat Bool)|) (BOUND_VARIABLE_1312732 tptp.nat) (BOUND_VARIABLE_1312733 tptp.code_integer)) (= (ho_11564 (ho_12168 (ho_12229 (ho_12228 k_12284 BOUND_VARIABLE_1312730) BOUND_VARIABLE_1354295) BOUND_VARIABLE_1312732) BOUND_VARIABLE_1312733) (and (ho_11567 (ho_11566 k_11565 BOUND_VARIABLE_1312733) BOUND_VARIABLE_1312730) (ho_11054 (ho_11551 BOUND_VARIABLE_1354295 BOUND_VARIABLE_1312733) BOUND_VARIABLE_1312732)))))) (let ((_let_4117 (forall ((BOUND_VARIABLE_1312721 tptp.int) (BOUND_VARIABLE_1312722 tptp.int)) (= (ho_11094 (ho_11093 k_12285 BOUND_VARIABLE_1312721) BOUND_VARIABLE_1312722) (= BOUND_VARIABLE_1312721 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312722) BOUND_VARIABLE_1312721)))))) (let ((_let_4118 (forall ((BOUND_VARIABLE_1312708 tptp.set_nat) (BOUND_VARIABLE_1354323 |u_(-> tptp.int tptp.nat Bool)|) (BOUND_VARIABLE_1312710 tptp.int) (BOUND_VARIABLE_1312711 tptp.nat)) (= (ho_11054 (ho_11574 (ho_11577 (ho_11576 k_12286 BOUND_VARIABLE_1312708) BOUND_VARIABLE_1354323) BOUND_VARIABLE_1312710) BOUND_VARIABLE_1312711) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1312711) BOUND_VARIABLE_1312708) (ho_11054 (ho_11574 BOUND_VARIABLE_1354323 BOUND_VARIABLE_1312710) BOUND_VARIABLE_1312711)))))) (let ((_let_4119 (forall ((BOUND_VARIABLE_1354340 |u_(-> tptp.int tptp.nat tptp.nat)|) (BOUND_VARIABLE_1312700 tptp.nat) (BOUND_VARIABLE_1312701 tptp.int)) (= (ho_11061 (ho_12184 (ho_12245 k_12287 BOUND_VARIABLE_1354340) BOUND_VARIABLE_1312700) BOUND_VARIABLE_1312701) (ho_11139 (ho_12187 BOUND_VARIABLE_1354340 BOUND_VARIABLE_1312701) BOUND_VARIABLE_1312700))))) (let ((_let_4120 (forall ((BOUND_VARIABLE_1312686 tptp.set_int) (BOUND_VARIABLE_1354354 |u_(-> tptp.int tptp.nat Bool)|) (BOUND_VARIABLE_1312688 tptp.nat) (BOUND_VARIABLE_1312689 tptp.int)) (= (ho_11094 (ho_11765 (ho_11764 (ho_11763 k_12288 BOUND_VARIABLE_1312686) BOUND_VARIABLE_1354354) BOUND_VARIABLE_1312688) BOUND_VARIABLE_1312689) (and (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1312689) BOUND_VARIABLE_1312686) (ho_11054 (ho_11574 BOUND_VARIABLE_1354354 BOUND_VARIABLE_1312689) BOUND_VARIABLE_1312688)))))) (let ((_let_4121 (forall ((BOUND_VARIABLE_1312673 tptp.set_nat) (BOUND_VARIABLE_1354372 |u_(-> Bool tptp.nat Bool)|) (BOUND_VARIABLE_1312675 Bool) (BOUND_VARIABLE_1312676 tptp.nat)) (= (ho_11054 (ho_11592 (ho_11595 (ho_11594 k_12289 BOUND_VARIABLE_1312673) BOUND_VARIABLE_1354372) BOUND_VARIABLE_1312675) BOUND_VARIABLE_1312676) (and (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1312676) BOUND_VARIABLE_1312673) (ho_11054 (ho_11592 BOUND_VARIABLE_1354372 BOUND_VARIABLE_1312675) BOUND_VARIABLE_1312676)))))) (let ((_let_4122 (forall ((BOUND_VARIABLE_1354389 |u_(-> Bool tptp.nat tptp.nat)|) (BOUND_VARIABLE_1312665 tptp.nat) (BOUND_VARIABLE_1312666 Bool)) (= (ho_12199 (ho_12195 (ho_12249 k_12290 BOUND_VARIABLE_1354389) BOUND_VARIABLE_1312665) BOUND_VARIABLE_1312666) (ho_11139 (ho_12198 BOUND_VARIABLE_1354389 BOUND_VARIABLE_1312666) BOUND_VARIABLE_1312665))))) (let ((_let_4123 (forall ((BOUND_VARIABLE_1312651 tptp.set_o) (BOUND_VARIABLE_1354403 |u_(-> Bool tptp.nat Bool)|) (BOUND_VARIABLE_1312653 tptp.nat) (BOUND_VARIABLE_1312654 Bool)) (= (ho_11194 (ho_12191 (ho_12237 (ho_12236 k_12291 BOUND_VARIABLE_1312651) BOUND_VARIABLE_1354403) BOUND_VARIABLE_1312653) BOUND_VARIABLE_1312654) (and (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1312654) BOUND_VARIABLE_1312651) (ho_11054 (ho_11592 BOUND_VARIABLE_1354403 BOUND_VARIABLE_1312654) BOUND_VARIABLE_1312653)))))) (let ((_let_4124 (forall ((BOUND_VARIABLE_1312643 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1312644 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12292 BOUND_VARIABLE_1312643) BOUND_VARIABLE_1312644) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1312644) BOUND_VARIABLE_1312643))))) (let ((_let_4125 (forall ((BOUND_VARIABLE_1312635 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1312636 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12293 BOUND_VARIABLE_1312635) BOUND_VARIABLE_1312636) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1312636) BOUND_VARIABLE_1312635))))) (let ((_let_4126 (forall ((BOUND_VARIABLE_1312627 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1312628 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12294 BOUND_VARIABLE_1312627) BOUND_VARIABLE_1312628) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1312628) BOUND_VARIABLE_1312627))))) (let ((_let_4127 (forall ((BOUND_VARIABLE_1312618 tptp.int) (BOUND_VARIABLE_1312619 tptp.int)) (= (ho_11094 (ho_11093 k_12295 BOUND_VARIABLE_1312618) BOUND_VARIABLE_1312619) (= BOUND_VARIABLE_1312618 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312619) BOUND_VARIABLE_1312618)))))) (let ((_let_4128 (forall ((BOUND_VARIABLE_1312610 tptp.set_int) (BOUND_VARIABLE_1312611 tptp.int)) (= (ho_11094 (ho_11234 k_12296 BOUND_VARIABLE_1312610) BOUND_VARIABLE_1312611) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1312611) BOUND_VARIABLE_1312610))))) (let ((_let_4129 (forall ((BOUND_VARIABLE_1312602 tptp.set_int) (BOUND_VARIABLE_1312603 tptp.int)) (= (ho_11094 (ho_11234 k_12297 BOUND_VARIABLE_1312602) BOUND_VARIABLE_1312603) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1312603) BOUND_VARIABLE_1312602))))) (let ((_let_4130 (forall ((BOUND_VARIABLE_1312594 tptp.set_int) (BOUND_VARIABLE_1312595 tptp.int)) (= (ho_11094 (ho_11234 k_12298 BOUND_VARIABLE_1312594) BOUND_VARIABLE_1312595) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1312595) BOUND_VARIABLE_1312594))))) (let ((_let_4131 (forall ((BOUND_VARIABLE_1312586 tptp.set_nat) (BOUND_VARIABLE_1312587 tptp.nat)) (= (ho_11054 (ho_11240 k_12299 BOUND_VARIABLE_1312586) BOUND_VARIABLE_1312587) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1312587) BOUND_VARIABLE_1312586))))) (let ((_let_4132 (forall ((BOUND_VARIABLE_1312578 tptp.set_nat) (BOUND_VARIABLE_1312579 tptp.nat)) (= (ho_11054 (ho_11240 k_12300 BOUND_VARIABLE_1312578) BOUND_VARIABLE_1312579) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1312579) BOUND_VARIABLE_1312578))))) (let ((_let_4133 (forall ((BOUND_VARIABLE_1312570 tptp.set_nat) (BOUND_VARIABLE_1312571 tptp.nat)) (= (ho_11054 (ho_11240 k_12301 BOUND_VARIABLE_1312570) BOUND_VARIABLE_1312571) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1312571) BOUND_VARIABLE_1312570))))) (let ((_let_4134 (forall ((BOUND_VARIABLE_1312561 tptp.int) (BOUND_VARIABLE_1312562 tptp.int)) (= (ho_11094 (ho_11093 k_12302 BOUND_VARIABLE_1312561) BOUND_VARIABLE_1312562) (= BOUND_VARIABLE_1312561 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312562) BOUND_VARIABLE_1312561)))))) (let ((_let_4135 (forall ((BOUND_VARIABLE_1312552 tptp.int) (BOUND_VARIABLE_1312553 tptp.int)) (= (ho_11094 (ho_11093 k_12303 BOUND_VARIABLE_1312552) BOUND_VARIABLE_1312553) (= BOUND_VARIABLE_1312552 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312553) BOUND_VARIABLE_1312552)))))) (let ((_let_4136 (forall ((BOUND_VARIABLE_1312543 tptp.int) (BOUND_VARIABLE_1312544 tptp.int)) (= (ho_11094 (ho_11093 k_12304 BOUND_VARIABLE_1312543) BOUND_VARIABLE_1312544) (= BOUND_VARIABLE_1312543 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312544) BOUND_VARIABLE_1312543)))))) (let ((_let_4137 (forall ((BOUND_VARIABLE_1312534 tptp.int) (BOUND_VARIABLE_1312535 tptp.int)) (= (ho_11094 (ho_11093 k_12305 BOUND_VARIABLE_1312534) BOUND_VARIABLE_1312535) (= BOUND_VARIABLE_1312534 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312535) BOUND_VARIABLE_1312534)))))) (let ((_let_4138 (forall ((BOUND_VARIABLE_1312525 tptp.int) (BOUND_VARIABLE_1312526 tptp.int)) (= (ho_11094 (ho_11093 k_12306 BOUND_VARIABLE_1312525) BOUND_VARIABLE_1312526) (= BOUND_VARIABLE_1312525 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312526) BOUND_VARIABLE_1312525)))))) (let ((_let_4139 (forall ((BOUND_VARIABLE_1312516 tptp.int) (BOUND_VARIABLE_1312517 tptp.int)) (= (ho_11094 (ho_11093 k_12307 BOUND_VARIABLE_1312516) BOUND_VARIABLE_1312517) (= BOUND_VARIABLE_1312516 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312517) BOUND_VARIABLE_1312516)))))) (let ((_let_4140 (forall ((BOUND_VARIABLE_1312507 tptp.int) (BOUND_VARIABLE_1312508 tptp.int)) (= (ho_11094 (ho_11093 k_12308 BOUND_VARIABLE_1312507) BOUND_VARIABLE_1312508) (= BOUND_VARIABLE_1312507 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312508) BOUND_VARIABLE_1312507)))))) (let ((_let_4141 (forall ((BOUND_VARIABLE_1312498 tptp.int) (BOUND_VARIABLE_1312499 tptp.int)) (= (ho_11094 (ho_11093 k_12309 BOUND_VARIABLE_1312498) BOUND_VARIABLE_1312499) (= BOUND_VARIABLE_1312498 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312499) BOUND_VARIABLE_1312498)))))) (let ((_let_4142 (forall ((BOUND_VARIABLE_1312489 tptp.int) (BOUND_VARIABLE_1312490 tptp.int)) (= (ho_11094 (ho_11093 k_12310 BOUND_VARIABLE_1312489) BOUND_VARIABLE_1312490) (= BOUND_VARIABLE_1312489 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312490) BOUND_VARIABLE_1312489)))))) (let ((_let_4143 (forall ((BOUND_VARIABLE_1312480 tptp.int) (BOUND_VARIABLE_1312481 tptp.int)) (= (ho_11094 (ho_11093 k_12311 BOUND_VARIABLE_1312480) BOUND_VARIABLE_1312481) (= BOUND_VARIABLE_1312480 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312481) BOUND_VARIABLE_1312480)))))) (let ((_let_4144 (forall ((BOUND_VARIABLE_1312471 tptp.int) (BOUND_VARIABLE_1312472 tptp.int)) (= (ho_11094 (ho_11093 k_12312 BOUND_VARIABLE_1312471) BOUND_VARIABLE_1312472) (= BOUND_VARIABLE_1312471 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312472) BOUND_VARIABLE_1312471)))))) (let ((_let_4145 (forall ((BOUND_VARIABLE_1312462 tptp.int) (BOUND_VARIABLE_1312463 tptp.int)) (= (ho_11094 (ho_11093 k_12313 BOUND_VARIABLE_1312462) BOUND_VARIABLE_1312463) (= BOUND_VARIABLE_1312462 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312463) BOUND_VARIABLE_1312462)))))) (let ((_let_4146 (forall ((BOUND_VARIABLE_1312453 tptp.int) (BOUND_VARIABLE_1312454 tptp.int)) (= (ho_11094 (ho_11093 k_12314 BOUND_VARIABLE_1312453) BOUND_VARIABLE_1312454) (= BOUND_VARIABLE_1312453 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312454) BOUND_VARIABLE_1312453)))))) (let ((_let_4147 (forall ((BOUND_VARIABLE_1312444 tptp.int) (BOUND_VARIABLE_1312445 tptp.int)) (= (ho_11094 (ho_11093 k_12315 BOUND_VARIABLE_1312444) BOUND_VARIABLE_1312445) (= BOUND_VARIABLE_1312444 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312445) BOUND_VARIABLE_1312444)))))) (let ((_let_4148 (forall ((BOUND_VARIABLE_1312435 tptp.int) (BOUND_VARIABLE_1312436 tptp.int)) (= (ho_11094 (ho_11093 k_12316 BOUND_VARIABLE_1312435) BOUND_VARIABLE_1312436) (= BOUND_VARIABLE_1312435 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312436) BOUND_VARIABLE_1312435)))))) (let ((_let_4149 (forall ((BOUND_VARIABLE_1312426 tptp.int) (BOUND_VARIABLE_1312427 tptp.int)) (= (ho_11094 (ho_11093 k_12317 BOUND_VARIABLE_1312426) BOUND_VARIABLE_1312427) (= BOUND_VARIABLE_1312426 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312427) BOUND_VARIABLE_1312426)))))) (let ((_let_4150 (forall ((BOUND_VARIABLE_1312417 tptp.int) (BOUND_VARIABLE_1312418 tptp.int)) (= (ho_11094 (ho_11093 k_12318 BOUND_VARIABLE_1312417) BOUND_VARIABLE_1312418) (= BOUND_VARIABLE_1312417 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312418) BOUND_VARIABLE_1312417)))))) (let ((_let_4151 (forall ((BOUND_VARIABLE_1312408 tptp.int) (BOUND_VARIABLE_1312409 tptp.int)) (= (ho_11094 (ho_11093 k_12319 BOUND_VARIABLE_1312408) BOUND_VARIABLE_1312409) (= BOUND_VARIABLE_1312408 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312409) BOUND_VARIABLE_1312408)))))) (let ((_let_4152 (forall ((BOUND_VARIABLE_1312399 tptp.int) (BOUND_VARIABLE_1312400 tptp.int)) (= (ho_11094 (ho_11093 k_12320 BOUND_VARIABLE_1312399) BOUND_VARIABLE_1312400) (= BOUND_VARIABLE_1312399 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312400) BOUND_VARIABLE_1312399)))))) (let ((_let_4153 (forall ((BOUND_VARIABLE_1312388 tptp.int) (BOUND_VARIABLE_1312389 tptp.nat)) (= (ho_11056 (ho_12276 k_12321 BOUND_VARIABLE_1312388) BOUND_VARIABLE_1312389) (ho_11059 (ho_12273 k_12324 BOUND_VARIABLE_1312389) (ho_12218 k_12323 (ho_11054 (ho_11574 k_12322 BOUND_VARIABLE_1312388) BOUND_VARIABLE_1312389))))))) (let ((_let_4154 (forall ((BOUND_VARIABLE_1354722 |u_(-> tptp.nat tptp.nat tptp.int)|) (BOUND_VARIABLE_1312366 tptp.nat) (BOUND_VARIABLE_1312367 tptp.nat)) (= (ho_11056 (ho_12325 BOUND_VARIABLE_1354722 BOUND_VARIABLE_1312367) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312366)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1312367))) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))))) (ho_11056 (ho_12325 (ho_12327 k_12326 BOUND_VARIABLE_1354722) BOUND_VARIABLE_1312366) BOUND_VARIABLE_1312367))))) (let ((_let_4155 (forall ((BOUND_VARIABLE_1312351 tptp.nat) (BOUND_VARIABLE_1312352 tptp.nat)) (= (ho_11054 (ho_11053 k_12328 BOUND_VARIABLE_1312351) BOUND_VARIABLE_1312352) (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1312351 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312352)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4156 (forall ((BOUND_VARIABLE_1354764 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1312329 tptp.nat) (BOUND_VARIABLE_1312330 tptp.nat)) (= (ho_11139 (ho_11479 BOUND_VARIABLE_1354764 BOUND_VARIABLE_1312330) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312329)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1312330))) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))))) (ho_11139 (ho_11479 (ho_12255 k_12329 BOUND_VARIABLE_1354764) BOUND_VARIABLE_1312329) BOUND_VARIABLE_1312330))))) (let ((_let_4157 (forall ((BOUND_VARIABLE_1312314 tptp.nat) (BOUND_VARIABLE_1312315 tptp.nat)) (= (ho_11054 (ho_11053 k_12330 BOUND_VARIABLE_1312314) BOUND_VARIABLE_1312315) (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1312314 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312315)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4158 (forall ((BOUND_VARIABLE_1312300 tptp.int) (BOUND_VARIABLE_1312301 tptp.int)) (= (ho_11094 (ho_11093 k_12331 BOUND_VARIABLE_1312300) BOUND_VARIABLE_1312301) (and (= BOUND_VARIABLE_1312300 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312301) BOUND_VARIABLE_1312300)) (not (= BOUND_VARIABLE_1312301 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312300) BOUND_VARIABLE_1312301)))))))) (let ((_let_4159 (forall ((BOUND_VARIABLE_1312278 tptp.nat) (BOUND_VARIABLE_1312279 tptp.nat)) (= (ho_11054 (ho_11053 k_12332 BOUND_VARIABLE_1312278) BOUND_VARIABLE_1312279) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1312278 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312279)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1312279 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312278)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4160 (forall ((BOUND_VARIABLE_1312264 tptp.int) (BOUND_VARIABLE_1312265 tptp.int)) (= (ho_11094 (ho_11093 k_12333 BOUND_VARIABLE_1312264) BOUND_VARIABLE_1312265) (and (= BOUND_VARIABLE_1312264 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312265) BOUND_VARIABLE_1312264)) (not (= BOUND_VARIABLE_1312265 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312264) BOUND_VARIABLE_1312265)))))))) (let ((_let_4161 (forall ((BOUND_VARIABLE_1312250 tptp.int) (BOUND_VARIABLE_1312251 tptp.int)) (= (or (= BOUND_VARIABLE_1312250 BOUND_VARIABLE_1312251) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1312251) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12334 BOUND_VARIABLE_1312250) BOUND_VARIABLE_1312251))))) (let ((_let_4162 (forall ((BOUND_VARIABLE_1312228 tptp.nat) (BOUND_VARIABLE_1312229 tptp.nat)) (= (ho_11054 (ho_11053 k_12335 BOUND_VARIABLE_1312228) BOUND_VARIABLE_1312229) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1312228 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312229)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1312229 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312228)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4163 (forall ((BOUND_VARIABLE_1312214 tptp.nat) (BOUND_VARIABLE_1312215 tptp.nat)) (= (or (= BOUND_VARIABLE_1312214 BOUND_VARIABLE_1312215) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1312215) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12336 BOUND_VARIABLE_1312214) BOUND_VARIABLE_1312215))))) (let ((_let_4164 (forall ((BOUND_VARIABLE_1312200 Bool) (BOUND_VARIABLE_1312201 Bool)) (= (or (= BOUND_VARIABLE_1312200 BOUND_VARIABLE_1312201) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1312201) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12337 BOUND_VARIABLE_1312200) BOUND_VARIABLE_1312201))))) (let ((_let_4165 (forall ((BOUND_VARIABLE_1312186 tptp.int) (BOUND_VARIABLE_1312187 tptp.int)) (= (ho_11094 (ho_11093 k_12338 BOUND_VARIABLE_1312186) BOUND_VARIABLE_1312187) (and (= BOUND_VARIABLE_1312186 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312187) BOUND_VARIABLE_1312186)) (not (= BOUND_VARIABLE_1312187 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312186) BOUND_VARIABLE_1312187)))))))) (let ((_let_4166 (forall ((BOUND_VARIABLE_1312172 tptp.int) (BOUND_VARIABLE_1312173 tptp.int)) (= (or (= BOUND_VARIABLE_1312172 BOUND_VARIABLE_1312173) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1312173) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12339 BOUND_VARIABLE_1312172) BOUND_VARIABLE_1312173))))) (let ((_let_4167 (forall ((BOUND_VARIABLE_1312158 tptp.int) (BOUND_VARIABLE_1312159 tptp.int)) (= (ho_11094 (ho_11093 k_12340 BOUND_VARIABLE_1312158) BOUND_VARIABLE_1312159) (and (= BOUND_VARIABLE_1312158 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312159) BOUND_VARIABLE_1312158)) (not (= BOUND_VARIABLE_1312159 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1312158) BOUND_VARIABLE_1312159)))))))) (let ((_let_4168 (forall ((BOUND_VARIABLE_1312144 tptp.int) (BOUND_VARIABLE_1312145 tptp.int)) (= (or (= BOUND_VARIABLE_1312144 BOUND_VARIABLE_1312145) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1312145) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12341 BOUND_VARIABLE_1312144) BOUND_VARIABLE_1312145))))) (let ((_let_4169 (forall ((BOUND_VARIABLE_1312116 tptp.nat) (BOUND_VARIABLE_1312117 tptp.nat) (BOUND_VARIABLE_1312118 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11064 k_12342 BOUND_VARIABLE_1312116) BOUND_VARIABLE_1312117) BOUND_VARIABLE_1312118) (and (not (forall ((K3 tptp.nat)) (not (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312116)) (ho_11056 k_11055 BOUND_VARIABLE_1312117))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312118)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1312118 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312116)) (ho_11056 k_11055 BOUND_VARIABLE_1312117))))) (ho_11056 k_11055 K3))))))))))) (let ((_let_4170 (forall ((BOUND_VARIABLE_1312102 tptp.nat) (BOUND_VARIABLE_1312103 tptp.nat)) (= (or (= BOUND_VARIABLE_1312102 BOUND_VARIABLE_1312103) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1312103) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12343 BOUND_VARIABLE_1312102) BOUND_VARIABLE_1312103))))) (let ((_let_4171 (forall ((BOUND_VARIABLE_1312080 tptp.nat) (BOUND_VARIABLE_1312081 tptp.nat)) (= (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1312080 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312081)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1312081 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312080)) (ho_11056 k_11055 K3))))))) (ho_11054 (ho_11053 k_12344 BOUND_VARIABLE_1312080) BOUND_VARIABLE_1312081))))) (let ((_let_4172 (forall ((BOUND_VARIABLE_1312066 tptp.nat) (BOUND_VARIABLE_1312067 tptp.nat)) (= (or (= BOUND_VARIABLE_1312066 BOUND_VARIABLE_1312067) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1312067) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12345 BOUND_VARIABLE_1312066) BOUND_VARIABLE_1312067))))) (let ((_let_4173 (forall ((BOUND_VARIABLE_1312044 tptp.nat) (BOUND_VARIABLE_1312045 tptp.nat)) (= (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1312044 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312045)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1312045 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312044)) (ho_11056 k_11055 K3))))))) (ho_11054 (ho_11053 k_12346 BOUND_VARIABLE_1312044) BOUND_VARIABLE_1312045))))) (let ((_let_4174 (forall ((BOUND_VARIABLE_1312024 tptp.nat) (BOUND_VARIABLE_1312025 tptp.nat) (BOUND_VARIABLE_1312026 tptp.nat)) (= (or (= BOUND_VARIABLE_1312026 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1312024)) (ho_11056 k_11055 BOUND_VARIABLE_1312025)))) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1312026) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 (ho_11064 k_12347 BOUND_VARIABLE_1312024) BOUND_VARIABLE_1312025) BOUND_VARIABLE_1312026))))) (let ((_let_4175 (forall ((BOUND_VARIABLE_1312012 tptp.assn) (BOUND_VARIABLE_1312013 tptp.assn) (BOUND_VARIABLE_1312014 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 (ho_11347 k_12348 BOUND_VARIABLE_1312012) BOUND_VARIABLE_1312013) BOUND_VARIABLE_1312014) (and (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1312012) BOUND_VARIABLE_1312014) (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1312013) BOUND_VARIABLE_1312014)))))) (let ((_let_4176 (forall ((BOUND_VARIABLE_1312000 tptp.assn) (BOUND_VARIABLE_1312001 tptp.assn) (BOUND_VARIABLE_1312002 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 (ho_11347 k_12349 BOUND_VARIABLE_1312000) BOUND_VARIABLE_1312001) BOUND_VARIABLE_1312002) (and (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1312000) BOUND_VARIABLE_1312002) (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1312001) BOUND_VARIABLE_1312002)))))) (let ((_let_4177 (forall ((BOUND_VARIABLE_1311988 tptp.assn) (BOUND_VARIABLE_1311989 tptp.assn) (BOUND_VARIABLE_1311990 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 (ho_11347 k_12350 BOUND_VARIABLE_1311988) BOUND_VARIABLE_1311989) BOUND_VARIABLE_1311990) (and (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1311988) BOUND_VARIABLE_1311990) (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1311989) BOUND_VARIABLE_1311990)))))) (let ((_let_4178 (forall ((BOUND_VARIABLE_1311976 tptp.assn) (BOUND_VARIABLE_1311977 tptp.assn) (BOUND_VARIABLE_1311978 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 (ho_11347 k_12351 BOUND_VARIABLE_1311976) BOUND_VARIABLE_1311977) BOUND_VARIABLE_1311978) (and (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1311976) BOUND_VARIABLE_1311978) (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1311977) BOUND_VARIABLE_1311978)))))) (let ((_let_4179 (forall ((BOUND_VARIABLE_1311962 Bool) (BOUND_VARIABLE_1311963 Bool)) (= (or (= BOUND_VARIABLE_1311962 BOUND_VARIABLE_1311963) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1311963) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12352 BOUND_VARIABLE_1311962) BOUND_VARIABLE_1311963))))) (let ((_let_4180 (forall ((BOUND_VARIABLE_1311948 Bool) (BOUND_VARIABLE_1311949 Bool)) (= (or (= BOUND_VARIABLE_1311948 BOUND_VARIABLE_1311949) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1311949) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12353 BOUND_VARIABLE_1311948) BOUND_VARIABLE_1311949))))) (let ((_let_4181 (forall ((BOUND_VARIABLE_1311926 tptp.nat) (BOUND_VARIABLE_1311927 tptp.nat)) (= (ho_11054 (ho_11053 k_12354 BOUND_VARIABLE_1311926) BOUND_VARIABLE_1311927) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311926 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311927)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311927 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311926)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4182 (forall ((BOUND_VARIABLE_1355164 |u_(-> tptp.nat tptp.nat tptp.int)|) (BOUND_VARIABLE_1311918 tptp.nat) (BOUND_VARIABLE_1311919 tptp.nat)) (= (ho_11056 (ho_12325 (ho_12327 k_12355 BOUND_VARIABLE_1355164) BOUND_VARIABLE_1311918) BOUND_VARIABLE_1311919) (ho_11056 (ho_12325 BOUND_VARIABLE_1355164 BOUND_VARIABLE_1311919) BOUND_VARIABLE_1311918))))) (let ((_let_4183 (forall ((BOUND_VARIABLE_1311895 tptp.nat) (BOUND_VARIABLE_1311896 tptp.nat)) (= (ho_11054 (ho_11053 k_12356 BOUND_VARIABLE_1311895) BOUND_VARIABLE_1311896) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311895 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311896)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311896 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311895)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4184 (forall ((BOUND_VARIABLE_1355200 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1311887 tptp.nat) (BOUND_VARIABLE_1311888 tptp.nat)) (= (ho_11139 (ho_11479 (ho_12255 k_12357 BOUND_VARIABLE_1355200) BOUND_VARIABLE_1311887) BOUND_VARIABLE_1311888) (ho_11139 (ho_11479 BOUND_VARIABLE_1355200 BOUND_VARIABLE_1311888) BOUND_VARIABLE_1311887))))) (let ((_let_4185 (forall ((BOUND_VARIABLE_1311864 tptp.nat) (BOUND_VARIABLE_1311865 tptp.nat)) (= (ho_11054 (ho_11053 k_12358 BOUND_VARIABLE_1311864) BOUND_VARIABLE_1311865) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311864 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311865)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311865 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311864)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4186 (forall ((BOUND_VARIABLE_1355236 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1311856 tptp.nat) (BOUND_VARIABLE_1311857 tptp.nat)) (= (ho_11139 (ho_11479 (ho_12255 k_12359 BOUND_VARIABLE_1355236) BOUND_VARIABLE_1311856) BOUND_VARIABLE_1311857) (ho_11139 (ho_11479 BOUND_VARIABLE_1355236 BOUND_VARIABLE_1311857) BOUND_VARIABLE_1311856))))) (let ((_let_4187 (forall ((BOUND_VARIABLE_1311846 tptp.int) (BOUND_VARIABLE_1311847 tptp.int)) (= (ho_11094 (ho_11093 k_12360 BOUND_VARIABLE_1311846) BOUND_VARIABLE_1311847) (= BOUND_VARIABLE_1311846 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311847) BOUND_VARIABLE_1311846)))))) (let ((_let_4188 (forall ((BOUND_VARIABLE_1311832 tptp.int) (BOUND_VARIABLE_1311833 tptp.int)) (= (ho_11094 (ho_11093 k_12361 BOUND_VARIABLE_1311832) BOUND_VARIABLE_1311833) (and (= BOUND_VARIABLE_1311832 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311833) BOUND_VARIABLE_1311832)) (not (= BOUND_VARIABLE_1311833 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311832) BOUND_VARIABLE_1311833)))))))) (let ((_let_4189 (forall ((BOUND_VARIABLE_1311818 tptp.nat) (BOUND_VARIABLE_1311819 tptp.nat)) (= (ho_11054 (ho_11053 k_12362 BOUND_VARIABLE_1311818) BOUND_VARIABLE_1311819) (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311818 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311819)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4190 (forall ((BOUND_VARIABLE_1311796 tptp.nat) (BOUND_VARIABLE_1311797 tptp.nat)) (= (ho_11054 (ho_11053 k_12363 BOUND_VARIABLE_1311796) BOUND_VARIABLE_1311797) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311796 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311797)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311797 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311796)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4191 (forall ((BOUND_VARIABLE_1355317 |u_(-> tptp.nat tptp.nat tptp.int)|) (BOUND_VARIABLE_1311774 tptp.nat) (BOUND_VARIABLE_1311775 tptp.nat)) (= (ho_11056 (ho_12325 BOUND_VARIABLE_1355317 BOUND_VARIABLE_1311775) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311774)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1311775))) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))))) (ho_11056 (ho_12325 (ho_12327 k_12364 BOUND_VARIABLE_1355317) BOUND_VARIABLE_1311774) BOUND_VARIABLE_1311775))))) (let ((_let_4192 (forall ((BOUND_VARIABLE_1311759 tptp.nat) (BOUND_VARIABLE_1311760 tptp.nat)) (= (ho_11054 (ho_11053 k_12365 BOUND_VARIABLE_1311759) BOUND_VARIABLE_1311760) (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311759 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311760)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4193 (forall ((BOUND_VARIABLE_1355353 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1311737 tptp.nat) (BOUND_VARIABLE_1311738 tptp.nat)) (= (ho_11139 (ho_11479 BOUND_VARIABLE_1355353 BOUND_VARIABLE_1311738) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311737)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1311738))) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))))) (ho_11139 (ho_11479 (ho_12255 k_12366 BOUND_VARIABLE_1355353) BOUND_VARIABLE_1311737) BOUND_VARIABLE_1311738))))) (let ((_let_4194 (forall ((BOUND_VARIABLE_1311722 tptp.nat) (BOUND_VARIABLE_1311723 tptp.nat)) (= (ho_11054 (ho_11053 k_12367 BOUND_VARIABLE_1311722) BOUND_VARIABLE_1311723) (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311722 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311723)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4195 (forall ((BOUND_VARIABLE_1311708 tptp.int) (BOUND_VARIABLE_1311709 tptp.int)) (= (ho_11094 (ho_11093 k_12368 BOUND_VARIABLE_1311708) BOUND_VARIABLE_1311709) (and (= BOUND_VARIABLE_1311708 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311709) BOUND_VARIABLE_1311708)) (not (= BOUND_VARIABLE_1311709 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311708) BOUND_VARIABLE_1311709)))))))) (let ((_let_4196 (forall ((BOUND_VARIABLE_1311686 tptp.nat) (BOUND_VARIABLE_1311687 tptp.nat)) (= (ho_11054 (ho_11053 k_12369 BOUND_VARIABLE_1311686) BOUND_VARIABLE_1311687) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311686 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311687)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311687 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311686)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4197 (forall ((BOUND_VARIABLE_1311672 tptp.int) (BOUND_VARIABLE_1311673 tptp.int)) (= (ho_11094 (ho_11093 k_12370 BOUND_VARIABLE_1311672) BOUND_VARIABLE_1311673) (and (= BOUND_VARIABLE_1311672 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311673) BOUND_VARIABLE_1311672)) (not (= BOUND_VARIABLE_1311673 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311672) BOUND_VARIABLE_1311673)))))))) (let ((_let_4198 (forall ((BOUND_VARIABLE_1311658 tptp.int) (BOUND_VARIABLE_1311659 tptp.int)) (= (ho_11094 (ho_11093 k_12371 BOUND_VARIABLE_1311658) BOUND_VARIABLE_1311659) (and (= BOUND_VARIABLE_1311658 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311659) BOUND_VARIABLE_1311658)) (not (= BOUND_VARIABLE_1311659 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311658) BOUND_VARIABLE_1311659)))))))) (let ((_let_4199 (forall ((BOUND_VARIABLE_1311644 tptp.int) (BOUND_VARIABLE_1311645 tptp.int)) (= (ho_11094 (ho_11093 k_12372 BOUND_VARIABLE_1311644) BOUND_VARIABLE_1311645) (and (= BOUND_VARIABLE_1311644 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311645) BOUND_VARIABLE_1311644)) (not (= BOUND_VARIABLE_1311645 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311644) BOUND_VARIABLE_1311645)))))))) (let ((_let_4200 (forall ((BOUND_VARIABLE_1311630 tptp.int) (BOUND_VARIABLE_1311631 tptp.int)) (= (ho_11094 (ho_11093 k_12373 BOUND_VARIABLE_1311630) BOUND_VARIABLE_1311631) (and (= BOUND_VARIABLE_1311630 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311631) BOUND_VARIABLE_1311630)) (not (= BOUND_VARIABLE_1311631 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311630) BOUND_VARIABLE_1311631)))))))) (let ((_let_4201 (forall ((BOUND_VARIABLE_1311608 tptp.nat) (BOUND_VARIABLE_1311609 tptp.nat)) (= (ho_11054 (ho_11053 k_12374 BOUND_VARIABLE_1311608) BOUND_VARIABLE_1311609) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311608 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311609)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311609 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311608)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4202 (forall ((BOUND_VARIABLE_1311586 tptp.nat) (BOUND_VARIABLE_1311587 tptp.nat)) (= (ho_11054 (ho_11053 k_12375 BOUND_VARIABLE_1311586) BOUND_VARIABLE_1311587) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311586 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311587)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311587 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311586)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4203 (forall ((BOUND_VARIABLE_1311572 tptp.int) (BOUND_VARIABLE_1311573 tptp.int)) (= (ho_11094 (ho_11093 k_12376 BOUND_VARIABLE_1311572) BOUND_VARIABLE_1311573) (and (= BOUND_VARIABLE_1311572 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311573) BOUND_VARIABLE_1311572)) (not (= BOUND_VARIABLE_1311573 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311572) BOUND_VARIABLE_1311573)))))))) (let ((_let_4204 (forall ((BOUND_VARIABLE_1311558 tptp.int) (BOUND_VARIABLE_1311559 tptp.int)) (= (ho_11094 (ho_11093 k_12377 BOUND_VARIABLE_1311558) BOUND_VARIABLE_1311559) (and (= BOUND_VARIABLE_1311558 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311559) BOUND_VARIABLE_1311558)) (not (= BOUND_VARIABLE_1311559 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1311558) BOUND_VARIABLE_1311559)))))))) (let ((_let_4205 (forall ((BOUND_VARIABLE_1311536 tptp.nat) (BOUND_VARIABLE_1311537 tptp.nat)) (= (ho_11054 (ho_11053 k_12378 BOUND_VARIABLE_1311536) BOUND_VARIABLE_1311537) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311536 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311537)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311537 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311536)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4206 (forall ((BOUND_VARIABLE_1311514 tptp.nat) (BOUND_VARIABLE_1311515 tptp.nat)) (= (ho_11054 (ho_11053 k_12379 BOUND_VARIABLE_1311514) BOUND_VARIABLE_1311515) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311514 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311515)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311515 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311514)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4207 (forall ((BOUND_VARIABLE_1311502 tptp.assn) (BOUND_VARIABLE_1311503 tptp.assn) (BOUND_VARIABLE_1311504 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 (ho_11347 k_12380 BOUND_VARIABLE_1311502) BOUND_VARIABLE_1311503) BOUND_VARIABLE_1311504) (and (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1311502) BOUND_VARIABLE_1311504) (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1311503) BOUND_VARIABLE_1311504)))))) (let ((_let_4208 (forall ((BOUND_VARIABLE_1311490 tptp.assn) (BOUND_VARIABLE_1311491 tptp.assn) (BOUND_VARIABLE_1311492 tptp.produc3658429121746597890et_nat)) (= (ho_11328 (ho_11327 (ho_11347 k_12381 BOUND_VARIABLE_1311490) BOUND_VARIABLE_1311491) BOUND_VARIABLE_1311492) (and (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1311490) BOUND_VARIABLE_1311492) (ho_11328 (ho_11327 k_11329 BOUND_VARIABLE_1311491) BOUND_VARIABLE_1311492)))))) (let ((_let_4209 (forall ((BOUND_VARIABLE_1311482 tptp.set_nat) (BOUND_VARIABLE_1311483 tptp.nat)) (= (ho_11054 (ho_11240 k_12382 BOUND_VARIABLE_1311482) BOUND_VARIABLE_1311483) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1311483) BOUND_VARIABLE_1311482))))) (let ((_let_4210 (forall ((BOUND_VARIABLE_1311474 tptp.set_nat) (BOUND_VARIABLE_1311475 tptp.nat)) (= (ho_11054 (ho_11240 k_12383 BOUND_VARIABLE_1311474) BOUND_VARIABLE_1311475) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1311475) BOUND_VARIABLE_1311474))))) (let ((_let_4211 (forall ((BOUND_VARIABLE_1355655 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1311452 tptp.nat) (BOUND_VARIABLE_1311453 tptp.nat)) (= (ho_11139 (ho_11479 BOUND_VARIABLE_1355655 BOUND_VARIABLE_1311453) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311452)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1311453))) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))))) (ho_11139 (ho_11479 (ho_12255 k_12384 BOUND_VARIABLE_1355655) BOUND_VARIABLE_1311452) BOUND_VARIABLE_1311453))))) (let ((_let_4212 (forall ((BOUND_VARIABLE_1311437 tptp.nat) (BOUND_VARIABLE_1311438 tptp.nat)) (= (ho_11054 (ho_11053 k_12385 BOUND_VARIABLE_1311437) BOUND_VARIABLE_1311438) (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1311437 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311438)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4213 (forall ((BOUND_VARIABLE_1311375 tptp.code_integer) (BOUND_VARIABLE_1311376 tptp.code_integer) (BOUND_VARIABLE_1311377 tptp.code_integer)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (let ((_let_2 (ho_11669 k_11668 (ho_11139 k_11138 _let_1)))) (let ((_let_3 (ho_12161 (ho_12160 (ho_12159 k_12158 k_12153) (ho_12157 (ho_12156 k_12155 k_12153) k_12152)) k_11057))) (let ((_let_4 (ho_11669 k_11668 _let_1))) (let ((_let_5 (ho_12154 k_12153 _let_4))) (let ((_let_6 (ho_12130 (ho_12129 _let_3 (ho_12130 k_12386 BOUND_VARIABLE_1311376)) _let_2))) (= (ho_12391 (ho_12390 (ho_12397 k_12396 BOUND_VARIABLE_1311375) BOUND_VARIABLE_1311376) BOUND_VARIABLE_1311377) (ho_12395 (ho_12394 (ho_12393 k_12392 (= BOUND_VARIABLE_1311377 _let_4)) (ho_12391 (ho_12390 k_12389 _let_6) _let_4)) (ho_12391 (ho_12390 k_12389 (ho_12130 (ho_12129 _let_3 _let_6) (ho_12130 (ho_12129 _let_3 (ho_12130 k_12386 _let_2)) _let_2))) (ho_12130 (ho_12129 _let_3 (ho_12130 (ho_12129 (ho_12388 k_12387 (= _let_5 (ho_11059 (ho_11058 k_11095 (ho_12154 k_12153 (ho_12130 (ho_12129 _let_3 BOUND_VARIABLE_1311375) _let_2))) _let_5))) (ho_12130 (ho_12129 _let_3 (ho_12130 k_12386 BOUND_VARIABLE_1311375)) _let_2)) BOUND_VARIABLE_1311375)) (ho_12130 (ho_12129 _let_3 (ho_12130 k_12386 BOUND_VARIABLE_1311377)) _let_2)))))))))))))) (let ((_let_4214 (forall ((BOUND_VARIABLE_1311335 tptp.code_integer) (BOUND_VARIABLE_1311336 tptp.code_integer) (BOUND_VARIABLE_1311337 tptp.code_integer)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (let ((_let_2 (ho_11669 k_11668 (ho_11139 k_11138 _let_1)))) (let ((_let_3 (ho_12161 (ho_12160 (ho_12159 k_12158 k_12153) (ho_12157 (ho_12156 k_12155 k_12153) k_12152)) k_11057))) (let ((_let_4 (ho_12130 (ho_12129 _let_3 (ho_12130 k_12386 BOUND_VARIABLE_1311336)) _let_2))) (let ((_let_5 (ho_11669 k_11668 _let_1))) (= (ho_12391 (ho_12390 (ho_12397 k_12398 BOUND_VARIABLE_1311335) BOUND_VARIABLE_1311336) BOUND_VARIABLE_1311337) (ho_12395 (ho_12394 (ho_12393 k_12392 (= BOUND_VARIABLE_1311337 _let_5)) (ho_12391 (ho_12390 k_12389 _let_4) _let_5)) (ho_12391 (ho_12390 k_12389 (ho_12130 (ho_12129 _let_3 _let_4) (ho_12130 (ho_12129 _let_3 (ho_12130 k_12386 _let_2)) _let_2))) (ho_12130 (ho_12129 _let_3 BOUND_VARIABLE_1311335) (ho_12130 (ho_12129 _let_3 (ho_12130 k_12386 BOUND_VARIABLE_1311337)) _let_2))))))))))))) (let ((_let_4215 (forall ((BOUND_VARIABLE_1311324 tptp.code_integer)) (= (ho_12130 (ho_12129 (ho_12161 (ho_12160 (ho_12159 k_12158 k_12153) (ho_12157 (ho_12156 k_12155 k_12153) k_12152)) k_11057) (ho_12130 k_12386 BOUND_VARIABLE_1311324)) (ho_11669 k_11668 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (ho_12130 k_12399 BOUND_VARIABLE_1311324))))) (let ((_let_4216 (forall ((BOUND_VARIABLE_1311279 tptp.code_integer) (BOUND_VARIABLE_1311280 tptp.code_integer) (BOUND_VARIABLE_1311281 tptp.code_integer)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (let ((_let_2 (ho_11669 k_11668 (ho_11139 k_11138 _let_1)))) (let ((_let_3 (ho_12161 (ho_12160 (ho_12159 k_12158 k_12153) (ho_12157 (ho_12156 k_12155 k_12153) k_12152)) k_11057))) (let ((_let_4 (ho_12130 (ho_12129 _let_3 (ho_12130 k_12386 BOUND_VARIABLE_1311280)) _let_2))) (let ((_let_5 (ho_11669 k_11668 _let_1))) (= (ho_12391 (ho_12390 (ho_12397 k_12400 BOUND_VARIABLE_1311279) BOUND_VARIABLE_1311280) BOUND_VARIABLE_1311281) (ho_12395 (ho_12394 (ho_12393 k_12392 (= BOUND_VARIABLE_1311281 _let_5)) (ho_12391 (ho_12390 k_12389 _let_4) _let_5)) (ho_12391 (ho_12390 k_12389 (ho_12130 (ho_12129 _let_3 _let_4) (ho_12130 (ho_12129 _let_3 (ho_12130 k_12386 _let_2)) _let_2))) (ho_12130 (ho_12129 _let_3 (ho_12130 (ho_12129 _let_3 (ho_12130 k_12386 BOUND_VARIABLE_1311279)) _let_2)) (ho_12130 (ho_12129 _let_3 (ho_12130 k_12386 BOUND_VARIABLE_1311281)) _let_2))))))))))))) (let ((_let_4217 (forall ((BOUND_VARIABLE_1311254 tptp.int) (BOUND_VARIABLE_1311255 tptp.nat) (BOUND_VARIABLE_1311256 tptp.nat)) (= (ho_11059 (ho_11058 k_11057 BOUND_VARIABLE_1311254) (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311255)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1311256))) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))))))) (ho_11056 (ho_12325 (ho_12402 k_12401 BOUND_VARIABLE_1311254) BOUND_VARIABLE_1311255) BOUND_VARIABLE_1311256))))) (let ((_let_4218 (forall ((BOUND_VARIABLE_1311222 tptp.nat) (BOUND_VARIABLE_1311223 tptp.nat) (BOUND_VARIABLE_1311224 tptp.nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311222)) (ho_11056 k_11055 (ho_11139 (ho_11479 (ho_12405 k_12404 k_12403) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311223)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1311224))) (ho_11056 k_11055 (ho_11139 k_11138 _let_1)))))) _let_1)))) (ho_11139 (ho_11479 (ho_12407 k_12406 BOUND_VARIABLE_1311222) BOUND_VARIABLE_1311223) BOUND_VARIABLE_1311224)))))) (let ((_let_4219 (forall ((BOUND_VARIABLE_1311197 tptp.code_integer) (BOUND_VARIABLE_1311198 tptp.nat) (BOUND_VARIABLE_1311199 tptp.nat)) (= (ho_12130 (ho_12129 (ho_12161 (ho_12160 (ho_12159 k_12158 k_12153) (ho_12157 (ho_12156 k_12155 k_12153) k_12152)) k_11057) BOUND_VARIABLE_1311197) (ho_11669 k_11668 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311198)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1311199))) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))))))) (ho_11669 (ho_12410 (ho_12409 k_12408 BOUND_VARIABLE_1311197) BOUND_VARIABLE_1311198) BOUND_VARIABLE_1311199))))) (let ((_let_4220 (forall ((BOUND_VARIABLE_1311171 tptp.rat) (BOUND_VARIABLE_1311172 tptp.nat) (BOUND_VARIABLE_1311173 tptp.nat)) (= (ho_11508 (ho_11511 (ho_12143 (ho_12142 (ho_12141 k_12140 k_11502) (ho_11506 (ho_11505 k_11504 k_11502) k_11116)) k_12139) BOUND_VARIABLE_1311171) (ho_11498 k_11497 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311172)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1311173))) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))))))) (ho_11498 (ho_12413 (ho_12412 k_12411 BOUND_VARIABLE_1311171) BOUND_VARIABLE_1311172) BOUND_VARIABLE_1311173))))) (let ((_let_4221 (forall ((BOUND_VARIABLE_1311149 tptp.int) (BOUND_VARIABLE_1311150 tptp.int) (BOUND_VARIABLE_1311151 tptp.int)) (= (or (= BOUND_VARIABLE_1311149 BOUND_VARIABLE_1311151) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1311151) (ho_12416 (ho_12415 k_12414 (ho_11059 (ho_11058 k_11057 BOUND_VARIABLE_1311149) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) BOUND_VARIABLE_1311150))) (ho_11094 (ho_11093 (ho_11104 k_12417 BOUND_VARIABLE_1311149) BOUND_VARIABLE_1311150) BOUND_VARIABLE_1311151))))) (let ((_let_4222 (forall ((BOUND_VARIABLE_1311135 tptp.int) (BOUND_VARIABLE_1311136 tptp.int)) (= (or (= BOUND_VARIABLE_1311135 BOUND_VARIABLE_1311136) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1311136) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12418 BOUND_VARIABLE_1311135) BOUND_VARIABLE_1311136))))) (let ((_let_4223 (forall ((BOUND_VARIABLE_1311115 tptp.nat) (BOUND_VARIABLE_1311116 tptp.nat) (BOUND_VARIABLE_1311117 tptp.nat)) (= (or (= BOUND_VARIABLE_1311117 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311115)) (ho_11056 k_11055 BOUND_VARIABLE_1311116)))) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1311117) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 (ho_11064 k_12419 BOUND_VARIABLE_1311115) BOUND_VARIABLE_1311116) BOUND_VARIABLE_1311117))))) (let ((_let_4224 (forall ((BOUND_VARIABLE_1311101 Bool) (BOUND_VARIABLE_1311102 Bool)) (= (or (= BOUND_VARIABLE_1311101 BOUND_VARIABLE_1311102) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1311102) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12420 BOUND_VARIABLE_1311101) BOUND_VARIABLE_1311102))))) (let ((_let_4225 (forall ((BOUND_VARIABLE_1355989 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1311093 tptp.nat) (BOUND_VARIABLE_1311094 tptp.nat)) (= (ho_11139 (ho_11479 (ho_12255 k_12421 BOUND_VARIABLE_1355989) BOUND_VARIABLE_1311093) BOUND_VARIABLE_1311094) (ho_11139 (ho_11479 BOUND_VARIABLE_1355989 BOUND_VARIABLE_1311094) BOUND_VARIABLE_1311093))))) (let ((_let_4226 (forall ((BOUND_VARIABLE_1311073 tptp.nat) (BOUND_VARIABLE_1311074 tptp.nat)) (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311073)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1311074))) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))))) (ho_11139 (ho_11479 k_12422 BOUND_VARIABLE_1311073) BOUND_VARIABLE_1311074))))) (let ((_let_4227 (forall ((BOUND_VARIABLE_1311068 tptp.nat)) (= BOUND_VARIABLE_1311068 (ho_11139 k_12423 BOUND_VARIABLE_1311068))))) (let ((_let_4228 (forall ((BOUND_VARIABLE_1311049 tptp.nat) (BOUND_VARIABLE_1311050 tptp.nat)) (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311049)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1311050))) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))))) (ho_11139 (ho_11479 k_12424 BOUND_VARIABLE_1311049) BOUND_VARIABLE_1311050))))) (let ((_let_4229 (forall ((BOUND_VARIABLE_1311044 tptp.nat)) (= BOUND_VARIABLE_1311044 (ho_11139 k_12425 BOUND_VARIABLE_1311044))))) (let ((_let_4230 (forall ((BOUND_VARIABLE_1311025 tptp.nat) (BOUND_VARIABLE_1311026 tptp.nat)) (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1311025)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1311026))) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))))) (ho_11139 (ho_11479 k_12426 BOUND_VARIABLE_1311025) BOUND_VARIABLE_1311026))))) (let ((_let_4231 (forall ((BOUND_VARIABLE_1311020 tptp.nat)) (= BOUND_VARIABLE_1311020 (ho_11139 k_12427 BOUND_VARIABLE_1311020))))) (let ((_let_4232 (forall ((BOUND_VARIABLE_1311005 tptp.rat) (BOUND_VARIABLE_1311006 tptp.nat)) (let ((_let_1 (ho_11506 (ho_11505 k_11504 k_11502) k_11116))) (= (ho_11508 (ho_11511 (ho_12143 (ho_12142 (ho_12141 k_12140 k_11502) _let_1) k_12139) BOUND_VARIABLE_1311005) (ho_11508 (ho_11507 _let_1 k_11500) (ho_11498 k_11497 BOUND_VARIABLE_1311006))) (ho_11498 (ho_12429 k_12428 BOUND_VARIABLE_1311005) BOUND_VARIABLE_1311006)))))) (let ((_let_4233 (forall ((BOUND_VARIABLE_1310972 tptp.rat) (BOUND_VARIABLE_1310973 tptp.nat) (BOUND_VARIABLE_1310974 tptp.nat)) (let ((_let_1 (ho_11506 (ho_11505 k_11504 k_11502) k_11116))) (= (ho_11508 (ho_11511 k_12430 (ho_11508 (ho_11511 (ho_12143 (ho_12142 (ho_12141 k_12140 k_11502) _let_1) k_12139) BOUND_VARIABLE_1310972) (ho_11508 (ho_11507 _let_1 k_11500) (ho_11498 k_11497 BOUND_VARIABLE_1310974)))) (ho_11498 k_11497 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1310973)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1310974))) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))))))) (ho_11498 (ho_12413 (ho_12412 k_12431 BOUND_VARIABLE_1310972) BOUND_VARIABLE_1310973) BOUND_VARIABLE_1310974)))))) (let ((_let_4234 (forall ((BOUND_VARIABLE_1310960 tptp.int) (BOUND_VARIABLE_1310961 tptp.nat) (BOUND_VARIABLE_1310962 tptp.int)) (= (ho_11059 (ho_12273 (ho_12433 k_12432 BOUND_VARIABLE_1310960) BOUND_VARIABLE_1310961) BOUND_VARIABLE_1310962) (ho_11059 (ho_11058 k_11085 (ho_11059 (ho_11058 k_11057 BOUND_VARIABLE_1310960) (ho_11056 k_11055 BOUND_VARIABLE_1310961))) BOUND_VARIABLE_1310962))))) (let ((_let_4235 (forall ((BOUND_VARIABLE_1310951 tptp.int) (BOUND_VARIABLE_1310952 tptp.nat)) (= (ho_11056 (ho_12276 k_12434 BOUND_VARIABLE_1310951) BOUND_VARIABLE_1310952) (ho_11059 (ho_11058 k_11057 BOUND_VARIABLE_1310951) (ho_11056 k_11055 BOUND_VARIABLE_1310952)))))) (let ((_let_4236 (forall ((BOUND_VARIABLE_1310921 tptp.nat) (BOUND_VARIABLE_1310922 tptp.nat) (BOUND_VARIABLE_1310923 tptp.nat)) (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11085 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1310921)) (ho_11056 k_11055 (ho_11139 (ho_11479 (ho_12405 k_12404 k_12403) BOUND_VARIABLE_1310922) (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))))) (ho_11056 k_11055 BOUND_VARIABLE_1310923))) (ho_11139 (ho_11479 (ho_12407 k_12435 BOUND_VARIABLE_1310921) BOUND_VARIABLE_1310922) BOUND_VARIABLE_1310923))))) (let ((_let_4237 (forall ((BOUND_VARIABLE_1310901 tptp.nat) (BOUND_VARIABLE_1310902 tptp.nat)) (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1310901)) (ho_11056 k_11055 (ho_11139 (ho_11479 (ho_12405 k_12404 k_12403) BOUND_VARIABLE_1310902) (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (ho_11139 (ho_11479 k_12436 BOUND_VARIABLE_1310901) BOUND_VARIABLE_1310902))))) (let ((_let_4238 (forall ((BOUND_VARIABLE_1310889 tptp.code_integer) (BOUND_VARIABLE_1310890 tptp.nat) (BOUND_VARIABLE_1310891 tptp.code_integer)) (= (ho_12130 (ho_12439 (ho_12438 k_12437 BOUND_VARIABLE_1310889) BOUND_VARIABLE_1310890) BOUND_VARIABLE_1310891) (ho_12130 (ho_12129 k_12128 (ho_12130 (ho_12129 (ho_12161 (ho_12160 (ho_12159 k_12158 k_12153) (ho_12157 (ho_12156 k_12155 k_12153) k_12152)) k_11057) BOUND_VARIABLE_1310889) (ho_11669 k_11668 BOUND_VARIABLE_1310890))) BOUND_VARIABLE_1310891))))) (let ((_let_4239 (forall ((BOUND_VARIABLE_1310880 tptp.code_integer) (BOUND_VARIABLE_1310881 tptp.nat)) (= (ho_11669 (ho_12441 k_12440 BOUND_VARIABLE_1310880) BOUND_VARIABLE_1310881) (ho_12130 (ho_12129 (ho_12161 (ho_12160 (ho_12159 k_12158 k_12153) (ho_12157 (ho_12156 k_12155 k_12153) k_12152)) k_11057) BOUND_VARIABLE_1310880) (ho_11669 k_11668 BOUND_VARIABLE_1310881)))))) (let ((_let_4240 (forall ((BOUND_VARIABLE_1310862 tptp.rat) (BOUND_VARIABLE_1310863 tptp.nat) (BOUND_VARIABLE_1310864 tptp.rat)) (let ((_let_1 (ho_12142 (ho_12141 k_12140 k_11502) (ho_11506 (ho_11505 k_11504 k_11502) k_11116)))) (= (ho_11508 (ho_11511 (ho_12143 _let_1 k_12442) (ho_11508 (ho_11511 (ho_12143 _let_1 k_12139) BOUND_VARIABLE_1310862) (ho_11498 k_11497 BOUND_VARIABLE_1310863))) BOUND_VARIABLE_1310864) (ho_11508 (ho_12445 (ho_12444 k_12443 BOUND_VARIABLE_1310862) BOUND_VARIABLE_1310863) BOUND_VARIABLE_1310864)))))) (let ((_let_4241 (forall ((BOUND_VARIABLE_1310849 tptp.rat) (BOUND_VARIABLE_1310850 tptp.nat)) (= (ho_11508 (ho_11511 (ho_12143 (ho_12142 (ho_12141 k_12140 k_11502) (ho_11506 (ho_11505 k_11504 k_11502) k_11116)) k_12139) BOUND_VARIABLE_1310849) (ho_11498 k_11497 BOUND_VARIABLE_1310850)) (ho_11498 (ho_12429 k_12446 BOUND_VARIABLE_1310849) BOUND_VARIABLE_1310850))))) (let ((_let_4242 (forall ((BOUND_VARIABLE_1356228 |u_(-> tptp.nat tptp.nat tptp.int)|) (BOUND_VARIABLE_1310841 tptp.nat) (BOUND_VARIABLE_1310842 tptp.nat)) (= (ho_11056 (ho_12325 (ho_12327 k_12447 BOUND_VARIABLE_1356228) BOUND_VARIABLE_1310841) BOUND_VARIABLE_1310842) (ho_11056 (ho_12325 BOUND_VARIABLE_1356228 BOUND_VARIABLE_1310842) BOUND_VARIABLE_1310841))))) (let ((_let_4243 (forall ((BOUND_VARIABLE_1356241 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1310832 tptp.nat) (BOUND_VARIABLE_1310833 tptp.nat)) (= (ho_11139 (ho_11479 (ho_12255 k_12448 BOUND_VARIABLE_1356241) BOUND_VARIABLE_1310832) BOUND_VARIABLE_1310833) (ho_11139 (ho_11479 BOUND_VARIABLE_1356241 BOUND_VARIABLE_1310833) BOUND_VARIABLE_1310832))))) (let ((_let_4244 (forall ((BOUND_VARIABLE_1356254 |u_(-> tptp.int tptp.int tptp.int)|) (BOUND_VARIABLE_1310823 tptp.int) (BOUND_VARIABLE_1310824 tptp.int)) (= (ho_11059 (ho_11058 (ho_12450 k_12449 BOUND_VARIABLE_1356254) BOUND_VARIABLE_1310823) BOUND_VARIABLE_1310824) (ho_11059 (ho_11058 BOUND_VARIABLE_1356254 BOUND_VARIABLE_1310824) BOUND_VARIABLE_1310823))))) (let ((_let_4245 (forall ((BOUND_VARIABLE_1356271 |u_(-> tptp.int tptp.nat tptp.int)|) (BOUND_VARIABLE_1310814 tptp.nat) (BOUND_VARIABLE_1310815 tptp.int)) (= (ho_11059 (ho_12273 (ho_12452 k_12451 BOUND_VARIABLE_1356271) BOUND_VARIABLE_1310814) BOUND_VARIABLE_1310815) (ho_11056 (ho_12276 BOUND_VARIABLE_1356271 BOUND_VARIABLE_1310815) BOUND_VARIABLE_1310814))))) (let ((_let_4246 (forall ((BOUND_VARIABLE_1356288 |u_(-> tptp.nat tptp.int tptp.int)|) (BOUND_VARIABLE_1310805 tptp.int) (BOUND_VARIABLE_1310806 tptp.nat)) (= (ho_11056 (ho_12276 (ho_12275 k_12453 BOUND_VARIABLE_1356288) BOUND_VARIABLE_1310805) BOUND_VARIABLE_1310806) (ho_11059 (ho_12273 BOUND_VARIABLE_1356288 BOUND_VARIABLE_1310806) BOUND_VARIABLE_1310805))))) (let ((_let_4247 (forall ((BOUND_VARIABLE_1356301 |u_(-> tptp.nat tptp.nat tptp.int)|) (BOUND_VARIABLE_1310796 tptp.nat) (BOUND_VARIABLE_1310797 tptp.nat)) (= (ho_11056 (ho_12325 (ho_12327 k_12454 BOUND_VARIABLE_1356301) BOUND_VARIABLE_1310796) BOUND_VARIABLE_1310797) (ho_11056 (ho_12325 BOUND_VARIABLE_1356301 BOUND_VARIABLE_1310797) BOUND_VARIABLE_1310796))))) (let ((_let_4248 (forall ((BOUND_VARIABLE_1356314 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1310787 tptp.nat) (BOUND_VARIABLE_1310788 tptp.nat)) (= (ho_11139 (ho_11479 (ho_12255 k_12455 BOUND_VARIABLE_1356314) BOUND_VARIABLE_1310787) BOUND_VARIABLE_1310788) (ho_11139 (ho_11479 BOUND_VARIABLE_1356314 BOUND_VARIABLE_1310788) BOUND_VARIABLE_1310787))))) (let ((_let_4249 (forall ((BOUND_VARIABLE_1310749 tptp.nat) (BOUND_VARIABLE_1310750 tptp.nat) (BOUND_VARIABLE_1310751 tptp.nat) (BOUND_VARIABLE_1310752 tptp.rat)) (let ((_let_1 (ho_11498 k_11497 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (let ((_let_2 (ho_11506 (ho_11505 k_11504 k_11502) k_11116))) (let ((_let_3 (ho_12142 (ho_12141 k_12140 k_11502) _let_2))) (let ((_let_4 (ho_12143 _let_3 k_12442))) (let ((_let_5 (ho_12143 _let_3 k_12139))) (= (ho_11508 (ho_11511 _let_4 (ho_11508 (ho_11511 _let_5 (ho_11508 (ho_11511 _let_5 (ho_11508 (ho_11511 _let_5 (ho_11508 (ho_11511 _let_5 (ho_11508 (ho_11511 _let_4 (ho_12457 k_12456 (ho_11030 k_11029 tptp.one))) (ho_11498 k_11497 BOUND_VARIABLE_1310749))) _let_1)) (ho_11508 (ho_11507 _let_2 k_11500) (ho_11498 k_11497 BOUND_VARIABLE_1310750)))) _let_1)) (ho_11498 k_11497 BOUND_VARIABLE_1310751))) BOUND_VARIABLE_1310752) (ho_11508 (ho_12445 (ho_12460 (ho_12459 k_12458 BOUND_VARIABLE_1310749) BOUND_VARIABLE_1310750) BOUND_VARIABLE_1310751) BOUND_VARIABLE_1310752)))))))))) (let ((_let_4250 (forall ((BOUND_VARIABLE_1310719 tptp.rat) (BOUND_VARIABLE_1310720 tptp.nat) (BOUND_VARIABLE_1310721 tptp.nat) (BOUND_VARIABLE_1310722 tptp.rat)) (let ((_let_1 (ho_11506 (ho_11505 k_11504 k_11502) k_11116))) (let ((_let_2 (ho_12142 (ho_12141 k_12140 k_11502) _let_1))) (let ((_let_3 (ho_12143 _let_2 k_12139))) (= (ho_11508 (ho_11511 (ho_12143 _let_2 k_12442) (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 BOUND_VARIABLE_1310719) (ho_11508 (ho_11507 _let_1 k_11500) (ho_11498 k_11497 BOUND_VARIABLE_1310720)))) (ho_11498 k_11497 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (ho_11498 k_11497 BOUND_VARIABLE_1310721))) BOUND_VARIABLE_1310722) (ho_11508 (ho_12445 (ho_12460 (ho_12462 k_12461 BOUND_VARIABLE_1310719) BOUND_VARIABLE_1310720) BOUND_VARIABLE_1310721) BOUND_VARIABLE_1310722)))))))) (let ((_let_4251 (forall ((BOUND_VARIABLE_1310692 tptp.nat) (BOUND_VARIABLE_1310693 tptp.nat) (BOUND_VARIABLE_1310694 tptp.set_nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310694) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 _let_1) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 _let_1)) (ho_11056 k_11055 BOUND_VARIABLE_1310692)))))) (= BOUND_VARIABLE_1310693 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310694))) (ho_11191 (ho_11190 (ho_12470 k_12469 BOUND_VARIABLE_1310692) BOUND_VARIABLE_1310693) BOUND_VARIABLE_1310694)))))) (let ((_let_4252 (forall ((BOUND_VARIABLE_1310665 tptp.nat) (BOUND_VARIABLE_1310666 tptp.nat) (BOUND_VARIABLE_1310667 tptp.set_nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310667) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 _let_1) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 _let_1)) (ho_11056 k_11055 BOUND_VARIABLE_1310665)))))) (= BOUND_VARIABLE_1310666 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310667))) (ho_11191 (ho_11190 (ho_12470 k_12471 BOUND_VARIABLE_1310665) BOUND_VARIABLE_1310666) BOUND_VARIABLE_1310667)))))) (let ((_let_4253 (forall ((BOUND_VARIABLE_1310638 tptp.nat) (BOUND_VARIABLE_1310639 tptp.nat) (BOUND_VARIABLE_1310640 tptp.set_nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310640) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 _let_1) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 _let_1)) (ho_11056 k_11055 BOUND_VARIABLE_1310638)))))) (= BOUND_VARIABLE_1310639 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310640))) (ho_11191 (ho_11190 (ho_12470 k_12472 BOUND_VARIABLE_1310638) BOUND_VARIABLE_1310639) BOUND_VARIABLE_1310640)))))) (let ((_let_4254 (forall ((BOUND_VARIABLE_1310616 tptp.nat) (BOUND_VARIABLE_1310617 tptp.nat) (BOUND_VARIABLE_1310618 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310618) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1310616))) (= BOUND_VARIABLE_1310617 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310618))) (ho_11191 (ho_11190 (ho_12470 k_12473 BOUND_VARIABLE_1310616) BOUND_VARIABLE_1310617) BOUND_VARIABLE_1310618))))) (let ((_let_4255 (forall ((BOUND_VARIABLE_1310585 tptp.nat) (BOUND_VARIABLE_1310586 tptp.nat) (BOUND_VARIABLE_1310587 tptp.set_nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310587) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 _let_1) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11085 (ho_11056 k_11055 (ho_11061 k_11060 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))))) (ho_11056 k_11055 BOUND_VARIABLE_1310585))))) (ho_11056 k_11055 (ho_11139 k_11138 _let_1))))))) (= BOUND_VARIABLE_1310586 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310587))) (ho_11191 (ho_11190 (ho_12470 k_12476 BOUND_VARIABLE_1310585) BOUND_VARIABLE_1310586) BOUND_VARIABLE_1310587)))))) (let ((_let_4256 (forall ((BOUND_VARIABLE_1310549 tptp.nat) (BOUND_VARIABLE_1310550 tptp.nat) (BOUND_VARIABLE_1310551 tptp.nat) (BOUND_VARIABLE_1310552 tptp.rat)) (let ((_let_1 (ho_11506 (ho_11505 k_11504 k_11502) k_11116))) (let ((_let_2 (ho_12142 (ho_12141 k_12140 k_11502) _let_1))) (let ((_let_3 (ho_12143 _let_2 k_12139))) (= (ho_11508 (ho_11511 (ho_12143 _let_2 k_12442) (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 (ho_11498 k_11497 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1310549)) (ho_11056 k_11055 BOUND_VARIABLE_1310550))))) (ho_11508 (ho_11507 _let_1 k_11500) (ho_11498 k_11497 BOUND_VARIABLE_1310550)))) (ho_11498 k_11497 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (ho_11498 k_11497 BOUND_VARIABLE_1310551))) BOUND_VARIABLE_1310552) (ho_11508 (ho_12445 (ho_12460 (ho_12459 k_12477 BOUND_VARIABLE_1310549) BOUND_VARIABLE_1310550) BOUND_VARIABLE_1310551) BOUND_VARIABLE_1310552)))))))) (let ((_let_4257 (forall ((BOUND_VARIABLE_1310527 tptp.nat) (BOUND_VARIABLE_1310528 tptp.nat) (BOUND_VARIABLE_1310529 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310529) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1310527))) (= BOUND_VARIABLE_1310528 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310529))) (ho_11191 (ho_11190 (ho_12470 k_12478 BOUND_VARIABLE_1310527) BOUND_VARIABLE_1310528) BOUND_VARIABLE_1310529))))) (let ((_let_4258 (forall ((BOUND_VARIABLE_1310505 tptp.nat) (BOUND_VARIABLE_1310506 tptp.nat) (BOUND_VARIABLE_1310507 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310507) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1310505))) (= BOUND_VARIABLE_1310506 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310507))) (ho_11191 (ho_11190 (ho_12470 k_12479 BOUND_VARIABLE_1310505) BOUND_VARIABLE_1310506) BOUND_VARIABLE_1310507))))) (let ((_let_4259 (forall ((BOUND_VARIABLE_1310483 tptp.nat) (BOUND_VARIABLE_1310484 tptp.nat) (BOUND_VARIABLE_1310485 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310485) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1310483))) (= BOUND_VARIABLE_1310484 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310485))) (ho_11191 (ho_11190 (ho_12470 k_12480 BOUND_VARIABLE_1310483) BOUND_VARIABLE_1310484) BOUND_VARIABLE_1310485))))) (let ((_let_4260 (forall ((BOUND_VARIABLE_1310447 tptp.nat) (BOUND_VARIABLE_1310448 tptp.rat) (BOUND_VARIABLE_1310449 tptp.nat) (BOUND_VARIABLE_1310450 tptp.nat) (BOUND_VARIABLE_1310451 tptp.rat)) (let ((_let_1 (ho_11506 (ho_11505 k_11504 k_11502) k_11116))) (let ((_let_2 (ho_12142 (ho_12141 k_12140 k_11502) _let_1))) (let ((_let_3 (ho_12143 _let_2 k_12139))) (= (ho_11508 (ho_11511 (ho_12143 _let_2 k_12442) (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 (ho_11498 k_11497 BOUND_VARIABLE_1310447)) BOUND_VARIABLE_1310448)) (ho_11508 (ho_11507 _let_1 k_11500) (ho_11498 k_11497 BOUND_VARIABLE_1310449)))) (ho_11498 k_11497 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (ho_11498 k_11497 BOUND_VARIABLE_1310450))) BOUND_VARIABLE_1310451) (ho_11508 (ho_12445 (ho_12460 (ho_12462 (ho_12482 k_12481 BOUND_VARIABLE_1310447) BOUND_VARIABLE_1310448) BOUND_VARIABLE_1310449) BOUND_VARIABLE_1310450) BOUND_VARIABLE_1310451)))))))) (let ((_let_4261 (forall ((BOUND_VARIABLE_1310409 tptp.rat) (BOUND_VARIABLE_1310410 tptp.nat) (BOUND_VARIABLE_1310411 tptp.nat) (BOUND_VARIABLE_1310412 tptp.rat)) (let ((_let_1 (ho_11498 k_11497 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (let ((_let_2 (ho_11498 k_11497 BOUND_VARIABLE_1310410))) (let ((_let_3 (ho_11506 (ho_11505 k_11504 k_11502) k_11116))) (let ((_let_4 (ho_11507 _let_3 k_11500))) (let ((_let_5 (ho_12142 (ho_12141 k_12140 k_11502) _let_3))) (let ((_let_6 (ho_12143 _let_5 k_12139))) (= (ho_11508 (ho_11511 (ho_12143 _let_5 k_12442) (ho_11508 (ho_11511 _let_6 (ho_11508 (ho_11511 _let_6 (ho_11508 (ho_11511 _let_6 (ho_11508 (ho_11511 _let_6 (ho_11508 (ho_11511 _let_6 _let_2) BOUND_VARIABLE_1310409)) (ho_11508 _let_4 _let_1))) (ho_11508 _let_4 _let_2))) _let_1)) (ho_11498 k_11497 BOUND_VARIABLE_1310411))) BOUND_VARIABLE_1310412) (ho_11508 (ho_12445 (ho_12460 (ho_12462 k_12483 BOUND_VARIABLE_1310409) BOUND_VARIABLE_1310410) BOUND_VARIABLE_1310411) BOUND_VARIABLE_1310412))))))))))) (let ((_let_4262 (forall ((BOUND_VARIABLE_1310378 tptp.nat) (BOUND_VARIABLE_1310379 tptp.nat) (BOUND_VARIABLE_1310380 tptp.nat) (BOUND_VARIABLE_1310381 tptp.rat)) (let ((_let_1 (ho_11506 (ho_11505 k_11504 k_11502) k_11116))) (let ((_let_2 (ho_12142 (ho_12141 k_12140 k_11502) _let_1))) (let ((_let_3 (ho_12143 _let_2 k_12139))) (= (ho_11508 (ho_11511 (ho_12143 _let_2 k_12442) (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 (ho_11498 k_11497 BOUND_VARIABLE_1310378)) (ho_11508 (ho_11507 _let_1 k_11500) (ho_11498 k_11497 BOUND_VARIABLE_1310379)))) (ho_11498 k_11497 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (ho_11498 k_11497 BOUND_VARIABLE_1310380))) BOUND_VARIABLE_1310381) (ho_11508 (ho_12445 (ho_12460 (ho_12459 k_12484 BOUND_VARIABLE_1310378) BOUND_VARIABLE_1310379) BOUND_VARIABLE_1310380) BOUND_VARIABLE_1310381)))))))) (let ((_let_4263 (forall ((BOUND_VARIABLE_1310342 tptp.nat) (BOUND_VARIABLE_1310343 tptp.rat) (BOUND_VARIABLE_1310344 tptp.nat) (BOUND_VARIABLE_1310345 tptp.nat) (BOUND_VARIABLE_1310346 tptp.rat)) (let ((_let_1 (ho_11506 (ho_11505 k_11504 k_11502) k_11116))) (let ((_let_2 (ho_12142 (ho_12141 k_12140 k_11502) _let_1))) (let ((_let_3 (ho_12143 _let_2 k_12139))) (= (ho_11508 (ho_11511 (ho_12143 _let_2 k_12442) (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 (ho_11498 k_11497 BOUND_VARIABLE_1310342)) BOUND_VARIABLE_1310343)) (ho_11508 (ho_11507 _let_1 k_11500) (ho_11498 k_11497 BOUND_VARIABLE_1310344)))) (ho_11498 k_11497 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (ho_11498 k_11497 BOUND_VARIABLE_1310345))) BOUND_VARIABLE_1310346) (ho_11508 (ho_12445 (ho_12460 (ho_12462 (ho_12482 k_12485 BOUND_VARIABLE_1310342) BOUND_VARIABLE_1310343) BOUND_VARIABLE_1310344) BOUND_VARIABLE_1310345) BOUND_VARIABLE_1310346)))))))) (let ((_let_4264 (forall ((BOUND_VARIABLE_1310310 tptp.rat) (BOUND_VARIABLE_1310311 tptp.nat) (BOUND_VARIABLE_1310312 tptp.nat) (BOUND_VARIABLE_1310313 tptp.rat)) (let ((_let_1 (ho_11506 (ho_11505 k_11504 k_11502) k_11116))) (let ((_let_2 (ho_11507 _let_1 k_11500))) (let ((_let_3 (ho_12142 (ho_12141 k_12140 k_11502) _let_1))) (let ((_let_4 (ho_12143 _let_3 k_12139))) (= (ho_11508 (ho_11511 (ho_12143 _let_3 k_12442) (ho_11508 (ho_11511 _let_4 (ho_11508 (ho_11511 _let_4 (ho_11508 (ho_11511 _let_4 (ho_11508 _let_2 BOUND_VARIABLE_1310310)) (ho_11508 _let_2 (ho_11498 k_11497 BOUND_VARIABLE_1310311)))) (ho_11498 k_11497 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (ho_11498 k_11497 BOUND_VARIABLE_1310312))) BOUND_VARIABLE_1310313) (ho_11508 (ho_12445 (ho_12460 (ho_12462 k_12486 BOUND_VARIABLE_1310310) BOUND_VARIABLE_1310311) BOUND_VARIABLE_1310312) BOUND_VARIABLE_1310313))))))))) (let ((_let_4265 (forall ((BOUND_VARIABLE_1310288 tptp.nat) (BOUND_VARIABLE_1310289 tptp.nat) (BOUND_VARIABLE_1310290 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310290) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1310288))) (= BOUND_VARIABLE_1310289 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310290))) (ho_11191 (ho_11190 (ho_12470 k_12487 BOUND_VARIABLE_1310288) BOUND_VARIABLE_1310289) BOUND_VARIABLE_1310290))))) (let ((_let_4266 (forall ((BOUND_VARIABLE_1310266 tptp.nat) (BOUND_VARIABLE_1310267 tptp.nat) (BOUND_VARIABLE_1310268 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310268) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1310266))) (= BOUND_VARIABLE_1310267 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310268))) (ho_11191 (ho_11190 (ho_12470 k_12488 BOUND_VARIABLE_1310266) BOUND_VARIABLE_1310267) BOUND_VARIABLE_1310268))))) (let ((_let_4267 (forall ((BOUND_VARIABLE_1310254 tptp.code_integer) (BOUND_VARIABLE_1310255 tptp.nat) (BOUND_VARIABLE_1310256 tptp.code_integer)) (= (ho_12130 (ho_12439 (ho_12438 k_12489 BOUND_VARIABLE_1310254) BOUND_VARIABLE_1310255) BOUND_VARIABLE_1310256) (ho_12130 (ho_12129 k_12128 (ho_12130 (ho_12129 (ho_12161 (ho_12160 (ho_12159 k_12158 k_12153) (ho_12157 (ho_12156 k_12155 k_12153) k_12152)) k_11057) BOUND_VARIABLE_1310254) (ho_11669 k_11668 BOUND_VARIABLE_1310255))) BOUND_VARIABLE_1310256))))) (let ((_let_4268 (forall ((BOUND_VARIABLE_1310242 tptp.code_integer) (BOUND_VARIABLE_1310243 tptp.nat) (BOUND_VARIABLE_1310244 tptp.code_integer)) (= (ho_12130 (ho_12439 (ho_12438 k_12490 BOUND_VARIABLE_1310242) BOUND_VARIABLE_1310243) BOUND_VARIABLE_1310244) (ho_12130 (ho_12129 k_12128 (ho_12130 (ho_12129 (ho_12161 (ho_12160 (ho_12159 k_12158 k_12153) (ho_12157 (ho_12156 k_12155 k_12153) k_12152)) k_11057) BOUND_VARIABLE_1310242) (ho_11669 k_11668 BOUND_VARIABLE_1310243))) BOUND_VARIABLE_1310244))))) (let ((_let_4269 (forall ((BOUND_VARIABLE_1310220 tptp.nat) (BOUND_VARIABLE_1310221 tptp.nat) (BOUND_VARIABLE_1310222 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310222) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1310220))) (= BOUND_VARIABLE_1310221 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310222))) (ho_11191 (ho_11190 (ho_12470 k_12491 BOUND_VARIABLE_1310220) BOUND_VARIABLE_1310221) BOUND_VARIABLE_1310222))))) (let ((_let_4270 (forall ((BOUND_VARIABLE_1310208 tptp.int) (BOUND_VARIABLE_1310209 tptp.nat) (BOUND_VARIABLE_1310210 tptp.int)) (= (ho_11059 (ho_12273 (ho_12433 k_12492 BOUND_VARIABLE_1310208) BOUND_VARIABLE_1310209) BOUND_VARIABLE_1310210) (ho_11059 (ho_11058 k_11085 (ho_11059 (ho_11058 k_11057 BOUND_VARIABLE_1310208) (ho_11056 k_11055 BOUND_VARIABLE_1310209))) BOUND_VARIABLE_1310210))))) (let ((_let_4271 (forall ((BOUND_VARIABLE_1310196 tptp.int) (BOUND_VARIABLE_1310197 tptp.nat) (BOUND_VARIABLE_1310198 tptp.int)) (= (ho_11059 (ho_12273 (ho_12433 k_12493 BOUND_VARIABLE_1310196) BOUND_VARIABLE_1310197) BOUND_VARIABLE_1310198) (ho_11059 (ho_11058 k_11085 (ho_11059 (ho_11058 k_11057 BOUND_VARIABLE_1310196) (ho_11056 k_11055 BOUND_VARIABLE_1310197))) BOUND_VARIABLE_1310198))))) (let ((_let_4272 (forall ((BOUND_VARIABLE_1310174 tptp.nat) (BOUND_VARIABLE_1310175 tptp.nat) (BOUND_VARIABLE_1310176 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310176) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1310174))) (= BOUND_VARIABLE_1310175 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310176))) (ho_11191 (ho_11190 (ho_12470 k_12494 BOUND_VARIABLE_1310174) BOUND_VARIABLE_1310175) BOUND_VARIABLE_1310176))))) (let ((_let_4273 (forall ((BOUND_VARIABLE_1310156 tptp.rat) (BOUND_VARIABLE_1310157 tptp.nat) (BOUND_VARIABLE_1310158 tptp.rat)) (let ((_let_1 (ho_12142 (ho_12141 k_12140 k_11502) (ho_11506 (ho_11505 k_11504 k_11502) k_11116)))) (= (ho_11508 (ho_11511 (ho_12143 _let_1 k_12442) (ho_11508 (ho_11511 (ho_12143 _let_1 k_12139) BOUND_VARIABLE_1310156) (ho_11498 k_11497 BOUND_VARIABLE_1310157))) BOUND_VARIABLE_1310158) (ho_11508 (ho_12445 (ho_12444 k_12495 BOUND_VARIABLE_1310156) BOUND_VARIABLE_1310157) BOUND_VARIABLE_1310158)))))) (let ((_let_4274 (forall ((BOUND_VARIABLE_1310138 tptp.rat) (BOUND_VARIABLE_1310139 tptp.nat) (BOUND_VARIABLE_1310140 tptp.rat)) (let ((_let_1 (ho_12142 (ho_12141 k_12140 k_11502) (ho_11506 (ho_11505 k_11504 k_11502) k_11116)))) (= (ho_11508 (ho_11511 (ho_12143 _let_1 k_12442) (ho_11508 (ho_11511 (ho_12143 _let_1 k_12139) BOUND_VARIABLE_1310138) (ho_11498 k_11497 BOUND_VARIABLE_1310139))) BOUND_VARIABLE_1310140) (ho_11508 (ho_12445 (ho_12444 k_12496 BOUND_VARIABLE_1310138) BOUND_VARIABLE_1310139) BOUND_VARIABLE_1310140)))))) (let ((_let_4275 (forall ((BOUND_VARIABLE_1310116 tptp.nat) (BOUND_VARIABLE_1310117 tptp.nat) (BOUND_VARIABLE_1310118 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310118) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1310116))) (= BOUND_VARIABLE_1310117 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310118))) (ho_11191 (ho_11190 (ho_12470 k_12497 BOUND_VARIABLE_1310116) BOUND_VARIABLE_1310117) BOUND_VARIABLE_1310118))))) (let ((_let_4276 (forall ((BOUND_VARIABLE_1310094 tptp.nat) (BOUND_VARIABLE_1310095 tptp.nat) (BOUND_VARIABLE_1310096 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310096) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1310094))) (= BOUND_VARIABLE_1310095 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310096))) (ho_11191 (ho_11190 (ho_12470 k_12498 BOUND_VARIABLE_1310094) BOUND_VARIABLE_1310095) BOUND_VARIABLE_1310096))))) (let ((_let_4277 (forall ((BOUND_VARIABLE_1310072 tptp.nat) (BOUND_VARIABLE_1310073 tptp.nat) (BOUND_VARIABLE_1310074 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310074) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1310072))) (= BOUND_VARIABLE_1310073 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310074))) (ho_11191 (ho_11190 (ho_12470 k_12499 BOUND_VARIABLE_1310072) BOUND_VARIABLE_1310073) BOUND_VARIABLE_1310074))))) (let ((_let_4278 (forall ((BOUND_VARIABLE_1310050 tptp.nat) (BOUND_VARIABLE_1310051 tptp.nat) (BOUND_VARIABLE_1310052 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310052) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1310050))) (= BOUND_VARIABLE_1310051 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310052))) (ho_11191 (ho_11190 (ho_12470 k_12500 BOUND_VARIABLE_1310050) BOUND_VARIABLE_1310051) BOUND_VARIABLE_1310052))))) (let ((_let_4279 (forall ((BOUND_VARIABLE_1310020 tptp.rat) (BOUND_VARIABLE_1310021 tptp.nat) (BOUND_VARIABLE_1310022 tptp.nat) (BOUND_VARIABLE_1310023 tptp.rat)) (let ((_let_1 (ho_11506 (ho_11505 k_11504 k_11502) k_11116))) (let ((_let_2 (ho_12142 (ho_12141 k_12140 k_11502) _let_1))) (let ((_let_3 (ho_12143 _let_2 k_12139))) (= (ho_11508 (ho_11511 (ho_12143 _let_2 k_12442) (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 BOUND_VARIABLE_1310020) (ho_11508 (ho_11507 _let_1 k_11500) (ho_11498 k_11497 BOUND_VARIABLE_1310021)))) (ho_11498 k_11497 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (ho_11498 k_11497 BOUND_VARIABLE_1310022))) BOUND_VARIABLE_1310023) (ho_11508 (ho_12445 (ho_12460 (ho_12462 k_12501 BOUND_VARIABLE_1310020) BOUND_VARIABLE_1310021) BOUND_VARIABLE_1310022) BOUND_VARIABLE_1310023)))))))) (let ((_let_4280 (forall ((BOUND_VARIABLE_1309998 tptp.nat) (BOUND_VARIABLE_1309999 tptp.nat) (BOUND_VARIABLE_1310000 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1310000) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1309998))) (= BOUND_VARIABLE_1309999 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1310000))) (ho_11191 (ho_11190 (ho_12470 k_12502 BOUND_VARIABLE_1309998) BOUND_VARIABLE_1309999) BOUND_VARIABLE_1310000))))) (let ((_let_4281 (forall ((BOUND_VARIABLE_1309976 tptp.nat) (BOUND_VARIABLE_1309977 tptp.nat) (BOUND_VARIABLE_1309978 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1309978) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1309976))) (= BOUND_VARIABLE_1309977 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1309978))) (ho_11191 (ho_11190 (ho_12470 k_12503 BOUND_VARIABLE_1309976) BOUND_VARIABLE_1309977) BOUND_VARIABLE_1309978))))) (let ((_let_4282 (forall ((BOUND_VARIABLE_1309954 tptp.nat) (BOUND_VARIABLE_1309955 tptp.nat) (BOUND_VARIABLE_1309956 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1309956) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1309954))) (= BOUND_VARIABLE_1309955 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1309956))) (ho_11191 (ho_11190 (ho_12470 k_12504 BOUND_VARIABLE_1309954) BOUND_VARIABLE_1309955) BOUND_VARIABLE_1309956))))) (let ((_let_4283 (forall ((BOUND_VARIABLE_1309920 tptp.nat) (BOUND_VARIABLE_1309921 tptp.nat) (BOUND_VARIABLE_1309922 tptp.nat) (BOUND_VARIABLE_1309923 tptp.set_nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (= (ho_11191 (ho_11190 (ho_12470 (ho_12506 k_12505 BOUND_VARIABLE_1309920) BOUND_VARIABLE_1309921) BOUND_VARIABLE_1309922) BOUND_VARIABLE_1309923) (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1309923) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 _let_1) BOUND_VARIABLE_1309920))) (= (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1309923) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1309921)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1309922))) (ho_11056 k_11055 (ho_11139 k_11138 _let_1)))))))))))) (let ((_let_4284 (forall ((BOUND_VARIABLE_1309877 tptp.nat) (BOUND_VARIABLE_1309878 tptp.nat) (BOUND_VARIABLE_1309879 tptp.nat) (BOUND_VARIABLE_1309880 tptp.set_nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (let ((_let_2 (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1309879))) (ho_11056 k_11055 (ho_11139 k_11138 _let_1))))) (let ((_let_3 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1309878)))) (= (ho_11191 (ho_11190 (ho_12470 (ho_12506 k_12507 BOUND_VARIABLE_1309877) BOUND_VARIABLE_1309878) BOUND_VARIABLE_1309879) BOUND_VARIABLE_1309880) (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1309880) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 _let_1) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_11059 _let_3 (ho_11056 k_11055 BOUND_VARIABLE_1309877))))) _let_2))))) (= (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1309880) (ho_11061 k_11060 (ho_11059 _let_3 _let_2))))))))))) (let ((_let_4285 (forall ((BOUND_VARIABLE_1357066 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1309855 tptp.nat) (BOUND_VARIABLE_1309856 tptp.nat)) (= (ho_11139 (ho_11479 BOUND_VARIABLE_1357066 BOUND_VARIABLE_1309856) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1309855)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1309856))) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))))) (ho_11139 (ho_11479 (ho_12255 k_12508 BOUND_VARIABLE_1357066) BOUND_VARIABLE_1309855) BOUND_VARIABLE_1309856))))) (let ((_let_4286 (forall ((BOUND_VARIABLE_1309840 tptp.nat) (BOUND_VARIABLE_1309841 tptp.nat)) (= (ho_11054 (ho_11053 k_12509 BOUND_VARIABLE_1309840) BOUND_VARIABLE_1309841) (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1309840 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1309841)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4287 (forall ((BOUND_VARIABLE_1309806 tptp.rat) (BOUND_VARIABLE_1309807 tptp.nat) (BOUND_VARIABLE_1309808 tptp.nat) (BOUND_VARIABLE_1309809 tptp.rat)) (let ((_let_1 (ho_11498 k_11497 BOUND_VARIABLE_1309807))) (let ((_let_2 (ho_11506 (ho_11505 k_11504 k_11502) k_11116))) (let ((_let_3 (ho_12142 (ho_12141 k_12140 k_11502) _let_2))) (let ((_let_4 (ho_12143 _let_3 k_12139))) (= (ho_11508 (ho_11511 (ho_12143 _let_3 k_12442) (ho_11508 (ho_11511 _let_4 (ho_11508 (ho_11511 _let_4 (ho_11508 (ho_11511 _let_4 (ho_11508 (ho_11511 _let_4 BOUND_VARIABLE_1309806) _let_1)) (ho_11508 (ho_11507 _let_2 k_11500) _let_1))) (ho_11498 k_11497 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (ho_11498 k_11497 BOUND_VARIABLE_1309808))) BOUND_VARIABLE_1309809) (ho_11508 (ho_12445 (ho_12460 (ho_12462 k_12510 BOUND_VARIABLE_1309806) BOUND_VARIABLE_1309807) BOUND_VARIABLE_1309808) BOUND_VARIABLE_1309809))))))))) (let ((_let_4288 (forall ((BOUND_VARIABLE_1309779 tptp.nat) (BOUND_VARIABLE_1309780 tptp.nat) (BOUND_VARIABLE_1309781 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1309781) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1309780)) (ho_11056 k_11055 BOUND_VARIABLE_1309779)))))) (= BOUND_VARIABLE_1309780 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1309781))) (ho_11191 (ho_11190 (ho_12470 k_12511 BOUND_VARIABLE_1309779) BOUND_VARIABLE_1309780) BOUND_VARIABLE_1309781))))) (let ((_let_4289 (forall ((BOUND_VARIABLE_1309752 tptp.nat) (BOUND_VARIABLE_1309753 tptp.nat) (BOUND_VARIABLE_1309754 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1309754) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1309753)) (ho_11056 k_11055 BOUND_VARIABLE_1309752)))))) (= BOUND_VARIABLE_1309753 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1309754))) (ho_11191 (ho_11190 (ho_12470 k_12512 BOUND_VARIABLE_1309752) BOUND_VARIABLE_1309753) BOUND_VARIABLE_1309754))))) (let ((_let_4290 (forall ((BOUND_VARIABLE_1309725 tptp.nat) (BOUND_VARIABLE_1309726 tptp.nat) (BOUND_VARIABLE_1309727 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1309727) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1309725)) (ho_11056 k_11055 BOUND_VARIABLE_1309726)))))) (= BOUND_VARIABLE_1309726 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1309727))) (ho_11191 (ho_11190 (ho_12470 k_12513 BOUND_VARIABLE_1309725) BOUND_VARIABLE_1309726) BOUND_VARIABLE_1309727))))) (let ((_let_4291 (forall ((BOUND_VARIABLE_1309703 tptp.nat) (BOUND_VARIABLE_1309704 tptp.nat) (BOUND_VARIABLE_1309705 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1309705) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1309703))) (= BOUND_VARIABLE_1309704 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1309705))) (ho_11191 (ho_11190 (ho_12470 k_12514 BOUND_VARIABLE_1309703) BOUND_VARIABLE_1309704) BOUND_VARIABLE_1309705))))) (let ((_let_4292 (forall ((BOUND_VARIABLE_1309694 tptp.int) (BOUND_VARIABLE_1309695 tptp.int)) (= (ho_11094 (ho_11093 k_12515 BOUND_VARIABLE_1309694) BOUND_VARIABLE_1309695) (= BOUND_VARIABLE_1309694 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1309695) BOUND_VARIABLE_1309694)))))) (let ((_let_4293 (forall ((BOUND_VARIABLE_1309685 tptp.int) (BOUND_VARIABLE_1309686 tptp.int)) (= (ho_11094 (ho_11093 k_12516 BOUND_VARIABLE_1309685) BOUND_VARIABLE_1309686) (= BOUND_VARIABLE_1309685 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1309686) BOUND_VARIABLE_1309685)))))) (let ((_let_4294 (forall ((BOUND_VARIABLE_1309671 tptp.nat) (BOUND_VARIABLE_1309672 tptp.nat)) (= (ho_11054 (ho_11053 k_12517 BOUND_VARIABLE_1309671) BOUND_VARIABLE_1309672) (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1309671 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1309672)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4295 (forall ((BOUND_VARIABLE_1309660 tptp.set_int) (BOUND_VARIABLE_1309661 tptp.set_int) (BOUND_VARIABLE_1309662 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1309662))) (= (ho_11094 (ho_11234 (ho_11339 k_12518 BOUND_VARIABLE_1309660) BOUND_VARIABLE_1309661) BOUND_VARIABLE_1309662) (or (ho_11180 _let_1 BOUND_VARIABLE_1309660) (ho_11180 _let_1 BOUND_VARIABLE_1309661))))))) (let ((_let_4296 (forall ((BOUND_VARIABLE_1309651 tptp.int) (BOUND_VARIABLE_1309652 tptp.int)) (= (ho_11094 (ho_11093 k_12519 BOUND_VARIABLE_1309651) BOUND_VARIABLE_1309652) (= BOUND_VARIABLE_1309651 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1309652) BOUND_VARIABLE_1309651)))))) (let ((_let_4297 (forall ((BOUND_VARIABLE_1309642 tptp.int) (BOUND_VARIABLE_1309643 tptp.int)) (= (ho_11094 (ho_11093 k_12520 BOUND_VARIABLE_1309642) BOUND_VARIABLE_1309643) (= BOUND_VARIABLE_1309642 (ho_11059 (ho_11058 k_11095 BOUND_VARIABLE_1309643) BOUND_VARIABLE_1309642)))))) (let ((_let_4298 (forall ((BOUND_VARIABLE_1309628 tptp.nat) (BOUND_VARIABLE_1309629 tptp.nat)) (= (ho_11054 (ho_11053 k_12521 BOUND_VARIABLE_1309628) BOUND_VARIABLE_1309629) (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1309628 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1309629)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4299 (forall ((BOUND_VARIABLE_1309614 tptp.nat) (BOUND_VARIABLE_1309615 tptp.nat)) (= (ho_11054 (ho_11053 k_12522 BOUND_VARIABLE_1309614) BOUND_VARIABLE_1309615) (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1309614 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1309615)) (ho_11056 k_11055 K3))))))))))) (let ((_let_4300 (forall ((BOUND_VARIABLE_1309603 tptp.set_int) (BOUND_VARIABLE_1309604 tptp.set_int) (BOUND_VARIABLE_1309605 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1309605))) (= (ho_11094 (ho_11234 (ho_11339 k_12523 BOUND_VARIABLE_1309603) BOUND_VARIABLE_1309604) BOUND_VARIABLE_1309605) (or (ho_11180 _let_1 BOUND_VARIABLE_1309603) (ho_11180 _let_1 BOUND_VARIABLE_1309604))))))) (let ((_let_4301 (forall ((BOUND_VARIABLE_1309592 tptp.set_int) (BOUND_VARIABLE_1309593 tptp.set_int) (BOUND_VARIABLE_1309594 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1309594))) (= (ho_11094 (ho_11234 (ho_11339 k_12524 BOUND_VARIABLE_1309592) BOUND_VARIABLE_1309593) BOUND_VARIABLE_1309594) (or (ho_11180 _let_1 BOUND_VARIABLE_1309592) (ho_11180 _let_1 BOUND_VARIABLE_1309593))))))) (let ((_let_4302 (forall ((BOUND_VARIABLE_1309581 tptp.set_int) (BOUND_VARIABLE_1309582 tptp.set_int) (BOUND_VARIABLE_1309583 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1309583))) (= (ho_11094 (ho_11234 (ho_11339 k_12525 BOUND_VARIABLE_1309581) BOUND_VARIABLE_1309582) BOUND_VARIABLE_1309583) (or (ho_11180 _let_1 BOUND_VARIABLE_1309581) (ho_11180 _let_1 BOUND_VARIABLE_1309582))))))) (let ((_let_4303 (forall ((BOUND_VARIABLE_1309570 tptp.set_nat) (BOUND_VARIABLE_1309571 tptp.set_nat) (BOUND_VARIABLE_1309572 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1309572))) (= (ho_11054 (ho_11240 (ho_11343 k_12526 BOUND_VARIABLE_1309570) BOUND_VARIABLE_1309571) BOUND_VARIABLE_1309572) (or (ho_11191 _let_1 BOUND_VARIABLE_1309570) (ho_11191 _let_1 BOUND_VARIABLE_1309571))))))) (let ((_let_4304 (forall ((BOUND_VARIABLE_1309540 tptp.rat) (BOUND_VARIABLE_1309541 tptp.nat) (BOUND_VARIABLE_1309542 tptp.nat) (BOUND_VARIABLE_1309543 tptp.rat)) (let ((_let_1 (ho_11506 (ho_11505 k_11504 k_11502) k_11116))) (let ((_let_2 (ho_12142 (ho_12141 k_12140 k_11502) _let_1))) (let ((_let_3 (ho_12143 _let_2 k_12139))) (= (ho_11508 (ho_11511 (ho_12143 _let_2 k_12442) (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 BOUND_VARIABLE_1309540) (ho_11508 (ho_11507 _let_1 k_11500) (ho_11498 k_11497 BOUND_VARIABLE_1309541)))) (ho_11498 k_11497 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (ho_11498 k_11497 BOUND_VARIABLE_1309542))) BOUND_VARIABLE_1309543) (ho_11508 (ho_12445 (ho_12460 (ho_12462 k_12527 BOUND_VARIABLE_1309540) BOUND_VARIABLE_1309541) BOUND_VARIABLE_1309542) BOUND_VARIABLE_1309543)))))))) (let ((_let_4305 (forall ((BOUND_VARIABLE_1309513 tptp.nat) (BOUND_VARIABLE_1309514 tptp.nat) (BOUND_VARIABLE_1309515 tptp.set_nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1309515) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 _let_1) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 _let_1)) (ho_11056 k_11055 BOUND_VARIABLE_1309513)))))) (= BOUND_VARIABLE_1309514 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1309515))) (ho_11191 (ho_11190 (ho_12470 k_12528 BOUND_VARIABLE_1309513) BOUND_VARIABLE_1309514) BOUND_VARIABLE_1309515)))))) (let ((_let_4306 (forall ((BOUND_VARIABLE_1309486 tptp.nat) (BOUND_VARIABLE_1309487 tptp.nat) (BOUND_VARIABLE_1309488 tptp.set_nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1309488) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 _let_1) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 _let_1)) (ho_11056 k_11055 BOUND_VARIABLE_1309486)))))) (= BOUND_VARIABLE_1309487 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1309488))) (ho_11191 (ho_11190 (ho_12470 k_12529 BOUND_VARIABLE_1309486) BOUND_VARIABLE_1309487) BOUND_VARIABLE_1309488)))))) (let ((_let_4307 (forall ((BOUND_VARIABLE_1309459 tptp.nat) (BOUND_VARIABLE_1309460 tptp.nat) (BOUND_VARIABLE_1309461 tptp.set_nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1309461) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 _let_1) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 _let_1)) (ho_11056 k_11055 BOUND_VARIABLE_1309459)))))) (= BOUND_VARIABLE_1309460 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1309461))) (ho_11191 (ho_11190 (ho_12470 k_12530 BOUND_VARIABLE_1309459) BOUND_VARIABLE_1309460) BOUND_VARIABLE_1309461)))))) (let ((_let_4308 (forall ((BOUND_VARIABLE_1309432 tptp.nat) (BOUND_VARIABLE_1309433 tptp.nat) (BOUND_VARIABLE_1309434 tptp.set_nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1309434) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 _let_1) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 _let_1)) (ho_11056 k_11055 BOUND_VARIABLE_1309432)))))) (= BOUND_VARIABLE_1309433 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1309434))) (ho_11191 (ho_11190 (ho_12470 k_12531 BOUND_VARIABLE_1309432) BOUND_VARIABLE_1309433) BOUND_VARIABLE_1309434)))))) (let ((_let_4309 (forall ((BOUND_VARIABLE_1309405 tptp.nat) (BOUND_VARIABLE_1309406 tptp.nat) (BOUND_VARIABLE_1309407 tptp.set_nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1309407) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 _let_1) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 _let_1)) (ho_11056 k_11055 BOUND_VARIABLE_1309405)))))) (= BOUND_VARIABLE_1309406 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1309407))) (ho_11191 (ho_11190 (ho_12470 k_12532 BOUND_VARIABLE_1309405) BOUND_VARIABLE_1309406) BOUND_VARIABLE_1309407)))))) (let ((_let_4310 (forall ((BOUND_VARIABLE_1309378 tptp.nat) (BOUND_VARIABLE_1309379 tptp.nat) (BOUND_VARIABLE_1309380 tptp.set_nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1309380) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 _let_1) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 _let_1)) (ho_11056 k_11055 BOUND_VARIABLE_1309378)))))) (= BOUND_VARIABLE_1309379 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1309380))) (ho_11191 (ho_11190 (ho_12470 k_12533 BOUND_VARIABLE_1309378) BOUND_VARIABLE_1309379) BOUND_VARIABLE_1309380)))))) (let ((_let_4311 (forall ((BOUND_VARIABLE_1309351 tptp.code_integer) (BOUND_VARIABLE_1309352 tptp.code_integer)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (let ((_let_2 (ho_11056 k_11055 (ho_12176 k_12534 BOUND_VARIABLE_1309351)))) (let ((_let_3 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 _let_2) _let_2)))) (= (ho_12176 (ho_12536 k_12535 BOUND_VARIABLE_1309351) BOUND_VARIABLE_1309352) (ho_11139 (ho_11479 (ho_12061 k_12060 (= BOUND_VARIABLE_1309352 (ho_11669 k_11668 _let_1))) _let_3) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 _let_3)) (ho_11056 k_11055 (ho_11139 k_11138 _let_1)))))))))))) (let ((_let_4312 (forall ((BOUND_VARIABLE_1357512 |u_(-> tptp.int tptp.int)|) (BOUND_VARIABLE_1309340 tptp.int) (BOUND_VARIABLE_1357511 |u_(-> tptp.int tptp.int)|) (BOUND_VARIABLE_1309342 tptp.int)) (= (ho_11059 (ho_12540 (ho_12539 (ho_12538 k_12537 BOUND_VARIABLE_1357512) BOUND_VARIABLE_1309340) BOUND_VARIABLE_1357511) BOUND_VARIABLE_1309342) (ho_11059 (ho_11058 k_11085 (ho_11059 BOUND_VARIABLE_1357512 BOUND_VARIABLE_1309340)) (ho_11059 BOUND_VARIABLE_1357511 BOUND_VARIABLE_1309342)))))) (let ((_let_4313 (forall ((BOUND_VARIABLE_1357541 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1309325 tptp.nat) (BOUND_VARIABLE_1357540 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_1309327 tptp.nat)) (= (ho_11139 (ho_12544 (ho_12543 (ho_12542 k_12541 BOUND_VARIABLE_1357541) BOUND_VARIABLE_1309325) BOUND_VARIABLE_1357540) BOUND_VARIABLE_1309327) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11085 (ho_11056 k_11055 (ho_11139 BOUND_VARIABLE_1357541 BOUND_VARIABLE_1309325))) (ho_11056 k_11055 (ho_11139 BOUND_VARIABLE_1357540 BOUND_VARIABLE_1309327)))))))) (let ((_let_4314 (forall ((BOUND_VARIABLE_1357571 |u_(-> tptp.int tptp.int tptp.int)|) (BOUND_VARIABLE_1309316 tptp.int) (BOUND_VARIABLE_1309317 tptp.int)) (= (ho_11059 (ho_11058 (ho_12450 k_12545 BOUND_VARIABLE_1357571) BOUND_VARIABLE_1309316) BOUND_VARIABLE_1309317) (ho_11059 (ho_11058 BOUND_VARIABLE_1357571 BOUND_VARIABLE_1309317) BOUND_VARIABLE_1309316))))) (let ((_let_4315 (forall ((BOUND_VARIABLE_1357584 |u_(-> tptp.nat tptp.nat tptp.nat)|) (BOUND_VARIABLE_1309307 tptp.nat) (BOUND_VARIABLE_1309308 tptp.nat)) (= (ho_11139 (ho_11479 (ho_12255 k_12546 BOUND_VARIABLE_1357584) BOUND_VARIABLE_1309307) BOUND_VARIABLE_1309308) (ho_11139 (ho_11479 BOUND_VARIABLE_1357584 BOUND_VARIABLE_1309308) BOUND_VARIABLE_1309307))))) (let ((_let_4316 (forall ((BOUND_VARIABLE_1309285 tptp.code_integer) (BOUND_VARIABLE_1309286 tptp.code_integer)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (let ((_let_2 (ho_11059 (ho_11058 k_11085 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))) (ho_12154 k_12153 BOUND_VARIABLE_1309285)))) (= (ho_12154 (ho_12550 k_12549 BOUND_VARIABLE_1309285) BOUND_VARIABLE_1309286) (ho_11059 (ho_11058 (ho_12548 k_12547 (= BOUND_VARIABLE_1309286 (ho_11669 k_11668 _let_1))) _let_2) (ho_11059 (ho_11058 k_11057 _let_2) (ho_11056 k_11055 (ho_11139 k_11138 _let_1)))))))))) (let ((_let_4317 (forall ((BOUND_VARIABLE_1309264 tptp.code_integer) (BOUND_VARIABLE_1309265 tptp.code_integer)) (let ((_let_1 (ho_12552 k_12551 BOUND_VARIABLE_1309264))) (let ((_let_2 (ho_11030 (ho_12554 k_12553 _let_1) _let_1))) (= (ho_12552 (ho_12558 k_12557 BOUND_VARIABLE_1309264) BOUND_VARIABLE_1309265) (ho_11030 (ho_12554 (ho_12556 k_12555 (= BOUND_VARIABLE_1309265 (ho_11669 k_11668 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) _let_2) (ho_11030 (ho_12554 k_12553 _let_2) tptp.one)))))))) (let ((_let_4318 (forall ((BOUND_VARIABLE_1309217 tptp.code_integer) (BOUND_VARIABLE_1309218 tptp.code_integer)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (let ((_let_2 (ho_11669 k_11668 (ho_11139 k_11138 _let_1)))) (let ((_let_3 (ho_12161 (ho_12160 (ho_12159 k_12158 k_12153) (ho_12157 (ho_12156 k_12155 k_12153) k_12152)) k_11057))) (let ((_let_4 (ho_12560 k_12559 (ho_11030 k_11029 tptp.one)))) (let ((_let_5 (ho_11669 k_11668 _let_1))) (let ((_let_6 (ho_12154 k_12153 _let_5))) (let ((_let_7 (ho_12130 (ho_12129 _let_3 (ho_12130 k_12386 BOUND_VARIABLE_1309217)) _let_2))) (= (ho_12391 (ho_12390 k_12561 BOUND_VARIABLE_1309217) BOUND_VARIABLE_1309218) (ho_12395 (ho_12394 (ho_12393 k_12392 (= BOUND_VARIABLE_1309218 _let_5)) (ho_12391 (ho_12390 k_12389 _let_7) _let_5)) (ho_12391 (ho_12390 k_12389 (ho_12130 (ho_12129 _let_3 _let_7) (ho_12130 (ho_12129 _let_3 (ho_12130 k_12386 _let_2)) _let_2))) (ho_12130 (ho_12129 _let_3 (ho_12130 (ho_12129 (ho_12388 k_12387 (= _let_6 (ho_11059 (ho_11058 k_11095 (ho_12154 k_12153 (ho_12130 (ho_12129 _let_3 _let_4) _let_2))) _let_6))) (ho_12130 (ho_12129 _let_3 (ho_12130 k_12386 _let_4)) _let_2)) _let_4)) (ho_12130 (ho_12129 _let_3 (ho_12130 k_12386 BOUND_VARIABLE_1309218)) _let_2))))))))))))))) (let ((_let_4319 (forall ((BOUND_VARIABLE_1309202 tptp.set_int) (BOUND_VARIABLE_1309203 tptp.int)) (= (or (= BOUND_VARIABLE_1309203 (ho_12563 k_12562 BOUND_VARIABLE_1309202)) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1309203) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11234 k_12564 BOUND_VARIABLE_1309202) BOUND_VARIABLE_1309203))))) (let ((_let_4320 (forall ((BOUND_VARIABLE_1309188 tptp.int) (BOUND_VARIABLE_1309189 tptp.int)) (= (or (= BOUND_VARIABLE_1309188 BOUND_VARIABLE_1309189) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1309189) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12565 BOUND_VARIABLE_1309188) BOUND_VARIABLE_1309189))))) (let ((_let_4321 (forall ((BOUND_VARIABLE_1309173 tptp.set_nat) (BOUND_VARIABLE_1309174 tptp.nat)) (= (or (= BOUND_VARIABLE_1309174 (ho_11109 k_12566 BOUND_VARIABLE_1309173)) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1309174) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11240 k_12567 BOUND_VARIABLE_1309173) BOUND_VARIABLE_1309174))))) (let ((_let_4322 (forall ((BOUND_VARIABLE_1309159 tptp.nat) (BOUND_VARIABLE_1309160 tptp.nat)) (= (or (= BOUND_VARIABLE_1309159 BOUND_VARIABLE_1309160) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1309160) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12568 BOUND_VARIABLE_1309159) BOUND_VARIABLE_1309160))))) (let ((_let_4323 (forall ((BOUND_VARIABLE_1309144 tptp.set_o) (BOUND_VARIABLE_1309145 Bool)) (= (or (= BOUND_VARIABLE_1309145 (ho_11199 k_12569 BOUND_VARIABLE_1309144)) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1309145) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_12571 k_12570 BOUND_VARIABLE_1309144) BOUND_VARIABLE_1309145))))) (let ((_let_4324 (forall ((BOUND_VARIABLE_1309130 Bool) (BOUND_VARIABLE_1309131 Bool)) (= (or (= BOUND_VARIABLE_1309130 BOUND_VARIABLE_1309131) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1309131) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12572 BOUND_VARIABLE_1309130) BOUND_VARIABLE_1309131))))) (let ((_let_4325 (forall ((BOUND_VARIABLE_1309115 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1309116 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1309116 (ho_12574 k_12573 BOUND_VARIABLE_1309115)) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1309116) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11237 k_12575 BOUND_VARIABLE_1309115) BOUND_VARIABLE_1309116))))) (let ((_let_4326 (forall ((BOUND_VARIABLE_1309101 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1309102 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1309101 BOUND_VARIABLE_1309102) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1309102) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12576 BOUND_VARIABLE_1309101) BOUND_VARIABLE_1309102))))) (let ((_let_4327 (forall ((BOUND_VARIABLE_1309090 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1309091 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11374 k_12577 BOUND_VARIABLE_1309090) BOUND_VARIABLE_1309091) (or (= BOUND_VARIABLE_1309091 (ho_12579 k_12578 BOUND_VARIABLE_1309090)) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1309091) tptp.bot_bo228742789529271731at_nat)))))) (let ((_let_4328 (forall ((BOUND_VARIABLE_1309080 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1309081 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1309080 BOUND_VARIABLE_1309081) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1309081) tptp.bot_bo228742789529271731at_nat)) (ho_11263 (ho_11262 k_12580 BOUND_VARIABLE_1309080) BOUND_VARIABLE_1309081))))) (let ((_let_4329 (forall ((BOUND_VARIABLE_1309066 tptp.int) (BOUND_VARIABLE_1309067 tptp.int)) (= (or (= BOUND_VARIABLE_1309066 BOUND_VARIABLE_1309067) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1309067) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12581 BOUND_VARIABLE_1309066) BOUND_VARIABLE_1309067))))) (let ((_let_4330 (forall ((BOUND_VARIABLE_1309052 tptp.nat) (BOUND_VARIABLE_1309053 tptp.nat)) (= (or (= BOUND_VARIABLE_1309052 BOUND_VARIABLE_1309053) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1309053) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12582 BOUND_VARIABLE_1309052) BOUND_VARIABLE_1309053))))) (let ((_let_4331 (forall ((BOUND_VARIABLE_1309038 Bool) (BOUND_VARIABLE_1309039 Bool)) (= (or (= BOUND_VARIABLE_1309038 BOUND_VARIABLE_1309039) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1309039) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12583 BOUND_VARIABLE_1309038) BOUND_VARIABLE_1309039))))) (let ((_let_4332 (forall ((BOUND_VARIABLE_1309024 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1309025 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1309024 BOUND_VARIABLE_1309025) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1309025) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12584 BOUND_VARIABLE_1309024) BOUND_VARIABLE_1309025))))) (let ((_let_4333 (forall ((BOUND_VARIABLE_1309014 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1309015 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11262 k_12585 BOUND_VARIABLE_1309014) BOUND_VARIABLE_1309015) (or (= BOUND_VARIABLE_1309014 BOUND_VARIABLE_1309015) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1309015) tptp.bot_bo228742789529271731at_nat)))))) (let ((_let_4334 (forall ((BOUND_VARIABLE_1308992 tptp.nat) (BOUND_VARIABLE_1308993 tptp.num)) (= (ho_11174 (ho_12588 (ho_12587 k_12586 (ho_11037 k_11036 k_11034)) (ho_11173 k_11172 BOUND_VARIABLE_1308993)) BOUND_VARIABLE_1308992) (ho_11028 (ho_11033 k_12589 BOUND_VARIABLE_1308992) BOUND_VARIABLE_1308993))))) (let ((_let_4335 (forall ((BOUND_VARIABLE_1308955 tptp.num) (BOUND_VARIABLE_1308956 tptp.code_integer) (BOUND_VARIABLE_1308957 tptp.code_integer)) (let ((_let_1 (ho_12130 (ho_12129 k_12128 (ho_12560 k_12559 (ho_11030 k_11029 tptp.one))) BOUND_VARIABLE_1308956))) (let ((_let_2 (ho_11669 k_11668 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (let ((_let_3 (ho_12560 k_12559 BOUND_VARIABLE_1308955))) (let ((_let_4 (ho_12161 (ho_12160 (ho_12159 k_12158 k_12153) (ho_12157 (ho_12156 k_12155 k_12153) k_12152)) k_11057))) (let ((_let_5 (ho_12154 k_12153 BOUND_VARIABLE_1308957))) (= (ho_12395 (ho_12394 (ho_12393 k_12392 (= _let_5 (ho_11059 (ho_11058 k_11095 (ho_12154 k_12153 _let_3)) _let_5))) (ho_12391 (ho_12390 k_12389 (ho_12130 (ho_12129 _let_4 _let_1) _let_2)) (ho_12130 (ho_12129 _let_4 BOUND_VARIABLE_1308957) (ho_12130 (ho_12129 _let_4 (ho_12130 k_12386 _let_3)) _let_2)))) (ho_12391 (ho_12390 k_12389 _let_1) BOUND_VARIABLE_1308957)) (ho_12391 (ho_12390 (ho_12591 k_12590 BOUND_VARIABLE_1308955) BOUND_VARIABLE_1308956) BOUND_VARIABLE_1308957)))))))))) (let ((_let_4336 (forall ((BOUND_VARIABLE_1308918 tptp.num) (BOUND_VARIABLE_1308919 tptp.code_integer) (BOUND_VARIABLE_1308920 tptp.code_integer)) (let ((_let_1 (ho_12130 (ho_12129 k_12128 (ho_12560 k_12559 (ho_11030 k_11029 tptp.one))) BOUND_VARIABLE_1308919))) (let ((_let_2 (ho_11669 k_11668 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (let ((_let_3 (ho_12560 k_12559 BOUND_VARIABLE_1308918))) (let ((_let_4 (ho_12161 (ho_12160 (ho_12159 k_12158 k_12153) (ho_12157 (ho_12156 k_12155 k_12153) k_12152)) k_11057))) (let ((_let_5 (ho_12154 k_12153 BOUND_VARIABLE_1308920))) (= (ho_12395 (ho_12394 (ho_12393 k_12392 (= _let_5 (ho_11059 (ho_11058 k_11095 (ho_12154 k_12153 _let_3)) _let_5))) (ho_12391 (ho_12390 k_12389 (ho_12130 (ho_12129 _let_4 _let_1) _let_2)) (ho_12130 (ho_12129 _let_4 BOUND_VARIABLE_1308920) (ho_12130 (ho_12129 _let_4 (ho_12130 k_12386 _let_3)) _let_2)))) (ho_12391 (ho_12390 k_12389 _let_1) BOUND_VARIABLE_1308920)) (ho_12391 (ho_12390 (ho_12591 k_12592 BOUND_VARIABLE_1308918) BOUND_VARIABLE_1308919) BOUND_VARIABLE_1308920)))))))))) (let ((_let_4337 (forall ((BOUND_VARIABLE_1308902 tptp.code_natural) (BOUND_VARIABLE_1357954 |u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (BOUND_VARIABLE_1308904 tptp.code_natural) (BOUND_VARIABLE_1308905 tptp.produc7822875418678951345atural)) (= (ho_11493 (ho_11492 (ho_12595 (ho_12594 k_12593 BOUND_VARIABLE_1308902) BOUND_VARIABLE_1357954) BOUND_VARIABLE_1308904) BOUND_VARIABLE_1308905) (ho_12600 (ho_12599 k_12598 (ho_12595 (ho_12594 k_12597 (ho_11477 (ho_11476 k_12596 BOUND_VARIABLE_1308902) tptp.one_one_Code_natural)) BOUND_VARIABLE_1357954)) (ho_11493 (ho_11492 BOUND_VARIABLE_1357954 BOUND_VARIABLE_1308904) BOUND_VARIABLE_1308905)))))) (let ((_let_4338 (forall ((BOUND_VARIABLE_1357994 |u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (BOUND_VARIABLE_1357993 |u_(-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural)|) (BOUND_VARIABLE_1308892 tptp.code_natural) (BOUND_VARIABLE_1308893 tptp.produc7822875418678951345atural)) (= (ho_11493 (ho_11492 (ho_12595 (ho_12602 k_12601 BOUND_VARIABLE_1357994) BOUND_VARIABLE_1357993) BOUND_VARIABLE_1308892) BOUND_VARIABLE_1308893) (ho_12600 (ho_12599 k_12598 BOUND_VARIABLE_1357994) (ho_11493 (ho_11492 BOUND_VARIABLE_1357993 BOUND_VARIABLE_1308892) BOUND_VARIABLE_1308893)))))) (let ((_let_4339 (forall ((BOUND_VARIABLE_1308876 tptp.nat) (BOUND_VARIABLE_1308877 tptp.nat)) (let ((_let_1 (ho_11061 k_11060 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))))) (= (ho_11054 (ho_11053 k_12603 BOUND_VARIABLE_1308876) BOUND_VARIABLE_1308877) (not (ho_11054 (ho_11053 k_11435 _let_1) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11523 (ho_11056 k_11055 BOUND_VARIABLE_1308876)) (ho_11056 k_11055 (ho_11139 (ho_11479 k_12604 _let_1) BOUND_VARIABLE_1308877))))))))))) (let ((_let_4340 (forall ((BOUND_VARIABLE_1308862 tptp.nat) (BOUND_VARIABLE_1308863 tptp.nat)) (let ((_let_1 (ho_11061 k_11060 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))))) (= (ho_11054 (ho_11053 k_12605 BOUND_VARIABLE_1308862) BOUND_VARIABLE_1308863) (not (ho_11054 (ho_11053 k_11435 _let_1) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11523 (ho_11056 k_11055 BOUND_VARIABLE_1308862)) (ho_11056 k_11055 (ho_11139 (ho_11479 k_12604 _let_1) BOUND_VARIABLE_1308863))))))))))) (let ((_let_4341 (forall ((BOUND_VARIABLE_1308848 tptp.nat) (BOUND_VARIABLE_1308849 tptp.nat)) (let ((_let_1 (ho_11061 k_11060 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))))) (= (ho_11054 (ho_11053 k_12606 BOUND_VARIABLE_1308848) BOUND_VARIABLE_1308849) (not (ho_11054 (ho_11053 k_11435 _let_1) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11523 (ho_11056 k_11055 BOUND_VARIABLE_1308848)) (ho_11056 k_11055 (ho_11139 (ho_11479 k_12604 _let_1) BOUND_VARIABLE_1308849))))))))))) (let ((_let_4342 (forall ((BOUND_VARIABLE_1308825 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1308826 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1308827 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1308828 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1308829 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (ho_12613 k_12612 BOUND_VARIABLE_1308826))) (= (ho_11070 (ho_12611 (ho_12610 (ho_12609 (ho_12608 k_12607 BOUND_VARIABLE_1308825) BOUND_VARIABLE_1308826) BOUND_VARIABLE_1308827) BOUND_VARIABLE_1308828) BOUND_VARIABLE_1308829) (and (or (ho_11260 (ho_11259 k_11258 (ho_11430 (ho_11429 k_11428 BOUND_VARIABLE_1308828) BOUND_VARIABLE_1308825)) _let_1) (= BOUND_VARIABLE_1308825 BOUND_VARIABLE_1308828)) (or (ho_11260 (ho_11259 k_11258 (ho_11430 (ho_11429 k_11428 BOUND_VARIABLE_1308827) BOUND_VARIABLE_1308829)) _let_1) (= BOUND_VARIABLE_1308827 BOUND_VARIABLE_1308829)))))))) (let ((_let_4343 (forall ((BOUND_VARIABLE_1308815 tptp.multis2468970476368604999at_nat) (BOUND_VARIABLE_1308816 tptp.multis2468970476368604999at_nat) (BOUND_VARIABLE_1308817 tptp.produc4166570645942440679at_nat)) (= (ho_11051 (ho_12616 (ho_12615 k_12614 BOUND_VARIABLE_1308815) BOUND_VARIABLE_1308816) BOUND_VARIABLE_1308817) (= BOUND_VARIABLE_1308817 (ho_12619 (ho_12618 k_12617 BOUND_VARIABLE_1308815) BOUND_VARIABLE_1308816)))))) (let ((_let_4344 (forall ((BOUND_VARIABLE_1308792 tptp.multis2468970476368604999at_nat) (BOUND_VARIABLE_1308793 tptp.set_Pr8551490117392284871at_nat) (BOUND_VARIABLE_1308794 tptp.multis2468970476368604999at_nat) (BOUND_VARIABLE_1308795 tptp.multis2468970476368604999at_nat) (BOUND_VARIABLE_1308796 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (ho_12627 k_12626 BOUND_VARIABLE_1308793))) (= (ho_12625 (ho_12624 (ho_12623 (ho_12622 (ho_12621 k_12620 BOUND_VARIABLE_1308792) BOUND_VARIABLE_1308793) BOUND_VARIABLE_1308794) BOUND_VARIABLE_1308795) BOUND_VARIABLE_1308796) (and (or (ho_11267 (ho_11266 k_11265 (ho_12619 (ho_12618 k_12617 BOUND_VARIABLE_1308795) BOUND_VARIABLE_1308792)) _let_1) (= BOUND_VARIABLE_1308792 BOUND_VARIABLE_1308795)) (or (ho_11267 (ho_11266 k_11265 (ho_12619 (ho_12618 k_12617 BOUND_VARIABLE_1308794) BOUND_VARIABLE_1308796)) _let_1) (= BOUND_VARIABLE_1308794 BOUND_VARIABLE_1308796)))))))) (let ((_let_4345 (forall ((BOUND_VARIABLE_1308781 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1308782 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1308783 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1308781 BOUND_VARIABLE_1308783) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1308783) BOUND_VARIABLE_1308782)) (ho_11184 (ho_11237 (ho_11236 k_12628 BOUND_VARIABLE_1308781) BOUND_VARIABLE_1308782) BOUND_VARIABLE_1308783))))) (let ((_let_4346 (forall ((BOUND_VARIABLE_1308770 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1308771 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1308772 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1308770 BOUND_VARIABLE_1308772) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1308772) BOUND_VARIABLE_1308771)) (ho_11263 (ho_11374 (ho_12630 k_12629 BOUND_VARIABLE_1308770) BOUND_VARIABLE_1308771) BOUND_VARIABLE_1308772))))) (let ((_let_4347 (forall ((BOUND_VARIABLE_1308762 tptp.set_int) (BOUND_VARIABLE_1308763 tptp.int)) (= (ho_11094 (ho_11234 k_12631 BOUND_VARIABLE_1308762) BOUND_VARIABLE_1308763) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308763) BOUND_VARIABLE_1308762))))) (let ((_let_4348 (forall ((BOUND_VARIABLE_1308739 tptp.int) (BOUND_VARIABLE_1308740 tptp.int)) (= (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308740) (ho_11177 k_11176 (ho_11093 k_11181 BOUND_VARIABLE_1308739))) (ho_11094 (ho_11093 k_12632 BOUND_VARIABLE_1308739) BOUND_VARIABLE_1308740))))) (let ((_let_4349 (forall ((BOUND_VARIABLE_1308725 tptp.int) (BOUND_VARIABLE_1308726 tptp.int)) (= (or (= BOUND_VARIABLE_1308725 BOUND_VARIABLE_1308726) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308726) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12633 BOUND_VARIABLE_1308725) BOUND_VARIABLE_1308726))))) (let ((_let_4350 (forall ((BOUND_VARIABLE_1308717 tptp.set_int) (BOUND_VARIABLE_1308718 tptp.int)) (= (ho_11094 (ho_11234 k_12634 BOUND_VARIABLE_1308717) BOUND_VARIABLE_1308718) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308718) BOUND_VARIABLE_1308717))))) (let ((_let_4351 (forall ((BOUND_VARIABLE_1308694 tptp.int) (BOUND_VARIABLE_1308695 tptp.int)) (= (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308695) (ho_11177 k_11176 (ho_11093 k_11182 BOUND_VARIABLE_1308694))) (ho_11094 (ho_11093 k_12635 BOUND_VARIABLE_1308694) BOUND_VARIABLE_1308695))))) (let ((_let_4352 (forall ((BOUND_VARIABLE_1308683 tptp.int) (BOUND_VARIABLE_1308684 tptp.set_int) (BOUND_VARIABLE_1308685 tptp.int)) (= (or (= BOUND_VARIABLE_1308683 BOUND_VARIABLE_1308685) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308685) BOUND_VARIABLE_1308684)) (ho_11094 (ho_11234 (ho_11233 k_12636 BOUND_VARIABLE_1308683) BOUND_VARIABLE_1308684) BOUND_VARIABLE_1308685))))) (let ((_let_4353 (forall ((BOUND_VARIABLE_1308672 tptp.int) (BOUND_VARIABLE_1308673 tptp.set_int) (BOUND_VARIABLE_1308674 tptp.int)) (= (or (= BOUND_VARIABLE_1308672 BOUND_VARIABLE_1308674) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308674) BOUND_VARIABLE_1308673)) (ho_11094 (ho_11234 (ho_11233 k_12637 BOUND_VARIABLE_1308672) BOUND_VARIABLE_1308673) BOUND_VARIABLE_1308674))))) (let ((_let_4354 (forall ((BOUND_VARIABLE_1308664 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1308665 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12638 BOUND_VARIABLE_1308664) BOUND_VARIABLE_1308665) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1308665) BOUND_VARIABLE_1308664))))) (let ((_let_4355 (forall ((BOUND_VARIABLE_1308641 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1308642 tptp.product_prod_nat_nat)) (= (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1308642) (ho_11186 k_11185 (ho_11188 k_11187 BOUND_VARIABLE_1308641))) (ho_11184 (ho_11188 k_12639 BOUND_VARIABLE_1308641) BOUND_VARIABLE_1308642))))) (let ((_let_4356 (forall ((BOUND_VARIABLE_1308627 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1308628 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1308627 BOUND_VARIABLE_1308628) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1308628) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12640 BOUND_VARIABLE_1308627) BOUND_VARIABLE_1308628))))) (let ((_let_4357 (forall ((BOUND_VARIABLE_1308616 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1308617 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1308618 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1308616 BOUND_VARIABLE_1308618) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1308618) BOUND_VARIABLE_1308617)) (ho_11184 (ho_11237 (ho_11236 k_12641 BOUND_VARIABLE_1308616) BOUND_VARIABLE_1308617) BOUND_VARIABLE_1308618))))) (let ((_let_4358 (forall ((BOUND_VARIABLE_1308608 tptp.set_nat) (BOUND_VARIABLE_1308609 tptp.nat)) (= (ho_11054 (ho_11240 k_12642 BOUND_VARIABLE_1308608) BOUND_VARIABLE_1308609) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1308609) BOUND_VARIABLE_1308608))))) (let ((_let_4359 (forall ((BOUND_VARIABLE_1308585 tptp.nat) (BOUND_VARIABLE_1308586 tptp.nat)) (= (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1308586) (ho_11107 k_11106 (ho_11053 k_11192 BOUND_VARIABLE_1308585))) (ho_11054 (ho_11053 k_12643 BOUND_VARIABLE_1308585) BOUND_VARIABLE_1308586))))) (let ((_let_4360 (forall ((BOUND_VARIABLE_1308574 tptp.nat) (BOUND_VARIABLE_1308575 tptp.set_nat) (BOUND_VARIABLE_1308576 tptp.nat)) (= (or (= BOUND_VARIABLE_1308574 BOUND_VARIABLE_1308576) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1308576) BOUND_VARIABLE_1308575)) (ho_11054 (ho_11240 (ho_11239 k_12644 BOUND_VARIABLE_1308574) BOUND_VARIABLE_1308575) BOUND_VARIABLE_1308576))))) (let ((_let_4361 (forall ((BOUND_VARIABLE_1308566 tptp.set_o) (BOUND_VARIABLE_1308567 Bool)) (= (ho_11194 (ho_12571 k_12645 BOUND_VARIABLE_1308566) BOUND_VARIABLE_1308567) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1308567) BOUND_VARIABLE_1308566))))) (let ((_let_4362 (forall ((BOUND_VARIABLE_1308543 Bool) (BOUND_VARIABLE_1308544 Bool)) (= (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1308544) (ho_11196 k_11195 (ho_11201 k_11200 BOUND_VARIABLE_1308543))) (ho_11194 (ho_11201 k_12646 BOUND_VARIABLE_1308543) BOUND_VARIABLE_1308544))))) (let ((_let_4363 (forall ((BOUND_VARIABLE_1308532 Bool) (BOUND_VARIABLE_1308533 tptp.set_o) (BOUND_VARIABLE_1308534 Bool)) (= (or (= BOUND_VARIABLE_1308532 BOUND_VARIABLE_1308534) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1308534) BOUND_VARIABLE_1308533)) (ho_11194 (ho_12571 (ho_12648 k_12647 BOUND_VARIABLE_1308532) BOUND_VARIABLE_1308533) BOUND_VARIABLE_1308534))))) (let ((_let_4364 (forall ((BOUND_VARIABLE_1308524 tptp.set_set_nat) (BOUND_VARIABLE_1308525 tptp.set_nat)) (= (ho_11191 (ho_12650 k_12649 BOUND_VARIABLE_1308524) BOUND_VARIABLE_1308525) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1308525) BOUND_VARIABLE_1308524))))) (let ((_let_4365 (forall ((BOUND_VARIABLE_1308501 tptp.set_nat) (BOUND_VARIABLE_1308502 tptp.set_nat)) (= (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1308502) (ho_11204 k_11203 (ho_11209 k_11208 BOUND_VARIABLE_1308501))) (ho_11191 (ho_11209 k_12651 BOUND_VARIABLE_1308501) BOUND_VARIABLE_1308502))))) (let ((_let_4366 (forall ((BOUND_VARIABLE_1308490 tptp.set_nat) (BOUND_VARIABLE_1308491 tptp.set_set_nat) (BOUND_VARIABLE_1308492 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1308490 BOUND_VARIABLE_1308492) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1308492) BOUND_VARIABLE_1308491)) (ho_11191 (ho_12650 (ho_12653 k_12652 BOUND_VARIABLE_1308490) BOUND_VARIABLE_1308491) BOUND_VARIABLE_1308492))))) (let ((_let_4367 (forall ((BOUND_VARIABLE_1308482 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1308483 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 k_12654 BOUND_VARIABLE_1308482) BOUND_VARIABLE_1308483) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1308483) BOUND_VARIABLE_1308482))))) (let ((_let_4368 (forall ((BOUND_VARIABLE_1308459 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1308460 tptp.set_Pr958786334691620121nt_int)) (= (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1308460) (ho_11213 k_11212 (ho_11218 k_11217 BOUND_VARIABLE_1308459))) (ho_11211 (ho_11218 k_12656 BOUND_VARIABLE_1308459) BOUND_VARIABLE_1308460))))) (let ((_let_4369 (forall ((BOUND_VARIABLE_1308448 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1308449 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1308450 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1308448 BOUND_VARIABLE_1308450) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1308450) BOUND_VARIABLE_1308449)) (ho_11211 (ho_12655 (ho_12658 k_12657 BOUND_VARIABLE_1308448) BOUND_VARIABLE_1308449) BOUND_VARIABLE_1308450))))) (let ((_let_4370 (forall ((BOUND_VARIABLE_1308438 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1308439 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1308438 BOUND_VARIABLE_1308439) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1308439) tptp.bot_bo228742789529271731at_nat)) (ho_11263 (ho_11262 k_12659 BOUND_VARIABLE_1308438) BOUND_VARIABLE_1308439))))) (let ((_let_4371 (forall ((BOUND_VARIABLE_1308427 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1308428 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1308429 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1308427 BOUND_VARIABLE_1308429) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1308429) BOUND_VARIABLE_1308428)) (ho_11263 (ho_11374 (ho_12630 k_12660 BOUND_VARIABLE_1308427) BOUND_VARIABLE_1308428) BOUND_VARIABLE_1308429))))) (let ((_let_4372 (forall ((BOUND_VARIABLE_1308413 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1308414 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1308413 BOUND_VARIABLE_1308414) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1308414) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12661 BOUND_VARIABLE_1308413) BOUND_VARIABLE_1308414))))) (let ((_let_4373 (forall ((BOUND_VARIABLE_1308402 tptp.int) (BOUND_VARIABLE_1308403 tptp.set_int) (BOUND_VARIABLE_1308404 tptp.int)) (= (or (= BOUND_VARIABLE_1308402 BOUND_VARIABLE_1308404) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308404) BOUND_VARIABLE_1308403)) (ho_11094 (ho_11234 (ho_11233 k_12662 BOUND_VARIABLE_1308402) BOUND_VARIABLE_1308403) BOUND_VARIABLE_1308404))))) (let ((_let_4374 (forall ((BOUND_VARIABLE_1308394 tptp.set_int) (BOUND_VARIABLE_1308395 tptp.int)) (= (ho_11094 (ho_11234 k_12663 BOUND_VARIABLE_1308394) BOUND_VARIABLE_1308395) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308395) BOUND_VARIABLE_1308394))))) (let ((_let_4375 (forall ((BOUND_VARIABLE_1308380 tptp.int) (BOUND_VARIABLE_1308381 tptp.int)) (= (or (= BOUND_VARIABLE_1308380 BOUND_VARIABLE_1308381) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308381) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12664 BOUND_VARIABLE_1308380) BOUND_VARIABLE_1308381))))) (let ((_let_4376 (forall ((BOUND_VARIABLE_1308369 tptp.nat) (BOUND_VARIABLE_1308370 tptp.set_nat) (BOUND_VARIABLE_1308371 tptp.nat)) (= (or (= BOUND_VARIABLE_1308369 BOUND_VARIABLE_1308371) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1308371) BOUND_VARIABLE_1308370)) (ho_11054 (ho_11240 (ho_11239 k_12665 BOUND_VARIABLE_1308369) BOUND_VARIABLE_1308370) BOUND_VARIABLE_1308371))))) (let ((_let_4377 (forall ((BOUND_VARIABLE_1308361 tptp.set_nat) (BOUND_VARIABLE_1308362 tptp.nat)) (= (ho_11054 (ho_11240 k_12666 BOUND_VARIABLE_1308361) BOUND_VARIABLE_1308362) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1308362) BOUND_VARIABLE_1308361))))) (let ((_let_4378 (forall ((BOUND_VARIABLE_1308347 tptp.nat) (BOUND_VARIABLE_1308348 tptp.nat)) (= (or (= BOUND_VARIABLE_1308347 BOUND_VARIABLE_1308348) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1308348) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12667 BOUND_VARIABLE_1308347) BOUND_VARIABLE_1308348))))) (let ((_let_4379 (forall ((BOUND_VARIABLE_1308336 Bool) (BOUND_VARIABLE_1308337 tptp.set_o) (BOUND_VARIABLE_1308338 Bool)) (= (or (= BOUND_VARIABLE_1308336 BOUND_VARIABLE_1308338) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1308338) BOUND_VARIABLE_1308337)) (ho_11194 (ho_12571 (ho_12648 k_12668 BOUND_VARIABLE_1308336) BOUND_VARIABLE_1308337) BOUND_VARIABLE_1308338))))) (let ((_let_4380 (forall ((BOUND_VARIABLE_1308328 tptp.set_o) (BOUND_VARIABLE_1308329 Bool)) (= (ho_11194 (ho_12571 k_12669 BOUND_VARIABLE_1308328) BOUND_VARIABLE_1308329) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1308329) BOUND_VARIABLE_1308328))))) (let ((_let_4381 (forall ((BOUND_VARIABLE_1308314 Bool) (BOUND_VARIABLE_1308315 Bool)) (= (or (= BOUND_VARIABLE_1308314 BOUND_VARIABLE_1308315) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1308315) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12670 BOUND_VARIABLE_1308314) BOUND_VARIABLE_1308315))))) (let ((_let_4382 (forall ((BOUND_VARIABLE_1308306 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1308307 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12671 BOUND_VARIABLE_1308306) BOUND_VARIABLE_1308307) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1308307) BOUND_VARIABLE_1308306))))) (let ((_let_4383 (forall ((BOUND_VARIABLE_1308283 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1308284 tptp.product_prod_nat_nat)) (= (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1308284) (ho_11186 k_11185 (ho_11188 k_11219 BOUND_VARIABLE_1308283))) (ho_11184 (ho_11188 k_12672 BOUND_VARIABLE_1308283) BOUND_VARIABLE_1308284))))) (let ((_let_4384 (forall ((BOUND_VARIABLE_1308269 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1308270 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1308269 BOUND_VARIABLE_1308270) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1308270) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12673 BOUND_VARIABLE_1308269) BOUND_VARIABLE_1308270))))) (let ((_let_4385 (forall ((BOUND_VARIABLE_1308261 tptp.set_int) (BOUND_VARIABLE_1308262 tptp.int)) (= (ho_11094 (ho_11234 k_12674 BOUND_VARIABLE_1308261) BOUND_VARIABLE_1308262) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308262) BOUND_VARIABLE_1308261))))) (let ((_let_4386 (forall ((BOUND_VARIABLE_1308238 tptp.int) (BOUND_VARIABLE_1308239 tptp.int)) (= (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308239) (ho_11177 k_11176 (ho_11093 k_11220 BOUND_VARIABLE_1308238))) (ho_11094 (ho_11093 k_12675 BOUND_VARIABLE_1308238) BOUND_VARIABLE_1308239))))) (let ((_let_4387 (forall ((BOUND_VARIABLE_1308224 tptp.int) (BOUND_VARIABLE_1308225 tptp.int)) (= (or (= BOUND_VARIABLE_1308224 BOUND_VARIABLE_1308225) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308225) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12676 BOUND_VARIABLE_1308224) BOUND_VARIABLE_1308225))))) (let ((_let_4388 (forall ((BOUND_VARIABLE_1308216 tptp.set_int) (BOUND_VARIABLE_1308217 tptp.int)) (= (ho_11094 (ho_11234 k_12677 BOUND_VARIABLE_1308216) BOUND_VARIABLE_1308217) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308217) BOUND_VARIABLE_1308216))))) (let ((_let_4389 (forall ((BOUND_VARIABLE_1308193 tptp.int) (BOUND_VARIABLE_1308194 tptp.int)) (= (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308194) (ho_11177 k_11176 (ho_11093 k_11221 BOUND_VARIABLE_1308193))) (ho_11094 (ho_11093 k_12678 BOUND_VARIABLE_1308193) BOUND_VARIABLE_1308194))))) (let ((_let_4390 (forall ((BOUND_VARIABLE_1308185 tptp.set_nat) (BOUND_VARIABLE_1308186 tptp.nat)) (= (ho_11054 (ho_11240 k_12679 BOUND_VARIABLE_1308185) BOUND_VARIABLE_1308186) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1308186) BOUND_VARIABLE_1308185))))) (let ((_let_4391 (forall ((BOUND_VARIABLE_1308162 tptp.nat) (BOUND_VARIABLE_1308163 tptp.nat)) (= (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1308163) (ho_11107 k_11106 (ho_11053 k_11222 BOUND_VARIABLE_1308162))) (ho_11054 (ho_11053 k_12680 BOUND_VARIABLE_1308162) BOUND_VARIABLE_1308163))))) (let ((_let_4392 (forall ((BOUND_VARIABLE_1308154 tptp.set_o) (BOUND_VARIABLE_1308155 Bool)) (= (ho_11194 (ho_12571 k_12681 BOUND_VARIABLE_1308154) BOUND_VARIABLE_1308155) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1308155) BOUND_VARIABLE_1308154))))) (let ((_let_4393 (forall ((BOUND_VARIABLE_1308131 Bool) (BOUND_VARIABLE_1308132 Bool)) (= (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1308132) (ho_11196 k_11195 (ho_11201 k_11223 BOUND_VARIABLE_1308131))) (ho_11194 (ho_11201 k_12682 BOUND_VARIABLE_1308131) BOUND_VARIABLE_1308132))))) (let ((_let_4394 (forall ((BOUND_VARIABLE_1308123 tptp.set_set_nat) (BOUND_VARIABLE_1308124 tptp.set_nat)) (= (ho_11191 (ho_12650 k_12683 BOUND_VARIABLE_1308123) BOUND_VARIABLE_1308124) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1308124) BOUND_VARIABLE_1308123))))) (let ((_let_4395 (forall ((BOUND_VARIABLE_1308100 tptp.set_nat) (BOUND_VARIABLE_1308101 tptp.set_nat)) (= (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1308101) (ho_11204 k_11203 (ho_11209 k_11224 BOUND_VARIABLE_1308100))) (ho_11191 (ho_11209 k_12684 BOUND_VARIABLE_1308100) BOUND_VARIABLE_1308101))))) (let ((_let_4396 (forall ((BOUND_VARIABLE_1308092 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1308093 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 k_12685 BOUND_VARIABLE_1308092) BOUND_VARIABLE_1308093) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1308093) BOUND_VARIABLE_1308092))))) (let ((_let_4397 (forall ((BOUND_VARIABLE_1308069 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1308070 tptp.set_Pr958786334691620121nt_int)) (= (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1308070) (ho_11213 k_11212 (ho_11218 k_11225 BOUND_VARIABLE_1308069))) (ho_11211 (ho_11218 k_12686 BOUND_VARIABLE_1308069) BOUND_VARIABLE_1308070))))) (let ((_let_4398 (forall ((BOUND_VARIABLE_1308059 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1308060 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1308059 BOUND_VARIABLE_1308060) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1308060) tptp.bot_bo228742789529271731at_nat)) (ho_11263 (ho_11262 k_12687 BOUND_VARIABLE_1308059) BOUND_VARIABLE_1308060))))) (let ((_let_4399 (forall ((BOUND_VARIABLE_1308051 tptp.set_int) (BOUND_VARIABLE_1308052 tptp.int)) (= (ho_11094 (ho_11234 k_12688 BOUND_VARIABLE_1308051) BOUND_VARIABLE_1308052) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308052) BOUND_VARIABLE_1308051))))) (let ((_let_4400 (forall ((BOUND_VARIABLE_1308028 tptp.int) (BOUND_VARIABLE_1308029 tptp.int)) (= (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308029) (ho_11177 k_11176 (ho_11093 k_11226 BOUND_VARIABLE_1308028))) (ho_11094 (ho_11093 k_12689 BOUND_VARIABLE_1308028) BOUND_VARIABLE_1308029))))) (let ((_let_4401 (forall ((BOUND_VARIABLE_1308017 tptp.int) (BOUND_VARIABLE_1308018 tptp.set_int) (BOUND_VARIABLE_1308019 tptp.int)) (= (or (= BOUND_VARIABLE_1308017 BOUND_VARIABLE_1308019) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1308019) BOUND_VARIABLE_1308018)) (ho_11094 (ho_11234 (ho_11233 k_12690 BOUND_VARIABLE_1308017) BOUND_VARIABLE_1308018) BOUND_VARIABLE_1308019))))) (let ((_let_4402 (forall ((BOUND_VARIABLE_1308003 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1308004 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1308003 BOUND_VARIABLE_1308004) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1308004) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12691 BOUND_VARIABLE_1308003) BOUND_VARIABLE_1308004))))) (let ((_let_4403 (forall ((BOUND_VARIABLE_1307995 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1307996 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12692 BOUND_VARIABLE_1307995) BOUND_VARIABLE_1307996) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307996) BOUND_VARIABLE_1307995))))) (let ((_let_4404 (forall ((BOUND_VARIABLE_1307972 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1307973 tptp.product_prod_nat_nat)) (= (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307973) (ho_11186 k_11185 (ho_11188 k_11227 BOUND_VARIABLE_1307972))) (ho_11184 (ho_11188 k_12693 BOUND_VARIABLE_1307972) BOUND_VARIABLE_1307973))))) (let ((_let_4405 (forall ((BOUND_VARIABLE_1307961 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1307962 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1307963 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1307961 BOUND_VARIABLE_1307963) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307963) BOUND_VARIABLE_1307962)) (ho_11184 (ho_11237 (ho_11236 k_12694 BOUND_VARIABLE_1307961) BOUND_VARIABLE_1307962) BOUND_VARIABLE_1307963))))) (let ((_let_4406 (forall ((BOUND_VARIABLE_1307953 tptp.set_nat) (BOUND_VARIABLE_1307954 tptp.nat)) (= (ho_11054 (ho_11240 k_12695 BOUND_VARIABLE_1307953) BOUND_VARIABLE_1307954) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307954) BOUND_VARIABLE_1307953))))) (let ((_let_4407 (forall ((BOUND_VARIABLE_1307930 tptp.nat) (BOUND_VARIABLE_1307931 tptp.nat)) (= (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307931) (ho_11107 k_11106 (ho_11053 k_11228 BOUND_VARIABLE_1307930))) (ho_11054 (ho_11053 k_12696 BOUND_VARIABLE_1307930) BOUND_VARIABLE_1307931))))) (let ((_let_4408 (forall ((BOUND_VARIABLE_1307919 tptp.nat) (BOUND_VARIABLE_1307920 tptp.set_nat) (BOUND_VARIABLE_1307921 tptp.nat)) (= (or (= BOUND_VARIABLE_1307919 BOUND_VARIABLE_1307921) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307921) BOUND_VARIABLE_1307920)) (ho_11054 (ho_11240 (ho_11239 k_12697 BOUND_VARIABLE_1307919) BOUND_VARIABLE_1307920) BOUND_VARIABLE_1307921))))) (let ((_let_4409 (forall ((BOUND_VARIABLE_1307905 Bool) (BOUND_VARIABLE_1307906 Bool)) (= (or (= BOUND_VARIABLE_1307905 BOUND_VARIABLE_1307906) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1307906) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12698 BOUND_VARIABLE_1307905) BOUND_VARIABLE_1307906))))) (let ((_let_4410 (forall ((BOUND_VARIABLE_1307895 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1307896 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1307895 BOUND_VARIABLE_1307896) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1307896) tptp.bot_bo228742789529271731at_nat)) (ho_11263 (ho_11262 k_12699 BOUND_VARIABLE_1307895) BOUND_VARIABLE_1307896))))) (let ((_let_4411 (forall ((BOUND_VARIABLE_1307884 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1307885 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1307886 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1307884 BOUND_VARIABLE_1307886) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1307886) BOUND_VARIABLE_1307885)) (ho_11263 (ho_11374 (ho_12630 k_12700 BOUND_VARIABLE_1307884) BOUND_VARIABLE_1307885) BOUND_VARIABLE_1307886))))) (let ((_let_4412 (forall ((BOUND_VARIABLE_1307876 tptp.set_int) (BOUND_VARIABLE_1307877 tptp.int)) (= (ho_11094 (ho_11234 k_12701 BOUND_VARIABLE_1307876) BOUND_VARIABLE_1307877) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307877) BOUND_VARIABLE_1307876))))) (let ((_let_4413 (forall ((BOUND_VARIABLE_1307853 tptp.int) (BOUND_VARIABLE_1307854 tptp.int)) (= (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307854) (ho_11177 k_11176 (ho_11093 k_11229 BOUND_VARIABLE_1307853))) (ho_11094 (ho_11093 k_12702 BOUND_VARIABLE_1307853) BOUND_VARIABLE_1307854))))) (let ((_let_4414 (forall ((BOUND_VARIABLE_1307842 tptp.int) (BOUND_VARIABLE_1307843 tptp.set_int) (BOUND_VARIABLE_1307844 tptp.int)) (= (or (= BOUND_VARIABLE_1307842 BOUND_VARIABLE_1307844) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307844) BOUND_VARIABLE_1307843)) (ho_11094 (ho_11234 (ho_11233 k_12703 BOUND_VARIABLE_1307842) BOUND_VARIABLE_1307843) BOUND_VARIABLE_1307844))))) (let ((_let_4415 (forall ((BOUND_VARIABLE_1307828 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1307829 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1307828 BOUND_VARIABLE_1307829) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307829) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12704 BOUND_VARIABLE_1307828) BOUND_VARIABLE_1307829))))) (let ((_let_4416 (forall ((BOUND_VARIABLE_1307820 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1307821 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12705 BOUND_VARIABLE_1307820) BOUND_VARIABLE_1307821) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307821) BOUND_VARIABLE_1307820))))) (let ((_let_4417 (forall ((BOUND_VARIABLE_1307797 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1307798 tptp.product_prod_nat_nat)) (= (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307798) (ho_11186 k_11185 (ho_11188 k_11230 BOUND_VARIABLE_1307797))) (ho_11184 (ho_11188 k_12706 BOUND_VARIABLE_1307797) BOUND_VARIABLE_1307798))))) (let ((_let_4418 (forall ((BOUND_VARIABLE_1307786 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1307787 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1307788 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1307786 BOUND_VARIABLE_1307788) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307788) BOUND_VARIABLE_1307787)) (ho_11184 (ho_11237 (ho_11236 k_12707 BOUND_VARIABLE_1307786) BOUND_VARIABLE_1307787) BOUND_VARIABLE_1307788))))) (let ((_let_4419 (forall ((BOUND_VARIABLE_1307778 tptp.set_nat) (BOUND_VARIABLE_1307779 tptp.nat)) (= (ho_11054 (ho_11240 k_12708 BOUND_VARIABLE_1307778) BOUND_VARIABLE_1307779) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307779) BOUND_VARIABLE_1307778))))) (let ((_let_4420 (forall ((BOUND_VARIABLE_1307755 tptp.nat) (BOUND_VARIABLE_1307756 tptp.nat)) (= (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307756) (ho_11107 k_11106 (ho_11053 k_11231 BOUND_VARIABLE_1307755))) (ho_11054 (ho_11053 k_12709 BOUND_VARIABLE_1307755) BOUND_VARIABLE_1307756))))) (let ((_let_4421 (forall ((BOUND_VARIABLE_1307744 tptp.nat) (BOUND_VARIABLE_1307745 tptp.set_nat) (BOUND_VARIABLE_1307746 tptp.nat)) (= (or (= BOUND_VARIABLE_1307744 BOUND_VARIABLE_1307746) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307746) BOUND_VARIABLE_1307745)) (ho_11054 (ho_11240 (ho_11239 k_12710 BOUND_VARIABLE_1307744) BOUND_VARIABLE_1307745) BOUND_VARIABLE_1307746))))) (let ((_let_4422 (forall ((BOUND_VARIABLE_1307730 Bool) (BOUND_VARIABLE_1307731 Bool)) (= (or (= BOUND_VARIABLE_1307730 BOUND_VARIABLE_1307731) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1307731) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12711 BOUND_VARIABLE_1307730) BOUND_VARIABLE_1307731))))) (let ((_let_4423 (forall ((BOUND_VARIABLE_1307716 tptp.set_nat) (BOUND_VARIABLE_1307717 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1307716 BOUND_VARIABLE_1307717) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1307717) (ho_11204 k_11203 k_11202))) (ho_11191 (ho_11209 k_12712 BOUND_VARIABLE_1307716) BOUND_VARIABLE_1307717))))) (let ((_let_4424 (forall ((BOUND_VARIABLE_1307702 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1307703 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1307702 BOUND_VARIABLE_1307703) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1307703) (ho_11213 k_11212 k_11210))) (ho_11211 (ho_11218 k_12713 BOUND_VARIABLE_1307702) BOUND_VARIABLE_1307703))))) (let ((_let_4425 (forall ((BOUND_VARIABLE_1307692 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1307693 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1307692 BOUND_VARIABLE_1307693) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1307693) tptp.bot_bo228742789529271731at_nat)) (ho_11263 (ho_11262 k_12714 BOUND_VARIABLE_1307692) BOUND_VARIABLE_1307693))))) (let ((_let_4426 (forall ((BOUND_VARIABLE_1307681 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1307682 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1307683 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1307681 BOUND_VARIABLE_1307683) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1307683) BOUND_VARIABLE_1307682)) (ho_11263 (ho_11374 (ho_12630 k_12715 BOUND_VARIABLE_1307681) BOUND_VARIABLE_1307682) BOUND_VARIABLE_1307683))))) (let ((_let_4427 (forall ((BOUND_VARIABLE_1307673 tptp.set_int) (BOUND_VARIABLE_1307674 tptp.int)) (= (ho_11094 (ho_11234 k_12716 BOUND_VARIABLE_1307673) BOUND_VARIABLE_1307674) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307674) BOUND_VARIABLE_1307673))))) (let ((_let_4428 (forall ((BOUND_VARIABLE_1307665 tptp.set_int) (BOUND_VARIABLE_1307666 tptp.int)) (= (ho_11094 (ho_11234 k_12717 BOUND_VARIABLE_1307665) BOUND_VARIABLE_1307666) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307666) BOUND_VARIABLE_1307665))))) (let ((_let_4429 (forall ((BOUND_VARIABLE_1307654 tptp.int) (BOUND_VARIABLE_1307655 tptp.set_int) (BOUND_VARIABLE_1307656 tptp.int)) (= (or (= BOUND_VARIABLE_1307654 BOUND_VARIABLE_1307656) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307656) BOUND_VARIABLE_1307655)) (ho_11094 (ho_11234 (ho_11233 k_12718 BOUND_VARIABLE_1307654) BOUND_VARIABLE_1307655) BOUND_VARIABLE_1307656))))) (let ((_let_4430 (forall ((BOUND_VARIABLE_1307646 tptp.set_int) (BOUND_VARIABLE_1307647 tptp.int)) (= (ho_11094 (ho_11234 k_12719 BOUND_VARIABLE_1307646) BOUND_VARIABLE_1307647) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307647) BOUND_VARIABLE_1307646))))) (let ((_let_4431 (forall ((BOUND_VARIABLE_1307618 tptp.int) (BOUND_VARIABLE_1307619 tptp.set_int) (BOUND_VARIABLE_1307620 tptp.int)) (= (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307620) (ho_11177 k_11176 (ho_11234 (ho_11233 k_11232 BOUND_VARIABLE_1307618) BOUND_VARIABLE_1307619))) (ho_11094 (ho_11234 (ho_11233 k_12720 BOUND_VARIABLE_1307618) BOUND_VARIABLE_1307619) BOUND_VARIABLE_1307620))))) (let ((_let_4432 (forall ((BOUND_VARIABLE_1307610 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1307611 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12721 BOUND_VARIABLE_1307610) BOUND_VARIABLE_1307611) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307611) BOUND_VARIABLE_1307610))))) (let ((_let_4433 (forall ((BOUND_VARIABLE_1307602 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1307603 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12722 BOUND_VARIABLE_1307602) BOUND_VARIABLE_1307603) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307603) BOUND_VARIABLE_1307602))))) (let ((_let_4434 (forall ((BOUND_VARIABLE_1307594 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1307595 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12723 BOUND_VARIABLE_1307594) BOUND_VARIABLE_1307595) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307595) BOUND_VARIABLE_1307594))))) (let ((_let_4435 (forall ((BOUND_VARIABLE_1307566 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1307567 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1307568 tptp.product_prod_nat_nat)) (= (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307568) (ho_11186 k_11185 (ho_11237 (ho_11236 k_11235 BOUND_VARIABLE_1307566) BOUND_VARIABLE_1307567))) (ho_11184 (ho_11237 (ho_11236 k_12724 BOUND_VARIABLE_1307566) BOUND_VARIABLE_1307567) BOUND_VARIABLE_1307568))))) (let ((_let_4436 (forall ((BOUND_VARIABLE_1307558 tptp.set_nat) (BOUND_VARIABLE_1307559 tptp.nat)) (= (ho_11054 (ho_11240 k_12725 BOUND_VARIABLE_1307558) BOUND_VARIABLE_1307559) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307559) BOUND_VARIABLE_1307558))))) (let ((_let_4437 (forall ((BOUND_VARIABLE_1307550 tptp.set_nat) (BOUND_VARIABLE_1307551 tptp.nat)) (= (ho_11054 (ho_11240 k_12726 BOUND_VARIABLE_1307550) BOUND_VARIABLE_1307551) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307551) BOUND_VARIABLE_1307550))))) (let ((_let_4438 (forall ((BOUND_VARIABLE_1307539 tptp.nat) (BOUND_VARIABLE_1307540 tptp.set_nat) (BOUND_VARIABLE_1307541 tptp.nat)) (= (or (= BOUND_VARIABLE_1307539 BOUND_VARIABLE_1307541) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307541) BOUND_VARIABLE_1307540)) (ho_11054 (ho_11240 (ho_11239 k_12727 BOUND_VARIABLE_1307539) BOUND_VARIABLE_1307540) BOUND_VARIABLE_1307541))))) (let ((_let_4439 (forall ((BOUND_VARIABLE_1307531 tptp.set_nat) (BOUND_VARIABLE_1307532 tptp.nat)) (= (ho_11054 (ho_11240 k_12728 BOUND_VARIABLE_1307531) BOUND_VARIABLE_1307532) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307532) BOUND_VARIABLE_1307531))))) (let ((_let_4440 (forall ((BOUND_VARIABLE_1307503 tptp.nat) (BOUND_VARIABLE_1307504 tptp.set_nat) (BOUND_VARIABLE_1307505 tptp.nat)) (= (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307505) (ho_11107 k_11106 (ho_11240 (ho_11239 k_11238 BOUND_VARIABLE_1307503) BOUND_VARIABLE_1307504))) (ho_11054 (ho_11240 (ho_11239 k_12729 BOUND_VARIABLE_1307503) BOUND_VARIABLE_1307504) BOUND_VARIABLE_1307505))))) (let ((_let_4441 (forall ((BOUND_VARIABLE_1307492 tptp.set_nat) (BOUND_VARIABLE_1307493 tptp.set_set_nat) (BOUND_VARIABLE_1307494 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1307492 BOUND_VARIABLE_1307494) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1307494) BOUND_VARIABLE_1307493)) (ho_11191 (ho_12650 (ho_12653 k_12730 BOUND_VARIABLE_1307492) BOUND_VARIABLE_1307493) BOUND_VARIABLE_1307494))))) (let ((_let_4442 (forall ((BOUND_VARIABLE_1307481 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1307482 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1307483 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1307481 BOUND_VARIABLE_1307483) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1307483) BOUND_VARIABLE_1307482)) (ho_11211 (ho_12655 (ho_12658 k_12731 BOUND_VARIABLE_1307481) BOUND_VARIABLE_1307482) BOUND_VARIABLE_1307483))))) (let ((_let_4443 (forall ((BOUND_VARIABLE_1307470 Bool) (BOUND_VARIABLE_1307471 tptp.set_o) (BOUND_VARIABLE_1307472 Bool)) (= (or (= BOUND_VARIABLE_1307470 BOUND_VARIABLE_1307472) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1307472) BOUND_VARIABLE_1307471)) (ho_11194 (ho_12571 (ho_12648 k_12732 BOUND_VARIABLE_1307470) BOUND_VARIABLE_1307471) BOUND_VARIABLE_1307472))))) (let ((_let_4444 (forall ((BOUND_VARIABLE_1307459 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1307460 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1307461 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1307459 BOUND_VARIABLE_1307461) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1307461) BOUND_VARIABLE_1307460)) (ho_11263 (ho_11374 (ho_12630 k_12733 BOUND_VARIABLE_1307459) BOUND_VARIABLE_1307460) BOUND_VARIABLE_1307461))))) (let ((_let_4445 (forall ((BOUND_VARIABLE_1307448 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1307449 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1307450 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1307448 BOUND_VARIABLE_1307450) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307450) BOUND_VARIABLE_1307449)) (ho_11184 (ho_11237 (ho_11236 k_12734 BOUND_VARIABLE_1307448) BOUND_VARIABLE_1307449) BOUND_VARIABLE_1307450))))) (let ((_let_4446 (forall ((BOUND_VARIABLE_1307440 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1307441 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12735 BOUND_VARIABLE_1307440) BOUND_VARIABLE_1307441) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307441) BOUND_VARIABLE_1307440))))) (let ((_let_4447 (forall ((BOUND_VARIABLE_1307432 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1307433 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12736 BOUND_VARIABLE_1307432) BOUND_VARIABLE_1307433) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307433) BOUND_VARIABLE_1307432))))) (let ((_let_4448 (forall ((BOUND_VARIABLE_1307418 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1307419 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1307418 BOUND_VARIABLE_1307419) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307419) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12737 BOUND_VARIABLE_1307418) BOUND_VARIABLE_1307419))))) (let ((_let_4449 (forall ((BOUND_VARIABLE_1307407 tptp.int) (BOUND_VARIABLE_1307408 tptp.set_int) (BOUND_VARIABLE_1307409 tptp.int)) (= (or (= BOUND_VARIABLE_1307407 BOUND_VARIABLE_1307409) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307409) BOUND_VARIABLE_1307408)) (ho_11094 (ho_11234 (ho_11233 k_12738 BOUND_VARIABLE_1307407) BOUND_VARIABLE_1307408) BOUND_VARIABLE_1307409))))) (let ((_let_4450 (forall ((BOUND_VARIABLE_1307399 tptp.set_int) (BOUND_VARIABLE_1307400 tptp.int)) (= (ho_11094 (ho_11234 k_12739 BOUND_VARIABLE_1307399) BOUND_VARIABLE_1307400) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307400) BOUND_VARIABLE_1307399))))) (let ((_let_4451 (forall ((BOUND_VARIABLE_1307391 tptp.set_int) (BOUND_VARIABLE_1307392 tptp.int)) (= (ho_11094 (ho_11234 k_12740 BOUND_VARIABLE_1307391) BOUND_VARIABLE_1307392) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307392) BOUND_VARIABLE_1307391))))) (let ((_let_4452 (forall ((BOUND_VARIABLE_1307377 tptp.int) (BOUND_VARIABLE_1307378 tptp.int)) (= (or (= BOUND_VARIABLE_1307377 BOUND_VARIABLE_1307378) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307378) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12741 BOUND_VARIABLE_1307377) BOUND_VARIABLE_1307378))))) (let ((_let_4453 (forall ((BOUND_VARIABLE_1307366 tptp.nat) (BOUND_VARIABLE_1307367 tptp.set_nat) (BOUND_VARIABLE_1307368 tptp.nat)) (= (or (= BOUND_VARIABLE_1307366 BOUND_VARIABLE_1307368) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307368) BOUND_VARIABLE_1307367)) (ho_11054 (ho_11240 (ho_11239 k_12742 BOUND_VARIABLE_1307366) BOUND_VARIABLE_1307367) BOUND_VARIABLE_1307368))))) (let ((_let_4454 (forall ((BOUND_VARIABLE_1307358 tptp.set_nat) (BOUND_VARIABLE_1307359 tptp.nat)) (= (ho_11054 (ho_11240 k_12743 BOUND_VARIABLE_1307358) BOUND_VARIABLE_1307359) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307359) BOUND_VARIABLE_1307358))))) (let ((_let_4455 (forall ((BOUND_VARIABLE_1307350 tptp.set_nat) (BOUND_VARIABLE_1307351 tptp.nat)) (= (ho_11054 (ho_11240 k_12744 BOUND_VARIABLE_1307350) BOUND_VARIABLE_1307351) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307351) BOUND_VARIABLE_1307350))))) (let ((_let_4456 (forall ((BOUND_VARIABLE_1307336 tptp.nat) (BOUND_VARIABLE_1307337 tptp.nat)) (= (or (= BOUND_VARIABLE_1307336 BOUND_VARIABLE_1307337) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307337) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12745 BOUND_VARIABLE_1307336) BOUND_VARIABLE_1307337))))) (let ((_let_4457 (forall ((BOUND_VARIABLE_1307325 Bool) (BOUND_VARIABLE_1307326 tptp.set_o) (BOUND_VARIABLE_1307327 Bool)) (= (or (= BOUND_VARIABLE_1307325 BOUND_VARIABLE_1307327) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1307327) BOUND_VARIABLE_1307326)) (ho_11194 (ho_12571 (ho_12648 k_12746 BOUND_VARIABLE_1307325) BOUND_VARIABLE_1307326) BOUND_VARIABLE_1307327))))) (let ((_let_4458 (forall ((BOUND_VARIABLE_1307317 tptp.set_o) (BOUND_VARIABLE_1307318 Bool)) (= (ho_11194 (ho_12571 k_12747 BOUND_VARIABLE_1307317) BOUND_VARIABLE_1307318) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1307318) BOUND_VARIABLE_1307317))))) (let ((_let_4459 (forall ((BOUND_VARIABLE_1307309 tptp.set_o) (BOUND_VARIABLE_1307310 Bool)) (= (ho_11194 (ho_12571 k_12748 BOUND_VARIABLE_1307309) BOUND_VARIABLE_1307310) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1307310) BOUND_VARIABLE_1307309))))) (let ((_let_4460 (forall ((BOUND_VARIABLE_1307295 Bool) (BOUND_VARIABLE_1307296 Bool)) (= (or (= BOUND_VARIABLE_1307295 BOUND_VARIABLE_1307296) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1307296) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12749 BOUND_VARIABLE_1307295) BOUND_VARIABLE_1307296))))) (let ((_let_4461 (forall ((BOUND_VARIABLE_1307287 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1307288 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12750 BOUND_VARIABLE_1307287) BOUND_VARIABLE_1307288) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307288) BOUND_VARIABLE_1307287))))) (let ((_let_4462 (forall ((BOUND_VARIABLE_1307264 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1307265 tptp.product_prod_nat_nat)) (= (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307265) (ho_11186 k_11185 (ho_11188 k_11241 BOUND_VARIABLE_1307264))) (ho_11184 (ho_11188 k_12751 BOUND_VARIABLE_1307264) BOUND_VARIABLE_1307265))))) (let ((_let_4463 (forall ((BOUND_VARIABLE_1307256 tptp.set_int) (BOUND_VARIABLE_1307257 tptp.int)) (= (ho_11094 (ho_11234 k_12752 BOUND_VARIABLE_1307256) BOUND_VARIABLE_1307257) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307257) BOUND_VARIABLE_1307256))))) (let ((_let_4464 (forall ((BOUND_VARIABLE_1307233 tptp.int) (BOUND_VARIABLE_1307234 tptp.int)) (= (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307234) (ho_11177 k_11176 (ho_11093 k_11242 BOUND_VARIABLE_1307233))) (ho_11094 (ho_11093 k_12753 BOUND_VARIABLE_1307233) BOUND_VARIABLE_1307234))))) (let ((_let_4465 (forall ((BOUND_VARIABLE_1307225 tptp.set_nat) (BOUND_VARIABLE_1307226 tptp.nat)) (= (ho_11054 (ho_11240 k_12754 BOUND_VARIABLE_1307225) BOUND_VARIABLE_1307226) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307226) BOUND_VARIABLE_1307225))))) (let ((_let_4466 (forall ((BOUND_VARIABLE_1307202 tptp.nat) (BOUND_VARIABLE_1307203 tptp.nat)) (= (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307203) (ho_11107 k_11106 (ho_11053 k_11243 BOUND_VARIABLE_1307202))) (ho_11054 (ho_11053 k_12755 BOUND_VARIABLE_1307202) BOUND_VARIABLE_1307203))))) (let ((_let_4467 (forall ((BOUND_VARIABLE_1307194 tptp.set_o) (BOUND_VARIABLE_1307195 Bool)) (= (ho_11194 (ho_12571 k_12756 BOUND_VARIABLE_1307194) BOUND_VARIABLE_1307195) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1307195) BOUND_VARIABLE_1307194))))) (let ((_let_4468 (forall ((BOUND_VARIABLE_1307171 Bool) (BOUND_VARIABLE_1307172 Bool)) (= (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1307172) (ho_11196 k_11195 (ho_11201 k_11244 BOUND_VARIABLE_1307171))) (ho_11194 (ho_11201 k_12757 BOUND_VARIABLE_1307171) BOUND_VARIABLE_1307172))))) (let ((_let_4469 (forall ((BOUND_VARIABLE_1307163 tptp.set_set_nat) (BOUND_VARIABLE_1307164 tptp.set_nat)) (= (ho_11191 (ho_12650 k_12758 BOUND_VARIABLE_1307163) BOUND_VARIABLE_1307164) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1307164) BOUND_VARIABLE_1307163))))) (let ((_let_4470 (forall ((BOUND_VARIABLE_1307140 tptp.set_nat) (BOUND_VARIABLE_1307141 tptp.set_nat)) (= (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1307141) (ho_11204 k_11203 (ho_11209 k_11245 BOUND_VARIABLE_1307140))) (ho_11191 (ho_11209 k_12759 BOUND_VARIABLE_1307140) BOUND_VARIABLE_1307141))))) (let ((_let_4471 (forall ((BOUND_VARIABLE_1307132 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1307133 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 k_12760 BOUND_VARIABLE_1307132) BOUND_VARIABLE_1307133) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1307133) BOUND_VARIABLE_1307132))))) (let ((_let_4472 (forall ((BOUND_VARIABLE_1307109 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1307110 tptp.set_Pr958786334691620121nt_int)) (= (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1307110) (ho_11213 k_11212 (ho_11218 k_11246 BOUND_VARIABLE_1307109))) (ho_11211 (ho_11218 k_12761 BOUND_VARIABLE_1307109) BOUND_VARIABLE_1307110))))) (let ((_let_4473 (forall ((BOUND_VARIABLE_1307099 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1307100 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11262 k_12762 BOUND_VARIABLE_1307099) BOUND_VARIABLE_1307100) (or (= BOUND_VARIABLE_1307099 BOUND_VARIABLE_1307100) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1307100) tptp.bot_bo228742789529271731at_nat)))))) (let ((_let_4474 (forall ((BOUND_VARIABLE_1307088 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1307089 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1307090 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1307088 BOUND_VARIABLE_1307090) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307090) BOUND_VARIABLE_1307089)) (ho_11184 (ho_11237 (ho_11236 k_12763 BOUND_VARIABLE_1307088) BOUND_VARIABLE_1307089) BOUND_VARIABLE_1307090))))) (let ((_let_4475 (forall ((BOUND_VARIABLE_1307080 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1307081 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12764 BOUND_VARIABLE_1307080) BOUND_VARIABLE_1307081) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307081) BOUND_VARIABLE_1307080))))) (let ((_let_4476 (forall ((BOUND_VARIABLE_1307057 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1307058 tptp.product_prod_nat_nat)) (= (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1307058) (ho_11186 k_11185 (ho_11188 k_11247 BOUND_VARIABLE_1307057))) (ho_11184 (ho_11188 k_12765 BOUND_VARIABLE_1307057) BOUND_VARIABLE_1307058))))) (let ((_let_4477 (forall ((BOUND_VARIABLE_1307046 tptp.int) (BOUND_VARIABLE_1307047 tptp.set_int) (BOUND_VARIABLE_1307048 tptp.int)) (= (or (= BOUND_VARIABLE_1307046 BOUND_VARIABLE_1307048) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307048) BOUND_VARIABLE_1307047)) (ho_11094 (ho_11234 (ho_11233 k_12766 BOUND_VARIABLE_1307046) BOUND_VARIABLE_1307047) BOUND_VARIABLE_1307048))))) (let ((_let_4478 (forall ((BOUND_VARIABLE_1307038 tptp.set_int) (BOUND_VARIABLE_1307039 tptp.int)) (= (ho_11094 (ho_11234 k_12767 BOUND_VARIABLE_1307038) BOUND_VARIABLE_1307039) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307039) BOUND_VARIABLE_1307038))))) (let ((_let_4479 (forall ((BOUND_VARIABLE_1307015 tptp.int) (BOUND_VARIABLE_1307016 tptp.int)) (= (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1307016) (ho_11177 k_11176 (ho_11093 k_11248 BOUND_VARIABLE_1307015))) (ho_11094 (ho_11093 k_12768 BOUND_VARIABLE_1307015) BOUND_VARIABLE_1307016))))) (let ((_let_4480 (forall ((BOUND_VARIABLE_1307004 tptp.nat) (BOUND_VARIABLE_1307005 tptp.set_nat) (BOUND_VARIABLE_1307006 tptp.nat)) (= (or (= BOUND_VARIABLE_1307004 BOUND_VARIABLE_1307006) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1307006) BOUND_VARIABLE_1307005)) (ho_11054 (ho_11240 (ho_11239 k_12769 BOUND_VARIABLE_1307004) BOUND_VARIABLE_1307005) BOUND_VARIABLE_1307006))))) (let ((_let_4481 (forall ((BOUND_VARIABLE_1306996 tptp.set_nat) (BOUND_VARIABLE_1306997 tptp.nat)) (= (ho_11054 (ho_11240 k_12770 BOUND_VARIABLE_1306996) BOUND_VARIABLE_1306997) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1306997) BOUND_VARIABLE_1306996))))) (let ((_let_4482 (forall ((BOUND_VARIABLE_1306973 tptp.nat) (BOUND_VARIABLE_1306974 tptp.nat)) (= (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1306974) (ho_11107 k_11106 (ho_11053 k_11249 BOUND_VARIABLE_1306973))) (ho_11054 (ho_11053 k_12771 BOUND_VARIABLE_1306973) BOUND_VARIABLE_1306974))))) (let ((_let_4483 (forall ((BOUND_VARIABLE_1306962 Bool) (BOUND_VARIABLE_1306963 tptp.set_o) (BOUND_VARIABLE_1306964 Bool)) (= (or (= BOUND_VARIABLE_1306962 BOUND_VARIABLE_1306964) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1306964) BOUND_VARIABLE_1306963)) (ho_11194 (ho_12571 (ho_12648 k_12772 BOUND_VARIABLE_1306962) BOUND_VARIABLE_1306963) BOUND_VARIABLE_1306964))))) (let ((_let_4484 (forall ((BOUND_VARIABLE_1306954 tptp.set_o) (BOUND_VARIABLE_1306955 Bool)) (= (ho_11194 (ho_12571 k_12773 BOUND_VARIABLE_1306954) BOUND_VARIABLE_1306955) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1306955) BOUND_VARIABLE_1306954))))) (let ((_let_4485 (forall ((BOUND_VARIABLE_1306931 Bool) (BOUND_VARIABLE_1306932 Bool)) (= (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1306932) (ho_11196 k_11195 (ho_11201 k_11250 BOUND_VARIABLE_1306931))) (ho_11194 (ho_11201 k_12774 BOUND_VARIABLE_1306931) BOUND_VARIABLE_1306932))))) (let ((_let_4486 (forall ((BOUND_VARIABLE_1306920 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1306921 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1306922 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1306920 BOUND_VARIABLE_1306922) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1306922) BOUND_VARIABLE_1306921)) (ho_11184 (ho_11237 (ho_11236 k_12775 BOUND_VARIABLE_1306920) BOUND_VARIABLE_1306921) BOUND_VARIABLE_1306922))))) (let ((_let_4487 (forall ((BOUND_VARIABLE_1306906 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1306907 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1306906 BOUND_VARIABLE_1306907) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1306907) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12776 BOUND_VARIABLE_1306906) BOUND_VARIABLE_1306907))))) (let ((_let_4488 (forall ((BOUND_VARIABLE_1306895 tptp.int) (BOUND_VARIABLE_1306896 tptp.set_int) (BOUND_VARIABLE_1306897 tptp.int)) (= (or (= BOUND_VARIABLE_1306895 BOUND_VARIABLE_1306897) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1306897) BOUND_VARIABLE_1306896)) (ho_11094 (ho_11234 (ho_11233 k_12777 BOUND_VARIABLE_1306895) BOUND_VARIABLE_1306896) BOUND_VARIABLE_1306897))))) (let ((_let_4489 (forall ((BOUND_VARIABLE_1306881 tptp.int) (BOUND_VARIABLE_1306882 tptp.int)) (= (or (= BOUND_VARIABLE_1306881 BOUND_VARIABLE_1306882) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1306882) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12778 BOUND_VARIABLE_1306881) BOUND_VARIABLE_1306882))))) (let ((_let_4490 (forall ((BOUND_VARIABLE_1306870 tptp.nat) (BOUND_VARIABLE_1306871 tptp.set_nat) (BOUND_VARIABLE_1306872 tptp.nat)) (= (or (= BOUND_VARIABLE_1306870 BOUND_VARIABLE_1306872) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1306872) BOUND_VARIABLE_1306871)) (ho_11054 (ho_11240 (ho_11239 k_12779 BOUND_VARIABLE_1306870) BOUND_VARIABLE_1306871) BOUND_VARIABLE_1306872))))) (let ((_let_4491 (forall ((BOUND_VARIABLE_1306856 tptp.nat) (BOUND_VARIABLE_1306857 tptp.nat)) (= (or (= BOUND_VARIABLE_1306856 BOUND_VARIABLE_1306857) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1306857) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12780 BOUND_VARIABLE_1306856) BOUND_VARIABLE_1306857))))) (let ((_let_4492 (forall ((BOUND_VARIABLE_1306845 Bool) (BOUND_VARIABLE_1306846 tptp.set_o) (BOUND_VARIABLE_1306847 Bool)) (= (or (= BOUND_VARIABLE_1306845 BOUND_VARIABLE_1306847) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1306847) BOUND_VARIABLE_1306846)) (ho_11194 (ho_12571 (ho_12648 k_12781 BOUND_VARIABLE_1306845) BOUND_VARIABLE_1306846) BOUND_VARIABLE_1306847))))) (let ((_let_4493 (forall ((BOUND_VARIABLE_1306831 Bool) (BOUND_VARIABLE_1306832 Bool)) (= (or (= BOUND_VARIABLE_1306831 BOUND_VARIABLE_1306832) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1306832) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12782 BOUND_VARIABLE_1306831) BOUND_VARIABLE_1306832))))) (let ((_let_4494 (forall ((BOUND_VARIABLE_1306820 tptp.set_nat) (BOUND_VARIABLE_1306821 tptp.set_set_nat) (BOUND_VARIABLE_1306822 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1306820 BOUND_VARIABLE_1306822) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1306822) BOUND_VARIABLE_1306821)) (ho_11191 (ho_12650 (ho_12653 k_12783 BOUND_VARIABLE_1306820) BOUND_VARIABLE_1306821) BOUND_VARIABLE_1306822))))) (let ((_let_4495 (forall ((BOUND_VARIABLE_1306806 tptp.set_nat) (BOUND_VARIABLE_1306807 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1306806 BOUND_VARIABLE_1306807) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1306807) (ho_11204 k_11203 k_11202))) (ho_11191 (ho_11209 k_12784 BOUND_VARIABLE_1306806) BOUND_VARIABLE_1306807))))) (let ((_let_4496 (forall ((BOUND_VARIABLE_1306795 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1306796 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1306797 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1306795 BOUND_VARIABLE_1306797) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1306797) BOUND_VARIABLE_1306796)) (ho_11211 (ho_12655 (ho_12658 k_12785 BOUND_VARIABLE_1306795) BOUND_VARIABLE_1306796) BOUND_VARIABLE_1306797))))) (let ((_let_4497 (forall ((BOUND_VARIABLE_1306781 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1306782 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1306781 BOUND_VARIABLE_1306782) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1306782) (ho_11213 k_11212 k_11210))) (ho_11211 (ho_11218 k_12786 BOUND_VARIABLE_1306781) BOUND_VARIABLE_1306782))))) (let ((_let_4498 (forall ((BOUND_VARIABLE_1306770 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1306771 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1306772 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1306770 BOUND_VARIABLE_1306772) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1306772) BOUND_VARIABLE_1306771)) (ho_11184 (ho_11237 (ho_11236 k_12787 BOUND_VARIABLE_1306770) BOUND_VARIABLE_1306771) BOUND_VARIABLE_1306772))))) (let ((_let_4499 (forall ((BOUND_VARIABLE_1306756 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1306757 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1306756 BOUND_VARIABLE_1306757) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1306757) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12788 BOUND_VARIABLE_1306756) BOUND_VARIABLE_1306757))))) (let ((_let_4500 (forall ((BOUND_VARIABLE_1306748 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1306749 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12789 BOUND_VARIABLE_1306748) BOUND_VARIABLE_1306749) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1306749) BOUND_VARIABLE_1306748))))) (let ((_let_4501 (forall ((BOUND_VARIABLE_1306725 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1306726 tptp.product_prod_nat_nat)) (= (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1306726) (ho_11186 k_11185 (ho_11188 k_11251 BOUND_VARIABLE_1306725))) (ho_11184 (ho_11188 k_12790 BOUND_VARIABLE_1306725) BOUND_VARIABLE_1306726))))) (let ((_let_4502 (forall ((BOUND_VARIABLE_1306714 tptp.int) (BOUND_VARIABLE_1306715 tptp.set_int) (BOUND_VARIABLE_1306716 tptp.int)) (= (or (= BOUND_VARIABLE_1306714 BOUND_VARIABLE_1306716) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1306716) BOUND_VARIABLE_1306715)) (ho_11094 (ho_11234 (ho_11233 k_12791 BOUND_VARIABLE_1306714) BOUND_VARIABLE_1306715) BOUND_VARIABLE_1306716))))) (let ((_let_4503 (forall ((BOUND_VARIABLE_1306700 tptp.int) (BOUND_VARIABLE_1306701 tptp.int)) (= (or (= BOUND_VARIABLE_1306700 BOUND_VARIABLE_1306701) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1306701) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12792 BOUND_VARIABLE_1306700) BOUND_VARIABLE_1306701))))) (let ((_let_4504 (forall ((BOUND_VARIABLE_1306692 tptp.set_int) (BOUND_VARIABLE_1306693 tptp.int)) (= (ho_11094 (ho_11234 k_12793 BOUND_VARIABLE_1306692) BOUND_VARIABLE_1306693) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1306693) BOUND_VARIABLE_1306692))))) (let ((_let_4505 (forall ((BOUND_VARIABLE_1306669 tptp.int) (BOUND_VARIABLE_1306670 tptp.int)) (= (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1306670) (ho_11177 k_11176 (ho_11093 k_11252 BOUND_VARIABLE_1306669))) (ho_11094 (ho_11093 k_12794 BOUND_VARIABLE_1306669) BOUND_VARIABLE_1306670))))) (let ((_let_4506 (forall ((BOUND_VARIABLE_1306658 tptp.nat) (BOUND_VARIABLE_1306659 tptp.set_nat) (BOUND_VARIABLE_1306660 tptp.nat)) (= (or (= BOUND_VARIABLE_1306658 BOUND_VARIABLE_1306660) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1306660) BOUND_VARIABLE_1306659)) (ho_11054 (ho_11240 (ho_11239 k_12795 BOUND_VARIABLE_1306658) BOUND_VARIABLE_1306659) BOUND_VARIABLE_1306660))))) (let ((_let_4507 (forall ((BOUND_VARIABLE_1306644 tptp.nat) (BOUND_VARIABLE_1306645 tptp.nat)) (= (or (= BOUND_VARIABLE_1306644 BOUND_VARIABLE_1306645) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1306645) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12796 BOUND_VARIABLE_1306644) BOUND_VARIABLE_1306645))))) (let ((_let_4508 (forall ((BOUND_VARIABLE_1306636 tptp.set_nat) (BOUND_VARIABLE_1306637 tptp.nat)) (= (ho_11054 (ho_11240 k_12797 BOUND_VARIABLE_1306636) BOUND_VARIABLE_1306637) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1306637) BOUND_VARIABLE_1306636))))) (let ((_let_4509 (forall ((BOUND_VARIABLE_1306613 tptp.nat) (BOUND_VARIABLE_1306614 tptp.nat)) (= (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1306614) (ho_11107 k_11106 (ho_11053 k_11253 BOUND_VARIABLE_1306613))) (ho_11054 (ho_11053 k_12798 BOUND_VARIABLE_1306613) BOUND_VARIABLE_1306614))))) (let ((_let_4510 (forall ((BOUND_VARIABLE_1306601 Bool) (BOUND_VARIABLE_1306602 tptp.set_o) (BOUND_VARIABLE_1306603 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_12799 BOUND_VARIABLE_1306601) BOUND_VARIABLE_1306602) BOUND_VARIABLE_1306603) (or (= BOUND_VARIABLE_1306603 (not BOUND_VARIABLE_1306601)) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1306603) BOUND_VARIABLE_1306602)))))) (let ((_let_4511 (forall ((BOUND_VARIABLE_1306587 Bool) (BOUND_VARIABLE_1306588 Bool)) (= (or (= BOUND_VARIABLE_1306587 BOUND_VARIABLE_1306588) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1306588) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12800 BOUND_VARIABLE_1306587) BOUND_VARIABLE_1306588))))) (let ((_let_4512 (forall ((BOUND_VARIABLE_1306579 tptp.set_o) (BOUND_VARIABLE_1306580 Bool)) (= (ho_11194 (ho_12571 k_12801 BOUND_VARIABLE_1306579) BOUND_VARIABLE_1306580) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1306580) BOUND_VARIABLE_1306579))))) (let ((_let_4513 (forall ((BOUND_VARIABLE_1306556 Bool) (BOUND_VARIABLE_1306557 Bool)) (= (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1306557) (ho_11196 k_11195 (ho_11201 k_11254 BOUND_VARIABLE_1306556))) (ho_11194 (ho_11201 k_12802 BOUND_VARIABLE_1306556) BOUND_VARIABLE_1306557))))) (let ((_let_4514 (forall ((BOUND_VARIABLE_1306546 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1306547 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11262 k_12803 BOUND_VARIABLE_1306546) BOUND_VARIABLE_1306547) (or (= BOUND_VARIABLE_1306546 BOUND_VARIABLE_1306547) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1306547) tptp.bot_bo228742789529271731at_nat)))))) (let ((_let_4515 (forall ((BOUND_VARIABLE_1306532 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1306533 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1306532 BOUND_VARIABLE_1306533) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1306533) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12804 BOUND_VARIABLE_1306532) BOUND_VARIABLE_1306533))))) (let ((_let_4516 (forall ((BOUND_VARIABLE_1306518 tptp.int) (BOUND_VARIABLE_1306519 tptp.int)) (= (or (= BOUND_VARIABLE_1306518 BOUND_VARIABLE_1306519) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1306519) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12805 BOUND_VARIABLE_1306518) BOUND_VARIABLE_1306519))))) (let ((_let_4517 (forall ((BOUND_VARIABLE_1306504 tptp.nat) (BOUND_VARIABLE_1306505 tptp.nat)) (= (or (= BOUND_VARIABLE_1306504 BOUND_VARIABLE_1306505) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1306505) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12806 BOUND_VARIABLE_1306504) BOUND_VARIABLE_1306505))))) (let ((_let_4518 (forall ((BOUND_VARIABLE_1306490 Bool) (BOUND_VARIABLE_1306491 Bool)) (= (or (= BOUND_VARIABLE_1306490 BOUND_VARIABLE_1306491) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1306491) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12807 BOUND_VARIABLE_1306490) BOUND_VARIABLE_1306491))))) (let ((_let_4519 (forall ((BOUND_VARIABLE_1306476 tptp.set_nat) (BOUND_VARIABLE_1306477 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1306476 BOUND_VARIABLE_1306477) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1306477) (ho_11204 k_11203 k_11202))) (ho_11191 (ho_11209 k_12808 BOUND_VARIABLE_1306476) BOUND_VARIABLE_1306477))))) (let ((_let_4520 (forall ((BOUND_VARIABLE_1306462 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1306463 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1306462 BOUND_VARIABLE_1306463) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1306463) (ho_11213 k_11212 k_11210))) (ho_11211 (ho_11218 k_12809 BOUND_VARIABLE_1306462) BOUND_VARIABLE_1306463))))) (let ((_let_4521 (forall ((BOUND_VARIABLE_1306455 tptp.produc4166570645942440679at_nat) (BOUND_VARIABLE_1306456 tptp.produc4166570645942440679at_nat)) (= (= BOUND_VARIABLE_1306455 BOUND_VARIABLE_1306456) (ho_11051 (ho_11050 k_12810 BOUND_VARIABLE_1306455) BOUND_VARIABLE_1306456))))) (let ((_let_4522 (forall ((BOUND_VARIABLE_1306448 tptp.produc4166570645942440679at_nat) (BOUND_VARIABLE_1306449 tptp.produc4166570645942440679at_nat)) (= (= BOUND_VARIABLE_1306448 BOUND_VARIABLE_1306449) (ho_11051 (ho_11050 k_12811 BOUND_VARIABLE_1306448) BOUND_VARIABLE_1306449))))) (let ((_let_4523 (forall ((BOUND_VARIABLE_1306421 tptp.int) (BOUND_VARIABLE_1306422 tptp.set_int) (BOUND_VARIABLE_1306423 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1306423))) (= (or (ho_11180 _let_1 (ho_11177 k_11176 (ho_11093 k_11255 BOUND_VARIABLE_1306421))) (ho_11180 _let_1 BOUND_VARIABLE_1306422)) (ho_11094 (ho_11234 (ho_11233 k_12812 BOUND_VARIABLE_1306421) BOUND_VARIABLE_1306422) BOUND_VARIABLE_1306423)))))) (let ((_let_4524 (forall ((BOUND_VARIABLE_1306394 tptp.nat) (BOUND_VARIABLE_1306395 tptp.set_nat) (BOUND_VARIABLE_1306396 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1306396))) (= (or (ho_11191 _let_1 (ho_11107 k_11106 (ho_11053 k_11256 BOUND_VARIABLE_1306394))) (ho_11191 _let_1 BOUND_VARIABLE_1306395)) (ho_11054 (ho_11240 (ho_11239 k_12813 BOUND_VARIABLE_1306394) BOUND_VARIABLE_1306395) BOUND_VARIABLE_1306396)))))) (let ((_let_4525 (forall ((BOUND_VARIABLE_1306367 Bool) (BOUND_VARIABLE_1306368 tptp.set_o) (BOUND_VARIABLE_1306369 Bool)) (let ((_let_1 (ho_11198 k_11197 BOUND_VARIABLE_1306369))) (= (or (ho_11199 _let_1 (ho_11196 k_11195 (ho_11201 k_11257 BOUND_VARIABLE_1306367))) (ho_11199 _let_1 BOUND_VARIABLE_1306368)) (ho_11194 (ho_12571 (ho_12648 k_12814 BOUND_VARIABLE_1306367) BOUND_VARIABLE_1306368) BOUND_VARIABLE_1306369)))))) (let ((_let_4526 (forall ((BOUND_VARIABLE_1306353 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1306354 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1306353 BOUND_VARIABLE_1306354) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1306354) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12815 BOUND_VARIABLE_1306353) BOUND_VARIABLE_1306354))))) (let ((_let_4527 (forall ((BOUND_VARIABLE_1306326 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1306327 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1306328 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (ho_11259 k_11258 BOUND_VARIABLE_1306328))) (= (or (ho_11260 _let_1 (ho_12817 k_12816 (ho_11262 k_11261 BOUND_VARIABLE_1306326))) (ho_11260 _let_1 BOUND_VARIABLE_1306327)) (ho_11263 (ho_11374 (ho_12630 k_12818 BOUND_VARIABLE_1306326) BOUND_VARIABLE_1306327) BOUND_VARIABLE_1306328)))))) (let ((_let_4528 (forall ((BOUND_VARIABLE_1306301 tptp.produc4166570645942440679at_nat) (BOUND_VARIABLE_1306302 tptp.set_Pr8551490117392284871at_nat) (BOUND_VARIABLE_1306303 tptp.produc4166570645942440679at_nat)) (let ((_let_1 (ho_11266 k_11265 BOUND_VARIABLE_1306303))) (= (or (ho_11267 _let_1 (ho_11269 k_11268 (ho_11050 k_11264 BOUND_VARIABLE_1306301))) (ho_11267 _let_1 BOUND_VARIABLE_1306302)) (ho_11051 (ho_11377 (ho_12820 k_12819 BOUND_VARIABLE_1306301) BOUND_VARIABLE_1306302) BOUND_VARIABLE_1306303)))))) (let ((_let_4529 (forall ((BOUND_VARIABLE_1306268 tptp.produc4166570645942440679at_nat) (BOUND_VARIABLE_1306269 tptp.set_Pr8551490117392284871at_nat) (BOUND_VARIABLE_1306270 tptp.produc4166570645942440679at_nat)) (let ((_let_1 (ho_11266 k_11265 BOUND_VARIABLE_1306270))) (= (or (ho_11267 _let_1 (ho_11269 k_11268 (ho_11050 k_11270 BOUND_VARIABLE_1306268))) (ho_11267 _let_1 BOUND_VARIABLE_1306269)) (ho_11051 (ho_11377 (ho_12820 k_12821 BOUND_VARIABLE_1306268) BOUND_VARIABLE_1306269) BOUND_VARIABLE_1306270)))))) (let ((_let_4530 (forall ((BOUND_VARIABLE_1306254 tptp.int) (BOUND_VARIABLE_1306255 tptp.int)) (= (or (= BOUND_VARIABLE_1306254 BOUND_VARIABLE_1306255) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1306255) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12822 BOUND_VARIABLE_1306254) BOUND_VARIABLE_1306255))))) (let ((_let_4531 (forall ((BOUND_VARIABLE_1306240 tptp.nat) (BOUND_VARIABLE_1306241 tptp.nat)) (= (or (= BOUND_VARIABLE_1306240 BOUND_VARIABLE_1306241) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1306241) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12823 BOUND_VARIABLE_1306240) BOUND_VARIABLE_1306241))))) (let ((_let_4532 (forall ((BOUND_VARIABLE_1306226 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1306227 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1306226 BOUND_VARIABLE_1306227) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1306227) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12824 BOUND_VARIABLE_1306226) BOUND_VARIABLE_1306227))))) (let ((_let_4533 (forall ((BOUND_VARIABLE_1306216 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1306217 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1306216 BOUND_VARIABLE_1306217) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1306217) tptp.bot_bo228742789529271731at_nat)) (ho_11263 (ho_11262 k_12825 BOUND_VARIABLE_1306216) BOUND_VARIABLE_1306217))))) (let ((_let_4534 (forall ((BOUND_VARIABLE_1306202 tptp.int) (BOUND_VARIABLE_1306203 tptp.int)) (= (or (= BOUND_VARIABLE_1306202 BOUND_VARIABLE_1306203) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1306203) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12826 BOUND_VARIABLE_1306202) BOUND_VARIABLE_1306203))))) (let ((_let_4535 (forall ((BOUND_VARIABLE_1306188 tptp.nat) (BOUND_VARIABLE_1306189 tptp.nat)) (= (or (= BOUND_VARIABLE_1306188 BOUND_VARIABLE_1306189) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1306189) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12827 BOUND_VARIABLE_1306188) BOUND_VARIABLE_1306189))))) (let ((_let_4536 (forall ((BOUND_VARIABLE_1306174 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1306175 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1306174 BOUND_VARIABLE_1306175) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1306175) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12828 BOUND_VARIABLE_1306174) BOUND_VARIABLE_1306175))))) (let ((_let_4537 (forall ((BOUND_VARIABLE_1306164 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1306165 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1306164 BOUND_VARIABLE_1306165) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1306165) tptp.bot_bo228742789529271731at_nat)) (ho_11263 (ho_11262 k_12829 BOUND_VARIABLE_1306164) BOUND_VARIABLE_1306165))))) (let ((_let_4538 (forall ((BOUND_VARIABLE_1306153 tptp.nat) (BOUND_VARIABLE_1306154 tptp.set_nat) (BOUND_VARIABLE_1306155 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_12830 BOUND_VARIABLE_1306153) BOUND_VARIABLE_1306154) BOUND_VARIABLE_1306155) (or (= BOUND_VARIABLE_1306153 BOUND_VARIABLE_1306155) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1306155) BOUND_VARIABLE_1306154)))))) (let ((_let_4539 (forall ((BOUND_VARIABLE_1306128 tptp.nat) (BOUND_VARIABLE_1306129 tptp.set_nat) (BOUND_VARIABLE_1306130 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1306130))) (= (or (ho_11191 _let_1 (ho_11107 k_11106 (ho_11053 k_11271 BOUND_VARIABLE_1306128))) (ho_11191 _let_1 BOUND_VARIABLE_1306129)) (ho_11054 (ho_11240 (ho_11239 k_12831 BOUND_VARIABLE_1306128) BOUND_VARIABLE_1306129) BOUND_VARIABLE_1306130)))))) (let ((_let_4540 (forall ((BOUND_VARIABLE_1306117 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1306118 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1306119 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11374 (ho_12630 k_12832 BOUND_VARIABLE_1306117) BOUND_VARIABLE_1306118) BOUND_VARIABLE_1306119) (or (= BOUND_VARIABLE_1306117 BOUND_VARIABLE_1306119) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1306119) BOUND_VARIABLE_1306118)))))) (let ((_let_4541 (forall ((BOUND_VARIABLE_1306092 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1306093 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1306094 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (ho_11259 k_11258 BOUND_VARIABLE_1306094))) (= (or (ho_11260 _let_1 (ho_12817 k_12816 (ho_11262 k_11272 BOUND_VARIABLE_1306092))) (ho_11260 _let_1 BOUND_VARIABLE_1306093)) (ho_11263 (ho_11374 (ho_12630 k_12833 BOUND_VARIABLE_1306092) BOUND_VARIABLE_1306093) BOUND_VARIABLE_1306094)))))) (let ((_let_4542 (forall ((BOUND_VARIABLE_1306081 tptp.int) (BOUND_VARIABLE_1306082 tptp.set_int) (BOUND_VARIABLE_1306083 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_12834 BOUND_VARIABLE_1306081) BOUND_VARIABLE_1306082) BOUND_VARIABLE_1306083) (or (= BOUND_VARIABLE_1306081 BOUND_VARIABLE_1306083) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1306083) BOUND_VARIABLE_1306082)))))) (let ((_let_4543 (forall ((BOUND_VARIABLE_1306056 tptp.int) (BOUND_VARIABLE_1306057 tptp.set_int) (BOUND_VARIABLE_1306058 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1306058))) (= (or (ho_11180 _let_1 (ho_11177 k_11176 (ho_11093 k_11273 BOUND_VARIABLE_1306056))) (ho_11180 _let_1 BOUND_VARIABLE_1306057)) (ho_11094 (ho_11234 (ho_11233 k_12835 BOUND_VARIABLE_1306056) BOUND_VARIABLE_1306057) BOUND_VARIABLE_1306058)))))) (let ((_let_4544 (forall ((BOUND_VARIABLE_1306045 tptp.set_nat) (BOUND_VARIABLE_1306046 tptp.set_set_nat) (BOUND_VARIABLE_1306047 tptp.set_nat)) (= (ho_11191 (ho_12650 (ho_12653 k_12836 BOUND_VARIABLE_1306045) BOUND_VARIABLE_1306046) BOUND_VARIABLE_1306047) (or (= BOUND_VARIABLE_1306045 BOUND_VARIABLE_1306047) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1306047) BOUND_VARIABLE_1306046)))))) (let ((_let_4545 (forall ((BOUND_VARIABLE_1306020 tptp.set_nat) (BOUND_VARIABLE_1306021 tptp.set_set_nat) (BOUND_VARIABLE_1306022 tptp.set_nat)) (let ((_let_1 (ho_11206 k_11205 BOUND_VARIABLE_1306022))) (= (or (ho_11207 _let_1 (ho_11204 k_11203 (ho_11209 k_11274 BOUND_VARIABLE_1306020))) (ho_11207 _let_1 BOUND_VARIABLE_1306021)) (ho_11191 (ho_12650 (ho_12653 k_12837 BOUND_VARIABLE_1306020) BOUND_VARIABLE_1306021) BOUND_VARIABLE_1306022)))))) (let ((_let_4546 (forall ((BOUND_VARIABLE_1306009 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1306010 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1306011 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 (ho_12658 k_12838 BOUND_VARIABLE_1306009) BOUND_VARIABLE_1306010) BOUND_VARIABLE_1306011) (or (= BOUND_VARIABLE_1306009 BOUND_VARIABLE_1306011) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1306011) BOUND_VARIABLE_1306010)))))) (let ((_let_4547 (forall ((BOUND_VARIABLE_1305984 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1305985 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1305986 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (ho_11215 k_11214 BOUND_VARIABLE_1305986))) (= (or (ho_11216 _let_1 (ho_11213 k_11212 (ho_11218 k_11275 BOUND_VARIABLE_1305984))) (ho_11216 _let_1 BOUND_VARIABLE_1305985)) (ho_11211 (ho_12655 (ho_12658 k_12839 BOUND_VARIABLE_1305984) BOUND_VARIABLE_1305985) BOUND_VARIABLE_1305986)))))) (let ((_let_4548 (forall ((BOUND_VARIABLE_1305973 tptp.list_nat) (BOUND_VARIABLE_1305974 tptp.set_list_nat) (BOUND_VARIABLE_1305975 tptp.list_nat)) (= (ho_11278 (ho_12842 (ho_12841 k_12840 BOUND_VARIABLE_1305973) BOUND_VARIABLE_1305974) BOUND_VARIABLE_1305975) (or (= BOUND_VARIABLE_1305973 BOUND_VARIABLE_1305975) (ho_11660 (ho_11659 k_11658 BOUND_VARIABLE_1305975) BOUND_VARIABLE_1305974)))))) (let ((_let_4549 (forall ((BOUND_VARIABLE_1305948 tptp.list_nat) (BOUND_VARIABLE_1305949 tptp.set_list_nat) (BOUND_VARIABLE_1305950 tptp.list_nat)) (let ((_let_1 (ho_11659 k_11658 BOUND_VARIABLE_1305950))) (= (or (ho_11660 _let_1 (ho_11657 k_11656 (ho_11277 k_11276 BOUND_VARIABLE_1305948))) (ho_11660 _let_1 BOUND_VARIABLE_1305949)) (ho_11278 (ho_12842 (ho_12841 k_12843 BOUND_VARIABLE_1305948) BOUND_VARIABLE_1305949) BOUND_VARIABLE_1305950)))))) (let ((_let_4550 (forall ((BOUND_VARIABLE_1305937 Bool) (BOUND_VARIABLE_1305938 tptp.set_o) (BOUND_VARIABLE_1305939 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_12844 BOUND_VARIABLE_1305937) BOUND_VARIABLE_1305938) BOUND_VARIABLE_1305939) (or (= BOUND_VARIABLE_1305937 BOUND_VARIABLE_1305939) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1305939) BOUND_VARIABLE_1305938)))))) (let ((_let_4551 (forall ((BOUND_VARIABLE_1305912 Bool) (BOUND_VARIABLE_1305913 tptp.set_o) (BOUND_VARIABLE_1305914 Bool)) (let ((_let_1 (ho_11198 k_11197 BOUND_VARIABLE_1305914))) (= (or (ho_11199 _let_1 (ho_11196 k_11195 (ho_11201 k_11279 BOUND_VARIABLE_1305912))) (ho_11199 _let_1 BOUND_VARIABLE_1305913)) (ho_11194 (ho_12571 (ho_12648 k_12845 BOUND_VARIABLE_1305912) BOUND_VARIABLE_1305913) BOUND_VARIABLE_1305914)))))) (let ((_let_4552 (forall ((BOUND_VARIABLE_1305901 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1305902 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305903 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_12846 BOUND_VARIABLE_1305901) BOUND_VARIABLE_1305902) BOUND_VARIABLE_1305903) (or (= BOUND_VARIABLE_1305901 BOUND_VARIABLE_1305903) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1305903) BOUND_VARIABLE_1305902)))))) (let ((_let_4553 (forall ((BOUND_VARIABLE_1305894 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1305895 tptp.product_prod_nat_nat)) (= (= BOUND_VARIABLE_1305894 BOUND_VARIABLE_1305895) (ho_11184 (ho_11188 k_12847 BOUND_VARIABLE_1305894) BOUND_VARIABLE_1305895))))) (let ((_let_4554 (forall ((BOUND_VARIABLE_1305883 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1305884 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305885 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1305883 BOUND_VARIABLE_1305885) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1305885) BOUND_VARIABLE_1305884)) (ho_11184 (ho_11237 (ho_11236 k_12848 BOUND_VARIABLE_1305883) BOUND_VARIABLE_1305884) BOUND_VARIABLE_1305885))))) (let ((_let_4555 (forall ((BOUND_VARIABLE_1305872 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1305873 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305874 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1305872 BOUND_VARIABLE_1305874) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1305874) BOUND_VARIABLE_1305873)) (ho_11184 (ho_11237 (ho_11236 k_12849 BOUND_VARIABLE_1305872) BOUND_VARIABLE_1305873) BOUND_VARIABLE_1305874))))) (let ((_let_4556 (forall ((BOUND_VARIABLE_1305864 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305865 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12850 BOUND_VARIABLE_1305864) BOUND_VARIABLE_1305865) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1305865) BOUND_VARIABLE_1305864))))) (let ((_let_4557 (forall ((BOUND_VARIABLE_1305856 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305857 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12851 BOUND_VARIABLE_1305856) BOUND_VARIABLE_1305857) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1305857) BOUND_VARIABLE_1305856))))) (let ((_let_4558 (forall ((BOUND_VARIABLE_1305845 tptp.int) (BOUND_VARIABLE_1305846 tptp.set_int) (BOUND_VARIABLE_1305847 tptp.int)) (= (or (= BOUND_VARIABLE_1305845 BOUND_VARIABLE_1305847) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1305847) BOUND_VARIABLE_1305846)) (ho_11094 (ho_11234 (ho_11233 k_12852 BOUND_VARIABLE_1305845) BOUND_VARIABLE_1305846) BOUND_VARIABLE_1305847))))) (let ((_let_4559 (forall ((BOUND_VARIABLE_1305834 tptp.int) (BOUND_VARIABLE_1305835 tptp.set_int) (BOUND_VARIABLE_1305836 tptp.int)) (= (or (= BOUND_VARIABLE_1305834 BOUND_VARIABLE_1305836) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1305836) BOUND_VARIABLE_1305835)) (ho_11094 (ho_11234 (ho_11233 k_12853 BOUND_VARIABLE_1305834) BOUND_VARIABLE_1305835) BOUND_VARIABLE_1305836))))) (let ((_let_4560 (forall ((BOUND_VARIABLE_1305826 tptp.set_int) (BOUND_VARIABLE_1305827 tptp.int)) (= (ho_11094 (ho_11234 k_12854 BOUND_VARIABLE_1305826) BOUND_VARIABLE_1305827) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1305827) BOUND_VARIABLE_1305826))))) (let ((_let_4561 (forall ((BOUND_VARIABLE_1305818 tptp.set_int) (BOUND_VARIABLE_1305819 tptp.int)) (= (ho_11094 (ho_11234 k_12855 BOUND_VARIABLE_1305818) BOUND_VARIABLE_1305819) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1305819) BOUND_VARIABLE_1305818))))) (let ((_let_4562 (forall ((BOUND_VARIABLE_1305807 tptp.nat) (BOUND_VARIABLE_1305808 tptp.set_nat) (BOUND_VARIABLE_1305809 tptp.nat)) (= (or (= BOUND_VARIABLE_1305807 BOUND_VARIABLE_1305809) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1305809) BOUND_VARIABLE_1305808)) (ho_11054 (ho_11240 (ho_11239 k_12856 BOUND_VARIABLE_1305807) BOUND_VARIABLE_1305808) BOUND_VARIABLE_1305809))))) (let ((_let_4563 (forall ((BOUND_VARIABLE_1305796 tptp.nat) (BOUND_VARIABLE_1305797 tptp.set_nat) (BOUND_VARIABLE_1305798 tptp.nat)) (= (or (= BOUND_VARIABLE_1305796 BOUND_VARIABLE_1305798) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1305798) BOUND_VARIABLE_1305797)) (ho_11054 (ho_11240 (ho_11239 k_12857 BOUND_VARIABLE_1305796) BOUND_VARIABLE_1305797) BOUND_VARIABLE_1305798))))) (let ((_let_4564 (forall ((BOUND_VARIABLE_1305788 tptp.set_nat) (BOUND_VARIABLE_1305789 tptp.nat)) (= (ho_11054 (ho_11240 k_12858 BOUND_VARIABLE_1305788) BOUND_VARIABLE_1305789) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1305789) BOUND_VARIABLE_1305788))))) (let ((_let_4565 (forall ((BOUND_VARIABLE_1305780 tptp.set_nat) (BOUND_VARIABLE_1305781 tptp.nat)) (= (ho_11054 (ho_11240 k_12859 BOUND_VARIABLE_1305780) BOUND_VARIABLE_1305781) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1305781) BOUND_VARIABLE_1305780))))) (let ((_let_4566 (forall ((BOUND_VARIABLE_1305769 tptp.set_nat) (BOUND_VARIABLE_1305770 tptp.set_set_nat) (BOUND_VARIABLE_1305771 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1305769 BOUND_VARIABLE_1305771) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1305771) BOUND_VARIABLE_1305770)) (ho_11191 (ho_12650 (ho_12653 k_12860 BOUND_VARIABLE_1305769) BOUND_VARIABLE_1305770) BOUND_VARIABLE_1305771))))) (let ((_let_4567 (forall ((BOUND_VARIABLE_1305758 tptp.set_nat) (BOUND_VARIABLE_1305759 tptp.set_set_nat) (BOUND_VARIABLE_1305760 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1305758 BOUND_VARIABLE_1305760) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1305760) BOUND_VARIABLE_1305759)) (ho_11191 (ho_12650 (ho_12653 k_12861 BOUND_VARIABLE_1305758) BOUND_VARIABLE_1305759) BOUND_VARIABLE_1305760))))) (let ((_let_4568 (forall ((BOUND_VARIABLE_1305750 tptp.set_set_nat) (BOUND_VARIABLE_1305751 tptp.set_nat)) (= (ho_11191 (ho_12650 k_12862 BOUND_VARIABLE_1305750) BOUND_VARIABLE_1305751) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1305751) BOUND_VARIABLE_1305750))))) (let ((_let_4569 (forall ((BOUND_VARIABLE_1305742 tptp.set_set_nat) (BOUND_VARIABLE_1305743 tptp.set_nat)) (= (ho_11191 (ho_12650 k_12863 BOUND_VARIABLE_1305742) BOUND_VARIABLE_1305743) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1305743) BOUND_VARIABLE_1305742))))) (let ((_let_4570 (forall ((BOUND_VARIABLE_1305731 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1305732 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1305733 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1305731 BOUND_VARIABLE_1305733) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1305733) BOUND_VARIABLE_1305732)) (ho_11211 (ho_12655 (ho_12658 k_12864 BOUND_VARIABLE_1305731) BOUND_VARIABLE_1305732) BOUND_VARIABLE_1305733))))) (let ((_let_4571 (forall ((BOUND_VARIABLE_1305720 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1305721 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1305722 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1305720 BOUND_VARIABLE_1305722) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1305722) BOUND_VARIABLE_1305721)) (ho_11211 (ho_12655 (ho_12658 k_12865 BOUND_VARIABLE_1305720) BOUND_VARIABLE_1305721) BOUND_VARIABLE_1305722))))) (let ((_let_4572 (forall ((BOUND_VARIABLE_1305712 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1305713 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 k_12866 BOUND_VARIABLE_1305712) BOUND_VARIABLE_1305713) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1305713) BOUND_VARIABLE_1305712))))) (let ((_let_4573 (forall ((BOUND_VARIABLE_1305704 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1305705 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 k_12867 BOUND_VARIABLE_1305704) BOUND_VARIABLE_1305705) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1305705) BOUND_VARIABLE_1305704))))) (let ((_let_4574 (forall ((BOUND_VARIABLE_1305693 Bool) (BOUND_VARIABLE_1305694 tptp.set_o) (BOUND_VARIABLE_1305695 Bool)) (= (or (= BOUND_VARIABLE_1305693 BOUND_VARIABLE_1305695) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1305695) BOUND_VARIABLE_1305694)) (ho_11194 (ho_12571 (ho_12648 k_12868 BOUND_VARIABLE_1305693) BOUND_VARIABLE_1305694) BOUND_VARIABLE_1305695))))) (let ((_let_4575 (forall ((BOUND_VARIABLE_1305682 Bool) (BOUND_VARIABLE_1305683 tptp.set_o) (BOUND_VARIABLE_1305684 Bool)) (= (or (= BOUND_VARIABLE_1305682 BOUND_VARIABLE_1305684) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1305684) BOUND_VARIABLE_1305683)) (ho_11194 (ho_12571 (ho_12648 k_12869 BOUND_VARIABLE_1305682) BOUND_VARIABLE_1305683) BOUND_VARIABLE_1305684))))) (let ((_let_4576 (forall ((BOUND_VARIABLE_1305674 tptp.set_o) (BOUND_VARIABLE_1305675 Bool)) (= (ho_11194 (ho_12571 k_12870 BOUND_VARIABLE_1305674) BOUND_VARIABLE_1305675) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1305675) BOUND_VARIABLE_1305674))))) (let ((_let_4577 (forall ((BOUND_VARIABLE_1305666 tptp.set_o) (BOUND_VARIABLE_1305667 Bool)) (= (ho_11194 (ho_12571 k_12871 BOUND_VARIABLE_1305666) BOUND_VARIABLE_1305667) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1305667) BOUND_VARIABLE_1305666))))) (let ((_let_4578 (forall ((BOUND_VARIABLE_1305655 tptp.nat) (BOUND_VARIABLE_1305656 tptp.set_nat) (BOUND_VARIABLE_1305657 tptp.nat)) (= (or (= BOUND_VARIABLE_1305655 BOUND_VARIABLE_1305657) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1305657) BOUND_VARIABLE_1305656)) (ho_11054 (ho_11240 (ho_11239 k_12872 BOUND_VARIABLE_1305655) BOUND_VARIABLE_1305656) BOUND_VARIABLE_1305657))))) (let ((_let_4579 (forall ((BOUND_VARIABLE_1305644 tptp.set_nat) (BOUND_VARIABLE_1305645 tptp.set_nat) (BOUND_VARIABLE_1305646 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1305646))) (= (ho_11054 (ho_11240 (ho_11343 k_12873 BOUND_VARIABLE_1305644) BOUND_VARIABLE_1305645) BOUND_VARIABLE_1305646) (and (ho_11191 _let_1 BOUND_VARIABLE_1305644) (ho_11191 _let_1 BOUND_VARIABLE_1305645))))))) (let ((_let_4580 (forall ((BOUND_VARIABLE_1305633 tptp.nat) (BOUND_VARIABLE_1305634 tptp.set_nat) (BOUND_VARIABLE_1305635 tptp.nat)) (= (or (= BOUND_VARIABLE_1305633 BOUND_VARIABLE_1305635) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1305635) BOUND_VARIABLE_1305634)) (ho_11054 (ho_11240 (ho_11239 k_12874 BOUND_VARIABLE_1305633) BOUND_VARIABLE_1305634) BOUND_VARIABLE_1305635))))) (let ((_let_4581 (forall ((BOUND_VARIABLE_1305622 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1305623 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305624 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1305622 BOUND_VARIABLE_1305624) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1305624) BOUND_VARIABLE_1305623)) (ho_11184 (ho_11237 (ho_11236 k_12875 BOUND_VARIABLE_1305622) BOUND_VARIABLE_1305623) BOUND_VARIABLE_1305624))))) (let ((_let_4582 (forall ((BOUND_VARIABLE_1305611 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305612 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305613 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1305613))) (= (ho_11184 (ho_11237 (ho_11365 k_12876 BOUND_VARIABLE_1305611) BOUND_VARIABLE_1305612) BOUND_VARIABLE_1305613) (and (ho_11070 _let_1 BOUND_VARIABLE_1305611) (ho_11070 _let_1 BOUND_VARIABLE_1305612))))))) (let ((_let_4583 (forall ((BOUND_VARIABLE_1305600 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1305601 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305602 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1305600 BOUND_VARIABLE_1305602) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1305602) BOUND_VARIABLE_1305601)) (ho_11184 (ho_11237 (ho_11236 k_12877 BOUND_VARIABLE_1305600) BOUND_VARIABLE_1305601) BOUND_VARIABLE_1305602))))) (let ((_let_4584 (forall ((BOUND_VARIABLE_1305589 tptp.int) (BOUND_VARIABLE_1305590 tptp.set_int) (BOUND_VARIABLE_1305591 tptp.int)) (= (or (= BOUND_VARIABLE_1305589 BOUND_VARIABLE_1305591) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1305591) BOUND_VARIABLE_1305590)) (ho_11094 (ho_11234 (ho_11233 k_12878 BOUND_VARIABLE_1305589) BOUND_VARIABLE_1305590) BOUND_VARIABLE_1305591))))) (let ((_let_4585 (forall ((BOUND_VARIABLE_1305578 tptp.set_int) (BOUND_VARIABLE_1305579 tptp.set_int) (BOUND_VARIABLE_1305580 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1305580))) (= (ho_11094 (ho_11234 (ho_11339 k_12879 BOUND_VARIABLE_1305578) BOUND_VARIABLE_1305579) BOUND_VARIABLE_1305580) (and (ho_11180 _let_1 BOUND_VARIABLE_1305578) (ho_11180 _let_1 BOUND_VARIABLE_1305579))))))) (let ((_let_4586 (forall ((BOUND_VARIABLE_1305567 tptp.int) (BOUND_VARIABLE_1305568 tptp.set_int) (BOUND_VARIABLE_1305569 tptp.int)) (= (or (= BOUND_VARIABLE_1305567 BOUND_VARIABLE_1305569) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1305569) BOUND_VARIABLE_1305568)) (ho_11094 (ho_11234 (ho_11233 k_12880 BOUND_VARIABLE_1305567) BOUND_VARIABLE_1305568) BOUND_VARIABLE_1305569))))) (let ((_let_4587 (forall ((BOUND_VARIABLE_1305556 tptp.set_nat) (BOUND_VARIABLE_1305557 tptp.set_set_nat) (BOUND_VARIABLE_1305558 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1305556 BOUND_VARIABLE_1305558) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1305558) BOUND_VARIABLE_1305557)) (ho_11191 (ho_12650 (ho_12653 k_12881 BOUND_VARIABLE_1305556) BOUND_VARIABLE_1305557) BOUND_VARIABLE_1305558))))) (let ((_let_4588 (forall ((BOUND_VARIABLE_1305545 tptp.set_set_nat) (BOUND_VARIABLE_1305546 tptp.set_set_nat) (BOUND_VARIABLE_1305547 tptp.set_nat)) (let ((_let_1 (ho_11206 k_11205 BOUND_VARIABLE_1305547))) (= (ho_11191 (ho_12650 (ho_12883 k_12882 BOUND_VARIABLE_1305545) BOUND_VARIABLE_1305546) BOUND_VARIABLE_1305547) (and (ho_11207 _let_1 BOUND_VARIABLE_1305545) (ho_11207 _let_1 BOUND_VARIABLE_1305546))))))) (let ((_let_4589 (forall ((BOUND_VARIABLE_1305534 tptp.set_nat) (BOUND_VARIABLE_1305535 tptp.set_set_nat) (BOUND_VARIABLE_1305536 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1305534 BOUND_VARIABLE_1305536) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1305536) BOUND_VARIABLE_1305535)) (ho_11191 (ho_12650 (ho_12653 k_12884 BOUND_VARIABLE_1305534) BOUND_VARIABLE_1305535) BOUND_VARIABLE_1305536))))) (let ((_let_4590 (forall ((BOUND_VARIABLE_1305523 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1305524 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1305525 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1305523 BOUND_VARIABLE_1305525) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1305525) BOUND_VARIABLE_1305524)) (ho_11211 (ho_12655 (ho_12658 k_12885 BOUND_VARIABLE_1305523) BOUND_VARIABLE_1305524) BOUND_VARIABLE_1305525))))) (let ((_let_4591 (forall ((BOUND_VARIABLE_1305512 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1305513 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1305514 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (ho_11215 k_11214 BOUND_VARIABLE_1305514))) (= (ho_11211 (ho_12655 (ho_12887 k_12886 BOUND_VARIABLE_1305512) BOUND_VARIABLE_1305513) BOUND_VARIABLE_1305514) (and (ho_11216 _let_1 BOUND_VARIABLE_1305512) (ho_11216 _let_1 BOUND_VARIABLE_1305513))))))) (let ((_let_4592 (forall ((BOUND_VARIABLE_1305501 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1305502 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1305503 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1305501 BOUND_VARIABLE_1305503) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1305503) BOUND_VARIABLE_1305502)) (ho_11211 (ho_12655 (ho_12658 k_12888 BOUND_VARIABLE_1305501) BOUND_VARIABLE_1305502) BOUND_VARIABLE_1305503))))) (let ((_let_4593 (forall ((BOUND_VARIABLE_1305490 Bool) (BOUND_VARIABLE_1305491 tptp.set_o) (BOUND_VARIABLE_1305492 Bool)) (= (or (= BOUND_VARIABLE_1305490 BOUND_VARIABLE_1305492) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1305492) BOUND_VARIABLE_1305491)) (ho_11194 (ho_12571 (ho_12648 k_12889 BOUND_VARIABLE_1305490) BOUND_VARIABLE_1305491) BOUND_VARIABLE_1305492))))) (let ((_let_4594 (forall ((BOUND_VARIABLE_1305479 tptp.set_o) (BOUND_VARIABLE_1305480 tptp.set_o) (BOUND_VARIABLE_1305481 Bool)) (let ((_let_1 (ho_11198 k_11197 BOUND_VARIABLE_1305481))) (= (ho_11194 (ho_12571 (ho_12891 k_12890 BOUND_VARIABLE_1305479) BOUND_VARIABLE_1305480) BOUND_VARIABLE_1305481) (and (ho_11199 _let_1 BOUND_VARIABLE_1305479) (ho_11199 _let_1 BOUND_VARIABLE_1305480))))))) (let ((_let_4595 (forall ((BOUND_VARIABLE_1305468 Bool) (BOUND_VARIABLE_1305469 tptp.set_o) (BOUND_VARIABLE_1305470 Bool)) (= (or (= BOUND_VARIABLE_1305468 BOUND_VARIABLE_1305470) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1305470) BOUND_VARIABLE_1305469)) (ho_11194 (ho_12571 (ho_12648 k_12892 BOUND_VARIABLE_1305468) BOUND_VARIABLE_1305469) BOUND_VARIABLE_1305470))))) (let ((_let_4596 (forall ((BOUND_VARIABLE_1305457 tptp.nat) (BOUND_VARIABLE_1305458 tptp.set_nat) (BOUND_VARIABLE_1305459 tptp.nat)) (= (or (= BOUND_VARIABLE_1305457 BOUND_VARIABLE_1305459) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1305459) BOUND_VARIABLE_1305458)) (ho_11054 (ho_11240 (ho_11239 k_12893 BOUND_VARIABLE_1305457) BOUND_VARIABLE_1305458) BOUND_VARIABLE_1305459))))) (let ((_let_4597 (forall ((BOUND_VARIABLE_1305446 tptp.set_nat) (BOUND_VARIABLE_1305447 tptp.set_nat) (BOUND_VARIABLE_1305448 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1305448))) (= (ho_11054 (ho_11240 (ho_11343 k_12894 BOUND_VARIABLE_1305446) BOUND_VARIABLE_1305447) BOUND_VARIABLE_1305448) (and (ho_11191 _let_1 BOUND_VARIABLE_1305446) (ho_11191 _let_1 BOUND_VARIABLE_1305447))))))) (let ((_let_4598 (forall ((BOUND_VARIABLE_1305435 tptp.nat) (BOUND_VARIABLE_1305436 tptp.set_nat) (BOUND_VARIABLE_1305437 tptp.nat)) (= (or (= BOUND_VARIABLE_1305435 BOUND_VARIABLE_1305437) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1305437) BOUND_VARIABLE_1305436)) (ho_11054 (ho_11240 (ho_11239 k_12895 BOUND_VARIABLE_1305435) BOUND_VARIABLE_1305436) BOUND_VARIABLE_1305437))))) (let ((_let_4599 (forall ((BOUND_VARIABLE_1305424 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1305425 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305426 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1305424 BOUND_VARIABLE_1305426) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1305426) BOUND_VARIABLE_1305425)) (ho_11184 (ho_11237 (ho_11236 k_12896 BOUND_VARIABLE_1305424) BOUND_VARIABLE_1305425) BOUND_VARIABLE_1305426))))) (let ((_let_4600 (forall ((BOUND_VARIABLE_1305413 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305414 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305415 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1305415))) (= (ho_11184 (ho_11237 (ho_11365 k_12897 BOUND_VARIABLE_1305413) BOUND_VARIABLE_1305414) BOUND_VARIABLE_1305415) (and (ho_11070 _let_1 BOUND_VARIABLE_1305413) (ho_11070 _let_1 BOUND_VARIABLE_1305414))))))) (let ((_let_4601 (forall ((BOUND_VARIABLE_1305402 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1305403 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305404 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1305402 BOUND_VARIABLE_1305404) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1305404) BOUND_VARIABLE_1305403)) (ho_11184 (ho_11237 (ho_11236 k_12898 BOUND_VARIABLE_1305402) BOUND_VARIABLE_1305403) BOUND_VARIABLE_1305404))))) (let ((_let_4602 (forall ((BOUND_VARIABLE_1305391 tptp.int) (BOUND_VARIABLE_1305392 tptp.set_int) (BOUND_VARIABLE_1305393 tptp.int)) (= (or (= BOUND_VARIABLE_1305391 BOUND_VARIABLE_1305393) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1305393) BOUND_VARIABLE_1305392)) (ho_11094 (ho_11234 (ho_11233 k_12899 BOUND_VARIABLE_1305391) BOUND_VARIABLE_1305392) BOUND_VARIABLE_1305393))))) (let ((_let_4603 (forall ((BOUND_VARIABLE_1305380 tptp.set_int) (BOUND_VARIABLE_1305381 tptp.set_int) (BOUND_VARIABLE_1305382 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1305382))) (= (ho_11094 (ho_11234 (ho_11339 k_12900 BOUND_VARIABLE_1305380) BOUND_VARIABLE_1305381) BOUND_VARIABLE_1305382) (and (ho_11180 _let_1 BOUND_VARIABLE_1305380) (ho_11180 _let_1 BOUND_VARIABLE_1305381))))))) (let ((_let_4604 (forall ((BOUND_VARIABLE_1305369 tptp.int) (BOUND_VARIABLE_1305370 tptp.set_int) (BOUND_VARIABLE_1305371 tptp.int)) (= (or (= BOUND_VARIABLE_1305369 BOUND_VARIABLE_1305371) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1305371) BOUND_VARIABLE_1305370)) (ho_11094 (ho_11234 (ho_11233 k_12901 BOUND_VARIABLE_1305369) BOUND_VARIABLE_1305370) BOUND_VARIABLE_1305371))))) (let ((_let_4605 (forall ((BOUND_VARIABLE_1305358 tptp.set_nat) (BOUND_VARIABLE_1305359 tptp.set_set_nat) (BOUND_VARIABLE_1305360 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1305358 BOUND_VARIABLE_1305360) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1305360) BOUND_VARIABLE_1305359)) (ho_11191 (ho_12650 (ho_12653 k_12902 BOUND_VARIABLE_1305358) BOUND_VARIABLE_1305359) BOUND_VARIABLE_1305360))))) (let ((_let_4606 (forall ((BOUND_VARIABLE_1305347 tptp.set_set_nat) (BOUND_VARIABLE_1305348 tptp.set_set_nat) (BOUND_VARIABLE_1305349 tptp.set_nat)) (let ((_let_1 (ho_11206 k_11205 BOUND_VARIABLE_1305349))) (= (ho_11191 (ho_12650 (ho_12883 k_12903 BOUND_VARIABLE_1305347) BOUND_VARIABLE_1305348) BOUND_VARIABLE_1305349) (and (ho_11207 _let_1 BOUND_VARIABLE_1305347) (ho_11207 _let_1 BOUND_VARIABLE_1305348))))))) (let ((_let_4607 (forall ((BOUND_VARIABLE_1305336 tptp.set_nat) (BOUND_VARIABLE_1305337 tptp.set_set_nat) (BOUND_VARIABLE_1305338 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1305336 BOUND_VARIABLE_1305338) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1305338) BOUND_VARIABLE_1305337)) (ho_11191 (ho_12650 (ho_12653 k_12904 BOUND_VARIABLE_1305336) BOUND_VARIABLE_1305337) BOUND_VARIABLE_1305338))))) (let ((_let_4608 (forall ((BOUND_VARIABLE_1305325 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1305326 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1305327 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1305325 BOUND_VARIABLE_1305327) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1305327) BOUND_VARIABLE_1305326)) (ho_11211 (ho_12655 (ho_12658 k_12905 BOUND_VARIABLE_1305325) BOUND_VARIABLE_1305326) BOUND_VARIABLE_1305327))))) (let ((_let_4609 (forall ((BOUND_VARIABLE_1305314 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1305315 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1305316 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (ho_11215 k_11214 BOUND_VARIABLE_1305316))) (= (ho_11211 (ho_12655 (ho_12887 k_12906 BOUND_VARIABLE_1305314) BOUND_VARIABLE_1305315) BOUND_VARIABLE_1305316) (and (ho_11216 _let_1 BOUND_VARIABLE_1305314) (ho_11216 _let_1 BOUND_VARIABLE_1305315))))))) (let ((_let_4610 (forall ((BOUND_VARIABLE_1305303 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1305304 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1305305 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1305303 BOUND_VARIABLE_1305305) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1305305) BOUND_VARIABLE_1305304)) (ho_11211 (ho_12655 (ho_12658 k_12907 BOUND_VARIABLE_1305303) BOUND_VARIABLE_1305304) BOUND_VARIABLE_1305305))))) (let ((_let_4611 (forall ((BOUND_VARIABLE_1305292 Bool) (BOUND_VARIABLE_1305293 tptp.set_o) (BOUND_VARIABLE_1305294 Bool)) (= (or (= BOUND_VARIABLE_1305292 BOUND_VARIABLE_1305294) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1305294) BOUND_VARIABLE_1305293)) (ho_11194 (ho_12571 (ho_12648 k_12908 BOUND_VARIABLE_1305292) BOUND_VARIABLE_1305293) BOUND_VARIABLE_1305294))))) (let ((_let_4612 (forall ((BOUND_VARIABLE_1305281 tptp.set_o) (BOUND_VARIABLE_1305282 tptp.set_o) (BOUND_VARIABLE_1305283 Bool)) (let ((_let_1 (ho_11198 k_11197 BOUND_VARIABLE_1305283))) (= (ho_11194 (ho_12571 (ho_12891 k_12909 BOUND_VARIABLE_1305281) BOUND_VARIABLE_1305282) BOUND_VARIABLE_1305283) (and (ho_11199 _let_1 BOUND_VARIABLE_1305281) (ho_11199 _let_1 BOUND_VARIABLE_1305282))))))) (let ((_let_4613 (forall ((BOUND_VARIABLE_1305270 Bool) (BOUND_VARIABLE_1305271 tptp.set_o) (BOUND_VARIABLE_1305272 Bool)) (= (or (= BOUND_VARIABLE_1305270 BOUND_VARIABLE_1305272) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1305272) BOUND_VARIABLE_1305271)) (ho_11194 (ho_12571 (ho_12648 k_12910 BOUND_VARIABLE_1305270) BOUND_VARIABLE_1305271) BOUND_VARIABLE_1305272))))) (let ((_let_4614 (forall ((BOUND_VARIABLE_1305259 tptp.int) (BOUND_VARIABLE_1305260 tptp.set_int) (BOUND_VARIABLE_1305261 tptp.int)) (= (or (= BOUND_VARIABLE_1305259 BOUND_VARIABLE_1305261) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1305261) BOUND_VARIABLE_1305260)) (ho_11094 (ho_11234 (ho_11233 k_12911 BOUND_VARIABLE_1305259) BOUND_VARIABLE_1305260) BOUND_VARIABLE_1305261))))) (let ((_let_4615 (forall ((BOUND_VARIABLE_1305248 tptp.nat) (BOUND_VARIABLE_1305249 tptp.set_nat) (BOUND_VARIABLE_1305250 tptp.nat)) (= (or (= BOUND_VARIABLE_1305248 BOUND_VARIABLE_1305250) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1305250) BOUND_VARIABLE_1305249)) (ho_11054 (ho_11240 (ho_11239 k_12912 BOUND_VARIABLE_1305248) BOUND_VARIABLE_1305249) BOUND_VARIABLE_1305250))))) (let ((_let_4616 (forall ((BOUND_VARIABLE_1305237 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1305238 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305239 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1305237 BOUND_VARIABLE_1305239) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1305239) BOUND_VARIABLE_1305238)) (ho_11184 (ho_11237 (ho_11236 k_12913 BOUND_VARIABLE_1305237) BOUND_VARIABLE_1305238) BOUND_VARIABLE_1305239))))) (let ((_let_4617 (forall ((BOUND_VARIABLE_1305226 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1305227 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1305228 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1305226 BOUND_VARIABLE_1305228) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1305228) BOUND_VARIABLE_1305227)) (ho_11263 (ho_11374 (ho_12630 k_12914 BOUND_VARIABLE_1305226) BOUND_VARIABLE_1305227) BOUND_VARIABLE_1305228))))) (let ((_let_4618 (forall ((BOUND_VARIABLE_1305215 tptp.int) (BOUND_VARIABLE_1305216 tptp.set_int) (BOUND_VARIABLE_1305217 tptp.int)) (= (or (= BOUND_VARIABLE_1305215 BOUND_VARIABLE_1305217) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1305217) BOUND_VARIABLE_1305216)) (ho_11094 (ho_11234 (ho_11233 k_12915 BOUND_VARIABLE_1305215) BOUND_VARIABLE_1305216) BOUND_VARIABLE_1305217))))) (let ((_let_4619 (forall ((BOUND_VARIABLE_1305204 tptp.nat) (BOUND_VARIABLE_1305205 tptp.set_nat) (BOUND_VARIABLE_1305206 tptp.nat)) (= (or (= BOUND_VARIABLE_1305204 BOUND_VARIABLE_1305206) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1305206) BOUND_VARIABLE_1305205)) (ho_11054 (ho_11240 (ho_11239 k_12916 BOUND_VARIABLE_1305204) BOUND_VARIABLE_1305205) BOUND_VARIABLE_1305206))))) (let ((_let_4620 (forall ((BOUND_VARIABLE_1305193 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1305194 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305195 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1305193 BOUND_VARIABLE_1305195) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1305195) BOUND_VARIABLE_1305194)) (ho_11184 (ho_11237 (ho_11236 k_12917 BOUND_VARIABLE_1305193) BOUND_VARIABLE_1305194) BOUND_VARIABLE_1305195))))) (let ((_let_4621 (forall ((BOUND_VARIABLE_1305182 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1305183 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1305184 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1305182 BOUND_VARIABLE_1305184) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1305184) BOUND_VARIABLE_1305183)) (ho_11263 (ho_11374 (ho_12630 k_12918 BOUND_VARIABLE_1305182) BOUND_VARIABLE_1305183) BOUND_VARIABLE_1305184))))) (let ((_let_4622 (forall ((BOUND_VARIABLE_1305171 tptp.int) (BOUND_VARIABLE_1305172 tptp.set_int) (BOUND_VARIABLE_1305173 tptp.int)) (= (or (= BOUND_VARIABLE_1305171 BOUND_VARIABLE_1305173) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1305173) BOUND_VARIABLE_1305172)) (ho_11094 (ho_11234 (ho_11233 k_12919 BOUND_VARIABLE_1305171) BOUND_VARIABLE_1305172) BOUND_VARIABLE_1305173))))) (let ((_let_4623 (forall ((BOUND_VARIABLE_1305160 tptp.nat) (BOUND_VARIABLE_1305161 tptp.set_nat) (BOUND_VARIABLE_1305162 tptp.nat)) (= (or (= BOUND_VARIABLE_1305160 BOUND_VARIABLE_1305162) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1305162) BOUND_VARIABLE_1305161)) (ho_11054 (ho_11240 (ho_11239 k_12920 BOUND_VARIABLE_1305160) BOUND_VARIABLE_1305161) BOUND_VARIABLE_1305162))))) (let ((_let_4624 (forall ((BOUND_VARIABLE_1305149 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1305150 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305151 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1305149 BOUND_VARIABLE_1305151) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1305151) BOUND_VARIABLE_1305150)) (ho_11184 (ho_11237 (ho_11236 k_12921 BOUND_VARIABLE_1305149) BOUND_VARIABLE_1305150) BOUND_VARIABLE_1305151))))) (let ((_let_4625 (forall ((BOUND_VARIABLE_1305138 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1305139 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1305140 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1305138 BOUND_VARIABLE_1305140) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1305140) BOUND_VARIABLE_1305139)) (ho_11263 (ho_11374 (ho_12630 k_12922 BOUND_VARIABLE_1305138) BOUND_VARIABLE_1305139) BOUND_VARIABLE_1305140))))) (let ((_let_4626 (forall ((BOUND_VARIABLE_1305127 tptp.int) (BOUND_VARIABLE_1305128 tptp.set_int) (BOUND_VARIABLE_1305129 tptp.int)) (= (or (= BOUND_VARIABLE_1305127 BOUND_VARIABLE_1305129) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1305129) BOUND_VARIABLE_1305128)) (ho_11094 (ho_11234 (ho_11233 k_12923 BOUND_VARIABLE_1305127) BOUND_VARIABLE_1305128) BOUND_VARIABLE_1305129))))) (let ((_let_4627 (forall ((BOUND_VARIABLE_1305116 tptp.nat) (BOUND_VARIABLE_1305117 tptp.set_nat) (BOUND_VARIABLE_1305118 tptp.nat)) (= (or (= BOUND_VARIABLE_1305116 BOUND_VARIABLE_1305118) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1305118) BOUND_VARIABLE_1305117)) (ho_11054 (ho_11240 (ho_11239 k_12924 BOUND_VARIABLE_1305116) BOUND_VARIABLE_1305117) BOUND_VARIABLE_1305118))))) (let ((_let_4628 (forall ((BOUND_VARIABLE_1305105 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1305106 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305107 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1305105 BOUND_VARIABLE_1305107) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1305107) BOUND_VARIABLE_1305106)) (ho_11184 (ho_11237 (ho_11236 k_12925 BOUND_VARIABLE_1305105) BOUND_VARIABLE_1305106) BOUND_VARIABLE_1305107))))) (let ((_let_4629 (forall ((BOUND_VARIABLE_1305094 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1305095 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1305096 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1305094 BOUND_VARIABLE_1305096) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1305096) BOUND_VARIABLE_1305095)) (ho_11263 (ho_11374 (ho_12630 k_12926 BOUND_VARIABLE_1305094) BOUND_VARIABLE_1305095) BOUND_VARIABLE_1305096))))) (let ((_let_4630 (forall ((BOUND_VARIABLE_1305083 tptp.int) (BOUND_VARIABLE_1305084 tptp.set_int) (BOUND_VARIABLE_1305085 tptp.int)) (= (or (= BOUND_VARIABLE_1305083 BOUND_VARIABLE_1305085) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1305085) BOUND_VARIABLE_1305084)) (ho_11094 (ho_11234 (ho_11233 k_12927 BOUND_VARIABLE_1305083) BOUND_VARIABLE_1305084) BOUND_VARIABLE_1305085))))) (let ((_let_4631 (forall ((BOUND_VARIABLE_1305072 tptp.int) (BOUND_VARIABLE_1305073 tptp.set_int) (BOUND_VARIABLE_1305074 tptp.int)) (= (or (= BOUND_VARIABLE_1305072 BOUND_VARIABLE_1305074) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1305074) BOUND_VARIABLE_1305073)) (ho_11094 (ho_11234 (ho_11233 k_12928 BOUND_VARIABLE_1305072) BOUND_VARIABLE_1305073) BOUND_VARIABLE_1305074))))) (let ((_let_4632 (forall ((BOUND_VARIABLE_1305061 tptp.nat) (BOUND_VARIABLE_1305062 tptp.set_nat) (BOUND_VARIABLE_1305063 tptp.nat)) (= (or (= BOUND_VARIABLE_1305061 BOUND_VARIABLE_1305063) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1305063) BOUND_VARIABLE_1305062)) (ho_11054 (ho_11240 (ho_11239 k_12929 BOUND_VARIABLE_1305061) BOUND_VARIABLE_1305062) BOUND_VARIABLE_1305063))))) (let ((_let_4633 (forall ((BOUND_VARIABLE_1305050 tptp.nat) (BOUND_VARIABLE_1305051 tptp.set_nat) (BOUND_VARIABLE_1305052 tptp.nat)) (= (or (= BOUND_VARIABLE_1305050 BOUND_VARIABLE_1305052) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1305052) BOUND_VARIABLE_1305051)) (ho_11054 (ho_11240 (ho_11239 k_12930 BOUND_VARIABLE_1305050) BOUND_VARIABLE_1305051) BOUND_VARIABLE_1305052))))) (let ((_let_4634 (forall ((BOUND_VARIABLE_1305039 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1305040 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305041 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1305039 BOUND_VARIABLE_1305041) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1305041) BOUND_VARIABLE_1305040)) (ho_11184 (ho_11237 (ho_11236 k_12931 BOUND_VARIABLE_1305039) BOUND_VARIABLE_1305040) BOUND_VARIABLE_1305041))))) (let ((_let_4635 (forall ((BOUND_VARIABLE_1305028 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1305029 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1305030 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1305028 BOUND_VARIABLE_1305030) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1305030) BOUND_VARIABLE_1305029)) (ho_11184 (ho_11237 (ho_11236 k_12932 BOUND_VARIABLE_1305028) BOUND_VARIABLE_1305029) BOUND_VARIABLE_1305030))))) (let ((_let_4636 (forall ((BOUND_VARIABLE_1305017 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1305018 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1305019 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1305017 BOUND_VARIABLE_1305019) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1305019) BOUND_VARIABLE_1305018)) (ho_11263 (ho_11374 (ho_12630 k_12933 BOUND_VARIABLE_1305017) BOUND_VARIABLE_1305018) BOUND_VARIABLE_1305019))))) (let ((_let_4637 (forall ((BOUND_VARIABLE_1305006 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1305007 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1305008 tptp.produc3843707927480180839at_nat)) (= (or (= BOUND_VARIABLE_1305006 BOUND_VARIABLE_1305008) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1305008) BOUND_VARIABLE_1305007)) (ho_11263 (ho_11374 (ho_12630 k_12934 BOUND_VARIABLE_1305006) BOUND_VARIABLE_1305007) BOUND_VARIABLE_1305008))))) (let ((_let_4638 (forall ((BOUND_VARIABLE_1304992 tptp.int) (BOUND_VARIABLE_1304993 tptp.int)) (= (or (= BOUND_VARIABLE_1304992 BOUND_VARIABLE_1304993) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304993) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12935 BOUND_VARIABLE_1304992) BOUND_VARIABLE_1304993))))) (let ((_let_4639 (forall ((BOUND_VARIABLE_1304978 tptp.int) (BOUND_VARIABLE_1304979 tptp.int)) (= (or (= BOUND_VARIABLE_1304978 BOUND_VARIABLE_1304979) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304979) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12936 BOUND_VARIABLE_1304978) BOUND_VARIABLE_1304979))))) (let ((_let_4640 (forall ((BOUND_VARIABLE_1304964 tptp.nat) (BOUND_VARIABLE_1304965 tptp.nat)) (= (or (= BOUND_VARIABLE_1304964 BOUND_VARIABLE_1304965) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304965) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12937 BOUND_VARIABLE_1304964) BOUND_VARIABLE_1304965))))) (let ((_let_4641 (forall ((BOUND_VARIABLE_1304950 tptp.nat) (BOUND_VARIABLE_1304951 tptp.nat)) (= (or (= BOUND_VARIABLE_1304950 BOUND_VARIABLE_1304951) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304951) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12938 BOUND_VARIABLE_1304950) BOUND_VARIABLE_1304951))))) (let ((_let_4642 (forall ((BOUND_VARIABLE_1304936 Bool) (BOUND_VARIABLE_1304937 Bool)) (= (or (= BOUND_VARIABLE_1304936 BOUND_VARIABLE_1304937) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1304937) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12939 BOUND_VARIABLE_1304936) BOUND_VARIABLE_1304937))))) (let ((_let_4643 (forall ((BOUND_VARIABLE_1304922 Bool) (BOUND_VARIABLE_1304923 Bool)) (= (or (= BOUND_VARIABLE_1304922 BOUND_VARIABLE_1304923) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1304923) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12940 BOUND_VARIABLE_1304922) BOUND_VARIABLE_1304923))))) (let ((_let_4644 (forall ((BOUND_VARIABLE_1304908 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1304909 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1304908 BOUND_VARIABLE_1304909) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1304909) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12941 BOUND_VARIABLE_1304908) BOUND_VARIABLE_1304909))))) (let ((_let_4645 (forall ((BOUND_VARIABLE_1304894 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1304895 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1304894 BOUND_VARIABLE_1304895) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1304895) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12942 BOUND_VARIABLE_1304894) BOUND_VARIABLE_1304895))))) (let ((_let_4646 (forall ((BOUND_VARIABLE_1304884 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1304885 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11262 k_12943 BOUND_VARIABLE_1304884) BOUND_VARIABLE_1304885) (or (= BOUND_VARIABLE_1304884 BOUND_VARIABLE_1304885) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1304885) tptp.bot_bo228742789529271731at_nat)))))) (let ((_let_4647 (forall ((BOUND_VARIABLE_1304874 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1304875 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11262 k_12944 BOUND_VARIABLE_1304874) BOUND_VARIABLE_1304875) (or (= BOUND_VARIABLE_1304874 BOUND_VARIABLE_1304875) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1304875) tptp.bot_bo228742789529271731at_nat)))))) (let ((_let_4648 (forall ((BOUND_VARIABLE_1304863 tptp.int) (BOUND_VARIABLE_1304864 tptp.set_int) (BOUND_VARIABLE_1304865 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_12945 BOUND_VARIABLE_1304863) BOUND_VARIABLE_1304864) BOUND_VARIABLE_1304865) (or (= BOUND_VARIABLE_1304863 BOUND_VARIABLE_1304865) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304865) BOUND_VARIABLE_1304864)))))) (let ((_let_4649 (forall ((BOUND_VARIABLE_1304852 tptp.int) (BOUND_VARIABLE_1304853 tptp.set_int) (BOUND_VARIABLE_1304854 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_12946 BOUND_VARIABLE_1304852) BOUND_VARIABLE_1304853) BOUND_VARIABLE_1304854) (or (= BOUND_VARIABLE_1304852 BOUND_VARIABLE_1304854) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304854) BOUND_VARIABLE_1304853)))))) (let ((_let_4650 (forall ((BOUND_VARIABLE_1304841 tptp.nat) (BOUND_VARIABLE_1304842 tptp.set_nat) (BOUND_VARIABLE_1304843 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_12947 BOUND_VARIABLE_1304841) BOUND_VARIABLE_1304842) BOUND_VARIABLE_1304843) (or (= BOUND_VARIABLE_1304841 BOUND_VARIABLE_1304843) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304843) BOUND_VARIABLE_1304842)))))) (let ((_let_4651 (forall ((BOUND_VARIABLE_1304830 tptp.nat) (BOUND_VARIABLE_1304831 tptp.set_nat) (BOUND_VARIABLE_1304832 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_12948 BOUND_VARIABLE_1304830) BOUND_VARIABLE_1304831) BOUND_VARIABLE_1304832) (or (= BOUND_VARIABLE_1304830 BOUND_VARIABLE_1304832) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304832) BOUND_VARIABLE_1304831)))))) (let ((_let_4652 (forall ((BOUND_VARIABLE_1304819 Bool) (BOUND_VARIABLE_1304820 tptp.set_o) (BOUND_VARIABLE_1304821 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_12949 BOUND_VARIABLE_1304819) BOUND_VARIABLE_1304820) BOUND_VARIABLE_1304821) (or (= BOUND_VARIABLE_1304819 BOUND_VARIABLE_1304821) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1304821) BOUND_VARIABLE_1304820)))))) (let ((_let_4653 (forall ((BOUND_VARIABLE_1304808 Bool) (BOUND_VARIABLE_1304809 tptp.set_o) (BOUND_VARIABLE_1304810 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_12950 BOUND_VARIABLE_1304808) BOUND_VARIABLE_1304809) BOUND_VARIABLE_1304810) (or (= BOUND_VARIABLE_1304808 BOUND_VARIABLE_1304810) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1304810) BOUND_VARIABLE_1304809)))))) (let ((_let_4654 (forall ((BOUND_VARIABLE_1304797 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1304798 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1304799 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_12951 BOUND_VARIABLE_1304797) BOUND_VARIABLE_1304798) BOUND_VARIABLE_1304799) (or (= BOUND_VARIABLE_1304797 BOUND_VARIABLE_1304799) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1304799) BOUND_VARIABLE_1304798)))))) (let ((_let_4655 (forall ((BOUND_VARIABLE_1304786 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1304787 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1304788 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_12952 BOUND_VARIABLE_1304786) BOUND_VARIABLE_1304787) BOUND_VARIABLE_1304788) (or (= BOUND_VARIABLE_1304786 BOUND_VARIABLE_1304788) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1304788) BOUND_VARIABLE_1304787)))))) (let ((_let_4656 (forall ((BOUND_VARIABLE_1304775 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1304776 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1304777 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11374 (ho_12630 k_12953 BOUND_VARIABLE_1304775) BOUND_VARIABLE_1304776) BOUND_VARIABLE_1304777) (or (= BOUND_VARIABLE_1304775 BOUND_VARIABLE_1304777) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1304777) BOUND_VARIABLE_1304776)))))) (let ((_let_4657 (forall ((BOUND_VARIABLE_1304764 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1304765 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1304766 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11374 (ho_12630 k_12954 BOUND_VARIABLE_1304764) BOUND_VARIABLE_1304765) BOUND_VARIABLE_1304766) (or (= BOUND_VARIABLE_1304764 BOUND_VARIABLE_1304766) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1304766) BOUND_VARIABLE_1304765)))))) (let ((_let_4658 (forall ((BOUND_VARIABLE_1304750 tptp.int) (BOUND_VARIABLE_1304751 tptp.int)) (= (or (= BOUND_VARIABLE_1304750 BOUND_VARIABLE_1304751) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304751) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12955 BOUND_VARIABLE_1304750) BOUND_VARIABLE_1304751))))) (let ((_let_4659 (forall ((BOUND_VARIABLE_1304727 tptp.int) (BOUND_VARIABLE_1304728 tptp.int)) (= (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304728) (ho_11177 k_11176 (ho_11093 k_11280 BOUND_VARIABLE_1304727))) (ho_11094 (ho_11093 k_12956 BOUND_VARIABLE_1304727) BOUND_VARIABLE_1304728))))) (let ((_let_4660 (forall ((BOUND_VARIABLE_1304713 tptp.nat) (BOUND_VARIABLE_1304714 tptp.nat)) (= (or (= BOUND_VARIABLE_1304713 BOUND_VARIABLE_1304714) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304714) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12957 BOUND_VARIABLE_1304713) BOUND_VARIABLE_1304714))))) (let ((_let_4661 (forall ((BOUND_VARIABLE_1304690 tptp.nat) (BOUND_VARIABLE_1304691 tptp.nat)) (= (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304691) (ho_11107 k_11106 (ho_11053 k_11281 BOUND_VARIABLE_1304690))) (ho_11054 (ho_11053 k_12958 BOUND_VARIABLE_1304690) BOUND_VARIABLE_1304691))))) (let ((_let_4662 (forall ((BOUND_VARIABLE_1304676 Bool) (BOUND_VARIABLE_1304677 Bool)) (= (or (= BOUND_VARIABLE_1304676 BOUND_VARIABLE_1304677) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1304677) (ho_11196 k_11195 k_11193))) (ho_11194 (ho_11201 k_12959 BOUND_VARIABLE_1304676) BOUND_VARIABLE_1304677))))) (let ((_let_4663 (forall ((BOUND_VARIABLE_1304662 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1304663 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1304662 BOUND_VARIABLE_1304663) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1304663) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12960 BOUND_VARIABLE_1304662) BOUND_VARIABLE_1304663))))) (let ((_let_4664 (forall ((BOUND_VARIABLE_1304648 tptp.set_nat) (BOUND_VARIABLE_1304649 tptp.set_nat)) (= (or (= BOUND_VARIABLE_1304648 BOUND_VARIABLE_1304649) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1304649) (ho_11204 k_11203 k_11202))) (ho_11191 (ho_11209 k_12961 BOUND_VARIABLE_1304648) BOUND_VARIABLE_1304649))))) (let ((_let_4665 (forall ((BOUND_VARIABLE_1304634 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1304635 tptp.set_Pr958786334691620121nt_int)) (= (or (= BOUND_VARIABLE_1304634 BOUND_VARIABLE_1304635) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1304635) (ho_11213 k_11212 k_11210))) (ho_11211 (ho_11218 k_12962 BOUND_VARIABLE_1304634) BOUND_VARIABLE_1304635))))) (let ((_let_4666 (forall ((BOUND_VARIABLE_1304624 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1304625 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11262 k_12963 BOUND_VARIABLE_1304624) BOUND_VARIABLE_1304625) (or (= BOUND_VARIABLE_1304624 BOUND_VARIABLE_1304625) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1304625) tptp.bot_bo228742789529271731at_nat)))))) (let ((_let_4667 (forall ((BOUND_VARIABLE_1304616 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1304617 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_12964 BOUND_VARIABLE_1304616) BOUND_VARIABLE_1304617) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1304617) BOUND_VARIABLE_1304616))))) (let ((_let_4668 (forall ((BOUND_VARIABLE_1304593 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1304594 tptp.product_prod_nat_nat)) (= (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1304594) (ho_11186 k_11185 (ho_11188 k_11282 BOUND_VARIABLE_1304593))) (ho_11184 (ho_11188 k_12965 BOUND_VARIABLE_1304593) BOUND_VARIABLE_1304594))))) (let ((_let_4669 (forall ((BOUND_VARIABLE_1304585 tptp.set_int) (BOUND_VARIABLE_1304586 tptp.int)) (= (ho_11094 (ho_11234 k_12966 BOUND_VARIABLE_1304585) BOUND_VARIABLE_1304586) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304586) BOUND_VARIABLE_1304585))))) (let ((_let_4670 (forall ((BOUND_VARIABLE_1304562 tptp.int) (BOUND_VARIABLE_1304563 tptp.int)) (= (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304563) (ho_11177 k_11176 (ho_11093 k_11283 BOUND_VARIABLE_1304562))) (ho_11094 (ho_11093 k_12967 BOUND_VARIABLE_1304562) BOUND_VARIABLE_1304563))))) (let ((_let_4671 (forall ((BOUND_VARIABLE_1304554 tptp.set_nat) (BOUND_VARIABLE_1304555 tptp.nat)) (= (ho_11054 (ho_11240 k_12968 BOUND_VARIABLE_1304554) BOUND_VARIABLE_1304555) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304555) BOUND_VARIABLE_1304554))))) (let ((_let_4672 (forall ((BOUND_VARIABLE_1304531 tptp.nat) (BOUND_VARIABLE_1304532 tptp.nat)) (= (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304532) (ho_11107 k_11106 (ho_11053 k_11284 BOUND_VARIABLE_1304531))) (ho_11054 (ho_11053 k_12969 BOUND_VARIABLE_1304531) BOUND_VARIABLE_1304532))))) (let ((_let_4673 (forall ((BOUND_VARIABLE_1304523 tptp.set_o) (BOUND_VARIABLE_1304524 Bool)) (= (ho_11194 (ho_12571 k_12970 BOUND_VARIABLE_1304523) BOUND_VARIABLE_1304524) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1304524) BOUND_VARIABLE_1304523))))) (let ((_let_4674 (forall ((BOUND_VARIABLE_1304500 Bool) (BOUND_VARIABLE_1304501 Bool)) (= (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1304501) (ho_11196 k_11195 (ho_11201 k_11285 BOUND_VARIABLE_1304500))) (ho_11194 (ho_11201 k_12971 BOUND_VARIABLE_1304500) BOUND_VARIABLE_1304501))))) (let ((_let_4675 (forall ((BOUND_VARIABLE_1304490 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1304491 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11262 k_12972 BOUND_VARIABLE_1304490) BOUND_VARIABLE_1304491) (or (= BOUND_VARIABLE_1304490 BOUND_VARIABLE_1304491) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1304491) tptp.bot_bo228742789529271731at_nat)))))) (let ((_let_4676 (forall ((BOUND_VARIABLE_1304479 tptp.int) (BOUND_VARIABLE_1304480 tptp.set_int) (BOUND_VARIABLE_1304481 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_12973 BOUND_VARIABLE_1304479) BOUND_VARIABLE_1304480) BOUND_VARIABLE_1304481) (or (= BOUND_VARIABLE_1304479 BOUND_VARIABLE_1304481) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304481) BOUND_VARIABLE_1304480)))))) (let ((_let_4677 (forall ((BOUND_VARIABLE_1304468 tptp.nat) (BOUND_VARIABLE_1304469 tptp.set_nat) (BOUND_VARIABLE_1304470 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_12974 BOUND_VARIABLE_1304468) BOUND_VARIABLE_1304469) BOUND_VARIABLE_1304470) (or (= BOUND_VARIABLE_1304468 BOUND_VARIABLE_1304470) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304470) BOUND_VARIABLE_1304469)))))) (let ((_let_4678 (forall ((BOUND_VARIABLE_1304457 Bool) (BOUND_VARIABLE_1304458 tptp.set_o) (BOUND_VARIABLE_1304459 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_12975 BOUND_VARIABLE_1304457) BOUND_VARIABLE_1304458) BOUND_VARIABLE_1304459) (or (= BOUND_VARIABLE_1304457 BOUND_VARIABLE_1304459) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1304459) BOUND_VARIABLE_1304458)))))) (let ((_let_4679 (forall ((BOUND_VARIABLE_1304446 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1304447 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1304448 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_12976 BOUND_VARIABLE_1304446) BOUND_VARIABLE_1304447) BOUND_VARIABLE_1304448) (or (= BOUND_VARIABLE_1304446 BOUND_VARIABLE_1304448) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1304448) BOUND_VARIABLE_1304447)))))) (let ((_let_4680 (forall ((BOUND_VARIABLE_1304435 tptp.set_nat) (BOUND_VARIABLE_1304436 tptp.set_set_nat) (BOUND_VARIABLE_1304437 tptp.set_nat)) (= (ho_11191 (ho_12650 (ho_12653 k_12977 BOUND_VARIABLE_1304435) BOUND_VARIABLE_1304436) BOUND_VARIABLE_1304437) (or (= BOUND_VARIABLE_1304435 BOUND_VARIABLE_1304437) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1304437) BOUND_VARIABLE_1304436)))))) (let ((_let_4681 (forall ((BOUND_VARIABLE_1304424 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1304425 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1304426 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 (ho_12658 k_12978 BOUND_VARIABLE_1304424) BOUND_VARIABLE_1304425) BOUND_VARIABLE_1304426) (or (= BOUND_VARIABLE_1304424 BOUND_VARIABLE_1304426) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1304426) BOUND_VARIABLE_1304425)))))) (let ((_let_4682 (forall ((BOUND_VARIABLE_1304413 tptp.int) (BOUND_VARIABLE_1304414 tptp.set_int) (BOUND_VARIABLE_1304415 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_12979 BOUND_VARIABLE_1304413) BOUND_VARIABLE_1304414) BOUND_VARIABLE_1304415) (or (= BOUND_VARIABLE_1304413 BOUND_VARIABLE_1304415) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304415) BOUND_VARIABLE_1304414)))))) (let ((_let_4683 (forall ((BOUND_VARIABLE_1304402 tptp.nat) (BOUND_VARIABLE_1304403 tptp.set_nat) (BOUND_VARIABLE_1304404 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_12980 BOUND_VARIABLE_1304402) BOUND_VARIABLE_1304403) BOUND_VARIABLE_1304404) (or (= BOUND_VARIABLE_1304402 BOUND_VARIABLE_1304404) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304404) BOUND_VARIABLE_1304403)))))) (let ((_let_4684 (forall ((BOUND_VARIABLE_1304391 Bool) (BOUND_VARIABLE_1304392 tptp.set_o) (BOUND_VARIABLE_1304393 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_12981 BOUND_VARIABLE_1304391) BOUND_VARIABLE_1304392) BOUND_VARIABLE_1304393) (or (= BOUND_VARIABLE_1304391 BOUND_VARIABLE_1304393) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1304393) BOUND_VARIABLE_1304392)))))) (let ((_let_4685 (forall ((BOUND_VARIABLE_1304380 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1304381 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1304382 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_12982 BOUND_VARIABLE_1304380) BOUND_VARIABLE_1304381) BOUND_VARIABLE_1304382) (or (= BOUND_VARIABLE_1304380 BOUND_VARIABLE_1304382) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1304382) BOUND_VARIABLE_1304381)))))) (let ((_let_4686 (forall ((BOUND_VARIABLE_1304369 tptp.set_nat) (BOUND_VARIABLE_1304370 tptp.set_set_nat) (BOUND_VARIABLE_1304371 tptp.set_nat)) (= (ho_11191 (ho_12650 (ho_12653 k_12983 BOUND_VARIABLE_1304369) BOUND_VARIABLE_1304370) BOUND_VARIABLE_1304371) (or (= BOUND_VARIABLE_1304369 BOUND_VARIABLE_1304371) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1304371) BOUND_VARIABLE_1304370)))))) (let ((_let_4687 (forall ((BOUND_VARIABLE_1304358 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1304359 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1304360 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 (ho_12658 k_12984 BOUND_VARIABLE_1304358) BOUND_VARIABLE_1304359) BOUND_VARIABLE_1304360) (or (= BOUND_VARIABLE_1304358 BOUND_VARIABLE_1304360) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1304360) BOUND_VARIABLE_1304359)))))) (let ((_let_4688 (forall ((BOUND_VARIABLE_1304347 tptp.int) (BOUND_VARIABLE_1304348 tptp.set_int) (BOUND_VARIABLE_1304349 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_12985 BOUND_VARIABLE_1304347) BOUND_VARIABLE_1304348) BOUND_VARIABLE_1304349) (or (= BOUND_VARIABLE_1304347 BOUND_VARIABLE_1304349) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304349) BOUND_VARIABLE_1304348)))))) (let ((_let_4689 (forall ((BOUND_VARIABLE_1304336 tptp.nat) (BOUND_VARIABLE_1304337 tptp.set_nat) (BOUND_VARIABLE_1304338 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_12986 BOUND_VARIABLE_1304336) BOUND_VARIABLE_1304337) BOUND_VARIABLE_1304338) (or (= BOUND_VARIABLE_1304336 BOUND_VARIABLE_1304338) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304338) BOUND_VARIABLE_1304337)))))) (let ((_let_4690 (forall ((BOUND_VARIABLE_1304325 Bool) (BOUND_VARIABLE_1304326 tptp.set_o) (BOUND_VARIABLE_1304327 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_12987 BOUND_VARIABLE_1304325) BOUND_VARIABLE_1304326) BOUND_VARIABLE_1304327) (or (= BOUND_VARIABLE_1304325 BOUND_VARIABLE_1304327) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1304327) BOUND_VARIABLE_1304326)))))) (let ((_let_4691 (forall ((BOUND_VARIABLE_1304314 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1304315 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1304316 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_12988 BOUND_VARIABLE_1304314) BOUND_VARIABLE_1304315) BOUND_VARIABLE_1304316) (or (= BOUND_VARIABLE_1304314 BOUND_VARIABLE_1304316) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1304316) BOUND_VARIABLE_1304315)))))) (let ((_let_4692 (forall ((BOUND_VARIABLE_1304303 tptp.set_nat) (BOUND_VARIABLE_1304304 tptp.set_set_nat) (BOUND_VARIABLE_1304305 tptp.set_nat)) (= (ho_11191 (ho_12650 (ho_12653 k_12989 BOUND_VARIABLE_1304303) BOUND_VARIABLE_1304304) BOUND_VARIABLE_1304305) (or (= BOUND_VARIABLE_1304303 BOUND_VARIABLE_1304305) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1304305) BOUND_VARIABLE_1304304)))))) (let ((_let_4693 (forall ((BOUND_VARIABLE_1304292 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1304293 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1304294 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 (ho_12658 k_12990 BOUND_VARIABLE_1304292) BOUND_VARIABLE_1304293) BOUND_VARIABLE_1304294) (or (= BOUND_VARIABLE_1304292 BOUND_VARIABLE_1304294) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1304294) BOUND_VARIABLE_1304293)))))) (let ((_let_4694 (forall ((BOUND_VARIABLE_1304281 tptp.int) (BOUND_VARIABLE_1304282 tptp.set_int) (BOUND_VARIABLE_1304283 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_12991 BOUND_VARIABLE_1304281) BOUND_VARIABLE_1304282) BOUND_VARIABLE_1304283) (or (= BOUND_VARIABLE_1304281 BOUND_VARIABLE_1304283) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304283) BOUND_VARIABLE_1304282)))))) (let ((_let_4695 (forall ((BOUND_VARIABLE_1304270 tptp.nat) (BOUND_VARIABLE_1304271 tptp.set_nat) (BOUND_VARIABLE_1304272 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_12992 BOUND_VARIABLE_1304270) BOUND_VARIABLE_1304271) BOUND_VARIABLE_1304272) (or (= BOUND_VARIABLE_1304270 BOUND_VARIABLE_1304272) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304272) BOUND_VARIABLE_1304271)))))) (let ((_let_4696 (forall ((BOUND_VARIABLE_1304259 Bool) (BOUND_VARIABLE_1304260 tptp.set_o) (BOUND_VARIABLE_1304261 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_12993 BOUND_VARIABLE_1304259) BOUND_VARIABLE_1304260) BOUND_VARIABLE_1304261) (or (= BOUND_VARIABLE_1304259 BOUND_VARIABLE_1304261) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1304261) BOUND_VARIABLE_1304260)))))) (let ((_let_4697 (forall ((BOUND_VARIABLE_1304248 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1304249 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1304250 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_12994 BOUND_VARIABLE_1304248) BOUND_VARIABLE_1304249) BOUND_VARIABLE_1304250) (or (= BOUND_VARIABLE_1304248 BOUND_VARIABLE_1304250) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1304250) BOUND_VARIABLE_1304249)))))) (let ((_let_4698 (forall ((BOUND_VARIABLE_1304237 tptp.set_nat) (BOUND_VARIABLE_1304238 tptp.set_set_nat) (BOUND_VARIABLE_1304239 tptp.set_nat)) (= (ho_11191 (ho_12650 (ho_12653 k_12995 BOUND_VARIABLE_1304237) BOUND_VARIABLE_1304238) BOUND_VARIABLE_1304239) (or (= BOUND_VARIABLE_1304237 BOUND_VARIABLE_1304239) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1304239) BOUND_VARIABLE_1304238)))))) (let ((_let_4699 (forall ((BOUND_VARIABLE_1304226 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1304227 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1304228 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 (ho_12658 k_12996 BOUND_VARIABLE_1304226) BOUND_VARIABLE_1304227) BOUND_VARIABLE_1304228) (or (= BOUND_VARIABLE_1304226 BOUND_VARIABLE_1304228) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1304228) BOUND_VARIABLE_1304227)))))) (let ((_let_4700 (forall ((BOUND_VARIABLE_1304212 tptp.int) (BOUND_VARIABLE_1304213 tptp.int)) (= (or (= BOUND_VARIABLE_1304212 BOUND_VARIABLE_1304213) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304213) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_12997 BOUND_VARIABLE_1304212) BOUND_VARIABLE_1304213))))) (let ((_let_4701 (forall ((BOUND_VARIABLE_1304198 tptp.nat) (BOUND_VARIABLE_1304199 tptp.nat)) (= (or (= BOUND_VARIABLE_1304198 BOUND_VARIABLE_1304199) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304199) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_12998 BOUND_VARIABLE_1304198) BOUND_VARIABLE_1304199))))) (let ((_let_4702 (forall ((BOUND_VARIABLE_1304184 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1304185 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1304184 BOUND_VARIABLE_1304185) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1304185) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_12999 BOUND_VARIABLE_1304184) BOUND_VARIABLE_1304185))))) (let ((_let_4703 (forall ((BOUND_VARIABLE_1304174 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1304175 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11262 k_13000 BOUND_VARIABLE_1304174) BOUND_VARIABLE_1304175) (or (= BOUND_VARIABLE_1304174 BOUND_VARIABLE_1304175) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1304175) tptp.bot_bo228742789529271731at_nat)))))) (let ((_let_4704 (forall ((BOUND_VARIABLE_1304160 tptp.int) (BOUND_VARIABLE_1304161 tptp.int)) (= (or (= BOUND_VARIABLE_1304160 BOUND_VARIABLE_1304161) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304161) (ho_11177 k_11176 k_11175))) (ho_11094 (ho_11093 k_13001 BOUND_VARIABLE_1304160) BOUND_VARIABLE_1304161))))) (let ((_let_4705 (forall ((BOUND_VARIABLE_1304146 tptp.nat) (BOUND_VARIABLE_1304147 tptp.nat)) (= (or (= BOUND_VARIABLE_1304146 BOUND_VARIABLE_1304147) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304147) (ho_11107 k_11106 k_11105))) (ho_11054 (ho_11053 k_13002 BOUND_VARIABLE_1304146) BOUND_VARIABLE_1304147))))) (let ((_let_4706 (forall ((BOUND_VARIABLE_1304132 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1304133 tptp.product_prod_nat_nat)) (= (or (= BOUND_VARIABLE_1304132 BOUND_VARIABLE_1304133) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1304133) (ho_11186 k_11185 k_11183))) (ho_11184 (ho_11188 k_13003 BOUND_VARIABLE_1304132) BOUND_VARIABLE_1304133))))) (let ((_let_4707 (forall ((BOUND_VARIABLE_1304122 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1304123 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11262 k_13004 BOUND_VARIABLE_1304122) BOUND_VARIABLE_1304123) (or (= BOUND_VARIABLE_1304122 BOUND_VARIABLE_1304123) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1304123) tptp.bot_bo228742789529271731at_nat)))))) (let ((_let_4708 (forall ((BOUND_VARIABLE_1304111 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1304112 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1304113 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_13005 BOUND_VARIABLE_1304111) BOUND_VARIABLE_1304112) BOUND_VARIABLE_1304113) (or (= BOUND_VARIABLE_1304111 BOUND_VARIABLE_1304113) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1304113) BOUND_VARIABLE_1304112)))))) (let ((_let_4709 (forall ((BOUND_VARIABLE_1304100 tptp.int) (BOUND_VARIABLE_1304101 tptp.set_int) (BOUND_VARIABLE_1304102 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_13006 BOUND_VARIABLE_1304100) BOUND_VARIABLE_1304101) BOUND_VARIABLE_1304102) (or (= BOUND_VARIABLE_1304100 BOUND_VARIABLE_1304102) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304102) BOUND_VARIABLE_1304101)))))) (let ((_let_4710 (forall ((BOUND_VARIABLE_1304089 tptp.nat) (BOUND_VARIABLE_1304090 tptp.set_nat) (BOUND_VARIABLE_1304091 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_13007 BOUND_VARIABLE_1304089) BOUND_VARIABLE_1304090) BOUND_VARIABLE_1304091) (or (= BOUND_VARIABLE_1304089 BOUND_VARIABLE_1304091) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304091) BOUND_VARIABLE_1304090)))))) (let ((_let_4711 (forall ((BOUND_VARIABLE_1304078 tptp.set_nat) (BOUND_VARIABLE_1304079 tptp.set_set_nat) (BOUND_VARIABLE_1304080 tptp.set_nat)) (= (ho_11191 (ho_12650 (ho_12653 k_13008 BOUND_VARIABLE_1304078) BOUND_VARIABLE_1304079) BOUND_VARIABLE_1304080) (or (= BOUND_VARIABLE_1304078 BOUND_VARIABLE_1304080) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1304080) BOUND_VARIABLE_1304079)))))) (let ((_let_4712 (forall ((BOUND_VARIABLE_1304067 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1304068 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1304069 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 (ho_12658 k_13009 BOUND_VARIABLE_1304067) BOUND_VARIABLE_1304068) BOUND_VARIABLE_1304069) (or (= BOUND_VARIABLE_1304067 BOUND_VARIABLE_1304069) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1304069) BOUND_VARIABLE_1304068)))))) (let ((_let_4713 (forall ((BOUND_VARIABLE_1304056 Bool) (BOUND_VARIABLE_1304057 tptp.set_o) (BOUND_VARIABLE_1304058 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_13010 BOUND_VARIABLE_1304056) BOUND_VARIABLE_1304057) BOUND_VARIABLE_1304058) (or (= BOUND_VARIABLE_1304056 BOUND_VARIABLE_1304058) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1304058) BOUND_VARIABLE_1304057)))))) (let ((_let_4714 (forall ((BOUND_VARIABLE_1304045 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1304046 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1304047 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_13011 BOUND_VARIABLE_1304045) BOUND_VARIABLE_1304046) BOUND_VARIABLE_1304047) (or (= BOUND_VARIABLE_1304045 BOUND_VARIABLE_1304047) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1304047) BOUND_VARIABLE_1304046)))))) (let ((_let_4715 (forall ((BOUND_VARIABLE_1304034 tptp.int) (BOUND_VARIABLE_1304035 tptp.set_int) (BOUND_VARIABLE_1304036 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_13012 BOUND_VARIABLE_1304034) BOUND_VARIABLE_1304035) BOUND_VARIABLE_1304036) (or (= BOUND_VARIABLE_1304034 BOUND_VARIABLE_1304036) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1304036) BOUND_VARIABLE_1304035)))))) (let ((_let_4716 (forall ((BOUND_VARIABLE_1304023 tptp.nat) (BOUND_VARIABLE_1304024 tptp.set_nat) (BOUND_VARIABLE_1304025 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_13013 BOUND_VARIABLE_1304023) BOUND_VARIABLE_1304024) BOUND_VARIABLE_1304025) (or (= BOUND_VARIABLE_1304023 BOUND_VARIABLE_1304025) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1304025) BOUND_VARIABLE_1304024)))))) (let ((_let_4717 (forall ((BOUND_VARIABLE_1304012 tptp.set_nat) (BOUND_VARIABLE_1304013 tptp.set_set_nat) (BOUND_VARIABLE_1304014 tptp.set_nat)) (= (ho_11191 (ho_12650 (ho_12653 k_13014 BOUND_VARIABLE_1304012) BOUND_VARIABLE_1304013) BOUND_VARIABLE_1304014) (or (= BOUND_VARIABLE_1304012 BOUND_VARIABLE_1304014) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1304014) BOUND_VARIABLE_1304013)))))) (let ((_let_4718 (forall ((BOUND_VARIABLE_1304001 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1304002 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1304003 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 (ho_12658 k_13015 BOUND_VARIABLE_1304001) BOUND_VARIABLE_1304002) BOUND_VARIABLE_1304003) (or (= BOUND_VARIABLE_1304001 BOUND_VARIABLE_1304003) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1304003) BOUND_VARIABLE_1304002)))))) (let ((_let_4719 (forall ((BOUND_VARIABLE_1303990 Bool) (BOUND_VARIABLE_1303991 tptp.set_o) (BOUND_VARIABLE_1303992 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_13016 BOUND_VARIABLE_1303990) BOUND_VARIABLE_1303991) BOUND_VARIABLE_1303992) (or (= BOUND_VARIABLE_1303990 BOUND_VARIABLE_1303992) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1303992) BOUND_VARIABLE_1303991)))))) (let ((_let_4720 (forall ((BOUND_VARIABLE_1303979 tptp.nat) (BOUND_VARIABLE_1303980 tptp.set_nat) (BOUND_VARIABLE_1303981 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_13017 BOUND_VARIABLE_1303979) BOUND_VARIABLE_1303980) BOUND_VARIABLE_1303981) (or (= BOUND_VARIABLE_1303979 BOUND_VARIABLE_1303981) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1303981) BOUND_VARIABLE_1303980)))))) (let ((_let_4721 (forall ((BOUND_VARIABLE_1303968 tptp.set_nat) (BOUND_VARIABLE_1303969 tptp.set_nat) (BOUND_VARIABLE_1303970 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1303970))) (= (ho_11054 (ho_11240 (ho_11343 k_13018 BOUND_VARIABLE_1303968) BOUND_VARIABLE_1303969) BOUND_VARIABLE_1303970) (or (ho_11191 _let_1 BOUND_VARIABLE_1303968) (ho_11191 _let_1 BOUND_VARIABLE_1303969))))))) (let ((_let_4722 (forall ((BOUND_VARIABLE_1303957 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1303958 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1303959 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11374 (ho_12630 k_13019 BOUND_VARIABLE_1303957) BOUND_VARIABLE_1303958) BOUND_VARIABLE_1303959) (or (= BOUND_VARIABLE_1303957 BOUND_VARIABLE_1303959) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1303959) BOUND_VARIABLE_1303958)))))) (let ((_let_4723 (forall ((BOUND_VARIABLE_1303946 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1303947 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1303948 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (ho_11259 k_11258 BOUND_VARIABLE_1303948))) (= (ho_11263 (ho_11374 (ho_11373 k_13020 BOUND_VARIABLE_1303946) BOUND_VARIABLE_1303947) BOUND_VARIABLE_1303948) (or (ho_11260 _let_1 BOUND_VARIABLE_1303946) (ho_11260 _let_1 BOUND_VARIABLE_1303947))))))) (let ((_let_4724 (forall ((BOUND_VARIABLE_1303921 tptp.produc4166570645942440679at_nat) (BOUND_VARIABLE_1303922 tptp.set_Pr8551490117392284871at_nat) (BOUND_VARIABLE_1303923 tptp.produc4166570645942440679at_nat)) (let ((_let_1 (ho_11266 k_11265 BOUND_VARIABLE_1303923))) (= (or (ho_11267 _let_1 (ho_11269 k_11268 (ho_11050 k_11286 BOUND_VARIABLE_1303921))) (ho_11267 _let_1 BOUND_VARIABLE_1303922)) (ho_11051 (ho_11377 (ho_12820 k_13021 BOUND_VARIABLE_1303921) BOUND_VARIABLE_1303922) BOUND_VARIABLE_1303923)))))) (let ((_let_4725 (forall ((BOUND_VARIABLE_1303914 tptp.produc4166570645942440679at_nat) (BOUND_VARIABLE_1303915 tptp.produc4166570645942440679at_nat)) (= (= BOUND_VARIABLE_1303914 BOUND_VARIABLE_1303915) (ho_11051 (ho_11050 k_13022 BOUND_VARIABLE_1303914) BOUND_VARIABLE_1303915))))) (let ((_let_4726 (forall ((BOUND_VARIABLE_1303903 tptp.set_Pr8551490117392284871at_nat) (BOUND_VARIABLE_1303904 tptp.set_Pr8551490117392284871at_nat) (BOUND_VARIABLE_1303905 tptp.produc4166570645942440679at_nat)) (let ((_let_1 (ho_11266 k_11265 BOUND_VARIABLE_1303905))) (= (ho_11051 (ho_11377 (ho_11376 k_13023 BOUND_VARIABLE_1303903) BOUND_VARIABLE_1303904) BOUND_VARIABLE_1303905) (or (ho_11267 _let_1 BOUND_VARIABLE_1303903) (ho_11267 _let_1 BOUND_VARIABLE_1303904))))))) (let ((_let_4727 (forall ((BOUND_VARIABLE_1303892 tptp.int) (BOUND_VARIABLE_1303893 tptp.set_int) (BOUND_VARIABLE_1303894 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_13024 BOUND_VARIABLE_1303892) BOUND_VARIABLE_1303893) BOUND_VARIABLE_1303894) (or (= BOUND_VARIABLE_1303892 BOUND_VARIABLE_1303894) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1303894) BOUND_VARIABLE_1303893)))))) (let ((_let_4728 (forall ((BOUND_VARIABLE_1303881 tptp.set_int) (BOUND_VARIABLE_1303882 tptp.set_int) (BOUND_VARIABLE_1303883 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1303883))) (= (ho_11094 (ho_11234 (ho_11339 k_13025 BOUND_VARIABLE_1303881) BOUND_VARIABLE_1303882) BOUND_VARIABLE_1303883) (or (ho_11180 _let_1 BOUND_VARIABLE_1303881) (ho_11180 _let_1 BOUND_VARIABLE_1303882))))))) (let ((_let_4729 (forall ((BOUND_VARIABLE_1303870 Bool) (BOUND_VARIABLE_1303871 tptp.set_o) (BOUND_VARIABLE_1303872 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_13026 BOUND_VARIABLE_1303870) BOUND_VARIABLE_1303871) BOUND_VARIABLE_1303872) (or (= BOUND_VARIABLE_1303870 BOUND_VARIABLE_1303872) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1303872) BOUND_VARIABLE_1303871)))))) (let ((_let_4730 (forall ((BOUND_VARIABLE_1303859 tptp.set_o) (BOUND_VARIABLE_1303860 tptp.set_o) (BOUND_VARIABLE_1303861 Bool)) (let ((_let_1 (ho_11198 k_11197 BOUND_VARIABLE_1303861))) (= (ho_11194 (ho_12571 (ho_12891 k_13027 BOUND_VARIABLE_1303859) BOUND_VARIABLE_1303860) BOUND_VARIABLE_1303861) (or (ho_11199 _let_1 BOUND_VARIABLE_1303859) (ho_11199 _let_1 BOUND_VARIABLE_1303860))))))) (let ((_let_4731 (forall ((BOUND_VARIABLE_1303848 tptp.nat) (BOUND_VARIABLE_1303849 tptp.set_nat) (BOUND_VARIABLE_1303850 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_13028 BOUND_VARIABLE_1303848) BOUND_VARIABLE_1303849) BOUND_VARIABLE_1303850) (or (= BOUND_VARIABLE_1303848 BOUND_VARIABLE_1303850) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1303850) BOUND_VARIABLE_1303849)))))) (let ((_let_4732 (forall ((BOUND_VARIABLE_1303837 tptp.set_nat) (BOUND_VARIABLE_1303838 tptp.set_nat) (BOUND_VARIABLE_1303839 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1303839))) (= (ho_11054 (ho_11240 (ho_11343 k_13029 BOUND_VARIABLE_1303837) BOUND_VARIABLE_1303838) BOUND_VARIABLE_1303839) (or (ho_11191 _let_1 BOUND_VARIABLE_1303837) (ho_11191 _let_1 BOUND_VARIABLE_1303838))))))) (let ((_let_4733 (forall ((BOUND_VARIABLE_1303826 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1303827 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1303828 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11374 (ho_12630 k_13030 BOUND_VARIABLE_1303826) BOUND_VARIABLE_1303827) BOUND_VARIABLE_1303828) (or (= BOUND_VARIABLE_1303826 BOUND_VARIABLE_1303828) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1303828) BOUND_VARIABLE_1303827)))))) (let ((_let_4734 (forall ((BOUND_VARIABLE_1303815 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1303816 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1303817 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (ho_11259 k_11258 BOUND_VARIABLE_1303817))) (= (ho_11263 (ho_11374 (ho_11373 k_13031 BOUND_VARIABLE_1303815) BOUND_VARIABLE_1303816) BOUND_VARIABLE_1303817) (or (ho_11260 _let_1 BOUND_VARIABLE_1303815) (ho_11260 _let_1 BOUND_VARIABLE_1303816))))))) (let ((_let_4735 (forall ((BOUND_VARIABLE_1303790 tptp.produc4166570645942440679at_nat) (BOUND_VARIABLE_1303791 tptp.set_Pr8551490117392284871at_nat) (BOUND_VARIABLE_1303792 tptp.produc4166570645942440679at_nat)) (let ((_let_1 (ho_11266 k_11265 BOUND_VARIABLE_1303792))) (= (or (ho_11267 _let_1 (ho_11269 k_11268 (ho_11050 k_11287 BOUND_VARIABLE_1303790))) (ho_11267 _let_1 BOUND_VARIABLE_1303791)) (ho_11051 (ho_11377 (ho_12820 k_13032 BOUND_VARIABLE_1303790) BOUND_VARIABLE_1303791) BOUND_VARIABLE_1303792)))))) (let ((_let_4736 (forall ((BOUND_VARIABLE_1303783 tptp.produc4166570645942440679at_nat) (BOUND_VARIABLE_1303784 tptp.produc4166570645942440679at_nat)) (= (= BOUND_VARIABLE_1303783 BOUND_VARIABLE_1303784) (ho_11051 (ho_11050 k_13033 BOUND_VARIABLE_1303783) BOUND_VARIABLE_1303784))))) (let ((_let_4737 (forall ((BOUND_VARIABLE_1303772 tptp.set_Pr8551490117392284871at_nat) (BOUND_VARIABLE_1303773 tptp.set_Pr8551490117392284871at_nat) (BOUND_VARIABLE_1303774 tptp.produc4166570645942440679at_nat)) (let ((_let_1 (ho_11266 k_11265 BOUND_VARIABLE_1303774))) (= (ho_11051 (ho_11377 (ho_11376 k_13034 BOUND_VARIABLE_1303772) BOUND_VARIABLE_1303773) BOUND_VARIABLE_1303774) (or (ho_11267 _let_1 BOUND_VARIABLE_1303772) (ho_11267 _let_1 BOUND_VARIABLE_1303773))))))) (let ((_let_4738 (forall ((BOUND_VARIABLE_1303761 tptp.int) (BOUND_VARIABLE_1303762 tptp.set_int) (BOUND_VARIABLE_1303763 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_13035 BOUND_VARIABLE_1303761) BOUND_VARIABLE_1303762) BOUND_VARIABLE_1303763) (or (= BOUND_VARIABLE_1303761 BOUND_VARIABLE_1303763) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1303763) BOUND_VARIABLE_1303762)))))) (let ((_let_4739 (forall ((BOUND_VARIABLE_1303750 tptp.set_int) (BOUND_VARIABLE_1303751 tptp.set_int) (BOUND_VARIABLE_1303752 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1303752))) (= (ho_11094 (ho_11234 (ho_11339 k_13036 BOUND_VARIABLE_1303750) BOUND_VARIABLE_1303751) BOUND_VARIABLE_1303752) (or (ho_11180 _let_1 BOUND_VARIABLE_1303750) (ho_11180 _let_1 BOUND_VARIABLE_1303751))))))) (let ((_let_4740 (forall ((BOUND_VARIABLE_1303739 Bool) (BOUND_VARIABLE_1303740 tptp.set_o) (BOUND_VARIABLE_1303741 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_13037 BOUND_VARIABLE_1303739) BOUND_VARIABLE_1303740) BOUND_VARIABLE_1303741) (or (= BOUND_VARIABLE_1303739 BOUND_VARIABLE_1303741) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1303741) BOUND_VARIABLE_1303740)))))) (let ((_let_4741 (forall ((BOUND_VARIABLE_1303728 tptp.set_o) (BOUND_VARIABLE_1303729 tptp.set_o) (BOUND_VARIABLE_1303730 Bool)) (let ((_let_1 (ho_11198 k_11197 BOUND_VARIABLE_1303730))) (= (ho_11194 (ho_12571 (ho_12891 k_13038 BOUND_VARIABLE_1303728) BOUND_VARIABLE_1303729) BOUND_VARIABLE_1303730) (or (ho_11199 _let_1 BOUND_VARIABLE_1303728) (ho_11199 _let_1 BOUND_VARIABLE_1303729))))))) (let ((_let_4742 (forall ((BOUND_VARIABLE_1303717 tptp.nat) (BOUND_VARIABLE_1303718 tptp.set_nat) (BOUND_VARIABLE_1303719 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_13039 BOUND_VARIABLE_1303717) BOUND_VARIABLE_1303718) BOUND_VARIABLE_1303719) (or (= BOUND_VARIABLE_1303717 BOUND_VARIABLE_1303719) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1303719) BOUND_VARIABLE_1303718)))))) (let ((_let_4743 (forall ((BOUND_VARIABLE_1303706 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1303707 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1303708 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_13040 BOUND_VARIABLE_1303706) BOUND_VARIABLE_1303707) BOUND_VARIABLE_1303708) (or (= BOUND_VARIABLE_1303706 BOUND_VARIABLE_1303708) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1303708) BOUND_VARIABLE_1303707)))))) (let ((_let_4744 (forall ((BOUND_VARIABLE_1303695 tptp.int) (BOUND_VARIABLE_1303696 tptp.set_int) (BOUND_VARIABLE_1303697 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_13041 BOUND_VARIABLE_1303695) BOUND_VARIABLE_1303696) BOUND_VARIABLE_1303697) (or (= BOUND_VARIABLE_1303695 BOUND_VARIABLE_1303697) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1303697) BOUND_VARIABLE_1303696)))))) (let ((_let_4745 (forall ((BOUND_VARIABLE_1303684 tptp.set_nat) (BOUND_VARIABLE_1303685 tptp.set_set_nat) (BOUND_VARIABLE_1303686 tptp.set_nat)) (= (ho_11191 (ho_12650 (ho_12653 k_13042 BOUND_VARIABLE_1303684) BOUND_VARIABLE_1303685) BOUND_VARIABLE_1303686) (or (= BOUND_VARIABLE_1303684 BOUND_VARIABLE_1303686) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1303686) BOUND_VARIABLE_1303685)))))) (let ((_let_4746 (forall ((BOUND_VARIABLE_1303673 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1303674 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1303675 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 (ho_12658 k_13043 BOUND_VARIABLE_1303673) BOUND_VARIABLE_1303674) BOUND_VARIABLE_1303675) (or (= BOUND_VARIABLE_1303673 BOUND_VARIABLE_1303675) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1303675) BOUND_VARIABLE_1303674)))))) (let ((_let_4747 (forall ((BOUND_VARIABLE_1303662 Bool) (BOUND_VARIABLE_1303663 tptp.set_o) (BOUND_VARIABLE_1303664 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_13044 BOUND_VARIABLE_1303662) BOUND_VARIABLE_1303663) BOUND_VARIABLE_1303664) (or (= BOUND_VARIABLE_1303662 BOUND_VARIABLE_1303664) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1303664) BOUND_VARIABLE_1303663)))))) (let ((_let_4748 (forall ((BOUND_VARIABLE_1303651 tptp.nat) (BOUND_VARIABLE_1303652 tptp.set_nat) (BOUND_VARIABLE_1303653 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_13045 BOUND_VARIABLE_1303651) BOUND_VARIABLE_1303652) BOUND_VARIABLE_1303653) (or (= BOUND_VARIABLE_1303651 BOUND_VARIABLE_1303653) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1303653) BOUND_VARIABLE_1303652)))))) (let ((_let_4749 (forall ((BOUND_VARIABLE_1303640 tptp.set_nat) (BOUND_VARIABLE_1303641 tptp.set_nat) (BOUND_VARIABLE_1303642 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1303642))) (= (ho_11054 (ho_11240 (ho_11343 k_13046 BOUND_VARIABLE_1303640) BOUND_VARIABLE_1303641) BOUND_VARIABLE_1303642) (and (ho_11191 _let_1 BOUND_VARIABLE_1303640) (ho_11191 _let_1 BOUND_VARIABLE_1303641))))))) (let ((_let_4750 (forall ((BOUND_VARIABLE_1303629 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1303630 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1303631 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_13047 BOUND_VARIABLE_1303629) BOUND_VARIABLE_1303630) BOUND_VARIABLE_1303631) (or (= BOUND_VARIABLE_1303629 BOUND_VARIABLE_1303631) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1303631) BOUND_VARIABLE_1303630)))))) (let ((_let_4751 (forall ((BOUND_VARIABLE_1303618 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1303619 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1303620 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1303620))) (= (ho_11184 (ho_11237 (ho_11365 k_13048 BOUND_VARIABLE_1303618) BOUND_VARIABLE_1303619) BOUND_VARIABLE_1303620) (and (ho_11070 _let_1 BOUND_VARIABLE_1303618) (ho_11070 _let_1 BOUND_VARIABLE_1303619))))))) (let ((_let_4752 (forall ((BOUND_VARIABLE_1303607 tptp.int) (BOUND_VARIABLE_1303608 tptp.set_int) (BOUND_VARIABLE_1303609 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_13049 BOUND_VARIABLE_1303607) BOUND_VARIABLE_1303608) BOUND_VARIABLE_1303609) (or (= BOUND_VARIABLE_1303607 BOUND_VARIABLE_1303609) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1303609) BOUND_VARIABLE_1303608)))))) (let ((_let_4753 (forall ((BOUND_VARIABLE_1303596 tptp.set_int) (BOUND_VARIABLE_1303597 tptp.set_int) (BOUND_VARIABLE_1303598 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1303598))) (= (ho_11094 (ho_11234 (ho_11339 k_13050 BOUND_VARIABLE_1303596) BOUND_VARIABLE_1303597) BOUND_VARIABLE_1303598) (and (ho_11180 _let_1 BOUND_VARIABLE_1303596) (ho_11180 _let_1 BOUND_VARIABLE_1303597))))))) (let ((_let_4754 (forall ((BOUND_VARIABLE_1303585 tptp.set_nat) (BOUND_VARIABLE_1303586 tptp.set_set_nat) (BOUND_VARIABLE_1303587 tptp.set_nat)) (= (ho_11191 (ho_12650 (ho_12653 k_13051 BOUND_VARIABLE_1303585) BOUND_VARIABLE_1303586) BOUND_VARIABLE_1303587) (or (= BOUND_VARIABLE_1303585 BOUND_VARIABLE_1303587) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1303587) BOUND_VARIABLE_1303586)))))) (let ((_let_4755 (forall ((BOUND_VARIABLE_1303574 tptp.set_set_nat) (BOUND_VARIABLE_1303575 tptp.set_set_nat) (BOUND_VARIABLE_1303576 tptp.set_nat)) (let ((_let_1 (ho_11206 k_11205 BOUND_VARIABLE_1303576))) (= (ho_11191 (ho_12650 (ho_12883 k_13052 BOUND_VARIABLE_1303574) BOUND_VARIABLE_1303575) BOUND_VARIABLE_1303576) (and (ho_11207 _let_1 BOUND_VARIABLE_1303574) (ho_11207 _let_1 BOUND_VARIABLE_1303575))))))) (let ((_let_4756 (forall ((BOUND_VARIABLE_1303563 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1303564 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1303565 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 (ho_12658 k_13053 BOUND_VARIABLE_1303563) BOUND_VARIABLE_1303564) BOUND_VARIABLE_1303565) (or (= BOUND_VARIABLE_1303563 BOUND_VARIABLE_1303565) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1303565) BOUND_VARIABLE_1303564)))))) (let ((_let_4757 (forall ((BOUND_VARIABLE_1303552 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1303553 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1303554 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (ho_11215 k_11214 BOUND_VARIABLE_1303554))) (= (ho_11211 (ho_12655 (ho_12887 k_13054 BOUND_VARIABLE_1303552) BOUND_VARIABLE_1303553) BOUND_VARIABLE_1303554) (and (ho_11216 _let_1 BOUND_VARIABLE_1303552) (ho_11216 _let_1 BOUND_VARIABLE_1303553))))))) (let ((_let_4758 (forall ((BOUND_VARIABLE_1303541 Bool) (BOUND_VARIABLE_1303542 tptp.set_o) (BOUND_VARIABLE_1303543 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_13055 BOUND_VARIABLE_1303541) BOUND_VARIABLE_1303542) BOUND_VARIABLE_1303543) (or (= BOUND_VARIABLE_1303541 BOUND_VARIABLE_1303543) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1303543) BOUND_VARIABLE_1303542)))))) (let ((_let_4759 (forall ((BOUND_VARIABLE_1303530 tptp.set_o) (BOUND_VARIABLE_1303531 tptp.set_o) (BOUND_VARIABLE_1303532 Bool)) (let ((_let_1 (ho_11198 k_11197 BOUND_VARIABLE_1303532))) (= (ho_11194 (ho_12571 (ho_12891 k_13056 BOUND_VARIABLE_1303530) BOUND_VARIABLE_1303531) BOUND_VARIABLE_1303532) (and (ho_11199 _let_1 BOUND_VARIABLE_1303530) (ho_11199 _let_1 BOUND_VARIABLE_1303531))))))) (let ((_let_4760 (forall ((BOUND_VARIABLE_1303519 tptp.nat) (BOUND_VARIABLE_1303520 tptp.set_nat) (BOUND_VARIABLE_1303521 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_13057 BOUND_VARIABLE_1303519) BOUND_VARIABLE_1303520) BOUND_VARIABLE_1303521) (or (= BOUND_VARIABLE_1303519 BOUND_VARIABLE_1303521) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1303521) BOUND_VARIABLE_1303520)))))) (let ((_let_4761 (forall ((BOUND_VARIABLE_1303508 tptp.nat) (BOUND_VARIABLE_1303509 tptp.set_nat) (BOUND_VARIABLE_1303510 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_13058 BOUND_VARIABLE_1303508) BOUND_VARIABLE_1303509) BOUND_VARIABLE_1303510) (or (= BOUND_VARIABLE_1303508 BOUND_VARIABLE_1303510) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1303510) BOUND_VARIABLE_1303509)))))) (let ((_let_4762 (forall ((BOUND_VARIABLE_1303497 tptp.set_nat) (BOUND_VARIABLE_1303498 tptp.set_nat) (BOUND_VARIABLE_1303499 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1303499))) (= (ho_11054 (ho_11240 (ho_11343 k_13059 BOUND_VARIABLE_1303497) BOUND_VARIABLE_1303498) BOUND_VARIABLE_1303499) (and (ho_11191 _let_1 BOUND_VARIABLE_1303497) (ho_11191 _let_1 BOUND_VARIABLE_1303498))))))) (let ((_let_4763 (forall ((BOUND_VARIABLE_1303486 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1303487 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1303488 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_13060 BOUND_VARIABLE_1303486) BOUND_VARIABLE_1303487) BOUND_VARIABLE_1303488) (or (= BOUND_VARIABLE_1303486 BOUND_VARIABLE_1303488) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1303488) BOUND_VARIABLE_1303487)))))) (let ((_let_4764 (forall ((BOUND_VARIABLE_1303475 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1303476 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1303477 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_13061 BOUND_VARIABLE_1303475) BOUND_VARIABLE_1303476) BOUND_VARIABLE_1303477) (or (= BOUND_VARIABLE_1303475 BOUND_VARIABLE_1303477) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1303477) BOUND_VARIABLE_1303476)))))) (let ((_let_4765 (forall ((BOUND_VARIABLE_1303464 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1303465 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1303466 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1303466))) (= (ho_11184 (ho_11237 (ho_11365 k_13062 BOUND_VARIABLE_1303464) BOUND_VARIABLE_1303465) BOUND_VARIABLE_1303466) (and (ho_11070 _let_1 BOUND_VARIABLE_1303464) (ho_11070 _let_1 BOUND_VARIABLE_1303465))))))) (let ((_let_4766 (forall ((BOUND_VARIABLE_1303453 tptp.int) (BOUND_VARIABLE_1303454 tptp.set_int) (BOUND_VARIABLE_1303455 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_13063 BOUND_VARIABLE_1303453) BOUND_VARIABLE_1303454) BOUND_VARIABLE_1303455) (or (= BOUND_VARIABLE_1303453 BOUND_VARIABLE_1303455) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1303455) BOUND_VARIABLE_1303454)))))) (let ((_let_4767 (forall ((BOUND_VARIABLE_1303442 tptp.int) (BOUND_VARIABLE_1303443 tptp.set_int) (BOUND_VARIABLE_1303444 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_13064 BOUND_VARIABLE_1303442) BOUND_VARIABLE_1303443) BOUND_VARIABLE_1303444) (or (= BOUND_VARIABLE_1303442 BOUND_VARIABLE_1303444) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1303444) BOUND_VARIABLE_1303443)))))) (let ((_let_4768 (forall ((BOUND_VARIABLE_1303431 tptp.set_int) (BOUND_VARIABLE_1303432 tptp.set_int) (BOUND_VARIABLE_1303433 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1303433))) (= (ho_11094 (ho_11234 (ho_11339 k_13065 BOUND_VARIABLE_1303431) BOUND_VARIABLE_1303432) BOUND_VARIABLE_1303433) (and (ho_11180 _let_1 BOUND_VARIABLE_1303431) (ho_11180 _let_1 BOUND_VARIABLE_1303432))))))) (let ((_let_4769 (forall ((BOUND_VARIABLE_1303420 Bool) (BOUND_VARIABLE_1303421 tptp.set_o) (BOUND_VARIABLE_1303422 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_13066 BOUND_VARIABLE_1303420) BOUND_VARIABLE_1303421) BOUND_VARIABLE_1303422) (or (= BOUND_VARIABLE_1303420 BOUND_VARIABLE_1303422) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1303422) BOUND_VARIABLE_1303421)))))) (let ((_let_4770 (forall ((BOUND_VARIABLE_1303409 Bool) (BOUND_VARIABLE_1303410 tptp.set_o) (BOUND_VARIABLE_1303411 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_13067 BOUND_VARIABLE_1303409) BOUND_VARIABLE_1303410) BOUND_VARIABLE_1303411) (or (= BOUND_VARIABLE_1303409 BOUND_VARIABLE_1303411) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1303411) BOUND_VARIABLE_1303410)))))) (let ((_let_4771 (forall ((BOUND_VARIABLE_1303398 tptp.set_o) (BOUND_VARIABLE_1303399 tptp.set_o) (BOUND_VARIABLE_1303400 Bool)) (let ((_let_1 (ho_11198 k_11197 BOUND_VARIABLE_1303400))) (= (ho_11194 (ho_12571 (ho_12891 k_13068 BOUND_VARIABLE_1303398) BOUND_VARIABLE_1303399) BOUND_VARIABLE_1303400) (and (ho_11199 _let_1 BOUND_VARIABLE_1303398) (ho_11199 _let_1 BOUND_VARIABLE_1303399))))))) (let ((_let_4772 (forall ((BOUND_VARIABLE_1303387 tptp.nat) (BOUND_VARIABLE_1303388 tptp.set_nat) (BOUND_VARIABLE_1303389 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_13069 BOUND_VARIABLE_1303387) BOUND_VARIABLE_1303388) BOUND_VARIABLE_1303389) (or (= BOUND_VARIABLE_1303387 BOUND_VARIABLE_1303389) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1303389) BOUND_VARIABLE_1303388)))))) (let ((_let_4773 (forall ((BOUND_VARIABLE_1303376 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1303377 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1303378 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_13070 BOUND_VARIABLE_1303376) BOUND_VARIABLE_1303377) BOUND_VARIABLE_1303378) (or (= BOUND_VARIABLE_1303376 BOUND_VARIABLE_1303378) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1303378) BOUND_VARIABLE_1303377)))))) (let ((_let_4774 (forall ((BOUND_VARIABLE_1303365 tptp.int) (BOUND_VARIABLE_1303366 tptp.set_int) (BOUND_VARIABLE_1303367 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_13071 BOUND_VARIABLE_1303365) BOUND_VARIABLE_1303366) BOUND_VARIABLE_1303367) (or (= BOUND_VARIABLE_1303365 BOUND_VARIABLE_1303367) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1303367) BOUND_VARIABLE_1303366)))))) (let ((_let_4775 (forall ((BOUND_VARIABLE_1303354 tptp.set_nat) (BOUND_VARIABLE_1303355 tptp.set_set_nat) (BOUND_VARIABLE_1303356 tptp.set_nat)) (= (ho_11191 (ho_12650 (ho_12653 k_13072 BOUND_VARIABLE_1303354) BOUND_VARIABLE_1303355) BOUND_VARIABLE_1303356) (or (= BOUND_VARIABLE_1303354 BOUND_VARIABLE_1303356) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1303356) BOUND_VARIABLE_1303355)))))) (let ((_let_4776 (forall ((BOUND_VARIABLE_1303343 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1303344 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1303345 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 (ho_12658 k_13073 BOUND_VARIABLE_1303343) BOUND_VARIABLE_1303344) BOUND_VARIABLE_1303345) (or (= BOUND_VARIABLE_1303343 BOUND_VARIABLE_1303345) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1303345) BOUND_VARIABLE_1303344)))))) (let ((_let_4777 (forall ((BOUND_VARIABLE_1303332 Bool) (BOUND_VARIABLE_1303333 tptp.set_o) (BOUND_VARIABLE_1303334 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_13074 BOUND_VARIABLE_1303332) BOUND_VARIABLE_1303333) BOUND_VARIABLE_1303334) (or (= BOUND_VARIABLE_1303332 BOUND_VARIABLE_1303334) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1303334) BOUND_VARIABLE_1303333)))))) (let ((_let_4778 (forall ((BOUND_VARIABLE_1303321 tptp.nat) (BOUND_VARIABLE_1303322 tptp.set_nat) (BOUND_VARIABLE_1303323 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_13075 BOUND_VARIABLE_1303321) BOUND_VARIABLE_1303322) BOUND_VARIABLE_1303323) (or (= BOUND_VARIABLE_1303321 BOUND_VARIABLE_1303323) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1303323) BOUND_VARIABLE_1303322)))))) (let ((_let_4779 (forall ((BOUND_VARIABLE_1303310 tptp.set_nat) (BOUND_VARIABLE_1303311 tptp.set_nat) (BOUND_VARIABLE_1303312 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1303312))) (= (ho_11054 (ho_11240 (ho_11343 k_13076 BOUND_VARIABLE_1303310) BOUND_VARIABLE_1303311) BOUND_VARIABLE_1303312) (and (ho_11191 _let_1 BOUND_VARIABLE_1303310) (ho_11191 _let_1 BOUND_VARIABLE_1303311))))))) (let ((_let_4780 (forall ((BOUND_VARIABLE_1303299 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1303300 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1303301 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_13077 BOUND_VARIABLE_1303299) BOUND_VARIABLE_1303300) BOUND_VARIABLE_1303301) (or (= BOUND_VARIABLE_1303299 BOUND_VARIABLE_1303301) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1303301) BOUND_VARIABLE_1303300)))))) (let ((_let_4781 (forall ((BOUND_VARIABLE_1303288 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1303289 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1303290 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1303290))) (= (ho_11184 (ho_11237 (ho_11365 k_13078 BOUND_VARIABLE_1303288) BOUND_VARIABLE_1303289) BOUND_VARIABLE_1303290) (and (ho_11070 _let_1 BOUND_VARIABLE_1303288) (ho_11070 _let_1 BOUND_VARIABLE_1303289))))))) (let ((_let_4782 (forall ((BOUND_VARIABLE_1303277 tptp.int) (BOUND_VARIABLE_1303278 tptp.set_int) (BOUND_VARIABLE_1303279 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_13079 BOUND_VARIABLE_1303277) BOUND_VARIABLE_1303278) BOUND_VARIABLE_1303279) (or (= BOUND_VARIABLE_1303277 BOUND_VARIABLE_1303279) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1303279) BOUND_VARIABLE_1303278)))))) (let ((_let_4783 (forall ((BOUND_VARIABLE_1303266 tptp.set_int) (BOUND_VARIABLE_1303267 tptp.set_int) (BOUND_VARIABLE_1303268 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1303268))) (= (ho_11094 (ho_11234 (ho_11339 k_13080 BOUND_VARIABLE_1303266) BOUND_VARIABLE_1303267) BOUND_VARIABLE_1303268) (and (ho_11180 _let_1 BOUND_VARIABLE_1303266) (ho_11180 _let_1 BOUND_VARIABLE_1303267))))))) (let ((_let_4784 (forall ((BOUND_VARIABLE_1303255 tptp.set_nat) (BOUND_VARIABLE_1303256 tptp.set_set_nat) (BOUND_VARIABLE_1303257 tptp.set_nat)) (= (ho_11191 (ho_12650 (ho_12653 k_13081 BOUND_VARIABLE_1303255) BOUND_VARIABLE_1303256) BOUND_VARIABLE_1303257) (or (= BOUND_VARIABLE_1303255 BOUND_VARIABLE_1303257) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1303257) BOUND_VARIABLE_1303256)))))) (let ((_let_4785 (forall ((BOUND_VARIABLE_1303244 tptp.set_set_nat) (BOUND_VARIABLE_1303245 tptp.set_set_nat) (BOUND_VARIABLE_1303246 tptp.set_nat)) (let ((_let_1 (ho_11206 k_11205 BOUND_VARIABLE_1303246))) (= (ho_11191 (ho_12650 (ho_12883 k_13082 BOUND_VARIABLE_1303244) BOUND_VARIABLE_1303245) BOUND_VARIABLE_1303246) (and (ho_11207 _let_1 BOUND_VARIABLE_1303244) (ho_11207 _let_1 BOUND_VARIABLE_1303245))))))) (let ((_let_4786 (forall ((BOUND_VARIABLE_1303233 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1303234 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1303235 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 (ho_12658 k_13083 BOUND_VARIABLE_1303233) BOUND_VARIABLE_1303234) BOUND_VARIABLE_1303235) (or (= BOUND_VARIABLE_1303233 BOUND_VARIABLE_1303235) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1303235) BOUND_VARIABLE_1303234)))))) (let ((_let_4787 (forall ((BOUND_VARIABLE_1303222 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1303223 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1303224 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (ho_11215 k_11214 BOUND_VARIABLE_1303224))) (= (ho_11211 (ho_12655 (ho_12887 k_13084 BOUND_VARIABLE_1303222) BOUND_VARIABLE_1303223) BOUND_VARIABLE_1303224) (and (ho_11216 _let_1 BOUND_VARIABLE_1303222) (ho_11216 _let_1 BOUND_VARIABLE_1303223))))))) (let ((_let_4788 (forall ((BOUND_VARIABLE_1303211 Bool) (BOUND_VARIABLE_1303212 tptp.set_o) (BOUND_VARIABLE_1303213 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_13085 BOUND_VARIABLE_1303211) BOUND_VARIABLE_1303212) BOUND_VARIABLE_1303213) (or (= BOUND_VARIABLE_1303211 BOUND_VARIABLE_1303213) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1303213) BOUND_VARIABLE_1303212)))))) (let ((_let_4789 (forall ((BOUND_VARIABLE_1303200 tptp.set_o) (BOUND_VARIABLE_1303201 tptp.set_o) (BOUND_VARIABLE_1303202 Bool)) (let ((_let_1 (ho_11198 k_11197 BOUND_VARIABLE_1303202))) (= (ho_11194 (ho_12571 (ho_12891 k_13086 BOUND_VARIABLE_1303200) BOUND_VARIABLE_1303201) BOUND_VARIABLE_1303202) (and (ho_11199 _let_1 BOUND_VARIABLE_1303200) (ho_11199 _let_1 BOUND_VARIABLE_1303201))))))) (let ((_let_4790 (forall ((BOUND_VARIABLE_1303189 tptp.int) (BOUND_VARIABLE_1303190 tptp.set_int) (BOUND_VARIABLE_1303191 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_13087 BOUND_VARIABLE_1303189) BOUND_VARIABLE_1303190) BOUND_VARIABLE_1303191) (or (= BOUND_VARIABLE_1303189 BOUND_VARIABLE_1303191) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1303191) BOUND_VARIABLE_1303190)))))) (let ((_let_4791 (forall ((BOUND_VARIABLE_1303178 tptp.nat) (BOUND_VARIABLE_1303179 tptp.set_nat) (BOUND_VARIABLE_1303180 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_13088 BOUND_VARIABLE_1303178) BOUND_VARIABLE_1303179) BOUND_VARIABLE_1303180) (or (= BOUND_VARIABLE_1303178 BOUND_VARIABLE_1303180) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1303180) BOUND_VARIABLE_1303179)))))) (let ((_let_4792 (forall ((BOUND_VARIABLE_1303167 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1303168 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1303169 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_13089 BOUND_VARIABLE_1303167) BOUND_VARIABLE_1303168) BOUND_VARIABLE_1303169) (or (= BOUND_VARIABLE_1303167 BOUND_VARIABLE_1303169) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1303169) BOUND_VARIABLE_1303168)))))) (let ((_let_4793 (forall ((BOUND_VARIABLE_1303156 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1303157 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1303158 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11374 (ho_12630 k_13090 BOUND_VARIABLE_1303156) BOUND_VARIABLE_1303157) BOUND_VARIABLE_1303158) (or (= BOUND_VARIABLE_1303156 BOUND_VARIABLE_1303158) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1303158) BOUND_VARIABLE_1303157)))))) (let ((_let_4794 (forall ((BOUND_VARIABLE_1303145 tptp.int) (BOUND_VARIABLE_1303146 tptp.set_int) (BOUND_VARIABLE_1303147 tptp.int)) (= (ho_11094 (ho_11234 (ho_11233 k_13091 BOUND_VARIABLE_1303145) BOUND_VARIABLE_1303146) BOUND_VARIABLE_1303147) (or (= BOUND_VARIABLE_1303145 BOUND_VARIABLE_1303147) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1303147) BOUND_VARIABLE_1303146)))))) (let ((_let_4795 (forall ((BOUND_VARIABLE_1303134 tptp.nat) (BOUND_VARIABLE_1303135 tptp.set_nat) (BOUND_VARIABLE_1303136 tptp.nat)) (= (ho_11054 (ho_11240 (ho_11239 k_13092 BOUND_VARIABLE_1303134) BOUND_VARIABLE_1303135) BOUND_VARIABLE_1303136) (or (= BOUND_VARIABLE_1303134 BOUND_VARIABLE_1303136) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1303136) BOUND_VARIABLE_1303135)))))) (let ((_let_4796 (forall ((BOUND_VARIABLE_1303123 Bool) (BOUND_VARIABLE_1303124 tptp.set_o) (BOUND_VARIABLE_1303125 Bool)) (= (ho_11194 (ho_12571 (ho_12648 k_13093 BOUND_VARIABLE_1303123) BOUND_VARIABLE_1303124) BOUND_VARIABLE_1303125) (or (= BOUND_VARIABLE_1303123 BOUND_VARIABLE_1303125) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1303125) BOUND_VARIABLE_1303124)))))) (let ((_let_4797 (forall ((BOUND_VARIABLE_1303112 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1303113 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1303114 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 (ho_11236 k_13094 BOUND_VARIABLE_1303112) BOUND_VARIABLE_1303113) BOUND_VARIABLE_1303114) (or (= BOUND_VARIABLE_1303112 BOUND_VARIABLE_1303114) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1303114) BOUND_VARIABLE_1303113)))))) (let ((_let_4798 (forall ((BOUND_VARIABLE_1303101 tptp.produc3843707927480180839at_nat) (BOUND_VARIABLE_1303102 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1303103 tptp.produc3843707927480180839at_nat)) (= (ho_11263 (ho_11374 (ho_12630 k_13095 BOUND_VARIABLE_1303101) BOUND_VARIABLE_1303102) BOUND_VARIABLE_1303103) (or (= BOUND_VARIABLE_1303101 BOUND_VARIABLE_1303103) (ho_11260 (ho_11259 k_11258 BOUND_VARIABLE_1303103) BOUND_VARIABLE_1303102)))))) (let ((_let_4799 (forall ((BOUND_VARIABLE_1303087 tptp.int)) (let ((_let_1 (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (= (ho_11094 k_13096 BOUND_VARIABLE_1303087) (or (= BOUND_VARIABLE_1303087 (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 _let_1)) _let_1)) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1303087) (ho_11177 k_11176 k_11175)))))))) (let ((_let_4800 (forall ((BOUND_VARIABLE_1363338 |u_(-> tptp.a tptp.heap_Time_Heap_a)|) (BOUND_VARIABLE_1303075 tptp.a) (BOUND_VARIABLE_1303076 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1303077 tptp.nat)) (= (ho_11293 (ho_11292 (ho_11291 (ho_11290 k_13097 BOUND_VARIABLE_1363338) BOUND_VARIABLE_1303075) BOUND_VARIABLE_1303076) BOUND_VARIABLE_1303077) (ho_11299 (ho_11298 k_11297 BOUND_VARIABLE_1303077) (ho_11296 (ho_11295 k_11294 (ho_11288 BOUND_VARIABLE_1363338 BOUND_VARIABLE_1303075)) BOUND_VARIABLE_1303076)))))) (let ((_let_4801 (forall ((BOUND_VARIABLE_1363352 |u_(-> tptp.a tptp.heap_Time_Heap_a)|) (BOUND_VARIABLE_1303046 tptp.a) (BOUND_VARIABLE_1303047 tptp.produc6653097349344004940it_nat)) (= (ho_13100 (ho_13099 k_13098 (ho_11291 (ho_11290 k_11289 BOUND_VARIABLE_1363352) BOUND_VARIABLE_1303046)) BOUND_VARIABLE_1303047) (ho_13100 (ho_13103 (ho_13102 k_13101 BOUND_VARIABLE_1363352) BOUND_VARIABLE_1303046) BOUND_VARIABLE_1303047))))) (let ((_let_4802 (forall ((BOUND_VARIABLE_1363386 |u_(-> tptp.b tptp.heap_Time_Heap_a)|) (BOUND_VARIABLE_1303033 tptp.b) (BOUND_VARIABLE_1303034 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1303035 tptp.nat)) (= (ho_11293 (ho_11292 (ho_11303 (ho_11302 k_13104 BOUND_VARIABLE_1363386) BOUND_VARIABLE_1303033) BOUND_VARIABLE_1303034) BOUND_VARIABLE_1303035) (ho_11299 (ho_11298 k_11297 BOUND_VARIABLE_1303035) (ho_11296 (ho_11295 k_11294 (ho_11300 BOUND_VARIABLE_1363386 BOUND_VARIABLE_1303033)) BOUND_VARIABLE_1303034)))))) (let ((_let_4803 (forall ((BOUND_VARIABLE_1363400 |u_(-> tptp.b tptp.heap_Time_Heap_a)|) (BOUND_VARIABLE_1303004 tptp.b) (BOUND_VARIABLE_1303005 tptp.produc6653097349344004940it_nat)) (= (ho_13100 (ho_13099 k_13098 (ho_11303 (ho_11302 k_11301 BOUND_VARIABLE_1363400) BOUND_VARIABLE_1303004)) BOUND_VARIABLE_1303005) (ho_13100 (ho_13107 (ho_13106 k_13105 BOUND_VARIABLE_1363400) BOUND_VARIABLE_1303004) BOUND_VARIABLE_1303005))))) (let ((_let_4804 (forall ((BOUND_VARIABLE_1363426 |u_(-> tptp.a tptp.heap_Time_Heap_b)|) (BOUND_VARIABLE_1302991 tptp.a) (BOUND_VARIABLE_1302992 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1302993 tptp.nat)) (= (ho_11309 (ho_11308 (ho_11307 (ho_11306 k_13108 BOUND_VARIABLE_1363426) BOUND_VARIABLE_1302991) BOUND_VARIABLE_1302992) BOUND_VARIABLE_1302993) (ho_11315 (ho_11314 k_11313 BOUND_VARIABLE_1302993) (ho_11312 (ho_11311 k_11310 (ho_11304 BOUND_VARIABLE_1363426 BOUND_VARIABLE_1302991)) BOUND_VARIABLE_1302992)))))) (let ((_let_4805 (forall ((BOUND_VARIABLE_1363440 |u_(-> tptp.a tptp.heap_Time_Heap_b)|) (BOUND_VARIABLE_1302962 tptp.a) (BOUND_VARIABLE_1302963 tptp.produc6653097349344004940it_nat)) (= (ho_13111 (ho_13110 k_13109 (ho_11307 (ho_11306 k_11305 BOUND_VARIABLE_1363440) BOUND_VARIABLE_1302962)) BOUND_VARIABLE_1302963) (ho_13111 (ho_13114 (ho_13113 k_13112 BOUND_VARIABLE_1363440) BOUND_VARIABLE_1302962) BOUND_VARIABLE_1302963))))) (let ((_let_4806 (forall ((BOUND_VARIABLE_1363474 |u_(-> tptp.b tptp.heap_Time_Heap_b)|) (BOUND_VARIABLE_1302949 tptp.b) (BOUND_VARIABLE_1302950 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1302951 tptp.nat)) (= (ho_11309 (ho_11308 (ho_11319 (ho_11318 k_13115 BOUND_VARIABLE_1363474) BOUND_VARIABLE_1302949) BOUND_VARIABLE_1302950) BOUND_VARIABLE_1302951) (ho_11315 (ho_11314 k_11313 BOUND_VARIABLE_1302951) (ho_11312 (ho_11311 k_11310 (ho_11316 BOUND_VARIABLE_1363474 BOUND_VARIABLE_1302949)) BOUND_VARIABLE_1302950)))))) (let ((_let_4807 (forall ((BOUND_VARIABLE_1363488 |u_(-> tptp.b tptp.heap_Time_Heap_b)|) (BOUND_VARIABLE_1302920 tptp.b) (BOUND_VARIABLE_1302921 tptp.produc6653097349344004940it_nat)) (= (ho_13111 (ho_13110 k_13109 (ho_11319 (ho_11318 k_11317 BOUND_VARIABLE_1363488) BOUND_VARIABLE_1302920)) BOUND_VARIABLE_1302921) (ho_13111 (ho_13118 (ho_13117 k_13116 BOUND_VARIABLE_1363488) BOUND_VARIABLE_1302920) BOUND_VARIABLE_1302921))))) (let ((_let_4808 (forall ((BOUND_VARIABLE_1302910 tptp.nat) (BOUND_VARIABLE_1302911 tptp.nat)) (= (ho_11067 (ho_11066 k_13119 BOUND_VARIABLE_1302910) BOUND_VARIABLE_1302911) (ho_11067 (ho_11066 k_11065 (ho_11139 k_11138 BOUND_VARIABLE_1302910)) BOUND_VARIABLE_1302911))))) (let ((_let_4809 (forall ((BOUND_VARIABLE_1302881 tptp.num) (BOUND_VARIABLE_1302882 tptp.num) (BOUND_VARIABLE_1302883 tptp.nat)) (= (ho_11059 (ho_12273 k_12324 BOUND_VARIABLE_1302883) (ho_12218 k_12323 (ho_11054 (ho_11574 k_12322 (ho_11059 (ho_11058 k_11057 (ho_11056 (ho_12276 k_13120 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))) (ho_11061 k_11060 (ho_12475 k_12474 BOUND_VARIABLE_1302881)))) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_12475 k_12474 BOUND_VARIABLE_1302882))) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))))) BOUND_VARIABLE_1302883))) (ho_11056 (ho_13123 (ho_13122 k_13121 BOUND_VARIABLE_1302881) BOUND_VARIABLE_1302882) BOUND_VARIABLE_1302883))))) (let ((_let_4810 (forall ((BOUND_VARIABLE_1302846 tptp.num) (BOUND_VARIABLE_1302847 tptp.int) (BOUND_VARIABLE_1302848 tptp.int)) (let ((_let_1 (ho_11059 (ho_11058 k_11085 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))) BOUND_VARIABLE_1302847))) (let ((_let_2 (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (let ((_let_3 (ho_12475 k_12474 BOUND_VARIABLE_1302846))) (= (ho_11501 (ho_11526 (ho_11525 k_11524 (= BOUND_VARIABLE_1302848 (ho_11059 (ho_11058 k_11095 _let_3) BOUND_VARIABLE_1302848))) (ho_11521 (ho_11115 k_11520 (ho_11059 (ho_11058 k_11057 _let_1) _let_2)) (ho_11059 (ho_11058 k_11057 BOUND_VARIABLE_1302848) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 _let_3)) _let_2)))) (ho_11521 (ho_11115 k_11520 _let_1) BOUND_VARIABLE_1302848)) (ho_11521 (ho_11115 (ho_13125 k_13124 BOUND_VARIABLE_1302846) BOUND_VARIABLE_1302847) BOUND_VARIABLE_1302848)))))))) (let ((_let_4811 (forall ((BOUND_VARIABLE_1302811 tptp.num) (BOUND_VARIABLE_1302812 tptp.int) (BOUND_VARIABLE_1302813 tptp.int)) (let ((_let_1 (ho_11059 (ho_11058 k_11085 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))) BOUND_VARIABLE_1302812))) (let ((_let_2 (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (let ((_let_3 (ho_12475 k_12474 BOUND_VARIABLE_1302811))) (= (ho_11501 (ho_11526 (ho_11525 k_11524 (= BOUND_VARIABLE_1302813 (ho_11059 (ho_11058 k_11095 _let_3) BOUND_VARIABLE_1302813))) (ho_11521 (ho_11115 k_11520 (ho_11059 (ho_11058 k_11057 _let_1) _let_2)) (ho_11059 (ho_11058 k_11057 BOUND_VARIABLE_1302813) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 _let_3)) _let_2)))) (ho_11521 (ho_11115 k_11520 _let_1) BOUND_VARIABLE_1302813)) (ho_11521 (ho_11115 (ho_13125 k_13126 BOUND_VARIABLE_1302811) BOUND_VARIABLE_1302812) BOUND_VARIABLE_1302813)))))))) (let ((_let_4812 (forall ((BOUND_VARIABLE_1302762 tptp.num) (BOUND_VARIABLE_1302763 tptp.nat) (BOUND_VARIABLE_1302764 tptp.nat)) (let ((_let_1 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11085 (ho_11056 k_11055 (ho_11061 k_11060 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))))) (ho_11056 k_11055 BOUND_VARIABLE_1302763))))) (let ((_let_2 (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (= (ho_11441 (ho_13129 (ho_13128 k_13127 (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1302764 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_12475 k_12474 BOUND_VARIABLE_1302762)))) (ho_11056 k_11055 K3)))))))) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 _let_1)) _let_2))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1302764)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 (ho_11061 k_11060 (ho_12475 k_12474 BOUND_VARIABLE_1302762))))) _let_2))))) (ho_11067 (ho_11066 k_11065 _let_1) BOUND_VARIABLE_1302764)) (ho_11067 (ho_11066 (ho_13131 k_13130 BOUND_VARIABLE_1302762) BOUND_VARIABLE_1302763) BOUND_VARIABLE_1302764))))))) (let ((_let_4813 (forall ((BOUND_VARIABLE_1302713 tptp.num) (BOUND_VARIABLE_1302714 tptp.nat) (BOUND_VARIABLE_1302715 tptp.nat)) (let ((_let_1 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11085 (ho_11056 k_11055 (ho_11061 k_11060 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))))) (ho_11056 k_11055 BOUND_VARIABLE_1302714))))) (let ((_let_2 (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (= (ho_11441 (ho_13129 (ho_13128 k_13127 (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1302715 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_12475 k_12474 BOUND_VARIABLE_1302713)))) (ho_11056 k_11055 K3)))))))) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 _let_1)) _let_2))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1302715)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 (ho_11061 k_11060 (ho_12475 k_12474 BOUND_VARIABLE_1302713))))) _let_2))))) (ho_11067 (ho_11066 k_11065 _let_1) BOUND_VARIABLE_1302715)) (ho_11067 (ho_11066 (ho_13131 k_13132 BOUND_VARIABLE_1302713) BOUND_VARIABLE_1302714) BOUND_VARIABLE_1302715))))))) (let ((_let_4814 (forall ((BOUND_VARIABLE_1302698 tptp.int) (BOUND_VARIABLE_1302699 tptp.nat) (BOUND_VARIABLE_1302700 tptp.nat)) (= (ho_11056 (ho_12325 (ho_12402 k_13133 BOUND_VARIABLE_1302698) BOUND_VARIABLE_1302699) BOUND_VARIABLE_1302700) (ho_11059 (ho_12273 k_12324 BOUND_VARIABLE_1302700) (ho_12218 k_12323 (ho_11054 (ho_11574 k_12322 (ho_11059 (ho_11058 k_11057 BOUND_VARIABLE_1302698) (ho_11056 (ho_12276 k_13120 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))) BOUND_VARIABLE_1302699))) BOUND_VARIABLE_1302700))))))) (let ((_let_4815 (forall ((BOUND_VARIABLE_1302687 tptp.int) (BOUND_VARIABLE_1302688 tptp.nat)) (= (ho_11056 (ho_12276 k_13134 BOUND_VARIABLE_1302687) BOUND_VARIABLE_1302688) (ho_11059 (ho_12273 k_12324 BOUND_VARIABLE_1302688) (ho_12218 k_12323 (ho_11054 (ho_11574 k_12322 BOUND_VARIABLE_1302687) BOUND_VARIABLE_1302688))))))) (let ((_let_4816 (forall ((BOUND_VARIABLE_1302676 tptp.int) (BOUND_VARIABLE_1302677 tptp.nat)) (= (ho_11056 (ho_12276 k_13135 BOUND_VARIABLE_1302676) BOUND_VARIABLE_1302677) (ho_11059 (ho_12273 k_12324 BOUND_VARIABLE_1302677) (ho_12218 k_12323 (ho_11054 (ho_11574 k_12322 BOUND_VARIABLE_1302676) BOUND_VARIABLE_1302677))))))) (let ((_let_4817 (forall ((BOUND_VARIABLE_1302661 tptp.int) (BOUND_VARIABLE_1302662 tptp.nat) (BOUND_VARIABLE_1302663 tptp.nat)) (= (ho_11056 (ho_12325 (ho_12402 k_13136 BOUND_VARIABLE_1302661) BOUND_VARIABLE_1302662) BOUND_VARIABLE_1302663) (ho_11059 (ho_12273 k_12324 BOUND_VARIABLE_1302663) (ho_12218 k_12323 (ho_11054 (ho_11574 k_12322 (ho_11059 (ho_11058 k_11057 BOUND_VARIABLE_1302661) (ho_11056 (ho_12276 k_13120 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))) BOUND_VARIABLE_1302662))) BOUND_VARIABLE_1302663))))))) (let ((_let_4818 (forall ((BOUND_VARIABLE_1302653 tptp.int) (BOUND_VARIABLE_1302654 tptp.int)) (= (ho_11094 (ho_11093 k_13137 BOUND_VARIABLE_1302653) BOUND_VARIABLE_1302654) (ho_11094 (ho_11093 k_11771 BOUND_VARIABLE_1302654) BOUND_VARIABLE_1302653))))) (let ((_let_4819 (forall ((BOUND_VARIABLE_1302645 tptp.int) (BOUND_VARIABLE_1302646 tptp.int)) (= (ho_11094 (ho_11093 k_13138 BOUND_VARIABLE_1302645) BOUND_VARIABLE_1302646) (ho_11094 (ho_11093 k_11771 BOUND_VARIABLE_1302646) BOUND_VARIABLE_1302645))))) (let ((_let_4820 (forall ((BOUND_VARIABLE_1302637 tptp.int) (BOUND_VARIABLE_1302638 tptp.int)) (= (ho_11094 (ho_11093 k_13139 BOUND_VARIABLE_1302637) BOUND_VARIABLE_1302638) (ho_11094 (ho_11093 k_11771 BOUND_VARIABLE_1302638) BOUND_VARIABLE_1302637))))) (let ((_let_4821 (forall ((BOUND_VARIABLE_1302629 tptp.int) (BOUND_VARIABLE_1302630 tptp.int)) (= (ho_11094 (ho_11093 k_13140 BOUND_VARIABLE_1302629) BOUND_VARIABLE_1302630) (ho_11094 (ho_11093 k_11771 BOUND_VARIABLE_1302630) BOUND_VARIABLE_1302629))))) (let ((_let_4822 (forall ((BOUND_VARIABLE_1302621 tptp.nat) (BOUND_VARIABLE_1302622 tptp.nat)) (= (ho_11054 (ho_11053 k_13141 BOUND_VARIABLE_1302621) BOUND_VARIABLE_1302622) (ho_11054 (ho_11053 k_11435 BOUND_VARIABLE_1302622) BOUND_VARIABLE_1302621))))) (let ((_let_4823 (forall ((BOUND_VARIABLE_1302613 tptp.nat) (BOUND_VARIABLE_1302614 tptp.nat)) (= (ho_11054 (ho_11053 k_13142 BOUND_VARIABLE_1302613) BOUND_VARIABLE_1302614) (ho_11054 (ho_11053 k_11435 BOUND_VARIABLE_1302614) BOUND_VARIABLE_1302613))))) (let ((_let_4824 (forall ((BOUND_VARIABLE_1302605 tptp.int) (BOUND_VARIABLE_1302606 tptp.int)) (= (ho_11094 (ho_11093 k_13143 BOUND_VARIABLE_1302605) BOUND_VARIABLE_1302606) (ho_11094 (ho_11093 k_11771 BOUND_VARIABLE_1302606) BOUND_VARIABLE_1302605))))) (let ((_let_4825 (forall ((BOUND_VARIABLE_1302597 tptp.int) (BOUND_VARIABLE_1302598 tptp.int)) (= (ho_11094 (ho_11093 k_13144 BOUND_VARIABLE_1302597) BOUND_VARIABLE_1302598) (ho_11094 (ho_11093 k_11771 BOUND_VARIABLE_1302598) BOUND_VARIABLE_1302597))))) (let ((_let_4826 (forall ((BOUND_VARIABLE_1302589 tptp.nat) (BOUND_VARIABLE_1302590 tptp.nat)) (= (ho_11054 (ho_11053 k_13145 BOUND_VARIABLE_1302589) BOUND_VARIABLE_1302590) (ho_11054 (ho_11053 k_11435 BOUND_VARIABLE_1302590) BOUND_VARIABLE_1302589))))) (let ((_let_4827 (forall ((BOUND_VARIABLE_1302581 tptp.nat) (BOUND_VARIABLE_1302582 tptp.nat)) (= (ho_11054 (ho_11053 k_13146 BOUND_VARIABLE_1302581) BOUND_VARIABLE_1302582) (ho_11054 (ho_11053 k_11435 BOUND_VARIABLE_1302582) BOUND_VARIABLE_1302581))))) (let ((_let_4828 (forall ((BOUND_VARIABLE_1363853 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (BOUND_VARIABLE_1302571 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302572 tptp.nat) (BOUND_VARIABLE_1302573 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11433 (ho_13149 k_13148 BOUND_VARIABLE_1363853) BOUND_VARIABLE_1302571) BOUND_VARIABLE_1302572) BOUND_VARIABLE_1302573) (ho_11184 (ho_13150 (ho_13147 BOUND_VARIABLE_1363853 BOUND_VARIABLE_1302572) BOUND_VARIABLE_1302573) BOUND_VARIABLE_1302571))))) (let ((_let_4829 (forall ((BOUND_VARIABLE_1363879 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (BOUND_VARIABLE_1302560 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302561 tptp.nat) (BOUND_VARIABLE_1302562 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11443 (ho_13153 k_13152 BOUND_VARIABLE_1363879) BOUND_VARIABLE_1302560) BOUND_VARIABLE_1302561) BOUND_VARIABLE_1302562) (ho_11441 (ho_13154 (ho_13151 BOUND_VARIABLE_1363879 BOUND_VARIABLE_1302561) BOUND_VARIABLE_1302562) BOUND_VARIABLE_1302560))))) (let ((_let_4830 (forall ((BOUND_VARIABLE_1363904 |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (BOUND_VARIABLE_1302548 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302549 tptp.nat) (BOUND_VARIABLE_1302550 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11433 (ho_13156 k_13155 BOUND_VARIABLE_1363904) BOUND_VARIABLE_1302548) BOUND_VARIABLE_1302549) BOUND_VARIABLE_1302550) (ho_11184 (ho_11188 BOUND_VARIABLE_1363904 (ho_11067 (ho_11066 k_11065 BOUND_VARIABLE_1302549) BOUND_VARIABLE_1302550)) BOUND_VARIABLE_1302548))))) (let ((_let_4831 (forall ((BOUND_VARIABLE_1363925 |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (BOUND_VARIABLE_1302536 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302537 tptp.nat) (BOUND_VARIABLE_1302538 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11443 (ho_13158 k_13157 BOUND_VARIABLE_1363925) BOUND_VARIABLE_1302536) BOUND_VARIABLE_1302537) BOUND_VARIABLE_1302538) (ho_11441 (ho_13129 BOUND_VARIABLE_1363925 (ho_11067 (ho_11066 k_11065 BOUND_VARIABLE_1302537) BOUND_VARIABLE_1302538)) BOUND_VARIABLE_1302536))))) (let ((_let_4832 (forall ((BOUND_VARIABLE_1363946 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (BOUND_VARIABLE_1302525 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302526 tptp.nat) (BOUND_VARIABLE_1302527 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11433 (ho_13149 k_13159 BOUND_VARIABLE_1363946) BOUND_VARIABLE_1302525) BOUND_VARIABLE_1302526) BOUND_VARIABLE_1302527) (ho_11184 (ho_13150 (ho_13147 BOUND_VARIABLE_1363946 BOUND_VARIABLE_1302526) BOUND_VARIABLE_1302527) BOUND_VARIABLE_1302525))))) (let ((_let_4833 (forall ((BOUND_VARIABLE_1363962 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (BOUND_VARIABLE_1302514 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302515 tptp.nat) (BOUND_VARIABLE_1302516 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11443 (ho_13153 k_13160 BOUND_VARIABLE_1363962) BOUND_VARIABLE_1302514) BOUND_VARIABLE_1302515) BOUND_VARIABLE_1302516) (ho_11441 (ho_13154 (ho_13151 BOUND_VARIABLE_1363962 BOUND_VARIABLE_1302515) BOUND_VARIABLE_1302516) BOUND_VARIABLE_1302514))))) (let ((_let_4834 (forall ((BOUND_VARIABLE_1363978 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (BOUND_VARIABLE_1302503 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302504 tptp.nat) (BOUND_VARIABLE_1302505 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11433 (ho_13149 k_13161 BOUND_VARIABLE_1363978) BOUND_VARIABLE_1302503) BOUND_VARIABLE_1302504) BOUND_VARIABLE_1302505) (ho_11184 (ho_13150 (ho_13147 BOUND_VARIABLE_1363978 BOUND_VARIABLE_1302504) BOUND_VARIABLE_1302505) BOUND_VARIABLE_1302503))))) (let ((_let_4835 (forall ((BOUND_VARIABLE_1363994 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (BOUND_VARIABLE_1302492 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302493 tptp.nat) (BOUND_VARIABLE_1302494 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11433 (ho_13149 k_13162 BOUND_VARIABLE_1363994) BOUND_VARIABLE_1302492) BOUND_VARIABLE_1302493) BOUND_VARIABLE_1302494) (ho_11184 (ho_13150 (ho_13147 BOUND_VARIABLE_1363994 BOUND_VARIABLE_1302493) BOUND_VARIABLE_1302494) BOUND_VARIABLE_1302492))))) (let ((_let_4836 (forall ((BOUND_VARIABLE_1364010 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (BOUND_VARIABLE_1302481 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302482 tptp.nat) (BOUND_VARIABLE_1302483 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11443 (ho_13153 k_13163 BOUND_VARIABLE_1364010) BOUND_VARIABLE_1302481) BOUND_VARIABLE_1302482) BOUND_VARIABLE_1302483) (ho_11441 (ho_13154 (ho_13151 BOUND_VARIABLE_1364010 BOUND_VARIABLE_1302482) BOUND_VARIABLE_1302483) BOUND_VARIABLE_1302481))))) (let ((_let_4837 (forall ((BOUND_VARIABLE_1364026 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (BOUND_VARIABLE_1302470 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302471 tptp.nat) (BOUND_VARIABLE_1302472 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11443 (ho_13153 k_13164 BOUND_VARIABLE_1364026) BOUND_VARIABLE_1302470) BOUND_VARIABLE_1302471) BOUND_VARIABLE_1302472) (ho_11441 (ho_13154 (ho_13151 BOUND_VARIABLE_1364026 BOUND_VARIABLE_1302471) BOUND_VARIABLE_1302472) BOUND_VARIABLE_1302470))))) (let ((_let_4838 (forall ((BOUND_VARIABLE_1364042 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (BOUND_VARIABLE_1302459 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302460 tptp.nat) (BOUND_VARIABLE_1302461 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11433 (ho_13149 k_13165 BOUND_VARIABLE_1364042) BOUND_VARIABLE_1302459) BOUND_VARIABLE_1302460) BOUND_VARIABLE_1302461) (ho_11184 (ho_13150 (ho_13147 BOUND_VARIABLE_1364042 BOUND_VARIABLE_1302460) BOUND_VARIABLE_1302461) BOUND_VARIABLE_1302459))))) (let ((_let_4839 (forall ((BOUND_VARIABLE_1364058 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (BOUND_VARIABLE_1302448 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302449 tptp.nat) (BOUND_VARIABLE_1302450 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11443 (ho_13153 k_13166 BOUND_VARIABLE_1364058) BOUND_VARIABLE_1302448) BOUND_VARIABLE_1302449) BOUND_VARIABLE_1302450) (ho_11441 (ho_13154 (ho_13151 BOUND_VARIABLE_1364058 BOUND_VARIABLE_1302449) BOUND_VARIABLE_1302450) BOUND_VARIABLE_1302448))))) (let ((_let_4840 (forall ((BOUND_VARIABLE_1302436 tptp.nat) (BOUND_VARIABLE_1302437 tptp.nat)) (= (ho_11139 (ho_11479 k_13167 BOUND_VARIABLE_1302436) BOUND_VARIABLE_1302437) (ho_11139 (ho_11479 k_13170 BOUND_VARIABLE_1302437) (ho_12199 k_13169 (ho_11054 (ho_11053 k_13168 BOUND_VARIABLE_1302436) BOUND_VARIABLE_1302437))))))) (let ((_let_4841 (forall ((BOUND_VARIABLE_1302425 tptp.nat) (BOUND_VARIABLE_1302426 tptp.nat)) (= (ho_11139 (ho_11479 k_13171 BOUND_VARIABLE_1302425) BOUND_VARIABLE_1302426) (ho_11139 (ho_11479 k_13170 BOUND_VARIABLE_1302426) (ho_12199 k_13169 (ho_11054 (ho_11053 k_13168 BOUND_VARIABLE_1302425) BOUND_VARIABLE_1302426))))))) (let ((_let_4842 (forall ((BOUND_VARIABLE_1302414 tptp.int) (BOUND_VARIABLE_1302415 tptp.nat)) (= (ho_11056 (ho_12276 k_13172 BOUND_VARIABLE_1302414) BOUND_VARIABLE_1302415) (ho_11059 (ho_12273 k_12324 BOUND_VARIABLE_1302415) (ho_12218 k_12323 (ho_11054 (ho_11574 k_12322 BOUND_VARIABLE_1302414) BOUND_VARIABLE_1302415))))))) (let ((_let_4843 (forall ((BOUND_VARIABLE_1302403 tptp.int) (BOUND_VARIABLE_1302404 tptp.nat)) (= (ho_11056 (ho_12276 k_13173 BOUND_VARIABLE_1302403) BOUND_VARIABLE_1302404) (ho_11059 (ho_12273 k_12324 BOUND_VARIABLE_1302404) (ho_12218 k_12323 (ho_11054 (ho_11574 k_12322 BOUND_VARIABLE_1302403) BOUND_VARIABLE_1302404))))))) (let ((_let_4844 (forall ((BOUND_VARIABLE_1364125 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (BOUND_VARIABLE_1302393 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302394 tptp.nat) (BOUND_VARIABLE_1302395 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11433 (ho_13149 k_13174 BOUND_VARIABLE_1364125) BOUND_VARIABLE_1302393) BOUND_VARIABLE_1302394) BOUND_VARIABLE_1302395) (ho_11184 (ho_13150 (ho_13147 BOUND_VARIABLE_1364125 BOUND_VARIABLE_1302394) BOUND_VARIABLE_1302395) BOUND_VARIABLE_1302393))))) (let ((_let_4845 (forall ((BOUND_VARIABLE_1364144 |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.product_prod_nat_nat Bool)|) (BOUND_VARIABLE_1364142 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (BOUND_VARIABLE_1302381 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302382 tptp.nat) (BOUND_VARIABLE_1302383 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11433 (ho_13149 (ho_13177 k_13176 BOUND_VARIABLE_1364144) BOUND_VARIABLE_1364142) BOUND_VARIABLE_1302381) BOUND_VARIABLE_1302382) BOUND_VARIABLE_1302383) (ho_11184 (ho_13175 BOUND_VARIABLE_1364144 (ho_13150 (ho_13147 BOUND_VARIABLE_1364142 BOUND_VARIABLE_1302382) BOUND_VARIABLE_1302383)) BOUND_VARIABLE_1302381))))) (let ((_let_4846 (forall ((BOUND_VARIABLE_1364168 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (BOUND_VARIABLE_1302369 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302370 tptp.nat) (BOUND_VARIABLE_1302371 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11433 (ho_13149 k_13178 BOUND_VARIABLE_1364168) BOUND_VARIABLE_1302369) BOUND_VARIABLE_1302370) BOUND_VARIABLE_1302371) (ho_11184 (ho_13150 (ho_13147 BOUND_VARIABLE_1364168 BOUND_VARIABLE_1302370) BOUND_VARIABLE_1302371) BOUND_VARIABLE_1302369))))) (let ((_let_4847 (forall ((BOUND_VARIABLE_1364184 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (BOUND_VARIABLE_1302358 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302359 tptp.nat) (BOUND_VARIABLE_1302360 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11433 (ho_13149 k_13179 BOUND_VARIABLE_1364184) BOUND_VARIABLE_1302358) BOUND_VARIABLE_1302359) BOUND_VARIABLE_1302360) (ho_11184 (ho_13150 (ho_13147 BOUND_VARIABLE_1364184 BOUND_VARIABLE_1302359) BOUND_VARIABLE_1302360) BOUND_VARIABLE_1302358))))) (let ((_let_4848 (forall ((BOUND_VARIABLE_1364200 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (BOUND_VARIABLE_1302347 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302348 tptp.nat) (BOUND_VARIABLE_1302349 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11443 (ho_13153 k_13180 BOUND_VARIABLE_1364200) BOUND_VARIABLE_1302347) BOUND_VARIABLE_1302348) BOUND_VARIABLE_1302349) (ho_11441 (ho_13154 (ho_13151 BOUND_VARIABLE_1364200 BOUND_VARIABLE_1302348) BOUND_VARIABLE_1302349) BOUND_VARIABLE_1302347))))) (let ((_let_4849 (forall ((BOUND_VARIABLE_1364216 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (BOUND_VARIABLE_1302336 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302337 tptp.nat) (BOUND_VARIABLE_1302338 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11443 (ho_13153 k_13181 BOUND_VARIABLE_1364216) BOUND_VARIABLE_1302336) BOUND_VARIABLE_1302337) BOUND_VARIABLE_1302338) (ho_11441 (ho_13154 (ho_13151 BOUND_VARIABLE_1364216 BOUND_VARIABLE_1302337) BOUND_VARIABLE_1302338) BOUND_VARIABLE_1302336))))) (let ((_let_4850 (forall ((BOUND_VARIABLE_1364232 |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|) (BOUND_VARIABLE_1302324 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302325 tptp.nat) (BOUND_VARIABLE_1302326 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11433 (ho_13156 k_13182 BOUND_VARIABLE_1364232) BOUND_VARIABLE_1302324) BOUND_VARIABLE_1302325) BOUND_VARIABLE_1302326) (ho_11184 (ho_13150 (ho_13147 (ho_13184 k_13183 BOUND_VARIABLE_1364232) BOUND_VARIABLE_1302325) BOUND_VARIABLE_1302326) BOUND_VARIABLE_1302324))))) (let ((_let_4851 (forall ((BOUND_VARIABLE_1364254 |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (BOUND_VARIABLE_1302312 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302313 tptp.nat) (BOUND_VARIABLE_1302314 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11443 (ho_13158 k_13185 BOUND_VARIABLE_1364254) BOUND_VARIABLE_1302312) BOUND_VARIABLE_1302313) BOUND_VARIABLE_1302314) (ho_11441 (ho_13154 (ho_13151 (ho_13187 k_13186 BOUND_VARIABLE_1364254) BOUND_VARIABLE_1302313) BOUND_VARIABLE_1302314) BOUND_VARIABLE_1302312))))) (let ((_let_4852 (forall ((BOUND_VARIABLE_1364276 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (BOUND_VARIABLE_1302301 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302302 tptp.nat) (BOUND_VARIABLE_1302303 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11433 (ho_13149 k_13188 BOUND_VARIABLE_1364276) BOUND_VARIABLE_1302301) BOUND_VARIABLE_1302302) BOUND_VARIABLE_1302303) (ho_11184 (ho_13150 (ho_13147 BOUND_VARIABLE_1364276 BOUND_VARIABLE_1302302) BOUND_VARIABLE_1302303) BOUND_VARIABLE_1302301))))) (let ((_let_4853 (forall ((BOUND_VARIABLE_1364292 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (BOUND_VARIABLE_1302290 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302291 tptp.nat) (BOUND_VARIABLE_1302292 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11443 (ho_13153 k_13189 BOUND_VARIABLE_1364292) BOUND_VARIABLE_1302290) BOUND_VARIABLE_1302291) BOUND_VARIABLE_1302292) (ho_11441 (ho_13154 (ho_13151 BOUND_VARIABLE_1364292 BOUND_VARIABLE_1302291) BOUND_VARIABLE_1302292) BOUND_VARIABLE_1302290))))) (let ((_let_4854 (forall ((BOUND_VARIABLE_1364308 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)|) (BOUND_VARIABLE_1302279 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302280 tptp.nat) (BOUND_VARIABLE_1302281 tptp.nat)) (= (ho_11054 (ho_11053 (ho_11433 (ho_13149 k_13190 BOUND_VARIABLE_1364308) BOUND_VARIABLE_1302279) BOUND_VARIABLE_1302280) BOUND_VARIABLE_1302281) (ho_11184 (ho_13150 (ho_13147 BOUND_VARIABLE_1364308 BOUND_VARIABLE_1302280) BOUND_VARIABLE_1302281) BOUND_VARIABLE_1302279))))) (let ((_let_4855 (forall ((BOUND_VARIABLE_1364324 |u_(-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)|) (BOUND_VARIABLE_1302268 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1302269 tptp.nat) (BOUND_VARIABLE_1302270 tptp.nat)) (= (ho_11067 (ho_11066 (ho_11443 (ho_13153 k_13191 BOUND_VARIABLE_1364324) BOUND_VARIABLE_1302268) BOUND_VARIABLE_1302269) BOUND_VARIABLE_1302270) (ho_11441 (ho_13154 (ho_13151 BOUND_VARIABLE_1364324 BOUND_VARIABLE_1302269) BOUND_VARIABLE_1302270) BOUND_VARIABLE_1302268))))) (let ((_let_4856 (forall ((BOUND_VARIABLE_1302256 tptp.nat) (BOUND_VARIABLE_1302257 tptp.nat)) (= (ho_11139 (ho_11479 k_13192 BOUND_VARIABLE_1302256) BOUND_VARIABLE_1302257) (ho_11139 (ho_11479 k_13170 BOUND_VARIABLE_1302257) (ho_12199 k_13169 (ho_11054 (ho_11053 k_13168 BOUND_VARIABLE_1302256) BOUND_VARIABLE_1302257))))))) (let ((_let_4857 (forall ((BOUND_VARIABLE_1302241 tptp.nat) (BOUND_VARIABLE_1302242 tptp.nat)) (= (ho_11139 (ho_11479 k_13193 BOUND_VARIABLE_1302241) BOUND_VARIABLE_1302242) (ho_11139 (ho_11479 k_13170 BOUND_VARIABLE_1302242) (ho_12199 k_13169 (ho_11054 (ho_11053 k_13168 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11523 (ho_11056 k_11055 BOUND_VARIABLE_1302241)) (ho_11056 k_11055 (ho_11061 k_11060 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))))))) BOUND_VARIABLE_1302242))))))) (let ((_let_4858 (forall ((BOUND_VARIABLE_1302230 tptp.int) (BOUND_VARIABLE_1302231 tptp.nat)) (= (ho_11056 (ho_12276 k_13194 BOUND_VARIABLE_1302230) BOUND_VARIABLE_1302231) (ho_11059 (ho_12273 k_12324 BOUND_VARIABLE_1302231) (ho_12218 k_12323 (ho_11054 (ho_11574 k_12322 BOUND_VARIABLE_1302230) BOUND_VARIABLE_1302231))))))) (let ((_let_4859 (forall ((BOUND_VARIABLE_1302217 tptp.int) (BOUND_VARIABLE_1302218 tptp.nat)) (= (ho_11056 (ho_12276 k_13195 BOUND_VARIABLE_1302217) BOUND_VARIABLE_1302218) (ho_11059 (ho_12273 k_12324 BOUND_VARIABLE_1302218) (ho_12218 k_12323 (ho_11054 (ho_11574 k_12322 (ho_11059 (ho_11058 k_11523 BOUND_VARIABLE_1302217) (ho_12475 k_12474 (ho_11030 k_11029 tptp.one)))) BOUND_VARIABLE_1302218))))))) (let ((_let_4860 (forall ((BOUND_VARIABLE_1302206 tptp.code_integer) (BOUND_VARIABLE_1302207 tptp.nat)) (= (ho_11669 (ho_12441 k_13196 BOUND_VARIABLE_1302206) BOUND_VARIABLE_1302207) (ho_12130 (ho_12439 k_13200 BOUND_VARIABLE_1302207) (ho_13199 k_13198 (ho_11054 (ho_11551 k_13197 BOUND_VARIABLE_1302206) BOUND_VARIABLE_1302207))))))) (let ((_let_4861 (forall ((BOUND_VARIABLE_1302193 tptp.code_integer) (BOUND_VARIABLE_1302194 tptp.nat)) (= (ho_11669 (ho_12441 k_13201 BOUND_VARIABLE_1302193) BOUND_VARIABLE_1302194) (ho_12130 (ho_12439 k_13200 BOUND_VARIABLE_1302194) (ho_13199 k_13198 (ho_11054 (ho_11551 k_13197 (ho_12130 (ho_12129 k_13202 BOUND_VARIABLE_1302193) (ho_12560 k_12559 (ho_11030 k_11029 tptp.one)))) BOUND_VARIABLE_1302194))))))) (let ((_let_4862 (forall ((BOUND_VARIABLE_1302156 tptp.num) (BOUND_VARIABLE_1302157 tptp.code_integer) (BOUND_VARIABLE_1302158 tptp.code_integer)) (let ((_let_1 (ho_12130 (ho_12129 k_12128 (ho_12560 k_12559 (ho_11030 k_11029 tptp.one))) BOUND_VARIABLE_1302157))) (let ((_let_2 (ho_11669 k_11668 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (let ((_let_3 (ho_12560 k_12559 BOUND_VARIABLE_1302156))) (let ((_let_4 (ho_12161 (ho_12160 (ho_12159 k_12158 k_12153) (ho_12157 (ho_12156 k_12155 k_12153) k_12152)) k_11057))) (let ((_let_5 (ho_12154 k_12153 BOUND_VARIABLE_1302158))) (= (ho_12395 (ho_12394 (ho_12393 k_12392 (= _let_5 (ho_11059 (ho_11058 k_11095 (ho_12154 k_12153 _let_3)) _let_5))) (ho_12391 (ho_12390 k_12389 (ho_12130 (ho_12129 _let_4 _let_1) _let_2)) (ho_12130 (ho_12129 _let_4 BOUND_VARIABLE_1302158) (ho_12130 (ho_12129 _let_4 (ho_12130 k_12386 _let_3)) _let_2)))) (ho_12391 (ho_12390 k_12389 _let_1) BOUND_VARIABLE_1302158)) (ho_12391 (ho_12390 (ho_12591 k_13203 BOUND_VARIABLE_1302156) BOUND_VARIABLE_1302157) BOUND_VARIABLE_1302158)))))))))) (let ((_let_4863 (forall ((BOUND_VARIABLE_1302121 tptp.num) (BOUND_VARIABLE_1302122 tptp.int) (BOUND_VARIABLE_1302123 tptp.int)) (let ((_let_1 (ho_11059 (ho_11058 k_11085 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))) BOUND_VARIABLE_1302122))) (let ((_let_2 (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (let ((_let_3 (ho_12475 k_12474 BOUND_VARIABLE_1302121))) (= (ho_11501 (ho_11526 (ho_11525 k_11524 (= BOUND_VARIABLE_1302123 (ho_11059 (ho_11058 k_11095 _let_3) BOUND_VARIABLE_1302123))) (ho_11521 (ho_11115 k_11520 (ho_11059 (ho_11058 k_11057 _let_1) _let_2)) (ho_11059 (ho_11058 k_11057 BOUND_VARIABLE_1302123) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 _let_3)) _let_2)))) (ho_11521 (ho_11115 k_11520 _let_1) BOUND_VARIABLE_1302123)) (ho_11521 (ho_11115 (ho_13125 k_13204 BOUND_VARIABLE_1302121) BOUND_VARIABLE_1302122) BOUND_VARIABLE_1302123)))))))) (let ((_let_4864 (forall ((BOUND_VARIABLE_1302072 tptp.num) (BOUND_VARIABLE_1302073 tptp.nat) (BOUND_VARIABLE_1302074 tptp.nat)) (let ((_let_1 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11085 (ho_11056 k_11055 (ho_11061 k_11060 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))))) (ho_11056 k_11055 BOUND_VARIABLE_1302073))))) (let ((_let_2 (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (= (ho_11441 (ho_13129 (ho_13128 k_13127 (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1302074 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_11061 k_11060 (ho_12475 k_12474 BOUND_VARIABLE_1302072)))) (ho_11056 k_11055 K3)))))))) (ho_11067 (ho_11066 k_11065 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 _let_1)) _let_2))) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1302074)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 (ho_11061 k_11060 (ho_12475 k_12474 BOUND_VARIABLE_1302072))))) _let_2))))) (ho_11067 (ho_11066 k_11065 _let_1) BOUND_VARIABLE_1302074)) (ho_11067 (ho_11066 (ho_13131 k_13205 BOUND_VARIABLE_1302072) BOUND_VARIABLE_1302073) BOUND_VARIABLE_1302074))))))) (let ((_let_4865 (forall ((BOUND_VARIABLE_1302061 tptp.int) (BOUND_VARIABLE_1302062 tptp.nat)) (= (ho_11056 (ho_12276 k_13206 BOUND_VARIABLE_1302061) BOUND_VARIABLE_1302062) (ho_11059 (ho_12273 k_12324 BOUND_VARIABLE_1302062) (ho_12218 k_12323 (ho_11054 (ho_11574 k_12322 BOUND_VARIABLE_1302061) BOUND_VARIABLE_1302062))))))) (let ((_let_4866 (forall ((BOUND_VARIABLE_1302039 tptp.nat) (BOUND_VARIABLE_1302040 tptp.nat) (BOUND_VARIABLE_1302041 tptp.set_nat)) (= (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1302041) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))) BOUND_VARIABLE_1302039))) (= BOUND_VARIABLE_1302040 (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1302041))) (ho_11191 (ho_11190 (ho_12470 k_13207 BOUND_VARIABLE_1302039) BOUND_VARIABLE_1302040) BOUND_VARIABLE_1302041))))) (let ((_let_4867 (forall ((BOUND_VARIABLE_1302006 tptp.nat) (BOUND_VARIABLE_1302007 tptp.nat) (BOUND_VARIABLE_1302008 tptp.set_nat)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (= (ho_11191 (ho_11190 (ho_12470 k_13208 BOUND_VARIABLE_1302006) BOUND_VARIABLE_1302007) BOUND_VARIABLE_1302008) (and (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1302008) (ho_12468 k_12467 (ho_11421 (ho_11420 k_12466 _let_1) BOUND_VARIABLE_1302006))) (= (ho_11109 (ho_12465 k_12464 k_12463) BOUND_VARIABLE_1302008) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1302006)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1302007))) (ho_11056 k_11055 (ho_11139 k_11138 _let_1)))))))))))) (let ((_let_4868 (forall ((BOUND_VARIABLE_1301987 tptp.nat) (BOUND_VARIABLE_1301988 tptp.nat)) (= (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1301987)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 (ho_11056 k_11055 BOUND_VARIABLE_1301988))) (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))))) (ho_11139 (ho_11479 k_13209 BOUND_VARIABLE_1301987) BOUND_VARIABLE_1301988))))) (let ((_let_4869 (forall ((BOUND_VARIABLE_1301952 tptp.rat) (BOUND_VARIABLE_1301953 tptp.product_prod_int_int)) (let ((_let_1 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))) (let ((_let_2 (ho_11056 k_11055 _let_1))) (let ((_let_3 (ho_11111 k_11110 BOUND_VARIABLE_1301953))) (let ((_let_4 (ho_11111 k_11112 BOUND_VARIABLE_1301953))) (= (ho_11130 (ho_11129 k_13210 BOUND_VARIABLE_1301952) BOUND_VARIABLE_1301953) (and (= (ho_11127 (ho_11126 (ho_11125 (ho_11124 (ho_11123 k_11122 k_11118) (ho_11121 (ho_11120 k_11119 k_11118) k_11116)) k_11114) _let_4) _let_3) (ho_11508 (ho_11511 (ho_12143 (ho_12142 (ho_12141 k_12140 k_11502) (ho_11506 (ho_11505 k_11504 k_11502) k_11116)) k_12139) BOUND_VARIABLE_1301952) (ho_11508 (ho_11511 k_12430 (ho_11498 k_11497 (ho_11139 k_11138 _let_1))) (ho_12457 k_12456 (ho_11030 k_11029 tptp.one))))) (ho_11094 (ho_11093 k_11113 _let_4) _let_3) (= _let_3 (ho_11059 (ho_11058 k_11095 _let_2) _let_3)) (not (= _let_2 (ho_11059 (ho_11058 k_11095 _let_3) _let_2)))))))))))) (let ((_let_4870 (forall ((BOUND_VARIABLE_1301921 tptp.rat) (BOUND_VARIABLE_1301922 tptp.product_prod_int_int)) (let ((_let_1 (ho_11056 k_11055 (ho_11109 k_11108 (ho_11107 k_11106 k_11105))))) (let ((_let_2 (ho_11111 k_11110 BOUND_VARIABLE_1301922))) (let ((_let_3 (ho_11111 k_11112 BOUND_VARIABLE_1301922))) (= (and (= BOUND_VARIABLE_1301921 (ho_11127 (ho_11126 (ho_11125 (ho_11124 (ho_11123 k_11122 k_11118) (ho_11121 (ho_11120 k_11119 k_11118) k_11116)) k_11114) _let_3) _let_2)) (ho_11094 (ho_11093 k_11113 _let_3) _let_2) (= _let_2 (ho_11059 (ho_11058 k_11095 _let_1) _let_2)) (not (= _let_1 (ho_11059 (ho_11058 k_11095 _let_2) _let_1)))) (ho_11130 (ho_11129 k_13211 BOUND_VARIABLE_1301921) BOUND_VARIABLE_1301922)))))))) (let ((_let_4871 (forall ((BOUND_VARIABLE_1301906 tptp.int) (BOUND_VARIABLE_1301907 tptp.nat) (BOUND_VARIABLE_1301908 tptp.nat)) (= (ho_11056 (ho_12325 (ho_12402 k_13212 BOUND_VARIABLE_1301906) BOUND_VARIABLE_1301907) BOUND_VARIABLE_1301908) (ho_11059 (ho_12273 k_12324 BOUND_VARIABLE_1301908) (ho_12218 k_12323 (ho_11054 (ho_11574 k_12322 (ho_11059 (ho_11058 k_11057 BOUND_VARIABLE_1301906) (ho_11056 (ho_12276 k_13120 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))) BOUND_VARIABLE_1301907))) BOUND_VARIABLE_1301908))))))) (let ((_let_4872 (forall ((BOUND_VARIABLE_1301891 tptp.int) (BOUND_VARIABLE_1301892 tptp.nat) (BOUND_VARIABLE_1301893 tptp.nat)) (= (ho_11056 (ho_12325 (ho_12402 k_13213 BOUND_VARIABLE_1301891) BOUND_VARIABLE_1301892) BOUND_VARIABLE_1301893) (ho_11059 (ho_12273 k_12324 BOUND_VARIABLE_1301893) (ho_12218 k_12323 (ho_11054 (ho_11574 k_12322 (ho_11059 (ho_11058 k_11057 BOUND_VARIABLE_1301891) (ho_11056 (ho_12276 k_13120 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))) BOUND_VARIABLE_1301892))) BOUND_VARIABLE_1301893))))))) (let ((_let_4873 (forall ((BOUND_VARIABLE_1301876 tptp.int) (BOUND_VARIABLE_1301877 tptp.nat) (BOUND_VARIABLE_1301878 tptp.nat)) (= (ho_11056 (ho_12325 (ho_12402 k_13214 BOUND_VARIABLE_1301876) BOUND_VARIABLE_1301877) BOUND_VARIABLE_1301878) (ho_11059 (ho_12273 k_12324 BOUND_VARIABLE_1301878) (ho_12218 k_12323 (ho_11054 (ho_11574 k_12322 (ho_11059 (ho_11058 k_11057 BOUND_VARIABLE_1301876) (ho_11056 (ho_12276 k_13120 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one))) BOUND_VARIABLE_1301877))) BOUND_VARIABLE_1301878))))))) (let ((_let_4874 (forall ((BOUND_VARIABLE_1301845 tptp.int) (BOUND_VARIABLE_1301846 tptp.nat) (BOUND_VARIABLE_1301847 tptp.nat)) (let ((_let_1 (ho_11056 k_11055 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (let ((_let_2 (ho_12475 k_12474 (ho_11030 k_11029 tptp.one)))) (= (ho_11059 (ho_12273 k_12324 BOUND_VARIABLE_1301847) (ho_12218 k_12323 (ho_11054 (ho_11574 k_12322 (ho_11059 (ho_11058 k_11057 (ho_11059 (ho_11058 k_11523 BOUND_VARIABLE_1301845) _let_2)) (ho_11056 (ho_12276 k_13120 _let_2) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1301846)) (ho_11059 (ho_11058 k_11057 (ho_11059 k_11499 _let_1)) _let_1)))))) BOUND_VARIABLE_1301847))) (ho_11056 (ho_12325 (ho_12402 k_13215 BOUND_VARIABLE_1301845) BOUND_VARIABLE_1301846) BOUND_VARIABLE_1301847))))))) (let ((_let_4875 (forall ((BOUND_VARIABLE_1301834 tptp.code_integer) (BOUND_VARIABLE_1301835 tptp.nat)) (= (ho_11669 (ho_12441 k_13216 BOUND_VARIABLE_1301834) BOUND_VARIABLE_1301835) (ho_12130 (ho_12439 k_13200 BOUND_VARIABLE_1301835) (ho_13199 k_13198 (ho_11054 (ho_11551 k_13197 BOUND_VARIABLE_1301834) BOUND_VARIABLE_1301835))))))) (let ((_let_4876 (forall ((BOUND_VARIABLE_1301821 tptp.code_integer) (BOUND_VARIABLE_1301822 tptp.nat)) (= (ho_11669 (ho_12441 k_13217 BOUND_VARIABLE_1301821) BOUND_VARIABLE_1301822) (ho_12130 (ho_12439 k_13200 BOUND_VARIABLE_1301822) (ho_13199 k_13198 (ho_11054 (ho_11551 k_13197 (ho_12130 (ho_12129 k_13202 BOUND_VARIABLE_1301821) (ho_12560 k_12559 (ho_11030 k_11029 tptp.one)))) BOUND_VARIABLE_1301822))))))) (let ((_let_4877 (forall ((BOUND_VARIABLE_1301771 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1301772 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1301773 tptp.product_prod_nat_nat) (BOUND_VARIABLE_1301774 tptp.nat) (BOUND_VARIABLE_1301775 tptp.nat)) (= (ho_11184 (ho_11424 k_11423 (ho_11324 (ho_11323 (ho_11322 (ho_11321 k_11320 BOUND_VARIABLE_1301771) BOUND_VARIABLE_1301774) BOUND_VARIABLE_1301775) BOUND_VARIABLE_1301772)) BOUND_VARIABLE_1301773) (ho_11054 (ho_11053 (ho_11433 (ho_13220 (ho_13219 k_13218 BOUND_VARIABLE_1301771) BOUND_VARIABLE_1301772) BOUND_VARIABLE_1301773) BOUND_VARIABLE_1301774) BOUND_VARIABLE_1301775))))) (let ((_let_4878 (forall ((BOUND_VARIABLE_1301750 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1301751 tptp.int) (BOUND_VARIABLE_1301752 tptp.int) (BOUND_VARIABLE_1301753 tptp.set_Pr958786334691620121nt_int) (BOUND_VARIABLE_1301754 tptp.int) (BOUND_VARIABLE_1301755 tptp.int)) (= (ho_11094 (ho_11093 (ho_13225 (ho_13224 (ho_13223 (ho_13222 k_13221 BOUND_VARIABLE_1301750) BOUND_VARIABLE_1301751) BOUND_VARIABLE_1301752) BOUND_VARIABLE_1301753) BOUND_VARIABLE_1301754) BOUND_VARIABLE_1301755) (or (ho_11211 (ho_13227 k_13226 (ho_11521 (ho_11115 k_11520 BOUND_VARIABLE_1301751) BOUND_VARIABLE_1301754)) BOUND_VARIABLE_1301750) (and (= BOUND_VARIABLE_1301751 BOUND_VARIABLE_1301754) (ho_11211 (ho_13227 k_13226 (ho_11521 (ho_11115 k_11520 BOUND_VARIABLE_1301752) BOUND_VARIABLE_1301755)) BOUND_VARIABLE_1301753))))))) (let ((_let_4879 (forall ((BOUND_VARIABLE_1301732 tptp.int) (BOUND_VARIABLE_1364810 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_1301734 tptp.int) (BOUND_VARIABLE_1364807 |u_(-> tptp.int tptp.set_Pr958786334691620121nt_int)|) (BOUND_VARIABLE_1301736 tptp.int) (BOUND_VARIABLE_1301737 tptp.int)) (= (ho_11094 (ho_11093 (ho_13233 (ho_13232 (ho_13231 (ho_13230 k_13229 BOUND_VARIABLE_1301732) BOUND_VARIABLE_1364810) BOUND_VARIABLE_1301734) BOUND_VARIABLE_1364807) BOUND_VARIABLE_1301736) BOUND_VARIABLE_1301737) (and (= BOUND_VARIABLE_1301732 BOUND_VARIABLE_1301736) (ho_11094 BOUND_VARIABLE_1364810 BOUND_VARIABLE_1301736) (ho_11211 (ho_13227 k_13226 (ho_11521 (ho_11115 k_11520 BOUND_VARIABLE_1301734) BOUND_VARIABLE_1301737)) (ho_13228 BOUND_VARIABLE_1364807 BOUND_VARIABLE_1301736))))))) (let ((_let_4880 (forall ((BOUND_VARIABLE_1301699 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1301700 tptp.heap_e7401611519738050253t_unit) (BOUND_VARIABLE_1301701 tptp.nat)) (= (ho_11054 (ho_13236 (ho_13235 k_13234 BOUND_VARIABLE_1301699) BOUND_VARIABLE_1301700) BOUND_VARIABLE_1301701) (and (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1301701 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_13238 k_13237 BOUND_VARIABLE_1301699))) (ho_11056 k_11055 K3))))))) (not (forall ((K3 tptp.nat)) (not (= (ho_13238 k_13237 BOUND_VARIABLE_1301700) (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 BOUND_VARIABLE_1301701)) (ho_11056 k_11055 K3))))))) (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_1301701 (ho_11061 k_11060 (ho_11059 (ho_11058 k_11057 (ho_11056 k_11055 (ho_13238 k_13237 BOUND_VARIABLE_1301700))) (ho_11056 k_11055 K3))))))))))) (let ((_let_4881 (forall ((BOUND_VARIABLE_1301669 tptp.rat) (BOUND_VARIABLE_1301670 tptp.nat) (BOUND_VARIABLE_1301671 tptp.nat) (BOUND_VARIABLE_1301672 tptp.rat)) (let ((_let_1 (ho_11506 (ho_11505 k_11504 k_11502) k_11116))) (let ((_let_2 (ho_12142 (ho_12141 k_12140 k_11502) _let_1))) (let ((_let_3 (ho_12143 _let_2 k_12139))) (= (ho_11508 (ho_11511 (ho_12143 _let_2 k_12442) (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 (ho_11508 (ho_11511 _let_3 BOUND_VARIABLE_1301669) (ho_11508 (ho_11507 _let_1 k_11500) (ho_11498 k_11497 BOUND_VARIABLE_1301670)))) (ho_11498 k_11497 (ho_11139 k_11138 (ho_11109 k_11108 (ho_11107 k_11106 k_11105)))))) (ho_11498 k_11497 BOUND_VARIABLE_1301671))) BOUND_VARIABLE_1301672) (ho_11508 (ho_12445 (ho_12460 (ho_12462 k_13239 BOUND_VARIABLE_1301669) BOUND_VARIABLE_1301670) BOUND_VARIABLE_1301671) BOUND_VARIABLE_1301672)))))))) (let ((_let_4882 (forall ((BOUND_VARIABLE_1301649 tptp.rat) (BOUND_VARIABLE_1301650 tptp.nat) (BOUND_VARIABLE_1301651 tptp.rat)) (let ((_let_1 (ho_11506 (ho_11505 k_11504 k_11502) k_11116))) (let ((_let_2 (ho_12142 (ho_12141 k_12140 k_11502) _let_1))) (= (ho_11508 (ho_11511 (ho_12143 _let_2 k_12442) (ho_11508 (ho_11511 (ho_12143 _let_2 k_12139) BOUND_VARIABLE_1301649) (ho_11508 (ho_11507 _let_1 k_11500) (ho_11498 k_11497 BOUND_VARIABLE_1301650)))) BOUND_VARIABLE_1301651) (ho_11508 (ho_12445 (ho_12444 k_13240 BOUND_VARIABLE_1301649) BOUND_VARIABLE_1301650) BOUND_VARIABLE_1301651))))))) (let ((_let_4883 (forall ((BOUND_VARIABLE_1301641 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1301642 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13241 BOUND_VARIABLE_1301641) BOUND_VARIABLE_1301642) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1301642) BOUND_VARIABLE_1301641))))) (let ((_let_4884 (forall ((BOUND_VARIABLE_1301633 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1301634 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13242 BOUND_VARIABLE_1301633) BOUND_VARIABLE_1301634) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1301634) BOUND_VARIABLE_1301633))))) (let ((_let_4885 (forall ((BOUND_VARIABLE_1301621 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1301622 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1301623 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1301623))) (= (ho_11184 (ho_11237 (ho_11365 k_13243 BOUND_VARIABLE_1301621) BOUND_VARIABLE_1301622) BOUND_VARIABLE_1301623) (and (ho_11070 _let_1 BOUND_VARIABLE_1301621) (not (ho_11070 _let_1 BOUND_VARIABLE_1301622)))))))) (let ((_let_4886 (forall ((BOUND_VARIABLE_1301613 tptp.set_int) (BOUND_VARIABLE_1301614 tptp.int)) (= (ho_11094 (ho_11234 k_13244 BOUND_VARIABLE_1301613) BOUND_VARIABLE_1301614) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1301614) BOUND_VARIABLE_1301613))))) (let ((_let_4887 (forall ((BOUND_VARIABLE_1301605 tptp.set_int) (BOUND_VARIABLE_1301606 tptp.int)) (= (ho_11094 (ho_11234 k_13245 BOUND_VARIABLE_1301605) BOUND_VARIABLE_1301606) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1301606) BOUND_VARIABLE_1301605))))) (let ((_let_4888 (forall ((BOUND_VARIABLE_1301593 tptp.set_int) (BOUND_VARIABLE_1301594 tptp.set_int) (BOUND_VARIABLE_1301595 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1301595))) (= (ho_11094 (ho_11234 (ho_11339 k_13246 BOUND_VARIABLE_1301593) BOUND_VARIABLE_1301594) BOUND_VARIABLE_1301595) (and (ho_11180 _let_1 BOUND_VARIABLE_1301593) (not (ho_11180 _let_1 BOUND_VARIABLE_1301594)))))))) (let ((_let_4889 (forall ((BOUND_VARIABLE_1301585 tptp.set_nat) (BOUND_VARIABLE_1301586 tptp.nat)) (= (ho_11054 (ho_11240 k_13247 BOUND_VARIABLE_1301585) BOUND_VARIABLE_1301586) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301586) BOUND_VARIABLE_1301585))))) (let ((_let_4890 (forall ((BOUND_VARIABLE_1301577 tptp.set_nat) (BOUND_VARIABLE_1301578 tptp.nat)) (= (ho_11054 (ho_11240 k_13248 BOUND_VARIABLE_1301577) BOUND_VARIABLE_1301578) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301578) BOUND_VARIABLE_1301577))))) (let ((_let_4891 (forall ((BOUND_VARIABLE_1301565 tptp.set_nat) (BOUND_VARIABLE_1301566 tptp.set_nat) (BOUND_VARIABLE_1301567 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1301567))) (= (ho_11054 (ho_11240 (ho_11343 k_13249 BOUND_VARIABLE_1301565) BOUND_VARIABLE_1301566) BOUND_VARIABLE_1301567) (and (ho_11191 _let_1 BOUND_VARIABLE_1301565) (not (ho_11191 _let_1 BOUND_VARIABLE_1301566)))))))) (let ((_let_4892 (forall ((BOUND_VARIABLE_1301557 tptp.set_set_nat) (BOUND_VARIABLE_1301558 tptp.set_nat)) (= (ho_11191 (ho_12650 k_13250 BOUND_VARIABLE_1301557) BOUND_VARIABLE_1301558) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1301558) BOUND_VARIABLE_1301557))))) (let ((_let_4893 (forall ((BOUND_VARIABLE_1301549 tptp.set_set_nat) (BOUND_VARIABLE_1301550 tptp.set_nat)) (= (ho_11191 (ho_12650 k_13251 BOUND_VARIABLE_1301549) BOUND_VARIABLE_1301550) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1301550) BOUND_VARIABLE_1301549))))) (let ((_let_4894 (forall ((BOUND_VARIABLE_1301537 tptp.set_set_nat) (BOUND_VARIABLE_1301538 tptp.set_set_nat) (BOUND_VARIABLE_1301539 tptp.set_nat)) (let ((_let_1 (ho_11206 k_11205 BOUND_VARIABLE_1301539))) (= (ho_11191 (ho_12650 (ho_12883 k_13252 BOUND_VARIABLE_1301537) BOUND_VARIABLE_1301538) BOUND_VARIABLE_1301539) (and (ho_11207 _let_1 BOUND_VARIABLE_1301537) (not (ho_11207 _let_1 BOUND_VARIABLE_1301538)))))))) (let ((_let_4895 (forall ((BOUND_VARIABLE_1301529 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1301530 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 k_13253 BOUND_VARIABLE_1301529) BOUND_VARIABLE_1301530) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1301530) BOUND_VARIABLE_1301529))))) (let ((_let_4896 (forall ((BOUND_VARIABLE_1301521 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1301522 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 k_13254 BOUND_VARIABLE_1301521) BOUND_VARIABLE_1301522) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1301522) BOUND_VARIABLE_1301521))))) (let ((_let_4897 (forall ((BOUND_VARIABLE_1301509 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1301510 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1301511 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (ho_11215 k_11214 BOUND_VARIABLE_1301511))) (= (ho_11211 (ho_12655 (ho_12887 k_13255 BOUND_VARIABLE_1301509) BOUND_VARIABLE_1301510) BOUND_VARIABLE_1301511) (and (ho_11216 _let_1 BOUND_VARIABLE_1301509) (not (ho_11216 _let_1 BOUND_VARIABLE_1301510)))))))) (let ((_let_4898 (forall ((BOUND_VARIABLE_1301501 tptp.set_list_nat) (BOUND_VARIABLE_1301502 tptp.list_nat)) (= (ho_11278 (ho_12842 k_13256 BOUND_VARIABLE_1301501) BOUND_VARIABLE_1301502) (ho_11660 (ho_11659 k_11658 BOUND_VARIABLE_1301502) BOUND_VARIABLE_1301501))))) (let ((_let_4899 (forall ((BOUND_VARIABLE_1301493 tptp.set_list_nat) (BOUND_VARIABLE_1301494 tptp.list_nat)) (= (ho_11278 (ho_12842 k_13257 BOUND_VARIABLE_1301493) BOUND_VARIABLE_1301494) (ho_11660 (ho_11659 k_11658 BOUND_VARIABLE_1301494) BOUND_VARIABLE_1301493))))) (let ((_let_4900 (forall ((BOUND_VARIABLE_1301481 tptp.set_list_nat) (BOUND_VARIABLE_1301482 tptp.set_list_nat) (BOUND_VARIABLE_1301483 tptp.list_nat)) (let ((_let_1 (ho_11659 k_11658 BOUND_VARIABLE_1301483))) (= (ho_11278 (ho_12842 (ho_13259 k_13258 BOUND_VARIABLE_1301481) BOUND_VARIABLE_1301482) BOUND_VARIABLE_1301483) (and (ho_11660 _let_1 BOUND_VARIABLE_1301481) (not (ho_11660 _let_1 BOUND_VARIABLE_1301482)))))))) (let ((_let_4901 (forall ((BOUND_VARIABLE_1301473 tptp.set_o) (BOUND_VARIABLE_1301474 Bool)) (= (ho_11194 (ho_12571 k_13260 BOUND_VARIABLE_1301473) BOUND_VARIABLE_1301474) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1301474) BOUND_VARIABLE_1301473))))) (let ((_let_4902 (forall ((BOUND_VARIABLE_1301465 tptp.set_o) (BOUND_VARIABLE_1301466 Bool)) (= (ho_11194 (ho_12571 k_13261 BOUND_VARIABLE_1301465) BOUND_VARIABLE_1301466) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1301466) BOUND_VARIABLE_1301465))))) (let ((_let_4903 (forall ((BOUND_VARIABLE_1301453 tptp.set_o) (BOUND_VARIABLE_1301454 tptp.set_o) (BOUND_VARIABLE_1301455 Bool)) (let ((_let_1 (ho_11198 k_11197 BOUND_VARIABLE_1301455))) (= (ho_11194 (ho_12571 (ho_12891 k_13262 BOUND_VARIABLE_1301453) BOUND_VARIABLE_1301454) BOUND_VARIABLE_1301455) (and (ho_11199 _let_1 BOUND_VARIABLE_1301453) (not (ho_11199 _let_1 BOUND_VARIABLE_1301454)))))))) (let ((_let_4904 (forall ((BOUND_VARIABLE_1301445 tptp.set_int) (BOUND_VARIABLE_1301446 tptp.int)) (= (ho_11094 (ho_11234 k_13263 BOUND_VARIABLE_1301445) BOUND_VARIABLE_1301446) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1301446) BOUND_VARIABLE_1301445))))) (let ((_let_4905 (forall ((BOUND_VARIABLE_1301436 tptp.set_int) (BOUND_VARIABLE_1301437 tptp.int)) (= (ho_11094 (ho_11234 k_13264 BOUND_VARIABLE_1301436) BOUND_VARIABLE_1301437) (not (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1301437) BOUND_VARIABLE_1301436)))))) (let ((_let_4906 (forall ((BOUND_VARIABLE_1301428 tptp.set_nat) (BOUND_VARIABLE_1301429 tptp.nat)) (= (ho_11054 (ho_11240 k_13265 BOUND_VARIABLE_1301428) BOUND_VARIABLE_1301429) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301429) BOUND_VARIABLE_1301428))))) (let ((_let_4907 (forall ((BOUND_VARIABLE_1301419 tptp.set_nat) (BOUND_VARIABLE_1301420 tptp.nat)) (= (ho_11054 (ho_11240 k_13266 BOUND_VARIABLE_1301419) BOUND_VARIABLE_1301420) (not (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301420) BOUND_VARIABLE_1301419)))))) (let ((_let_4908 (forall ((BOUND_VARIABLE_1301411 tptp.set_set_nat) (BOUND_VARIABLE_1301412 tptp.set_nat)) (= (ho_11191 (ho_12650 k_13267 BOUND_VARIABLE_1301411) BOUND_VARIABLE_1301412) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1301412) BOUND_VARIABLE_1301411))))) (let ((_let_4909 (forall ((BOUND_VARIABLE_1301402 tptp.set_set_nat) (BOUND_VARIABLE_1301403 tptp.set_nat)) (= (ho_11191 (ho_12650 k_13268 BOUND_VARIABLE_1301402) BOUND_VARIABLE_1301403) (not (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1301403) BOUND_VARIABLE_1301402)))))) (let ((_let_4910 (forall ((BOUND_VARIABLE_1301394 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1301395 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 k_13269 BOUND_VARIABLE_1301394) BOUND_VARIABLE_1301395) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1301395) BOUND_VARIABLE_1301394))))) (let ((_let_4911 (forall ((BOUND_VARIABLE_1301385 tptp.set_se6260736226359567993nt_int) (BOUND_VARIABLE_1301386 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_12655 k_13270 BOUND_VARIABLE_1301385) BOUND_VARIABLE_1301386) (not (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1301386) BOUND_VARIABLE_1301385)))))) (let ((_let_4912 (forall ((BOUND_VARIABLE_1301377 tptp.set_list_nat) (BOUND_VARIABLE_1301378 tptp.list_nat)) (= (ho_11278 (ho_12842 k_13271 BOUND_VARIABLE_1301377) BOUND_VARIABLE_1301378) (ho_11660 (ho_11659 k_11658 BOUND_VARIABLE_1301378) BOUND_VARIABLE_1301377))))) (let ((_let_4913 (forall ((BOUND_VARIABLE_1301368 tptp.set_list_nat) (BOUND_VARIABLE_1301369 tptp.list_nat)) (= (ho_11278 (ho_12842 k_13272 BOUND_VARIABLE_1301368) BOUND_VARIABLE_1301369) (not (ho_11660 (ho_11659 k_11658 BOUND_VARIABLE_1301369) BOUND_VARIABLE_1301368)))))) (let ((_let_4914 (forall ((BOUND_VARIABLE_1301360 tptp.set_o) (BOUND_VARIABLE_1301361 Bool)) (= (ho_11194 (ho_12571 k_13273 BOUND_VARIABLE_1301360) BOUND_VARIABLE_1301361) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1301361) BOUND_VARIABLE_1301360))))) (let ((_let_4915 (forall ((BOUND_VARIABLE_1301351 tptp.set_o) (BOUND_VARIABLE_1301352 Bool)) (= (ho_11194 (ho_12571 k_13274 BOUND_VARIABLE_1301351) BOUND_VARIABLE_1301352) (not (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1301352) BOUND_VARIABLE_1301351)))))) (let ((_let_4916 (forall ((BOUND_VARIABLE_1301343 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1301344 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13275 BOUND_VARIABLE_1301343) BOUND_VARIABLE_1301344) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1301344) BOUND_VARIABLE_1301343))))) (let ((_let_4917 (forall ((BOUND_VARIABLE_1301335 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1301336 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13276 BOUND_VARIABLE_1301335) BOUND_VARIABLE_1301336) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1301336) BOUND_VARIABLE_1301335))))) (let ((_let_4918 (forall ((BOUND_VARIABLE_1301327 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1301328 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13277 BOUND_VARIABLE_1301327) BOUND_VARIABLE_1301328) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1301328) BOUND_VARIABLE_1301327))))) (let ((_let_4919 (forall ((BOUND_VARIABLE_1301319 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1301320 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13278 BOUND_VARIABLE_1301319) BOUND_VARIABLE_1301320) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1301320) BOUND_VARIABLE_1301319))))) (let ((_let_4920 (forall ((BOUND_VARIABLE_1301311 tptp.set_int) (BOUND_VARIABLE_1301312 tptp.int)) (= (ho_11094 (ho_11234 k_13279 BOUND_VARIABLE_1301311) BOUND_VARIABLE_1301312) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1301312) BOUND_VARIABLE_1301311))))) (let ((_let_4921 (forall ((BOUND_VARIABLE_1301303 tptp.set_int) (BOUND_VARIABLE_1301304 tptp.int)) (= (ho_11094 (ho_11234 k_13280 BOUND_VARIABLE_1301303) BOUND_VARIABLE_1301304) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1301304) BOUND_VARIABLE_1301303))))) (let ((_let_4922 (forall ((BOUND_VARIABLE_1301295 tptp.set_int) (BOUND_VARIABLE_1301296 tptp.int)) (= (ho_11094 (ho_11234 k_13281 BOUND_VARIABLE_1301295) BOUND_VARIABLE_1301296) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1301296) BOUND_VARIABLE_1301295))))) (let ((_let_4923 (forall ((BOUND_VARIABLE_1301287 tptp.set_int) (BOUND_VARIABLE_1301288 tptp.int)) (= (ho_11094 (ho_11234 k_13282 BOUND_VARIABLE_1301287) BOUND_VARIABLE_1301288) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1301288) BOUND_VARIABLE_1301287))))) (let ((_let_4924 (forall ((BOUND_VARIABLE_1301279 tptp.set_nat) (BOUND_VARIABLE_1301280 tptp.nat)) (= (ho_11054 (ho_11240 k_13283 BOUND_VARIABLE_1301279) BOUND_VARIABLE_1301280) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301280) BOUND_VARIABLE_1301279))))) (let ((_let_4925 (forall ((BOUND_VARIABLE_1301271 tptp.set_nat) (BOUND_VARIABLE_1301272 tptp.nat)) (= (ho_11054 (ho_11240 k_13284 BOUND_VARIABLE_1301271) BOUND_VARIABLE_1301272) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301272) BOUND_VARIABLE_1301271))))) (let ((_let_4926 (forall ((BOUND_VARIABLE_1301263 tptp.set_o) (BOUND_VARIABLE_1301264 Bool)) (= (ho_11194 (ho_12571 k_13285 BOUND_VARIABLE_1301263) BOUND_VARIABLE_1301264) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1301264) BOUND_VARIABLE_1301263))))) (let ((_let_4927 (forall ((BOUND_VARIABLE_1301255 tptp.set_o) (BOUND_VARIABLE_1301256 Bool)) (= (ho_11194 (ho_12571 k_13286 BOUND_VARIABLE_1301255) BOUND_VARIABLE_1301256) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1301256) BOUND_VARIABLE_1301255))))) (let ((_let_4928 (forall ((BOUND_VARIABLE_1301247 tptp.set_int) (BOUND_VARIABLE_1301248 tptp.int)) (= (ho_11094 (ho_11234 k_13287 BOUND_VARIABLE_1301247) BOUND_VARIABLE_1301248) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1301248) BOUND_VARIABLE_1301247))))) (let ((_let_4929 (forall ((BOUND_VARIABLE_1301239 tptp.set_nat) (BOUND_VARIABLE_1301240 tptp.nat)) (= (ho_11054 (ho_11240 k_13288 BOUND_VARIABLE_1301239) BOUND_VARIABLE_1301240) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301240) BOUND_VARIABLE_1301239))))) (let ((_let_4930 (forall ((BOUND_VARIABLE_1301228 tptp.set_nat) (BOUND_VARIABLE_1301229 tptp.set_nat) (BOUND_VARIABLE_1301230 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1301230))) (= (ho_11054 (ho_11240 (ho_11343 k_13289 BOUND_VARIABLE_1301228) BOUND_VARIABLE_1301229) BOUND_VARIABLE_1301230) (or (ho_11191 _let_1 BOUND_VARIABLE_1301228) (ho_11191 _let_1 BOUND_VARIABLE_1301229))))))) (let ((_let_4931 (forall ((BOUND_VARIABLE_1301220 tptp.set_nat) (BOUND_VARIABLE_1301221 tptp.nat)) (= (ho_11054 (ho_11240 k_13290 BOUND_VARIABLE_1301220) BOUND_VARIABLE_1301221) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301221) BOUND_VARIABLE_1301220))))) (let ((_let_4932 (forall ((BOUND_VARIABLE_1301212 tptp.set_nat) (BOUND_VARIABLE_1301213 tptp.nat)) (= (ho_11054 (ho_11240 k_13291 BOUND_VARIABLE_1301212) BOUND_VARIABLE_1301213) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301213) BOUND_VARIABLE_1301212))))) (let ((_let_4933 (forall ((BOUND_VARIABLE_1301201 tptp.set_nat) (BOUND_VARIABLE_1301202 tptp.set_nat) (BOUND_VARIABLE_1301203 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1301203))) (= (ho_11054 (ho_11240 (ho_11343 k_13292 BOUND_VARIABLE_1301201) BOUND_VARIABLE_1301202) BOUND_VARIABLE_1301203) (and (ho_11191 _let_1 BOUND_VARIABLE_1301201) (ho_11191 _let_1 BOUND_VARIABLE_1301202))))))) (let ((_let_4934 (forall ((BOUND_VARIABLE_1301193 tptp.set_nat) (BOUND_VARIABLE_1301194 tptp.nat)) (= (ho_11054 (ho_11240 k_13293 BOUND_VARIABLE_1301193) BOUND_VARIABLE_1301194) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301194) BOUND_VARIABLE_1301193))))) (let ((_let_4935 (forall ((BOUND_VARIABLE_1301185 tptp.set_nat) (BOUND_VARIABLE_1301186 tptp.nat)) (= (ho_11054 (ho_11240 k_13294 BOUND_VARIABLE_1301185) BOUND_VARIABLE_1301186) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301186) BOUND_VARIABLE_1301185))))) (let ((_let_4936 (forall ((BOUND_VARIABLE_1301177 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1301178 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13295 BOUND_VARIABLE_1301177) BOUND_VARIABLE_1301178) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1301178) BOUND_VARIABLE_1301177))))) (let ((_let_4937 (forall ((BOUND_VARIABLE_1301169 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1301170 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13296 BOUND_VARIABLE_1301169) BOUND_VARIABLE_1301170) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1301170) BOUND_VARIABLE_1301169))))) (let ((_let_4938 (forall ((BOUND_VARIABLE_1301161 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1301162 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13297 BOUND_VARIABLE_1301161) BOUND_VARIABLE_1301162) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1301162) BOUND_VARIABLE_1301161))))) (let ((_let_4939 (forall ((BOUND_VARIABLE_1301150 tptp.set_nat) (BOUND_VARIABLE_1301151 tptp.set_nat) (BOUND_VARIABLE_1301152 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1301152))) (= (ho_11054 (ho_11240 (ho_11343 k_13298 BOUND_VARIABLE_1301150) BOUND_VARIABLE_1301151) BOUND_VARIABLE_1301152) (or (ho_11191 _let_1 BOUND_VARIABLE_1301150) (ho_11191 _let_1 BOUND_VARIABLE_1301151))))))) (let ((_let_4940 (forall ((BOUND_VARIABLE_1301142 tptp.set_nat) (BOUND_VARIABLE_1301143 tptp.nat)) (= (ho_11054 (ho_11240 k_13299 BOUND_VARIABLE_1301142) BOUND_VARIABLE_1301143) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301143) BOUND_VARIABLE_1301142))))) (let ((_let_4941 (forall ((BOUND_VARIABLE_1301134 tptp.set_nat) (BOUND_VARIABLE_1301135 tptp.nat)) (= (ho_11054 (ho_11240 k_13300 BOUND_VARIABLE_1301134) BOUND_VARIABLE_1301135) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301135) BOUND_VARIABLE_1301134))))) (let ((_let_4942 (forall ((BOUND_VARIABLE_1301126 tptp.set_nat) (BOUND_VARIABLE_1301127 tptp.nat)) (= (ho_11054 (ho_11240 k_13301 BOUND_VARIABLE_1301126) BOUND_VARIABLE_1301127) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301127) BOUND_VARIABLE_1301126))))) (let ((_let_4943 (forall ((BOUND_VARIABLE_1301115 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1301116 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1301117 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1301117))) (= (ho_11184 (ho_11237 (ho_11365 k_13302 BOUND_VARIABLE_1301115) BOUND_VARIABLE_1301116) BOUND_VARIABLE_1301117) (and (ho_11070 _let_1 BOUND_VARIABLE_1301115) (ho_11070 _let_1 BOUND_VARIABLE_1301116))))))) (let ((_let_4944 (forall ((BOUND_VARIABLE_1301104 tptp.set_nat) (BOUND_VARIABLE_1301105 tptp.set_nat) (BOUND_VARIABLE_1301106 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1301106))) (= (ho_11054 (ho_11240 (ho_11343 k_13303 BOUND_VARIABLE_1301104) BOUND_VARIABLE_1301105) BOUND_VARIABLE_1301106) (and (ho_11191 _let_1 BOUND_VARIABLE_1301104) (ho_11191 _let_1 BOUND_VARIABLE_1301105))))))) (let ((_let_4945 (forall ((BOUND_VARIABLE_1301096 tptp.set_nat) (BOUND_VARIABLE_1301097 tptp.nat)) (= (ho_11054 (ho_11240 k_13304 BOUND_VARIABLE_1301096) BOUND_VARIABLE_1301097) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301097) BOUND_VARIABLE_1301096))))) (let ((_let_4946 (forall ((BOUND_VARIABLE_1301088 tptp.set_nat) (BOUND_VARIABLE_1301089 tptp.nat)) (= (ho_11054 (ho_11240 k_13305 BOUND_VARIABLE_1301088) BOUND_VARIABLE_1301089) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301089) BOUND_VARIABLE_1301088))))) (let ((_let_4947 (forall ((BOUND_VARIABLE_1301080 tptp.set_nat) (BOUND_VARIABLE_1301081 tptp.nat)) (= (ho_11054 (ho_11240 k_13306 BOUND_VARIABLE_1301080) BOUND_VARIABLE_1301081) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301081) BOUND_VARIABLE_1301080))))) (let ((_let_4948 (forall ((BOUND_VARIABLE_1301069 tptp.set_nat) (BOUND_VARIABLE_1301070 tptp.set_nat) (BOUND_VARIABLE_1301071 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1301071))) (= (ho_11054 (ho_11240 (ho_11343 k_13307 BOUND_VARIABLE_1301069) BOUND_VARIABLE_1301070) BOUND_VARIABLE_1301071) (and (ho_11191 _let_1 BOUND_VARIABLE_1301069) (ho_11191 _let_1 BOUND_VARIABLE_1301070))))))) (let ((_let_4949 (forall ((BOUND_VARIABLE_1301061 tptp.set_nat) (BOUND_VARIABLE_1301062 tptp.nat)) (= (ho_11054 (ho_11240 k_13308 BOUND_VARIABLE_1301061) BOUND_VARIABLE_1301062) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301062) BOUND_VARIABLE_1301061))))) (let ((_let_4950 (forall ((BOUND_VARIABLE_1301053 tptp.set_nat) (BOUND_VARIABLE_1301054 tptp.nat)) (= (ho_11054 (ho_11240 k_13309 BOUND_VARIABLE_1301053) BOUND_VARIABLE_1301054) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301054) BOUND_VARIABLE_1301053))))) (let ((_let_4951 (forall ((BOUND_VARIABLE_1301045 tptp.set_nat) (BOUND_VARIABLE_1301046 tptp.nat)) (= (ho_11054 (ho_11240 k_13310 BOUND_VARIABLE_1301045) BOUND_VARIABLE_1301046) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301046) BOUND_VARIABLE_1301045))))) (let ((_let_4952 (forall ((BOUND_VARIABLE_1301037 tptp.set_nat) (BOUND_VARIABLE_1301038 tptp.nat)) (= (ho_11054 (ho_11240 k_13311 BOUND_VARIABLE_1301037) BOUND_VARIABLE_1301038) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301038) BOUND_VARIABLE_1301037))))) (let ((_let_4953 (forall ((BOUND_VARIABLE_1301026 tptp.set_nat) (BOUND_VARIABLE_1301027 tptp.set_nat) (BOUND_VARIABLE_1301028 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1301028))) (= (ho_11054 (ho_11240 (ho_11343 k_13312 BOUND_VARIABLE_1301026) BOUND_VARIABLE_1301027) BOUND_VARIABLE_1301028) (and (ho_11191 _let_1 BOUND_VARIABLE_1301026) (ho_11191 _let_1 BOUND_VARIABLE_1301027))))))) (let ((_let_4954 (forall ((BOUND_VARIABLE_1301018 tptp.set_int) (BOUND_VARIABLE_1301019 tptp.int)) (= (ho_11094 (ho_11234 k_13313 BOUND_VARIABLE_1301018) BOUND_VARIABLE_1301019) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1301019) BOUND_VARIABLE_1301018))))) (let ((_let_4955 (forall ((BOUND_VARIABLE_1301010 tptp.set_int) (BOUND_VARIABLE_1301011 tptp.int)) (= (ho_11094 (ho_11234 k_13314 BOUND_VARIABLE_1301010) BOUND_VARIABLE_1301011) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1301011) BOUND_VARIABLE_1301010))))) (let ((_let_4956 (forall ((BOUND_VARIABLE_1301002 tptp.set_nat) (BOUND_VARIABLE_1301003 tptp.nat)) (= (ho_11054 (ho_11240 k_13315 BOUND_VARIABLE_1301002) BOUND_VARIABLE_1301003) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1301003) BOUND_VARIABLE_1301002))))) (let ((_let_4957 (forall ((BOUND_VARIABLE_1300994 tptp.set_nat) (BOUND_VARIABLE_1300995 tptp.nat)) (= (ho_11054 (ho_11240 k_13316 BOUND_VARIABLE_1300994) BOUND_VARIABLE_1300995) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300995) BOUND_VARIABLE_1300994))))) (let ((_let_4958 (forall ((BOUND_VARIABLE_1300983 tptp.set_int) (BOUND_VARIABLE_1300984 tptp.set_int) (BOUND_VARIABLE_1300985 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1300985))) (= (ho_11094 (ho_11234 (ho_11339 k_13317 BOUND_VARIABLE_1300983) BOUND_VARIABLE_1300984) BOUND_VARIABLE_1300985) (or (ho_11180 _let_1 BOUND_VARIABLE_1300983) (ho_11180 _let_1 BOUND_VARIABLE_1300984))))))) (let ((_let_4959 (forall ((BOUND_VARIABLE_1300975 tptp.set_int) (BOUND_VARIABLE_1300976 tptp.int)) (= (ho_11094 (ho_11234 k_13318 BOUND_VARIABLE_1300975) BOUND_VARIABLE_1300976) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300976) BOUND_VARIABLE_1300975))))) (let ((_let_4960 (forall ((BOUND_VARIABLE_1300967 tptp.set_int) (BOUND_VARIABLE_1300968 tptp.int)) (= (ho_11094 (ho_11234 k_13319 BOUND_VARIABLE_1300967) BOUND_VARIABLE_1300968) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300968) BOUND_VARIABLE_1300967))))) (let ((_let_4961 (forall ((BOUND_VARIABLE_1300959 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300960 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13320 BOUND_VARIABLE_1300959) BOUND_VARIABLE_1300960) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300960) BOUND_VARIABLE_1300959))))) (let ((_let_4962 (forall ((BOUND_VARIABLE_1300951 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300952 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13321 BOUND_VARIABLE_1300951) BOUND_VARIABLE_1300952) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300952) BOUND_VARIABLE_1300951))))) (let ((_let_4963 (forall ((BOUND_VARIABLE_1300940 tptp.set_nat) (BOUND_VARIABLE_1300941 tptp.set_nat) (BOUND_VARIABLE_1300942 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1300942))) (= (ho_11054 (ho_11240 (ho_11343 k_13322 BOUND_VARIABLE_1300940) BOUND_VARIABLE_1300941) BOUND_VARIABLE_1300942) (or (ho_11191 _let_1 BOUND_VARIABLE_1300940) (ho_11191 _let_1 BOUND_VARIABLE_1300941))))))) (let ((_let_4964 (forall ((BOUND_VARIABLE_1300932 tptp.set_nat) (BOUND_VARIABLE_1300933 tptp.nat)) (= (ho_11054 (ho_11240 k_13323 BOUND_VARIABLE_1300932) BOUND_VARIABLE_1300933) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300933) BOUND_VARIABLE_1300932))))) (let ((_let_4965 (forall ((BOUND_VARIABLE_1300924 tptp.set_nat) (BOUND_VARIABLE_1300925 tptp.nat)) (= (ho_11054 (ho_11240 k_13324 BOUND_VARIABLE_1300924) BOUND_VARIABLE_1300925) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300925) BOUND_VARIABLE_1300924))))) (let ((_let_4966 (forall ((BOUND_VARIABLE_1300913 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1300914 tptp.set_Pr4329608150637261639at_nat) (BOUND_VARIABLE_1300915 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (ho_11259 k_11258 BOUND_VARIABLE_1300915))) (= (ho_11263 (ho_11374 (ho_11373 k_13325 BOUND_VARIABLE_1300913) BOUND_VARIABLE_1300914) BOUND_VARIABLE_1300915) (or (ho_11260 _let_1 BOUND_VARIABLE_1300913) (ho_11260 _let_1 BOUND_VARIABLE_1300914))))))) (let ((_let_4967 (forall ((BOUND_VARIABLE_1300902 tptp.set_Pr8551490117392284871at_nat) (BOUND_VARIABLE_1300903 tptp.set_Pr8551490117392284871at_nat) (BOUND_VARIABLE_1300904 tptp.produc4166570645942440679at_nat)) (let ((_let_1 (ho_11266 k_11265 BOUND_VARIABLE_1300904))) (= (ho_11051 (ho_11377 (ho_11376 k_13326 BOUND_VARIABLE_1300902) BOUND_VARIABLE_1300903) BOUND_VARIABLE_1300904) (or (ho_11267 _let_1 BOUND_VARIABLE_1300902) (ho_11267 _let_1 BOUND_VARIABLE_1300903))))))) (let ((_let_4968 (forall ((BOUND_VARIABLE_1300891 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300892 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300893 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1300893))) (= (ho_11184 (ho_11237 (ho_11365 k_13327 BOUND_VARIABLE_1300891) BOUND_VARIABLE_1300892) BOUND_VARIABLE_1300893) (and (ho_11070 _let_1 BOUND_VARIABLE_1300891) (ho_11070 _let_1 BOUND_VARIABLE_1300892))))))) (let ((_let_4969 (forall ((BOUND_VARIABLE_1300883 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300884 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13328 BOUND_VARIABLE_1300883) BOUND_VARIABLE_1300884) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300884) BOUND_VARIABLE_1300883))))) (let ((_let_4970 (forall ((BOUND_VARIABLE_1300875 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300876 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13329 BOUND_VARIABLE_1300875) BOUND_VARIABLE_1300876) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300876) BOUND_VARIABLE_1300875))))) (let ((_let_4971 (forall ((BOUND_VARIABLE_1300864 tptp.set_int) (BOUND_VARIABLE_1300865 tptp.set_int) (BOUND_VARIABLE_1300866 tptp.int)) (let ((_let_1 (ho_11179 k_11178 BOUND_VARIABLE_1300866))) (= (ho_11094 (ho_11234 (ho_11339 k_13330 BOUND_VARIABLE_1300864) BOUND_VARIABLE_1300865) BOUND_VARIABLE_1300866) (and (ho_11180 _let_1 BOUND_VARIABLE_1300864) (ho_11180 _let_1 BOUND_VARIABLE_1300865))))))) (let ((_let_4972 (forall ((BOUND_VARIABLE_1300856 tptp.set_int) (BOUND_VARIABLE_1300857 tptp.int)) (= (ho_11094 (ho_11234 k_13331 BOUND_VARIABLE_1300856) BOUND_VARIABLE_1300857) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300857) BOUND_VARIABLE_1300856))))) (let ((_let_4973 (forall ((BOUND_VARIABLE_1300848 tptp.set_int) (BOUND_VARIABLE_1300849 tptp.int)) (= (ho_11094 (ho_11234 k_13332 BOUND_VARIABLE_1300848) BOUND_VARIABLE_1300849) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300849) BOUND_VARIABLE_1300848))))) (let ((_let_4974 (forall ((BOUND_VARIABLE_1300837 tptp.set_nat) (BOUND_VARIABLE_1300838 tptp.set_nat) (BOUND_VARIABLE_1300839 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1300839))) (= (ho_11054 (ho_11240 (ho_11343 k_13333 BOUND_VARIABLE_1300837) BOUND_VARIABLE_1300838) BOUND_VARIABLE_1300839) (and (ho_11191 _let_1 BOUND_VARIABLE_1300837) (ho_11191 _let_1 BOUND_VARIABLE_1300838))))))) (let ((_let_4975 (forall ((BOUND_VARIABLE_1300829 tptp.set_nat) (BOUND_VARIABLE_1300830 tptp.nat)) (= (ho_11054 (ho_11240 k_13334 BOUND_VARIABLE_1300829) BOUND_VARIABLE_1300830) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300830) BOUND_VARIABLE_1300829))))) (let ((_let_4976 (forall ((BOUND_VARIABLE_1300821 tptp.set_nat) (BOUND_VARIABLE_1300822 tptp.nat)) (= (ho_11054 (ho_11240 k_13335 BOUND_VARIABLE_1300821) BOUND_VARIABLE_1300822) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300822) BOUND_VARIABLE_1300821))))) (let ((_let_4977 (forall ((BOUND_VARIABLE_1300810 tptp.set_o) (BOUND_VARIABLE_1300811 tptp.set_o) (BOUND_VARIABLE_1300812 Bool)) (let ((_let_1 (ho_11198 k_11197 BOUND_VARIABLE_1300812))) (= (ho_11194 (ho_12571 (ho_12891 k_13336 BOUND_VARIABLE_1300810) BOUND_VARIABLE_1300811) BOUND_VARIABLE_1300812) (and (ho_11199 _let_1 BOUND_VARIABLE_1300810) (ho_11199 _let_1 BOUND_VARIABLE_1300811))))))) (let ((_let_4978 (forall ((BOUND_VARIABLE_1300802 tptp.set_o) (BOUND_VARIABLE_1300803 Bool)) (= (ho_11194 (ho_12571 k_13337 BOUND_VARIABLE_1300802) BOUND_VARIABLE_1300803) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1300803) BOUND_VARIABLE_1300802))))) (let ((_let_4979 (forall ((BOUND_VARIABLE_1300794 tptp.set_o) (BOUND_VARIABLE_1300795 Bool)) (= (ho_11194 (ho_12571 k_13338 BOUND_VARIABLE_1300794) BOUND_VARIABLE_1300795) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1300795) BOUND_VARIABLE_1300794))))) (let ((_let_4980 (forall ((BOUND_VARIABLE_1300786 tptp.set_int) (BOUND_VARIABLE_1300787 tptp.int)) (= (ho_11094 (ho_11234 k_13339 BOUND_VARIABLE_1300786) BOUND_VARIABLE_1300787) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300787) BOUND_VARIABLE_1300786))))) (let ((_let_4981 (forall ((BOUND_VARIABLE_1300778 tptp.set_nat) (BOUND_VARIABLE_1300779 tptp.nat)) (= (ho_11054 (ho_11240 k_13340 BOUND_VARIABLE_1300778) BOUND_VARIABLE_1300779) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300779) BOUND_VARIABLE_1300778))))) (let ((_let_4982 (forall ((BOUND_VARIABLE_1365923 |u_(-> tptp.nat Bool)|) (BOUND_VARIABLE_1300770 tptp.nat)) (= (ho_11054 (ho_11956 k_13341 BOUND_VARIABLE_1365923) BOUND_VARIABLE_1300770) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300770) (ho_11107 k_11106 BOUND_VARIABLE_1365923)))))) (let ((_let_4983 (forall ((BOUND_VARIABLE_1365935 |u_(-> tptp.int Bool)|) (BOUND_VARIABLE_1300761 tptp.int)) (= (ho_11094 (ho_11785 k_13342 BOUND_VARIABLE_1365935) BOUND_VARIABLE_1300761) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300761) (ho_11177 k_11176 BOUND_VARIABLE_1365935)))))) (let ((_let_4984 (forall ((BOUND_VARIABLE_1365947 |u_(-> tptp.set_nat Bool)|) (BOUND_VARIABLE_1300752 tptp.set_nat)) (= (ho_11191 (ho_13344 k_13343 BOUND_VARIABLE_1365947) BOUND_VARIABLE_1300752) (ho_11207 (ho_11206 k_11205 BOUND_VARIABLE_1300752) (ho_11204 k_11203 BOUND_VARIABLE_1365947)))))) (let ((_let_4985 (forall ((BOUND_VARIABLE_1365962 |u_(-> tptp.set_Pr958786334691620121nt_int Bool)|) (BOUND_VARIABLE_1300743 tptp.set_Pr958786334691620121nt_int)) (= (ho_11211 (ho_13346 k_13345 BOUND_VARIABLE_1365962) BOUND_VARIABLE_1300743) (ho_11216 (ho_11215 k_11214 BOUND_VARIABLE_1300743) (ho_11213 k_11212 BOUND_VARIABLE_1365962)))))) (let ((_let_4986 (forall ((BOUND_VARIABLE_1365977 |u_(-> tptp.list_nat Bool)|) (BOUND_VARIABLE_1300734 tptp.list_nat)) (= (ho_11278 (ho_11966 k_13347 BOUND_VARIABLE_1365977) BOUND_VARIABLE_1300734) (ho_11660 (ho_11659 k_11658 BOUND_VARIABLE_1300734) (ho_11657 k_11656 BOUND_VARIABLE_1365977)))))) (let ((_let_4987 (forall ((BOUND_VARIABLE_1300725 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300726 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13348 BOUND_VARIABLE_1300725) BOUND_VARIABLE_1300726) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300726) BOUND_VARIABLE_1300725))))) (let ((_let_4988 (forall ((BOUND_VARIABLE_1300717 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300718 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13349 BOUND_VARIABLE_1300717) BOUND_VARIABLE_1300718) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300718) BOUND_VARIABLE_1300717))))) (let ((_let_4989 (forall ((BOUND_VARIABLE_1300709 tptp.set_nat) (BOUND_VARIABLE_1300710 tptp.nat)) (= (ho_11054 (ho_11240 k_13350 BOUND_VARIABLE_1300709) BOUND_VARIABLE_1300710) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300710) BOUND_VARIABLE_1300709))))) (let ((_let_4990 (forall ((BOUND_VARIABLE_1300701 tptp.set_nat) (BOUND_VARIABLE_1300702 tptp.nat)) (= (ho_11054 (ho_11240 k_13351 BOUND_VARIABLE_1300701) BOUND_VARIABLE_1300702) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300702) BOUND_VARIABLE_1300701))))) (let ((_let_4991 (forall ((BOUND_VARIABLE_1300690 tptp.set_nat) (BOUND_VARIABLE_1300691 tptp.set_nat) (BOUND_VARIABLE_1300692 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1300692))) (= (ho_11054 (ho_11240 (ho_11343 k_13352 BOUND_VARIABLE_1300690) BOUND_VARIABLE_1300691) BOUND_VARIABLE_1300692) (or (ho_11191 _let_1 BOUND_VARIABLE_1300690) (ho_11191 _let_1 BOUND_VARIABLE_1300691))))))) (let ((_let_4992 (forall ((BOUND_VARIABLE_1300679 tptp.set_nat) (BOUND_VARIABLE_1300680 tptp.set_nat) (BOUND_VARIABLE_1300681 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1300681))) (= (ho_11054 (ho_11240 (ho_11343 k_13353 BOUND_VARIABLE_1300679) BOUND_VARIABLE_1300680) BOUND_VARIABLE_1300681) (or (ho_11191 _let_1 BOUND_VARIABLE_1300679) (ho_11191 _let_1 BOUND_VARIABLE_1300680))))))) (let ((_let_4993 (forall ((BOUND_VARIABLE_1300671 tptp.set_nat) (BOUND_VARIABLE_1300672 tptp.nat)) (= (ho_11054 (ho_11240 k_13354 BOUND_VARIABLE_1300671) BOUND_VARIABLE_1300672) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300672) BOUND_VARIABLE_1300671))))) (let ((_let_4994 (forall ((BOUND_VARIABLE_1300663 tptp.set_nat) (BOUND_VARIABLE_1300664 tptp.nat)) (= (ho_11054 (ho_11240 k_13355 BOUND_VARIABLE_1300663) BOUND_VARIABLE_1300664) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300664) BOUND_VARIABLE_1300663))))) (let ((_let_4995 (forall ((BOUND_VARIABLE_1300655 tptp.set_nat) (BOUND_VARIABLE_1300656 tptp.nat)) (= (ho_11054 (ho_11240 k_13356 BOUND_VARIABLE_1300655) BOUND_VARIABLE_1300656) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300656) BOUND_VARIABLE_1300655))))) (let ((_let_4996 (forall ((BOUND_VARIABLE_1300644 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300645 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300646 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1300646))) (= (ho_11184 (ho_11237 (ho_11365 k_13357 BOUND_VARIABLE_1300644) BOUND_VARIABLE_1300645) BOUND_VARIABLE_1300646) (and (ho_11070 _let_1 BOUND_VARIABLE_1300644) (ho_11070 _let_1 BOUND_VARIABLE_1300645))))))) (let ((_let_4997 (forall ((BOUND_VARIABLE_1300636 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300637 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13358 BOUND_VARIABLE_1300636) BOUND_VARIABLE_1300637) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300637) BOUND_VARIABLE_1300636))))) (let ((_let_4998 (forall ((BOUND_VARIABLE_1300628 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300629 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13359 BOUND_VARIABLE_1300628) BOUND_VARIABLE_1300629) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300629) BOUND_VARIABLE_1300628))))) (let ((_let_4999 (forall ((BOUND_VARIABLE_1300617 tptp.set_nat) (BOUND_VARIABLE_1300618 tptp.set_nat) (BOUND_VARIABLE_1300619 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1300619))) (= (ho_11054 (ho_11240 (ho_11343 k_13360 BOUND_VARIABLE_1300617) BOUND_VARIABLE_1300618) BOUND_VARIABLE_1300619) (and (ho_11191 _let_1 BOUND_VARIABLE_1300617) (ho_11191 _let_1 BOUND_VARIABLE_1300618))))))) (let ((_let_5000 (forall ((BOUND_VARIABLE_1300609 tptp.set_nat) (BOUND_VARIABLE_1300610 tptp.nat)) (= (ho_11054 (ho_11240 k_13361 BOUND_VARIABLE_1300609) BOUND_VARIABLE_1300610) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300610) BOUND_VARIABLE_1300609))))) (let ((_let_5001 (forall ((BOUND_VARIABLE_1300601 tptp.set_nat) (BOUND_VARIABLE_1300602 tptp.nat)) (= (ho_11054 (ho_11240 k_13362 BOUND_VARIABLE_1300601) BOUND_VARIABLE_1300602) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300602) BOUND_VARIABLE_1300601))))) (let ((_let_5002 (forall ((BOUND_VARIABLE_1300590 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300591 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300592 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1300592))) (= (ho_11184 (ho_11237 (ho_11365 k_13363 BOUND_VARIABLE_1300590) BOUND_VARIABLE_1300591) BOUND_VARIABLE_1300592) (and (ho_11070 _let_1 BOUND_VARIABLE_1300590) (ho_11070 _let_1 BOUND_VARIABLE_1300591))))))) (let ((_let_5003 (forall ((BOUND_VARIABLE_1300579 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300580 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300581 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1300581))) (= (ho_11184 (ho_11237 (ho_11365 k_13364 BOUND_VARIABLE_1300579) BOUND_VARIABLE_1300580) BOUND_VARIABLE_1300581) (and (ho_11070 _let_1 BOUND_VARIABLE_1300579) (ho_11070 _let_1 BOUND_VARIABLE_1300580))))))) (let ((_let_5004 (forall ((BOUND_VARIABLE_1300568 tptp.set_nat) (BOUND_VARIABLE_1300569 tptp.set_nat) (BOUND_VARIABLE_1300570 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1300570))) (= (ho_11054 (ho_11240 (ho_11343 k_13365 BOUND_VARIABLE_1300568) BOUND_VARIABLE_1300569) BOUND_VARIABLE_1300570) (and (ho_11191 _let_1 BOUND_VARIABLE_1300568) (ho_11191 _let_1 BOUND_VARIABLE_1300569))))))) (let ((_let_5005 (forall ((BOUND_VARIABLE_1300557 tptp.set_nat) (BOUND_VARIABLE_1300558 tptp.set_nat) (BOUND_VARIABLE_1300559 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1300559))) (= (ho_11054 (ho_11240 (ho_11343 k_13366 BOUND_VARIABLE_1300557) BOUND_VARIABLE_1300558) BOUND_VARIABLE_1300559) (and (ho_11191 _let_1 BOUND_VARIABLE_1300557) (ho_11191 _let_1 BOUND_VARIABLE_1300558))))))) (let ((_let_5006 (forall ((BOUND_VARIABLE_1300549 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300550 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13367 BOUND_VARIABLE_1300549) BOUND_VARIABLE_1300550) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300550) BOUND_VARIABLE_1300549))))) (let ((_let_5007 (forall ((BOUND_VARIABLE_1300541 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300542 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13368 BOUND_VARIABLE_1300541) BOUND_VARIABLE_1300542) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300542) BOUND_VARIABLE_1300541))))) (let ((_let_5008 (forall ((BOUND_VARIABLE_1300533 tptp.set_nat) (BOUND_VARIABLE_1300534 tptp.nat)) (= (ho_11054 (ho_11240 k_13369 BOUND_VARIABLE_1300533) BOUND_VARIABLE_1300534) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300534) BOUND_VARIABLE_1300533))))) (let ((_let_5009 (forall ((BOUND_VARIABLE_1300525 tptp.set_nat) (BOUND_VARIABLE_1300526 tptp.nat)) (= (ho_11054 (ho_11240 k_13370 BOUND_VARIABLE_1300525) BOUND_VARIABLE_1300526) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300526) BOUND_VARIABLE_1300525))))) (let ((_let_5010 (forall ((BOUND_VARIABLE_1300517 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300518 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13371 BOUND_VARIABLE_1300517) BOUND_VARIABLE_1300518) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300518) BOUND_VARIABLE_1300517))))) (let ((_let_5011 (forall ((BOUND_VARIABLE_1300509 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300510 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13372 BOUND_VARIABLE_1300509) BOUND_VARIABLE_1300510) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300510) BOUND_VARIABLE_1300509))))) (let ((_let_5012 (forall ((BOUND_VARIABLE_1300498 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300499 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300500 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1300500))) (= (ho_11184 (ho_11237 (ho_11365 k_13373 BOUND_VARIABLE_1300498) BOUND_VARIABLE_1300499) BOUND_VARIABLE_1300500) (and (ho_11070 _let_1 BOUND_VARIABLE_1300498) (ho_11070 _let_1 BOUND_VARIABLE_1300499))))))) (let ((_let_5013 (forall ((BOUND_VARIABLE_1300487 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300488 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300489 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1300489))) (= (ho_11184 (ho_11237 (ho_11365 k_13374 BOUND_VARIABLE_1300487) BOUND_VARIABLE_1300488) BOUND_VARIABLE_1300489) (and (ho_11070 _let_1 BOUND_VARIABLE_1300487) (ho_11070 _let_1 BOUND_VARIABLE_1300488))))))) (let ((_let_5014 (forall ((BOUND_VARIABLE_1300479 tptp.set_nat) (BOUND_VARIABLE_1300480 tptp.nat)) (= (ho_11054 (ho_11240 k_13375 BOUND_VARIABLE_1300479) BOUND_VARIABLE_1300480) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300480) BOUND_VARIABLE_1300479))))) (let ((_let_5015 (forall ((BOUND_VARIABLE_1300471 tptp.set_nat) (BOUND_VARIABLE_1300472 tptp.nat)) (= (ho_11054 (ho_11240 k_13376 BOUND_VARIABLE_1300471) BOUND_VARIABLE_1300472) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300472) BOUND_VARIABLE_1300471))))) (let ((_let_5016 (forall ((BOUND_VARIABLE_1300460 tptp.set_nat) (BOUND_VARIABLE_1300461 tptp.set_nat) (BOUND_VARIABLE_1300462 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1300462))) (= (ho_11054 (ho_11240 (ho_11343 k_13377 BOUND_VARIABLE_1300460) BOUND_VARIABLE_1300461) BOUND_VARIABLE_1300462) (and (ho_11191 _let_1 BOUND_VARIABLE_1300460) (ho_11191 _let_1 BOUND_VARIABLE_1300461))))))) (let ((_let_5017 (forall ((BOUND_VARIABLE_1300449 tptp.set_nat) (BOUND_VARIABLE_1300450 tptp.set_nat) (BOUND_VARIABLE_1300451 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1300451))) (= (ho_11054 (ho_11240 (ho_11343 k_13378 BOUND_VARIABLE_1300449) BOUND_VARIABLE_1300450) BOUND_VARIABLE_1300451) (and (ho_11191 _let_1 BOUND_VARIABLE_1300449) (ho_11191 _let_1 BOUND_VARIABLE_1300450))))))) (let ((_let_5018 (forall ((BOUND_VARIABLE_1300441 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300442 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13379 BOUND_VARIABLE_1300441) BOUND_VARIABLE_1300442) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300442) BOUND_VARIABLE_1300441))))) (let ((_let_5019 (forall ((BOUND_VARIABLE_1300433 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300434 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13380 BOUND_VARIABLE_1300433) BOUND_VARIABLE_1300434) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300434) BOUND_VARIABLE_1300433))))) (let ((_let_5020 (forall ((BOUND_VARIABLE_1300422 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300423 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300424 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1300424))) (= (ho_11184 (ho_11237 (ho_11365 k_13381 BOUND_VARIABLE_1300422) BOUND_VARIABLE_1300423) BOUND_VARIABLE_1300424) (and (ho_11070 _let_1 BOUND_VARIABLE_1300422) (ho_11070 _let_1 BOUND_VARIABLE_1300423))))))) (let ((_let_5021 (forall ((BOUND_VARIABLE_1300411 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300412 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300413 tptp.product_prod_nat_nat)) (let ((_let_1 (ho_11069 k_11068 BOUND_VARIABLE_1300413))) (= (ho_11184 (ho_11237 (ho_11365 k_13382 BOUND_VARIABLE_1300411) BOUND_VARIABLE_1300412) BOUND_VARIABLE_1300413) (and (ho_11070 _let_1 BOUND_VARIABLE_1300411) (ho_11070 _let_1 BOUND_VARIABLE_1300412))))))) (let ((_let_5022 (forall ((BOUND_VARIABLE_1300403 tptp.set_nat) (BOUND_VARIABLE_1300404 tptp.nat)) (= (ho_11054 (ho_11240 k_13383 BOUND_VARIABLE_1300403) BOUND_VARIABLE_1300404) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300404) BOUND_VARIABLE_1300403))))) (let ((_let_5023 (forall ((BOUND_VARIABLE_1300395 tptp.set_nat) (BOUND_VARIABLE_1300396 tptp.nat)) (= (ho_11054 (ho_11240 k_13384 BOUND_VARIABLE_1300395) BOUND_VARIABLE_1300396) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300396) BOUND_VARIABLE_1300395))))) (let ((_let_5024 (forall ((BOUND_VARIABLE_1300384 tptp.set_nat) (BOUND_VARIABLE_1300385 tptp.set_nat) (BOUND_VARIABLE_1300386 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1300386))) (= (ho_11054 (ho_11240 (ho_11343 k_13385 BOUND_VARIABLE_1300384) BOUND_VARIABLE_1300385) BOUND_VARIABLE_1300386) (and (ho_11191 _let_1 BOUND_VARIABLE_1300384) (ho_11191 _let_1 BOUND_VARIABLE_1300385))))))) (let ((_let_5025 (forall ((BOUND_VARIABLE_1300373 tptp.set_nat) (BOUND_VARIABLE_1300374 tptp.set_nat) (BOUND_VARIABLE_1300375 tptp.nat)) (let ((_let_1 (ho_11190 k_11189 BOUND_VARIABLE_1300375))) (= (ho_11054 (ho_11240 (ho_11343 k_13386 BOUND_VARIABLE_1300373) BOUND_VARIABLE_1300374) BOUND_VARIABLE_1300375) (and (ho_11191 _let_1 BOUND_VARIABLE_1300373) (ho_11191 _let_1 BOUND_VARIABLE_1300374))))))) (let ((_let_5026 (forall ((BOUND_VARIABLE_1300365 tptp.set_int) (BOUND_VARIABLE_1300366 tptp.int)) (= (ho_11094 (ho_11234 k_13387 BOUND_VARIABLE_1300365) BOUND_VARIABLE_1300366) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300366) BOUND_VARIABLE_1300365))))) (let ((_let_5027 (forall ((BOUND_VARIABLE_1300357 tptp.set_int) (BOUND_VARIABLE_1300358 tptp.int)) (= (ho_11094 (ho_11234 k_13388 BOUND_VARIABLE_1300357) BOUND_VARIABLE_1300358) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300358) BOUND_VARIABLE_1300357))))) (let ((_let_5028 (forall ((BOUND_VARIABLE_1300349 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300350 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13389 BOUND_VARIABLE_1300349) BOUND_VARIABLE_1300350) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300350) BOUND_VARIABLE_1300349))))) (let ((_let_5029 (forall ((BOUND_VARIABLE_1300341 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300342 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13390 BOUND_VARIABLE_1300341) BOUND_VARIABLE_1300342) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300342) BOUND_VARIABLE_1300341))))) (let ((_let_5030 (forall ((BOUND_VARIABLE_1300333 tptp.set_int) (BOUND_VARIABLE_1300334 tptp.int)) (= (ho_11094 (ho_11234 k_13391 BOUND_VARIABLE_1300333) BOUND_VARIABLE_1300334) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300334) BOUND_VARIABLE_1300333))))) (let ((_let_5031 (forall ((BOUND_VARIABLE_1300325 tptp.set_int) (BOUND_VARIABLE_1300326 tptp.int)) (= (ho_11094 (ho_11234 k_13392 BOUND_VARIABLE_1300325) BOUND_VARIABLE_1300326) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300326) BOUND_VARIABLE_1300325))))) (let ((_let_5032 (forall ((BOUND_VARIABLE_1300317 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300318 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13393 BOUND_VARIABLE_1300317) BOUND_VARIABLE_1300318) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300318) BOUND_VARIABLE_1300317))))) (let ((_let_5033 (forall ((BOUND_VARIABLE_1300309 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300310 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13394 BOUND_VARIABLE_1300309) BOUND_VARIABLE_1300310) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300310) BOUND_VARIABLE_1300309))))) (let ((_let_5034 (forall ((BOUND_VARIABLE_1300301 tptp.set_int) (BOUND_VARIABLE_1300302 tptp.int)) (= (ho_11094 (ho_11234 k_13395 BOUND_VARIABLE_1300301) BOUND_VARIABLE_1300302) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300302) BOUND_VARIABLE_1300301))))) (let ((_let_5035 (forall ((BOUND_VARIABLE_1300293 tptp.set_int) (BOUND_VARIABLE_1300294 tptp.int)) (= (ho_11094 (ho_11234 k_13396 BOUND_VARIABLE_1300293) BOUND_VARIABLE_1300294) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300294) BOUND_VARIABLE_1300293))))) (let ((_let_5036 (forall ((BOUND_VARIABLE_1300285 tptp.set_int) (BOUND_VARIABLE_1300286 tptp.int)) (= (ho_11094 (ho_11234 k_13397 BOUND_VARIABLE_1300285) BOUND_VARIABLE_1300286) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300286) BOUND_VARIABLE_1300285))))) (let ((_let_5037 (forall ((BOUND_VARIABLE_1300277 tptp.set_int) (BOUND_VARIABLE_1300278 tptp.int)) (= (ho_11094 (ho_11234 k_13398 BOUND_VARIABLE_1300277) BOUND_VARIABLE_1300278) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300278) BOUND_VARIABLE_1300277))))) (let ((_let_5038 (forall ((BOUND_VARIABLE_1300269 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300270 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13399 BOUND_VARIABLE_1300269) BOUND_VARIABLE_1300270) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300270) BOUND_VARIABLE_1300269))))) (let ((_let_5039 (forall ((BOUND_VARIABLE_1300261 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300262 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13400 BOUND_VARIABLE_1300261) BOUND_VARIABLE_1300262) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300262) BOUND_VARIABLE_1300261))))) (let ((_let_5040 (forall ((BOUND_VARIABLE_1300253 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300254 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13401 BOUND_VARIABLE_1300253) BOUND_VARIABLE_1300254) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300254) BOUND_VARIABLE_1300253))))) (let ((_let_5041 (forall ((BOUND_VARIABLE_1300245 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300246 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13402 BOUND_VARIABLE_1300245) BOUND_VARIABLE_1300246) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300246) BOUND_VARIABLE_1300245))))) (let ((_let_5042 (forall ((BOUND_VARIABLE_1300237 tptp.set_int) (BOUND_VARIABLE_1300238 tptp.int)) (= (ho_11094 (ho_11234 k_13403 BOUND_VARIABLE_1300237) BOUND_VARIABLE_1300238) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300238) BOUND_VARIABLE_1300237))))) (let ((_let_5043 (forall ((BOUND_VARIABLE_1300229 tptp.set_nat) (BOUND_VARIABLE_1300230 tptp.nat)) (= (ho_11054 (ho_11240 k_13404 BOUND_VARIABLE_1300229) BOUND_VARIABLE_1300230) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300230) BOUND_VARIABLE_1300229))))) (let ((_let_5044 (forall ((BOUND_VARIABLE_1300221 tptp.set_o) (BOUND_VARIABLE_1300222 Bool)) (= (ho_11194 (ho_12571 k_13405 BOUND_VARIABLE_1300221) BOUND_VARIABLE_1300222) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1300222) BOUND_VARIABLE_1300221))))) (let ((_let_5045 (forall ((BOUND_VARIABLE_1300213 tptp.set_int) (BOUND_VARIABLE_1300214 tptp.int)) (= (ho_11094 (ho_11234 k_13406 BOUND_VARIABLE_1300213) BOUND_VARIABLE_1300214) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300214) BOUND_VARIABLE_1300213))))) (let ((_let_5046 (forall ((BOUND_VARIABLE_1300205 tptp.set_nat) (BOUND_VARIABLE_1300206 tptp.nat)) (= (ho_11054 (ho_11240 k_13407 BOUND_VARIABLE_1300205) BOUND_VARIABLE_1300206) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300206) BOUND_VARIABLE_1300205))))) (let ((_let_5047 (forall ((BOUND_VARIABLE_1300197 tptp.set_o) (BOUND_VARIABLE_1300198 Bool)) (= (ho_11194 (ho_12571 k_13408 BOUND_VARIABLE_1300197) BOUND_VARIABLE_1300198) (ho_11199 (ho_11198 k_11197 BOUND_VARIABLE_1300198) BOUND_VARIABLE_1300197))))) (let ((_let_5048 (forall ((BOUND_VARIABLE_1300189 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300190 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13409 BOUND_VARIABLE_1300189) BOUND_VARIABLE_1300190) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300190) BOUND_VARIABLE_1300189))))) (let ((_let_5049 (forall ((BOUND_VARIABLE_1300181 tptp.set_Pr1261947904930325089at_nat) (BOUND_VARIABLE_1300182 tptp.product_prod_nat_nat)) (= (ho_11184 (ho_11237 k_13410 BOUND_VARIABLE_1300181) BOUND_VARIABLE_1300182) (ho_11070 (ho_11069 k_11068 BOUND_VARIABLE_1300182) BOUND_VARIABLE_1300181))))) (let ((_let_5050 (forall ((BOUND_VARIABLE_1300173 tptp.set_int) (BOUND_VARIABLE_1300174 tptp.int)) (= (ho_11094 (ho_11234 k_13411 BOUND_VARIABLE_1300173) BOUND_VARIABLE_1300174) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300174) BOUND_VARIABLE_1300173))))) (let ((_let_5051 (forall ((BOUND_VARIABLE_1300165 tptp.set_int) (BOUND_VARIABLE_1300166 tptp.int)) (= (ho_11094 (ho_11234 k_13412 BOUND_VARIABLE_1300165) BOUND_VARIABLE_1300166) (ho_11180 (ho_11179 k_11178 BOUND_VARIABLE_1300166) BOUND_VARIABLE_1300165))))) (let ((_let_5052 (forall ((BOUND_VARIABLE_1300157 tptp.set_nat) (BOUND_VARIABLE_1300158 tptp.nat)) (= (ho_11054 (ho_11240 k_13413 BOUND_VARIABLE_1300157) BOUND_VARIABLE_1300158) (ho_11191 (ho_11190 k_11189 BOUND_VARIABLE_1300158) BOUND_VARIABLE_1300157))))) (let ((_let_5